C ALGORITHM 764, COLLECTED ALGORITHMS FROM ACM. C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE, C VOL. 23, NO. 1, March, 1997, P. 1--15. C #! /bin/sh # This is a shell archive, meaning: # 1. Remove everything above the #! /bin/sh line. # 2. Save the resulting text in a file. # 3. Execute the file with /bin/sh (not csh) to create the files: # Src # Doc # This archive created: Sat Apr 19 22:37:40 1997 export PATH; PATH=/bin:$PATH if test ! -d 'Src' then mkdir 'Src' fi cd 'Src' if test ! -d 'Cubpack++' then mkdir 'Cubpack++' fi cd 'Cubpack++' if test ! -d 'Drivers' then mkdir 'Drivers' fi cd 'Drivers' if test -f 'CONTENTS' then echo shar: will not over-write existing file "'CONTENTS'" else cat << \SHAR_EOF > 'CONTENTS' What you find in the current directory -------------------------------------- CONTENTS : this file Small examples of main programs illustrating the use of different geometries. You can start playing with Cubpack++ by modifying these. ---------------------- ------------------------------ source region output ------ ------ ------ vb1.c : TRIANGLE : vb1.out vb2.c : CIRCLE : vb2.out vb3.c : PLANE_SECTOR (wedge) : vb3.out vb4.c : GENERALIZED_RECTANGLE (parabola) : vb4.out vb5.c : GENERALIZED_RECTANGLE (lemniscate) : vb5.out vb6.c : SEMI_INFINITE_STRIP : vb6.out vb7.c : SEMI_INFINITE_STRIP : vb7.out vb8.c : INFINITE_STRIP : vb8.out vb9.c : RECTANGLE : vb9.out vb10.c : TRIANGLE : vb10.out vb11.c : PLANE_SECTOR (half plane) : vb11.out vb12.c : PLANE_SECTOR (quadrant) : vb12.out vb13.c : House = TRIANGLE + RECTANGLE : vb13.out vb14.c : SEMI_INFINITE_STRIP (see vb6) : vb14.out vb15.c : House (see vb13) : vb15.out vb16.c : House (see vb13) : vb16.out vb17.c : GENERALIZED_RECTANGLE (see vb4) : vb17.out vb18.c : PLANE_SECTOR (Bivariate normal distribution) vb_hankel.c: call of Fortran function from C++, see User Manual. The output files where generated using the xlC compiler on an IBM RS6000 running AIX version 3.2.5 SHAR_EOF fi # end of overwriting check if test -f 'EXAMPLES' then echo shar: will not over-write existing file "'EXAMPLES'" else cat << \SHAR_EOF > 'EXAMPLES' Nr File Integration region -- ----- ---------------------------------- 0 interactive choice 1 vb1.c TRIANGLE 2 vb2.c CIRCLE 3 vb3.c PLANE_SECTOR (wedge) 4 vb4.c GENERALIZED_RECTANGLE (parabola) 5 vb5.c GENERALIZED_RECTANGLE (lemniscate) 6 vb6.c SEMI_INFINITE_STRIP 7 vb7.c SEMI_INFINITE_STRIP 8 vb8.c INFINITE_STRIP 9 vb9.c RECTANGLE 10 vb10.c TRIANGLE 11 vb11.c PLANE_SECTOR (half plane) 12 vb12.c PLANE_SECTOR (quadrant) 13 vb13.c House = TRIANGLE + RECTANGLE 14 vb14.c SEMI_INFINITE_STRIP (variant of vb6) 15 vb15.c House (variant of vb13) 16 vb16.c House (variant of vb13) 17 vb17.c GENERALIZED_RECTANGLE (variant of vb4) 18 vb18.c PLANE_SECTOR (Bivariate normal distribution) SHAR_EOF fi # end of overwriting check if test -f 'vb1.c' then echo shar: will not over-write existing file "'vb1.c'" else cat << \SHAR_EOF > 'vb1.c' #include #include real f(const Point& p) { real x=p.X(); return x*x; } int main() { Point p1(0,0), p2(1,1), p3(2,0); TRIANGLE T(p1,p2,p3); cout << "The integral is " << Integrate(f,T) << endl; return 0; } SHAR_EOF fi # end of overwriting check if test -f 'vb10.c' then echo shar: will not over-write existing file "'vb10.c'" else cat << \SHAR_EOF > 'vb10.c' // Example 20 from ditamo // exact value = 4/15 #include #include real f(const Point& p) { real x=p.X() , y=p.Y() ; return sqrt(1-x-y); } int main () { Point origin(0,0),p1(1,0),p2(0,1); TRIANGLE ditamo20(origin,p1,p2); EvaluationCounter count; count.Start(); cout <<"The integral is " << Integrate(f,ditamo20,0,0.5e-4,10000); cout <<" with absolute error " << ditamo20.AbsoluteError() << endl; count.Stop(); cout << count.Read() << " function evaluations were used." << endl; return 0; } SHAR_EOF fi # end of overwriting check if test -f 'vb11.c' then echo shar: will not over-write existing file "'vb11.c'" else cat << \SHAR_EOF > 'vb11.c' // This example assumes that math.h contains the function erfc. // The erfc function is only used to compute the exact value. // Problem posted in sci.math.num-analysis on 9 Feb 1995 // by N. Sukumar (E-mail: n-sukumar@nwu.edu), // Theoretical & Applied Mechanics, Northwestern U, Evanston IL 60208. // Exact value = 1/2 - (1/2) * erf (h/sqrt(2)) // where h = b / sqrt (1 + a^2) #include #include real f(const Point& p) { real x=p.X() , y=p.Y(); return exp(-(x*x+y*y)/2.0)/(2*M_PI); } int main () { real a=1,b=1,h=b/sqrt(1.0+a*a),t=h/sqrt(2.0); Point A(0,b),B(1,a+b),D=2*A-B; PLANE_SECTOR halfplane(A,B,D); EvaluationCounter count; count.Start(); cout <<"The estimated integral is " << Integrate(f,halfplane,0,0.5e-6)< 'vb12.c' // Example 34 from DITAMO // The function is rescaled such that the solution is 1. #include #include real f(const Point& p) { real x=p.X() , y=p.Y(),z , a=1.0/3.0 , b=2.0/3.0 ; if (x*y < 1e-15) return 0.0; z = x + y + 1/(x*y); if ((z > 100) || (z < -100)) { return 0.0;} else { return exp(-z) / (pow(x,b)*pow(y,a)*0.1806075059054343159);} } int main () { // Using the first constructor: Point origin(0,0),p1(1,0),p2(0,1); PLANE_SECTOR quadrant(origin,p1,p2); // Using the second constructor: // Point origin(0,0); // PLANE_SECTOR quadrant(origin,0.0, 0.0, M_PI/2); EvaluationCounter count; count.Start(); cout <<"The integral is " << Integrate(f,quadrant,0,0.5e-4); cout <<" with absolute error " << quadrant.AbsoluteError() << endl; count.Stop(); cout << count.Read() << " function evaluations were used." << endl; return 0; } SHAR_EOF fi # end of overwriting check if test -f 'vb13.c' then echo shar: will not over-write existing file "'vb13.c'" else cat << \SHAR_EOF > 'vb13.c' // Example suggested by a referee, who called this `reasonable'. // One can easily see, e.g. by substituting y=1, that this // integral involves severe difficulties such as fast oscillations // in the neighbourhood of the line x+y=2, and discontinuous derivatives. #include #include #define sqr(x) ((x)*(x)) static const real sqrt_PI = sqrt(M_PI), p35_PI = pow(M_PI,0.35e0); real f(const Point& p) { real x=p.X() , y=p.Y() ; return ( sqrt( sqr(x-sqrt_PI) + sqr(y-1) + 0.00001) + pow(pow(y-p35_PI,4) + sqr(x-1) + 0.00002,1.0/3.0) ) * sin( (x-y-sqrt_PI+p35_PI)/(sqr(x+y-2) + 0.01) ); } int main () { TRIANGLE Roof( Point(0,1), Point(2,1), Point(1,2)); RECTANGLE Walls( Point(0,0), Point(0,1), Point(2,0)); REGION_COLLECTION House = Walls + Roof; EvaluationCounter count; count.Start(); cout <<"The integral is " << Integrate(f,House,0,0.5e-1,1000000); cout <<" with absolute error " << House.AbsoluteError() << endl; count.Stop(); cout << count.Read() << " function evaluations were used." << endl; return 0; } SHAR_EOF fi # end of overwriting check if test -f 'vb14.c' then echo shar: will not over-write existing file "'vb14.c'" else cat << \SHAR_EOF > 'vb14.c' // Example 28 from ditamo #include #include real f(const Point& p) { real y=p.Y(); return 1/(y*y); } int main () { Point A(2,-1), B(1,-1); SEMI_INFINITE_STRIP langelat(A,B); real Integral_est, Error_est; Boolean Success; EvaluationCounter TikTak; TikTak.Start(); cout.setf(ios::scientific,ios::floatfield); do { Integrate(f,langelat,Integral_est,Error_est,Success,0,0.5e-7,10000); cout <<"The integral is " << Integral_est; cout <<" with estimated absolute error " << Error_est << endl; cout <<"The real error is " << Integral_est - 1 < 'vb15.c' // The `House' example with on each subregion a different integrand. #include #include real f1(const Point& p) { return ( p.X()*p.X() ); } real f2(const Point& p) { return ( p.Y()*p.Y() ); } int main () { TRIANGLE Roof( Point(0,1), Point(2,1), Point(1,2)); RECTANGLE Walls( Point(0,0), Point(0,1), Point(2,0)); REGION_COLLECTION House = Walls + Roof; Roof.LocalIntegrand(f1); Walls.LocalIntegrand(f2); EvaluationCounter count; count.Start(); cout <<"The integral is " << Integrate(House); cout <<" with estimated absolute error " << House.AbsoluteError() << endl; cout <<"The contributions of the subregions are:"< 'vb16.c' // Example suggested by a referee, who called this `reasonable'. // One can easily see, e.g. by substituting y=1, that this // integral involves severe difficulties such as fast oscillations // in the neighbourhood of the line x+y=2, and discontinuous derivatives. #include #include #define sqr(x) ((x)*(x)) static const real sqrt_PI = sqrt(M_PI), p35_PI = pow(M_PI,0.35e0); real f(const Point& p) { real x=p.X() , y=p.Y() ; return ( sqrt( sqr(x-sqrt_PI) + sqr(y-1) + 0.00001) + pow(pow(y-p35_PI,4) + sqr(x-1) + 0.00002,1.0/3.0) ) * sin( (x-y-sqrt_PI+p35_PI)/(sqr(x+y-2) + 0.01) ); } int main () { TRIANGLE T1( Point(0,0), Point(1,0), Point(0,1)), T2( Point(1,0), Point(2,0), Point(1.5,0.5)), T3( Point(2,0), Point(2,1), Point(1.5,0.5)); RECTANGLE R1( Point(1,0), Point(0,1), Point(2,1)); REGION_COLLECTION House1 = T1 + T2 + T3 + R1; RECTANGLE R3( Point(1,0), Point(0,1), Point(2,1)), R2( Point(1.8,0), Point(1.4,0.4), Point(2,0.2)); TRIANGLE T4( Point(1,0), Point(1.8,0), Point(1.4,0.4)), T7( Point(0,0), Point(1,0), Point(0,1)), T5( Point(1.8,0), Point(2,0), Point(2,0.2)), T6( Point(2,0.2), Point(2,1), Point(1.6,0.6)); REGION_COLLECTION House2 = T7 + R3 + R2 + T4 + T5 + T6; EvaluationCounter count; count.Start(); cout <<"The integral is " << Integrate(f,House1,0,0.5e-1,1000000); cout <<" with absolute error " << House1.AbsoluteError() << endl; count.Stop(); cout << count.Read() << " function evaluations were used." << endl; cout << "Contribution of the different parts:" << endl; cout << "R1: integral and error are " << R1.Integral() << " and " << R1.AbsoluteError() < 'vb17.c' // Example 23 from ditamo // The function is rescaled such that the solution is 1. #include #include real f(const Point& p) { real x=p.X() , y=p.Y(); return 0.25/sqrt(x*(2.0-x)); } real Height(const Point& p) { return sqrt(4-2*p.X()); } int main () { real Integral_est, Error_est; Boolean Success; Point A(0,0), B(2,0); GENERALIZED_RECTANGLE parabola(Height,A,B); do { Integrate(f,parabola,Integral_est,Error_est,Success,0,0.5e-1,10000); cout <<"The integral is " << Integral_est < 'vb18.c' // Bivariate normal distribution // Note that special purpose methods exist for this type of integral. #include #include // The integral depends on the following 3 parameters: real rho, a, b; real N; // This is used to save work real f(const Point& p) { real x=p.X() , y=p.Y(); return exp(N*(-x*x+2*rho*x*y-y*y)) ; } int main () { EvaluationCounter count; real c; // Read the 3 parameters from standard input: cout << "Give a,b and rho ( |rho| < 1 ): "; cin >> a >> b >> rho; // Define the region of integration: Point Center(a,b); PLANE_SECTOR quadrant(Center,0.0, M_PI , 3*M_PI/2); c = 1.0/(2.0*M_PI*sqrt(1.0 - rho*rho)); N = 1.0/(2.0 - 2.0*rho*rho); count.Start(); cout <<"The integral is " << Integrate(f,quadrant,0,0.5e-6)*c; cout <<" with absolute error " << quadrant.AbsoluteError()*c << endl; count.Stop(); cout << count.Read() << " function evaluations were used." << endl; return 0; } SHAR_EOF fi # end of overwriting check if test -f 'vb2.c' then echo shar: will not over-write existing file "'vb2.c'" else cat << \SHAR_EOF > 'vb2.c' #include #include real f(const Point& p) { real r=p.Length(); return 1.0/(1.0+r*r*r*r); } int main () { Point origin(0,0); real radius=1; CIRCLE cir(origin,radius); cout <<"The integral is " << Integrate(f, cir, 0, 1.0e-6, 10000); cout <<" with absolute error " << cir.AbsoluteError() << endl; return 0; } SHAR_EOF fi # end of overwriting check if test -f 'vb3.c' then echo shar: will not over-write existing file "'vb3.c'" else cat << \SHAR_EOF > 'vb3.c' // Example 33 from ditamo // Exact value = arctan(2) // Note that the "exact" value in the original paper is wrong. #include #include #include real f(const Point& p) { real x=p.X() , y=p.Y(); return exp(0.5*(-x*x -y*y)); } int main () { Point origin(0,0); real innerradius=0, alfa=0, beta=atan(2.0); PLANE_SECTOR wedge(origin,innerradius,alfa,beta); EvaluationCounter count; cout.setf(ios::scientific,ios::floatfield); cout<<"req. rel. error est integral est error abs error evaluations" <1e-12; req_err/=10) { cout << setprecision(1) << " <" << req_err <<" " << setprecision(10) << Integrate(f,wedge,0,req_err) << " "; cout << setprecision(1) << wedge.AbsoluteError() << " " << fabs(wedge.Integral() - atan(2.0)) << " " << count.Read() << endl; } count.Stop(); return 0; } SHAR_EOF fi # end of overwriting check if test -f 'vb4.c' then echo shar: will not over-write existing file "'vb4.c'" else cat << \SHAR_EOF > 'vb4.c' // Example 23 from ditamo // The function is rescaled such that the solution is 1. #include #include real f(const Point& p) { real x=p.X() , y=p.Y(); return 0.25/sqrt(x*(2.0-x)); } real Height(const Point& p) { return sqrt(4-2*p.X()); } int main () { Point A(0,0), B(2,0); GENERALIZED_RECTANGLE parabola(Height,A,B); Chrono TikTak; TikTak.Start(); cout <<"The integral is " << Integrate(f,parabola,0,0.5e-4); TikTak.Stop(); cout <<" with absolute error " << parabola.AbsoluteError() << endl; cout <<"Elapsed Time: " << TikTak.Read()/1000<<" seconds" << endl; return 0; } SHAR_EOF fi # end of overwriting check if test -f 'vb5.c' then echo shar: will not over-write existing file "'vb5.c'" else cat << \SHAR_EOF > 'vb5.c' // Example 5 from ditamo #include #include real f(const Point& p) { real x=p.X() , y=p.Y(); return p.Y(); } real Height(const Point& p) { real x=p.X(); return sqrt(4*cos(x)*cos(x)/9 - 16*sin(x)*sin(x)/25); } int main () { Point A(0,0), B(atan(5.0/6.0),0); GENERALIZED_RECTANGLE lemniscate(Height,A,B); EvaluationCounter TikTak; TikTak.Start(); // cout.setf(ios::left,ios::adjustfield); cout.setf(ios::scientific,ios::floatfield); cout <<"The integral is " << Integrate(f,lemniscate,0,0.5e-7,10000); cout <<" with estimated absolute error " << lemniscate.AbsoluteError() << endl; cout <<"The real error is " << lemniscate.Integral() - (2-11*atan(5.0/6.0)/15)/15 < 'vb6.c' // Example 28 from ditamo #include #include real f(const Point& p) { real y=p.Y(); return 1/(y*y); } int main () { Point A(2,-1), B(1,-1); SEMI_INFINITE_STRIP langelat(A,B); EvaluationCounter TikTak; TikTak.Start(); // cout.setf(ios::left,ios::adjustfield); cout.setf(ios::scientific,ios::floatfield); cout <<"The integral is " << Integrate(f,langelat,0,0.5e-7,20000); cout <<" with estimated absolute error " << langelat.AbsoluteError() << endl; cout <<"The real error is " << langelat.Integral() - 1 < 'vb7.c' // Example 29 from ditamo #include #include real f(const Point& p) { return fabs(p.Y())*exp(-p.Y()*p.Y()/2); } int main () { Point A(0,0), B(1.107148717794090503,0); SEMI_INFINITE_STRIP langelat(A,B); EvaluationCounter TikTak; TikTak.Start(); // cout.setf(ios::left,ios::adjustfield); cout.setf(ios::scientific,ios::floatfield); cout <<"The integral is " << Integrate(f,langelat,0,0.5e-4,10000); cout <<" with estimated absolute error " << langelat.AbsoluteError() << endl; TikTak.Stop(); cout<<"Number of evaluations = "< 'vb8.c' // Example #include #include #include real f(const Point& p) { return exp(-p.Y()*p.Y()); } int main () { Point A(0,0), B(1,0); INFINITE_STRIP langelat(A,B); EvaluationCounter TikTak; TikTak.Start(); // cout.setf(ios::left,ios::adjustfield); cout.setf(ios::scientific,ios::floatfield); cout <<"The integral is " << Integrate(f,langelat,0,0.5e-3,10000); cout <<" with estimated absolute error " << langelat.AbsoluteError() << endl; cout <<"The real error is " << langelat.Integral() - sqrt(M_PI) < 'vb9.c' // This example comes from Problem 94-7 by D.E. Loper // Siam Review, Vol. 36 (1994) page 277 #include #include #include static real q; real A(const Point& p) { real m=p.X() , f=p.Y(); real t=(1-m*m)*(1-m*m), s = sin(f); s = s*s; return (t*s)/(t*s*s+q*q*m*m); } real B(const Point& p) { real m=p.X() , f=p.Y(); real t=(1-m*m), s = sin(f); s = s*s; return (t*s*(t*s+m*m))/(t*t*s*s+q*q*m*m); } int main () { Point Origin(0,0), mu(1,0),phi(0,M_PI/2); cout<<"q A(q) B(q) A(q)/B(q)"< 'vb_hankel.c' #include #include extern "C" {void zbesh_ (real&, real&, real&, int&, int&, int&, real[], real[], int&, int&);} real AbsHankel1 ( const Point& z) { real x=z.X(), y=z.Y(), cr[10], ci[10], fnu=0; int kode=1, m=1, n=1, nz, ierr; zbesh_(x,y,fnu,kode,m,n,cr,ci,nz,ierr); return sqrt(cr[0]*cr[0]+ci[0]*ci[0]); } real AbsHankel2 ( const Point& z) { real x=(z.X()*0.8+z.Y()*0.6), y=(0.8*z.Y()-z.X()*0.6), cr[10], ci[10], fnu=0; int kode=1, m=1, n=1, nz, ierr; zbesh_(x,y,fnu,kode,m,n,cr,ci,nz,ierr); return sqrt(cr[0]*cr[0]+ci[0]*ci[0]); } int main() { Point O(0,0), A(-1,0),B(-0.8,-0.6); EvaluationCounter count; cout << " Omega = 1"< 'vb1.out' The integral is 1.16667 SHAR_EOF fi # end of overwriting check if test -f 'vb10.out' then echo shar: will not over-write existing file "'vb10.out'" else cat << \SHAR_EOF > 'vb10.out' The integral is 0.266677 with absolute error 1.16825e-05 925 function evaluations were used. SHAR_EOF fi # end of overwriting check if test -f 'vb11.out' then echo shar: will not over-write existing file "'vb11.out'" else cat << \SHAR_EOF > 'vb11.out' The estimated integral is 0.23975 The exact value is 0.23975 17620 function evaluations were used. SHAR_EOF fi # end of overwriting check if test -f 'vb12.out' then echo shar: will not over-write existing file "'vb12.out'" else cat << \SHAR_EOF > 'vb12.out' The integral is 1 with absolute error 4.27146e-05 5091 function evaluations were used. SHAR_EOF fi # end of overwriting check if test -f 'vb13.out' then echo shar: will not over-write existing file "'vb13.out'" else cat << \SHAR_EOF > 'vb13.out' The integral is -0.40791 with absolute error 0.0203924 266548 function evaluations were used. SHAR_EOF fi # end of overwriting check if test -f 'vb14.out' then echo shar: will not over-write existing file "'vb14.out'" else cat << \SHAR_EOF > 'vb14.out' The integral is 1.000000e+00 with estimated absolute error 3.035122e-05 The real error is 1.779739e-07 ------------------------------------------------- The integral is 1.000000e+00 with estimated absolute error 4.073745e-07 The real error is 5.862995e-10 ------------------------------------------------- The integral is 1.000000e+00 with estimated absolute error 6.832923e-08 The real error is 2.741229e-11 ------------------------------------------------- The integral is 1.000000e+00 with estimated absolute error 4.986300e-08 The real error is 2.816547e-11 ------------------------------------------------- Total number of evaluations = 32067 SHAR_EOF fi # end of overwriting check if test -f 'vb15.out' then echo shar: will not over-write existing file "'vb15.out'" else cat << \SHAR_EOF > 'vb15.out' The integral is 1.83333 with estimated absolute error 2.03541e-14 The contributions of the subregions are: Walls: integral = 0.666667, error = 7.40149e-15 Roof: integral = 1.16667, error = 1.29526e-14 The exact value is 2/3 + 7/6 = 11/6 74 function evaluations were used. SHAR_EOF fi # end of overwriting check if test -f 'vb16.out' then echo shar: will not over-write existing file "'vb16.out'" else cat << \SHAR_EOF > 'vb16.out' The integral is -0.407393 with absolute error 0.0203507 105968 function evaluations were used. Contribution of the different parts: R1: integral and error are -0.283031 and 0.00816722 T1: integral and error are -0.221416 and 1.09496e-06 T2: integral and error are 0.068406 and 0.0055473 T3: integral and error are 0.0286485 and 0.00663513 The integral is -0.407853 with absolute error 0.0203784 94572 function evaluations were used. SHAR_EOF fi # end of overwriting check if test -f 'vb17.out' then echo shar: will not over-write existing file "'vb17.out'" else cat << \SHAR_EOF > 'vb17.out' The integral is 0.996521 with estimated absolute error 0.151082 ------------------------------------------------- The integral is 0.997535 with estimated absolute error 0.107081 ------------------------------------------------- The integral is 0.997926 with estimated absolute error 0.0900689 ------------------------------------------------- The integral is 0.998255 with estimated absolute error 0.0758062 ------------------------------------------------- The integral is 0.998393 with estimated absolute error 0.0697915 ------------------------------------------------- The integral is 0.998532 with estimated absolute error 0.0637768 ------------------------------------------------- The integral is 0.99867 with estimated absolute error 0.0577621 ------------------------------------------------- The integral is 0.998765 with estimated absolute error 0.0536343 ------------------------------------------------- The integral is 0.998814 with estimated absolute error 0.0515078 ------------------------------------------------- The integral is 0.998851 with estimated absolute error 0.0499129 ------------------------------------------------- SHAR_EOF fi # end of overwriting check if test -f 'vb18.out' then echo shar: will not over-write existing file "'vb18.out'" else cat << \SHAR_EOF > 'vb18.out' Give a,b and rho ( |rho| < 1 ): 1.0 1.0 0.5 The integral is 0.745204 with absolute error 3.68313e-07 17194 function evaluations were used. SHAR_EOF fi # end of overwriting check if test -f 'vb2.out' then echo shar: will not over-write existing file "'vb2.out'" else cat << \SHAR_EOF > 'vb2.out' The integral is 2.4674 with absolute error 5.77166e-08 SHAR_EOF fi # end of overwriting check if test -f 'vb3.out' then echo shar: will not over-write existing file "'vb3.out'" else cat << \SHAR_EOF > 'vb3.out' req. rel. error est integral est error abs error evaluations <5.0e-02 1.1096504402e+00 3.4e-02 2.5e-03 292 <5.0e-03 1.1071935478e+00 4.1e-03 4.5e-05 1181 <5.0e-04 1.1071470438e+00 5.1e-04 1.7e-06 3105 <5.0e-05 1.1071488562e+00 5.3e-05 1.4e-07 5657 <5.0e-06 1.1071486939e+00 5.3e-06 2.4e-08 11239 <5.0e-07 1.1071487183e+00 5.3e-07 5.5e-10 16377 <5.0e-08 1.1071487178e+00 5.5e-08 1.0e-12 25553 <5.0e-09 1.1071487178e+00 5.5e-09 1.1e-11 38577 <5.0e-10 1.1071487178e+00 5.4e-10 5.2e-13 53081 <5.0e-11 1.1071487178e+00 5.5e-11 2.6e-13 73949 <5.0e-12 1.1071487178e+00 5.5e-12 1.8e-15 117794 SHAR_EOF fi # end of overwriting check if test -f 'vb4.out' then echo shar: will not over-write existing file "'vb4.out'" else cat << \SHAR_EOF > 'vb4.out' The integral is 0.99886 with absolute error 0.0495064 Elapsed Time: 0 seconds SHAR_EOF fi # end of overwriting check if test -f 'vb5.out' then echo shar: will not over-write existing file "'vb5.out'" else cat << \SHAR_EOF > 'vb5.out' The integral is 9.936835e-02 with estimated absolute error 7.230197e-14 The real error is 1.387779e-17 Number of evaluations = 37 SHAR_EOF fi # end of overwriting check if test -f 'vb6.out' then echo shar: will not over-write existing file "'vb6.out'" else cat << \SHAR_EOF > 'vb6.out' The integral is 1.000000e+00 with estimated absolute error 4.173926e-07 The real error is 5.863554e-10 Number of evaluations = 20079 SHAR_EOF fi # end of overwriting check if test -f 'vb7.out' then echo shar: will not over-write existing file "'vb7.out'" else cat << \SHAR_EOF > 'vb7.out' The integral is 1.107149e+00 with estimated absolute error 5.263967e-05 Number of evaluations = 5657 SHAR_EOF fi # end of overwriting check if test -f 'vb8.out' then echo shar: will not over-write existing file "'vb8.out'" else cat << \SHAR_EOF > 'vb8.out' The integral is 1.772455e+00 with estimated absolute error 6.976425e-04 The real error is 1.067348e-06 Number of evaluations = 1183 SHAR_EOF fi # end of overwriting check if test -f 'vb9.out' then echo shar: will not over-write existing file "'vb9.out'" else cat << \SHAR_EOF > 'vb9.out' q A(q) B(q) A(q)/B(q) 1 1.513682 0.7568409 2 2 0.9107223 0.4553611 2 3 0.6587322 0.3293661 2 4 0.5176153 0.2588077 2 5 0.4268288 0.2134144 2 6 0.3633539 0.181677 2 7 0.3164155 0.1582078 2 8 0.2802695 0.1401347 2 9 0.2515646 0.1257823 2 10 0.2282109 0.1141055 2 11 0.2088359 0.104418 2 12 0.1925005 0.09625026 2 13 0.1785401 0.08927006 2 14 0.166471 0.08323551 2 15 0.1559327 0.07796635 2 16 0.1466509 0.07332547 2 17 0.1384134 0.06920668 2 18 0.131053 0.06552649 2 19 0.1244366 0.06221831 2 SHAR_EOF fi # end of overwriting check cd .. if test ! -d 'Documentation' then mkdir 'Documentation' fi cd 'Documentation' if test -f 'CONTENTS' then echo shar: will not over-write existing file "'CONTENTS'" else cat << \SHAR_EOF > 'CONTENTS' What you find in the current directory -------------------------------------- CONTENTS : this file COMPILERS : overview of compilers used to test Cubpack++ MACHINE_DEPEND : list of machine dependable source files paper.dvi : copy of submitted paper in dvi format paper.ps : copy of submitted paper in Postscript format userman.dvi : copy of User Manual in dvi format userman.ps : copy of User Manual in Postscript format SHAR_EOF fi # end of overwriting check if test -f 'COMPILERS' then echo shar: will not over-write existing file "'COMPILERS'" else cat << \SHAR_EOF > 'COMPILERS' Systems for which Cubpack++ has proven it works =============================================== Compiler Version Operating System Machine type -------------------------------------------------------------- g++/gcc 2.5.8 Ultrix 4.4 DECstation 5000 SunOS 5.3 Sparcenter 1000 Linux 1.0 i586 2.6.0 HP-UX 2.6.2 SunOS 5.3 Sparcenter 1000 2.6.3* MSDOS 2.7.2 Ultrix 4.4 DECstation 5000 Solaris2.3 Sparcenter 1000 -------------------------------------------------------------- xlC AIX Version 3.2 IBM RS6000 -------------------------------------------------------------- cxx OSF/1 V1.3 DECalpha -------------------------------------------------------------- CC SC3.0.1 SunOS 5.3 Sparcenter 1000 -------------------------------------------------------------- Borland C++ 4.0 Windows -------------------------------------------------------------- Turbo C++ 3.0 MSDOS 5.0 386SX -------------------------------------------------------------- *) DJGPP 1.12m4 Systems for which a workaround is provided ========================================== Compiler Version Operating System Machine type -------------------------------------------------------------- CC SC3.0 SunOS 5.3 Sparcenter 1000 (15 Dec 1993) Workaround activated with compiler option -DSOLARIS Note that this bug was removed from CC in version SC3.0.1. -------------------------------------------------------------- Systems for which Cubpack++ is too complex ========================================== Compiler Version Operating System Machine type -------------------------------------------------------------- CC SC2.0.1 SunOS 4. Sun4 -------------------------------------------------------------- The answer from vendors to these problems is: upgrade. SHAR_EOF fi # end of overwriting check if test -f 'MACHINE_DEPEND' then echo shar: will not over-write existing file "'MACHINE_DEPEND'" else cat << \SHAR_EOF > 'MACHINE_DEPEND' MACHINE DEPENDENT FILES: ------------------------ chrono.c real.h templist.h -> For details we refer to the User Manual, section 11. Users might need to change these. deccxxtp.c -> This file is only used by the cxx compiler on DECalpha OSF/1 V1.3 Users should not change this. gnu262tp.c -> This file is only used by the gnu compiler version at least 2.6.2 Users should not change this. SHAR_EOF fi # end of overwriting check cd .. if test ! -d 'Tools' then mkdir 'Tools' fi cd 'Tools' if test -f 'CONTENTS' then echo shar: will not over-write existing file "'CONTENTS'" else cat << \SHAR_EOF > 'CONTENTS' What you find in the current directory -------------------------------------- CONTENTS : this file c2C : change from suffix .c to .C c2cpp : change from suffix .c to .cpp The following makefile-s are used by quick_install and quick_run. mkfile.decalpha : makefile for cxx compiler on DECalpha OSF mkfile.gn1 : makefile for gnu compiler at most v2.6.0 mkfile.gn2 : makefile for gnu compiler v2.6.2 mkfile.gn3 : makefile for gnu compiler v2.7.0 mkfile.rs6000 : makefile for xlC compiler on RS6000 AIX mkfile.solaris : makefile for CC compiler on Solaris 2.* mkfile.tc : makefile for Turbo C++ under MS-DOS The following Makefile-s are models which can be modified by users. Mk.decalpha : makefile for cxx compiler on DECalpha OSF Mk.gn1 : makefile for gnu compiler at most v2.6.0 Mk.gn2 : makefile for gnu compiler v2.6.2 Mk.gn3 : makefile for gnu compiler v2.7.0 Mk.solaris : makefile for CC compiler on Solaris 2.* Mk.tc : makefile for Turbo C++ under MS-DOS SHAR_EOF fi # end of overwriting check if test -f 'c2C' then echo shar: will not over-write existing file "'c2C'" else cat << \SHAR_EOF > 'c2C' #!/bin/sh SRC_DIR=Src cd ../$SRC_DIR for i in s_adapt.h set.h stack.h vector.h vstack.h heap.h atomic.h div.h passbuck.h pointer.h regproc.h rule.h samediv.h userint.h do cat $i | sed 's/\.c>/.C>/' > tmp mv tmp $i done # for i in `ls *.c` do a=`echo $i | sed "s/\.c$/.C/"` mv $i $a done SHAR_EOF chmod +x 'c2C' fi # end of overwriting check if test -f 'c2cpp' then echo shar: will not over-write existing file "'c2cpp'" else cat << \SHAR_EOF > 'c2cpp' #!/bin/sh SRC_DIR=Src cd ../$SRC_DIR for i in s_adapt.h set.h stack.h vector.h vstack.h heap.h atomic.h div.h passbuck.h pointer.h regproc.h rule.h samediv.h userint.h do cat $i | sed 's/\.c>/.cpp>/' > tmp mv tmp $i done # for i in `ls *.c` do a=`echo $i | sed "s/\.c$/.cpp/"` mv $i $a done SHAR_EOF chmod +x 'c2cpp' fi # end of overwriting check if test -f 'mkfile.decalpha' then echo shar: will not over-write existing file "'mkfile.decalpha'" else cat << \SHAR_EOF > 'mkfile.decalpha' .SUFFIXES: .o .C .C.o: ; $(CC) $(CFLAGS) -c $*.C CC = cxx CFLAGS = -I. libdir = -L. libs = -lcubpack -lm MYTESTPROG = main.o OBJS = \ deccxxtp.o \ point2D.o \ C2.o \ C2dv2.o \ C2dv4.o \ C2interf.o \ C2prc.o \ C2rule13.o \ C2toS2.o \ C2togr.o \ E2tostrp.o \ E2.o \ E2adapt.o \ E2interf.o \ E2sec.o \ E2secitf.o \ E2secprc.o \ S2.o \ S2adapt.o \ S2interf.o \ S2rule13.o \ T2.o \ T2dv4.o \ T2interf.o \ T2rule13.o \ T2tops.o \ atomreg.o \ boolean.o \ chrono.o \ compreg.o \ eval_ctr.o \ geometry.o \ gr.o \ gritf.o \ gs.o \ gsitf.o \ gsprc.o \ integran.o \ integrat.o \ invert.o \ outS2.o \ outS2itf.o \ polC2.o \ polC2itf.o \ polC2prc.o \ ps.o \ psitf.o \ refcount.o \ regcoll.o \ reginfo.o \ region.o \ semstitf.o \ semistrp.o \ sttosmst.o \ strip.o \ stripitf.o \ translat.o \ trnsfrm.o all:: libcubpack.a libcubpack.a: $(OBJS) ar rus libcubpack.a $(OBJS) tst: $(MYTESTPROG) $(CC) $(MYTESTPROG) $(libdir) $(libs) -o tst clean: /bin/rm -f *.o tst core SHAR_EOF fi # end of overwriting check if test -f 'mkfile.gn1' then echo shar: will not over-write existing file "'mkfile.gn1'" else cat << \SHAR_EOF > 'mkfile.gn1' CC = gcc CFLAGS = -x c++ -I. # COPTIONS = -DEGTRUSAGE COPTIONS = libdir = -L. libs = -lcubpack -lm -lg++ MYTESTPROG = main.o .c.o: ; $(CC) $(CFLAGS) -c $*.c chrono.o: chrono.c $(CC) $(CFLAGS) $(COPTIONS) -c chrono.c OBJS = \ point2D.o \ C2.o \ C2dv2.o \ C2dv4.o \ C2interf.o \ C2prc.o \ C2rule13.o \ C2toS2.o \ C2togr.o \ E2tostrp.o \ E2.o \ E2adapt.o \ E2interf.o \ E2sec.o \ E2secitf.o \ E2secprc.o \ S2.o \ S2adapt.o \ S2interf.o \ S2rule13.o \ T2.o \ T2dv4.o \ T2interf.o \ T2rule13.o \ T2tops.o \ atomreg.o \ boolean.o \ chrono.o \ compreg.o \ eval_ctr.o \ geometry.o \ gr.o \ gritf.o \ gs.o \ gsitf.o \ gsprc.o \ integran.o \ integrat.o \ invert.o \ outS2.o \ outS2itf.o \ polC2.o \ polC2itf.o \ polC2prc.o \ ps.o \ psitf.o \ refcount.o \ regcoll.o \ reginfo.o \ region.o \ semstitf.o \ semistrp.o \ sttosmst.o \ strip.o \ stripitf.o \ translat.o \ trnsfrm.o all:: libcubpack.a libcubpack.a: $(OBJS) ar ru libcubpack.a $(OBJS) ranlib libcubpack.a tst: $(MYTESTPROG) $(CC) $(MYTESTPROG) $(libdir) $(libs) -o tst clean: /bin/rm -f *.o tst core SHAR_EOF fi # end of overwriting check if test -f 'mkfile.gn2' then echo shar: will not over-write existing file "'mkfile.gn2'" else cat << \SHAR_EOF > 'mkfile.gn2' CC = gcc CFLAGS = -x c++ -I. -fno-implicit-templates # COPTIONS = -DEGTRUSAGE COPTIONS = libdir = -L. libs = -lcubpack -lm -lg++ MYTESTPROG = main.o .c.o: ; $(CC) $(CFLAGS) -c $*.c chrono.o: chrono.c $(CC) $(CFLAGS) $(COPTIONS) -c chrono.c OBJS = \ point2D.o \ C2.o \ C2dv2.o \ C2dv4.o \ C2interf.o \ C2prc.o \ C2rule13.o \ C2toS2.o \ C2togr.o \ E2tostrp.o \ E2.o \ E2adapt.o \ E2interf.o \ E2sec.o \ E2secitf.o \ E2secprc.o \ S2.o \ S2adapt.o \ S2interf.o \ S2rule13.o \ T2.o \ T2dv4.o \ T2interf.o \ T2rule13.o \ T2tops.o \ atomreg.o \ boolean.o \ chrono.o \ compreg.o \ eval_ctr.o \ geometry.o \ gr.o \ gritf.o \ gs.o \ gsitf.o \ gsprc.o \ integran.o \ integrat.o \ invert.o \ outS2.o \ outS2itf.o \ polC2.o \ polC2itf.o \ polC2prc.o \ ps.o \ psitf.o \ refcount.o \ regcoll.o \ reginfo.o \ region.o \ semstitf.o \ semistrp.o \ sttosmst.o \ strip.o \ stripitf.o \ translat.o \ trnsfrm.o \ gnu262tp.o all:: libcubpack.a libcubpack.a: $(OBJS) ar rus libcubpack.a $(OBJS) tst: $(MYTESTPROG) $(CC) $(MYTESTPROG) $(libdir) $(libs) -o tst clean: /bin/rm -f *.o tst core SHAR_EOF fi # end of overwriting check if test -f 'mkfile.gn3' then echo shar: will not over-write existing file "'mkfile.gn3'" else cat << \SHAR_EOF > 'mkfile.gn3' CC = g++ CFLAGS = -I. -fno-implicit-templates # COPTIONS = -DEGTRUSAGE COPTIONS = libdir = -L. libs = -lcubpack -lm MYTESTPROG = main.o .c.o: ; $(CC) $(CFLAGS) -c $*.c chrono.o: chrono.c $(CC) $(CFLAGS) $(COPTIONS) -c chrono.c OBJS = \ point2D.o \ C2.o \ C2dv2.o \ C2dv4.o \ C2interf.o \ C2prc.o \ C2rule13.o \ C2toS2.o \ C2togr.o \ E2tostrp.o \ E2.o \ E2adapt.o \ E2interf.o \ E2sec.o \ E2secitf.o \ E2secprc.o \ S2.o \ S2adapt.o \ S2interf.o \ S2rule13.o \ T2.o \ T2dv4.o \ T2interf.o \ T2rule13.o \ T2tops.o \ atomreg.o \ boolean.o \ chrono.o \ compreg.o \ eval_ctr.o \ geometry.o \ gr.o \ gritf.o \ gs.o \ gsitf.o \ gsprc.o \ integran.o \ integrat.o \ invert.o \ outS2.o \ outS2itf.o \ polC2.o \ polC2itf.o \ polC2prc.o \ ps.o \ psitf.o \ refcount.o \ regcoll.o \ reginfo.o \ region.o \ semstitf.o \ semistrp.o \ sttosmst.o \ strip.o \ stripitf.o \ translat.o \ trnsfrm.o \ gnu262tp.o all:: libcubpack.a libcubpack.a: $(OBJS) ar rus libcubpack.a $(OBJS) tst: $(MYTESTPROG) $(CC) $(MYTESTPROG) $(libdir) $(libs) -o tst clean: /bin/rm -f *.o tst core SHAR_EOF fi # end of overwriting check if test -f 'mkfile.rs6000' then echo shar: will not over-write existing file "'mkfile.rs6000'" else cat << \SHAR_EOF > 'mkfile.rs6000' CC = xlC -+ #CFLAGS = -O CFLAGS = -I. libdir = libs = -lm MYTESTPROG = main.o .c.o: ; $(CC) $(CFLAGS) -c $*.c OBJS = \ point2D.o \ C2.o \ C2dv2.o \ C2dv4.o \ C2interf.o \ C2prc.o \ C2rule13.o \ C2toS2.o \ C2togr.o \ E2tostrp.o \ E2.o \ E2adapt.o \ E2interf.o \ E2sec.o \ E2secitf.o \ E2secprc.o \ S2.o \ S2adapt.o \ S2interf.o \ S2rule13.o \ T2.o \ T2dv4.o \ T2interf.o \ T2rule13.o \ T2tops.o \ atomreg.o \ boolean.o \ chrono.o \ compreg.o \ eval_ctr.o \ geometry.o \ gr.o \ gritf.o \ gs.o \ gsitf.o \ gsprc.o \ integran.o \ integrat.o \ invert.o \ outS2.o \ outS2itf.o \ polC2.o \ polC2itf.o \ polC2prc.o \ ps.o \ psitf.o \ refcount.o \ regcoll.o \ reginfo.o \ region.o \ semstitf.o \ semistrp.o \ sttosmst.o \ strip.o \ stripitf.o \ translat.o \ trnsfrm.o all:: $(OBJS) tst: $(MYTESTPROG) $(CC) $(CFLAGS) $(MYTESTPROG) $(OBJS) $(libdir) $(libs) -o tst clean: /bin/rm -f *.o run tst core SHAR_EOF fi # end of overwriting check if test -f 'mkfile.solaris' then echo shar: will not over-write existing file "'mkfile.solaris'" else cat << \SHAR_EOF > 'mkfile.solaris' CC = CC # If you have CC version SC3.0 of 15 Dec 1993, then use the following # to activated the workaround # CFLAGS = -I. -DSOLARIS # If you have CC version SC3.0.1 of 13 Jul 1994, then use CFLAGS = -I. libdir = -L. libs = -lcubpack -lm MYTESTPROG = main.o .c.o: ; $(CC) $(CFLAGS) -c $*.c OBJS = \ point2D.o \ C2.o \ C2dv2.o \ C2dv4.o \ C2interf.o \ C2prc.o \ C2rule13.o \ C2toS2.o \ C2togr.o \ E2tostrp.o \ E2.o \ E2adapt.o \ E2interf.o \ E2sec.o \ E2secitf.o \ E2secprc.o \ S2.o \ S2adapt.o \ S2interf.o \ S2rule13.o \ T2.o \ T2dv4.o \ T2interf.o \ T2rule13.o \ T2tops.o \ atomreg.o \ boolean.o \ chrono.o \ compreg.o \ eval_ctr.o \ geometry.o \ gr.o \ gritf.o \ gs.o \ gsitf.o \ gsprc.o \ integran.o \ integrat.o \ invert.o \ outS2.o \ outS2itf.o \ polC2.o \ polC2itf.o \ polC2prc.o \ ps.o \ psitf.o \ refcount.o \ regcoll.o \ reginfo.o \ region.o \ semstitf.o \ semistrp.o \ sttosmst.o \ strip.o \ stripitf.o \ translat.o \ trnsfrm.o all:: libcubpack.a libcubpack.a: $(OBJS) $(CC) -xar -o libcubpack.a $(OBJS) tst: $(MYTESTPROG) $(CC) $(MYTESTPROG) $(libdir) $(libs) -o tst clean: /bin/rm -f *.o run tst core /bin/rm -r -f Templates.DB SHAR_EOF fi # end of overwriting check if test -f 'mkfile.tc' then echo shar: will not over-write existing file "'mkfile.tc'" else cat << \SHAR_EOF > 'mkfile.tc' # Makefile for Cubpack++ installation using Turbo C++ under MS-DOS # File suffixes C = .c # C++ code H = .h # C++ header O = .obj # Compiled code X = .exe # Executable # File delete utility RM = del # Compiler name and flags CC = tcc # Must be 3.0 or later CFLAGS = -v -P -I. -ml # This combination works. Many others don't. # COPTIONS = -DEGTRUSAGE COPTIONS = MYTESTPROG = main$(O) $(C)$(O): $(CC) $(CFLAGS) -c $*$(C) chrono$(O): chrono$(C) $(CC) $(CFLAGS) $(COPTIONS) -c chrono$(C) main$(O): main$(C) $(CC) $(CFLAGS) -c main$(C) OBJS = \ point2D$(O) \ C2$(O) \ C2dv2$(O) \ C2dv4$(O) \ C2interf$(O) \ C2prc$(O) \ C2rule13$(O) \ C2toS2$(O) \ C2togr$(O) \ E2tostrp$(O) \ E2$(O) \ E2adapt$(O) \ E2interf$(O) \ E2sec$(O) \ E2secitf$(O) \ E2secprc$(O) \ S2$(O) \ S2adapt$(O) \ S2interf$(O) \ S2rule13$(O) \ T2$(O) \ T2dv4$(O) \ T2interf$(O) \ T2rule13$(O) \ T2tops$(O) \ atomreg$(O) \ boolean$(O) \ chrono$(O) \ compreg$(O) \ eval_ctr$(O) \ geometry$(O) \ gr$(O) \ gritf$(O) \ gs$(O) \ gsitf$(O) \ gsprc$(O) \ integran$(O) \ integrat$(O) \ invert$(O) \ outS2$(O) \ outS2itf$(O) \ polC2$(O) \ polC2itf$(O) \ polC2prc$(O) \ ps$(O) \ psitf$(O) \ refcount$(O) \ regcoll$(O) \ reginfo$(O) \ region$(O) \ semstitf$(O) \ semistrp$(O) \ sttosmst$(O) \ strip$(O) \ stripitf$(O) \ translat$(O) \ trnsfrm$(O) all: cubpack.lib cubpack.lib: $(OBJS) tlib.rsp tlib cubpack @tlib.rsp tst$(X): $(MYTESTPROG) $(CC) $(CFLAGS) -etst$(X) cubpack.lib $(MYTESTPROG) tst.out: tst$(X) tst > tst.out type tst.out clean: $(RM) *$(O) $(RM) tst$(X) $(RM) cubpack.lib $(RM) tlib.rsp $(RM) *.out tlib.rsp: # TLIB response file copy &&| /C & /P64 & +point2D$(O) & +C2$(O) & +C2dv2$(O) & +C2dv4$(O) & +C2interf$(O) & +C2prc$(O) & +C2rule13$(O) & +C2toS2$(O) & +C2togr$(O) & +E2tostrp$(O) & +E2$(O) & +E2adapt$(O) & +E2interf$(O) & +E2sec$(O) & +E2secitf$(O) & +E2secprc$(O) & +S2$(O) & +S2adapt$(O) & +S2interf$(O) & +S2rule13$(O) & +T2$(O) & +T2dv4$(O) & +T2interf$(O) & +T2rule13$(O) & +T2tops$(O) & +atomreg$(O) & +boolean$(O) & +chrono$(O) & +compreg$(O) & +eval_ctr$(O) & +geometry$(O) & +gr$(O) & +gritf$(O) & +gs$(O) & +gsitf$(O) & +gsprc$(O) & +integran$(O) & +integrat$(O) & +invert$(O) & +outS2$(O) & +outS2itf$(O) & +polC2$(O) & +polC2itf$(O) & +polC2prc$(O) & +ps$(O) & +psitf$(O) & +refcount$(O) & +regcoll$(O) & +reginfo$(O) & +region$(O) & +semstitf$(O) & +semistrp$(O) & +sttosmst$(O) & +strip$(O) & +stripitf$(O) & +translat$(O) & +trnsfrm$(O) | tlib.rsp SHAR_EOF fi # end of overwriting check if test -f 'Mk.decalpha' then echo shar: will not over-write existing file "'Mk.decalpha'" else cat << \SHAR_EOF > 'Mk.decalpha' CUBPACK = /home/ronald/Research/Cubpack++ MYTESTPROG = tmp.o TARGET = tst ######################################################### LIB_DIR=$(CUBPACK)/Src INCLUDE_DIR=$(CUBPACK)/Src CC = cxx CFLAGS = -I$(INCLUDE_DIR) libdir = -L$(LIB_DIR) libs = -lcubpack -lm .SUFFIXES: .o .C .C.o: ; $(CC) $(CFLAGS) -c $*.C $(TARGET): $(MYTESTPROG) $(CC) $(MYTESTPROG) $(libdir) $(libs) -o $(TARGET) clean: /bin/rm -f *.o $(TARGET) core SHAR_EOF fi # end of overwriting check if test -f 'Mk.gn1' then echo shar: will not over-write existing file "'Mk.gn1'" else cat << \SHAR_EOF > 'Mk.gn1' CUBPACK = /home/ronald/Research/Cubpack++ MYTESTPROG = vb5.o TARGET = tst ######################################################### LIB_DIR=$(CUBPACK)/Src INCLUDE_DIR=$(CUBPACK)/Src CC = gcc CFLAGS = -x c++ -I$(INCLUDE_DIR) libdir = -L$(LIB_DIR) libs = -lcubpack -lm -lg++ .c.o: ; $(CC) $(CFLAGS) -c $*.c $(TARGET): $(MYTESTPROG) $(CC) $(MYTESTPROG) $(libdir) $(libs) -o $(TARGET) clean: /bin/rm -f *.o $(TARGET) core SHAR_EOF fi # end of overwriting check if test -f 'Mk.gn2' then echo shar: will not over-write existing file "'Mk.gn2'" else cat << \SHAR_EOF > 'Mk.gn2' CUBPACK = /home/ronald/Research/Cubpack++ MYTESTPROG = vb5.o TARGET = tst ######################################################### LIB_DIR=$(CUBPACK)/Src INCLUDE_DIR=$(CUBPACK)/Src CC = gcc CFLAGS = -x c++ -I$(INCLUDE_DIR) -fno-implicit-templates libdir = -L$(LIB_DIR) libs = -lcubpack -lm -lg++ .c.o: ; $(CC) $(CFLAGS) -c $*.c $(TARGET): $(MYTESTPROG) $(CC) $(MYTESTPROG) $(libdir) $(libs) -o $(TARGET) clean: /bin/rm -f *.o $(TARGET) core SHAR_EOF fi # end of overwriting check if test -f 'Mk.gn3' then echo shar: will not over-write existing file "'Mk.gn3'" else cat << \SHAR_EOF > 'Mk.gn3' CUBPACK = /home/ronald/Research/Cubpack++ MYTESTPROG = vb5.o TARGET = tst ######################################################### LIB_DIR=$(CUBPACK)/Src INCLUDE_DIR=$(CUBPACK)/Src CC = g++ CFLAGS = -I$(INCLUDE_DIR) -fno-implicit-templates libdir = -L$(LIB_DIR) libs = -lcubpack -lm .c.o: ; $(CC) $(CFLAGS) -c $*.c $(TARGET): $(MYTESTPROG) $(CC) $(MYTESTPROG) $(libdir) $(libs) -o $(TARGET) clean: /bin/rm -f *.o $(TARGET) core SHAR_EOF fi # end of overwriting check if test -f 'Mk.solaris' then echo shar: will not over-write existing file "'Mk.solaris'" else cat << \SHAR_EOF > 'Mk.solaris' CUBPACK = /home/ronald/Cubpack++ MYTESTPROG = vb7.o TARGET = tst ######################################################### LIB_DIR=$(CUBPACK)/Src INCLUDE_DIR=$(CUBPACK)/Src CC = CC CFLAGS = -I$(INCLUDE_DIR) libdir = -L$(LIB_DIR) libs = -lcubpack -lm .c.o: ; $(CC) $(CFLAGS) -c $*.c $(TARGET): $(MYTESTPROG) $(CC) $(MYTESTPROG) $(libdir) $(libs) -o $(TARGET) clean: /bin/rm -f *.o $(TARGET) core SHAR_EOF fi # end of overwriting check if test -f 'Mk.tc' then echo shar: will not over-write existing file "'Mk.tc'" else cat << \SHAR_EOF > 'Mk.tc' # Makefile for running Cubpack++ applications using Turbo C++ under MS-DOS CUBPACK = D:\CUBPACK MYTESTPROG = C2toquad.obj quadril.obj quadritf.obj testquad.obj TARGET = tst.exe # You should not need to change anything after this ############################################################################# LIB_DIR=$(CUBPACK)/Src INCLUDE_DIR=$(CUBPACK)/Src # File suffixes C = .c # C++ code H = .h # C++ header O = .obj # Compiled code X = .exe # Executable # File delete utility RM = del # Compiler name and flags. The given compiler options work with # Turbo C++ 3.0. Many others don't. CC = tcc CFLAGS = -v -P -I$(INCLUDE_DIR) -ml libdir = -L$(LIB_DIR) $(C)$(O): $(CC) $(CFLAGS) -c $*$(C) >> compiler.log $(TARGET): $(MYTESTPROG) $(CC) $(CFLAGS) -e$(TARGET) $(libdir) cubpack.lib $(MYTESTPROG) clean: $(RM) *.$(O) $(TARGET) SHAR_EOF fi # end of overwriting check cd .. if test -f 'README.1st' then echo shar: will not over-write existing file "'README.1st'" else cat << \SHAR_EOF > 'README.1st' ////////////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools (ronald@cs.kuleuven.ac.be) // // Dirk Laurie (dirk@calvyn.puk.ac.za) // // Luc Pluym // // // ////////////////////////////////////////////////////////////// // // // Last modification of source code: April 4, 1996 // // Last modification of text : May 23, 1996 // // // ////////////////////////////////////////////////////////////// This version is available by anonymous ftp from ftp.cs.kuleuven.ac.be in /pub/NumAnal-ApplMath/Cubpack/all.tar.gz or /pub/NumAnal-ApplMath/Cubpack/all.zip and also by using a World Wide Web browser such as xmosaic via "http://www.cs.kuleuven.ac.be/~ronald/". If you tell us who you are, we promise to keep you informed about corrections, updates and extensions. If you need assistance, please always mention the two dates above. The next file to read is named INSTALL. Enjoy Cubpack++ ! SHAR_EOF fi # end of overwriting check if test -f 'README.DOS' then echo shar: will not over-write existing file "'README.DOS'" else cat << \SHAR_EOF > 'README.DOS' [ If you are using UNIX, read the file README instead of this one. ] 23 May 1996 The current version of Cubpack++ is Version 0.1h = 1.0 ====================================================== |The complete Cubpack++ distribution is in the file all.zip . | |Switch your ftp to binary mode before you get this file. | |Once you have this file on your machine, you have to execute | unzip -aL all.zip |You now have a directory named CUBPACK . --------------------------------------------------------------------- Start by reading CUBPACK\DOCUMENT\PAPER.* and CUBPACK\DOCUMENT\USERMAN.* and CUBPACK\README.1ST Enjoy Cubpack++! SHAR_EOF fi # end of overwriting check if test -f 'README' then echo shar: will not over-write existing file "'README'" else cat << \SHAR_EOF > 'README' [ If you are using MSDOS, read the file README.DOS instead of this one. ] 23 May 1996 The current version of Cubpack++ is Version 0.1h = 1.0 ====================================================== First check which decompression program is available on your machine. IF you have gunzip and tar THEN |The complete Cubpack++ distribution is in the file all.tar.gz . |(Yes, all patches are already included in this.) | |Switch your ftp to binary mode before you get this file. | |Once you have this file on your machine, you have to execute | gunzip all.tar.gz | tar xf all.tar |You now have a directory named Cubpack++ . --------------------------------------------------------------------- IF you have unzip THEN |The complete Cubpack++ distribution is in the file all.zip . | |Switch your ftp to binary mode before you get this file. | |Once you have this file on your machine, you have to execute | unzip all.zip |You now have a directory named Cubpack . --------------------------------------------------------------------- Start by reading Cubpack{++}/Documentation/paper.* and Cubpack{++}/Documentation/userman.* and Cubpack{++}/README.1st Enjoy Cubpack++! SHAR_EOF fi # end of overwriting check if test -f 'CONTENTS' then echo shar: will not over-write existing file "'CONTENTS'" else cat << \SHAR_EOF > 'CONTENTS' What you find in the current directory -------------------------------------- README.1st : information you should first look at CONTENTS : this file INSTALL : hints to get Cubpack++ up and running Makefile : primitive Makefile for unix systems INSTALL.BAT : installation for MS-DOS systems TESTCASE.BAT : running test cases on MS-DOS systems quick_install : script invoked by `make install' quick_run : script invoked by `make run' Src : directory with all source code Documentation : directory with documentation See Documentation/CONTENTS for details. Drivers : directory with example programs See Documentation/CONTENTS for details. Tools : directory with unix tools to change suffixes and makefiles for several systems See Documentation/CONTENTS for details. Note that on MSDOS systems, the file names are all in the same case and truncated to conform to the 8.3 naming restriction. We have taken care to ensure that no conflicts arise. SHAR_EOF fi # end of overwriting check if test -f 'INSTALL' then echo shar: will not over-write existing file "'INSTALL'" else cat << \SHAR_EOF > 'INSTALL' How to get Cubpack++ up and running? ------------------------------------ 1) Getting the suffix right --------------------------- At this stage of C++, a uniform installation procedure is impossible (one of the reasons is that templates are treated differently by different systems). With this file we provide some help. At the moment all source code is located in one directory, named `Src'. All C++ source files have suffix .c on the distribution. Start with verifying what suffix your compiler expects. - If this is .c, you have nothing to change. (This is the case with e.g. gcc (gnu), xlC (IBM), CC (Sun). With some other compilers (e.g. Turbo C++) this is not the default, but you can specify it with a compiler option.) - If there is absolutely no way to persuade your compiler to accept .c files as C++ code, you have to change not only the suffixes of the files itself but also inside the header files of template classes where .c files are included. For those working on Unix systems, we provided some shell scripts to do this. These are located in the directory `Tools'. Change your current working directory to `Tools', learn from the file `CONTENTS' which script you need and execute if from where you are. Other users can learn from these scripts (e.g. c2C) which files they have to modify. 2) Compile the package ---------------------- Those working on a Unix system can now try to execute make install in the parent directory. Then you can choose between the several compilers we used. Those working on MSDOS can now try to execute INSTALL in the parent directory, and choose a compiler. Now you can go for coffee or lunch, depending on your platform. Some timings to give you an idea: IBM RS6000 AIX 3.2.5, xlC compiler - 181.0u 34.0s 6:09 58% i586 90 MHz Linux1.2.4, g++ compiler (gcc v2.7.2) - 208.79u 36.69s 4:29.19 91% DECalpha OSF/1 V1.3, cxx compiler - 272.08u 62.45s 13:00 42% Sparccenter 1000, SunOS 5.3, g++ compiler ( gcc v2.7.2) - 296.0u 49.0s 7:28 76% DECstation 5000/240 ULTRIX V4.4 , g++ compiler (gcc v2.7.2) - 366.3u 85.6s 15:31 48% Sparccenter 1000, SunOS 5.3, CC compiler - 286.0u 186.0s 28:49 27% i486 33MHz MS-DOS Turbo C++ 3.0 compiler - 7min38s elapsed time HP, HP-UX, g++ compiler (gcc v2.6.0) - 499.2u 41.3s 10:36 84% DECstation 5000/120 ULTRIX V4.4 , g++ compiler (gcc v2.7.2) - 747.8u 148.6s 19:45 75% --------------- | If you use one of the platforms on which we tested Cubpack++ no | problem should occur. If it does, please let us know. | | If you use another Unix platform, writing a specific makefile (by | modifying one of those we provided in the directory Tools) and | extending the script quick_install, should be straitforward. If | you are not feeling that familiar with makefiles, please ask and | we will help. | | If you are not using a Unix platform, we hope you know enough | about your system to get Cubpack++ at work. Probably you can | still find useful information in the makefiles we provided in the | directory Tools. --------------- This was the time consuming part which never has to be done again if you continue to use the same platform. 3) Trying some examples ----------------------- Those working on a Unix system can now try to execute make run in the parent directory. You are requested to select a main program. You can choose among the examples we provided or enter the name of your own main program. When the compilation finished successfully, an executable named `tst' is available in the parent directory. Those working on MSDOS can now try to execute TESTCASE n in the parent directory, where n is a number in the range 1 to 11. (Executing TESTCASE without a number will give a menu.) The corresponding main program will be copied into the CODE directory, compiled, linked and executed. The output will be written to the file CODE\VBn.OUT and may be compared with EXAMPLES\VBn.OUT. --------------- | If you have problems linking with libcubpack.a you can replace | this with $(OBJS) in the lines that define tst. --------------- 4) Using Cubpack++ ------------------ It is of course far from ideal that the user program has to be copied into the directory where the Cubpack++ source code is located. Because templates are treated differently on different platforms, we cannot (yet) provide a good alternative for all platforms. The ideal solution we have in mind can be realized for those using the gnu gcc compiler, the cxx compiler on DECalpha OSF or the CC compiler on Solaris. In the directory Tools we provided a Makefile which a user can copy into his working directory. He should modify the values of the constants CUBPACK, MYTESTPROG and TARGET in the beginning of these files, depending on his situation and wishes. 5) Cleaning up -------------- To remove all object files, archive, the template data base, execute make clean in the parent directory. 6) In case of problems ---------------------- In case of installation problems, please don't wait to contact one of the authors: ----------------------------------------------------------------------------- | Name : Ronald Cools | | Email : ronald.cools@cs.kuleuven.ac.be Katholieke Universiteit Leuven | | ronald@cs.kuleuven.ac.be Department of Computer Science | | Celestijnenlaan 200 A | | Fax : +(32) 16 32 79 96 B-3001 HEVERLEE | | Phone : +(32) 16 32 75 62 BELGIUM | ----------------------------------------------------------------------------- For MSDOS installation, contact: ----------------------------------------------------------------------------- | Name : Dirk Laurie | | Email : dirk@calvyn.puk.ac.za Potchefstroomse Universiteit vir CHO | | na.dlaurie@na-net.ornl.gov Department of Mathematics | | P.O.Box 1174 | | Fax : +(27) 16 807 3614 1900 VANDERBIJLPARK | | Phone : +(27) 16 807 3600 South Africa | ----------------------------------------------------------------------------- SHAR_EOF fi # end of overwriting check if test -f 'INSTALL.BAT' then echo shar: will not over-write existing file "'INSTALL.BAT'" else cat << \SHAR_EOF > 'INSTALL.BAT' @echo off if "%1"=="" goto 1 rem Quick installation on MS-DOS systems using Turbo C++ copy tools\mkfile.%1 code\makefile echo --------------------------------------------------- echo Compilation will now start. This will take a while. echo --------------------------------------------------- chdir code make clean rem The REM'd lines below record start/finish times, and require an rem empty file called CR in the root directory rem type ..\cr|time>time make all rem type ..\cr|time>>time chdir .. goto 2 :1 echo 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴커 echo � Available makefiles under MSDOS � echo � � echo � tc Turbo C++ version 3.00 and later � echo � gnu Gnu C++ version 2.6.0 and earlier � echo � gn2 Gnu C++ version 2.6.2 and later � echo � � echo � Type 'install OPTION' at the DOS prompt to install � echo � the chosen OPTION; e.g. 'install tc'. � echo 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸 :2 SHAR_EOF fi # end of overwriting check if test -f 'TESTCASE.BAT' then echo shar: will not over-write existing file "'TESTCASE.BAT'" else cat << \SHAR_EOF > 'TESTCASE.BAT' @echo off if "%1"=="" goto 1 copy examples\vb%1.c code\main.c chdir code del main.obj del tst.* make tst.out rename tst.out vb%1.out chdir .. goto 2 :1 echo 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� echo � Available examples for Cubpack++ � echo � � echo � vb1 CIRCLE � echo � vb2 PLANE_SECTOR (quadrant) � echo � vb3 PLANE_SECTOR (wedge) � echo � vb4 GENERALIZED_RECTANGLE (parabola) � echo � vb5 GENERALIZED_RECTANGLE (lemniscate) � echo � vb6 SEMI_INFINITE_STRIP � echo � vb7 SEMI_INFINITE_STRIP � echo � vb8 INFINITE_STRIP � echo � vb9 RECTANGLE � echo � vb10 TRIANGLE � echo � vb10 TRIANGLE � echo � vb11 PLANE_SECTOR (wedge) � echo � � echo � Type 'testcase 1' etc. at the DOS � echo � prompt to activate one of these options. � echo 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� :2 SHAR_EOF fi # end of overwriting check if test -f 'quick_install' then echo shar: will not over-write existing file "'quick_install'" else cat << \SHAR_EOF > 'quick_install' #!/bin/sh # # Constants that must be adjusted # SRC_DIR=Src TOOL_DIR=Tools # ####################################################################### echo "This script should make it easier for you to install Cubpack++." echo "An appropriate makefile is selected based on the brand of unix" echo "you use." echo "Available are" echo " (1) IBM RS6000 - AIX - XlC compiler" echo " (2) DEC alpha - DEC OSF - cxx compiler" echo " (3) Unix gnu - gcc or g++ compiler" echo " (4) Solaris 2.* - CC compiler version 4.*" echo echo "Make your choice. \c" read x case $x in 1) cp $TOOL_DIR/mkfile.rs6000 $SRC_DIR/makefile;; 2) cp $TOOL_DIR/mkfile.decalpha $SRC_DIR/makefile;; 3) OLDVERSION1=2.6.0 OLDVERSION2=2.7.0 gcc -v 2> tmp$$ v=`tail -1 tmp$$ | sed "s/^.*version //" | sed "s/ .*$//"` /bin/rm tmp$$ echo "You are using gcc version $v" a=`expr "$v" ">" "$OLDVERSION2"` if test $a = "1" then cp $TOOL_DIR/mkfile.gn3 $SRC_DIR/makefile else a=`expr "$v" ">" "$OLDVERSION1"` if test $a = "1" then cp $TOOL_DIR/mkfile.gn2 $SRC_DIR/makefile else cp $TOOL_DIR/mkfile.gn1 $SRC_DIR/makefile fi fi;; 4) cp $TOOL_DIR/mkfile.solaris $SRC_DIR/makefile;; *) echo "This was an illegal choice!" exit 1 ;; esac ####################################################################### if test -f .lastinstall then y=`cat .lastinstall` /bin/rm -f .lastinstall if test $x != $y then echo "Removing the remains of a previous compilation which might interfere ..." cd $SRC_DIR make clean cd .. echo "... Done." fi fi echo $x > .lastinstall ####################################################################### echo "Do you want to edit the makefile first? [n/y] \c" read a case $a in [Yy]*) vi $SRC_DIR/makefile ;; esac ####################################################################### # echo echo "Compilation will now start. This will take a while." echo cd $SRC_DIR make all SHAR_EOF chmod +x 'quick_install' fi # end of overwriting check if test -f 'quick_run' then echo shar: will not over-write existing file "'quick_run'" else cat << \SHAR_EOF > 'quick_run' #!/bin/sh # # Constants that must be adjusted # SRC_DIR=Src # ####################################################################### if test -f .lastinstall then y=`cat .lastinstall` case $y in 1|3|4) SUFFIX=c;; 2) SUFFIX=C;; *) echo "Unknown compiler used for installation." exit 1;; esac else echo "make install must be executed first." exit 1 fi ####################################################################### echo "Choose a main program from the following list." echo cat Drivers/EXAMPLES echo echo "Make your choice. \c" read a case $a in 0) echo "Give the name of your example file." echo "(Full pathname from current position.)" read a cp $a $SRC_DIR/main.$SUFFIX ;; [1-9]|1[0-8]) cp Drivers/vb${a}.c $SRC_DIR/main.$SUFFIX ;; *) echo "That was an illegal choice!" exit 1 ;; esac ####################################################################### # echo echo "Compilation will now start." echo cd $SRC_DIR make tst SHAR_EOF chmod +x 'quick_run' fi # end of overwriting check if test -f 'Makefile' then echo shar: will not over-write existing file "'Makefile'" else cat << \SHAR_EOF > 'Makefile' SRC_DIR = Src install: ./quick_install run: ./quick_run mv $(SRC_DIR)/tst . echo 'executable "tst" is available.' clean: cd $(SRC_DIR) ; /bin/rm -f *.o tst core makefile cd $(SRC_DIR) ; /bin/rm -f main.c libcubpack.a cd $(SRC_DIR) ; /bin/rm -r -f ptrepository tempinc Templates.DB SHAR_EOF fi # end of overwriting check if test ! -d 'Src' then mkdir 'Src' fi cd 'Src' if test -f 'C2.c' then echo shar: will not over-write existing file "'C2.c'" else cat << \SHAR_EOF > 'C2.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////// //File C2.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////////////////////////////////////// #include #include ////////////////////////////////////////////// Parallelogram::Parallelogram (const Point& p1,const Point& p2,const Point& p3) : Geometry(2),Vertices(3),TheVolumeKnown(False) { Vertices[0] = p1; Vertices[1] = p2; Vertices[2] = p3; } ////////////////////////////////////////////// void Parallelogram::ComputeVolume() { TheVolume = fabs( ((Vertices[0][0]*Vertices[1][1]-Vertices[1][0]*Vertices[0][1]) +(Vertices[1][0]*Vertices[2][1]-Vertices[2][0]*Vertices[1][1]) +(Vertices[2][0]*Vertices[0][1]-Vertices[0][0]*Vertices[2][1])) ); TheVolumeKnown = True; } /////////////////////////////////////////////// const Point& Parallelogram::Vertex(int i) const { return Vertices[i]; } ////////////////////////////////////////////////// real Parallelogram::Volume() const { Parallelogram* P = (Parallelogram*) this; if (!TheVolumeKnown) { P->ComputeVolume(); }; return P->TheVolume; } /////////////////////////////////////////////// void Parallelogram::Volume(real v) { TheVolume = v; TheVolumeKnown = True; } //////////////////////////////////////////////// //Processor* //Parallelogram::DefaultProcessor() //const //{ //return new SimpleAdaptive //(new Parallelogram_Rule13, //new Parallelogram_Divide4); //} /////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'C2dv2.c' then echo shar: will not over-write existing file "'C2dv2.c'" else cat << \SHAR_EOF > 'C2dv2.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////////////// //File C2dv2.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(long lines split) ///////////////////////////////////////////////// #include #include #include #include ////////////////////////////////////////////////// void Parallelogram_Divide2::Apply (const Parallelogram& t, Stack& Offspring, const Vector& DiffOrder) { Point m12 = (t.Vertex(0)+t.Vertex(DiffOrder[0]))/2; Point m34 = t.Vertex(DiffOrder[1])+(t.Vertex(DiffOrder[0])-t.Vertex(0))/2; Parallelogram* t1 = new Parallelogram(t.Vertex(0),m12,t.Vertex(DiffOrder[1])); Parallelogram* t2 = new Parallelogram(m12,t.Vertex(DiffOrder[0]),m34); Offspring.Push(t1); Offspring.Push(t2); } ////////////////////////////////////////////////// Parallelogram_Divide2::Parallelogram_Divide2() :SameShapeDivisor() { } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'C2dv4.c' then echo shar: will not over-write existing file "'C2dv4.c'" else cat << \SHAR_EOF > 'C2dv4.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////////////// //File C2dv4.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(long lines split) ///////////////////////////////////////////////// #include #include #include ////////////////////////////////////////////////// void Parallelogram_Divide4::Apply (const Parallelogram& t, Stack& Offspring, const Vector& DiffOrder) { Point m12 = (t.Vertex(0)+t.Vertex(1))/2; Point m13 = (t.Vertex(0)+t.Vertex(2))/2; Point m23 = (t.Vertex(2)+t.Vertex(1))/2; Point m24 = t.Vertex(1)+(t.Vertex(2)-t.Vertex(0))/2; Point m34 = t.Vertex(2)+(t.Vertex(1)-t.Vertex(0))/2; Parallelogram* t1 = new Parallelogram(t.Vertex(0),m12,m13); Parallelogram* t2 = new Parallelogram(m12,t.Vertex(1),m23); Parallelogram* t3 = new Parallelogram(m13,m23,t.Vertex(2)); Parallelogram* t4 = new Parallelogram(m23,m24,m34); Offspring.Push(t1); Offspring.Push(t2); Offspring.Push(t3); Offspring.Push(t4); } ////////////////////////////////////////////////// Parallelogram_Divide4::Parallelogram_Divide4() :SameShapeDivisor() { } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'C2interf.c' then echo shar: will not over-write existing file "'C2interf.c'" else cat << \SHAR_EOF > 'C2interf.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////////// //File C2interf.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(typedef introduced) //////////////////////////////////////////////// #include #include #include #include #include #include #include /////////////////////////////////////////////// typedef Rule RuleParallelogram; typedef SameShapeDivisor SameShapeDivisorParallelogram; PARALLELOGRAM::PARALLELOGRAM(const Point& p1, const Point& p2, const Point& p3) :USERINTERFACE() {Pointer R13(new Parallelogram_Rule13); Pointer D4(new Parallelogram_Divide4); Processor *SAP(new SimpleAdaptive(R13,D4)); StoreAtomic(new Parallelogram(p1,p2,p3),SAP); } /////////////////////////////////////////////// RECTANGLE::RECTANGLE(const Point& p1, const Point& p2, const Point& p3) :USERINTERFACE() { Error( fabs((p2-p1)*(p3-p1)) > 100*REAL_EPSILON, "Sides of RECTANGLE not orthogonal"); StoreAtomic(new Parallelogram(p1,p2,p3), //new SimpleAdaptive( //new Parallelogram_Rule13, //new Parallelogram_Divide4)); new Parallelogram_Processor); } /////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'C2prc.c' then echo shar: will not over-write existing file "'C2prc.c'" else cat << \SHAR_EOF > 'C2prc.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //File C2prc.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(typedef introduced and long lines split) //////////////////////////////////////////////////////////// #include #include #include #include #include #include //////////////////////////////////////////////////////// Pointer < Parallelogram_Processor::RuleParallelogram > Parallelogram_Processor::TheRule = new Parallelogram_Rule13; Pointer < Parallelogram_Processor::SameShapeDivisorParallelogram > Parallelogram_Processor::TheDivisor2 = new Parallelogram_Divide2; Pointer < Parallelogram_Processor::SameShapeDivisorParallelogram > Parallelogram_Processor::TheDivisor4 = new Parallelogram_Divide4; //////////////////////////////////////////////////////// Parallelogram_Processor::Parallelogram_Processor() :TimesCalled(0), Diffs(2) { } ///////////////////////////////////////////////////////////// Parallelogram_Processor* Parallelogram_Processor::Descendant() const { Parallelogram_Processor* r = new Parallelogram_Processor; return r; } //////////////////////////////////////////////// void Parallelogram_Processor::Process( Stack& Offspring) { TimesCalled ++; if (TimesCalled == 1) { TheRule->ApplyWithDiffs(LocalIntegrand(),Geometry(),Integral(), AbsoluteError(),Diffs); Offspring.MakeEmpty(); return; }; if(TimesCalled == 2) { real NewVolume = Geometry().Volume()/2; Stack Parts; Vector DiffOrder(Diffs.Size()); const real difffac = 1.81818, difftreshold = 0.00004; if (max(Diffs[0],Diffs[1]) < difftreshold) { TheDivisor4->Apply(Geometry(),Parts,DiffOrder); NewVolume /=2; } else if (Diffs[0]>difffac*Diffs[1]) { DiffOrder[0] = 1 ; DiffOrder[1] = 2; TheDivisor2->Apply (Geometry(),Parts,DiffOrder); } else if (Diffs[1]>difffac*Diffs[0]) { DiffOrder[0] = 2; DiffOrder[1] =1; TheDivisor2->Apply (Geometry(),Parts,DiffOrder); } else { TheDivisor4->Apply(Geometry(),Parts,DiffOrder); NewVolume /=2; }; unsigned int N = Parts.Size(); for (unsigned int i =0;iVolume(NewVolume); Processor* p = Descendant(); Atomic* a = new Atomic(g,p); a->LocalIntegrand(&LocalIntegrand()); Offspring.Push(a); }; return; }; Error(TimesCalled > 2, "Parallelogram_Processor : more than two calls of Process()"); } /////////////////////////////////////////////// Processor* Parallelogram_Processor::NewCopy() const { return new Parallelogram_Processor(*this); } /////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'C2rule13.c' then echo shar: will not over-write existing file "'C2rule13.c'" else cat << \SHAR_EOF > 'C2rule13.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// // //File C2rule13.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(long lines split) ///////////////////////////////////////////////////////// // // A cubature formula of degree 13 with 37 points and associated // null rules. // The cubature formula, from Rabinowitz & Richter, was recomputed // to obtain higher accuracy. // ///////////////////////////////////////////////////////// #include static int K[]={1,2,3,2}; const int NumberOfPoints=K[0]+4*K[1]+4*K[2]+8*K[3]; const int Orbits=K[0]+K[1]+K[2]+K[3]; static real Type1[]={ 0.9909890363004326469792722978603e+00, 0.6283940712305315063814483471116e+00}; static real l1sdl2s = Type1[1]*Type1[1]/Type1[0]/Type1[0]; static real Type2[]={ 0.9194861553393073086142137772149e+00, 0.6973201917871173078084506730937e+00, 0.3805687186904854497424188074662e+00}; static real Type3[2][2]={{0.9708504361720225062147290554088e+00, 0.6390348393207252159077623446225e+00}, {0.8623637916722781475018696425693e+00, 0.3162277660168700033875075593701e+00}}; static real Weight[8][8]={{0.2995235559387052215463143056692e+00, 0.3311006686692356205977471655046e-01, 0.1802214941550624038355347399683e+00, 0.3916727896035153300761243260674e-01, 0.1387748348777288706306435595057e+00, 0.2268881207335707037147066705814e+00, 0.3657395765508995601240002438981e-01, 0.1169047000557533546701746277951e+00}, {7.610781847149629154716409791983e-2, 1.486101247399760261471935168346e-1, -2.077685631717747007172983323970e-1, 6.850758313011924198538315395405e-2, 2.024205813317813585572881715385e-1, 1.108627473745508429879249169864e-1, -1.187411393304862640859204217487e-1, -5.208857468077715683772080394959e-2}, {4.016494861405949747097510013162e-2, -1.093132962444079541048635452881e-1, -2.270251673633777452624380129694e-1, 1.231674163356097016086203579325e-2, -1.420402526499201540699111172200e-1, 1.189080551229557928776504129312e-1, -4.482039658150474743804189300793e-3, 1.730383808319875827592824151609e-1}, {-5.643905795781771973971259866415e-1, 2.878418073676293225652331648545e-2, 1.159354231997583294689565314470e-1, 1.376081498690624477894043101438e-1, -7.909780225340130915490382973570e-2, 1.174335441429478112778176601234e-1, -1.107251942334134124782600707843e-1, 2.094226883312045633400182488252e-2}, {-2.269001713589584730602581694579e-1, 2.976190892690301120078774620049e-2, -7.440193483272787588251423144751e-2, -1.224665989043784131260454301280e-1, -4.857910454732976198562745578156e-2, 2.228157325962656425537280474671e-1, 1.459764751457503859063666414952e-1, -1.211789553452468781539987084682e-1}, {-3.326760468009974589269134283992e-1, 1.796655319904795478676993902115e-1, -4.389976396805911868560791966472e-2, -2.295841771339316497310760908889e-1, 6.182618387692816082856552878852e-2, -1.202703885325137746461829140891e-1, 5.109536580363550180208564374234e-3, 1.126062761533095493689566169969e-1}, {2.290638530086106512999345512401e-1, 2.702070398116919449911037051753e-1, -9.078047988731123605988441792069e-3, 4.618480310858703283999169489655e-2, -2.598231009547631799096616255056e-1, -2.518433931146441037986247681820e-2, -1.257796993152456033984707367389e-2, -2.720818902721190304043617320910e-2}, {2.746908885094872977794932213372e-1, -1.149427039769738298032807785523e-2, 1.596178537820019535731955591283e-1, -2.180626972663360443142752377527e-1, -8.711748038292630173597899697063e-3, 1.902786182960269617633915869710e-1, -1.189840649092108827784089292890e-1, 2.883382565767354162177931122471e-2}}; // // The error estimator constants // static const real crival=0.4 , facmed=8.0; static const real facopt = facmed/(crival*crival); #include #include #include #include #define sqr(x) ((x)*(x)) void Parallelogram_Rule13::ApplyWithDiffs(Integrand& F,Parallelogram& R, real& TheResult,real& TheError, Vector& DiffOrder) { int i,j,p,Type,nr,number; real Null[7]; real Tres = -1.0; real noise,r,r1,r2,r3,Deg5,Deg3,Deg1,Deg7,z1,z2,sumval; real D1,D2; real F0; real FE[2][2][2]; // [l1,l2][vertex1,vertex2][plus,minus] Point x[8]; if (Tres <= 0) { Tres=50*REAL_EPSILON; } TheResult = 0.0; for (i=0;i<7;i++){Null[i]=0;} p=0; for (Type=0;Type <=3;Type++){ for (nr=0;nr= 1) { TheError =facmed*Deg7; } else { if (r>=crival) { TheError = facmed*r*Deg7; } else { TheError = facopt *r*r*r*Deg7; } } TheError = max(noise,TheError); } TheError *= R.Volume()/4; TheResult *=R.Volume()/4; } ////////////////////////////////////////////////// Parallelogram_Rule13::Parallelogram_Rule13() :Rule() { } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'C2toS2.c' then echo shar: will not over-write existing file "'C2toS2.c'" else cat << \SHAR_EOF > 'C2toS2.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////// //File C2toS2.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ////////////////////////////////////////// #include #include #include ////////////////////////////////////////// void PolarToRectangular::Transform(real& w, Point& p) { Point P(p.R()*cos(p.Theta()),p.R()*sin(p.Theta())); w *= p.R(); p = P; } /////////////////////////////////////////// PolarToRectangular::PolarToRectangular() : Transformation() { } /////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'C2togr.c' then echo shar: will not over-write existing file "'C2togr.c'" else cat << \SHAR_EOF > 'C2togr.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////// //File gr.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////////////////////////////////////// #include #include //////////////////////////////////////////// void C2toGR::Transform(real& w, Point& p) { GeneralizedRectangle& G = *GR_ptr; Point M = G.B()-G.A(); Point C = G.A() + p.X()*M; real ml = M.Length(); real dist = G.Boundary(C), ratio=dist/ml; Point P(-ratio*M.Y(),ratio*M.X()); w *= dist*ml; p = C+p.Y()*P; } /////////////////////////////////////////////////// C2toGR::C2toGR(GeneralizedRectangle* g) : Transformation(),GR_ptr(g) { } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'E2.c' then echo shar: will not over-write existing file "'E2.c'" else cat << \SHAR_EOF > 'E2.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// //File E2.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Nov 1994 V0.1d(re-ordering of member initializers) ///////////////////////////////////////////////////////// #include #include #include #include ///////////////////////////////////////////////////////// Plane::Plane () : Geometry(2), xscale(1.0), yscale(1.0), TheCenter(0,0) { } ///////////////////////////////////////////////////////// Plane::Plane (const Point& center) : Geometry(2), xscale(1.0), yscale(1.0), TheCenter(center) { } ///////////////////////////////////////////////////////// Plane::Plane(const Point& center, real x, real y) : Geometry(2), xscale(x), yscale(y), TheCenter(center) { } ///////////////////////////////////////////////////////// real Plane::ScaleX() const { return xscale; } ///////////////////////////////////////////////////////// real Plane::ScaleY() const { return yscale; } ///////////////////////////////////////////////////////// //Processor* //Plane::DefaultProcessor() //const //{ //return new PlaneAdaptive; //} ///////////////////////////////////////////////////////// const Point& Plane::Center() const { return TheCenter; } ///////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'E2adapt.c' then echo shar: will not over-write existing file "'E2adapt.c'" else cat << \SHAR_EOF > 'E2adapt.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////// //File E2.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////////////////////////////////////// #include #include #include #include #include #include #include #include /////////////////////////////////////////////// #define sqr(x) ((x)*(x)) static int K[]={0,3,2,2}; const int NumberOfPoints=K[0]+4*K[1]+4*K[2]+8*K[3]; const int Orbits=K[0]+K[1]+K[2]+K[3]; static real Type1[]= {0.5460844152585403666984417e+00 , 0.1376486679696350642323050e+01 , 0.2358932261980680967828022e+01}; static real Type2[]= {0.8462499884480199068814807e+00 , 0.1985531339917884990890422e+01}; static real Type3[2][2]= {{0.1779246738905319006374908e+01 , 0.9318240227761998500475049e+00}, {0.3030436065368579151664045e+01 , 0.9962534261727632104611162e+00}}; static real OrigWeight[7]= {0.1418036987406628465242303e+00, 0.3807850175899473939094384e-01, 0.1290856883945041937607418e-02, 0.5772571826901623901546648e-01, 0.1620590503146543183518239e-03, 0.5445472363593369147167489e-02, 0.2411028493987025953260209e-04}; static int d[]={0,3,1,5,2,4,6}; static real Weight[7][7]= {{0.6002713316445080080142126, 0.7955990316249109629216728, 1.0584888443837658614605899, 0.7595383160846588054989698, 1.3523576929325600784468914, 0.9663531601396869556259704, 1.9895758469520118113052969}, {-0.1714120818975139, -1.4261615934658296, 20.9491066359021694, 1.7029699666146943, 57.2013795938251143, -4.3332227154742827, -175.0624620496226842}, {-0.2883800695213331, 2.5450105556734605, 2.8699527274413806, 0.304671504643251, 138.1913876850488233, -8.5573830821954439, -18.7930973279112966}, {-0.250456836419066, 0.3273926337592694, -83.9551965137636766, 0.4609375440071548, -365.1974538111883157, 10.4127651350263225, 1537.3605596124529503}, {-0.2595143739988262, 0.1255865390202144, 85.4652862386879934, -0.2489288730337109, -712.5513360902265439, 6.3018929219370941, -645.6559424743654782}, {-0.24820543230912, -0.2143965818640334, 8.5337065366470588, -0.2238393816932916, 867.6556565044116888, 7.6084037588845301, -4712.804729866979117}, {0.3052968227487744, 1.0011209710514362, -6.3357177267870899, 0.7227067892680122, -358.0249035190603089, 2.7469614313645364, -6407.2910382311609777}}; // Radii of rings associated with weights of published formula static real RingRadius[]= {0.9151577658134376, 1.2649388389767648, 1.7333214530567136, 2.2616892861784437, 2.6609731353556634, 2.9246248487342039, 6.0979478618219725}; //This is `infinity'. Never used actually // // The error estimator constants // const real crival=0.5 , facmed=5.0; const real facopt = facmed/(crival*crival); ////////////////////////////////////////////////////// void PlaneAdaptive::Rule(Integrand& F,Plane& R,real& TheResult,real& TheError,real& HalfValueRadius) { int i,j,p,Type,nr,number; real Null[6],OrbitContrib[7],below,above,fraction; real Tres = 50*REAL_EPSILON; real noise,r,r1,r2,r3,Deg5,Deg3,Deg7,Deg1,sumval; real A=1.0/R.ScaleX() , B=1.0/R.ScaleY(); Point x[8]; TheResult = 0.0; for (i=0;i<6;i++){Null[i]=0;} p=0; for (Type=0;Type <=3;Type++){ for (nr=0;nr= 1) { TheError =facmed*Deg7; } else { if (r>=crival) { TheError = facmed*r*Deg7; } else { TheError = facopt *r*r*r*Deg7; } } TheError = max(noise,TheError); } TheResult *= (A*B); TheError *= (A*B); // cout <<"=> Error = "<& Offspring) { TimesCalled++; if (TimesCalled==1) { Rule(LocalIntegrand(),Geometry(),Integral(),AbsoluteError(),HalfValueRadius); } else { const Point& C=Geometry().Center(); Offspring.Push(( AtomicRegion*) CIRCLE(C,HalfValueRadius)); Offspring.Push(( AtomicRegion*) OUT_CIRCLE(C,HalfValueRadius)); Offspring.IteratorReset(); while (!Offspring.IteratorAtEnd()) { Offspring.IteratorNext()->LocalIntegrand(&LocalIntegrand()); }; } } /////////////////////////////////////////////////// PlaneAdaptive::PlaneAdaptive() :Processor(),TimesCalled(0),HalfValueRadius(0) { } //////////////////////////////////////////////////// Processor* PlaneAdaptive::NewCopy() const { return new PlaneAdaptive(*this); } ////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'E2interf.c' then echo shar: will not over-write existing file "'E2interf.c'" else cat << \SHAR_EOF > 'E2interf.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// /////////// //File E2interf.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////// #include #include /////////////////////// PLANE::PLANE() { StoreAtomic(new Plane,new PlaneAdaptive); } ////////////////////////////////////////////// PLANE::PLANE(const Point& Center) { StoreAtomic(new Plane(Center),new PlaneAdaptive); } ////////////////////////////////////////////// PLANE::PLANE(const Point& Center, real ScaleX, real ScaleY) { StoreAtomic(new Plane(Center,ScaleX, ScaleY),new PlaneAdaptive); } /////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'E2sec.c' then echo shar: will not over-write existing file "'E2sec.c'" else cat << \SHAR_EOF > 'E2sec.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////// //File E2sec.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 14 Feb 1995 V0.1e(bug fix in transformation) ////////////////////////////////////////// #include #include #include ////////////////////////////////////////// PlaneSector::PlaneSector( const Point& A, const Point& B, const Point& C) :Geometry(2) { if(C==B) { TheCenter=A; } else { real dp = (C-B)*(A-B); Error(dp==0, "Error: trying to construct a plane sector with centre at infinity"); TheCenter = (A+(A-B)*((C-B)*((C+B)/2-A))/dp); }; TheInnerRadius=(TheCenter-A).Length(); Point BB(B-TheCenter), CC(C-TheCenter); TheSmallAngle=atan2(BB.Y(),BB.X()); TheBigAngle=atan2(CC.Y(),CC.X()); if (TheBigAngle<=TheSmallAngle) TheBigAngle += 2*M_PI; } /////////////////////////////////////////////////// PlaneSector::PlaneSector(const Point& O,real r, real theta1, real theta2) : Geometry(2) { TheCenter = O; TheInnerRadius = r; TheSmallAngle = theta1; TheBigAngle = theta2; if (TheSmallAngle == TheBigAngle) TheBigAngle += 2*M_PI; } ///////////////////////////////////////////////////// real PlaneSector::InnerRadius() const { return TheInnerRadius; } //////////////////////////////////////////////////// real PlaneSector::SmallAngle() const { return TheSmallAngle; } ///////////////////////////////////////////////////// real PlaneSector::BigAngle() const { return TheBigAngle; } //////////////////////////////////////////////////// const Point& PlaneSector::Center() const { return TheCenter; } //////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'E2secitf.c' then echo shar: will not over-write existing file "'E2secitf.c'" else cat << \SHAR_EOF > 'E2secitf.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////////// //File E2secitf.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ////////////////////////////////////////////// #include #include ////////////////////////////////////////////// PLANE_SECTOR::PLANE_SECTOR (const Point& A, const Point& B,const Point& C) { StoreAtomic(new PlaneSector(A,B,C),new PlaneSector_Processor); } ////////////////////////////////////////////// PLANE_SECTOR::PLANE_SECTOR (const Point& O, real r , real theta1, real theta2) { StoreAtomic(new PlaneSector(O,r,theta1,theta2), new PlaneSector_Processor); } /////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'E2secprc.c' then echo shar: will not over-write existing file "'E2secprc.c'" else cat << \SHAR_EOF > 'E2secprc.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////////////// //File E2secprc.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// #include #include #include #include #include #include #include //////////////////////////////////////////////////////// void PlaneSector_Processor::Process( Stack& Offspring) { PlaneSector& G = Geometry(); Point P1(G.InnerRadius(),G.BigAngle()), P2(G.InnerRadius(),G.SmallAngle()); AtomicRegion* A ; A= (AtomicRegion*) SEMI_INFINITE_STRIP(P1,P2); Integrand I1(LocalIntegrand(),new Translation(G.Center())); A->LocalIntegrand(new Integrand(I1, new PolarToRectangular)); Offspring.Push(A); } ///////////////////////////////////////////////// PlaneSector_Processor::PlaneSector_Processor() :Processor() { } ///////////////////////////////////////////////// Processor* PlaneSector_Processor::NewCopy() const { return new PlaneSector_Processor(*this); } //////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'E2tostrp.c' then echo shar: will not over-write existing file "'E2tostrp.c'" else cat << \SHAR_EOF > 'E2tostrp.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////// //File E2tostrp.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////////////////////////////////////// #include #include #include //////////////////////////////////////////// void E2toIS::Transform(real& w, Point& p) { InfiniteStrip& s = *IS_ptr; Point D = s.B()- s.A(); Point C(-D.Y(),D.X()); C = C/C.Length(); w *= D.Length()*.5*(1-tanh(p.X())*tanh(p.X())); p = s.A() + p.Y()*C + (.5*(1+tanh(p.X())))*D; } /////////////////////////////////////////////////// E2toIS::E2toIS(InfiniteStrip* g) : Transformation(),IS_ptr(g) { } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'S2.c' then echo shar: will not over-write existing file "'S2.c'" else cat << \SHAR_EOF > 'S2.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////// //File S2.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ////////////////////////////////////////// #include #include #include #include #include #include #include #include #include //////////////////////////////////////////// Circle::Circle(const Point& Center, real Radius) : Geometry(2), TheCenter(Center), TheRadius(fabs(Radius)) {} /////////////////////////////////////////////// Circle::Circle(const Point& Center, const Point& Boundary) : Geometry(2), TheCenter(Center), TheRadius(sqrt((Center.X()-Boundary.X())*(Center.X()-Boundary.X()) +(Center.Y()-Boundary.Y())*(Center.Y()-Boundary.Y()))) {} /////////////////////////////////////////////// real Circle::Volume() const { return M_PI*TheRadius*TheRadius; } ////////////////////////////////////////////// const Point& Circle::Center() const { return TheCenter; } ///////////////////////////////////////////// real Circle::Radius() const { return TheRadius; } ////////////////////////////////////////////// //Processor* //Circle::DefaultProcessor() //const //{ //return new CircleAdaptive(new Circle_Rule13); //} ///////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'S2adapt.c' then echo shar: will not over-write existing file "'S2adapt.c'" else cat << \SHAR_EOF > 'S2adapt.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////// //File S2adapt.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 30 Jan 1996 V0.1g(no longer compare signed and unsigned) ////////////////////////////////////////// #include #include #include #include #include //////////////////////////////////////////////// void CircleAdaptive::Process(Stack& Offspring) { Circle& C = Geometry(); static unsigned int mxgen=2; //if (mxgen == 0) //{ //cerr<<"How many times may I apply the circle rule? "; //cin>>mxgen; //}; TimesCalled++; if(TimesCalled ==1) { if (GenerationNumber < mxgen) { TheRule->Apply(LocalIntegrand(),C,Integral(),AbsoluteError()); } else { Point rv (C.Radius(),0); Point bp = C.Center()+rv; AtomicRegion* A ; A= (AtomicRegion*) POLAR_RECTANGLE(C.Center(),bp,bp); A->LocalIntegrand(&(LocalIntegrand())); Offspring.Push(A); }; } else { const real CircleRatio = 0.44721359549995793928; Point m1(C.Radius()*CircleRatio ,0.); Point m2(C.Radius() , 0.); Point m3(0.,C.Radius()); Point m4(0.,C.Radius()*CircleRatio); Point origin=C.Center(); AtomicRegion* t1=(AtomicRegion*) POLAR_RECTANGLE(origin+m1,origin+m2,origin+m3); AtomicRegion* t2=(AtomicRegion*) POLAR_RECTANGLE(origin+m4,origin+m3,origin-m2); AtomicRegion* t3=(AtomicRegion*) POLAR_RECTANGLE(origin-m1,origin-m2,origin-m3); AtomicRegion* t4=(AtomicRegion*) POLAR_RECTANGLE(origin-m4,origin-m3,origin+m2); Offspring.Push(t1); Offspring.Push(t2); Offspring.Push(t3); Offspring.Push(t4); Offspring.IteratorReset(); while (!Offspring.IteratorAtEnd()) { Offspring.IteratorNext()->LocalIntegrand(&LocalIntegrand()); }; if (CircleRatio != 0.0) { Circle* tmp = new Circle(origin,C.Radius()*CircleRatio); Atomic* a =new Atomic(tmp,Descendant()); a->LocalIntegrand(&LocalIntegrand()); Offspring.Push(a); }; }; } ////////////////////////////////////////////////// CircleAdaptive::CircleAdaptive(Rule * R) :Processor(),TheRule(R),TimesCalled(0),GenerationNumber(0) { } ///////////////////////////////////////////////////// CircleAdaptive* CircleAdaptive::Descendant() const { CircleAdaptive * CA = new CircleAdaptive (&(*(TheRule))); CA->GenerationNumber = GenerationNumber+1; return CA; } ////////////////////////////////////////////////////// Processor* CircleAdaptive::NewCopy() const { return new CircleAdaptive(*this); } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'S2interf.c' then echo shar: will not over-write existing file "'S2interf.c'" else cat << \SHAR_EOF > 'S2interf.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// //File S2interf.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// #include #include #include ///////////////////////////////////////////////////////// CIRCLE::CIRCLE(const Point& c,const Point& b) { StoreAtomic(new Circle(c,b),new CircleAdaptive(new Circle_Rule13)); } ///////////////////////////////////////////////////////// CIRCLE::CIRCLE(const Point& c, real Radius) { StoreAtomic(new Circle(c,Radius),new CircleAdaptive(new Circle_Rule13)); } ///////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'S2rule13.c' then echo shar: will not over-write existing file "'S2rule13.c'" else cat << \SHAR_EOF > 'S2rule13.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //File S2rule13.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // // A cubature formula of degree 13 with 36 points and associated // null rules (Cools & Haegemans). // #include static real facmed = 1.5; static real crival = 0.3; static int K[]={0,3,2,2}; const int NumberOfPoints=K[0]+4*K[1]+4*K[2]+8*K[3]; const int Orbits=K[0]+K[1]+K[2]+K[3]; static real Type1[]= {0.283402832348840340260055531925e+00, 0.649007230578023857142954047869e+00, 0.920575474036255978410400945265e+00}; static real Type2[]= {0.677355106028069632559870394597e+00, 0.412672216763278882147845015245e+00}; static real Type3[2][2]= {{0.335767600829543545504321849367e+00, 0.938694583835106683089433405007e+00}, {0.752042776803937943743749637665e+00, 0.379717011170079696840056017956e+00}}; static real Weight[7][7]= {{0.497326951852944153115255529183e-01, 0.439732090591084987635001867639e-01, 0.221057969395291114959209696751e-01, 0.138071954801617944635783199052e-01, 0.478191639416850908138653549756e-01, 0.579302409092634509107760741653e-02, 0.304879456061841994847272004644e-01}, // Nullrule exact for the first 6 basispolynomials, {-0.8073879159066197e-02, -0.2498315518214109e-01, 0.5349170539028515e-01, 0.3595547716318644e-01, 0.4320518775944201e-01, -0.1967607360410405e-01, -0.3012159438174910e-01}, // Nullrule exact for the first 5 basispolynomials, {0.2175100120594341e-01, -0.7117820786684134e-01, 0.1801191272610644e-01, -0.1775642346529020e-01, -0.2754333027079005e-02, -0.1170796597217573e-01, 0.3767099118575607e-01}, // Nullrule exact for the first 4 basispolynomials, {0.2413156434309756e-01, 0.2327141313816948e-01, 0.3438009174891747e-01, 0.3084063431284037e-01, -0.6858211678704531e-01, -0.2561913343310581e-01, 0.3598340055116032e-02}, // Nullrule exact for the first 3 basispolynomials, {-0.4853627844062673e-01, 0.3645578330411178e-01, 0.4003943562394422e-01, -0.4494496660283691e-01, 0.1266357696444992e-01, -0.2028566592818438e-01, 0.2244689050366323e-01}, // Nullrule exact for the first 2 basispolynomials, {-0.2979266039117054e-01, 0.3977474716810517e-02, -0.4396076050818155e-01, 0.5463380585542593e-01, 0.1777067704103634e-01, -0.2876745680547196e-01, 0.2745318844851159e-01}, // Nullrule exact for the first 1 basispolynomials, {0.6246499865107039e-01, 0.2624836264288300e-01, -0.1903648724133519e-01, -0.2649038633167001e-01, 0.3481279195257287e-01, -0.3459307949232926e-01, -0.4406560344431272e-02}}; // // The error estimator constants // #include #include #include #include //#include #define sqr(x) ((x)*(x)) void Circle_Rule13::Apply(Integrand& F,Circle& R,real& TheResult,real& TheError) { //if (crival<0 || facmed <0) // { // cerr << " crival,facmed? " << endl; // cin >> crival; // cin >> facmed; // }; const real facopt = facmed/(crival*crival); int i,j,p,Type,nr,number; real Null[6]; real Tres = -1.0; real noise,r,r1,r2,Deg5,Deg3,Deg7,sumval; Point x[8]; if (Tres <= 0) { Tres=50*REAL_EPSILON; } TheResult = 0.0; for (i=0;i<6;i++){Null[i]=0;} p=0; for (Type=0;Type <=3;Type++){ for (nr=0;nr= 1) { TheError =10*Deg7; } else { if (r>=crival) { TheError = facmed*r*Deg7; } else { TheError = facopt *r*r*r*Deg7; } } TheError = max(noise,TheError); } TheError *= R.Volume(); TheResult *= R.Volume(); // cout <<"=> Error = "<() { } /////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'T2.c' then echo shar: will not over-write existing file "'T2.c'" else cat << \SHAR_EOF > 'T2.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////// //File T2.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////////////////////////////////////// #include #include ////////////////////////////////////////////// Triangle::Triangle (const Point& p1,const Point& p2,const Point& p3) : Geometry(2),Vertices(3),TheVolumeKnown(False) { Vertices[0] = p1; Vertices[1] = p2; Vertices[2] = p3; } ////////////////////////////////////////////// void Triangle::ComputeVolume() { TheVolume = fabs( 0.5* ((Vertices[0][0]*Vertices[1][1]-Vertices[1][0]*Vertices[0][1]) +(Vertices[1][0]*Vertices[2][1]-Vertices[2][0]*Vertices[1][1]) +(Vertices[2][0]*Vertices[0][1]-Vertices[0][0]*Vertices[2][1])) ); TheVolumeKnown = True; } /////////////////////////////////////////////// const Point& Triangle::Vertex(int i) const { return Vertices[i]; } ////////////////////////////////////////////////// real Triangle::Volume() const { Triangle* T= (Triangle*) this; if (!TheVolumeKnown) { T->ComputeVolume(); }; return T->TheVolume; } /////////////////////////////////////////////// void Triangle::Volume(real v) { TheVolume = v; TheVolumeKnown = True; } //////////////////////////////////////////////// //Processor* //Triangle::DefaultProcessor() //const //{ //return new SimpleAdaptive( //new Triangle_Rule13, //new Triangle_Divide4); //} //////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'T2dv4.c' then echo shar: will not over-write existing file "'T2dv4.c'" else cat << \SHAR_EOF > 'T2dv4.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////////////// //File T2dv4.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////// #include #include #include ////////////////////////////////////////////////// void Triangle_Divide4::Apply (const Triangle& t,Stack& Offspring, const Vector& D) { Point m12 = (t.Vertex(0)+t.Vertex(1))/2; Point m13 = (t.Vertex(0)+t.Vertex(2))/2; Point m23 = (t.Vertex(2)+t.Vertex(1))/2; Triangle* t1 = new Triangle(t.Vertex(0),m12,m13); Triangle* t2 = new Triangle(t.Vertex(1),m12,m23); Triangle* t3 = new Triangle(t.Vertex(2),m23,m13); Triangle* t4 = new Triangle(m23,m12,m13); Offspring.Push(t1); Offspring.Push(t2); Offspring.Push(t3); Offspring.Push(t4); } ////////////////////////////////////////////////// Triangle_Divide4::Triangle_Divide4() :SameShapeDivisor() { } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'T2interf.c' then echo shar: will not over-write existing file "'T2interf.c'" else cat << \SHAR_EOF > 'T2interf.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////////// //File T2interf.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(typedef introduced) //////////////////////////////////////////////// #include #include #include #include /////////////////////////////////////////////// typedef Rule RuleTriangle; typedef SameShapeDivisor SameShapeDivisorTriangle; TRIANGLE::TRIANGLE(const Point& p1,const Point& p2, const Point& p3) { Pointer R13 (new Triangle_Rule13); Pointer D4 (new Triangle_Divide4); StoreAtomic(new Triangle(p1,p2,p3), new SimpleAdaptive(R13,D4) ); } /////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'T2rule13.c' then echo shar: will not over-write existing file "'T2rule13.c'" else cat << \SHAR_EOF > 'T2rule13.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// //File T2rule13.c //Authors: Berntsen & Espelid (DRLTRI) //C++Translation: Luc Pluym/Ronald Cools // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 28 Mar 1996 V0.1h(redundant variable removed) ///////////////////////////////////////////////////////// #include #include #include #define sqr(x) ((x)*(x)) // coordinates of the quadrature rule static real G1[] = { 0.333333333333333333333333333333e0, 0.950275662924105565450352089520e0, 0.171614914923835347556304795551e0, 0.539412243677190440263092985511e0, 0.772160036676532561750285570113e0, 0.009085399949835353883572964740e0, 0.062277290305886993497083640527e0, 0.022076289653624405142446876931e0, 0.018620522802520968955913511549e0, 0.096506481292159228736516560903e0, 0.851306504174348550389457672223e0, 0.689441970728591295496647976487e0, 0.635867859433872768286976979827e0}; static real G2[] = { 0.333333333333333333333333333333e0, 0.024862168537947217274823955239e0, 0.414192542538082326221847602214e0, 0.230293878161404779868453507244e0, 0.113919981661733719124857214943e0, 0.495457300025082323058213517632e0, 0.468861354847056503251458179727e0, 0.851306504174348550389457672223e0, 0.689441970728591295496647976487e0, 0.635867859433872768286976979827e0, 0.022076289653624405142446876931e0, 0.018620522802520968955913511549e0, 0.096506481292159228736516560903e0}; // // Weights of the degree 13 quadrature rule. // static real W[] = {0.051739766065744133555179145422e0, 0.008007799555564801597804123460e0, 0.046868898981821644823226732071e0, 0.046590940183976487960361770070e0, 0.031016943313796381407646220131e0, 0.010791612736631273623178240136e0, 0.032195534242431618819414482205e0, 0.015445834210701583817692900053e0, 0.017822989923178661888748319485e0, 0.037038683681384627918546472190e0, 0.015445834210701583817692900053e0, 0.017822989923178661888748319485e0, 0.037038683681384627918546472190e0}; // Weights of the first null rule of degree 7. static real W71[] = {-0.077738051051462052051304462750e0, 0.001640389740236881582083124927e0, 0.078124083459915167386776552733e0, -0.030706528522391137165581298102e0, 0.010246307817678312345028512621e0, 0.012586300774453821540476193059e0, -0.043630506151410607808929481439e0, -0.004567055157220063810223671248e0, 0.003393373439889186878847613140e0, 0.000000000000000000000000000000e0, -0.004567055157220063810223671248e0, 0.003393373439889186878847613140e0, 0.000000000000000000000000000000e0}; // Weights of the second null rule of degree 7. static real W72[] = {-0.064293709240668260928898888457e0, 0.003134665264639380635175608661e0, 0.007822550509742830478456728602e0, 0.048653051907689492781049400973e0, 0.032883327334384971735434067029e0, -0.017019508374229390108580829589e0, 0.025973557893399824586684707198e0, -0.010716753326806275930657622320e0, 0.018315629578968063765722278290e0, -0.047607080313197299401024682666e0, -0.010716753326806275930657622320e0, 0.018315629578968063765722278290e0, -0.047607080313197299401024682666e0}; // Weights of the first degree 5 null rule. static real W51[] = {0.021363205584741860993131879186e0, 0.022716410154120323440432428315e0, -0.026366191271182090678117381002e0, 0.029627021479068212693155637482e0, 0.004782834546596399307634111034e0, 0.004178667433984132052378990240e0, -0.065398996748953861618846710897e0, -0.033589813176131630980793760168e0, 0.033018320112481615757912576257e0, 0.012241086002709814125707333127e0, -0.033589813176131630980793760168e0, 0.033018320112481615757912576257e0, 0.012241086002709814125707333127e0}; // Weights of the second degree 5 null rule. static real W52[] = { -0.046058756832790538620830792345e0, 0.005284159186732627192774759959e0, 0.009325799301158899112648198129e0, -0.006101110360950124560783393745e0, -0.056223328794664871336486737231e0, -0.062516479198185693171971930698e0, 0.022428226812039547178810743269e0, -0.000026014926110604563130107142e0, 0.032882099937471182365626663487e0, 0.018721740987705986426812755881e0, -0.000026014926110604563130107142e0, 0.032882099937471182365626663487e0, 0.018721740987705986426812755881e0}; // Weights of first degree 3 null rule. static real W31[] = {0.080867117677405246540283712799e0, -0.033915806661511608094988607349e0, 0.014813362053697845461526433401e0, 0.001442315416337389214102507204e0, -0.024309696484708683486455879210e0, -0.005135085639122398522835391664e0, -0.034649417896235909885490654650e0, 0.035748423431577326597742956780e0, 0.024548155266816447583155562333e0, -0.032897267038856299280541675107e0, 0.035748423431577326597742956780e0, 0.024548155266816447583155562333e0, -0.032897267038856299280541675107e0}; // Weights of second degree 3 null rule. static real W32[] = {-0.038457863913548248582247346193e0, -0.055143631258696406147982448269e0, -0.021536994314510083845999131455e0, 0.001547467894857008228010564582e0, 0.057409361764652373776043522086e0, -0.040636938884669694118908764512e0, -0.020801144746964801777584428369e0, 0.019490770404993674256256421103e0, 0.002606109985826399625043764771e0, 0.023893703367437102825618048130e0, 0.019490770404993674256256421103e0, 0.002606109985826399625043764771e0, 0.023893703367437102825618048130e0}; // Weights of first degree 1 null rule. static real W11[] = {0.074839568911184074117081012527e0, -0.004270103034833742737299816615e0, 0.049352639555084484177095781183e0, 0.048832124609719176627453278550e0, 0.001042698696559292759051590242e0, -0.044445273029113458906055765365e0, -0.004670751812662861209726508477e0, -0.015613390485814379318605247424e0, -0.030581651696100000521074498679e0, 0.010801113204340588798240297593e0, -0.015613390485814379318605247424e0, -0.030581651696100000521074498679e0, 0.010801113204340588798240297593e0}; // Weights of second degree 1 null rule. static real W12[] = {0.009373028261842556370231264134e0, -0.074249368848508554545399978725e0, 0.014709707700258308001897299938e0, 0.009538502545163567494354463302e0, -0.014268362488069444905870465047e0, 0.040126396495352694403045023109e0, 0.028737181842214741174950928350e0, -0.031618075834734607275229608099e0, 0.016879961075872039084307382161e0, 0.010878914758683152984395046434e0, -0.031618075834734607275229608099e0, 0.016879961075872039084307382161e0, 0.010878914758683152984395046434e0}; void Triangle_Rule13::Apply(Integrand& F,Triangle& t,real& TheResult,real& TheError) { real Null71,Null72,Null51,Null52,Null31,Null32,Null11,Null12; const int Wtleng =13; real Tres = -1.0; real tune = 1.0; real f,Z1,Z2,Z3; real noise,r,r1,r2,r3,DEG1,DEG3,DEG5,DEG7; Point X[3],Center; int i,l; real cvmax,cvmin,fmmax,fmmin, crival,facmed,facopt; // // The abscissas are given in homogeneous coordinates. // // *FIRST EXECUTABLE STATEMENT DRLT2A cvmax = 0.5; cvmin = 0.9; crival = tune*cvmax + (1-tune)*cvmin; fmmax = 10; fmmin = 0.1; facmed = tune*fmmax + (1-tune)*fmmin; facopt = facmed/(crival*crival); if (Tres <= 0) { Tres=50*REAL_EPSILON; }; // Compute contributions from the center of the triangle. Center = (t.Vertex(0)+t.Vertex(1)+t.Vertex(2))/3; f = F(Center); TheResult = W[0]*f; Null71 = W71[0]*f; Null72 = W72[0]*f; Null51 = W51[0]*f; Null52 = W52[0]*f; Null31 = W31[0]*f; Null32 = W32[0]*f; Null11 = W11[0]*f; Null12 = W12[0]*f; // Compute contributions from points with // multiplicity 3. for (i=1;i= 1) { TheError =10*max(max(max(DEG1,DEG3),DEG5),DEG7); } else { if (r>=crival) { TheError = facmed*r*DEG7; } else { TheError = facopt *r*r*r*DEG7; }; }; TheError = max(noise,TheError); }; TheError *= t.Volume(); TheResult *=t.Volume(); TheError = min(fabs(TheResult),TheError); // **END DRLTRI } ///////////////////////////////////////////////////////// Triangle_Rule13::Triangle_Rule13() :Rule() { } ///////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'T2tops.c' then echo shar: will not over-write existing file "'T2tops.c'" else cat << \SHAR_EOF > 'T2tops.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : T2tops.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// #include ///////////////////////////////////////////////////////// T2toPS::T2toPS(ParabolicSegment* p) : Transformation(), P(p->P()), M((p->A()+p->B())/2), H((p->B()-p->A())/2) { a= -0.5* (P-M).Length(); k= H.X()*(P.Y()-M.Y())-H.Y()*(P.X()-M.X()); k*=a; } //////////////////////////////////////////////////////// void T2toPS::Transform(real & w, Point& p) { if (p.X()<0) { real X = p.X(); real Y = a*(X-1)*p.Y(); p= M+X*H+Y*(P-M); w *= k*(X-1); } else { real X = p.X(); real Y = -a*(X+1)*p.Y(); p= M+X*H+Y*(P-M); w *= -k*(X+1); }; } ///////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'atomic.c' then echo shar: will not over-write existing file "'atomic.c'" else cat << \SHAR_EOF > 'atomic.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////////// //File atomic.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////// #include ///////////////////////////////////////////// template Atomic::Atomic(GEOMETRY* g, Processor* p) :AtomicRegion(),G_ptr(g),RP_ptr(p),I_ptr( new Integrand) { p->LocalAtomic(this); } ////////////////////////////////////////////// template void Atomic::Use(Processor* p) { RP_ptr =p; p->LocalAtomic(this); } //////////////////////////////////////////// template void Atomic::Process(Stack& Offspring) { RP_ptr->Process(Offspring); } //////////////////////////////////////////// template void Atomic::LocalIntegrand(Integrand* i) { I_ptr = i; } ////////////////////////////////////////////// template RegionInfo* Atomic::LocalRegionInfo() { return &(LocalInfo()); } /////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'atomreg.c' then echo shar: will not over-write existing file "'atomreg.c'" else cat << \SHAR_EOF > 'atomreg.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////////// //File atomreg.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////////////////////////////////////// #include //////////////////////////////////////////////// AtomicRegion::AtomicRegion() :Region() { } ///////////////////////////////////////////////// AtomicRegion::~AtomicRegion() { } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'boolean.c' then echo shar: will not over-write existing file "'boolean.c'" else cat << \SHAR_EOF > 'boolean.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////////// //File boolean.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////////////////////////////////////// #include #include ostream& operator << (ostream& os, const Boolean& b) { if (b==False) { os<< "False "; } else { os<< "True "; }; return os; } SHAR_EOF fi # end of overwriting check if test -f 'chrono.c' then echo shar: will not over-write existing file "'chrono.c'" else cat << \SHAR_EOF > 'chrono.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// //File chrono.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 28 Mar 1996 V0.1h(long instead of int) ///////////////////////////////////////////////////////// #include #ifdef GETRUSAGE #include #include #endif ///////////////////////////////////////////////////////// Chrono::Chrono() { Reset(); } ///////////////////////////////////////////////////////// void Chrono::Start() { if ( !Running) { Time= OldTime = times_(); Running =True; }; } ///////////////////////////////////////////////////////// void Chrono::Stop() { if (Running) { Time = times_(); Running =False; }; } ///////////////////////////////////////////////////////// void Chrono::Reset() { Time=0; OldTime=0; Running = False; } ///////////////////////////////////////////////////////// unsigned long Chrono::Read() { if (Running) { return (times_() - OldTime); } else { return (Time -OldTime); }; } ///////////////////////////////////////////////////////// long Chrono::times_ () { long t=0; #ifdef GETRUSAGE struct rusage info ; struct timeval *user_t = &(info.ru_utime), *sys_t = &(info.ru_stime) ; getrusage (0, &info) ; t += user_t->tv_sec * 1000 + user_t->tv_usec / 1000 ; t += sys_t->tv_sec * 1000 + sys_t->tv_usec / 1000 ; #endif return t; } ///////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'compreg.c' then echo shar: will not over-write existing file "'compreg.c'" else cat << \SHAR_EOF > 'compreg.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////// //File compreg.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ////////////////////////////////////////////////// #include #include ///////////////////////////////////////////////// COMPOUND_REGION::COMPOUND_REGION() : Region(),TheStatus(Virgin) { } ////////////////////////////////////////////////// void COMPOUND_REGION::Process() { Error(Hopeless(),"Processing a hopeless COMPOUND_REGION"); if (TheStatus==Virgin) { TheStatus= Active; Preprocess(); } else { Improve(); } } //////////////////////////////////////////////////// COMPOUND_REGION::~COMPOUND_REGION() { } ///////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'deccxxtp.c' then echo shar: will not over-write existing file "'deccxxtp.c'" else cat << \SHAR_EOF > 'deccxxtp.c' // This file is needed by cxx, The Decalpha C++ compiler. // // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // #include #include #include #include #include #include #include /////////////////////////////////////////////////////////////// #include #pragma define_template SimpleAdaptive #pragma define_template SimpleAdaptive /////////////////////////////////////////////////////////////// #include #pragma define_template Set /////////////////////////////////////////////////////////////// #include #pragma define_template Stack #pragma define_template Stack #pragma define_template Stack #pragma define_template Stack /////////////////////////////////////////////////////////////// #include #pragma define_template Vector #pragma define_template Vector #pragma define_template Vector #pragma define_template Vector< Pointer > /////////////////////////////////////////////////////////////// #include #pragma define_template VectorStack< Pointer < Transformation > > /////////////////////////////////////////////////////////////// #include #pragma define_template SubHeap #pragma define_template Heap /////////////////////////////////////////////////////////////// #include #pragma define_template Atomic #pragma define_template Atomic #pragma define_template Atomic #pragma define_template Atomic #pragma define_template Atomic #pragma define_template Atomic #pragma define_template Atomic #pragma define_template Atomic #pragma define_template Atomic #pragma define_template Atomic #pragma define_template Atomic #pragma define_template Atomic /////////////////////////////////////////////////////////////// #include #pragma define_template Divisor #pragma define_template Divisor /////////////////////////////////////////////////////////////// #include #pragma define_template PassTheBuck #pragma define_template PassTheBuck #pragma define_template PassTheBuck #pragma define_template PassTheBuck #pragma define_template PassTheBuck /////////////////////////////////////////////////////////////// #include #pragma define_template Pointer > #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer > #pragma define_template Pointer /////////////////////////////////////////////////////////////// #include #pragma define_template Processor #pragma define_template Processor #pragma define_template Processor #pragma define_template Processor #pragma define_template Processor #pragma define_template Processor #pragma define_template Processor #pragma define_template Processor #pragma define_template Processor #pragma define_template Processor #pragma define_template Processor #pragma define_template Processor /////////////////////////////////////////////////////////////// #include #pragma define_template Rule #pragma define_template Rule #pragma define_template Rule /////////////////////////////////////////////////////////////// #include #pragma define_template SameShapeDivisor #pragma define_template SameShapeDivisor /////////////////////////////////////////////////////////////// #include #pragma define_template USERINTERFACE #pragma define_template USERINTERFACE #pragma define_template USERINTERFACE #pragma define_template USERINTERFACE #pragma define_template USERINTERFACE #pragma define_template USERINTERFACE #pragma define_template USERINTERFACE #pragma define_template USERINTERFACE #pragma define_template USERINTERFACE #pragma define_template USERINTERFACE #pragma define_template USERINTERFACE #pragma define_template USERINTERFACE /////////////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'div.c' then echo shar: will not over-write existing file "'div.c'" else cat << \SHAR_EOF > 'div.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////// //File div.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////// #include ///////////////////////////////////////////////// template Divisor::Divisor() :ReferenceCounting() { } ////////////////////////////////////////////////// template Divisor::~Divisor() { } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'eval_ctr.c' then echo shar: will not over-write existing file "'eval_ctr.c'" else cat << \SHAR_EOF > 'eval_ctr.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////// //File eval_ctr.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 28 Mar 1996 V0.1h(long instead of int) ///////////////////////////////////////////// #include #include ///////////////////////////////////////////// EvaluationCounter::EvaluationCounter() { Reset(); } ///////////////////////////////////////////// void EvaluationCounter::Start() { if (!Running) { Strt = Integrand::NumberOfEvaluations(); End =Strt; Running = True; }; } ///////////////////////////////////////////// void EvaluationCounter::Stop() { if (Running) { End =Integrand::NumberOfEvaluations(); Running = False; }; } ///////////////////////////////////////////// void EvaluationCounter::Reset() { Bias =0; Strt=Integrand::NumberOfEvaluations(); End =Strt; Running = False; } ///////////////////////////////////////////// void EvaluationCounter::Reset(unsigned long v) { Bias =v; Strt=Integrand::NumberOfEvaluations(); End =Strt; Running = False; } ///////////////////////////////////////////// unsigned long EvaluationCounter::Read() { if (Running) { return Integrand::NumberOfEvaluations()-Strt+ Bias; } else { return End - Strt+ Bias; }; } ///////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'geometry.c' then echo shar: will not over-write existing file "'geometry.c'" else cat << \SHAR_EOF > 'geometry.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////////////// //File geometry.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) /////////////////////////////////////////////////// #include /////////////////////////////////////////////////// Geometry::Geometry(unsigned int Dim) :ReferenceCounting(),TheDimension(Dim) { } /////////////////////////////////////////////////// unsigned int Geometry::Dimension() const { return TheDimension; } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'gnu262tp.c' then echo shar: will not over-write existing file "'gnu262tp.c'" else cat << \SHAR_EOF > 'gnu262tp.c' // This file is needed by gcc v2.6.2 . // One has to compile with option -fno-implicit-templates. // // History: // (date) (version) // 28 Nov 1994 V0.1 (first limited distribution) // #include #include #include #include #include #include #include /////////////////////////////////////////////////////////////// #include template class SimpleAdaptive; template class SimpleAdaptive; /////////////////////////////////////////////////////////////// #include template class Set; /////////////////////////////////////////////////////////////// #include template class Stack; template class Stack; template class Stack; template class Stack; /////////////////////////////////////////////////////////////// #include template class Vector; template class Vector; template class Vector; template class Vector< Pointer >; /////////////////////////////////////////////////////////////// #include template class VectorStack< Pointer < Transformation > >; /////////////////////////////////////////////////////////////// #include template class SubHeap; template class Heap; /////////////////////////////////////////////////////////////// #include template class Atomic; template class Atomic; template class Atomic; template class Atomic; template class Atomic; template class Atomic; template class Atomic; template class Atomic; template class Atomic; template class Atomic; template class Atomic; template class Atomic; /////////////////////////////////////////////////////////////// #include template class Divisor; template class Divisor; /////////////////////////////////////////////////////////////// #include template class PassTheBuck; template class PassTheBuck; template class PassTheBuck; template class PassTheBuck; template class PassTheBuck; /////////////////////////////////////////////////////////////// #include template class Pointer >; template class Pointer; template class Pointer; template class Pointer; template class Pointer; template class Pointer; template class Pointer; template class Pointer; template class Pointer; template class Pointer; template class Pointer; template class Pointer; template class Pointer; template class Pointer; template class Pointer; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer >; template class Pointer; /////////////////////////////////////////////////////////////// #include template class Processor; template class Processor; template class Processor; template class Processor; template class Processor; template class Processor; template class Processor; template class Processor; template class Processor; template class Processor; template class Processor; template class Processor; /////////////////////////////////////////////////////////////// #include template class Rule; template class Rule; template class Rule; /////////////////////////////////////////////////////////////// #include template class SameShapeDivisor; template class SameShapeDivisor; /////////////////////////////////////////////////////////////// #include template class USERINTERFACE; template class USERINTERFACE; template class USERINTERFACE; template class USERINTERFACE; template class USERINTERFACE; template class USERINTERFACE; template class USERINTERFACE; template class USERINTERFACE; template class USERINTERFACE; template class USERINTERFACE; template class USERINTERFACE; template class USERINTERFACE; /////////////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'gr.c' then echo shar: will not over-write existing file "'gr.c'" else cat << \SHAR_EOF > 'gr.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////// //File gr.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////// #include #include #include #include ////////////////////////////////////////////// GeneralizedRectangle::GeneralizedRectangle(Function f,const Point& a,const Point& b) :Geometry(2),TheBoundary(f),TheA(a),TheB(b) { } //////////////////////////////////////////// const Point& GeneralizedRectangle::A() const { return TheA; } /////////////////////////////////////////// const Point& GeneralizedRectangle::B() const { return TheB; } ///////////////////////////////////////////// real GeneralizedRectangle::Boundary(const Point& p) const { return ((GeneralizedRectangle*)this)->TheBoundary(p); } ////////////////////////////////////////// //Processor* //GeneralizedRectangle::DefaultProcessor() //const //{ //Point a(0,0),b(1,0),c(0,1); //Parallelogram* R= new Parallelogram(a,b,c); //return new //PassTheBuck(R); //} //////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'gritf.c' then echo shar: will not over-write existing file "'gritf.c'" else cat << \SHAR_EOF > 'gritf.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////////// //File gritf.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ////////////////////////////////////////////// #include #include #include #include #include #include ////////////////////////////////////////////// GENERALIZED_RECTANGLE::GENERALIZED_RECTANGLE(Function f,const Point& a,const Point& b) :USERINTERFACE() { Point A(0,0),B(1,0),C(0,1); PARALLELOGRAM R(A,B,C); StoreAtomic(new GeneralizedRectangle(f,a,b), new PassTheBuck((AtomicRegion*)R)); } /////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'gs.c' then echo shar: will not over-write existing file "'gs.c'" else cat << \SHAR_EOF > 'gs.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : gs.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// #include //////////////////////////////////////////////////////// GeneralizedSector::GeneralizedSector(real (*f)(real) ,real a,real b,const Point& C) :Geometry(2),TheCenter(C),TheAlpha(a),TheBeta(b),TheBoundary(f) { } ///////////////////////////////////////////////////////// real GeneralizedSector::Alpha() const { return TheAlpha; } ////////////////////////////////////////////////////////// real GeneralizedSector::Beta() const { return TheBeta; } ////////////////////////////////////////////////////////// const Point& GeneralizedSector::Center() const { return TheCenter; } ////////////////////////////////////////////////////////// real GeneralizedSector::Boundary(real p) const { GeneralizedSector* G= (GeneralizedSector*) this; return G->TheBoundary(p); } /////////////////////////////////////////////////////////// RealFunction GeneralizedSector::Boundary() const { return TheBoundary; } ///////////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'gsitf.c' then echo shar: will not over-write existing file "'gsitf.c'" else cat << \SHAR_EOF > 'gsitf.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////////// //File gsitf.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ////////////////////////////////////////////// #include #include #include ////////////////////////////////////////////// GENERALIZED_SECTOR::GENERALIZED_SECTOR(real (*F)(real), real a, real b, const Point& Center) :USERINTERFACE() { StoreAtomic(new GeneralizedSector(F,a,b,Center), new GeneralizedSector_Processor); } /////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'gsprc.c' then echo shar: will not over-write existing file "'gsprc.c'" else cat << \SHAR_EOF > 'gsprc.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////////////// //File polC2prc.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// #include #include #include #include #include #include #include //////////////////////////////////////////////////////// // LOCAL CLASS ////////////////////////////////////////// class VariableScaling : public Transformation { private: real (*B) (real); public: VariableScaling(real(*b)(real)) :Transformation(),B(b) {}; void Transform( real& w, Point& p) { p.R() = B(p.Theta())*p.R(); w*= B(p.Theta()); }; }; /////////////////////////////////////////////////////////// void GeneralizedSector_Processor::Process( Stack& Offspring) { GeneralizedSector& G = Geometry(); Point P1(0,G.Alpha()), P2(0,G.Beta()), P3(1,G.Alpha()); AtomicRegion* A ; A= (AtomicRegion*) PARALLELOGRAM(P1,P2,P3); Integrand I1(LocalIntegrand(),new Translation(G.Center())); Integrand I2(I1, new PolarToRectangular); A->LocalIntegrand(new Integrand(I2, new VariableScaling(G.Boundary()))); Offspring.Push(A); } ///////////////////////////////////////////////// GeneralizedSector_Processor::GeneralizedSector_Processor() :Processor() { } ///////////////////////////////////////////////// Processor* GeneralizedSector_Processor::NewCopy() const { return new GeneralizedSector_Processor(*this); } ///////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'heap.c' then echo shar: will not over-write existing file "'heap.c'" else cat << \SHAR_EOF > 'heap.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// /////////////////////////////////////////////// //File heap.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 30 Jan 1996 V0.1g(good for old and new ANSI for-scope) /////////////////////////////////////////////// #include #include #include #include ////////////////////////////////////////////// template SubHeap::SubHeap() :Set() { ActiveChild = -1; LastChild = -1; } //////////////////////////////////////////////// template SubHeap::~SubHeap() { Clear(); } /////////////////////////////////////////////// template T* SubHeap::Get() { Error(Number == 0,"error:get from empty heap"); if(Number ==1) { Number--; return Contents[1]; }; T* B =Bottom(); if (LastChild == CAPACITY && Children[ActiveChild]->Saturated()) { ActiveChild--; if(ActiveChild<0) ActiveChild =CAPACITY; }; T* Result = Contents[1]; int Hole = 1; int First= 2; int Second= 3; while (Second <= Number) { if ((*B >= *Contents[First]) &&(*B >= *Contents[Second])) { goto putinhole; } else { if(*Contents[First] >= *Contents[Second]) { Contents[Hole] = Contents[First]; Hole = First; First = 2*Hole; Second = First +1; } else { Contents[Hole] = Contents [Second]; Hole = Second; First = 2*Hole; Second = First+1; }; }; }; if (First == Number) { if (*B >= *Contents[First]) { goto putinhole; } else { Contents[Hole] = Contents [First]; Hole = First; }; }; putinhole: Contents[Hole] = B; if((CAPACITY+1)/2<=Hole && Hole <=CAPACITY) { First =LeftChild(Hole); Second =RightChild(Hole); if (LastChild >=Second) { if( *Contents[Hole] < *Children[Second]->Look() ||*Contents[Hole] < *Children[First]->Look()) { if(*Children[First]->Look() > *Children[Second]->Look()) { B=Children[First]->Swap(Contents[Hole]); Contents[Hole]=B; } else { B=Children[Second]->Swap(Contents[Hole]); Contents[Hole]=B; }; }; }; if(LastChild ==First) { if (*Contents[Hole] <*Children[First]->Look()) { B=Children[First]->Swap(Contents[Hole]); Contents[Hole]=B; }; }; }; return Result; } /////////////////////////////////////////////////// template T* SubHeap::Look() { Error(Number==0,"Looking at empty heap"); return Contents [1]; } /////////////////////////////////////////////////// template T* SubHeap::Swap(T* B) { T* Result = Contents[1]; int Hole =1; int First =2; int Second =3; while (Second <= Number) { if ((*B > *Contents[First]) &&(*B > *Contents[Second])) { goto putinhole; } else { if(*Contents[First] > *Contents[Second]) { Contents[Hole] = Contents[First]; Hole = First; First = 2*Hole; Second = First +1; } else { Contents[Hole] = Contents [Second]; Hole = Second; First = 2*Hole; Second = First+1; }; }; }; if (First == Number-1) { if (*B > *Contents[First]) { goto putinhole; } else { Contents[Hole] = Contents [First]; Hole = Number-1; }; }; putinhole: Contents[Hole] = B; if((CAPACITY+1)/2<=Hole && Hole <=CAPACITY) { First =LeftChild(Hole); Second =RightChild(Hole); if (LastChild >=Second) { if( *Contents[Hole] < *Children[Second]->Look() ||*Contents[Hole] < *Children[First]->Look()) { if(*Children[First]->Look() > *Children[Second]->Look()) { B=Children[First]->Swap(Contents[Hole]); Contents[Hole]=B; } else { B=Children[Second]->Swap(Contents[Hole]); Contents[Hole]=B; }; }; }; if(LastChild ==First) { if (*Contents[Hole] <*Children[First]->Look()) { B=Children[First]->Swap(Contents[Hole]); Contents[Hole]=B; }; }; }; return Result; } /////////////////////////////////////////////////// template Boolean SubHeap::Saturated() const { if (Number!=CAPACITY) return False; if (LastChild <0) return True; if (LastChild !=CAPACITY) return False; Boolean Return = True; for (int i=0;iSaturated()); }; return Return; } //////////////////////////////////////////////////// template T* SubHeap::Bottom() { Error(Number==0,"error:Bottom of empty subheap"); if (ActiveChild >=0) { T* Return = Children[ActiveChild]->Bottom(); if(Children[ActiveChild]->Size()==0) { delete Children[ActiveChild]; ActiveChild--; LastChild--; }; return Return; } else { T* Return =Contents[Number]; Number--; return Return; }; } //////////////////////////////////////////////////// template void SubHeap::operator +=(T* t) { T* NewT; int Hole; if(ActiveChild>=0) { if(Children[ActiveChild]->Saturated()) { ActiveChild++; ActiveChild%=(CAPACITY+1); if (ActiveChild>LastChild) { LastChild=ActiveChild; Children[ActiveChild]=new SubHeap; Error(!Children[ActiveChild],"heap:allocation failed"); }; }; *Children[ActiveChild] +=t; if (*Children[ActiveChild]->Look() > *Contents[FatherOfChild(ActiveChild)]) { NewT =Children[ActiveChild]->Swap(Contents[FatherOfChild(ActiveChild)]); Hole =FatherOfChild(ActiveChild); } else { return; }; } else { if (Number==CAPACITY) { ActiveChild=LastChild=0; Children[ActiveChild] = new SubHeap; Error(!Children[ActiveChild],"heap:allocation failed"); *Children[ActiveChild] +=t; if (*t > *Contents[FatherOfChild(ActiveChild)]) { NewT =Children[ActiveChild]->Swap(Contents[FatherOfChild(ActiveChild)]); Hole =FatherOfChild(ActiveChild); } else { return; }; } else { Number++; NewT = t; Hole = Number; }; }; int Father = Hole/2; while (Father > 0) { if (*Contents[Father] > *NewT) { break; } else { Contents [Hole] = Contents[Father]; Hole = Father; Father = Hole / 2; }; }; Contents [Hole] = NewT; } //////////////////////////////////////////////////// template void SubHeap::Clear() { int i; for (i=0;i<=LastChild;i++) { Children [i] ->Clear(); delete Children[i]; }; for (i=1;i<=Number;i++) { delete Contents [i]; }; ActiveChild=-1; LastChild =-1; Number =0; } //////////////////////////////////////////////////// template void SubHeap::Print() const { int i; for (i=1;i<=Number;i++) { cout <AbsoluteError()<Print(); }; } /////////////////////////////////////////////////// template int SubHeap::FatherOfChild(int i) const { return i/2 + (CAPACITY +1)/2; } /////////////////////////////////////////////////// template int SubHeap::LeftChild(int i) const { return 2*(i-(CAPACITY+1)/2); } ////////////////////////////////////////////////// template int SubHeap::RightChild(int i) const { return LeftChild(i) +1; } //////////////////////////////////////////////////// ///HEAP //////////////////////////////////////////////////// template Heap::Heap() :Set() { } //////////////////////////////////////////////// template T* Heap::Look() { return TheSubHeap.Look(); } /////////////////////////////////////////////////// template T* Heap::Get() { Error(Number == 0,"error:get from empty heap"); Number--; return TheSubHeap.Get(); } /////////////////////////////////////////////////// template void Heap::operator +=( T* t) { Number++; TheSubHeap +=t; } //////////////////////////////////////////////////// template void Heap::Clear() { Number =0; TheSubHeap.Clear(); } //////////////////////////////////////////////////// template void Heap::operator+=(Heap& h) { int n = h.Number; for (int i=0;i void Heap::Print() const { cout<< "Heap"< Heap::~Heap() { Clear(); } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'integran.c' then echo shar: will not over-write existing file "'integran.c'" else cat << \SHAR_EOF > 'integran.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// /////////////////////////////////////////////////// //File integran.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 9 Sep 1994 V0.1a(operator added) // 10 Sep 1994 V0.1b(constructors of ReferenceCounting added) // 25 Jan 1996 V0.1f(unused parameter removed) // 30 Jan 1996 V0.1g(no longer compare signed and unsigned) // 28 Mar 1996 V0.1h(long instead of int) ////////////////////////////////////////////////// #include #include #include #include #include ////////////////////////////////////////////////// long Integrand::Number = 0; ////////////////////////////////////////////////////// Integrand::Integrand (real (*f)(const Point&)) :TheFunction(f),AppliedTransformations() ,ReferenceCounting() { } //////////////////////////////////////////////// Integrand::Integrand(const Integrand& I, Transformation* T) : TheFunction(I.TheFunction), AppliedTransformations(I.AppliedTransformations) ,ReferenceCounting(I) { Pointer p=T; AppliedTransformations += p; } ///////////////////////////////////////////////////////// Integrand::Integrand(const Integrand& I) : TheFunction(I.TheFunction), AppliedTransformations(I.AppliedTransformations) ,ReferenceCounting(I) { } //////////////////////////////////////////////// long Integrand::NumberOfEvaluations() { return Number; } ////////////////////////////////////////////////////// real Integrand::operator() (const Point& StartingPoint) { real JacProd =1; Point p =StartingPoint; for (unsigned int i=0; JacProd!=0 && iTransform(JacProd,p); }; if (JacProd == 0) return 0.0; real R = TheFunction(p)*fabs(JacProd); Number++; return R; } //////////////////////////////////////////////// real ErrorMessage(const Point&) { Error(True,"Error : Attempt to integrate without knowing integrand"); return 0; } Integrand::Integrand() :TheFunction(ErrorMessage),AppliedTransformations() ,ReferenceCounting() { } /////////////////////////////////////////////// Boolean Integrand::operator==(const Integrand& i) const { if ((AppliedTransformations.Size() > 0 ) || (i.AppliedTransformations.Size() > 0 )) return False; return (Boolean)(TheFunction == i.TheFunction); } /////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'integrat.c' then echo shar: will not over-write existing file "'integrat.c'" else cat << \SHAR_EOF > 'integrat.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////// //File integrat.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////// #include #include #include #include #include #include //////////////////////////////////////////////// void Integrate ( COMPOUND_REGION& R, real& Integral, real& AbsError, Boolean& Success, real AbsErrReq, real RelErrReq, unsigned long MaxEval) { EvaluationCounter E; E.Start(); do { if (R.Hopeless()) break; R.Process(); } while (R.AbsoluteError() > AbsErrReq && R.AbsoluteError() > fabs(R.Integral())*RelErrReq && E.Read() < MaxEval); Success = (Boolean)(R.AbsoluteError() <= AbsErrReq || R.AbsoluteError() <= fabs(R.Integral()*RelErrReq)); Integral = R.Integral(); AbsError = R.AbsoluteError(); } ///////////////////////////////////////////////////////// real Integrate ( COMPOUND_REGION& R, real AbsErrReq, real RelErrReq, unsigned long MaxEval) { real Integral; real AbsError; Boolean Success; Integrate(R,Integral,AbsError,Success,AbsErrReq,RelErrReq,MaxEval); return Integral; } ///////////////////////////////////////////////////////// void Integrate ( Function f, COMPOUND_REGION& R, real& Integral, real& AbsError, Boolean& Success, real AbsErrReq, real RelErrReq, unsigned long MaxEval) { R.LocalIntegrand(new Integrand(f)); Integrate(R,Integral,AbsError,Success,AbsErrReq,RelErrReq,MaxEval); } ///////////////////////////////////////////////////////// real Integrate ( Function f, COMPOUND_REGION& R, real AbsErrReq, real RelErrReq, unsigned long MaxEval) { R.LocalIntegrand(new Integrand(f)); real Integral; real AbsError; Boolean Success; Integrate(R,Integral,AbsError,Success,AbsErrReq,RelErrReq,MaxEval); return Integral; } ///////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'invert.c' then echo shar: will not over-write existing file "'invert.c'" else cat << \SHAR_EOF > 'invert.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////// //File invert.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////////////////////////////////////////////// #include /////////////////////////////////////////////////////// Invert::Invert(Circle* C) :Transformation(), C_ptr(C), RadiusSq(C->Radius()*C->Radius()) { } ////////////////////////////////////////// void Invert::Transform (real &w, Point& p) { const Point diff = p-C_ptr->Center(); real r=diff.Length(); real ratio=RadiusSq/(r*r); p = C_ptr->Center()+diff*ratio; w *= ratio*ratio; } ///////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'outS2.c' then echo shar: will not over-write existing file "'outS2.c'" else cat << \SHAR_EOF > 'outS2.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// /////////////////////////////////////////////// //File outS2.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////////////////////////////////////// #include #include #include //////////////////////////////////////////////// OutCircle::OutCircle(const Point& C,const Point& B) :Circle(C,B) { } /////////////////////////////////////////////// OutCircle::OutCircle(const Point& C,real r) :Circle(C,r) { } /////////////////////////////////////////////// //Processor* //OutCircle::DefaultProcessor() //const // { //return new PassTheBuck( // new Circle(*this)); //} //////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'outS2itf.c' then echo shar: will not over-write existing file "'outS2itf.c'" else cat << \SHAR_EOF > 'outS2itf.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// /////////// //File outs2itf.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////// #include #include #include #include #include #include /////////////////////// OUT_CIRCLE::OUT_CIRCLE(const Point& c,const Point& b) { StoreAtomic(new OutCircle(c,b), new PassTheBuck((AtomicRegion*)CIRCLE(c,b))); } ////////////////////////////////////////////// OUT_CIRCLE::OUT_CIRCLE(const Point& c, real Radius) { StoreAtomic(new OutCircle(c,Radius), new PassTheBuck((AtomicRegion*)CIRCLE(c,Radius))); } ////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'passbuck.c' then echo shar: will not over-write existing file "'passbuck.c'" else cat << \SHAR_EOF > 'passbuck.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// //File passbuck.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// #include #include #include #include ////////////////////////////////////////////////// template PassTheBuck::PassTheBuck(AtomicRegion* a) :Processor(), AR_ptr(a) { } ////////////////////////////////////////////////// template void PassTheBuck::Process( Stack& Offspring) { Transformation* T = new VIA(&Geometry()); Integrand* I = new Integrand(LocalIntegrand(),T); AR_ptr->LocalIntegrand(I); Offspring.Push(AR_ptr); } ///////////////////////////////////////////////// template Processor* PassTheBuck::NewCopy() const { return new PassTheBuck(*this); } //////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'point2D.c' then echo shar: will not over-write existing file "'point2D.c'" else cat << \SHAR_EOF > 'point2D.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////// //File point2D.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(file name changed) ///////////////////////////////////////////// #include ////////////////////////////////////////////////////// Point_2D::Point_2D() { } ////////////////////////////////////////////////////// Point_2D::Point_2D(const Point_2D& v) :x(v.x),y(v.y) { } ////////////////////////////////////////////////////// Point_2D::Point_2D(const real X, const real Y) :x(X),y(Y) { } ////////////////////////////////////////////////////// Point_2D::~Point_2D() { } ////////////////////////////////////////////////// // Other functions are inlined ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'pointer.c' then echo shar: will not over-write existing file "'pointer.c'" else cat << \SHAR_EOF > 'pointer.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// //File pointer.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 11 Sep 1994 V0.1b(bug removed from destructor) // 14 Sep 1994 V0.1c(inlines removed) // 25 Jan 1996 V0.1f(code moved from .c to .h) ///////////////////////////////////////////////////////// #include //////////////////////////////////////////////// template Pointer::Pointer() { ptr = 0; } //////////////////////////////////////////////// template Pointer::Pointer(const Pointer& p) { ptr = p.ptr; if (ptr !=0) ptr->Refer(); } /////////////////////////////////////////////// template Pointer::Pointer(T* p) { ptr = p; if (ptr !=0) ptr->Refer(); } //////////////////////////////////////////////// template Pointer& Pointer::operator=(const Pointer& p) { if (ptr !=0) { ptr->UnRefer(); if(ptr->NumberOfReferences() == 0 && (ptr != p.ptr)) { delete ptr; }; }; ptr = p.ptr; if (ptr !=0) ptr->Refer(); return *this; } //////////////////////////////////////////////// template Pointer& Pointer::operator=(T* p) { if (ptr !=0) { ptr->UnRefer(); if(ptr->NumberOfReferences() == 0 && (p != ptr)) { delete ptr; }; }; ptr = p; if (ptr !=0) ptr->Refer(); return *this; } //////////////////////////////////////////////// //////////////////////////////////////////////// template T& Pointer::operator[] (int i) const { return ptr[i]; } /////////////////////////////////////////////// template Pointer::~Pointer() { if (ptr ==0) return; ptr->UnRefer(); if(ptr->NumberOfReferences() == 0) { delete ptr; }; } /////////////////////////////////////////////// template Boolean Pointer::operator == (const Pointer& tp) const { return (ptr == tp.ptr) ? True : False; } //////////////////////////////////////////////// template Boolean Pointer::operator != (const Pointer& tp) const { return (ptr != tp.ptr)? True : False; } //////////////////////////////////////////////// template T& Pointer::operator *() const { return *ptr; } //////////////////////////////////////////////// template T* Pointer::operator ->() const { return ptr; } //////////////////////////////////////////////// //template //Pointer::operator T*() // { // return ptr; // } //////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'polC2.c' then echo shar: will not over-write existing file "'polC2.c'" else cat << \SHAR_EOF > 'polC2.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////// //File POLC2.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 14 Feb 1995 V0.1e(bug fix in transformation) ////////////////////////////////////////// #include #include #include #include #include ////////////////////////////////////////// #include //////////////////////////////////////////// PolarRectangle::PolarRectangle( const Point& A, const Point& B, const Point& C) :Geometry(2) { if(C==B) { TheCenter=A; } else { real dp = (C-B)*(A-B); Error(dp==0, "Error: trying to construct a polar rectangle with centre at infinity"); TheCenter = (A+(A-B)*((C-B)*((C+B)/2-A))/dp); }; TheInnerRadius=(TheCenter-A).Length(); TheOuterRadius=(TheCenter-B).Length(); Point BB(B-TheCenter), CC(C-TheCenter); TheSmallAngle=atan2(BB.Y(),BB.X()); TheBigAngle=atan2(CC.Y(),CC.X()); if (TheBigAngle<=TheSmallAngle) TheBigAngle += 2*M_PI; } /////////////////////////////////////////////////// PolarRectangle::PolarRectangle(const Point& O, real r1, real r2, real t1, real t2) : Geometry(2) { TheCenter = O; if (r1 > r2) { TheInnerRadius = r2; TheOuterRadius = r1; } else { TheInnerRadius = r1; TheOuterRadius = r2; }; TheSmallAngle = t1; TheBigAngle = t2; } ///////////////////////////////////////////////////// real PolarRectangle::InnerRadius() const { return TheInnerRadius; } //////////////////////////////////////////////////// real PolarRectangle::OuterRadius() const { return TheOuterRadius; } /////////////////////////////////////////////////// real PolarRectangle::SmallAngle() const { return TheSmallAngle; } ///////////////////////////////////////////////////// real PolarRectangle::BigAngle() const { return TheBigAngle; } //////////////////////////////////////////////////// const Point& PolarRectangle::Center() const { return TheCenter; } //////////////////////////////////////////////////// //Processor* //PolarRectangle::DefaultProcessor() //const //{ //return new PolarRectangle_Processor; //} //////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'polC2itf.c' then echo shar: will not over-write existing file "'polC2itf.c'" else cat << \SHAR_EOF > 'polC2itf.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////////// //File polC2itf.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ////////////////////////////////////////////// #include #include ////////////////////////////////////////////// POLAR_RECTANGLE::POLAR_RECTANGLE (const Point& A, const Point& B,const Point& C) { StoreAtomic(new PolarRectangle(A,B,C),new PolarRectangle_Processor); } ////////////////////////////////////////////// POLAR_RECTANGLE::POLAR_RECTANGLE (const Point& O, real r1, real r2, real t1, real t2) { StoreAtomic(new PolarRectangle(O,r1,r2,t1,t2),new PolarRectangle_Processor); } ////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'polC2prc.c' then echo shar: will not over-write existing file "'polC2prc.c'" else cat << \SHAR_EOF > 'polC2prc.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// //File polC2prc.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// #include #include #include #include #include #include #include //////////////////////////////////////////////////////// void PolarRectangle_Processor::Process( Stack& Offspring) { PolarRectangle& G = Geometry(); Point P1(G.InnerRadius(),G.SmallAngle()), P2(G.OuterRadius(),G.SmallAngle()), P3(G.OuterRadius(),G.BigAngle()); AtomicRegion* A ; A= (AtomicRegion*) PARALLELOGRAM(P2,P1,P3); Integrand I1(LocalIntegrand(),new Translation(G.Center())); A->LocalIntegrand(new Integrand(I1, new PolarToRectangular)); Offspring.Push(A); } ///////////////////////////////////////////////// PolarRectangle_Processor::PolarRectangle_Processor() :Processor() { } ///////////////////////////////////////////////// Processor* PolarRectangle_Processor::NewCopy() const { return new PolarRectangle_Processor(*this); } //////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'ps.c' then echo shar: will not over-write existing file "'ps.c'" else cat << \SHAR_EOF > 'ps.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : ps.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// #include ///////////////////////////////////////////////////////// ParabolicSegment::ParabolicSegment(const Point& a, const Point& b, const Point& p) :Geometry(2),TheA(a),TheB(b),TheP(p) { } ///////////////////////////////////////////////////////// const Point& ParabolicSegment::A() const { return TheA; } ////////////////////////////////////////////////////////// const Point& ParabolicSegment::B() const { return TheB; } ////////////////////////////////////////////////////////// const Point& ParabolicSegment::P() const { return TheP; } ////////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'psitf.c' then echo shar: will not over-write existing file "'psitf.c'" else cat << \SHAR_EOF > 'psitf.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : psitf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// #include #include #include #include ///////////////////////////////////////////////////////// PARABOLIC_SEGMENT::PARABOLIC_SEGMENT(const Point& A, const Point& B, const Point& P) :USERINTERFACE() { Point p(-1,0),q(0,1),r(1,0); TRIANGLE T(p,q,r); StoreAtomic ( new ParabolicSegment(A,B,P), new PassTheBuck ( (AtomicRegion*) T ) ); } ////////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'rule.c' then echo shar: will not over-write existing file "'rule.c'" else cat << \SHAR_EOF > 'rule.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// /////////////////////////////////////////////// //File rule.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 30 Jan 1996 V0.1g(no longer compare signed and unsigned) ///////////////////////////////////// #include //////////////////////////////////// template Rule::Rule() :ReferenceCounting() { } //////////////////////////////////////////////// template Rule::~Rule() { } ///////////////////////////////////////////////// template void Rule::Apply(Integrand& F,GEOMETRY& G, real& i, real&d) { } /////////////////////////////////////////////////// template void Rule::ApplyWithDiffs(Integrand& F,GEOMETRY& G, real& r, real&e, Vector& D) { for (unsigned int i= 0; i 'refcount.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////////// //File refcount.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(unused parameter removed) ///////////////////////////////////////////// #include ////////////////////////////////////////////// ReferenceCounting::ReferenceCounting() { numref = 0; } ////////////////////////////////////////////// ReferenceCounting::ReferenceCounting(const ReferenceCounting&) { //numref isn't copied! numref = 0; } ///////////////////////////////////////////// ReferenceCounting& ReferenceCounting::operator= (const ReferenceCounting&) { //numref isn't copied! return *this; } //////////////////////////////////////////// void ReferenceCounting::Refer () { numref++; } //////////////////////////////////////////// void ReferenceCounting::UnRefer() { numref--; } /////////////////////////////////////////////// unsigned int ReferenceCounting::NumberOfReferences() const { return numref; } /////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'regcoll.c' then echo shar: will not over-write existing file "'regcoll.c'" else cat << \SHAR_EOF > 'regcoll.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////// //File regcoll.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ////////////////////////////////////////////////// #include #include /////////////////////////////////////////////////// void REGION_COLLECTION::LocalIntegrand(Integrand* ip) { SCR_ptr->IteratorReset(); while(!SCR_ptr->IteratorAtEnd()) { SCR_ptr->IteratorNext()->LocalIntegrand(ip); }; } /////////////////////////////////////////////////// void REGION_COLLECTION::LocalIntegrand(Function f) { LocalIntegrand(new Integrand(f)); } /////////////////////////////////////////////////// REGION_COLLECTION& REGION_COLLECTION::operator+= (const COMPOUND_REGION& C) { SCR_ptr->Push( C.NewCopy()); return *this; } ////////////////////////////////////////////////// REGION_COLLECTION REGION_COLLECTION::operator+ (const COMPOUND_REGION& C) { REGION_COLLECTION r; r+= (*this); r+= C; return r; } /////////////////////////////////////////////////// REGION_COLLECTION::REGION_COLLECTION() :COMPOUND_REGION() { SCR_ptr = new Stack; } ///////////////////////////////////////////////// REGION_COLLECTION::REGION_COLLECTION(const REGION_COLLECTION& rc) :COMPOUND_REGION(rc),SCR_ptr(rc.SCR_ptr) { } ////////////////////////////////////////////////////// void REGION_COLLECTION::Preprocess() { SCR_ptr->IteratorReset(); while(!SCR_ptr->IteratorAtEnd()) { COMPOUND_REGION* C =SCR_ptr->IteratorNext(); real OldIntegral = C->Integral(); real OldError = C->AbsoluteError(); C->Preprocess(); LocalInfo().Integral() += C->Integral()-OldIntegral; LocalInfo().AbsoluteError ()+= C->AbsoluteError()-OldError; }; // if all parts are hopeless then the result is // hopeless too: SCR_ptr->IteratorReset(); while (!SCR_ptr->IteratorAtEnd()) { COMPOUND_REGION* C = SCR_ptr->IteratorNext(); if(!C->Hopeless()) return; }; LocalInfo().Hopeless() = True; } //////////////////////////////////////////////////// void REGION_COLLECTION::Improve() { real MaxCompoundError = 0; COMPOUND_REGION* MaxCompoundErrorAtRegion =0; SCR_ptr->IteratorReset(); while (!SCR_ptr->IteratorAtEnd()) { COMPOUND_REGION* C = SCR_ptr->IteratorNext(); real e =C->MaxAtomicError(); if (e > MaxCompoundError && !C->Hopeless()) { MaxCompoundError = e; MaxCompoundErrorAtRegion = C; }; }; LocalInfo().Integral() -= MaxCompoundErrorAtRegion->Integral(); LocalInfo().AbsoluteError() -= MaxCompoundErrorAtRegion->AbsoluteError(); MaxCompoundErrorAtRegion->Process(); LocalInfo().Integral() += MaxCompoundErrorAtRegion->Integral(); LocalInfo().AbsoluteError() += MaxCompoundErrorAtRegion->AbsoluteError(); // if all parts are hopeless then the result is // hopeless too: SCR_ptr->IteratorReset(); while (!SCR_ptr->IteratorAtEnd()) { COMPOUND_REGION* C = SCR_ptr->IteratorNext(); if(!C->Hopeless()) return; }; LocalInfo().Hopeless() = True; } ///////////////////////////////////////////////////// real REGION_COLLECTION::MaxAtomicError() const { real MaxError=0; SCR_ptr->IteratorReset(); while(!SCR_ptr->IteratorAtEnd()) { real m = SCR_ptr->IteratorNext()->MaxAtomicError(); if(m > MaxError) { MaxError = m; }; }; return MaxError; } ///////////////////////////////////////////////////// COMPOUND_REGION* REGION_COLLECTION::NewCopy() const { return new REGION_COLLECTION(*this); } /////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'reginfo.c' then echo shar: will not over-write existing file "'reginfo.c'" else cat << \SHAR_EOF > 'reginfo.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// //File reginfo.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Nov 1994 V0.1d(re-ordering of member initializers) ///////////////////////////////////////////////////////// #include //////////////////////////////////////////////////////// RegionInfo::RegionInfo() :ReferenceCounting(), TheIntegral(0), TheAbsoluteError(0), IsHopeless(False) { } ///////////////////////////////////////////////////////// Boolean RegionInfo::Hopeless() const { return IsHopeless; } //////////////////////////////////////////////////////////// Boolean& RegionInfo::Hopeless() { return IsHopeless; } ///////////////////////////////////////////////////////////// real RegionInfo::Integral() const { return TheIntegral; } ////////////////////////////////////////////////////////// real& RegionInfo::Integral() { return TheIntegral; } //////////////////////////////////////////////////////// real RegionInfo::AbsoluteError() const { return TheAbsoluteError; } /////////////////////////////////////////////////////////// real& RegionInfo::AbsoluteError() { return TheAbsoluteError; } //////////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'region.c' then echo shar: will not over-write existing file "'region.c'" else cat << \SHAR_EOF > 'region.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////////// //File region.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ////////////////////////////////////////////// #include #include #include #include ///////////////////////////////////////////// real Region::AbsoluteError() const { return RI_ptr->AbsoluteError(); } /////////////////////////////////////////////// real Region::Integral() const { return RI_ptr->Integral(); } /////////////////////////////////////////////// Boolean Region::operator< (const Region& r) const { return (Boolean)(AbsoluteError() < r.AbsoluteError()); } /////////////////////////////////////////////// Boolean Region::operator<=(const Region& r) const { return (Boolean)(AbsoluteError() <= r.AbsoluteError()); } /////////////////////////////////////////////// Boolean Region::operator>(const Region& r) const { return (Boolean)(AbsoluteError() > r.AbsoluteError()); } /////////////////////////////////////////////// Boolean Region::operator>=(const Region& r) const { return (Boolean)(AbsoluteError() >= r.AbsoluteError()); } /////////////////////////////////////////////// RegionInfo& Region::LocalInfo() { return *RI_ptr; } //////////////////////////////////////////////// Region::Region() :RI_ptr( new RegionInfo) { } //////////////////////////////////////////////// Boolean Region::Hopeless() const { return RI_ptr->Hopeless(); } //////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'regproc.c' then echo shar: will not over-write existing file "'regproc.c'" else cat << \SHAR_EOF > 'regproc.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// /////////////////////////////////////////////// //File regproc.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) /////////////////////////////////////////////// #include #include /////////////////////////////////////////////// template Processor::Processor() :ReferenceCounting() { } /////////////////////////////////////////////// template Processor::~Processor() { } //////////////////////////////////////////// template Integrand& Processor::LocalIntegrand() const { return (*(A_ptr->I_ptr)); } /////////////////////////////////////////// template GEOMETRY& Processor::Geometry() const { return (*(A_ptr->G_ptr)); } /////////////////////////////////////////// template void Processor::LocalAtomic(Atomic* a) { A_ptr = a; } //////////////////////////////////////////// template Atomic& Processor::LocalAtomic() const { return *A_ptr; } ////////////////////////////////////////////// template real& Processor::Integral() { return A_ptr->LocalRegionInfo()->Integral(); } ////////////////////////////////////////////////// template real& Processor::AbsoluteError() { return A_ptr->LocalRegionInfo()->AbsoluteError(); } ///////////////////////////////////////////////// template RegionInfo& Processor::LocalRegionInfo() const { return *(A_ptr->LocalRegionInfo()); } //////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 's_adapt.c' then echo shar: will not over-write existing file "'s_adapt.c'" else cat << \SHAR_EOF > 's_adapt.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////// //File s_adapt.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(typedef introduced, code from .c to .h) ////////////////////////////////////////////// #include #include #include #include ///////////////////////////////////////////// //template //SimpleAdaptive::SimpleAdaptive(const Pointer& R, // const Pointer& D) // :Processor(), // TimesCalled(0), // Diffs(2), // TheRule(R), // TheDivisor(D) // { // } /////////////////////////////////////////////// template SimpleAdaptive::SimpleAdaptive(Rule* R, SameShapeDivisor* D) :Processor(), TimesCalled(0), Diffs(2), TheRule(R), TheDivisor(D) { } /////////////////////////////////////////////// template SimpleAdaptive* SimpleAdaptive::Descendant() const { SimpleAdaptive* r = new SimpleAdaptive(TheRule,TheDivisor); return r; } //////////////////////////////////////////////// template void SimpleAdaptive::Process( Stack& Offspring) { TimesCalled ++; if (TimesCalled == 1) { TheRule->ApplyWithDiffs(LocalIntegrand(),Geometry(),Integral(), AbsoluteError(),Diffs); Offspring.MakeEmpty(); return; }; if(TimesCalled == 2) { real NewVolume = Geometry().Volume()/TheDivisor->NumberOfParts(); Stack Parts; Vector DiffOrder(Diffs.Size()); if (Diffs[0]>Diffs[1]) { DiffOrder[0] = 1 ; DiffOrder[1] = 2; } else { DiffOrder[0] = 2; DiffOrder[1] =1; }; TheDivisor->Apply (Geometry(),Parts,DiffOrder); unsigned int N = Parts.Size(); for (unsigned int i =0;iVolume(NewVolume); Processor* p = Descendant(); Atomic* a = new Atomic(g,p); a->LocalIntegrand(&LocalIntegrand()); Offspring.Push(a); }; return; }; Error(TimesCalled > 2, "SimpleAdaptive : more than two calls of Process()"); } /////////////////////////////////////////////// template Processor* SimpleAdaptive::NewCopy() const { return new SimpleAdaptive(*this); } ///////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'samediv.c' then echo shar: will not over-write existing file "'samediv.c'" else cat << \SHAR_EOF > 'samediv.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////// //File samediv.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////// #include ///////////////////////////////////////////////// template SameShapeDivisor::SameShapeDivisor() :Divisor() { } ////////////////////////////////////////////////// template SameShapeDivisor::~SameShapeDivisor() { } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'semistrp.c' then echo shar: will not over-write existing file "'semistrp.c'" else cat << \SHAR_EOF > 'semistrp.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////// //File semistrp.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////// #include ////////////////////////////////////////////// SemiInfiniteStrip::SemiInfiniteStrip(const Point& a,const Point& b) :Geometry(2),TheA(a),TheB(b) { } //////////////////////////////////////////// const Point& SemiInfiniteStrip::A() const { return TheA; } /////////////////////////////////////////// const Point& SemiInfiniteStrip::B() const { return TheB; } /////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'semstitf.c' then echo shar: will not over-write existing file "'semstitf.c'" else cat << \SHAR_EOF > 'semstitf.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////////// //File stripitf.c ////////////////////////////////////////////// #include #include #include #include ////////////////////////////////////////////// SEMI_INFINITE_STRIP::SEMI_INFINITE_STRIP(const Point& a,const Point& b) :USERINTERFACE() { Point or(0,0),one(1,0); INFINITE_STRIP I(or,one); StoreAtomic(new SemiInfiniteStrip(a,b), new PassTheBuck((AtomicRegion*)I)); } /////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'set.c' then echo shar: will not over-write existing file "'set.c'" else cat << \SHAR_EOF > 'set.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// /////////////////////////////////////////////////////// //File set.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ////////////////////////////////////////////////////// #include #include /////////////////////////////////////////////////////// template Set::Set() :ReferenceCounting() { Number = 0; } //////////////////////////////////////////////////////////// template Set::~Set() { } /////////////////////////////////////////////////////// template unsigned int Set::Size() const { return(Number); } //////////////////////////////////////////////////////////// template Boolean Set::Empty() const { return (Number == 0)? True : False ; } ///////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'stack.c' then echo shar: will not over-write existing file "'stack.c'" else cat << \SHAR_EOF > 'stack.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// /////////////////////////////////////////////////////// //File stack.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 30 Jan 1996 V0.1g(no longer compare signed and unsigned) ////////////////////////////////////////////////////// #include #include #include //////////////////////////////////////////////////////////// template Stack::Stack () :ReferenceCounting() { TheTop = new SElement; Error(!TheTop,"Stack:Allocation Failed"); TheTop ->Next =TheTop; Number = 0; } //////////////////////////////////////////////////////////// template void Stack::Push( T* r) { TheTop->Contents = r; SElement* w1 = TheTop; SElement* w2 = w1->Next; w1->Next = new SElement; Error(!w1->Next,"Stack:Allocation Failed"); w1->Next->Contents = TheTop->Contents; w1->Next->Next = w2; Number++; } //////////////////////////////////////////////////////////// template void Stack::Merge (Stack& r) { if(&r == this) return; SElement *w = r.TheTop->Next; for (unsigned int i =0; iContents); w->Contents = 0; w=w->Next; }; r.MakeEmpty(); } //////////////////////////////////////////////////////////// template T* Stack::Pop() { Error(Number==0,"Attempt to pop empty stack"); Number--; T* R=(TheTop->Next->Contents); SElement *w =TheTop->Next; TheTop->Next = TheTop->Next->Next; delete w; return R; } ///////////////////////////////////////////////////// template T* Stack::Top() const { Error(Number==0,"Attempt to access top of empty Stack"); return (TheTop->Next->Contents); } //////////////////////////////////////////////////////////// //template //ostream& //operator<<(ostream& os,const Stack& s) //{ //os << "Stack\n"; //SElement *w = s.TheTop->Next; //for (int i =0; iContents); //w=w->Next; //}; //return os; //} //////////////////////////////////////////////////////////// template void Stack::MakeEmpty() { if (Number == 0) return; SElement* w1 = TheTop->Next; SElement* w2 = w1 ->Next; for (unsigned int i=0 ;iContents; delete w1; w1 = w2; w2 = w1->Next; }; TheTop->Next = TheTop; Number = 0; } ////////////////////////////////////////////////////////// template Stack::~Stack () { MakeEmpty(); delete TheTop; } ////////////////////////////////////////////////////////// template unsigned int Stack::Size() const { return Number; } ////////////////////////////////////////////////////// template Boolean Stack::Empty() const { return (Number == 0) ? True : False ; } ////////////////////////////////////////////////////// template void Stack::IteratorReset() { Current = TheTop->Next; } //////////////////////////////////////////////////// template Boolean Stack::IteratorAtEnd() const { return (Current == TheTop) ? True : False; } //////////////////////////////////////////////////// template T* Stack::IteratorNext() { T*r = Current->Contents; Current = Current->Next; return r; } ///////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'strip.c' then echo shar: will not over-write existing file "'strip.c'" else cat << \SHAR_EOF > 'strip.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////// //File strip.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////// #include #include #include ////////////////////////////////////////////// InfiniteStrip::InfiniteStrip(const Point& a,const Point& b) :Geometry(2),TheA(a),TheB(b) { } //////////////////////////////////////////// const Point& InfiniteStrip::A() const { return TheA; } /////////////////////////////////////////// const Point& InfiniteStrip::B() const { return TheB; } /////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'stripitf.c' then echo shar: will not over-write existing file "'stripitf.c'" else cat << \SHAR_EOF > 'stripitf.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////////// //File stripitf.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ////////////////////////////////////////////// #include #include #include #include ////////////////////////////////////////////// INFINITE_STRIP::INFINITE_STRIP(const Point& a,const Point& b) :USERINTERFACE() { PLANE P; StoreAtomic(new InfiniteStrip(a,b), new PassTheBuck((AtomicRegion*)P)); } /////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'sttosmst.c' then echo shar: will not over-write existing file "'sttosmst.c'" else cat << \SHAR_EOF > 'sttosmst.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////// //File sttosmt.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////////////////////////////////////// #include #include #include #include //////////////////////////////////////////// void IStoSIS::Transform(real& w, Point& p) { // cout << p; SemiInfiniteStrip& s = *SIS_ptr; Point D = s.B()- s.A(); Point C(-D.Y(),D.X()); // if (p.Y() > 600) // goed voor double // if (p.Y() > 60) if (p.Y() > log(REAL_MAX)*6.0/7.0) { w = 0; return; }; C = C/C.Length(); w *= D.Length()*exp(p.Y()); p = s.A() + exp(p.Y())*C + p.X()*D; // cout << p << endl; } /////////////////////////////////////////////////// IStoSIS::IStoSIS(SemiInfiniteStrip* g) : Transformation(),SIS_ptr(g) { } ////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'translat.c' then echo shar: will not over-write existing file "'translat.c'" else cat << \SHAR_EOF > 'translat.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////////// //File translat.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(unused parameter removed) //////////////////////////////////////////////// #include /////////////////////////////////////////////// Translation::Translation( const Point& Offset) :Transformation(),TheOffset(Offset) { } ///////////////////////////////////////////// void Translation::Transform (real &, Point& p) { p += TheOffset; } ///////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'trnsfrm.c' then echo shar: will not over-write existing file "'trnsfrm.c'" else cat << \SHAR_EOF > 'trnsfrm.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// //////////////////////////////////////////////////////// //File trnsfrm.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) //////////////////////////////////////////////////////// #include //////////////////////////////////////////////////////// Transformation::Transformation() :ReferenceCounting() { } ///////////////////////////////////////////////////////// Transformation::~Transformation() { } //////////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'userint.c' then echo shar: will not over-write existing file "'userint.c'" else cat << \SHAR_EOF > 'userint.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ////////////////////////////////////////////////// //File userint.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 9 Sep 1994 V0.1a(operator added) // 10 Sep 1994 V0.1b(initialisation of Int_ptr added) // 25 Jan 1996 V0.1f(typedef introduced, code from .c to .h) /////////////////////////////////////////////////// #include #include /////////////////////////////////////////////////// template USERINTERFACE::USERINTERFACE() :COMPOUND_REGION() { SAR_ptr = new Stack; HAR_ptr = new Heap; HopelessAR_ptr = new Stack; Int_ptr = (Pointer) (0); } ////////////////////////////////////////////////// template USERINTERFACE::USERINTERFACE(const USERINTERFACE& u) :COMPOUND_REGION(u) { SAR_ptr = u.SAR_ptr; HAR_ptr = u.HAR_ptr; HopelessAR_ptr = u.HopelessAR_ptr; Int_ptr = u.Int_ptr; } /////////////////////////////////////////////////// template USERINTERFACE::~USERINTERFACE() { } /////////////////////////////////////////////////// template void USERINTERFACE::Use(Processor* rp) { Error(SAR_ptr-> Size() != 1, "Attempt to specify region processor for multiple regions" ); Atomic* A =(Atomic*)(SAR_ptr->Top()); A->Use(rp); } ////////////////////////////////////////////////// template void USERINTERFACE ::StoreAtomic (GEOMETRY* g, Processor* p) { Atomic* A = new Atomic(g,p); SAR_ptr->Push(A); } ////////////////////////////////////////////////// //template //void //USERINTERFACE ::StoreAtomic (GEOMETRY* g) //{ //Atomic* A = new Atomic(g); //SAR_ptr->Push(A); //} ////////////////////////////////////////////////// template void USERINTERFACE::Preprocess() { while(!SAR_ptr->Empty()) { AtomicRegion* A; A = SAR_ptr->Pop(); Stack Offspring; A->Process(Offspring); if( Offspring.Empty()) { if (!A->Hopeless()) { (*HAR_ptr) += A; } else { HopelessAR_ptr->Push( A); }; LocalInfo().Integral() += A->Integral(); LocalInfo().AbsoluteError () += A->AbsoluteError(); } else { delete A; SAR_ptr->Merge(Offspring); }; }; if (HAR_ptr->Empty()) { LocalInfo().Hopeless() = True; }; } ///////////////////////////////////////////////////// template void USERINTERFACE::Improve() { // (*this) shouldn't be Hopeless() AtomicRegion* A = HAR_ptr->Get(); //HAR_ptr->Print(); //cout << A->Integral()<<" "<AbsoluteError()<Integral(); LocalInfo().AbsoluteError() -= A->AbsoluteError(); Stack Offspring; A->Process(Offspring); if( Offspring.Empty()) { if (!A->Hopeless()) { (*HAR_ptr) += A; } else { HopelessAR_ptr->Push( A); }; LocalInfo().Integral() += A->Integral(); LocalInfo().AbsoluteError() += A->AbsoluteError(); } else { delete A; SAR_ptr->Merge(Offspring); Preprocess(); }; if (HAR_ptr->Empty()) { LocalInfo().Hopeless() = True; }; } ////////////////////////////////////////////////////// template void USERINTERFACE::LocalIntegrand(Integrand* ip) { if (Int_ptr == (Pointer) (0)) Int_ptr = ip; else { Error(!(*Int_ptr == *ip), "Attempt to modify integrand during integration"); } // Error(!HAR_ptr->Empty(), // "Attempt to modify integrand during integration"); if ( !(SAR_ptr->Empty()) ) { SAR_ptr->IteratorReset(); while(!SAR_ptr->IteratorAtEnd()) { SAR_ptr->IteratorNext()->LocalIntegrand(ip); }; } } ////////////////////////////////////////////////////// template void USERINTERFACE::LocalIntegrand(Function f) { LocalIntegrand(new Integrand(f)); } /////////////////////////////////////////////////////// template REGION_COLLECTION USERINTERFACE::operator+( const COMPOUND_REGION& C) { REGION_COLLECTION r; r += (*this); r += C; return r; } ////////////////////////////////////////////////////// template real USERINTERFACE::MaxAtomicError() const { real MaxError=0; if (!HAR_ptr->Empty()) { AtomicRegion* t = HAR_ptr->Look(); MaxError = t->AbsoluteError(); }; return MaxError; } //////////////////////////////////////////////////////// template COMPOUND_REGION* USERINTERFACE::NewCopy() const { return new USERINTERFACE(*this); } /////////////////////////////////////////////////////// //template //USERINTERFACE::operator AtomicRegion*() // { // Error (SAR_ptr->Empty(), // "converting empty compound region to atomic."); // return SAR_ptr->Pop(); // } //////////////////////////////////////////////////// SHAR_EOF fi # end of overwriting check if test -f 'vector.c' then echo shar: will not over-write existing file "'vector.c'" else cat << \SHAR_EOF > 'vector.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////// //File vector.c // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////// #include #include #include #include //////////////////////////////////////////////////// template Vector::Vector(unsigned int s) { TheSize =s; if (s>0) { Contents = new T[TheSize]; Error(!Contents,"Vector:allocation failed"); }; } ////////////////////////////////////////////////////// template Vector::Vector() { TheSize = 0; } ////////////////////////////////////////////////////// template Vector::~Vector() { if (TheSize>0) delete [] Contents; } ////////////////////////////////////////////////////// template Vector::Vector(const Vector& v) { TheSize = v.TheSize; if (TheSize ==0) { Contents = 0; return; }; Contents = new T[TheSize]; Error(!Contents,"Vectorcopyconst:allocation failed"); for (unsigned int i =0;i Vector::Vector( unsigned int s,T* v) { TheSize = s; Contents = new T[TheSize]; for (unsigned int i =0;i const T& Vector::operator[](unsigned int i) const { Error( i>=TheSize,"arrayindex constraint violation"); return Contents[i]; } ////////////////////////////////////////////////////// template T& Vector::operator[](unsigned int i) { Error( i>=TheSize,"array index constraint violation"); return Contents[i]; } ////////////////////////////////////////////////////// template Vector& Vector::operator=(const Vector& v) { if (TheSize == 0) { TheSize = v.TheSize; Contents = new T[TheSize]; Error(!Contents,"Vectorassign:allocation failed"); }; Error( (TheSize != v.TheSize),"lengths of arrays incompatible"); for (unsigned int i =0;i Boolean Vector::operator==(const Vector& v) const { if (TheSize !=v.TheSize) { return False; } else { Boolean b = True; for (unsigned int i=0;i Boolean Vector::operator!=(const Vector& v) const { return (Boolean)!( (*this) == v); } /////////////////////////////////////////////////// template unsigned int Vector::Size() const { return TheSize; } ////////////////////////////////////////////// //template //ostream& //operator << (ostream& os,const Vector& v) //{ //os << "Vector"; //for (unsigned int i=0;i 'vstack.c' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////// //File vstack.cpp // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////// #include #include #include #include #include template VectorStack::VectorStack() :Vector() { } /////////////////////////////////////////////////// template VectorStack::VectorStack(const VectorStack& v) :Vector(v) { } /////////////////////////////////////////////////// template VectorStack& VectorStack::operator=(const VectorStack& v) { if (TheSize == 0) { TheSize = v.TheSize; Contents = new T[TheSize]; Error(!Contents,"Vectorassign:allocation failed"); }; Error( (TheSize != v.TheSize),"lengths of arrays incompatible"); for (unsigned int i =0;i void VectorStack::operator += (const T& t) { T* New = new T[TheSize+1]; for(unsigned int i=0;i 'C2.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : C2.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Parallelogram // ------------------------------------------------- // // BASECLASSES: // Geometry // // PURPOSE: // the geometry of a 2D parallelogram // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1)Parallelogram(const Point& A, // const Point& B, // const Point& C) // ------------------------------- // constructs a parallelogram with vertices // A, B, C and D= B+C-A. // // SELECTORS: // 1) const Point& Vertex (int i ) const // ------------------------------------- // returns the i-th vertex. 0<=i<3 // referring to the constructor, i=0 returns A, // i=1 B and i=2 C. D can't be retrieved. // // 2) real Volume() const // ---------------------- // // 3) Processor* DefaultProcessor()const // ---------------------------------------------------- // // // MODIFIERS: // 1) void Volume(real) // -------------------- // informs the par. about its volume, in order to // avoid computation of it // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// #ifndef C2_H #define C2_H ///////////////////////////////////////////////////////// #include #include #include #include #include #include ///////////////////////////////////////////////////////// class Parallelogram : public Geometry { public: Parallelogram (const Point&,const Point&, const Point&); const Point& Vertex(int)const ; real Volume ()const ; void Volume(real); private: Vector Vertices; real TheVolume; Boolean TheVolumeKnown; void ComputeVolume(); }; ///////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'C2dv2.h' then echo shar: will not over-write existing file "'C2dv2.h'" else cat << \SHAR_EOF > 'C2dv2.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : C2dv2.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(long lines split) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Parallelogram_Divide2 // ------------------------------------------------- // // BASECLASSES: // SameShapeDivisor // // PURPOSE: // to cut a Parallelogram in 2 new ones // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Parallelogram_Divide4() // ------------------------ // // SELECTORS: // 1) int NumberOfParts() const // ---------------------------- // returns 2 // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Apply(const Parallelogram& P, Stack& S // , const Vector& DiffOrder) // ---------------------------------------------------------- // divides P by halving its sides. the new parts are // returned in S. If DiffOrder[0] > DiffOrder[1] then P // is divided by halving the edge {Vertex(0),Vertex(1)} // otherwise the edge {Vertex(0),Vertex(2)} is halved. // ///////////////////////////////////////////////////////// #ifndef C2DV2_H #define C2DV2_H ////////////////////////////////////////// #include #include //////////////////////////////////////// class Parallelogram_Divide2 :public SameShapeDivisor { public: Parallelogram_Divide2(); void Apply(const Parallelogram&, Stack&, const Vector&); int NumberOfParts() const {return 2;}; }; ////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'C2dv4.h' then echo shar: will not over-write existing file "'C2dv4.h'" else cat << \SHAR_EOF > 'C2dv4.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : C2dv4.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(long lines split) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Parallelogram_Divide4 // ------------------------------------------------- // // BASECLASSES: // SameShapeDivisor // // PURPOSE: // Divides a Parallelogram in 4 new ones. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Parallelogram_Divide4() // ------------------------ // // SELECTORS: // 1) int NumberOfParts() const // ---------------------------- // returns 4 // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Apply(const Parallelogram& P, Stack& S // , const Vector& DiffOrder) // ---------------------------------------------------------- // divides P by halving its sides. the new parts are // returned in S,DiffOrder isn't used. // ///////////////////////////////////////////////////////// #ifndef C2DV4_H #define C2DV4_H ////////////////////////////////////////// #include #include //////////////////////////////////////// class Parallelogram_Divide4 :public SameShapeDivisor { public: Parallelogram_Divide4(); void Apply(const Parallelogram&, Stack&, const Vector&); int NumberOfParts() const {return 4;}; }; ////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'C2interf.h' then echo shar: will not over-write existing file "'C2interf.h'" else cat << \SHAR_EOF > 'C2interf.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : C2interf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS PARALLELOGRAM // ------------------------------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // End-user interface to a parallelogram. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) PARALLELOGRAM(const Point& A, // const Point& B, // const Point& C) // ------------------------------ // constructs a parallelogram with 4 vertices // A, B, C, and D=B+C-A // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// // DEFINITION OF CLASS RECTANGLE // ------------------------------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // End-user interface to a parallelogram. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) RECTANGLE(const Point& A, // const Point& B, // const Point& C) // ------------------------------ // constructs a parallelogram with 4 vertices // A, B, C, and D=B+C-A // AB should be orthogonal to BC // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef C2INTERF_H #define C2INTERF_H /////////////////////////////////////////////////// #include #include /////////////////////////////////////////////////// class PARALLELOGRAM : public USERINTERFACE { public: PARALLELOGRAM(const Point&,const Point&,const Point&); }; ////////////////////////////////////////////////// class RECTANGLE : public USERINTERFACE { public: RECTANGLE(const Point&,const Point&,const Point&); }; ////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'C2prc.h' then echo shar: will not over-write existing file "'C2prc.h'" else cat << \SHAR_EOF > 'C2prc.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : C2prc.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(typedef introduced) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Parallelogram_Processor // ------------------------------------------------- // // BASECLASSES: // Processor // // PURPOSE: // A processor for two-dimensional parallelograms. // first a degree 13 rule is applied to the region // Fourth order divided differences along the axes are // computed. If they're very much different, the region // is cut in two, otherwise it is cut in four. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Parallelogram_Processor(); // ----------------------------- // // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Process(Stack&); // -------------------------------------------------- // see class Processor // // 2) virtual Processor* NewCopy() const=0 // ------------------------------------------------- // // makes a new copy (using the copy constructor) and // returns a pointer to it. ///////////////////////////////////////////////////////// #ifndef C2PRC_H #define C2PRC_H ////////////////////////////////////////////// #include #include #include #include #include ///////////////////////////////////////////// class Parallelogram_Processor : public Processor { public: typedef Rule RuleParallelogram; typedef SameShapeDivisor SameShapeDivisorParallelogram; Parallelogram_Processor(); void Process(Stack&); Processor* NewCopy() const; protected: static Pointer TheRule; static Pointer TheDivisor4; static Pointer TheDivisor2; unsigned int TimesCalled; Parallelogram_Processor* Descendant() const; Vector Diffs; }; ///////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'C2rule13.h' then echo shar: will not over-write existing file "'C2rule13.h'" else cat << \SHAR_EOF > 'C2rule13.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : C2rule13.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(long lines split) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Parallelogram_Rule13 // ------------------------------------ // // BASECLASSES: // Rule // // // PURPOSE: // A degree 13 rule for a rectangle. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // None // SELECTORS: // 1) int Degree() const // --------------------- // returns 13 // // 2) int NumberOfPoints(int ) const // -------------------------------------- // returns 37. // // MODIFIERS: // None // OPERATORS: // None // SPECIAL: // 1) ApplyWithDiffs(Integrand & I, // Parallelogram& H,real& Result,real& Error // Vector& D) // ------------------------------------------------- // Input parameters: // I: Integrand // H: rectangle to be integrated. H.Dimension() // should be 2. // Output parameters: // Result: approximation to the integral // Error: absolute error estimation // D: Fourth order divided differences in each direction // D[0] refers to {Vertex(0),Vertex(1)}; // D[1] refers to {Vertex(0),Vertex(2)}; // // /////////////////////////////////////////////////////////// #ifndef C2RULE13_H #define C2RULE13_H ///////////////////////////////////////// #include #include ////////////////////////////////////////// class Parallelogram_Rule13 : public Rule { public: Parallelogram_Rule13(); void ApplyWithDiffs(Integrand&,Parallelogram&,real& Result, real& Error,Vector&); int NumberOfPoints() const {return 37;}; int Degree () const {return 13;}; }; //////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'C2toS2.h' then echo shar: will not over-write existing file "'C2toS2.h'" else cat << \SHAR_EOF > 'C2toS2.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : C2toS2.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// //////////////////////////////////////////////////////// // DEFINITION OF CLASS PolarToRectangular // ------------------------------- // // BASECLASSES: // Transformation // // // PURPOSE: // implements a transformation from polar to // rectangular coordinates // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) PolarToRectangular() // ------------------------ // // SELECTORS: // None // MODIFIERS: // None // OPERATORS: // None // SPECIAL: // 1) void Transform (real& w, Point& p) // --------------------------------------- // Multiplies w by the Jacobian at p and then replaces p by // the transformed point. // /////////////////////////////////////////////////////////// #ifndef C2TOS2_H #define C2TOS2_H //////////////////////////////////////////////////////// #include #include /////////////////////////////////////////////////////// class PolarToRectangular :public Transformation { public: PolarToRectangular(); void Transform (real &w, Point& p); }; //////////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'C2togr.h' then echo shar: will not over-write existing file "'C2togr.h'" else cat << \SHAR_EOF > 'C2togr.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : C2togr.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS C2toGR // ------------------------------------------------- // // BASECLASSES: // Transformation // // PURPOSE: // transformation from parallelogram to generalized // rectangle // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) C2toGR(GeneralizedRectangle*) // ------------ // The target region has to be supplied // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Transform(real & w, Point & p) // -------------------------------------- // multiplies w by the Jacobian at p and then // replaces p by the transformed point // ///////////////////////////////////////////////////////// #ifndef C2TOGR_H #define C2TOGR_H ///////////////////////////////////////////////////////// #include #include #include #include /////////////////////////////////////////////////// class C2toGR : public Transformation { public: C2toGR( GeneralizedRectangle*); void Transform(real& w, Point& p); private: Pointer GR_ptr; }; ////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'E2.h' then echo shar: will not over-write existing file "'E2.h'" else cat << \SHAR_EOF > 'E2.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : E2.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Plane // ---------------------------- // // BASECLASSES: // Geometry // // PURPOSE: // implements the geometry of a plane // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Plane() // ---------------------------- // constructs a plane with center=(0,0) and the unit // on both coordinate axis = 1. // // 2) Plane(const Point& center) // --------------------------------------------------- // Constructs a plane given an integrand an a center point. // the unit on both axis = 1. // // 3) Plane(const Point& center, // const real& xscale, const real& yscale) // ---------------------------------------------------- // same as above, but now the scales can be set. // // // SELECTORS: // 1) real ScaleX() const // --------------------------- // returns a scale factor for the X coordinate. // // 2) real ScaleX() const // --------------------------- // returns a scale factor for the X coordinate. // // 3) const Point& Center() const // ------------------------------ // // 4) Processor* DefaultProcessor() const // --------------------------------------------- // // MODIFIERS: // None // OPERATORS: // None // SPECIAL: // None // /////////////////////////////////////////////////////////// #ifndef E2_H #define E2_H ////////////////////////////////////////////////// #include #include #include #include ////////////////////////////////////////////////// class Plane : public Geometry { public: Plane (); Plane (const Point&); Plane (const Point&, real, real); real ScaleX() const ; real ScaleY() const ; const Point& Center()const; private: real xscale,yscale; Point TheCenter; }; ////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'E2adapt.h' then echo shar: will not over-write existing file "'E2adapt.h'" else cat << \SHAR_EOF > 'E2adapt.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : E2adapt.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Nov 1994 V0.1d(re-ordering of member declarations) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS PlaneAdaptive // ------------------------------------------------- // // BASECLASSES: // Processor // // PURPOSE: // during the first call of Process() a degree 13 rule // is applied to the plane. during the second call // the plane is divided into a CIRCLE and an OUT_CIRCLE // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) PlaneAdaptive() // ---------------- // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Process( Stack&) // ------------------------------------------------------- // see Processor<> // // 2) virtual Processor* NewCopy() const=0 // ------------------------------------------------- // // makes a new copy (using the copy constructor) and // returns a pointer to it. ///////////////////////////////////////////////////////// #ifndef E2ADAPT_H #define E2ADAPT_H ///////////////////////////////////////////////////// #include #include #include //////////////////////////////////////////////////// class PlaneAdaptive: public Processor { public: PlaneAdaptive(); void Process(Stack&); Processor* NewCopy() const; private: static void Rule(Integrand&,Plane&,real&,real&,real&); unsigned int TimesCalled; real HalfValueRadius; } ; ///////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'E2interf.h' then echo shar: will not over-write existing file "'E2interf.h'" else cat << \SHAR_EOF > 'E2interf.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : E2interf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS PLANE // ------------------------------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // End-user interface to planes // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1)PLANE() // -------- // // 2)PLANE(const Point& Center) // ---------------------------- // Center indicates where in the plane the // activity is the greatest. // // 3)PLANE(const Point& Center, // real ScaleX, real ScaleY) // ------------------------------------ // same as 2) but with an indication of scales. // // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef E2INTERF_H #define E2INTERF_H //////////////////////////////////////////////// #include #include #include #include //////////////////////////////////////////////// class PLANE : public USERINTERFACE { public: PLANE(); PLANE(const Point&); PLANE(const Point&, real, real); }; //////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'E2sec.h' then echo shar: will not over-write existing file "'E2sec.h'" else cat << \SHAR_EOF > 'E2sec.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : E2sec.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS PlaneSector // ------------------------------------------------- // // BASECLASSES: // Geometry // // PURPOSE: // the geometry of a plane sector // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) PlaneSector(const Point& A, const Point& B, // const Point& C) // ------------------------------------------------- // constructs a PlaneSector. AB should not be // perpendicular to BC. // // 2) PlaneSector(const Point& O,real r,real theta1,real,theta2) // ------------------------------------------------ // // SELECTORS: // 1) const Point& Center() const // ------------------------------ // // 2) real InnerRadius() const // --------------------------- // // 3) real SmallAngle() const // -------------------------- // // 4) real BigAngle() const // ------------------------ // // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef E2SEC_H #define E2SEC_H ///////////////////////////////////////// #include #include #include ///////////////////////////////////////// class PlaneSector : public Geometry { public: PlaneSector( const Point& A, const Point& B, const Point& C); PlaneSector( const Point& O,real r,real theta1,real theta2); const Point& Center() const; real InnerRadius() const; real OuterRadius() const; real SmallAngle () const; real BigAngle () const; private: Point TheCenter; real TheInnerRadius, TheSmallAngle, TheBigAngle; }; ////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'E2secitf.h' then echo shar: will not over-write existing file "'E2secitf.h'" else cat << \SHAR_EOF > 'E2secitf.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : E2secitf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS PLANE_SECTOR // ------------------------------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // End-user interface to PlaneSectors // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) PLANE_SECTOR(const Point& A, // const Point& B, // const Point& C) // --------------------------------- // constructs a plane sector with vertices A,B,C // AB shouldn't be perpendicular to BC // // 2) PLANE_SECTOR(const Point& O,real r,real theta1,real theta2) // --------------------------------------------------------------- // // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef E2SECITF_H #define E2SECITF_H ///////////////////////////////////////// #include #include ///////////////////////////////////////// class PLANE_SECTOR : public USERINTERFACE { public: PLANE_SECTOR(const Point&,const Point&, const Point&); PLANE_SECTOR(const Point&,real,real,real); }; ///////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'E2secprc.h' then echo shar: will not over-write existing file "'E2secprc.h'" else cat << \SHAR_EOF > 'E2secprc.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : E2secprc.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS PlaneSector_Processor // ------------------------------------------------- // // BASECLASSES: // Processor // // PURPOSE: // transforms the plane sector into a semi-infinite strip // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1)PlaneSector_Processor() // ---------------------------- // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Process(Stack&) // ------------------------------------------------- // see Processor<> // // 2) virtual Processor* NewCopy() const=0 // ------------------------------------------------- // // makes a new copy (using the copy constructor) and // returns a pointer to it. ///////////////////////////////////////////////////////// #ifndef E2SECPRC_H #define E2SECPRC_H ////////////////////////////////////////////// #include #include ///////////////////////////////////////////// class PlaneSector_Processor: public Processor { public: PlaneSector_Processor(); void Process(Stack&); Processor* NewCopy() const; }; ///////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'E2tostrp.h' then echo shar: will not over-write existing file "'E2tostrp.h'" else cat << \SHAR_EOF > 'E2tostrp.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : E2tostrp.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS E2toIS // ------------------------------------------------- // // BASECLASSES: // Transformation // // PURPOSE: // transformation from plane to infinite strip // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) E2toIS(InfiniteStrip*) // ------------ // The target region has to be supplied // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Transform(real & w, Point & p) // -------------------------------------- // multiplies w by the Jacobian at p and then // replaces p by the transformed point // ///////////////////////////////////////////////////////// #ifndef E2TOSTRP_H #define E2TOSTRP_H ///////////////////////////////////////////////////////// #include #include #include #include /////////////////////////////////////////////////// class E2toIS : public Transformation { public: E2toIS( InfiniteStrip*); void Transform(real& w, Point& p); private: Pointer IS_ptr; }; ////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'S2.h' then echo shar: will not over-write existing file "'S2.h'" else cat << \SHAR_EOF > 'S2.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : S2.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Circle // -------------------------------- // // BASECLASSES: // Geometry // // PURPOSE: // Circle is a 2D circle with arbitrary center and // radius. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Circle(const Point& Center, real Radius) // -------------------------------- // defines the region. // // 2) Circle( const Point& Center, Point Boundary) // -------------------------------- // defines the region using its center and a point on the boundary. // SELECTORS: // 1) const Point& Center()const // ------------------------------ // // 2) real Radius() const // ----------------------- // // 3) real Volume() const // ---------------------- // // 4) Processor* DefaultProcessor()const // --------------------------------------------- // // MODIFIERS: // None // OPERATORS: // None // SPECIAL: // None // /////////////////////////////////////////////////////////// #ifndef S2_H #define S2_H ///////////////////////////////////////// #include #include #include #include ///////////////////////////////////////// class Circle : public Geometry { public: Circle(const Point& Center,real Radius); Circle(const Point& Center,const Point& Boundary); real Volume()const ; const Point& Center()const; real Radius() const; private: Point TheCenter; real TheRadius; }; ////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'S2adapt.h' then echo shar: will not over-write existing file "'S2adapt.h'" else cat << \SHAR_EOF > 'S2adapt.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : S2adapt.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Nov 1994 V0.1d(re-ordering of member declarations) // 25 Jan 1996 V0.1f(typedef introduced) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS CircleAdaptive // ------------------------------------------------- // // BASECLASSES: // Processor // // PURPOSE: // A circle processor. First a rule is // applied to the circle. Afterwards the circle is // divided into a central circle and some // polar rectangles. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1)CircleAdaptive(Rule*) // ------------------------------- // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Process( Stack) // ------------------------------------------------- // see class Processor // // 2) virtual Processor* NewCopy() const=0 // ------------------------------------------------- // // makes a new copy (using the copy constructor) and // returns a pointer to it. ///////////////////////////////////////////////////////// #ifndef S2ADAPT_H #define S2ADAPT_H ///////////////////////////////////////////////// #include #include #include #include ///////////////////////////////////////////////// class CircleAdaptive : public Processor { public: typedef Rule RuleCircle; CircleAdaptive( Rule * ); void Process(Stack& ); Processor* NewCopy() const; private: Pointer< RuleCircle > TheRule; CircleAdaptive* Descendant()const; unsigned int TimesCalled; unsigned int GenerationNumber; }; /////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'S2interf.h' then echo shar: will not over-write existing file "'S2interf.h'" else cat << \SHAR_EOF > 'S2interf.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : S2interf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS CIRCLE // ------------------------------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // end-user interface to circles // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) CIRCLE(const Point& Center, const Point& B) // ---------------------------------------------- // constructs a circle with Center as its origin // and B a point on the boundary. // // 2) CIRCLE(const Point& Center, real Radius) // ------------------------------------------- // // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef S2INTERF_H #define S2INTERF_H //////////////////////////////////////////////// #include #include //////////////////////////////////////////////// class CIRCLE : public USERINTERFACE { public: CIRCLE(const Point&,const Point&); CIRCLE(const Point&, real); }; //////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'S2rule13.h' then echo shar: will not over-write existing file "'S2rule13.h'" else cat << \SHAR_EOF > 'S2rule13.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : S2rule13.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Circle_Rule13 // ------------------------------------ // // BASECLASSES: // Rule // // // PURPOSE: // A degree 13 rule for a circle. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1)Circle_Rule13() // ------------------ // // SELECTORS: // 1) int Degree() const // --------------------- // returns 13 // // 2) int NumberOfPoints() const // -------------------------------------- // returns 36. // // MODIFIERS: // None // OPERATORS: // None // SPECIAL: // 1) Apply(Integrand& I,Circle& H, // real& Result,real& Error) // ------------------------------------------------- // Inputparameters: // I: the integrand // H: circle to be integrated. H.Dimension() // should be 2. // Outputparameters: // Result: approximation to the integral // Error: absolute error estimation // /////////////////////////////////////////////////////////// #ifndef S2RULE13_H #define S2RULE13_H ///////////////////////////////////////// #include #include ////////////////////////////////////////// class Circle_Rule13 : public Rule { public: Circle_Rule13(); void Apply(Integrand&,Circle&,real& Result ,real& Error); int NumberOfPoints() const {return 36;}; int Degree () const {return 13;}; }; //////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'T2.h' then echo shar: will not over-write existing file "'T2.h'" else cat << \SHAR_EOF > 'T2.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : T2.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Triangle // ------------------------------------------------- // // BASECLASSES: // Geometry // // PURPOSE: // implements the geometry of a simple triangle // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Triangle (const Point&,const Point&,const Point&) // ---------------------------------------------------- // constructs a 2D Triangle given its 3 vertices // // SELECTORS: // 1) const Point& Vertex(int i) const // ----------------------------------- // returns the i-th vertex, 0<=i<3 // // 2) real Volume() const // ----------------------- // // 3) Processor* DefaultProcessor() const // ------------------------------------------------ // // MODIFIERS: // 1) void Volume(real) // -------------------- // informs the triangle about its volume, to avoid // future computations of it // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef T2_H #define T2_H ////////////////////////////////////////////////// #include #include #include #include #include #include ////////////////////////////////////////////////// class Triangle : public Geometry { public : Triangle(const Point&,const Point&,const Point&); const Point& Vertex (int) const; real Volume() const; void Volume(real); private: Vector Vertices; real TheVolume; Boolean TheVolumeKnown; void ComputeVolume(); }; //////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'T2dv4.h' then echo shar: will not over-write existing file "'T2dv4.h'" else cat << \SHAR_EOF > 'T2dv4.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : T2dv4.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Triangle_Divide4 // ------------------------------------------ // // BASECLASSES: // SameShapeDivisor // // // PURPOSE: // provides a means to cut Triangles in 4. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Triangle_Divide4() // --------------------- // // SELECTORS: // 1) NumberOfParts() const // ------------------------ // returns 4 // // MODIFIERS: // None // OPERATORS: // None // SPECIAL: // 1) void Apply(Triangle& H, // Stack& S,const Vector& D) // -------------------------------- // divides H into parts and returns them in S // /////////////////////////////////////////////////////////// #ifndef T2DV4_H #define T2DV4_H ////////////////////////////////////////// #include #include //////////////////////////////////////// class Triangle_Divide4 :public SameShapeDivisor { public: Triangle_Divide4(); void Apply(const Triangle&, Stack&, const Vector&); int NumberOfParts() const {return 4;}; }; ////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'T2interf.h' then echo shar: will not over-write existing file "'T2interf.h'" else cat << \SHAR_EOF > 'T2interf.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : T2interf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS TRIANGLE // ---------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // an end-user interface to Triangle // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1)TRIANGLE(const Point& , const Point&, const Point&) // --------------------------------------------------- // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef T2INTERF_H #define T2INTERF_H /////////////////////////////////////////////////// #include #include /////////////////////////////////////////////////// class TRIANGLE : public USERINTERFACE { public: TRIANGLE(const Point&,const Point&,const Point&); }; ////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'T2rule13.h' then echo shar: will not over-write existing file "'T2rule13.h'" else cat << \SHAR_EOF > 'T2rule13.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : T2rule13.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Triangle_Rule13 // ------------------------------------ // // BASECLASSES: // Rule // // // PURPOSE: // A degree 13 rule for a rectangle. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1)Triangle_Rule13() // ------------------- // // SELECTORS: // 1) int Degree() const // --------------------- // returns 13 // // 2) int NumberOfPoints() const // -------------------------------------- // returns 37. // // MODIFIERS: // None // OPERATORS: // None // SPECIAL: // 1) Apply(Integrand& I,Triangle& H,real& Result,real& // Error) // ------------------------------------------------- // Input parameters: // I: the integrand // H: Triangle to be integrated. // Output parameters: // Result: approximation to the integral // Error: absolute error estimation // /////////////////////////////////////////////////////////// #ifndef T2_RULE13 #define T2_RULE13 /////////////////////////////////////////// #include #include /////////////////////////////////////////// class Triangle_Rule13 :public Rule { public: Triangle_Rule13(); void Apply(Integrand&,Triangle& ,real&,real& ); int Degree() const {return 13;}; int NumberOfPoints () const {return 37;}; }; /////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'T2tops.h' then echo shar: will not over-write existing file "'T2tops.h'" else cat << \SHAR_EOF > 'T2tops.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : T2tops.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Nov 1994 V0.1d(re-ordering of member declarations) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS C2toGR // ------------------------------------------------- // // BASECLASSES: // Transformation // // PURPOSE: // transformation from triangle to parabolic segment // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) T2toPS(ParabolicSegment* g) // ------------ // the target region has to be supplied // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Transform(real & w, Point & p) // -------------------------------------- // multiplies w by the Jacobian at p and then // replaces p by the transformed point // ///////////////////////////////////////////////////////// #ifndef T2TOPS_H #define T2TOPS_H ///////////////////////////////////////////////////////// #include #include #include #include /////////////////////////////////////////////////// class T2toPS : public Transformation { public: T2toPS( ParabolicSegment*); void Transform(real& w, Point& p); private: Point P,M,H; real a,k; }; ////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'atomic.h' then echo shar: will not over-write existing file "'atomic.h'" else cat << \SHAR_EOF > 'atomic.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : atomic.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(typedef introduced) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Atomic // ------------------------------------------------- // // BASECLASSES: // AtomicRegion // // PURPOSE: // provides a base class to all atomic regions. // provides a means for constructing them, as well // as for altering their integrand or processor // provides a method for processing them // // TEMPLATES: // it should be instantiated with a class GEOMETRY // derived from Geometry // this GEOMETRY should have a member // Processor* DefaultProcessor() const. // // METHODS: // CONSTRUCTORS: // 1) Atomic(GEOMETRY* G, Processor* P ) // ------------------------------------------ // constructs an atomic region with *G as its geometry // and *P as its processor // // // SELECTORS: // None // // MODIFIERS: // 1) Use(Processor* P) // ----------------------------- // to change the processor to be used // // 2) LocalIntegrand(Integrand* I) // ------------------------------- // to change the integrand // // OPERATORS: // None // // SPECIAL: // 1) Process( Stack& Offspring) // ------------------------------------------- // attempts to compute an integral and an error // estimate. possible offspring is returned. // ///////////////////////////////////////////////////////// #ifndef ATOMIC_H #define ATOMIC_H //////////////////////////////////////////// #include #include ////////////////////////////////////////// template class Atomic : public AtomicRegion { friend class Processor; public: typedef Processor ProcessorGEOMETRY; Atomic(GEOMETRY*, Processor*); void Use(Processor*); void Process(Stack& Offspring); void LocalIntegrand(Integrand*); private: Pointer G_ptr; Pointer< ProcessorGEOMETRY> RP_ptr; Pointer I_ptr; RegionInfo* LocalRegionInfo() ; }; /////////////////////////////////////////////// #include #ifdef TEMPLATEINCLUDE #include #endif /////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'atomreg.h' then echo shar: will not over-write existing file "'atomreg.h'" else cat << \SHAR_EOF > 'atomreg.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : atomreg.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS AtomicRegion // -------------------------------- // // BASECLASSES: // Region // // PURPOSE: // common base class to all Atomic<> regions, merely // to be able to group them in a single set. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) AtomicRegion() // ----------------- // // SELECTORS: // None // // MODIFIERS: // 1) void LocalIntegrand(Integrand*) // ---------------------------------- // to change the integrand // // // OPERATORS: // None // // SPECIAL: // 1) void Process(Stack& Offspring) // ----------------------------------------------- // attempts to compute integral and error over // the region. possible Offspring is returned. // ///////////////////////////////////////////////////////// #ifndef ATOMREG_H #define ATOMREG_H /////////////////////////////////////////////// #include #include #include /////////////////////////////////////////////// class AtomicRegion : public Region { public: AtomicRegion(); virtual void LocalIntegrand(Integrand*)=0; virtual void Process(Stack& Offspring)=0; virtual ~AtomicRegion(); }; ///////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'boolean.h' then echo shar: will not over-write existing file "'boolean.h'" else cat << \SHAR_EOF > 'boolean.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : boolean.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// #ifndef BOOLEAN_H #define BOOLEAN_H ///////////////////////////////////////////////// #include ///////////////////////////////////////////////// enum Boolean {False, True}; extern ostream& operator<<(ostream&,const Boolean&); ////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'chrono.h' then echo shar: will not over-write existing file "'chrono.h'" else cat << \SHAR_EOF > 'chrono.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : chrono.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 28 Mar 1996 V0.1h(long instead of int) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Chrono // -------------------------- // // BASECLASSES: // Counter // // PURPOSE: // Chrono implements a simple stop-watch; it can be used for // all sorts of timings. At the moment it will only give // useful results when compiled with -DGETRUSAGE on a // system that has a getrusage() system call. If // GETRUSAGE is not defined, Read() will always return 0. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Chrono() // ----------- // Default constructor. The stop-watch isn't running after // construction. // SELECTORS: // 1) unsigned long Read() // ---------------- // Read reads out the time in milliseconds. Currently it // is accurate up to one millisecond. // MODIFIERS: // 1) void Start() // --------------- // Start() makes the stop-watch running. Successive calls // of Start() have no effect. // 2) void Stop() // --------------- // Stops the stop-watch. After Stop(), Read() will always // read out the same value, until the stop-watch is started // again. Stopping a stopped stop-watch has no effect. // 3) void Reset() // --------------- // After a call of Reset(), Read() will read out zero, // until the stop-watch is started again. A running // stop-watch should not be Reset(). // // OPERATORS: // None // SPECIAL: // None ////////////////////////////////////////////////////////// #ifndef CHRONO_H #define CHRONO_H ////////////////////////////////////////////////////////// #include #include ////////////////////////////////////////////////////////// class Chrono :public Counter { public: Chrono(); void Start(); void Stop(); void Reset(); unsigned long Read(); private: long Time; long OldTime; Boolean Running; long times_(); }; ///////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'compreg.h' then echo shar: will not over-write existing file "'compreg.h'" else cat << \SHAR_EOF > 'compreg.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : compreg.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS COMPOUND_REGION // ------------------------------------------------- // // BASECLASSES: // Region // // PURPOSE: // groups regions and their eventual offspring. applies // the global adaptive algorithm. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) COMPOUND_REGION() // ------------------- // an empty compound region is created. the integral // and error over it will be 0. calls of Process() // will have no effect. // // 2) COMPOUNDERGION(const COMPOUND_REGION& C) // ------------------------------------------ // implements sharing semantics !! // // SELECTORS: // None // // MODIFIERS: // 1) void LocalIntegrand (Integrand* I) // ------------------------------------ // establishes *I as the integrand to be integrated // on all subregions that are contained in *this. // When subsequent calls are made, only the last one // has effect. It's an error to call this function // after the first call of Process(). // // // 2) void Process() // ----------------- // performs one step in the global adaptive algorithm. // the first call of Process() will compute an initial // approximation; subsequent calls will try to improve // this // // OPERATORS: // // 1) COMPOUND_REGION& operator= // (const COMPOUND_REGION& C) // --------------------------------- // implements sharing semantics !! // // SPECIAL: // None // // NOTE: The other public members are not to be // used by normal clients. ///////////////////////////////////////////////////////// #ifndef COMPREG_H #define COMPREG_H ///////////////////////////////////////////// #include #include #include #include #include ///////////////////////////////////////////// ///////////////////////////////////////////// class COMPOUND_REGION : public Region { public: virtual void LocalIntegrand(Integrand*)=0; void Process(); COMPOUND_REGION(); virtual ~COMPOUND_REGION(); virtual void Preprocess()=0; virtual void Improve()=0; virtual real MaxAtomicError()const=0; virtual COMPOUND_REGION* NewCopy()const =0; private: enum Status {Virgin,Active}; Status TheStatus; }; /////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'counter.h' then echo shar: will not over-write existing file "'counter.h'" else cat << \SHAR_EOF > 'counter.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : counter.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 28 Mar 1996 V0.1h(long instead of int) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Counter // --------------------------- // // BASECLASSES: // None // // // PURPOSE: // Counter is a pure virtual base class for implementing // stop-watch-like classes. // // TEMPLATES: // None // METHODS: // CONSTRUCTORS: // None // // SELECTORS: // 1) virtual unsigned long Read()=0 // -------------------------- // Read reads out the counter // MODIFIERS: // 1) virtual void Start()=0 // ------------------------- // Start() makes the stop-watch running. Successive calls // of Start() have no effect. // 2) virtual void Stop()=0 // ------------------------- // Stops the stop-watch. After Stop(), Read() will always // read out the same value, until the stop-watch is started // again. Stopping a stopped stop-watch has no effect. // 3) virtual void Reset()=0 // ------------------------- // After a call of Reset(), Read() will read out zero, // until the stop-watch is started again. A running // stop-watch should not be Reset(). // // OPERATORS: // None // SPECIAL: // None /////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////// #ifndef COUNTER_H #define COUNTER_H ////////////////////////////////////////////// class Counter { public: virtual void Start()=0; virtual void Stop()=0; virtual void Reset()=0; virtual unsigned long Read()=0; }; ////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'cubpack.h' then echo shar: will not over-write existing file "'cubpack.h'" else cat << \SHAR_EOF > 'cubpack.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : cubpack.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // PURPOSE: // an include file for the end-user ///////////////////////////////////////////////////////// #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include SHAR_EOF fi # end of overwriting check if test -f 'div.h' then echo shar: will not over-write existing file "'div.h'" else cat << \SHAR_EOF > 'div.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : div.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Divisor // --------------------------- // // BASECLASSES: // ReferenceCounting // // // PURPOSE: // Divisor is a pure virtual base class for implementing // dividing-procedures. Information on the number of // parts the divisor produces, can be retrieved. // // TEMPLATES: // The type of region T which has to be divided is // templated. Currently it is assumed that the parts // after division also are of type T. T should be // derived from class Region. // // METHODS: // CONSTRUCTORS: // 1) Divisor() // ------------ // // SELECTORS: // 1) virtual int NumberOfParts() const=0 // --------------------------------------------------- // returns the number of parts the divisor produces. // // MODIFIERS: // None // OPERATORS: // None // SPECIAL: // None /////////////////////////////////////////////////////////// #ifndef DIV_H #define DIV_H ///////////////////////////////////////// #include ////////////////////////////////////////// template class Divisor: public ReferenceCounting { public: Divisor(); virtual int NumberOfParts() const =0; virtual ~Divisor(); }; /////////////////////////////////////////// #include #ifdef TEMPLATEINCLUDE #include #endif ////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'error.h' then echo shar: will not over-write existing file "'error.h'" else cat << \SHAR_EOF > 'error.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : error.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // PURPOSE // void Error(Boolean b,char* message) is an error // checking and reporting routine. if b is true then // message is printed on stderr and the program is // aborted. ///////////////////////////////////////////////////////// #ifndef ERROR_H #define ERROR_H //////////////////////////////////////// #include #include #include //////////////////////////////////////// inline void Error(int b,char* message) { if (b) { cerr << message < 'eval_ctr.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : eval_ctr.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 28 Mar 1996 V0.1h(long instead of int) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS EvaluationCounter // ------------------------------------- // // BASECLASSES: // Counter // // // PURPOSE: // EvaluationCounter acts as a kind of stop-watch // counting the number of Integrand evaluations // during the time it's running. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) EvaluationCounter() // ---------------------- // Default constructor. The stop-watch isn't running after // construction. // SELECTORS: // 1) unsigned long Read() // ---------------- // Read reads out the number of // IntegrandEvaluations made since Start() was // called. This value remains constant after Stop() is // called. // MODIFIERS: // 1) void Start() // --------------- // Start() makes the stop-watch running. Successive calls // of Start() have no effect. // 2) void Stop() // --------------- // Stops the stop-watch. After Stop(), Read() will always // read out the same value, until the stop-watch is started // again. Stopping a stopped stop-watch has no effect. // 3) void Reset() // --------------- // After a call of Reset(), Read() will read out zero, // until the stop-watch is started again. A running // stop-watch should not be Reset(). // // 4) void Reset(unsigned long value) // ---------------------------------- // allows you to reset the counter to some other // value than zero. Counting will start from this value. // // OPERATORS: // None // SPECIAL: // None /////////////////////////////////////////////////////////// #ifndef EVAL_CTR_H #define EVAL_CTR_H ///////////////////////////////// #include #include //////////////////////////////////////////////// class EvaluationCounter : public Counter { public: EvaluationCounter(); void Start(); void Stop(); void Reset(); void Reset(unsigned long); unsigned long Read(); private: long Strt; long End; unsigned long Bias; Boolean Running; }; //////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'function.h' then echo shar: will not over-write existing file "'function.h'" else cat << \SHAR_EOF > 'function.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : function.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // PURPOSE: // mapping from a Point to a real ///////////////////////////////////////////////////////// #ifndef FUNCTION_H #define FUNCTION_H ///////////////////////////////////////////////////////// #include #include ///////////////////////////////////////////////////////// typedef real (*Function)(const Point&); ///////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'geometry.h' then echo shar: will not over-write existing file "'geometry.h'" else cat << \SHAR_EOF > 'geometry.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : geometry.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Geometry // ------------------------------------------------- // // BASECLASSES: // ReferenceCounting // // PURPOSE: // common base for all geometries // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Geometry( unsigned int Dim) // ------------------------------ // the Dimension must be provided. // // SELECTORS: // 1) unsigned int Dimension() const // --------------------------------- // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef GEOMETRY_H #define GEOMETRY_H ///////////////////////////////////////////////////////// #include ////////////////////////////////////////////////// class Geometry : public ReferenceCounting { public: Geometry (unsigned int Dim); unsigned int Dimension()const; private: unsigned int TheDimension; }; ////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'gr.h' then echo shar: will not over-write existing file "'gr.h'" else cat << \SHAR_EOF > 'gr.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : gr.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Nov 1994 V0.1d(re-ordering of member declarations) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Generalized Rectangle // ----------------------------------------- // // BASECLASSES: // Geometry // // PURPOSE: // implements a generalized rectangle // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) GeneralizedRectangle(Function f, // const Point& A, const Point& B) // --------------------------------------------------- // constructs a generalized rectangle with two points // and a function; f(P) is the length of the // perpendicular to // the boundary from a point P on the line AB. // // SELECTORS: // 1) const Point& A() const // ------------------------- // returns the point A (see constructor) // // 2) const Point& B() const // ------------------------- // returns the point B (see constructor) // // 3) real Boundary(const Point& P)const // ------------------------------------- // evaluates the boundary function at P(see constructor) // // 4) Processor* // DefaultProcessor() const // ----------------------------------- // // MODIFIERS: // None // // OPERATORS: // None // SPECIAL: // None // /////////////////////////////////////////////////////////// #ifndef gr2_H #define gr2_H ////////////////////////////////////////////////// #include #include #include #include ////////////////////////////////////////////////// class GeneralizedRectangle : public Geometry { public: GeneralizedRectangle (Function, const Point&,const Point&); const Point& A() const; const Point& B() const; real Boundary(const Point&) const; private: const Function TheBoundary; Point TheA; Point TheB; }; ////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'gritf.h' then echo shar: will not over-write existing file "'gritf.h'" else cat << \SHAR_EOF > 'gritf.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : gritf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS GENERALIZED_RECTANGLE // ------------------------------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // End-user interface to Generalized Rectangles // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) GENERALIZED_RECTANGLE(Function f, // const Point& A, const Point& B) // --------------------------------------------------- // constructs a generalized rectangle with two points // and a function; f(P) is the length of the // perpendicular to // the boundary from a point P on the line AB. // // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef GRITF_H #define GRITF_H //////////////////////////////////////////// #include #include //////////////////////////////////////////// class GENERALIZED_RECTANGLE : public USERINTERFACE { public: GENERALIZED_RECTANGLE(Function, const Point&,const Point&); }; //////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'gs.h' then echo shar: will not over-write existing file "'gs.h'" else cat << \SHAR_EOF > 'gs.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : gs.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Generalized Sector // ----------------------------------------- // // BASECLASSES: // Geometry // // PURPOSE: // implements a generalized sector // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) GeneralizedSector(Function f, // real alpha, real beta, const Point& Center) // --------------------------------------------------- // the region is bounded by 2 straight lines going // through Center and having an angle of alpha and // beta respectively with the positive X-axis. a // third boundary line is provided by f, which denotes // the distance from the Center to the boundary for // all angles between alpha and beta. // // SELECTORS: // 1) real Alpha() const // ------------------------- // returns alpha (see constructor) // // 2) real Beta() const // ------------------------- // returns beta (see constructor) // // 3) real Boundary(real P)const // ------------------------------------- // evaluates the boundary function at P(see constructor) // // 4) const Point& Center() const // ------------------------------- // MODIFIERS: // None // // OPERATORS: // None // SPECIAL: // None // /////////////////////////////////////////////////////////// #ifndef GS_H #define GS_H ////////////////////////////////////////////////// #include #include ////////////////////////////////////////////////// typedef real (*RealFunction)(real); ////////////////////////////////////////////////// class GeneralizedSector : public Geometry { public: GeneralizedSector (real(*)(real), real,real,const Point&); real Alpha() const; real Beta() const; real Boundary(real) const; RealFunction Boundary() const; const Point& Center() const; private: Point TheCenter; real TheAlpha,TheBeta; real(*TheBoundary)(real); }; ////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'gsitf.h' then echo shar: will not over-write existing file "'gsitf.h'" else cat << \SHAR_EOF > 'gsitf.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : gritf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS GENERALIZED_SECTOR // ------------------------------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // End-user interface to Generalized Rectangles // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) GENERALIZED_SECTOR(real (*F) real, // real Alpha, real Beta, const Point& Center) // --------------------------------------------------- // the region is bounded by 2 straight lines going // through Center and having an angle of alpha and // beta respectively with the positive X-axis. a // third boundary line is provided by f, which denotes // the distance from the Center to the boundary for // all angles between alpha and beta. // // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef GSITF_H #define GSITF_H //////////////////////////////////////////// #include #include //////////////////////////////////////////// class GENERALIZED_SECTOR : public USERINTERFACE { public: GENERALIZED_SECTOR( real(*)(real), real,real,const Point&); }; /////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'gsprc.h' then echo shar: will not over-write existing file "'gsprc.h'" else cat << \SHAR_EOF > 'gsprc.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : gsprc.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS GeneralizedSector_Processor // ------------------------------------------------- // // BASECLASSES: // Processor // // PURPOSE: // transforms the generalized sector into a rectangle // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1)GeneralizedSector_Processor() // ---------------------------- // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Process(Stack&) // ------------------------------------------------- // see Processor<> // // 2) virtual Processor* NewCopy() const=0 // ------------------------------------------------- // // makes a new copy (using the copy constructor) and // returns a pointer to it. ///////////////////////////////////////////////////////// #ifndef GSPRC_H #define GSPRC_H ////////////////////////////////////////////// #include #include ///////////////////////////////////////////// class GeneralizedSector_Processor : public Processor { public: GeneralizedSector_Processor(); void Process(Stack&); Processor* NewCopy() const ; }; ///////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'heap.h' then echo shar: will not over-write existing file "'heap.h'" else cat << \SHAR_EOF > 'heap.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : heap.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Heap // ------------------------ // // BASECLASSES: // Set // // // PURPOSE: // implements a heap. elements can be added and the // largest element can be accessed. // // TEMPLATES: // The type T of the elements is templated. T must // provide a T* NewCopy() as well as relational // operators <,>,<= and >= // // METHODS: // CONSTRUCTORS: // 1) Heap() // --------- // default constructor // SELECTORS: // 1) T* Look() // ------------ // returns a pointer to the largest element. this // element is not removed from the heap. No copy // is made, so modifications of the element are // potentially dangerous. // MODIFIERS: // 1) T* Get() // ----------- // returns a pointer to the largest element. this // element is removed from the heap. // // 2) void Clear() // -------------- // makes the heap empty and destroys all of its // elements // // OPERATORS: // 1) void operator+=(T* R) // ------------------------------ // Puts a pointer to *R into the heap. // // 2) void operator+=(Heap& H) // ------------------------------ // puts all elements of H in the heap. no copies are // made and the state of H is not defined afterwards. // // SPECIAL: // None // NOTE: // Heap uses a class SubHeap in its implementation. // This class should be thought of as being local to // Heap. However the current compiler we used did not // support nested classes within templates. Direct use // of SubHeap is not recommended, since it will // eventually become local to Heap. /////////////////////////////////////////////////////////// #ifndef HEAP_H #define HEAP_H #include ////////////////////////////////////////////// #include #include #include ///////////////////////////////////////////// template class SubHeap : public Set { public: SubHeap(); ~SubHeap(); T* Get(); T* Look() ; T* Swap( T*); T* Bottom() ; void Clear(); void operator +=( T*); Boolean Saturated() const; void Print() const ; int LeftChild(int) const; int RightChild(int) const; int FatherOfChild(int) const; private: #ifdef SOLARIS T* Contents[256]; SubHeap* Children[256]; #else T* Contents[CAPACITY+1]; SubHeap* Children[CAPACITY+1]; #endif int ActiveChild; int LastChild; }; //////////////////////////////////////////// template class Heap : public Set { public: Heap(); ~Heap(); T* Get(); T* Look() ; void Clear(); void operator+= ( T*); void operator+= (Heap&); void Print() const; private: SubHeap TheSubHeap; }; //////////////////////////////////////////// #ifdef TEMPLATEINCLUDE #include #endif #endif SHAR_EOF fi # end of overwriting check if test -f 'integran.h' then echo shar: will not over-write existing file "'integran.h'" else cat << \SHAR_EOF > 'integran.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : integran.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 8 Sep 1994 V0.1a(operator added) // 25 Jan 1996 V0.1f(typedef introduced) // 28 Mar 1996 V0.1h(long instead of int) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Integrand // ----------------------------- // // BASECLASSES: // ReferenceCounting // // PURPOSE: // implements an integrand class. Apart from evaluating // integrands, it takes care of counting the number of // evaluations and it permits the integrand to be // transformed. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Integrand( Function f) // --------------------------------- // constructs the Integrand. The function to be // integrated is f. // // 2) Integrand( const Integrand& I) // --------------------------------- // copy constructor // // 3) Integrand( const Integrand& I, // const Transformation& T) // -------------------------------------- // constructs a new Integrand by applying T to I // // 4) Integrand() // -------------- // constructs an Integrand without the function // to be integrated being known. an evaluation of // this Integrand results in an error. // // SELECTORS: // 1)static long NumberOfEvaluations() // ---------------------------------- // returns the total number of function evaluations // since the program was started. // See also class EvaluationCounter. // // MODIFIERS: // None // OPERATORS: // 1) real operator() (const Point& p) // ------------------------------------- // evaluates the Integrand at Point p. // // SPECIAL: // None /////////////////////////////////////////////////////////// #ifndef INTEGRAN_H #define INTEGRAN_H #include #include #include #include #include #include #include /////////////////////////////////////////////////////// class Integrand : public ReferenceCounting { public: typedef Pointer< Transformation > PointerTransformation; Integrand(); Integrand(Function); Integrand(const Integrand&,Transformation* ); Integrand(const Integrand&); real operator()(const Point&); Boolean operator==(const Integrand&) const; static long NumberOfEvaluations(); private: static long Number; Function TheFunction; VectorStack< PointerTransformation > AppliedTransformations; }; #endif SHAR_EOF fi # end of overwriting check if test -f 'integrat.h' then echo shar: will not over-write existing file "'integrat.h'" else cat << \SHAR_EOF > 'integrat.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : integrat.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 28 Mar 1996 V0.1h(DefaultMaxEval = unsigned long) ///////////////////////////////////////////////////////// // PURPOSE: // Integrate is the algorithm controller of Cubpack++. // 4 different versions are supplied: // // 1)real Integrate( // Function f, // COMPOUND_REGION& TheCollection, // real RequestedAbsolute, // real RequestedRelative, // unsigned long MaxEval, // ); // ----------------------------------------------- // input parameters: // RequestedAbsolute: absolute error request // RequestedRelative: relative error request // MaxEval: bound on the number of function // evaluations. // f:the integrand // return value: // the approximation of the integral is returned // in-out parameters: // TheCollection: collection of regions over which the // integration is to take place. // On return, TheCollection.Integral() // will contain an approximation of the // integral. // // // 2)real Integrate( // COMPOUND_REGION& TheCollection, // real RequestedAbsolute, // real RequestedRelative, // unsigned long MaxEval, // ); // ----------------------------------------------- // input parameters: // RequestedAbsolute: absolute error request // RequestedRelative: relative error request // MaxEval: bound on the number of function // evaluations. // return value: // the approximation of the integral is returned // in-out parameters: // TheCollection: collection of regions over which the // integration is to take place. // Before the call of Integrate() // a local integrand must have been // specified for all members of TheCollection // On return, TheCollection.Integral() // will contain an approximation of the // integral. // // // 3)void Integrate( // Function f, // COMPOUND_REGION& TheCollection, // real& Integral, // real& AbsErr, // real RequestedAbsolute, // real RequestedRelative, // unsigned long MaxEval, // ); // ----------------------------------------------- // input parameters: // RequestedAbsolute: absolute error request // RequestedRelative: relative error request // MaxEval: bound on the number of function // evaluations. // f:the integrand // output parameters: // Integral: approximation of the integral // AbsError: estimate of the error // in-out parameters: // TheCollection: collection of regions over which the // integration is to take place. // On return, TheCollection.Integral() // will contain an approximation of the // integral. // // // 4)void Integrate( // COMPOUND_REGION& TheCollection, // real& Integral, // real& AbsErr, // real RequestedAbsolute, // real RequestedRelative, // unsigned long MaxEval, // ); // ----------------------------------------------- // input parameters: // RequestedAbsolute: absolute error request // RequestedRelative: relative error request // MaxEval: bound on the number of function // evaluations. // output parameters: // Integral: approximation of the integral // AbsError: estimate of the error // in-out parameters: // TheCollection: collection of regions over which the // integration is to take place. // Before the call of Integrate() // a local integrand must have been // specified for all members of TheCollection // On return, TheCollection.Integral() // will contain an approximation of the // integral. /////////////////////////////////////////////////////// #include #ifndef INTEGRAT_H #define INTEGRAT_H const unsigned long DefaultMaxEval = 100000; const real DefaultAbsErrReq = 0.0; const real DefaultRelErrReq = DEFAULT_REL_ERR_REQ; extern real Integrate( Function f, COMPOUND_REGION& R, real AbsErrReq = DefaultAbsErrReq, real RelErrReq = DefaultRelErrReq, unsigned long MaxEval = DefaultMaxEval); extern real Integrate( COMPOUND_REGION& R, real AbsErrReq = DefaultAbsErrReq, real RelErrReq = DefaultRelErrReq, unsigned long MaxEval = DefaultMaxEval); extern void Integrate( Function f, COMPOUND_REGION& R, real& Integral, real& AbsError, Boolean& Success, real AbsErrReq , real RelErrReq , unsigned long MaxEval ); extern void Integrate( COMPOUND_REGION& R, real& Integral, real& AbsError, Boolean& Success, real AbsErrReq , real RelErrReq , unsigned long MaxEval ); #endif SHAR_EOF fi # end of overwriting check if test -f 'invert.h' then echo shar: will not over-write existing file "'invert.h'" else cat << \SHAR_EOF > 'invert.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : invert.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Invert // -------------------------- // // BASECLASSES: // Transformation // // // PURPOSE: // Inverts with respect to a given (arbitrary) circle // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Invert(Circle* ) // -------------------- // // SELECTORS: // None // MODIFIERS: // None // OPERATORS: // None // SPECIAL: // 1) void Transform (real& w, Point& p) // --------------------------------------- // Multiplies w by the Jacobian at p and then replaces p by // the transformed point. // /////////////////////////////////////////////////////////// #ifndef INVERT_H #define INVERT_H //////////////////////////////////////////////////////// #include #include #include /////////////////////////////////////////////////////// class Invert :public Transformation { public: Invert(Circle*); void Transform (real &w, Point& p); private: Pointer C_ptr; real RadiusSq; }; //////////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'outS2.h' then echo shar: will not over-write existing file "'outS2.h'" else cat << \SHAR_EOF > 'outS2.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : outS2.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS OutCircle // ------------------------------------------------- // // BASECLASSES: // Circle // // PURPOSE: // the complement of a circle // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) OutCircle(const Point& C, const Point& B) // -------------------------------------------- // the complement of a circle centred at C and having // B as a point on its boundary. // // 2) OutCircle(const Point& C,real Radius) // ---------------------------------------- // the complement of a circle centred at C and having // Radius as its radius. // // SELECTORS: // 1) Processor* DefaultProcessor() const // ------------------------------------------------- // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef OUTS2_H #define OUTS2_H //////////////////////////////////////////////// #include /////////////////////////////////////////////// class OutCircle : public Circle { public: OutCircle(const Point&,const Point&); OutCircle(const Point&,real); }; //////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'outS2itf.h' then echo shar: will not over-write existing file "'outS2itf.h'" else cat << \SHAR_EOF > 'outS2itf.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : outS2itf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS OUT_CIRCLE // ------------------------------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // end-user interface to OutCircle // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) OUT_CIRCLE(const Point& Center, const Point& B) // ---------------------------------------------- // constructs a OutCircle with Center as its origin // and B a point on the boundary. // // 2) OUT_CIRCLE(const Point& Center, real Radius) // ------------------------------------------- // // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef OUTS2ITF_H #define OUTS2ITF_H //////////////////////////////////////////////// #include #include #include //////////////////////////////////////////////// class OUT_CIRCLE : public USERINTERFACE { public: OUT_CIRCLE(const Point&,const Point&); OUT_CIRCLE(const Point&, real); }; //////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'passbuck.h' then echo shar: will not over-write existing file "'passbuck.h'" else cat << \SHAR_EOF > 'passbuck.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : passbuck.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS PassTheBuck // ------------------------------------------------- // // BASECLASSES: // Processor // // PURPOSE: // a processor for all regions that are immediately // transformed into new ones. // // TEMPLATES: // FROM: the new region, an Atomic<> // TO: the present Geometry // VIA: a Transformation from FROM to TO; it should have // a constructor with a TO* as its only argument. // // METHODS: // CONSTRUCTORS: // 1) PassTheBuck(AtomicRegion*) // --------------------- // The new region must be provided . // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Process(Stack&) // ------------------------------------------------- // see Processor<> // // 2) virtual Processor* NewCopy() const=0 // ------------------------------------------------- // // makes a new copy (using the copy constructor) and // returns a pointer to it. ///////////////////////////////////////////////////////// #ifndef PASSBUCK_H #define PASSBUCK_H /////////////////////////////////////////// #include #include /////////////////////////////////////////// template class PassTheBuck : public Processor { public: PassTheBuck(AtomicRegion*); void Process(Stack&); Processor* NewCopy() const; private: AtomicRegion* AR_ptr; }; ////////////////////////////////////////// #include #ifdef TEMPLATEINCLUDE #include #endif ////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'patchlevel.h' then echo shar: will not over-write existing file "'patchlevel.h'" else cat << \SHAR_EOF > 'patchlevel.h' #define PATCHLEVEL 6 SHAR_EOF fi # end of overwriting check if test -f 'point.h' then echo shar: will not over-write existing file "'point.h'" else cat << \SHAR_EOF > 'point.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : point.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(file name changed) ///////////////////////////////////////////////////////// #ifndef POINT_H #define POINT_H ////////////////////////////////////// #include /////////////////////////////////////// typedef Point_2D Point; ///////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'point2D.h' then echo shar: will not over-write existing file "'point2D.h'" else cat << \SHAR_EOF > 'point2D.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : point2D.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(file name changed) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Point_2D // ------------------------- // // BASECLASSES: // None // // PURPOSE: // Implements 2-dimensional points. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Point_2D() // ---------- // default constructor. // the point must be initialized afterwards with an // assignment. // // 2) Point_2D(const Point_2D&) // ---------------------- // copy constructor // // 3) Point_2D(const real, const real) // ------------------------------------ // constructor. Two Cartesian coordinates are given. // // 4) Point_2D (int l) // --------------------- // constructs a point of dimension l, l must be 2 // // SELECTORS: // 1) real X()const // -------------------- // returns the first component of the Point_2D. // // 2) real Y() const // -------------------- // returns the second component of the Point_2D. // // 3) real R()const // -------------------- // returns the first component of the Point_2D. // not to be confused with Length() // // 4) real Theta() const // ------------------------ // returns the second component of the Point_2D. // not to be confused with Angle() // // 5) real operator[] (int i) const // -------------------------------- // returns the i-th component. 0<=i<=1. // // 6) real Length() const // ---------------------- // returns the length of the vector from (0,0) to point. // // 7) real Angle() const // ----------------------- // returns the angle (in [0, 2pi) ) between the // vector and positive X-axis // // 8) Point_2D Proj(const Point_2D& d) const // ----------------------------------------- // returns the projection of the point on a // line with direction d // // 9) int Size() const // -------------------- // returns the dimension of the point. (=2) // // MODIFIERS: // 1) real& X() // ------------ // returns the first component of the Point_2D. // // 2) real& Y() // ------------ // returns the second component of the Point_2D. // // 3) real& R() // ----------- // returns the first component of the Point_2D. // not to be confused with Length() // // 4) real& Theta() // ---------------- // returns the second component of the Point_2D. // not to be confused with Angle() // // 5) real& operator[] (int i) // ---------------------------- // returns the i-th component. 0<=i<=1. // // OPERATORS: // 1)Point_2D& operator=(const Point_2D&); // -------------------------------- // assignment operator // // 2)Point_2D operator+(const Point_2D&) const; // -------------------------------- // point addition // // 3)Point_2D operator-(const Point_2D&) const; // -------------------------------- // point subtraction // // 4)Point_2D operator-() const; // -------------------------------- // multiplication by -1 // // 5)Point_2D operator*( const real) const; // -------------------------------- // multiplication with scalar // // 6)Point_2D operator/(const real) const; // -------------------------------- // division by scalar // // 7)real operator*(const Point_2D& ) const; // -------------------------------- // dot-product of two point // // 8)Point_2D& operator+=(const Point_2D&); // -------------------------------- // addition and assignment // // 9)Point_2D& operator-=(const Point_2D&); // -------------------------------- // subtraction and assignment // // 10)Point_2D& operator*=(real); // -------------------------------- // scalar multiply and assignment // // 11)Point_2D& operator/=(real); // -------------------------------- // division and assignment // // 12)Boolean operator==(const Point_2D&); // --------------------------------------- // // 13)Boolean operator!=(const Point_2D&); // --------------------------------------- // // SPECIAL: // 1) friend Point_2D operator*(real d,const Point_2D& p) // ---------------------------------------------------- // product of the point with the scalar d // // 2) friend ostream& operator<<(ostream&,const Point_2D&p) // -------------------------------------------------------- // output function /////////////////////////////////////////////////////////// #ifndef _2DPOINT_H #define _2DPOINT_H ///////////////////////////////////////////////////////// // IMPORT FOR INTERFACE ///////////////////////////////////////////////////////// #include #include // introduction class Point_2D; static Point_2D operator*(real,const Point_2D&); static ostream& operator<<(ostream&,const Point_2D& ); ///////////////////////////////////////////////////////// // EXPORT ///////////////////////////////////////////////////////// class Point_2D { friend Point_2D operator*(real,const Point_2D&); friend ostream& operator<<(ostream&,const Point_2D& ); public: Point_2D(const Point_2D&); Point_2D(const real, const real); Point_2D(int n); Point_2D(); ~Point_2D(); Point_2D& operator=(const Point_2D&); Point_2D operator+(const Point_2D&) const; Point_2D operator-(const Point_2D&) const; Point_2D operator-() const; Point_2D operator*( const real) const; Point_2D operator/(const real) const; real operator*(const Point_2D& ) const; Point_2D& operator+=(const Point_2D&); Point_2D& operator-=(const Point_2D&); Point_2D& operator*=(real); Point_2D& operator/=(real); real X() const; real Y() const; real R() const; real Theta() const; real operator[](int i) const; real& X() ; real& Y() ; real& R() ; real& Theta() ; real& operator[](int i) ; real/* in[0,2pi] */ Angle() const; real Length() const; Boolean operator == (const Point_2D&) const; Boolean operator != (const Point_2D&) const; int Size() const; Point_2D Proj(const Point_2D& p)const; private: real x,y; }; ///////////////////////////////////////////// //INLINE DEFINITIONS ///////////////////////////////////////////// #include #include #include ////////////////////////////////////////////////////// inline Point_2D& Point_2D::operator=(const Point_2D& v) { x = v.x; y = v.y; return *this; } /////////////////////////////////////////////// inline Point_2D operator*(real d ,const Point_2D& v) { Point_2D r(v); r.x *= d; r.y *= d; return r; } ///////////////////////////////////////////////// inline real Point_2D::X() const { return x; } //////////////////////////////////////////////////// inline real Point_2D::Y() const { return y; } //////////////////////////////////////////////////// inline real Point_2D::R() const { return x; } //////////////////////////////////////////////////// inline real Point_2D::Theta() const { return y; } ///////////////////////////////////////////////// inline real& Point_2D::X() { return x; } //////////////////////////////////////////////////// inline real& Point_2D::Y() { return y; } //////////////////////////////////////////////////// inline real& Point_2D::R() { return x; } //////////////////////////////////////////////////// inline real& Point_2D::Theta() { return y; } //////////////////////////////////////////////////// inline real Point_2D::Angle() const { real Return; if (x==0) { Return = M_PI-M_PI/2*sign(y); }; if (x<0) { Return = M_PI + atan(y/x); } else { real a=2*M_PI +atan(y/x); Return = (a>=2*M_PI) ? a-2*M_PI : a; }; return Return ; } ///////////////////////////////////////////////////// inline ostream& operator<< (ostream& os,const Point_2D& p) { os<< "Point_2D(" <x) //{ //return y*sqrt((x/y)*(x/y)+1); //} //else //{ //return x*sqrt((y/x)*(y/x)+1); //}; } //////////////////////////////////////////////////// inline real Point_2D::operator *(const Point_2D& v) const { real inprod =x*v.x+y*v.y; return inprod; } //////////////////////////////////////////////////// inline Point_2D& Point_2D::operator +=(const Point_2D& v) { x += v.x; y += v.y; return (*this); } /////////////////////////////////////////////////// inline Point_2D& Point_2D::operator -=(const Point_2D& v) { x -= v.x; y -= v.y; return (*this); } /////////////////////////////////////////////////// inline Point_2D& Point_2D::operator *=(real d) { x *=d; y *=d; return (*this); } /////////////////////////////////////////////////// inline Point_2D& Point_2D::operator /=(real d) { Error(d==0,"Point_2D:division by zero error"); x /= d; y /= d; return (*this); } /////////////////////////////////////////////////// inline real Point_2D::operator[](int i) const { return i ? y : x; } /////////////////////////////////////////////// inline real& Point_2D::operator[](int i) { return i ? y : x; } /////////////////////////////////////////////// inline Boolean Point_2D::operator==(const Point_2D& v) const { int b = (x == v.x)&&(y == v.y); return (Boolean) b; } //////////////////////////////////////////////////// inline Boolean Point_2D::operator!=(const Point_2D& v) const { int b = (x != v.x)||(y != v.y); return (Boolean) b; } //////////////////////////////////////////////////// inline int Point_2D::Size() const { return 2; } ////////////////////////////////////////////////// inline Point_2D Point_2D::Proj(const Point_2D& v) const { Point_2D r(v); r *= (*this) *v; r /= (*this) * (*this); return r; } ////////////////////////////////////////////////// inline Point_2D::Point_2D(int n) { Error(n != 2, "a Point_2D should be two-dimensional"); } ///////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'pointer.h' then echo shar: will not over-write existing file "'pointer.h'" else cat << \SHAR_EOF > 'pointer.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : pointer // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 14 Sep 1994 V0.1c(inlines removed) // 25 Jan 1996 V0.1f(code moved from .c to .h) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Pointer // ------------------------------------------------- // // BASECLASSES: // None // // PURPOSE: // a device for storing pointers, managing reference // counts to the pointed objects and controlling the // deletion of the pointed objects . Once a T* // has been stored as a Pointer you can use it // as if C++ had garbage collection. // some compilers have problems converting // Pointers to normal pointers. // // TEMPLATES: // a Pointer stores a T*. T should be derived from // ReferenceCounting // ///////////////////////////////////////////////////////// #ifndef POINTER_H #define POINTER_H ///////////////////////////////////////////////////// #include ///////////////////////////////////////////////////// template class Pointer { public: Pointer(); Pointer(const Pointer&); Pointer(T* tp); Pointer& operator=(const Pointer& tp); Pointer& operator=(T* tp); Boolean operator==(const Pointer& tp) const; Boolean operator!=(const Pointer& tp) const; T& operator* () const; T* operator->() const; T& operator [](int i) const; operator T*(){return ptr;} ~Pointer(); private: T* ptr; }; ///////////////////////////////////////////////////// #include #ifdef TEMPLATEINCLUDE #include #endif ///////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'polC2.h' then echo shar: will not over-write existing file "'polC2.h'" else cat << \SHAR_EOF > 'polC2.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : polC2.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS PolarRectangle // ------------------------------------------------- // // BASECLASSES: // Geometry // // PURPOSE: // the geometry of a polar rectangle // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) PolarRectangle(const Point& A, const Point& B, // const Point& C) // ------------------------------------------------- // constructs a Polar rectangle. AB should not be // perpendicular to BC. // // 2) PolarRectangle(const Point& O, real R1, real R2, // real Theta1, real Theta2) // --------------------------------------------------- // // SELECTORS: // 1) const Point& Center() const // ------------------------------ // // 2) real InnerRadius() const // --------------------------- // // 3) real OuterRadius() const // --------------------------- // // 4) real SmallAngle() const // -------------------------- // // 5) real BigAngle() const // ------------------------ // // 6)Processor DefaultProcessor() const // ----------------------------------------------------- // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef POLC2_H #define POLC2_H ///////////////////////////////////////// #include #include #include #include ///////////////////////////////////////// class PolarRectangle : public Geometry { public: PolarRectangle( const Point& A, const Point& B, const Point& C); PolarRectangle( const Point& O, real r1, real r2, real theta1,real theta2); const Point& Center() const; real InnerRadius() const; real OuterRadius() const; real SmallAngle () const; real BigAngle () const; private: Point TheCenter; real TheInnerRadius, TheOuterRadius, TheSmallAngle, TheBigAngle; }; ////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'polC2itf.h' then echo shar: will not over-write existing file "'polC2itf.h'" else cat << \SHAR_EOF > 'polC2itf.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : polC2itf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS POLAR_RECTANGLE // ------------------------------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // End-user interface to PolarRectangles // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) POLAR_RECTANGLE(const Point& A, // const Point& B, // const Point& C) // --------------------------------- // constructs a polar rectangle with vertices A,B,C // AB shouldn't be perpendicular to BC // // 2) POLAR_RECTANGLE( const& Point& O, // real r1, real r2, real theta1,real theta2) // ---------------------------------------------- // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef POLC2ITF_H #define POLC2ITF_H ///////////////////////////////////////// #include #include ///////////////////////////////////////// class POLAR_RECTANGLE : public USERINTERFACE { public: POLAR_RECTANGLE(const Point&,const Point&, const Point&); POLAR_RECTANGLE(const Point&,real,real,real,real); }; ///////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'polC2prc.h' then echo shar: will not over-write existing file "'polC2prc.h'" else cat << \SHAR_EOF > 'polC2prc.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : polC2prc.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS PolarRectangle_Processor // ------------------------------------------------- // // BASECLASSES: // Processor // // PURPOSE: // transforms the polar rectangle into a rectangle // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1)PolarRectangle_Processor() // ---------------------------- // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Process(Stack&) // ------------------------------------------------- // see Processor<> // // 2) virtual Processor* NewCopy() const=0 // ------------------------------------------------- // // makes a new copy (using the copy constructor) and // returns a pointer to it. ///////////////////////////////////////////////////////// #ifndef POLC2PRC_H #define POLC2PRC_H ////////////////////////////////////////////// #include #include ///////////////////////////////////////////// class PolarRectangle_Processor: public Processor { public: PolarRectangle_Processor(); void Process(Stack&); Processor* NewCopy() const; }; ///////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'ps.h' then echo shar: will not over-write existing file "'ps.h'" else cat << \SHAR_EOF > 'ps.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : ps.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS ParabolicSegment // ------------------------------------------------- // // BASECLASSES: // Geometry // // PURPOSE: // the geometry of a parabolic segment // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) ParabolicSegment(const Point& A, const Point& B, // const Point& P) // --------------------------------------------------- // the region is bounded by the straight line AB and the // parabolic arc through A and B such that AP and BP are // tangents // // // SELECTORS: // 1) const Point& A() const // -------------------------- // // 1) const Point& B() const // -------------------------- // // 1) const Point& P() const // -------------------------- // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef PS_H #define PS_H ///////////////////////////////////////////////////////// #include #include ///////////////////////////////////////////////////////// class ParabolicSegment : public Geometry { public: ParabolicSegment(const Point&,const Point&,const Point&); const Point& A() const; const Point& B() const; const Point& P() const; private: Point TheA; Point TheB; Point TheP; }; ///////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'psitf.h' then echo shar: will not over-write existing file "'psitf.h'" else cat << \SHAR_EOF > 'psitf.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : psitf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS PARABOLIC_SEGMENT // ------------------------------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // end-user interface to a parabolic segment. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) PARABOLIC_SEGMENT(const Point& A, // const Point& B, // const Point& P) // ------------------------------------- // the region is bounded by the straight line AB // and the parabolic arc through A and B such that // AP and BP are tangents. // // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef PSITF_H #define PSITF_H ///////////////////////////////////////////////////////// #include #include ///////////////////////////////////////////////////////// class PARABOLIC_SEGMENT : public USERINTERFACE { public: PARABOLIC_SEGMENT(const Point& A,const Point& B,const Point& p); }; //////////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'real.h' then echo shar: will not over-write existing file "'real.h'" else cat << \SHAR_EOF > 'real.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : real.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// #ifndef REAL_H #define REAL_H ///////////////////////////////////////////////////////// #include #ifdef FLOAT typedef float real; #define REAL_MAX FLT_MAX #define REAL_MIN FLT_MIN #define REAL_EPSILON FLT_EPSILON #define REAL_MAX_EXP FLT_MAX_EPS #define DEFAULT_REL_ERR_REQ (1.0e-4) #else typedef double real; #define REAL_MAX DBL_MAX #define REAL_MIN DBL_MIN #define REAL_EPSILON DBL_EPSILON #define REAL_MAX_EXP DBL_MAX_EXP #define DEFAULT_REL_ERR_REQ (1.0e-6) #endif ///////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'refcount.h' then echo shar: will not over-write existing file "'refcount.h'" else cat << \SHAR_EOF > 'refcount.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : refcount.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS ReferenceCounting // ------------------------------------------------- // // BASECLASSES: // None // // PURPOSE: // provides a means to count references to an object. // it is to be used preferably together with // class Pointer<>, which automatically calls // Refer() and Unrefer() wherever necessary. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) ReferenceCounting() // ---------------------- // initialises the reference count to zero. // // 2) ReferenceCounting(const ReferenceCounting&) // ---------------------------------------------- // also initialises the count to zero // // SELECTORS: // 1) unsigned int NumberOfReferences() const // ------------------------------------------ // // MODIFIERS: // 1) void Refer() // --------------- // increments the reference count. // // 2) void UnRefer() // ----------------- // decrements the reference count // // OPERATORS: // 1) ReferenceCounting& operator= // (const ReferenceCounting&) // ------------------------------------------------- // resets the reference count. // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef REFCOUNT_H #define REFCOUNT_H /////////////////////////////////////////////////// class ReferenceCounting { public: ReferenceCounting(); ReferenceCounting(const ReferenceCounting&); void Refer(); void UnRefer(); ReferenceCounting& operator=(const ReferenceCounting&); unsigned int NumberOfReferences()const; private: unsigned int numref; }; //////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'regcoll.h' then echo shar: will not over-write existing file "'regcoll.h'" else cat << \SHAR_EOF > 'regcoll.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : regcoll.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Jan 1996 V0.1f(typedef introduced) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS REGION_COLLECTION // ------------------------------------------------- // // BASECLASSES: // COMPOUND_REGION // // PURPOSE: // groups regions and their eventual offspring. applies // the global adaptive algorithm. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) REGION_COLLECTION() // ---------------------- // // 2) REGION_COLLECTION(const REGION_COLLECTION&) // ---------------------------------------------- // // SELECTORS: // None // // MODIFIERS: // 1) LocalIntegrand(Integrand* I) // ------------------------------ // sets the local integrand of all members to I // only to be called before Process(). // // 2) LocalIntegrand(Function F) // ------------------------------ // sets the local integrand of all members to F // only to be called before Process(). // // OPERATORS: // 1) REGION_COLLECTION operator+(const COMPOUND_REGION&) // ---------------------------------------------------- // // 2) REGION_COLLECTION& operator+=(const COMPOUND_REGION&) // ---------------------------------------------------- // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef REGCOLL_H #define REGCOLL_H ///////////////////////////////////////////// #include #include #include #include #include #include ///////////////////////////////////////////// class REGION_COLLECTION : public COMPOUND_REGION { public: typedef Stack < COMPOUND_REGION> StackCOMPOUND_REGION; void LocalIntegrand(Integrand*); void LocalIntegrand(Function); REGION_COLLECTION& operator+=(const COMPOUND_REGION&) ; REGION_COLLECTION operator+(const COMPOUND_REGION&) ; REGION_COLLECTION(); REGION_COLLECTION(const REGION_COLLECTION&); protected: Pointer < StackCOMPOUND_REGION > SCR_ptr; void Preprocess(); void Improve(); real MaxAtomicError()const; COMPOUND_REGION* NewCopy()const; }; /////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'reginfo.h' then echo shar: will not over-write existing file "'reginfo.h'" else cat << \SHAR_EOF > 'reginfo.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : reginfo.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS RegionInfo // ------------------------------------------------- // // BASECLASSES: // ReferenceCounting // // PURPOSE: // to store integral and error of a specific region // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) RegionInfo() // --------------- // after construction Integral() and AbsoluteError() // will both return zero // // SELECTORS: // 1) real Integral() const // ------------------------ // // 2) real AbsoluteError() const // ----------------------------- // 3) Boolean Hopeless() const // --------------------------- // // MODIFIERS: // 1) real& Integral() // -------------------- // // 2) real& AbsoluteError() // ------------------------ // // 3) Boolean& Hopeless() // ---------------------- // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef REGINFO_H #define REGINFO_H ////////////////////////////////////////// #include #include #include ////////////////////////////////////////// class RegionInfo : public ReferenceCounting { public : RegionInfo(); real Integral()const; real& Integral(); real AbsoluteError()const; real& AbsoluteError(); Boolean Hopeless() const; Boolean& Hopeless() ; private: real TheIntegral; real TheAbsoluteError; Boolean IsHopeless; }; ///////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'region.h' then echo shar: will not over-write existing file "'region.h'" else cat << \SHAR_EOF > 'region.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : region.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Region // ------------------------------------------------- // // BASECLASSES: // None // // PURPOSE: // base class for all regions, providing storage for // integral and error approximations // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Region() // ----------- // // SELECTORS: // 1) real Integral() const // ----------------------- // // 2) real AbsoluteError() const // ----------------------------- // // 3) Boolean Hopeless() const // --------------------------- // // MODIFIERS: // None // // OPERATORS: // 1) Boolean operator<(const Region&)const // ---------------------------------------- // compares the absolute errors // // 2) Boolean operator>(const Region&)const // ---------------------------------------- // compares the absolute errors // // 3) Boolean operator<=(const Region&)const // ---------------------------------------- // compares the absolute errors // // 4) Boolean operator>=(const Region&)const // ---------------------------------------- // compares the absolute errors // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef REGION_H #define REGION_H ////////////////////////////////////////////////// #include #include #include #include ///////////////////////////////////////////////// class Region { public: Region(); real Integral() const; real AbsoluteError() const ; Boolean Hopeless()const; Boolean operator<(const Region&) const; Boolean operator<=(const Region&) const; Boolean operator>(const Region&) const; Boolean operator>=(const Region&) const; protected : RegionInfo& LocalInfo(); private: Pointer RI_ptr; }; /////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'rule.h' then echo shar: will not over-write existing file "'rule.h'" else cat << \SHAR_EOF > 'rule.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : rule.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Rule // ------------------------ // // BASECLASSES: // ReferenceCounting // // // PURPOSE: // provides a pure virtual base class as a common // interface to all rules. // // TEMPLATES: // T: type of region on which the rule has to be // applied. T should be derived from // class Region . // // METHODS: // CONSTRUCTORS: // None // SELECTORS: // 1) int Degree() const // --------------------- // returns the degree of the formula // // 2) int NumberOfPoints() const // ------------------------------------------ // returns the number of points the rule uses. // this might depend on Dimension // // MODIFIERS: // None // OPERATORS: // None // SPECIAL: // 1) Apply(Integrand& I,T& H,real& Result,real& // Error) // ------------------------------------------------- // Input parameters: // I: the integrand // H: Region to be integrated. H.Dimension() // should be 2. // Output parameters: // Result: approximation to the integral // Error: absolute error estimation // // 2) ApplyWithDiffs(Integrand& I,T& H,real& Result,real& // Error,Vector& D) // ------------------------------------------------- // Input parameters: // I: the integrand // H: Region to be integrated. H.Dimension() // should be 2. // Output parameters: // Result: approximation to the integral // Error: absolute error estimation // D: order of indices regarding a higher order difference. /////////////////////////////////////////////////////////// #ifndef RULE_H #define RULE_H ///////////////////////////////////////// #include #include #include ////////////////////////////////////////// template class Rule : public ReferenceCounting { public: Rule(); virtual void ApplyWithDiffs(Integrand&,GEOMETRY&,real&,real&,Vector&) ; virtual void Apply(Integrand&,GEOMETRY&,real&,real&); virtual int Degree() const =0; virtual int NumberOfPoints () const =0; virtual ~Rule(); }; ////////////////////////////////////////// #include #ifdef TEMPLATEINCLUDE #include #endif ////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'regproc.h' then echo shar: will not over-write existing file "'regproc.h'" else cat << \SHAR_EOF > 'regproc.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : regproc.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Processor // ------------------------------------------------- // // BASECLASSES: // ReferenceCounting // // PURPOSE: // abstract base class for region processors. these // either compute an integral or an error over a given // GEOMETRY or convert it to another GEOMETRY. // the processor has access to the GEOMETRY through // a pointer to an atomic region. // // TEMPLATES: // the GEOMETRY that the Processor is meant to operate // on must be specified as a template argument. // // METHODS: // CONSTRUCTORS: // 1) Processor() // -------------- // // SELECTORS: // None // // MODIFIERS: // 1) void LocalAtomic(Atomic* G) // ------------------------------------------- // specifies the AtomicRegion to process // this should happen before the first call of Process() // // // OPERATORS: // None // // SPECIAL: // 1) virtual void Process( Stack& Offspring) // ----------------------------------------------------- // after a call of Process() one of the following // statements will be true: // I) Offspring is empty. // The processor will have computed new // values for integral and error. // They will be stored in the RegionInfo // of the atomic region, possibly along // with some other information like // hopelessness. // II)Offspring is non-empty. // The region has produced // offspring and can be deleted. // // 2) virtual Processor* NewCopy() const=0 // ------------------------------------------------- // // makes a new copy (using the copy constructor) and // returns a pointer to it. ///////////////////////////////////////////////////////// #ifndef REGPROC_H #define REGPROC_H //////////////////////////////////////////// #include #include #include #include #include #include ///////////////////////////////////////////// template class Atomic; template class Processor: public ReferenceCounting { public: Processor(); void LocalAtomic(Atomic* ); virtual Processor* NewCopy() const=0; virtual void Process( Stack& Offspring)=0; virtual ~Processor(); protected: Integrand& LocalIntegrand() const; GEOMETRY& Geometry() const; real& Integral(); real& AbsoluteError(); Atomic& LocalAtomic() const; RegionInfo& LocalRegionInfo() const; private: Atomic* A_ptr; }; ///////////////////////////////////////////// #include #ifdef TEMPLATEINCLUDE #include #endif ///////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 's_adapt.h' then echo shar: will not over-write existing file "'s_adapt.h'" else cat << \SHAR_EOF > 's_adapt.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : s_adapt.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 25 Nov 1994 V0.1d(re-ordering of member declarations) // 25 Jan 1996 V0.1f(typedef introduced, code from .c to .h) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS SimpleAdaptive // ------------------------------------------------- // // BASECLASSES: // Processor // // PURPOSE: // Simple Adaptive means applying a rule once // (during the first call of Process()) // and then cutting the region into subregions with // the same shape as the original (during the second // call of Process()). // // TEMPLATES: // the Geometry T to work with // // METHODS: // CONSTRUCTORS: // 1) SimpleAdaptive( Rule* , // SameShapeDivisor* ) // ------------------------------------------------- // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Process(Stack&) // ------------------------------------------------- // see Processor // // 2) virtual Processor* NewCopy() const=0 // ------------------------------------------------- // // makes a new copy (using the copy constructor) and // returns a pointer to it. ///////////////////////////////////////////////////////// #ifndef S_ADAPT_H #define S_ADAPT_H /////////////////////////////////////////// #include #include #include /////////////////////////////////////////// template class SimpleAdaptive : public Processor { public: typedef Rule RuleGEOMETRY; typedef SameShapeDivisor SameShapeDivisorGEOMETRY; SimpleAdaptive(const Pointer &R, const Pointer& D) :Processor(), TimesCalled(0), Diffs(2), TheRule(R), TheDivisor(D) { } SimpleAdaptive(Rule*, SameShapeDivisor*); void Process( Stack& Offspring); Processor* NewCopy() const; protected: SimpleAdaptive* Descendant() const; unsigned int TimesCalled; Vector Diffs; Pointer TheRule; Pointer TheDivisor; }; ///////////////////////////////////////////////// #include #ifdef TEMPLATEINCLUDE #include #endif ///////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'samediv.h' then echo shar: will not over-write existing file "'samediv.h'" else cat << \SHAR_EOF > 'samediv.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : samediv.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS SameShapeDivisor // ------------------------------------------------- // // BASECLASSES: // Divisor // // PURPOSE: // a divisor that produces parts of the same shape as // the original // // TEMPLATES: // T, the Geometry to be divided. // // METHODS: // CONSTRUCTORS: // 1) SameShapeDivisor() // --------------------- // // SELECTORS: // 1) virtual int NumberOfParts() const // ------------------------------- // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) virtual void Apply( const T& , // Stack& Offspring) // -------------------------------------------------- // performs the division // ///////////////////////////////////////////////////////// #ifndef SAMEDIV_H #define SAMEDIV_H //////////////////////////////////////////// #include #include #include //////////////////////////////////////////// template class SameShapeDivisor : public Divisor { public: SameShapeDivisor(); virtual int NumberOfParts() const =0; virtual void Apply( const GEOMETRY&,Stack&,const Vector&)=0; virtual ~SameShapeDivisor(); }; ///////////////////////////////////////////// #include #ifdef TEMPLATEINCLUDE #include #endif ///////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'semistrp.h' then echo shar: will not over-write existing file "'semistrp.h'" else cat << \SHAR_EOF > 'semistrp.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : semistrp.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS SemiInfiniteStrip // ----------------------------------------- // // BASECLASSES: // Geometry // // PURPOSE: // implements a semi-infinite strip // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) SemiInfiniteStrip( // const Point& A, const Point& B) // --------------------------------------------------- // the region lies to the left of AB // // SELECTORS: // 1) const Point& A() const // ------------------------- // returns the point A (see constructor) // // 2) const Point& B() const // ------------------------- // returns the point B (see constructor) // // MODIFIERS: // None // // OPERATORS: // None // SPECIAL: // None // /////////////////////////////////////////////////////////// #ifndef SEMISTRP_H #define SEMISTRP_H ////////////////////////////////////////////////// #include #include ////////////////////////////////////////////////// class SemiInfiniteStrip : public Geometry { public: SemiInfiniteStrip ( const Point&,const Point&); const Point& A() const; const Point& B() const; private: Point TheA; Point TheB; }; ////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'semstitf.h' then echo shar: will not over-write existing file "'semstitf.h'" else cat << \SHAR_EOF > 'semstitf.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : semstitf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS SEMI_INFINITE_STRIP // ------------------------------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // End-user interface to semi-infinite strips // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) SEMI_INFINITE_STRIP( // const Point& A, const Point& B) // --------------------------------------------------- // the region will be to the left of AB. // // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef SEMSTITF_H #define SEMSTITF_H //////////////////////////////////////////// #include #include //////////////////////////////////////////// class SEMI_INFINITE_STRIP : public USERINTERFACE { public: SEMI_INFINITE_STRIP(const Point&,const Point&); }; //////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'set.h' then echo shar: will not over-write existing file "'set.h'" else cat << \SHAR_EOF > 'set.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : set.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Set // ----------------------- // // BASECLASSES: // ReferenceCounting // // // PURPOSE: // provides a pure virtual base class for all // collection classes. // // TEMPLATES: // the type T of the Set elements is templated. it // should have a method T* NewCopy () defined. // // METHODS: // CONSTRUCTORS: // 1) Set() // -------- // Default constructor // // SELECTORS: // 1) virtual T* Look() =0 // ------------------------ // returns a pointer to an element of the Set. // // 2) int NumberOfElements() const // -------------------------------- // returns the number of elements in the set. // // MODIFIERS: // 1) virtual T* Get()=0 // ----------------------- // returns a pointer to an element of the Set and // removes them. // // 2) virtual void Clear()=0 // --------------------------- // removes all of the elements // // OPERATORS: // 1) virtual void operator+=(T*) =0 // ------------------------------------------- // adds a reference to an element to the set // // SPECIAL: // None /////////////////////////////////////////////////////////// #ifndef SET_H #define SET_H #include #include #include template class Set: public ReferenceCounting { public: Set(); virtual ~Set(); virtual void Clear()=0; virtual T* Get () =0; virtual T* Look() =0; virtual void operator+=( T*) =0; unsigned int Size() const; Boolean Empty() const; protected: int Number; }; #ifdef TEMPLATEINCLUDE #include #endif #endif SHAR_EOF fi # end of overwriting check if test -f 'stack.h' then echo shar: will not over-write existing file "'stack.h'" else cat << \SHAR_EOF > 'stack.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : stack.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Stack // ------------------------- // // BASECLASSES: // ReferenceCounting // // PURPOSE: // implements a stack. an iterator over all the elements // is provided. // // TEMPLATES: // The type T of the elements to be stacked is // templated. T should have T* NewCopy() defined. // // // METHODS: // CONSTRUCTORS: // 1) Stack() // ----------- // default constructor // // SELECTORS: // 1) T* Top() const // ----------------- // returns a pointer to the top-element of the stack. // this element is not removed so modifications of it // are potentially dangerous. // not to be called when Size() == 0 // // 2) Boolean Empty() const // -------------------------- // // 3) unsigned int Size() const // ------------------------------ // // 4) Boolean IteratorAtEnd() const // --------------------------------- // returns True if the iterator has passed the // bottom element of the Stack or if Size() == 0 // // MODIFIERS: // 1) T* Pop() // ----------- // gets the top-element of the stack. it is removed. // not to be called when Size() == 0 // // 2) void MakeEmpty() // --------------- // Empties the Stack // // 3) IteratorReset() // ------------------ // a subsequent call of IteratorNext() will return the // top of the stack, unless the stack is empty. // // 4) T* IteratorNext() // -------------------- // advances the iterator and returns the next element. // not to be called when IteratorAtEnd() // // 5) void Push(T* t) // ---------------------------- // pushes a pointer to *t on the stack // // 6) void Merge(Stack& S) // ------------------------------- // pushes all elements of S on the Stack. The order in // which they are pushed is not defined. The state of // S afterwards is not defined. // // OPERATORS: // None // SPECIAL: // None /////////////////////////////////////////////////////////// #ifndef SELEMENT #define SELEMENT template< class T> struct SElement { SElement* Next; T* Contents; }; #endif /////////////////////////////////////////////////// #ifndef STACK_H #define STACK_H /////////////////////////////////////////////////// #include #include #include /////////////////////////////////////////////////// template class Stack :public ReferenceCounting { public: Stack(); ~Stack(); void MakeEmpty(); Boolean Empty () const; void Push (T*); T* Pop(); T* Top()const; void Merge (Stack& Source); void IteratorReset(); Boolean IteratorAtEnd() const; T* IteratorNext(); unsigned int Size() const; private: SElement* TheTop; SElement* Current; unsigned int Number; }; ///////////////////////////////////////////////// #include #ifdef TEMPLATEINCLUDE #include #endif #endif SHAR_EOF fi # end of overwriting check if test -f 'strip.h' then echo shar: will not over-write existing file "'strip.h'" else cat << \SHAR_EOF > 'strip.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : strip.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS InfiniteStrip Rectangle // ----------------------------------------- // // BASECLASSES: // Geometry // // PURPOSE: // implements an infinite strip // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) GeneralizedRectangle( // const Point& A, const Point& B) // --------------------------------------------------- // the line segment AB is the diameter of the strip // // SELECTORS: // 1) const Point& A() const // ------------------------- // returns the point A (see constructor) // // 2) const Point& B() const // ------------------------- // returns the point B (see constructor) // // MODIFIERS: // None // // OPERATORS: // None // SPECIAL: // None // /////////////////////////////////////////////////////////// #ifndef STRIP_H #define STRIP_H ////////////////////////////////////////////////// #include #include ////////////////////////////////////////////////// class InfiniteStrip : public Geometry { public: InfiniteStrip ( const Point&,const Point&); const Point& A() const; const Point& B() const; private: Point TheA; Point TheB; }; ////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'stripitf.h' then echo shar: will not over-write existing file "'stripitf.h'" else cat << \SHAR_EOF > 'stripitf.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : stripitf.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS INFINITE_STRIP // ------------------------------------------------- // // BASECLASSES: // USERINTERFACE // // PURPOSE: // End user interface to infinite strips // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) INFINITE_STRIP( // const Point& A, const Point& B) // --------------------------------------------------- // AB will be the diameter of the strip // // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef STRIPITF_H #define STRIPITF_H //////////////////////////////////////////// #include #include //////////////////////////////////////////// class INFINITE_STRIP : public USERINTERFACE { public: INFINITE_STRIP(const Point&,const Point&); }; //////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'sttosmst.h' then echo shar: will not over-write existing file "'sttosmst.h'" else cat << \SHAR_EOF > 'sttosmst.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : sttosmst.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS E2toIS // ------------------------------------------------- // // BASECLASSES: // Transformation // // PURPOSE: // transformation from strip to semistrip // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) IStoSIS(SemiInfiniteStrip*) // ------------ // The target region has to be supplied // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // None // // SPECIAL: // 1) void Transform(real & w, Point & p) // -------------------------------------- // multiplies w by the Jacobian at p and then // replaces p by the transformed point // ///////////////////////////////////////////////////////// #ifndef STTOSMST_H #define STTOSMST_H ///////////////////////////////////////////////////////// #include #include #include #include /////////////////////////////////////////////////// class IStoSIS : public Transformation { public: IStoSIS( SemiInfiniteStrip*); void Transform(real& w, Point& p); private: Pointer SIS_ptr; }; ////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'templist.h' then echo shar: will not over-write existing file "'templist.h'" else cat << \SHAR_EOF > 'templist.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : templist.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // PURPOSE: // to enumerate the compilers that need inclusion of // template implementations ///////////////////////////////////////////////////////// #ifndef TEMPLIST_H #define TEMPLIST_H #ifdef __GNUG__ #define TEMPLATEINCLUDE #endif #ifdef __TCPLUSPLUS__ #define TEMPLATEINCLUDE #endif #ifdef __DECCXX #define TEMPLATEINCLUDE #endif #endif SHAR_EOF fi # end of overwriting check if test -f 'tools.h' then echo shar: will not over-write existing file "'tools.h'" else cat << \SHAR_EOF > 'tools.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : tools.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // PURPOSE : this file contains some simple tools ////////////////////////////////////////////////// #ifndef TOOLS_H #define TOOLS_H #include /////////////////////////////////////////////////////// inline real min (real a,real b) { return (ab) ? a : b ; } inline real sign (real x) { return (x>0) ? 1.0 : -1.0; } /////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'translat.h' then echo shar: will not over-write existing file "'translat.h'" else cat << \SHAR_EOF > 'translat.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : translat.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Translation // ------------------------------- // // BASECLASSES: // Transformation // // // PURPOSE: // implements translations. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Translation(const Point& Offset) // ----------------------------------- // constructs the translation by specifying the // Offset that has to be added by T() // // SELECTORS: // None // MODIFIERS: // None // OPERATORS: // None // SPECIAL: // 1) void Transform (real& w, Point& p) // --------------------------------------- // Leaves w unchanged and replaces p by p+Offset. // /////////////////////////////////////////////////////////// #ifndef TRANSLAT_H #define TRANSLAT_H //////////////////////////////////////////////////////// #include #include /////////////////////////////////////////////////////// class Translation :public Transformation { public: Translation( const Point& Offset); //Translation::T(p) ADDS Offset to p void Transform(real& w, Point& p); private: Point TheOffset; }; //////////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'trnsfrm.h' then echo shar: will not over-write existing file "'trnsfrm.h'" else cat << \SHAR_EOF > 'trnsfrm.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : trnsfrm.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Transformation // ---------------------------------- // // BASECLASSES: // ReferenceCounting // // // PURPOSE: // a pure virtual base class providing a common interface // to all transformations. // // TEMPLATES: // None // // METHODS: // CONSTRUCTORS: // 1) Transformation() // -------------------- // // SELECTORS: // None // MODIFIERS: // None // OPERATORS: // None // SPECIAL: // 1) virtual void Transform (real& w, Point& p) // ----------------------------------------------- // Multiplies w by the Jacobian at p and then replaces p by // the transformed point. // /////////////////////////////////////////////////////////// #ifndef TRNSFRM_H #define TRNSFRM_H #include #include class Transformation: public ReferenceCounting { public: Transformation(); virtual void Transform (real& w, Point& p) =0; virtual ~Transformation(); }; #endif SHAR_EOF fi # end of overwriting check if test -f 'userint.h' then echo shar: will not over-write existing file "'userint.h'" else cat << \SHAR_EOF > 'userint.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : userint.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) // 8 Sep 1994 V0.1a(operator added) // 25 Jan 1996 V0.1f(typedef introduced, code from .c to .h) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS USERINTERFACE // ------------------------------------------------- // // BASECLASSES: // COMPOUND_REGION // // PURPOSE: // base class for end-user interfaces to geometries // // TEMPLATES: // a specific GEOMETRY (derived from Geometry) // must be provided // // METHODS: // CONSTRUCTORS: // 1) USERINTERFACE() // ------------------ // // 2) USERINTERFACE(const USERINTERFACE&) // ------------------------------------------------ // // SELECTORS: // None // // MODIFIERS: // 1) void Use(Processor* P) // ----------------------------------- // forces P to be used for Process()ing. // // 2) LocalIntegrand(Integrand* I) // ------------------------------ // sets the local integrand of all members to I // only to be called before Process(). // // 3) LocalIntegrand(Function F) // ------------------------------ // sets the local integrand of all members to F // only to be called before Process(). // // // OPERATORS: // 1) REGION_COLLECTION operator+(const COMPOUND_REGION&) // ----------------------------------------------------- // // SPECIAL: // 1)operator AtomicRegion*() // --------------------------- // conversion to an AtomicRegion. The USERINTERFACE // can't be used after a call of this operator. // ///////////////////////////////////////////////////////// #ifndef USERINT_H #define USERINT_H ///////////////////////////////////////////////// #include #include #include #include #include #include #include #include ///////////////////////////////////////////////// template class USERINTERFACE : public COMPOUND_REGION { public: typedef Stack StackAtomicRegion; typedef Heap HeapAtomicRegion; USERINTERFACE(); USERINTERFACE(const USERINTERFACE&); ~USERINTERFACE(); void Use( Processor*); REGION_COLLECTION operator+(const COMPOUND_REGION&); void LocalIntegrand(Integrand*); void LocalIntegrand(Function); operator AtomicRegion* () { Error (SAR_ptr->Empty(), "converting empty compound region to atomic."); return SAR_ptr->Pop(); } protected: Pointer< StackAtomicRegion> HopelessAR_ptr; Pointer< StackAtomicRegion> SAR_ptr; Pointer< HeapAtomicRegion > HAR_ptr; Pointer< Integrand > Int_ptr; void StoreAtomic(GEOMETRY*,Processor*); //void StoreAtomic(GEOMETRY*); void Preprocess(); void Improve(); real MaxAtomicError() const; COMPOUND_REGION* NewCopy() const; }; ////////////////////////////////////////////////// #include #ifdef TEMPLATEINCLUDE #include #endif /////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'vector.h' then echo shar: will not over-write existing file "'vector.h'" else cat << \SHAR_EOF > 'vector.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : vector.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS Vector // -------------------------- // // BASECLASSES: // None // // // PURPOSE: // implements vectors of arbitrary length. // // TEMPLATES: // The type T of the elements is templated. T can be any // class with a copy constructor, a default constructor // and an assignment operator. // // METHODS: // CONSTRUCTORS: // 1) Vector() // ------------- // default constructor. the length is not defined so // the Vector must be initialized afterwards by an // assignment operation. use before this assignment // will result in an error. // // 2) Vector(const Vector&) // ----------------------- // copy constructor. // // 3) Vector(unsigned int n) // --------------------------- // constructs a vector of length n; // // 4) Vector(unsigned int n,T* p) // ------------------- // assumes p is pointing to a classical C array and // copies its elements. if the array has not the // expected dimension n, an error might occur . // // // SELECTORS: // 1) unsigned int Size() const // ---------------- // returns the length of a vector. // // MODIFIERS: // None // OPERATORS: // 1) Vector& operator=(const Vector&) // ----------------------------------------- // assignment operator. Sizes must be equal, // unless the lefthandside hasn't got // a Size. // // 2) Boolean operator ==(const Vector&) // ------------------------------------- // equality operator. Sizes must be equal // // 3) Boolean operator !=(const Vector&) // ------------------------------------- // !(==). Sizes must be equal // // 4) T& operator[](unsigned int) const // --------------------------- // selects the ith component. 0<=i ///////////////////////////////////////////////// template class Vector { public: Vector(); Vector(unsigned int length); Vector(unsigned int,T*); Vector(const Vector&); T& operator[](unsigned int) ; const T& operator[](unsigned int) const; Vector& operator=(const Vector&); Boolean operator == (const Vector&) const; Boolean operator != (const Vector&) const; ~Vector(); unsigned int Size() const; protected: unsigned int TheSize; T* Contents; }; /////////////////////////////////////////////////// #include #ifdef TEMPLATEINCLUDE #include #endif #endif SHAR_EOF fi # end of overwriting check if test -f 'vstack.h' then echo shar: will not over-write existing file "'vstack.h'" else cat << \SHAR_EOF > 'vstack.h' ///////////////////////////////////////////////////////// // // // Cubpack++ // // // // A Package For Automatic Cubature // // // // Authors : Ronald Cools // // Dirk Laurie // // Luc Pluym // // // ///////////////////////////////////////////////////////// ///////////////////////////////////////////////////////// // File : vstack.h // History: // (date) (version) // 19 Aug 1994 V0.1 (first limited distribution) ///////////////////////////////////////////////////////// // DEFINITION OF CLASS VectorStack // ------------------------------------------------- // // BASECLASSES: // Vector // // PURPOSE: // implements a stack of elements T, with individual // access possible. // // TEMPLATES: // The type T of the elements to be stacked is // templated. They must have a copy constructor // // METHODS: // CONSTRUCTORS: // 1) VectorStack() // ----------------- // creates an empty VectorStack // // 2) VectorStack(const VectorStack& V) // ------------------------------------- // // SELECTORS: // None // // MODIFIERS: // None // // OPERATORS: // 1) void operator+=(const T& t) ; // ------------------------------ // pushes a copy of t on top of the stack. // // SPECIAL: // None // ///////////////////////////////////////////////////////// #ifndef VSTACK_H #define VSTACK_H ///////////////////////////////////////////////// #include #include ///////////////////////////////////////////////// template class VectorStack: public Vector { public: VectorStack(); VectorStack(const VectorStack&); VectorStack& operator=(const VectorStack&); void operator+=(const T&); }; /////////////////////////////////////////////////// #include #ifdef TEMPLATEINCLUDE #include #endif /////////////////////////////////////////////////////// #endif SHAR_EOF fi # end of overwriting check if test -f 'makefile' then echo shar: will not over-write existing file "'makefile'" else cat << \SHAR_EOF > 'makefile' CC = gcc CFLAGS = -x c++ -I. # COPTIONS = -DEGTRUSAGE COPTIONS = libdir = -L. libs = -lcubpack -lm -lg++ MYTESTPROG = main.o .c.o: ; $(CC) $(CFLAGS) -c $*.c chrono.o: chrono.c $(CC) $(CFLAGS) $(COPTIONS) -c chrono.c OBJS = \ point2D.o \ C2.o \ C2dv2.o \ C2dv4.o \ C2interf.o \ C2prc.o \ C2rule13.o \ C2toS2.o \ C2togr.o \ E2tostrp.o \ E2.o \ E2adapt.o \ E2interf.o \ E2sec.o \ E2secitf.o \ E2secprc.o \ S2.o \ S2adapt.o \ S2interf.o \ S2rule13.o \ T2.o \ T2dv4.o \ T2interf.o \ T2rule13.o \ T2tops.o \ atomreg.o \ boolean.o \ chrono.o \ compreg.o \ eval_ctr.o \ geometry.o \ gr.o \ gritf.o \ gs.o \ gsitf.o \ gsprc.o \ integran.o \ integrat.o \ invert.o \ outS2.o \ outS2itf.o \ polC2.o \ polC2itf.o \ polC2prc.o \ ps.o \ psitf.o \ refcount.o \ regcoll.o \ reginfo.o \ region.o \ semstitf.o \ semistrp.o \ sttosmst.o \ strip.o \ stripitf.o \ translat.o \ trnsfrm.o all:: libcubpack.a libcubpack.a: $(OBJS) ar ru libcubpack.a $(OBJS) ranlib libcubpack.a tst: $(MYTESTPROG) $(CC) $(MYTESTPROG) $(libdir) $(libs) -o tst clean: /bin/rm -f *.o tst core SHAR_EOF fi # end of overwriting check if test -f 'main.c' then echo shar: will not over-write existing file "'main.c'" else cat << \SHAR_EOF > 'main.c' // Example 28 from ditamo #include #include real f(const Point& p) { real y=p.Y(); return 1/(y*y); } int main () { Point A(2,-1), B(1,-1); SEMI_INFINITE_STRIP langelat(A,B); real Integral_est, Error_est; Boolean Success; EvaluationCounter TikTak; TikTak.Start(); cout.setf(ios::scientific,ios::floatfield); do { Integrate(f,langelat,Integral_est,Error_est,Success,0,0.5e-7,10000); cout <<"The integral is " << Integral_est; cout <<" with estimated absolute error " << Error_est << endl; cout <<"The real error is " << Integral_est - 1 < 'userman.ps' %!PS-Adobe-2.0 %%Creator: dvips 5.58 Copyright 1986, 1994 Radical Eye Software %%Title: userman.dvi 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1746 y(.)518 1744 y(.)518 1743 y(.)517 1741 y(.)516 1740 y(.)515 1739 y(.)514 1737 y(.)513 1736 y(.)512 1735 y(.)511 1733 y(.)510 1732 y(.)509 1731 y(.)508 1729 y(.)507 1728 y(.)506 1727 y(.)505 1725 y(.)504 1724 y(.)503 1723 y(.)502 1721 y(.)501 1720 y(.)500 1719 y(.)499 1717 y(.)498 1716 y(.)497 1715 y(.)496 1713 y(.)495 1712 y(.)494 1711 y(.)493 1710 y(.)p 291 1968 300 3 v 262 1902 a(.)264 1901 y(.)265 1900 y(.)266 1899 y(.)267 1898 y(.)269 1897 y(.)270 1895 y(.)271 1894 y(.)273 1893 y(.)274 1892 y(.)275 1891 y(.)276 1890 y(.)278 1889 y(.)279 1888 y(.)280 1887 y(.)281 1886 y(.)283 1885 y(.)284 1884 y(.)285 1883 y(.)287 1882 y(.)288 1880 y(.)289 1879 y(.)290 1878 y(.)292 1877 y(.)293 1876 y(.)294 1875 y(.)296 1874 y(.)297 1873 y(.)298 1872 y(.)299 1871 y(.)301 1870 y(.)302 1869 y(.)303 1868 y(.)304 1867 y(.)306 1865 y(.)307 1864 y(.)308 1863 y(.)310 1862 y(.)311 1861 y(.)312 1860 y(.)313 1859 y(.)315 1858 y(.)316 1857 y(.)317 1856 y(.)318 1855 y(.)320 1854 y(.)321 1853 y(.)322 1852 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y(\014)1659 1798 y(\032)p Ft(\()p Fm(\022)q Ft(\))1434 2004 y Fm(\022)272 1067 y Ft(T)l(riangle)400 b(P)o(arallelogram)344 b(Rectangle)534 992 y Fj(C)-404 b(A)441 711 y(B)722 748 y(B)778 992 y(A)1359 748 y(B)1359 973 y(A)1416 2117 y Ft(Generalized)17 b(sector)1341 1629 y(Generalized)g(rectangle)422 1723 y Fj(D)1809 973 y(C)1172 992 y(C)805 2117 y Ft(P)o(arab)q(olic)f (segmen)o(t)p 809 2067 2 2 v 810 2064 V 812 2062 V 813 2060 V 815 2057 V 816 2055 V 818 2053 V 820 2050 V 821 2048 V 823 2046 V 824 2044 V 826 2041 V 827 2039 V 829 2037 V 830 2035 V 832 2033 V 834 2031 V 835 2028 V 837 2026 V 838 2024 V 840 2022 V 841 2020 V 843 2018 V 844 2016 V 846 2014 V 848 2012 V 849 2010 V 851 2008 V 852 2006 V 854 2004 V 855 2002 V 857 2000 V 858 1998 V 860 1996 V 861 1994 V 863 1992 V 864 1991 V 866 1989 V 867 1987 V 869 1985 V 870 1983 V 872 1981 V 874 1980 V 875 1978 V 877 1976 V 878 1974 V 880 1973 V 881 1971 V 883 1969 V 884 1967 V 886 1966 V 887 1964 V 889 1963 V 890 1961 V 892 1959 V 893 1958 V 895 1956 V 896 1955 V 898 1953 V 899 1951 V 901 1950 V 902 1948 V 904 1947 V 905 1945 V 907 1944 V 908 1942 V 910 1941 V 911 1940 V 913 1938 V 914 1937 V 916 1935 V 917 1934 V 919 1933 V 920 1931 V 921 1930 V 923 1929 V 924 1927 V 926 1926 V 927 1925 V 929 1923 V 930 1922 V 932 1921 V 933 1920 V 935 1918 V 936 1917 V 938 1916 V 939 1915 V 941 1914 V 942 1913 V 944 1911 V 945 1910 V 946 1909 V 948 1908 V 949 1907 V 951 1906 V 952 1905 V 954 1904 V 955 1903 V 957 1902 V 958 1901 V 959 1900 V 961 1899 V 962 1898 V 964 1897 V 965 1896 V 967 1895 V 968 1894 V 970 1893 V 971 1893 V 972 1892 V 974 1891 V 975 1890 V 977 1889 V 978 1888 V 980 1888 V 981 1887 V 982 1886 V 984 1885 V 985 1885 V 987 1884 V 988 1883 V 990 1883 V 991 1882 V 992 1881 V 994 1881 V 995 1880 V 997 1879 V 998 1879 V 999 1878 V 1001 1878 V 1002 1877 V 1004 1876 V 1005 1876 V 1006 1875 V 1008 1875 V 1009 1874 V 1011 1874 V 1012 1873 V 1013 1873 V 1015 1873 V 1016 1872 V 1018 1872 V 1019 1871 V 1020 1871 V 1022 1871 V 1023 1870 V 1024 1870 V 1026 1870 V 1027 1869 V 1029 1869 V 1030 1869 V 1031 1868 V 1033 1868 V 1034 1868 V 1036 1868 V 1037 1868 V 1038 1867 V 1040 1867 V 1041 1867 V 1042 1867 V 1044 1867 V 1045 1867 V 1046 1866 V 1048 1866 V 1049 1866 V 1051 1866 V 1052 1866 V 1053 1866 V 1055 1866 V 1056 1866 V 1057 1866 V 1059 1866 V 1060 1866 V 1061 1866 V 1063 1866 V 1064 1866 V 1065 1866 V 1067 1866 V 1068 1866 V 1069 1867 V 1071 1867 V 1072 1867 V 1073 1867 V 1075 1867 V 1076 1867 V 1077 1868 V 1079 1868 V 1080 1868 V 1081 1868 V 1083 1869 V 1084 1869 V 1085 1869 V 1087 1869 V 1088 1870 V 1089 1870 V 1091 1870 V 1092 1871 V 1093 1871 V 1095 1872 V 1096 1872 V 1097 1872 V 1099 1873 V 1100 1873 V 1101 1874 V 1103 1874 V 1104 1875 V 1105 1875 V 1106 1876 V 1108 1876 V 1109 1877 V 1110 1877 V 1112 1878 V 1113 1878 V 1114 1879 V 1116 1880 V 1117 1880 V 1118 1881 V 1119 1881 V 1121 1882 V 1122 1883 V 1123 1883 V 1125 1884 V 1126 1885 V 1127 1886 V 1128 1886 V 1130 1887 V 1131 1888 V 1132 1889 V 1134 1890 V 1135 1890 V 1136 1891 V 1137 1892 V 1139 1893 V 1140 1894 V 1141 1895 V 1142 1896 V 1144 1896 V 1145 1897 V 1146 1898 V 1147 1899 V 1149 1900 V 1150 1901 V 1151 1902 V 1152 1903 V 1154 1904 V 1155 1905 V 1156 1906 V 1158 1907 V 1159 1909 V 1160 1910 V 1161 1911 V 1162 1912 V 1164 1913 V 1165 1914 V 1166 1915 V 1167 1916 V 1169 1918 V 1170 1919 V 1171 1920 V 1172 1921 V 1174 1923 V 1175 1924 V 1176 1925 V 1177 1926 V 1179 1928 V 1180 1929 V 1181 1930 V 1182 1932 V 1183 1933 V 1185 1934 V 1186 1936 V 1187 1937 V 1188 1939 V 1190 1940 V 1191 1941 V 1192 1943 V 1193 1944 V 1194 1946 V 1196 1947 V 1197 1949 V 1198 1950 V 1199 1952 V 1200 1954 V 1202 1955 V 1203 1957 V 1204 1958 V 1205 1960 V 1206 1961 V 1208 1963 V 1209 1965 V 1210 1966 V 1211 1968 V 1212 1970 V 1214 1972 V 1215 1973 V 1216 1975 V 1217 1977 V 1218 1978 V 1220 1980 V 1221 1982 V 1222 1984 V 801 2067 a Fi(.)-6 b(.)804 2066 y(.)g(.)g(.)809 2065 y(.)g(.)f(.)814 2064 y(.)h(.)f(.)819 2063 y(.)h(.)f(.)824 2062 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y(.)g(.)f(.)h(.)1064 2015 y(.)f(.)h(.)1069 2014 y(.)f(.)h(.)1073 2013 y(.)g(.)g(.)1078 2012 y(.)g(.)g(.)1083 2011 y(.)g(.)g(.)1088 2010 y(.)g(.)f(.)1093 2009 y(.)h(.)f(.)1098 2008 y(.)h(.)f(.)1103 2007 y(.)g(.)h(.)g(.)1109 2006 y(.)g(.)g(.)1114 2005 y(.)g(.)g(.)1119 2004 y(.)g(.)f(.)1124 2003 y(.)h(.)f(.)1129 2002 y(.)h(.)f(.)1134 2001 y(.)g(.)h(.)1139 2000 y(.)f(.)h(.)1144 1999 y(.)f(.)h(.)1149 1998 y(.)f(.)h(.)f(.)1155 1997 y(.)h(.)f(.)1160 1996 y(.)h(.)f(.)1165 1995 y(.)g(.)h(.)1170 1994 y(.)f(.)h(.)1175 1993 y(.)f(.)h(.)1180 1992 y(.)f(.)h(.)1184 1991 y(.)g(.)g(.)1189 1990 y(.)g(.)g(.)1194 1989 y(.)g(.)f(.)h(.)1201 1988 y(.)f(.)h(.)1206 1987 y(.)f(.)h(.)1211 1986 y(.)f(.)h(.)1215 1985 y(.)g(.)g(.)1220 1984 y(.)801 2067 y(.)802 2066 y(.)803 2064 y(.)804 2063 y(.)805 2061 y(.)806 2060 y(.)807 2059 y(.)807 2057 y(.)808 2056 y(.)809 2055 y(.)818 2042 y(.)819 2041 y(.)820 2039 y(.)820 2038 y(.)821 2037 y(.)822 2035 y(.)823 2034 y(.)824 2032 y(.)825 2031 y(.)826 2030 y(.)834 2017 y(.)835 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y(.)1478 918 y(.)1479 917 y(.)1481 916 y(.)1482 915 y(.)1483 914 y(.)1485 913 y(.)1486 912 y(.)1487 911 y(.)1489 910 y(.)1490 909 y(.)1491 908 y(.)1492 907 y(.)1494 906 y(.)1495 905 y(.)1496 904 y(.)1498 903 y(.)1499 902 y(.)1500 901 y(.)1502 900 y(.)1503 899 y(.)1504 897 y(.)1505 896 y(.)1507 895 y(.)1508 894 y(.)1509 893 y(.)1511 892 y(.)1512 891 y(.)1513 890 y(.)1515 889 y(.)1516 888 y(.)1517 887 y(.)1519 886 y(.)1520 885 y(.)1521 884 y(.)1522 883 y(.)1524 882 y(.)1525 881 y(.)1526 880 y(.)1528 879 y(.)1529 878 y(.)1530 877 y(.)1532 876 y(.)1533 875 y(.)1534 874 y(.)1536 873 y(.)1537 872 y(.)1538 871 y(.)1539 870 y(.)1541 869 y(.)1542 868 y(.)1543 867 y(.)1545 866 y(.)1546 865 y(.)1547 864 y(.)1549 863 y(.)1550 862 y(.)1551 861 y(.)1552 860 y(.)1554 858 y(.)1555 857 y(.)1556 856 y(.)1558 855 y(.)1559 854 y(.)1560 853 y(.)1562 852 y(.)1563 851 y(.)1564 850 y(.)1566 849 y(.)1567 848 y(.)1568 847 y(.)1569 846 y(.)1571 845 y(.)1572 844 y(.)1573 843 y(.)1575 842 y(.)1576 841 y(.)1577 840 y(.)1579 839 y(.)1580 838 y(.)1581 837 y(.)1583 836 y(.)1584 835 y(.)1585 834 y(.)1586 833 y(.)1588 832 y(.)1589 831 y(.)1590 830 y(.)1592 829 y(.)1593 828 y(.)1594 827 y(.)1596 826 y(.)1597 825 y(.)1598 824 y(.)1599 823 y(.)1601 822 y(.)1602 821 y(.)1603 820 y(.)1605 818 y(.)1606 817 y(.)1607 816 y(.)1609 815 y(.)1610 814 y(.)1611 813 y(.)1613 812 y(.)1614 811 y(.)1615 810 y(.)1616 809 y(.)1618 808 y(.)1619 807 y(.)1620 806 y(.)1622 805 y(.)1623 804 y(.)1624 803 y(.)1626 802 y(.)1627 801 y(.)1628 800 y(.)1630 799 y(.)1631 798 y(.)1632 797 y(.)1633 796 y(.)1635 795 y(.)1636 794 y(.)1637 793 y(.)1639 792 y(.)1640 791 y(.)1641 790 y(.)1643 789 y(.)1644 788 y(.)1645 787 y(.)1646 786 y(.)1648 785 y(.)1649 784 y(.)1650 783 y(.)1652 782 y(.)1653 781 y(.)1654 780 y(.)1656 778 y(.)1657 777 y(.)1658 776 y(.)1660 775 y(.)1661 774 y(.)1662 773 y(.)1663 772 y(.)1665 771 y(.)1666 770 y(.)1667 769 y(.)1669 768 y(.)1670 767 y(.)1671 766 y(.)1673 765 y(.)1674 764 y(.)1675 763 y(.)1677 762 y(.)1678 761 y(.)1679 760 y(.)1680 759 y(.)1682 758 y(.)1683 757 y(.)1684 756 y(.)1665 780 y(.)1667 779 y(.)1668 778 y(.)1669 776 y(.)1670 775 y(.)1671 774 y(.)1672 772 y(.)1673 771 y(.)1674 769 y(.)1675 768 y(.)1676 767 y(.)1677 765 y(.)1678 764 y(.)1679 763 y(.)1680 761 y(.)1681 760 y(.)1682 759 y(.)1683 757 y(.)1684 756 y(.)-8 b(.)1683 757 y(.)e(.)1680 758 y(.)1678 759 y(.)h(.)1675 760 y(.)1673 761 y(.)1672 762 y(.)f(.)1669 763 y(.)1667 764 y(.)h(.)1664 765 y(.)1662 766 y(.)g(.)1659 767 y(.)1658 768 y(.)1656 769 y(.)1309 1056 y(.)1311 1055 y(.)1312 1054 y(.)1313 1053 y(.)1314 1052 y(.)1316 1051 y(.)1317 1050 y(.)1318 1048 y(.)1320 1047 y(.)1321 1046 y(.)1332 1037 y(.)1334 1036 y(.)1335 1035 y(.)1336 1034 y(.)1338 1032 y(.)1339 1031 y(.)1340 1030 y(.)1341 1029 y(.)1343 1028 y(.)1344 1027 y(.)1355 1017 y(.)1357 1016 y(.)1358 1015 y(.)1359 1014 y(.)1361 1013 y(.)1362 1012 y(.)1363 1011 y(.)1364 1010 y(.)1366 1009 y(.)1367 1008 y(.)1379 998 y(.)1380 997 y(.)1381 996 y(.)1382 995 y(.)1384 994 y(.)1385 993 y(.)1386 992 y(.)1387 991 y(.)1389 990 y(.)1390 989 y(.)1402 979 y(.)1403 978 y(.)1404 977 y(.)1405 976 y(.)1407 975 y(.)1408 974 y(.)1409 973 y(.)1410 972 y(.)1412 971 y(.)1413 970 y(.)p 37 1205 3 1050 v 339 942 a Ft(C)339 830 y(R)920 942 y(C)789 773 y(B)837 1167 y(Out-circle)-785 b(Out-circle)170 755 y Fg(X)919 b(X)170 605 y(In\014nite)15 b(strip)132 380 y Ft(A)276 b(B)732 605 y(Semi-in\014nite)18 b(strip)294 286 y(X)568 b(X)750 511 y(A)248 b(B)1464 605 y(Plane)1745 886 y(X)1482 1036 y(A)191 b(B)1595 792 y(D)1428 1167 y(Plane)16 b(sector)1459 1056 y Fi(.)1459 1054 y(.)1459 1053 y(.)1459 1051 y(.)1459 1049 y(.)1459 1048 y(.)1459 1046 y(.)1459 1044 y(.)1459 1043 y(.)1459 1041 y(.)1458 1039 y(.)1458 1038 y(.)1458 1036 y(.)1458 1034 y(.)1458 1033 y(.)1457 1031 y(.)1457 1029 y(.)1457 1028 y(.)1456 1026 y(.)1456 1025 y(.)1456 1023 y(.)1455 1021 y(.)1455 1020 y(.)1455 1018 y(.)1454 1017 y(.)1454 1015 y(.)1453 1013 y(.)1453 1012 y(.)1452 1010 y(.)1452 1009 y(.)1451 1007 y(.)1451 1005 y(.)1450 1004 y(.)1449 1002 y(.)1449 1001 y(.)1448 999 y(.)1448 998 y(.)1447 996 y(.)1446 995 y(.)1446 993 y(.)1445 992 y(.)1444 990 y(.)1443 989 y(.)1443 987 y(.)1442 986 y(.)1441 984 y(.)1440 983 y(.)1440 981 y(.)1439 980 y(.)1438 978 y(.)1437 977 y(.)1436 976 y(.)1435 974 y(.)1434 973 y(.)1433 971 y(.)1432 970 y(.)1431 969 y(.)1430 967 y(.)1429 966 y(.)1428 965 y(.)1427 963 y(.)1426 962 y(.)1425 961 y(.)1424 960 y(.)1666 1056 y(.)1666 1054 y(.)1666 1053 y(.)1666 1051 y(.)1666 1049 y(.)1666 1048 y(.)1666 1046 y(.)1666 1044 y(.)1665 1043 y(.)1665 1041 y(.)1664 1026 y(.)1664 1024 y(.)1664 1023 y(.)1664 1021 y(.)1664 1019 y(.)1664 1018 y(.)1663 1016 y(.)1663 1014 y(.)1663 1013 y(.)1663 1011 y(.)1661 996 y(.)1660 995 y(.)1660 993 y(.)1660 991 y(.)1659 990 y(.)1659 988 y(.)1659 986 y(.)1659 985 y(.)1658 983 y(.)1658 982 y(.)1654 967 y(.)1654 965 y(.)1654 964 y(.)1653 962 y(.)1653 960 y(.)1652 959 y(.)1652 957 y(.)1651 956 y(.)1651 954 y(.)1650 952 y(.)1646 938 y(.)1645 937 y(.)1645 935 y(.)1644 933 y(.)1643 932 y(.)1643 930 y(.)1642 929 y(.)1642 927 y(.)1641 926 y(.)1640 924 y(.)1635 910 y(.)1634 909 y(.)1633 907 y(.)1633 906 y(.)1632 904 y(.)1631 903 y(.)1630 901 y(.)1630 900 y(.)1629 898 y(.)1628 897 y(.)1621 883 y(.)1620 882 y(.)1620 881 y(.)1619 879 y(.)1618 878 y(.)1617 876 y(.)1616 875 y(.)1615 873 y(.)1615 872 y(.)1614 871 y(.)1606 858 y(.)1605 856 y(.)1604 855 y(.)1603 854 y(.)1602 852 y(.)1601 851 y(.)1600 850 y(.)1599 848 y(.)1598 847 y(.)1597 846 y(.)1588 834 y(.)1587 832 y(.)1586 831 y(.)1585 830 y(.)1584 828 y(.)1583 827 y(.)451 1304 y Ft(Figure)f(2:)20 b(In\014nite)c(regions)g(a)o(v)m(ailable)h(in)f Fr(Cubpac)o(k)p Fn(++)p Ft(.)60 1442 y Fn(OUT)p 135 1442 15 2 v 17 w(CIRCLE)32 b Ft(The)17 b(same)f(as)g Fn(CIRCLE)p Ft(,)f(except)i(that)e(the)i(in)o (tegration)f(region)h(is)g(the)f(complemen)o(t)h(of)151 1498 y(the)e(disk.)60 1594 y Fn(PLANE)39 b Ft(The)20 b(in)o(tegration)g(region)g(is)g(the)g(whole)h(t)o(w)o(o-dimensional)f (plane.)35 b(Strictly)21 b(sp)q(eaking,)g(no)151 1650 y(parameters)13 b(are)g(necessary)l(,)h(but)g(the)f(in)o(tegration)h (routines)g(use)g(form)o(ulas)f(with)h(appro)o(ximately)151 1706 y(half)e(their)g(p)q(oin)o(ts)g(inside)h(an)f(ellipse)i(cen)o (tred)e(at)e Fn(Center)h Ft(and)h(ha)o(ving)g(axes)f Fn(ScaleX)f Ft(and)i Fn(ScaleY)o Fm(:)151 1763 y Ft(If)21 b(y)o(ou)g(kno)o(w)f(where)h(in)h(the)f(plane)h(the)f(action)g(tak)o (es)f(place,)j(y)o(ou)d(can)h(sa)o(v)o(e)g(some)f(function)151 1819 y(ev)m(aluations)15 b(b)o(y)f(supplying)h(these.)20 b(Otherwise)14 b(the)g(v)m(alue)h(giv)o(en)f(for)f(the)h(ellipse)i (defaults)e(to)f(the)151 1876 y(unit)j(circle.)151 1952 y(A)o(t)10 b(this)g(p)q(oin)o(t,)i(some)e(users)g(migh)o(t)g(\014nd)h (it)f(useful)h(to)f(kno)o(w)g(more)f(details.)19 b(The)11 b(cubature)f(form)o(ula)151 2008 y(that)17 b(is)h(initially)i(applied)f (for)e(this)h(region)g(can)f(b)q(e)h(transformed)f(b)o(y)g(an)g (a\014ne)h(transformation)151 2065 y(to)d(giv)o(e)g(an)g(appro)o (ximation)g(to)598 2126 y Ff(Z)640 2139 y Fe(1)621 2220 y(\0001)693 2126 y Ff(Z)735 2139 y Fe(1)717 2220 y(\0001)789 2183 y Fm(e)810 2164 y Fl(\()p Fd(a)p Fl(\()p Fd(x)p Fe(\000)p Fd(c)919 2168 y Fc(x)938 2164 y Fl(\)\))966 2153 y Fb(2)983 2164 y Fl(+\()p Fd(b)p Fl(\()p Fd(y)q Fe(\000)p Fd(c)1113 2168 y Fc(y)1133 2164 y Fl(\)\))1161 2153 y Fb(2)1180 2183 y Fm(f)5 b Ft(\()p Fm(x;)j(y)r Ft(\))g(d)p Fm(x)g Ft(d)p Fm(y)151 2306 y Ft(while)20 b(the)f(cubature)g(form)o(ula)f(main)o(tains)h(its)g(degree.)31 b(W)l(e)19 b(use)g(this)g(with)g Fm(a)g Ft(=)f Fn(ScaleX)p Ft(,)h Fm(b)f Ft(=)151 2362 y Fn(ScaleY)e Ft(and)g Fm(c)420 2369 y Fd(x)456 2362 y Ft(=)f Fn(Center)p Fm(:)p Fn(X)n Fm(;)8 b(c)726 2369 y Fd(y)760 2362 y Ft(=)15 b Fn(Center)p Fm(:)p Fn(Y)o Ft(.)23 b(The)16 b(fact)g(that)g Fn(Center)p Ft(,)f Fn(ScaleX)g Ft(and)i Fn(ScaleY)151 2419 y Ft(are)12 b(related)g(to)f(an)h(ellipse)i(with)e(appro)o(ximately)g(the)g(same)g (n)o(um)o(b)q(er)g(of)f(p)q(oin)o(ts)i(inside)g(as)f(outside,)151 2475 y(is)h(used)g(to)e(determine)j(a)e(sub)q(division)j(of)c(the)i (plane.)20 b(F)l(or)11 b(details)j(of)d(this)i(algorithm,)g(see)f (Section)151 2532 y(5.4)i(of)h(the)g(pap)q(er)h([2)o(].)60 2627 y Fn(GENERALIZED)p 327 2627 V 16 w(RECTANGLE)33 b Ft(This)18 b(region)f(has)g(three)g(straigh)o(t)g(sides)h(that)e (meet)h(at)g(righ)o(t)g(angles)g(in)151 2683 y(the)f(p)q(oin)o(ts)h Fj(A)f Ft(and)g Fj(B)q Ft(,)g(and)g(one)g(curv)o(ed)h(side.)23 b(The)16 b(p)q(erp)q(endicul)q(ar)i(distance)f(b)q(et)o(w)o(een)g(a)e (p)q(oin)o(t)151 2740 y Fj(P)h Ft(on)g(the)h(directed)g(line)h(segmen)o (t)e Fj(AB)h Ft(and)f(the)g(p)q(oin)o(t)h(on)f(the)g(curv)o(e)h (orthogonally)f(to)f(the)i(left)151 2796 y(of)e Fj(P)g Ft(is)h Fn(Height\()p Fj(P)o Fn(\).)k Ft(It)15 b(is)h(necessary)f(that) g Fn(Height\()p Fj(P)o Fn(\))d Fq(\025)h Ft(0)i(for)g(all)h Fj(P)f Ft(b)q(et)o(w)o(een)g Fj(A)h Ft(and)f Fj(B)q Ft(.)p eop %%Page: 6 9 6 8 bop 37 50 a Ft(6)1136 b Fo(R.)15 b(Co)q(ols,)g(D.)g(Laurie)h(and)f (L.)g(Pluym)60 199 y Fn(POLAR)p 183 199 15 2 v 17 w(RECTANGLE)29 b Ft(This)17 b(region)e(is)i(b)q(ounded)f(b)o(y)g(the)g(ra)o(ys)e Fm(\022)h Ft(=)f Fm(\013)h Ft(and)h Fm(\022)f Ft(=)e Fm(\014)18 b Ft(\(where)d Fm(\014)h(>)d(\013)p Ft(\))j(and)151 256 y(the)e(arcs)f Fm(r)h Ft(=)f Fn(InnerRadius)f Ft(and)i Fm(r)f Ft(=)g Fn(OuterRadius)f Ft(\(where)i Fn(OuterRadius)d Fm(>)i Fn(InnerRadius)n Ft(\))151 312 y(in)j(p)q(olar)g(co)q(ordinates) f(with)h(origin)g Fn(Center)p Ft(.)j(An)c(ann)o(ulus)h(\()p Fm(\014)f Ft(=)e Fm(\013)d Ft(+)h(2)p Fm(\031)r Ft(\))j(is)h(a)g(sp)q (ecial)i(case.)151 387 y(Alternativ)o(ely)l(,)i(y)o(ou)e(ma)o(y)f(sp)q (ecify)j(the)e(region)h(in)g(terms)f(of)g Fn(Point)p Ft(s:)23 b Fj(A)17 b Ft(and)h Fj(B)f Ft(are)g(the)h(p)q(oin)o(ts)151 444 y(on)g(the)g(ra)o(y)f Fm(\022)h Ft(=)g Fm(\013)g Ft(at)f Fn(InnerRadius)f Ft(and)i Fn(OuterRadius)p Ft(,)f(resp)q(ectiv) o(ely)l(,)j(and)e Fj(D)f Ft(is)i(the)e(p)q(oin)o(t)151 500 y(on)k(the)g(ra)o(y)f Fm(\022)j Ft(=)g Fm(\014)g Ft(at)d Fn(OuterRadius.)35 b Ft(Y)l(ou)21 b(need)h(not)e(sp)q(ecify)i Fj(Center)q Ft(:)31 b(the)21 b(other)g(p)q(oin)o(ts)151 557 y(determine)d(it)f(fully)l(,)h(except)g(when)f Fj(AB)f Fq(?)g Fj(BD)p Fm(:)g Ft(In)i(that)e(case,)h(the)f(region)i(should)f(b) q(e)h(sp)q(eci\014ed)151 613 y(as)f(a)f Fn(RECTANGLE)g Ft(and)h(not)g(as)g(a)f(limiting)j(case)e(of)g(a)g Fn(POLAR)p 1236 613 V 16 w(RECTANGLE)p Ft(.)f(Y)l(ou)h(cannot)g(sp)q(ecify)151 670 y(an)e(ann)o(ulus)i(in)f(terms)e(of)h Fn(Point)p Ft(s.)20 b(Sp)q(ecial)d(cases)e(are)g(a)g(sector)g(\()p Fj(Center)e Ft(=)g Fj(A)q Ft(\))i(and)g(a)g(cut)g(circle)151 726 y(\()p Fj(Center)e Ft(=)g Fj(A)q Ft(,)h Fj(D)e Ft(=)h Fj(B)q Ft(\).)19 b(F)l(rom)14 b(a)g(top)q(ological)h(p)q(oin)o(t)g(of)f (view,)h(p)q(oin)o(ts)g(on)g(either)g(side)h(of)e(the)g(line)151 782 y Fj(AB)h Ft(in)h(a)e(cut)h(circle)i(are)d(not)g(though)o(t)g(of)h (as)f(close)h(to)f(eac)o(h)h(other.)20 b(In)15 b Fq(x)p Ft(10.3)f(w)o(e)g(shall)i(later)f(giv)o(e)151 839 y(an)g(example)h (that)f(illustrates)h(the)f(di\013erence)i(b)q(et)o(w)o(een)e(a)g (circle)i(and)e(a)g(cut)g(circle.)60 933 y Fn(GENERALIZED)p 327 933 V 16 w(SECTOR)25 b Ft(This)13 b(region)g(has)g(t)o(w)o(o)f (straigh)o(t)g(sides)h(and)g(one)g(curv)o(ed)h(side.)20 b(It)13 b(is)g(describ)q(ed)151 989 y(in)23 b(p)q(olar)g(co)q (ordinates)g(measured)g(from)f Fn(Center.)41 b Ft(The)23 b(straigh)o(t)e(sides)j(run)e(along)h(ra)o(ys)f(at)151 1046 y(angles)16 b Fn(Alpha)e Ft(and)h Fn(Beta)g Ft(resp)q(ectiv)o(ely) l(,)i(and)e(the)g(curv)o(ed)h(side)g(is)g(de\014ned)g(b)o(y)f(the)g (function)h Fn(Rho)151 1102 y Ft(as)i(follo)o(ws:)26 b(the)18 b(distance)h(from)f Fn(Center)f Ft(to)h(the)g(curv)o(e)h (along)f(a)g(ra)o(y)f(at)h(an)g(angle)h Fm(\022)h Ft(b)q(et)o(w)o(een) 151 1159 y Fn(Alpha)15 b Ft(and)g Fn(Beta)g Ft(is)g(giv)o(en)h(b)o(y)f Fn(Rho\()p Fm(\022)q Fn(\).)60 1252 y(PARABOLIC)p 279 1252 V 16 w(SEGMENT)28 b Ft(This)14 b(region)h(is)g(b)q(ounded)g(b)o(y) g(a)f(straigh)o(t)f(line)j Fj(AB)f Ft(and)f(a)g(parab)q(olic)h(arc.)20 b(The)151 1309 y(arc)15 b(is)h(de\014ned)g(b)o(y)f(an)h(external)f(p)q (oin)o(t)h Fj(P)f Ft(suc)o(h)h(that)e Fj(AP)i Ft(and)f Fj(BP)g Ft(are)g(tangen)o(ts.)60 1403 y Fn(INFINITE)p 255 1403 V 16 w(STRIP)30 b Ft(The)15 b(line)i(segmen)o(t)e Fj(AB)h Ft(is)f(a)g(diameter)h(of)f(the)g(strip.)60 1496 y Fn(SEMI-INFINITE)p 375 1496 V 16 w(STRIP)34 b Ft(The)18 b(strip)g(lies)h(orthogonally)e(to)g(the)h(left)g(of)f(the)g(directed)i (line)g(segmen)o(t)151 1553 y Fj(AB)q Ft(.)60 1647 y Fn(PLANE)p 183 1647 V 17 w(SECTOR)h Ft(This)11 b(region)g(is)g(b)q (ounded)h(b)o(y)e(the)h(ra)o(ys)f Fm(\022)k Ft(=)f Fm(\013)e Ft(and)f Fm(\022)15 b Ft(=)e Fm(\014)f Ft(\(where)f Fm(\014)j(>)f(\013) p Ft(\))e(and)g(the)f(arc)151 1703 y Fm(r)k Ft(=)f Fj(InnerRadius)i Ft(in)f(p)q(olar)g(co)q(ordinates)g(with)h(origin)f Fn(Center)p Fm(:)e Ft(Alternativ)o(ely)l(,)j(y)o(ou)f(ma)o(y)f(sp)q(ecify)151 1760 y(the)k(region)h(in)g(terms)e(of)h Fn(Point)p Ft(s:)22 b Fj(A)c Ft(is)f(the)h(p)q(oin)o(t)f(on)g(the)g(ra)o(y)f(at)h Fm(\022)g Ft(=)f Fm(\013)i Ft(at)e Fm(r)h Ft(=)f Fj(InnerRadius)q Fm(;)151 1816 y Ft(and)i Fj(B)h Ft(and)f Fj(D)f Ft(are)h(p)q(oin)o(ts)h (on)e(an)h(arc)g Fm(r)g Ft(=)g Fj(OuterRadius)i Ft(\(with)e Fj(OuterRadius)i Fm(>)e Fj(InnerRadius)q Ft(\))151 1873 y(at)k Fm(\022)k Ft(=)f Fm(\013)e Ft(and)g Fm(\022)j Ft(=)f Fm(\014)f Ft(resp)q(ectiv)o(ely)l(.)44 b(Y)l(ou)23 b(need)g(not)f(sp)q(ecify)i Fj(Center)q Ft(:)34 b(the)22 b(other)h(p)q(oin)o(ts)151 1929 y(determine)18 b(it)f(fully)l(,)h (except)g(when)f Fj(AB)f Fq(?)g Fj(BD)p Fm(:)g Ft(In)i(that)e(case,)h (the)f(region)i(should)f(b)q(e)h(sp)q(eci\014ed)151 1985 y(as)d(a)f Fn(SEMI)p 343 1985 V 17 w(INFINITE)p 552 1985 V 16 w(STRIP)g Ft(and)h(not)f(as)h(a)f(limiting)j(case)e(of)f(a)h Fn(PLANE)p 1437 1985 V 16 w(SECTOR)p Ft(.)f(Sp)q(ecial)j(cases)151 2042 y(include)h(the)d(half-plane)i(\()p Fj(D)12 b Ft(=)h(2)p Fj(A)d Fq(\000)h Fj(B)p Ft(\))k(and)g(cut)g(plane)i(\()p Fj(Center)c Ft(=)g Fj(A)p Fm(;)i Fj(D)d Ft(=)h Fj(B)q Ft(\).)108 2148 y(Small)h(example)g(programs)e(that)h(illustrate)h(the) f(use)h(of)f(these)g(simple)i(regions)e(are)g(pro)o(vided)h(in)g(the)37 2205 y(directory)i(Examples.)k(W)l(e)c(refer)f(to)f(the)h(\014le)i Fn(Examples/CONTENTS)c Ft(for)h(its)h(con)o(ten)o(ts.)108 2261 y(As)g(y)o(ou)f(see)h(all)g(names)g(of)f(simple)i(regions)f(con)o (tain)f(upp)q(er)i(case)e(letters)h(only)l(,)g(the)g(comp)q(onen)o(ts)f (of)37 2318 y(comp)q(ound)i(w)o(ords)f(b)q(eing)h(separated)f(b)o(y)g (underscores.)20 b(All)d(classes)f(represen)o(ting)f(simple)i(regions)e (are)37 2374 y(deriv)o(ed)g(from)e(a)g(class)h Fn(COMPOUND)p 637 2374 V 16 w(REGION)p Ft(,)f(whic)o(h)h(also)g(comprises)g(the)g (transformed)e(and)i(sub)q(divided)37 2430 y(regions)i(that)e(arise)i (during)g(the)f(computation.)p eop %%Page: 7 10 7 9 bop 37 50 a Fo(A)16 b(User)f(Man)o(ual)g(for)g(Cubpac)o(k++)1182 b Ft(7)37 199 y Fp(5)67 b(The)23 b(in)n(tegrators)37 301 y Fr(Cubpac)o(k)p Fn(++)16 b Ft(uses)h(only)g(one)g(global)g (adaptiv)o(e)g(in)o(tegration)g(algorithm,)f(but)h(to)f(meet)g (di\013ering)i(user)37 357 y(requiremen)o(ts)e(w)o(e)f(ha)o(v)o(e)g (supplied)i(four)e(v)o(ersions)g(of)g(the)g(cen)o(tral)h(routine)f Fn(Integrate)p Ft(.)k(These)c(will)i(b)q(e)37 414 y(discussed)g(in)f (this)g(and)f(the)h(follo)o(wing)f(section.)37 532 y Fs(5.1)56 b(No-fuss)19 b(in)n(tegration)37 618 y Ft(When)e(y)o(ou)f (just)g(w)o(an)o(t)f(to)h(kno)o(w)g(the)g(in)o(tegral)h(of)f(a)g Fn(Function)f(f)h Ft(o)o(v)o(er)f(a)h Fn(COMPOUND)p 1555 618 15 2 v 16 w(REGION)g(CR)p Ft(,)f(y)o(ou)37 675 y(can)h(use)h(the)e (function)i Fn(Integrate\(f,)22 b(CR\))16 b Ft(as)f(in)i(the)e(example) i(in)g(Section)f(2.)22 b(The)16 b(v)m(alue)h(returned)37 731 y(will)g(then)f(b)q(e)g(an)f(appro)o(ximation)g(of)g(the)g(in)o (tegral.)108 788 y(This)20 b(simple)h(v)o(ersion)e(of)g(the)g(in)o (tegrator)f(uses)i(default)g(v)m(alues)g(for)f(the)g(accuracy)g(to)g (whic)o(h)h(the)37 844 y(in)o(tegral)c(should)g(b)q(e)g(ev)m(aluated)g (and)f(the)g(amoun)o(t)g(of)f(w)o(ork)g(p)q(ermitted.)21 b(If)15 b(y)o(ou)g(w)o(an)o(t)f(explicit)j(con)o(trol)37 901 y(o)o(v)o(er)i(the)h(in)o(tegration)f(pro)q(cess,)i(y)o(ou)e(can)h (supply)h(these)e(v)m(alues:)30 b(the)20 b(full)h(header)f(with)g(its)f (default)37 957 y(argumen)o(ts)c(is:)37 1045 y Fn(real)24 b(Integrate\()228 1101 y(Function)f(f,)228 1158 y(COMPOUND_REGION&)f (CR,)228 1214 y(real)i(AbsoluteErrorRequest)d(=)j(0.0,)228 1271 y(real)g(RelativeErrorRequest)d(=)j(DEFAULT_REL_ERR_REQ)d(,)228 1327 y(unsigned)i(long)g(MaxEval)g(=)h(100000\);)37 1415 y Ft(The)19 b(constan)o(t)e Fn(DEFAULT_REL_ERR_REQ)f Ft(is)j(de\014ned)g(in)g(the)g(\014le)g Fn(real.h)p Ft(.)28 b(As)18 b(usual)h(with)g(C)p Fn(++)25 b Ft(y)o(ou)37 1472 y(ma)o(y)15 b(omit)g(an)o(y)g(n)o(um)o(b)q(er)g(of)g(trailing)h (argumen)o(ts)f(for)f(whic)o(h)i(defaults)g(are)f(giv)o(en.)108 1528 y(The)e(in)o(tegrator)e(tries)h(to)g(compute)g(an)h(appro)o (ximation)f(to)f(the)i(in)o(tegral)f(of)g Fn(f)g Ft(on)h Fn(CR)f Ft(whic)o(h)h(satis\014es)520 1612 y Fq(j)p Fn(AbsoluteError)m Fq(j)g(\024)g Fn(AbsoluteErrorRequest)37 1695 y Ft(or)377 1752 y Fq(j)p Fn(AbsoluteError)n Fq(j)g(\024)f(j)p Fn(Integral)o Fq(j)e(\002)g Fn(RelativeErrorRequest)m Fm(;)37 1826 y Ft(whic)o(hev)o(er)15 b(it)e(reac)o(hes)h(\014rst.)19 b(The)13 b(result)h(is)g(returned)g(via)g Fn(Integral)e Ft(and)h Fn(AbsoluteError)p Ft(.)18 b(Ho)o(w)o(ev)o(er)37 1883 y(it)e(will)h(at)d(most)h(do)g Fn(MaxEval)f Ft(function)i(ev)m (aluations.)37 2001 y Fs(5.2)56 b(Adv)m(anced)19 b(in)n(tegration)37 2087 y Ft(If)d(the)g(automatic)f(in)o(tegrator)f(cannot)h(satisfy)h (one)f(of)g(the)h(error)f(requests,)g(the)g(\015ag)h Fn(Success)e Ft(will)j(b)q(e)37 2144 y(set)d(to)f Fn(False)p Ft(;)g(otherwise)h(it)g(will)h(b)q(e)g(set)e(to)g Fn(True)p Ft(.)19 b(The)14 b(\015ag)f Fn(Success)g Ft(cannot)g(b)q(e)i(seen)f (when)g(y)o(ou)g(use)37 2200 y(the)i(simple)g(in)o(tegrator)e(whose)h (only)h(output)e(is)i(a)f(function)g(v)m(alue.)22 b(If)15 b(y)o(ou)f(wish)i(to)f(see)g(it,)g(or)f(to)h(store)37 2257 y(the)h(in)o(tegral)f(and)h(error)e(estimates)h(in)h(v)m(ariables) h(of)d(y)o(our)h(o)o(wn)g(c)o(hoice,)h(the)f(header)g(of)g Fn(Integrate)f Ft(is:)37 2345 y Fn(void)24 b(Integrate\()228 2401 y(Function)f(f,)228 2457 y(COMPOUND_REGION&)f(CR,)228 2514 y(real&)i(Integral,)228 2570 y(real&)g(AbsoluteError,)228 2627 y(Boolean&)f(Success,)228 2683 y(real)h(AbsoluteErrorRequest,)228 2740 y(real)g(RelativeErrorRequest,)228 2796 y(unsigned)f(long)g (MaxEval\);)p eop %%Page: 8 11 8 10 bop 37 50 a Ft(8)1136 b Fo(R.)15 b(Co)q(ols,)g(D.)g(Laurie)h(and)f (L.)g(Pluym)37 199 y Ft(Note)g(that)g(this)g(v)o(ersion)h(requires)g(y) o(ou)e(to)h(sp)q(ecify)h(all)h(the)e(argumen)o(ts:)k(no)c(default)h(v)m (alues)g(are)f(giv)o(en.)37 256 y(The)h(three)f(reference)h(parameters) e(are)h(used)h(to)f(return)g(computed)g(quan)o(tities.)108 312 y(Tw)o(o)20 b(further)h(v)o(ersions)g(of)g Fn(Integrate)p Ft(,)g(in)o(tended)h(for)e(more)h(complicated)h(situations,)h(are)d (de-)37 369 y(scrib)q(ed)d(in)f(the)f(next)h(section.)108 425 y(F)l(or)j(all)h(four)e(v)o(ersions)i(of)e Fn(Integrate)p Ft(,)h(the)g(in)o(tegral)g(and)h(error)e(estimate)h(are)g(stored)f (with)i(the)37 482 y(region)g Fn(CR)f Ft(itself,)i(and)f(can)f(b)q(e)h (retriev)o(ed)g(at)e(an)o(y)h(stage)g(after)f(in)o(tegration)i(b)o(y)f (the)g Fn(real)g Ft(functions)37 538 y Fn(CR.Integral\(\))14 b Ft(and)h Fn(CR.AbsoluteError\(\))e Ft(resp)q(ectiv)o(ely)l(.)37 679 y Fp(6)67 b(Handling)24 b(collections)f(of)f(regions)37 781 y Ft(Sometimes)f(y)o(ou)e(w)o(an)o(t)g(to)h(in)o(tegrate)f(o)o(v)o (er)g(a)h(collection)i(of)d(regions,)i(rather)e(than)h(o)o(v)o(er)f (one)h(of)g(the)37 837 y(simple)f(regions)d(men)o(tioned)i(ab)q(o)o(v)o (e.)23 b(Supp)q(ose)18 b(for)e(instance)h(that)f(y)o(ou)g(w)o(ould)h (lik)o(e)h(to)e(in)o(tegrate)g(o)o(v)o(er)37 894 y(the)h(house-shap)q (ed)h(region)g(sho)o(wn)e(in)i(Figure)f(3.)24 b(In)17 b Fr(Cubpac)o(k)p Fn(++)f Ft(y)o(ou)h(w)o(ould)g(use)g(a)g (generalization)37 950 y(of)e(a)g Fn(COMPOUND)p 322 950 15 2 v 16 w(REGION)p Ft(,)f(called)j(a)e Fn(REGION)p 820 950 V 16 w(COLLECTION)p Ft(.)f(It)h(go)q(es)g(lik)o(e)h(this:)37 1033 y Fn(REGION_COLLECTION)22 b(House;)37 1090 y(TRIANGLE)h(Roof\()g (Point\(0,1\),)g(Point\(2,1\),)f(Point\(1,2\)\);)37 1146 y(RECTANGLE)h(Walls\()g(Point\(0,0\),)g(Point\(0,1\),)f (Point\(2,0\)\);)37 1259 y(House)i(=)f(Roof)h(+)f(Walls;)37 1372 y(cout)h(<<)f("integral)g(over)g(the)h(house-shaped)e(region)h(")h (<<)f(Integrate\(f,House\);)108 1455 y Ft(Y)l(ou)14 b(can)g(add)f(as)g (man)o(y)h Fn(COMPOUND)p 740 1455 V 16 w(REGION)p Ft(s)e(as)h(y)o(ou)h (lik)o(e,)g(giving)h(a)e Fn(REGION)p 1477 1455 V 16 w(COLLECTION)f Ft(\(whic)o(h)37 1512 y(is)k(itself)h(a)e Fn(COMPOUND)p 427 1512 V 16 w(REGION)p Ft(\).)f(The)i(addition)g(can)g(either)g(use)g (the)f Fn(+)g Ft(op)q(erator)g(as)g(ab)q(o)o(v)o(e,)g(or)g(the)g Fn(+=)37 1568 y Ft(op)q(erator)g(as)g(in)h(C.)108 1625 y(Y)l(ou)g(needn't)f(use)h Fn(REGION)p 589 1625 V 16 w(COLLECTION)e Ft(explicitly)l(,)k(y)o(ou)c(can)i(also)f(do)g(it)h(lik) o(e)g(this:)37 1708 y Fn(...)37 1764 y(cout)24 b(<<)f (Integrate\(f,Roof+Walls\);)p 790 2098 250 4 v 789 2096 4 125 v 1038 2096 V 790 1971 a Fa(\000)832 1930 y(\000)873 1888 y(\000)998 1971 y(@)956 1930 y(@)915 1888 y(@)p 790 1972 250 2 v 776 2244 a Ft(Figure)16 b(3:)j(A)d(house)108 2345 y(After)d(calling)i Fn(Integrate)e Ft(y)o(ou)g(can)g(access)h(the) f(in)o(tegral)h(and)g(error)f(on)g(eac)o(h)g(part)g(of)g(a)h (collection,)37 2401 y(i.e.)e(y)o(ou)f(kno)o(w)g Fn(Roof.Integral\(\))f Ft(as)h(w)o(ell)h(as)f Fn(Walls.Integral\(\))f Ft(et)h(cetera.)19 b(This)12 b(is)g(made)f(p)q(ossible)37 2457 y(b)o(y)k(the)g(implemen)o (tation)i(of)d(the)h(addition)h(op)q(erators)e(for)g Fn(COMPOUND)p 1276 2457 15 2 v 17 w(REGION)p Ft(s.)k(Rather)d(than)g (adding)37 2514 y(a)e(cop)o(y)g(of)g(the)g(original)h Fn(COMPOUND)p 660 2514 V 16 w(REGION)f Ft(to)f(the)h Fn(REGION)p 1106 2514 V 17 w(COLLECTION)e Ft(a)i(reference)h(to)e(its)i (con)o(ten)o(ts)37 2570 y(is)i(stored.)108 2627 y(Y)l(ou)47 b(are)f(allo)o(w)o(ed)h(to)g(in)o(tegrate)f(di\013eren)o(t)h(functions) g(o)o(v)o(er)f(di\013eren)o(t)h(parts)f(of)g(a)37 2683 y Fn(REGION)p 184 2683 V 17 w(COLLECTION)p Ft(,)18 b(whic)o(h)j(ma)o(y) f(for)f(instance)i(b)q(e)g(useful)g(when)g(y)o(our)f(in)o(tegrand)g(is) h(discon)o(tin)o(u-)37 2740 y(ous.)34 b(In)21 b(that)e(case,)h(y)o(ou)g (use)g(a)f(v)o(ersion)h(of)g Fn(Integrate)e Ft(that)h(omits)h(the)g (\014rst)f(argumen)o(t)g(\(i.e.)h(the)37 2796 y(in)o(tegrand\),)15 b(and)h(instead)f(asso)q(ciate)h(an)f(in)o(tegrand)g(with)h(eac)o(h)f (region,)g(lik)o(e)h(this:)p eop %%Page: 9 12 9 11 bop 37 50 a Fo(A)16 b(User)f(Man)o(ual)g(for)g(Cubpac)o(k++)1182 b Ft(9)37 199 y Fn(Roof.LocalIntegrand\(f1\);)37 256 y(Walls.LocalIntegrand\(f2\);)37 312 y(cout)24 b(<<)f("the)h(result)f (is)g(")h(<<)g(Integrate\(Roof+Walls\);)37 406 y Ft(The)16 b(full)g(header)g(for)f(this)g(in)o(tegrator)f(is:)37 500 y Fn(real)24 b(Integrate\()228 556 y(COMPOUND_REGION&)e(CR,)228 613 y(real)i(AbsoluteErrorRequest)d(=)j(0.0,)228 669 y(real)g(RelativeErrorRequest)d(=)j(DEFAULT_REL_ERR_REQ)d(,)228 726 y(unsigned)i(long)g(MaxEval)g(=)h(100000\);)37 819 y Ft(A)16 b(complete)g(example)g(is)f(giv)o(en)h(in)g(the)f(\014le)i Fn(Examples/vb15.c)p Ft(.)108 876 y(If)i(y)o(ou)g(forgot)e(to)i(sp)q (ecify)h(the)f(in)o(tegrand)g(using)h Fn(LocalIntegrand\(\))d Ft(for)h(eac)o(h)h(region)h(in)f(y)o(our)37 932 y Fn(REGION)p 184 932 15 2 v 17 w(COLLECTION)11 b Ft(b)q(efore)i(calling)h Fn(Integrate\(\))p Ft(,)d Fr(Cubpac)o(k)p Fn(++)h Ft(will)i(generate)e (an)g(error)g(message.)108 989 y(Similarly)l(,)j(there)e(exists)g(a)g (v)o(ersion)g(of)g(the)g(more)f(elab)q(orate)h Fn(Integrate\(\))e Ft(without)i(the)g Fn(Function)37 1045 y Ft(argumen)o(t.)20 b(The)15 b(full)i(header)e(is:)37 1139 y Fn(void)24 b(Integrate\()228 1196 y(COMPOUND_REGION&)e(CR,)228 1252 y(real&)i(Integral,)228 1308 y(real&)g(AbsoluteError,)228 1365 y(Boolean&)f(Success,)228 1421 y(real)h(AbsoluteErrorRequest,)228 1478 y(real)g (RelativeErrorRequest,)228 1534 y(unsigned)f(long)g(MaxEval\);)37 1628 y Ft(Although)e(the)f(four)g(v)o(ersions)g(of)g Fn(Integrate)f Ft(ha)o(v)o(e)g(the)i(same)e(name,)i(C)p Fn(++)f Ft(deduces)h(whic)o(h)g(one)f(is)37 1685 y(required)d(b)o(y)e (its)g(actual)h(argumen)o(ts.)p eop %%Page: 10 13 10 12 bop 37 50 a Ft(10)1113 b Fo(R.)15 b(Co)q(ols,)g(D.)g(Laurie)h (and)f(L.)g(Pluym)37 199 y Fp(7)67 b(A)23 b(p)r(ossible)f(pitfall)37 301 y Ft(One)c(feature)e(of)f(the)i(automatic)f(in)o(tegrator)f (requires)i(further)f(men)o(tion.)24 b(If)16 b(y)o(ou)g(e.g.)g(create)g (a)g(trian-)37 357 y(gular)j(region)g(b)o(y)f(sa)o(ying)h Fn(TRIANGLE)k(T1\(A,B,C\))p Ft(,)16 b(then)j(the)g(pac)o(k)m(age)f (will)j(construct)d(an)g(ob)s(ject)g Fn(T1)37 414 y Ft(that)13 b(con)o(tains)h(a)f(data-store)f(to)h(b)q(e)h(used)g(to)f(store)f(all)j (regions)e(created)h(when)g(one)f(in)o(tegrates)g(o)o(v)o(er)g(the)37 470 y(triangle.)21 b(Apart)15 b(from)g(this)h(data-store,)d(the)j(ob)s (ject)f Fn(T1)g Ft(also)g(con)o(tains)g(a)g(n)o(um)o(b)q(er)h(of)f (attributes)g(\(the)37 527 y(total)e(appro)o(ximate)f(in)o(tegral)h (and)g(error)f(estimate,)h(requested)g(absolute)g(and)g(relativ)o(e)h (tolerances,)f(and)37 583 y(a)18 b(coun)o(t)g(of)f(the)h(n)o(um)o(b)q (er)g(of)f(functions)i(ev)m(aluations\))f(all)h(with)f(resp)q(ect)g(to) f(the)h(triangle)h(men)o(tioned.)37 639 y(After)c(in)o(tegration,)g (the)g(original)h(region)f(is)h(no)f(longer)g(a)o(v)m(ailable,)h(but)f (it)g(will)i(ha)o(v)o(e)e(b)q(een)h(replaced)g(b)o(y)37 696 y(a)e Fn(COMPOUND)p 269 696 15 2 v 16 w(REGION)e Ft(consisting)j(of)e(all)h(the)g(transformations)e(and)i(sub)q (divisions)i(that)d(the)h(automatic)37 752 y(in)o(tegrator)h(made.)108 809 y(The)c(adv)m(an)o(tage)f(of)g(this)h(feature)f(is)h(that)f(y)o(ou) g(can)g(no)o(w)g(con)o(tin)o(ue)h(in)o(tegrating)g(\(i.e.)f(without)g (w)o(asting)37 865 y(previous)16 b(computations\))f(if)g(y)o(ou)g (require)h(higher)f(precision:)22 b(for)14 b(example,)i(if)f(the)g(b)q (eha)o(viour)h(of)e(y)o(our)37 922 y(in)o(tegrand)22 b(is)g(unfamiliar)h(to)d(y)o(ou,)i(y)o(ou)f(will)i(b)q(e)f(able)g(to)f (assess)g(the)g(reliabili)q(t)o(y)i(of)e(the)h(computed)37 978 y(in)o(tegrals)13 b(b)o(y)f(prin)o(ting)h(them)f(out)g(for)g (requested)g(tolerances)h(of)f(10)1211 962 y Fe(\000)p Fl(2)1257 978 y Fm(;)c Ft(10)1324 962 y Fe(\000)p Fl(3)1370 978 y Fm(;)g(:)g(:)g(:)h Ft(un)o(til)14 b(y)o(ou)e(are)f(satis\014ed)37 1035 y(with)16 b(the)f(result.)21 b(Details)15 b(on)g(ho)o(w)g(this)h (can)f(b)q(e)h(done)g(are)e(giv)o(en)i(in)g Fq(x)p Ft(8.)108 1091 y(W)l(e)f(are)f(a)o(w)o(are)g(that)g(some)g(users)h(migh)o(t)g (\014nd)g(this)h(a)e(bit)h(di\016cult)i(to)d(liv)o(e)i(with)f(in)g(the) g(b)q(eginning.)37 1148 y(They)e(should)h(remem)o(b)q(er)f(that)f Fr(Cubpac)o(k)p Fn(++)g Ft(is)h(a)g(pac)o(k)m(age)f(to)g(compute)h(in)o (tegrals)g(and)g(not)g(a)f(pac)o(k)m(age)37 1204 y(to)k(manipulate)i (geometric)f(ob)s(jects.)23 b(They)17 b(should)g(k)o(eep)g(in)h(mind)f (that)f(a)g Fn(TRIANGLE)g Ft(is)h(m)o(uc)o(h)f(more)37 1260 y(than)g(just)f(the)h(geometric)f(ob)s(ject.)20 b(Compared)15 b(to)g(existing)i(F)l(ortran)d(77)h(co)q(des,)h(an)f(ob)s (ject)g Fn(TRIANGLE)37 1317 y Ft(replaces)d(at)e(least)h(6)f (parameters)g(in)h(the)g(calling)h(sequence,)g(including)i(a)c(real)h (and)f(an)h(in)o(teger)g(w)o(ork)m(arra)o(y)37 1373 y(F)l(ortran)k(77)f (users)h(ha)o(v)o(e)g(to)g(pro)o(vide.)108 1430 y(As)g(a)g(consequence) i(of)d(this)i(side-e\013ect)g(a)f(sequence)h(of)f(co)q(de)h(lik)o(e)37 1524 y Fn(TRIANGLE)23 b(T1\(A,B,C\);)37 1580 y(Integrate)g(\(f,T1\);)37 1637 y(Integrate)g(\(g,T1\);)37 1730 y Ft(will)17 b(pro)q(duce)f(an)g (error)e(\(A)o(ttempt)g(to)h(mo)q(dify)g(in)o(tegrand)h(during)g(in)o (tegration\).)108 1787 y(If)f(y)o(ou)f(need)h(a)g(cop)o(y)f(of)g(the)h (original)g(region)g(after)f(in)o(tegration)h(\(for)e(example,)i(when)g (y)o(ou)f(wish)i(to)37 1843 y(in)o(tegrate)f(another)g(function)h(o)o (v)o(er)f(the)g(same)g(region\),)g(y)o(ou)g(m)o(ust)f(construct)h(a)g (separate)g(instance.)21 b(It)37 1900 y(is)16 b(not)f(su\016cien)o(t)h (to)e(sa)o(y)37 1994 y Fn(TRIANGLE)23 b(T1\(A,B,C\),)g(T2=T1;)37 2087 y Ft(b)q(ecause)17 b(class)f Fn(COMPOUND)p 508 2087 V 16 w(REGION)f Ft(uses)h(reference)g(seman)o(tics)g(ev)o(erywhere.)21 b Fn(T2)16 b Ft(will)h(not)e(b)q(e)h(another)37 2144 y(triangle)g(with)g(the)g(same)f(sp)q(eci\014cations)i(as)e Fn(T1)g Ft(but)g(another)g(reference)h(to)f(the)g(same)g(triangle.)21 b(After)37 2200 y(calling)e Fn(Integrate\(f,T1\))c Ft(y)o(ou)i(will)h (\014nd)g(that)e Fn(T1.Integral\(\))g Ft(and)h Fn(T2.Integral\(\))e Ft(return)i(the)37 2257 y(same)i(v)m(alue.)32 b(If)19 b(either)h(of)e(the)h(t)o(w)o(o)f(ob)s(jects)g(is)i(destructed)f(or)f 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(Integrate\(COMPOUND_REGION&)k(CR,)k(...\);)151 1876 y Ft(are)15 b(allo)o(w)o(ed)h(if)f Fn(CR)g Ft(is)h(not)f(c)o(hanged)g (b)o(y)g Fk(you)p Ft(.)37 1970 y(Although)23 b(w)o(e)f(cannot)f(stop)h (y)o(ou,)h(y)o(ou)e(should)i(nev)o(er)f(c)o(hange)g(the)g(in)o(tegrand) g Fn(f)g Ft(b)q(et)o(w)o(een)g(succes-)37 2027 y(siv)o(e)c(calls)g(b)o (y)g(c)o(hanging)f(global)h(v)m(ariables)h(that)d(are)h(used)h(b)o(y)f Fn(f)p Ft(.)26 b(Remem)o(b)q(er)18 b(that)e(after)h(one)g(call)h(of)37 2083 y Fn(Integrate)e Ft(the)g(original)i(region)e(is)h(replaced)h(b)o (y)e(a)h Fn(COMPOUND)p 1178 2083 15 2 v 16 w(REGION)e Ft(consisting)j(of)e(all)h(the)f(trans-)37 2140 y(formations)f(and)g (sub)q(divisions)i(that)d(the)h(automatic)f(in)o(tegrator)g(made.)20 b Fr(Cubpac)o(k)p Fn(++)14 b Ft(detects)h(if)g(y)o(ou)37 2196 y(call)f Fn(Integrate)d Ft(with)i(suc)o(h)g(a)f Fn(COMPOUND)p 776 2196 V 16 w(REGION)g Ft(with)h(a)f(di\013eren)o(t)h (function)g(than)f(y)o(ou)h(used)g(the)f(\014rst)37 2253 y(time)k(but)g(it)f(cannot)g(detect)h(situations)g(where)f(y)o(ou)g(mo) q(dify)h(the)f(function)i(b)q(et)o(w)o(een)e(calls.)22 b(Complete)37 2309 y(examples)16 b(are)f(giv)o(en)h(in)g(the)f(\014les) i Fn(Examples/vb14.c)c Ft(and)i Fn(Examples/vb17.c)p Ft(.)p eop %%Page: 12 15 12 14 bop 37 50 a Ft(12)1113 b Fo(R.)15 b(Co)q(ols,)g(D.)g(Laurie)h (and)f(L.)g(Pluym)37 199 y Fp(9)67 b(Measuring)23 b(the)g(p)r (erformance)37 301 y Ft(If)d(y)o(ou)e(w)o(an)o(t)g(to)g(kno)o(w)g(ho)o (w)h(m)o(uc)o(h)g(w)o(ork)e Fr(Cubpac)o(k)p Fn(++)i Ft(has)f(done)h(to) g(ev)m(aluate)g(y)o(our)g(in)o(tegral,)g(y)o(ou)37 357 y(should)k(de\014ne)g(a)e(v)m(ariable)h(\(sa)o(y)f Fn(Count)p Ft(\))f(of)h(the)h(class)g Fn(EvaluationCounter)p Ft(.)36 b(This)22 b(v)m(ariable)h(can)37 414 y(b)q(e)h(though)o(t)e(of)g(as)g (a)g(stop-w)o(atc)o(h:)34 b(after)22 b(y)o(ou)g(ha)o(v)o(e)g(said)h Fn(Count.Start\(\),)g Ft(a)f(coun)o(ter)h(is)g(incre-)37 470 y(men)o(ted)c(whenev)o(er)f(a)g(function)h(ev)m(aluation)g(has)f(b) 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