C ALGORITHM 822, COLLECTED ALGORITHMS FROM ACM. C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE, C VOL. 28,NO. 4, December, 2002, P. 436--447. #! /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: # Doc/ # Doc/Makefile # Fortran77/ # Fortran77/Drivers/ # Fortran77/Drivers/Dp/ # Fortran77/Drivers/Dp/driver.f # Fortran77/Drivers/Dp/port.f # Fortran77/Drivers/Dp/res1 # Fortran77/Drivers/Dp/res2 # Fortran77/Drivers/Dp/res3 # Fortran77/Drivers/Dp/res4 # Fortran77/Src/ # Fortran77/Src/Dp/ # Fortran77/Src/Dp/src.f # Fortran77/Src/Dp/src_819.f # This archive created: Wed Apr 16 10:42:34 2003 export PATH; PATH=/bin:$PATH if test ! -d 'Doc' then mkdir 'Doc' fi cd 'Doc' if test -f 'Makefile' then echo shar: will not over-write existing file "'Makefile'" else cat << "SHAR_EOF" > 'Makefile' FFLAGS= -sloppy -C -d5 -g -temp=/tmp -u FC=epcf90 OBJS = driver.o src.o airy.f port.f res : $(OBJS) $(FC) $(FFLAGS) $(OBJS) a.out SHAR_EOF fi # end of overwriting check cd .. if test ! -d 'Fortran77' then mkdir 'Fortran77' fi cd 'Fortran77' if test ! -d 'Drivers' then mkdir 'Drivers' fi cd 'Drivers' if test ! -d 'Dp' then mkdir 'Dp' fi cd 'Dp' if test -f 'driver.f' then echo shar: will not over-write existing file "'driver.f'" else cat << "SHAR_EOF" > 'driver.f' PROGRAM SCTEST CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC TEST PROGRAM OF HIZ, GIZ. TEST OF THE ADDITION FORMULAS: CCC A) UNSCALED FUNCTIONS: CCC HI(Z+W)=SUM_K W**K/K!HI^(K)(Z) (SAME FOR GI(Z)) CCC B) SCALED FUNCTIONS: CCC HI(Z+W)=EXP((2/3)*Z**(3/2))* CCC EXP(-(2/3)*(Z+W)**(3/2))* CCC SUM_K W**K/K!HI^(K)(Z) (SAME FOR GI(Z)) CCC CCC REMEMBER THAT HI(Z) IS SCALED IN THE SECTOR |ARG(Z)|<=PI/3 CCC WHILE GI(Z) IS SCALED IN THE SECTOR PI/3<=ARG(Z)<=PI. CCC BOTH THE UNSCALED AND SCALED FUNCTIONS ARE TESTED. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC WARNING: LOSS OF RELATIVE ACCURACY FOR THE TEST OF THE CCC PHASE IS UNAVOIDABLE WHEN THE REAL OR IMAGINARY CCC PART VANISHES. CCC LOSS OF RELATIVE ACCURACY FOR THE TEST OF THE CCC MODULUS IS UNAVOIDABLE NEAR THE ZEROS OF THE CCC FUNCTION. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC WE TEST THE RELATIONS FOR Z=R*EXP(I*PHI) WHERE CCC 0<=R<=30, 0<=PHI<=PI CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION PI,X,Y,R,PH,W DOUBLE PRECISION ERRO1M,ERRO1P,ERRO2M,ERRO2P,ERRO3M, + ERRO3P,ERRO4M,ERRO4P DOUBLE PRECISION EM1MAX,EM2MAX,EM3MAX,EM4MAX,EP1MAX, + EP2MAX,EP3MAX,EP4MAX INTEGER I,J,IFAC PI=3.1415926535897932385D0 OPEN(UNIT=10,FILE='Res3',STATUS='UNKNOWN') WRITE(10,*)' ' WRITE(10,*)'TEST OF THE UNSCALED HI(Z)' WRITE(10,*)'CHECK THE FOLLOWING RELATION:' WRITE(10,*)' ' WRITE(10,*)' HI(Z+W)=SUM_K W**K/K!HI^(K)(Z) ' WRITE(10,*)' ' WRITE(10,30)'X','Y','MODULUS','PHASE' OPEN(UNIT=11,FILE='Res4',STATUS='UNKNOWN') WRITE(11,*)' ' WRITE(11,*)'TEST OF THE SCALED HI(Z)' WRITE(11,*)'CHECK THE FOLLOWING RELATION:' WRITE(11,*)' ' WRITE(11,*)' HI(Z+W)=EXP((2/3)*Z**(3/2))* ' WRITE(11,*)' EXP(-(2/3)*(Z+W)**(3/2))*' WRITE(11,*)' SUM_K W**K/K!HI^(K)(Z) ' WRITE(11,30)'X','Y','MODULUS','PHASE' OPEN(UNIT=12,FILE='Res1',STATUS='UNKNOWN') WRITE(12,*)' ' WRITE(12,*)' ' WRITE(12,*)'TEST OF THE UNSCALED GI(Z)' WRITE(12,*)'CHECK THE FOLLOWING RELATION:' WRITE(12,*)' ' WRITE(12,*)' GI(Z+W)=SUM_K W**K/K!GI^(K)(Z) ' WRITE(12,*)' ' WRITE(12,30)'X','Y','MODULUS','PHASE' OPEN(UNIT=14,FILE='Res2',STATUS='UNKNOWN') WRITE(14,*)' ' WRITE(14,*)'TEST OF THE SCALED GI(Z)' WRITE(14,*)'CHECK THE FOLLOWING RELATION:' WRITE(14,*)' ' WRITE(14,*)' GI(Z+W)=EXP((2/3)*Z**(3/2))* ' WRITE(14,*)' EXP(-(2/3)*(Z+W)**(3/2))*' WRITE(14,*)' SUM_K W**K/K!GI^(K)(Z) ' WRITE(14,30)'X','Y','MODULUS','PHASE' EM1MAX=0.D0 EM2MAX=0.D0 EM3MAX=0.D0 EM4MAX=0.D0 EP1MAX=0.D0 EP2MAX=0.D0 EP3MAX=0.D0 EP4MAX=0.D0 W=0.1D0 DO 1 I=1,300,6 R=I*0.1D0 DO 2 J=10,1800,6 PH=J*PI/1800.D0 X=R*COS(PH) Y=R*SIN(PH) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CHECK THE UNSCALED HI(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC IFAC=1 CALL HITEST(IFAC,X,Y,W,ERRO1M,ERRO1P) IF (ERRO1M.GT.EM1MAX) THEN EM1MAX=ERRO1M ENDIF IF (ERRO1P.GT.EP1MAX) THEN EP1MAX=ERRO1P ENDIF WRITE(10,33)X,Y,ERRO1M,ERRO1P IF (PH.LE.PI/3.D0) THEN CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CHECK THE SCALED HI(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC IFAC=2 CALL HITEST(IFAC,X,Y,W,ERRO2M,ERRO2P) IF (ERRO2M.GT.EM2MAX) THEN EM2MAX=ERRO2M ENDIF IF (ERRO2P.GT.EP2MAX) THEN EP2MAX=ERRO2P ENDIF WRITE(11,33)X,Y,ERRO2M,ERRO2P ENDIF CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CHECK THE UNSCALED GI(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC IFAC=1 CALL GITEST(IFAC,X,Y,W,ERRO3M,ERRO3P) IF (ERRO3M.GT.EM3MAX) THEN EM3MAX=ERRO3M ENDIF IF (ERRO3P.GT.EP3MAX) THEN EP3MAX=ERRO3P ENDIF WRITE(12,33)X,Y,ERRO3M,ERRO3P IF (R.GT.0.D0) THEN IF ((PH.GT.PI/3.D0).AND.(PH.LT.PI)) THEN CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CHECK THE SCALED GI(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC IFAC=2 CALL GITEST(IFAC,X,Y,-W,ERRO4M,ERRO4P) IF (ERRO4M.GT.EM4MAX) THEN EM4MAX=ERRO4M ENDIF IF (ERRO4P.GT.EP4MAX) THEN EP4MAX=ERRO4P ENDIF WRITE(14,33)X,Y,ERRO4M,ERRO4P ENDIF ENDIF 2 CONTINUE 1 CONTINUE WRITE(10,*)' ' WRITE(10,*)'MAXIMUM VALUE OF THE MODULUS OF THE CHECK =',EM1MAX WRITE(10,*)' ' WRITE(10,*)'MAXIMUM VALUE OF THE PHASE OF THE CHECK =',EP1MAX WRITE(11,*)' ' WRITE(11,*)'MAXIMUM VALUE OF THE MODULUS OF THE CHECK =',EM2MAX WRITE(11,*)' ' WRITE(11,*)'MAXIMUM VALUE OF THE PHASE OF THE CHECK =',EP2MAX WRITE(12,*)' ' WRITE(12,*)'MAXIMUM VALUE OF THE MODULUS OF THE CHECK =',EM3MAX WRITE(12,*)' ' WRITE(12,*)'MAXIMUM VALUE OF THE PHASE OF THE CHECK =',EP3MAX WRITE(14,*)' ' WRITE(14,*)'MAXIMUM VALUE OF THE MODULUS OF THE CHECK =',EM4MAX WRITE(14,*)' ' WRITE(14,*)'MAXIMUM VALUE OF THE PHASE OF THE CHECK =',EP4MAX 30 FORMAT(6X,A1,18X,A1,12X,A5,11X,A5) C31 FORMAT(6X,A1,18X,A1,12X,A6) 33 FORMAT(D16.9,1X,D16.9,1X,D16.9,1X,D16.9) END SUBROUTINE HITEST(IFAC,X,Y,W,ERROR1,ERROR2) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCC TEST FOR HI(Z): CCCC IFAC=1: CCCC THE TEST IS BASED ON THE ADDITION CCCC FORMULA: CCCC HI(Z+W)=SUM(K=0,INFTY)W**K/K!HI(K)(Z) CCCC IFAC=2: CCCC TEST FOR NORMALIZED FUNCTIONS. CCCC THE ADDITION FORMULA READS NOW: CCCC HI(Z+W)=EXP((2/3*Z**3/2)* CCCC (1-(1+W/Z)**(3/2)))* CCCC SUM(K=0,INFTY)W**K/K!HI(K)(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,Y,W DOUBLE PRECISION EPS,D1MACH,PI,F23,RH0,RH1,RH2,RH3,IH0,IH1, +IH2,IH3,RES,IMS,D,T,P,Q,IMSU DOUBLE PRECISION PH,PHASE,R,R2,R32,TH15,TH2,S1,C1,F23R,DF1, +DF2,S11,C11,DEX,DRE,DIMA,RZ32,RZ2 DOUBLE PRECISION W2,W3,RZW32,RDENO,RNUME,DMDENO,DRE2,DIMA2, +DRE3,DIMA3,RESU DOUBLE PRECISION DMODU1,DMODU2,DPHAS1,DPHAS2,ERROR1,ERROR2 DOUBLE PRECISION IZ2,IZ32,IZW32,IDENO,INUME INTEGER IFAC,K,N,IERROH EPS=D1MACH(3) PI=ACOS(-1.D0) F23=.6666666666666667D0 IF (IFAC.EQ.2) THEN PH=PHASE(X,Y) IF (PH.GT.PI/3.D0) THEN WRITE(*,*)'WARNING: THE TEST IS MEANINGLESS FOR H' WRITE(*,*)'Z IS OUTSIDE THE NORMALIZATION SECTOR' ENDIF ENDIF CALL HIZ(IFAC,X,Y,RH0,IH0,RH1,IH1,IERROH) IF (IFAC.EQ.1) THEN RH2=X*RH0-Y*IH0+1.D0/PI IH2=Y*RH0+X*IH0 ELSE PH=PHASE(X,Y) R=SQRT(X*X+Y*Y) R2=R*R R32=R*SQRT(R) TH15=1.5D0*PH TH2=2.D0*PH S1=SIN(TH15) C1=COS(TH15) F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(-DF1) DRE=DEX*C11 DIMA=-DEX*S11 RH2=X*RH0-Y*IH0+DRE/PI IH2=Y*RH0+X*IH0+DIMA/PI RZ32=R32*C1 IZ32=R32*S1 RZ2=R2*COS(TH2) IZ2=R2*SIN(TH2) ENDIF T=W RES=RH0+T*RH1 IMS=IH0+T*IH1 T=T*W/2.D0 RES=RES+T*RH2 IMS=IMS+T*IH2 K=0 N=3 D=1.D0 50 RH3=X*RH1-Y*IH1+(K+1)*RH0 IH3=Y*RH1+X*IH1+(K+1)*IH0 T=T*W/N N=N+1 K=K+1 P=T*RH3 Q=T*IH3 D=ABS(P)+ABS(Q) RES=RES+P IMS=IMS+Q RH0=RH1 IH0=IH1 RH1=RH2 IH1=IH2 RH2=RH3 IH2=IH3 IF (RES.NE.0) THEN IF (ABS(P/RES).GT.EPS) GOTO 50 ENDIF IF (IMS.NE.0) THEN IF (ABS(Q/IMS).GT.EPS) GOTO 50 ENDIF CALL HIZ(IFAC,X+W,Y,RH0,IH0,RH1,IH1,IERROH) IF (IFAC.EQ.2) THEN W2=W*W W3=W2*W PH=PHASE(X+W,Y) R=SQRT((X+W)*(X+W)+Y*Y) R32=R*SQRT(R) TH15=1.5D0*PH S1=SIN(TH15) C1=COS(TH15) RZW32=R32*C1 IZW32=R32*S1 RDENO=RZ32+RZW32 IDENO=IZ32+IZW32 RNUME=-(2.D0*RZ2*W+2.D0*X*W2+2.D0/3.D0*W3) INUME=-(2.D0*IZ2*W+2.D0*Y*W2) DMDENO=RDENO*RDENO+IDENO*IDENO DRE2=(RNUME*RDENO+INUME*IDENO)/DMDENO DIMA2=(INUME*RDENO-RNUME*IDENO)/DMDENO DRE3=EXP(DRE2)*COS(DIMA2) DIMA3=EXP(DRE2)*SIN(DIMA2) RESU=RES*DRE3-IMS*DIMA3 IMSU=RES*DIMA3+IMS*DRE3 RES=RESU IMS=IMSU ENDIF DMODU1=ABS(RH0)+ABS(IH0) DMODU2=ABS(RES)+ABS(IMS) DPHAS1=IH0/RH0 DPHAS2=IMS/RES IF (DMODU2.NE.0.D0) THEN ERROR1=ABS(1.D0-DMODU1/DMODU2) ENDIF IF (DPHAS2.NE.0.D0) THEN ERROR2=ABS(1.D0-DPHAS1/DPHAS2) ENDIF END SUBROUTINE GITEST(IFAC,X,Y,W,ERROR1,ERROR2) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCC TEST FOR GI(Z): CCCC IFAC=1: CCCC THE TEST IS BASED ON THE ADDITION CCCC FORMULA: CCCC GI(Z+W)=SUM(K=0,INFTY)W**K/K!GI(K)(Z) CCCC IFAC=2: CCCC TEST FOR NORMALIZED FUNCTIONS. CCCC THE ADDITION FORMULA READS NOW: CCCC GI(Z+W)=EXP(-(2/3*Z**3/2)* CCCC (1-(1+W/Z)**(3/2)))* CCCC SUM(K=0,INFTY)W**K/K!GI(K)(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,Y,W DOUBLE PRECISION EPS,D1MACH,PI,F23,RH0,RH1,RH2,RH3,IH0,IH1, +IH2,IH3,RES,IMS,D,T,P,Q,IMSU DOUBLE PRECISION PH,PHASE,R,R2,R32,TH15,TH2,S1,C1,F23R,DF1, +DF2,S11,C11,DEX,DRE,DIMA,RZ32,RZ2 DOUBLE PRECISION W2,W3,RZW32,RDENO,RNUME,DMDENO,DRE2,DIMA2, +DRE3,DIMA3,RESU DOUBLE PRECISION DMODU1,DMODU2,DPHAS1,DPHAS2,ERROR1,ERROR2 DOUBLE PRECISION IZ2,IZ32,IZW32,IDENO,INUME INTEGER IFAC,K,N,IERROH EPS=D1MACH(3) PI=ACOS(-1.D0) F23=.6666666666666667D0 IF (IFAC.EQ.2) THEN PH=PHASE(X,Y) IF (PH.LT.PI/3.D0) THEN WRITE(*,*)'WARNING: THE TEST IS MEANINGLESS FOR G' WRITE(*,*)'Z IS OUTSIDE THE NORMALIZATION SECTOR' ENDIF ENDIF CALL GIZ(IFAC,X,Y,RH0,IH0,RH1,IH1,IERROH) IF (IFAC.EQ.1) THEN RH2=X*RH0-Y*IH0-1.D0/PI IH2=Y*RH0+X*IH0 ELSE PH=PHASE(X,Y) R=SQRT(X*X+Y*Y) R2=R*R R32=R*SQRT(R) TH15=1.5D0*PH TH2=2.D0*PH S1=SIN(TH15) C1=COS(TH15) F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(DF1) DRE=DEX*C11 DIMA=DEX*S11 RH2=X*RH0-Y*IH0-DRE/PI IH2=Y*RH0+X*IH0-DIMA/PI RZ32=R32*C1 IZ32=R32*S1 RZ2=R2*COS(TH2) IZ2=R2*SIN(TH2) ENDIF T=W RES=RH0+T*RH1 IMS=IH0+T*IH1 T=T*W/2.D0 RES=RES+T*RH2 IMS=IMS+T*IH2 K=0 N=3 D=1.D0 51 RH3=X*RH1-Y*IH1+(K+1)*RH0 IH3=Y*RH1+X*IH1+(K+1)*IH0 T=T*W/N N=N+1 K=K+1 P=T*RH3 Q=T*IH3 D=ABS(P)+ABS(Q) RES=RES+P IMS=IMS+Q RH0=RH1 IH0=IH1 RH1=RH2 IH1=IH2 RH2=RH3 IH2=IH3 IF (RES.NE.0) THEN IF (ABS(P/RES).GT.EPS) GOTO 51 ENDIF IF (IMS.NE.0) THEN IF (ABS(Q/IMS).GT.EPS) GOTO 51 ENDIF CALL GIZ(IFAC,X+W,Y,RH0,IH0,RH1,IH1,IERROH) IF (IFAC.EQ.2) THEN W2=W*W W3=W2*W PH=PHASE(X+W,Y) R=SQRT((X+W)*(X+W)+Y*Y) R32=R*SQRT(R) TH15=1.5D0*PH S1=SIN(TH15) C1=COS(TH15) RZW32=R32*C1 IZW32=R32*S1 RDENO=RZ32+RZW32 IDENO=IZ32+IZW32 RNUME=(2.D0*RZ2*W+2.D0*X*W2+2.D0/3.D0*W3) INUME=(2.D0*IZ2*W+2.D0*Y*W2) DMDENO=RDENO*RDENO+IDENO*IDENO DRE2=(RNUME*RDENO+INUME*IDENO)/DMDENO DIMA2=(INUME*RDENO-RNUME*IDENO)/DMDENO DRE3=EXP(DRE2)*COS(DIMA2) DIMA3=EXP(DRE2)*SIN(DIMA2) RESU=RES*DRE3-IMS*DIMA3 IMSU=RES*DIMA3+IMS*DRE3 RES=RESU IMS=IMSU ENDIF DMODU1=ABS(RH0)+ABS(IH0) DMODU2=ABS(RES)+ABS(IMS) DPHAS1=IH0/RH0 DPHAS2=IMS/RES IF (DMODU2.NE.0.D0) THEN ERROR1=ABS(1.D0-DMODU1/DMODU2) ENDIF IF (DPHAS2.NE.0.D0) THEN ERROR2=ABS(1.D0-DPHAS1/DPHAS2) ENDIF END SHAR_EOF fi # end of overwriting check if test -f 'port.f' then echo shar: will not over-write existing file "'port.f'" else cat << "SHAR_EOF" > 'port.f' DOUBLE PRECISION FUNCTION D1MACH(I) INTEGER I C C DOUBLE-PRECISION MACHINE CONSTANTS C D1MACH( 1) = B**(EMIN-1), THE SMALLEST POSITIVE MAGNITUDE. C D1MACH( 2) = B**EMAX*(1 - B**(-T)), THE LARGEST MAGNITUDE. C D1MACH( 3) = B**(-T), THE SMALLEST RELATIVE SPACING. C D1MACH( 4) = B**(1-T), THE LARGEST RELATIVE SPACING. C D1MACH( 5) = LOG10(B) C INTEGER SMALL(2) INTEGER LARGE(2) INTEGER RIGHT(2) INTEGER DIVER(2) INTEGER LOG10(2) INTEGER SC, CRAY1(38), J COMMON /D9MACH/ CRAY1 SAVE SMALL, LARGE, RIGHT, DIVER, LOG10, SC DOUBLE PRECISION DMACH(5) EQUIVALENCE (DMACH(1),SMALL(1)) EQUIVALENCE (DMACH(2),LARGE(1)) EQUIVALENCE (DMACH(3),RIGHT(1)) EQUIVALENCE (DMACH(4),DIVER(1)) EQUIVALENCE (DMACH(5),LOG10(1)) C THIS VERSION ADAPTS AUTOMATICALLY TO MOST CURRENT MACHINES. C R1MACH CAN HANDLE AUTO-DOUBLE COMPILING, BUT THIS VERSION OF C D1MACH DOES NOT, BECAUSE WE DO NOT HAVE QUAD CONSTANTS FOR C MANY MACHINES YET. C TO COMPILE ON OLDER MACHINES, ADD A C IN COLUMN 1 C ON THE NEXT LINE DATA SC/0/ C AND REMOVE THE C FROM COLUMN 1 IN ONE OF THE SECTIONS BELOW. C CONSTANTS FOR EVEN OLDER MACHINES CAN BE OBTAINED BY C mail netlib@research.bell-labs.com C send old1mach from blas C PLEASE SEND CORRECTIONS TO dmg OR ehg@bell-labs.com. C C MACHINE CONSTANTS FOR THE HONEYWELL DPS 8/70 SERIES. C DATA SMALL(1),SMALL(2) / O402400000000, O000000000000 / C DATA LARGE(1),LARGE(2) / O376777777777, O777777777777 / C DATA RIGHT(1),RIGHT(2) / O604400000000, O000000000000 / C DATA DIVER(1),DIVER(2) / O606400000000, O000000000000 / C DATA LOG10(1),LOG10(2) / O776464202324, O117571775714 /, SC/987/ C C MACHINE CONSTANTS FOR PDP-11 FORTRANS SUPPORTING C 32-BIT INTEGERS. C DATA SMALL(1),SMALL(2) / 8388608, 0 / C DATA LARGE(1),LARGE(2) / 2147483647, -1 / C DATA RIGHT(1),RIGHT(2) / 612368384, 0 / C DATA DIVER(1),DIVER(2) / 620756992, 0 / C DATA LOG10(1),LOG10(2) / 1067065498, -2063872008 /, SC/987/ C C MACHINE CONSTANTS FOR THE UNIVAC 1100 SERIES. C DATA SMALL(1),SMALL(2) / O000040000000, O000000000000 / C DATA LARGE(1),LARGE(2) / O377777777777, O777777777777 / C DATA RIGHT(1),RIGHT(2) / O170540000000, O000000000000 / C DATA DIVER(1),DIVER(2) / O170640000000, O000000000000 / C DATA LOG10(1),LOG10(2) / O177746420232, O411757177572 /, SC/987/ C C ON FIRST CALL, IF NO DATA UNCOMMENTED, TEST MACHINE TYPES. IF (SC .NE. 987) THEN DMACH(1) = 1.D13 IF ( SMALL(1) .EQ. 1117925532 * .AND. SMALL(2) .EQ. -448790528) THEN * *** IEEE BIG ENDIAN *** SMALL(1) = 1048576 SMALL(2) = 0 LARGE(1) = 2146435071 LARGE(2) = -1 RIGHT(1) = 1017118720 RIGHT(2) = 0 DIVER(1) = 1018167296 DIVER(2) = 0 LOG10(1) = 1070810131 LOG10(2) = 1352628735 ELSE IF ( SMALL(2) .EQ. 1117925532 * .AND. SMALL(1) .EQ. -448790528) THEN * *** IEEE LITTLE ENDIAN *** SMALL(2) = 1048576 SMALL(1) = 0 LARGE(2) = 2146435071 LARGE(1) = -1 RIGHT(2) = 1017118720 RIGHT(1) = 0 DIVER(2) = 1018167296 DIVER(1) = 0 LOG10(2) = 1070810131 LOG10(1) = 1352628735 ELSE IF ( SMALL(1) .EQ. -2065213935 * .AND. SMALL(2) .EQ. 10752) THEN * *** VAX WITH D_FLOATING *** SMALL(1) = 128 SMALL(2) = 0 LARGE(1) = -32769 LARGE(2) = -1 RIGHT(1) = 9344 RIGHT(2) = 0 DIVER(1) = 9472 DIVER(2) = 0 LOG10(1) = 546979738 LOG10(2) = -805796613 ELSE IF ( SMALL(1) .EQ. 1267827943 * .AND. SMALL(2) .EQ. 704643072) THEN * *** IBM MAINFRAME *** SMALL(1) = 1048576 SMALL(2) = 0 LARGE(1) = 2147483647 LARGE(2) = -1 RIGHT(1) = 856686592 RIGHT(2) = 0 DIVER(1) = 873463808 DIVER(2) = 0 LOG10(1) = 1091781651 LOG10(2) = 1352628735 ELSE IF ( SMALL(1) .EQ. 1120022684 * .AND. SMALL(2) .EQ. -448790528) THEN * *** CONVEX C-1 *** SMALL(1) = 1048576 SMALL(2) = 0 LARGE(1) = 2147483647 LARGE(2) = -1 RIGHT(1) = 1019215872 RIGHT(2) = 0 DIVER(1) = 1020264448 DIVER(2) = 0 LOG10(1) = 1072907283 LOG10(2) = 1352628735 ELSE IF ( SMALL(1) .EQ. 815547074 * .AND. SMALL(2) .EQ. 58688) THEN * *** VAX G-FLOATING *** SMALL(1) = 16 SMALL(2) = 0 LARGE(1) = -32769 LARGE(2) = -1 RIGHT(1) = 15552 RIGHT(2) = 0 DIVER(1) = 15568 DIVER(2) = 0 LOG10(1) = 1142112243 LOG10(2) = 2046775455 ELSE DMACH(2) = 1.D27 + 1 DMACH(3) = 1.D27 LARGE(2) = LARGE(2) - RIGHT(2) IF (LARGE(2) .EQ. 64 .AND. SMALL(2) .EQ. 0) THEN CRAY1(1) = 67291416 DO 10 J = 1, 20 CRAY1(J+1) = CRAY1(J) + CRAY1(J) 10 CONTINUE CRAY1(22) = CRAY1(21) + 321322 DO 20 J = 22, 37 CRAY1(J+1) = CRAY1(J) + CRAY1(J) 20 CONTINUE IF (CRAY1(38) .EQ. SMALL(1)) THEN * *** CRAY *** CALL I1MCRY(SMALL(1), J, 8285, 8388608, 0) SMALL(2) = 0 CALL I1MCRY(LARGE(1), J, 24574, 16777215, 16777215) CALL I1MCRY(LARGE(2), J, 0, 16777215, 16777214) CALL I1MCRY(RIGHT(1), J, 16291, 8388608, 0) RIGHT(2) = 0 CALL I1MCRY(DIVER(1), J, 16292, 8388608, 0) DIVER(2) = 0 CALL I1MCRY(LOG10(1), J, 16383, 10100890, 8715215) CALL I1MCRY(LOG10(2), J, 0, 16226447, 9001388) ELSE WRITE(*,9000) STOP 779 END IF ELSE WRITE(*,9000) STOP 779 END IF END IF SC = 987 END IF * SANITY CHECK IF (DMACH(4) .GE. 1.0D0) STOP 778 IF (I .LT. 1 .OR. I .GT. 5) THEN WRITE(*,*) 'D1MACH(I): I =',I,' is out of bounds.' STOP END IF D1MACH = DMACH(I) RETURN 9000 FORMAT(/' Adjust D1MACH by uncommenting data statements'/ *' appropriate for your machine.') * /* Standard C source for D1MACH -- remove the * in column 1 */ *#include *#include *#include *double d1mach_(long *i) *{ * switch(*i){ * case 1: return DBL_MIN; * case 2: return DBL_MAX; * case 3: return DBL_EPSILON/FLT_RADIX; * case 4: return DBL_EPSILON; * case 5: return log10((double)FLT_RADIX); * } * fprintf(stderr, "invalid argument: d1mach(%ld)\n", *i); * exit(1); return 0; /* some compilers demand return values */ *} END SUBROUTINE I1MCRY(A, A1, B, C, D) **** SPECIAL COMPUTATION FOR OLD CRAY MACHINES **** INTEGER A, A1, B, C, D A1 = 16777216*B + C A = 16777216*A1 + D END SHAR_EOF fi # end of overwriting check if test -f 'res1' then echo shar: will not over-write existing file "'res1'" else cat << "SHAR_EOF" > 'res1' TEST OF THE UNSCALED GI(Z) CHECK THE FOLLOWING RELATION: GI(Z+W)=SUM_K W**K/K!GI^(K)(Z) X Y MODUL PHASE 0.999847695D-01 0.174524064D-02 0.111022302D-15 0.333066907D-15 0.999610115D-01 0.279216387D-02 0.111022302D-15 0.666133815D-15 0.999262916D-01 0.383878091D-02 0.111022302D-15 0.222044605D-15 0.998806137D-01 0.488497698D-02 0.000000000D+00 0.777156117D-15 0.998239828D-01 0.593063736D-02 0.777156117D-15 0.666133815D-15 0.997564050D-01 0.697564737D-02 0.222044605D-15 0.222044605D-15 0.996778878D-01 0.801989243D-02 0.333066907D-15 0.444089210D-15 0.995884399D-01 0.906325802D-02 0.222044605D-15 0.444089210D-15 0.994880709D-01 0.101056297D-01 0.222044605D-15 0.222044605D-15 0.993767919D-01 0.111468932D-01 0.444089210D-15 0.444089210D-15 0.992546152D-01 0.121869343D-01 0.000000000D+00 0.444089210D-15 0.991215540D-01 0.132256390D-01 0.555111512D-15 0.888178420D-15 0.989776231D-01 0.142628934D-01 0.000000000D+00 0.222044605D-15 0.988228381D-01 0.152985836D-01 0.444089210D-15 0.111022302D-15 0.986572162D-01 0.163325962D-01 0.000000000D+00 0.444089210D-15 0.984807753D-01 0.173648178D-01 0.333066907D-15 0.666133815D-15 0.982935349D-01 0.183951351D-01 0.444089210D-15 0.000000000D+00 0.980955155D-01 0.194234351D-01 0.222044605D-15 0.333066907D-15 0.978867389D-01 0.204496052D-01 0.000000000D+00 0.222044605D-15 0.976672278D-01 0.214735327D-01 0.000000000D+00 0.222044605D-15 0.974370065D-01 0.224951054D-01 0.222044605D-15 0.555111512D-15 0.971961001D-01 0.235142113D-01 0.000000000D+00 0.888178420D-15 0.969445350D-01 0.245307386D-01 0.111022302D-15 0.222044605D-15 0.966823389D-01 0.255445758D-01 0.222044605D-15 0.555111512D-15 0.964095404D-01 0.265556117D-01 0.000000000D+00 0.333066907D-15 0.961261696D-01 0.275637356D-01 0.222044605D-15 0.111022302D-14 0.958322574D-01 0.285688367D-01 0.111022302D-15 0.000000000D+00 0.955278362D-01 0.295708050D-01 0.111022302D-15 0.777156117D-15 0.952129393D-01 0.305695305D-01 0.444089210D-15 0.666133815D-15 0.948876012D-01 0.315649037D-01 0.333066907D-15 0.444089210D-15 0.945518576D-01 0.325568154D-01 0.222044605D-15 0.222044605D-15 0.942057453D-01 0.335451570D-01 0.666133815D-15 0.111022302D-14 0.938493023D-01 0.345298199D-01 0.222044605D-15 0.333066907D-15 0.934825676D-01 0.355106962D-01 0.444089210D-15 0.777156117D-15 0.931055816D-01 0.364876784D-01 0.222044605D-15 0.222044605D-15 0.927183855D-01 0.374606593D-01 0.222044605D-15 0.333066907D-15 0.923210217D-01 0.384295323D-01 0.222044605D-15 0.000000000D+00 0.919135339D-01 0.393941910D-01 0.000000000D+00 0.444089210D-15 0.914959668D-01 0.403545296D-01 0.222044605D-15 0.666133815D-15 0.910683661D-01 0.413104430D-01 0.444089210D-15 0.777156117D-15 0.906307787D-01 0.422618262D-01 0.222044605D-15 0.444089210D-15 0.901832526D-01 0.432085749D-01 0.222044605D-15 0.444089210D-15 0.897258370D-01 0.441505853D-01 0.222044605D-15 0.777156117D-15 0.892585818D-01 0.450877541D-01 0.222044605D-15 0.000000000D+00 0.887815385D-01 0.460199785D-01 0.222044605D-15 0.000000000D+00 0.882947593D-01 0.469471563D-01 0.000000000D+00 0.222044605D-15 0.877982975D-01 0.478691858D-01 0.333066907D-15 0.444089210D-15 0.872922077D-01 0.487859659D-01 0.000000000D+00 0.444089210D-15 0.867765453D-01 0.496973961D-01 0.333066907D-15 0.666133815D-15 0.862513669D-01 0.506033764D-01 0.000000000D+00 0.222044605D-15 0.857167301D-01 0.515038075D-01 0.000000000D+00 0.111022302D-15 0.851726934D-01 0.523985906D-01 0.444089210D-15 0.444089210D-15 0.846193166D-01 0.532876276D-01 0.000000000D+00 0.333066907D-15 0.840566603D-01 0.541708210D-01 0.222044605D-15 0.000000000D+00 0.834847863D-01 0.550480740D-01 0.444089210D-15 0.888178420D-15 0.829037573D-01 0.559192903D-01 0.000000000D+00 0.111022302D-15 0.823136369D-01 0.567843745D-01 0.000000000D+00 0.000000000D+00 0.817144898D-01 0.576432316D-01 0.444089210D-15 0.888178420D-15 0.811063819D-01 0.584957675D-01 0.222044605D-15 0.444089210D-15 0.804893797D-01 0.593418887D-01 0.222044605D-15 0.222044605D-15 0.798635510D-01 0.601815023D-01 0.222044605D-15 0.444089210D-15 0.792289643D-01 0.610145164D-01 0.333066907D-15 0.888178420D-15 0.785856893D-01 0.618408395D-01 0.222044605D-15 0.888178420D-15 0.779337965D-01 0.626603811D-01 0.000000000D+00 0.222044605D-15 0.772733573D-01 0.634730513D-01 0.222044605D-15 0.333066907D-15 0.766044443D-01 0.642787610D-01 0.000000000D+00 0.666133815D-15 0.759271307D-01 0.650774217D-01 0.222044605D-15 0.666133815D-15 0.752414909D-01 0.658689460D-01 0.000000000D+00 0.444089210D-15 0.745476000D-01 0.666532470D-01 0.000000000D+00 0.666133815D-15 0.738455341D-01 0.674302388D-01 0.333066907D-15 0.222044605D-15 0.731353702D-01 0.681998360D-01 0.222044605D-15 0.777156117D-15 0.724171861D-01 0.689619544D-01 0.111022302D-15 0.222044605D-15 0.716910608D-01 0.697165103D-01 0.000000000D+00 0.111022302D-15 0.709570737D-01 0.704634210D-01 0.222044605D-15 0.333066907D-15 0.702153053D-01 0.712026046D-01 0.222044605D-15 0.666133815D-15 0.694658370D-01 0.719339800D-01 0.000000000D+00 0.666133815D-15 0.687087511D-01 0.726574671D-01 0.222044605D-15 0.222044605D-15 0.679441304D-01 0.733729865D-01 0.222044605D-15 0.000000000D+00 0.671720589D-01 0.740804596D-01 0.666133815D-15 0.444089210D-15 0.663926213D-01 0.747798090D-01 0.222044605D-15 0.222044605D-15 0.656059029D-01 0.754709580D-01 0.444089210D-15 0.000000000D+00 0.648119901D-01 0.761538308D-01 0.222044605D-15 0.222044605D-15 0.640109699D-01 0.768283524D-01 0.444089210D-15 0.666133815D-15 0.632029303D-01 0.774944489D-01 0.222044605D-15 0.666133815D-15 0.623879597D-01 0.781520472D-01 0.222044605D-15 0.000000000D+00 0.615661475D-01 0.788010754D-01 0.111022302D-15 0.222044605D-15 0.607375840D-01 0.794414621D-01 0.222044605D-15 0.000000000D+00 0.599023599D-01 0.800731371D-01 0.222044605D-15 0.000000000D+00 0.590605668D-01 0.806960312D-01 0.333066907D-15 0.222044605D-15 0.582122970D-01 0.813100761D-01 0.222044605D-15 0.333066907D-15 0.573576436D-01 0.819152044D-01 0.333066907D-15 0.444089210D-15 0.564967003D-01 0.825113498D-01 0.111022302D-15 0.000000000D+00 0.556295616D-01 0.830984469D-01 0.222044605D-15 0.000000000D+00 0.547563223D-01 0.836764313D-01 0.333066907D-15 0.555111512D-15 0.538770785D-01 0.842452397D-01 0.222044605D-15 0.000000000D+00 0.529919264D-01 0.848048096D-01 0.222044605D-15 0.222044605D-15 0.521009632D-01 0.853550797D-01 0.000000000D+00 0.222044605D-15 0.512042865D-01 0.858959897D-01 0.444089210D-15 0.222044605D-15 0.503019947D-01 0.864274802D-01 0.222044605D-15 0.999200722D-15 0.493941867D-01 0.869494930D-01 0.222044605D-15 0.333066907D-15 0.484809620D-01 0.874619707D-01 0.111022302D-15 0.666133815D-15 0.475624209D-01 0.879648573D-01 0.444089210D-15 0.000000000D+00 0.466386640D-01 0.884580975D-01 0.222044605D-15 0.444089210D-15 0.457097927D-01 0.889416373D-01 0.111022302D-15 0.666133815D-15 0.447759088D-01 0.894154237D-01 0.222044605D-15 0.000000000D+00 0.438371147D-01 0.898794046D-01 0.222044605D-15 0.222044605D-15 0.428935133D-01 0.903335293D-01 0.111022302D-15 0.111022302D-15 0.419452082D-01 0.907777479D-01 0.111022302D-15 0.222044605D-15 0.409923034D-01 0.912120116D-01 0.000000000D+00 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0.555111512D-14 0.538458167D-13 -0.258012814D+02 0.143018838D+02 0.766053887D-14 0.177635684D-14 -0.259496329D+02 0.140309142D+02 0.167643677D-13 0.135447209D-13 -0.260951388D+02 0.137584059D+02 0.288657986D-14 0.350386387D-12 -0.262377830D+02 0.134843888D+02 0.115463195D-13 0.592859095D-13 -0.263775500D+02 0.132088931D+02 0.632827124D-14 0.135447209D-13 -0.265144244D+02 0.129319488D+02 0.200950367D-13 0.512923037D-13 -0.266483911D+02 0.126535864D+02 0.299760217D-13 0.421884749D-14 -0.267794356D+02 0.123738364D+02 0.306421555D-13 0.144328993D-13 -0.269075434D+02 0.120927295D+02 0.203170814D-13 0.126565425D-12 -0.270327005D+02 0.118102965D+02 0.159872116D-13 0.242028619D-13 -0.271548932D+02 0.115265683D+02 0.650590692D-13 0.255351296D-13 -0.272741080D+02 0.112415761D+02 0.222044605D-13 0.335287353D-13 -0.273903319D+02 0.109553511D+02 0.355271368D-14 0.417443857D-13 -0.275035521D+02 0.106679248D+02 0.404121181D-13 0.333066907D-12 -0.276137563D+02 0.103793286D+02 0.163202785D-13 0.555111512D-13 -0.277209323D+02 0.100895942D+02 0.223154828D-13 0.444089210D-13 -0.278250684D+02 0.979875339D+01 0.195399252D-13 0.406341627D-13 -0.279261532D+02 0.950683801D+01 0.176525461D-13 0.865973959D-14 -0.280241755D+02 0.921388010D+01 0.599520433D-14 0.197619698D-13 -0.281191247D+02 0.891991178D+01 0.116573418D-13 0.103028697D-12 -0.282109903D+02 0.862496529D+01 0.448530102D-13 0.470734562D-13 -0.282997622D+02 0.832907298D+01 0.437427872D-13 0.818567436D-12 -0.283854308D+02 0.803226729D+01 0.222044605D-14 0.270894418D-13 -0.284679866D+02 0.773458077D+01 0.177635684D-13 0.110245146D-12 -0.285474205D+02 0.743604607D+01 0.488498131D-14 0.222044605D-14 -0.286237239D+02 0.713669592D+01 0.215383267D-13 0.281996648D-13 -0.286968884D+02 0.683656315D+01 0.510702591D-14 0.170974346D-13 -0.287669060D+02 0.653568068D+01 0.297539771D-13 0.353050922D-13 -0.288337689D+02 0.623408150D+01 0.131006317D-13 0.225375274D-13 -0.288974699D+02 0.593179867D+01 0.346389584D-13 0.250910404D-12 -0.289580019D+02 0.562886536D+01 0.488498131D-14 0.532907052D-14 -0.290153584D+02 0.532531478D+01 0.399680289D-14 0.610622664D-14 -0.290695330D+02 0.502118023D+01 0.164313008D-13 0.236255460D-12 -0.291205198D+02 0.471649504D+01 0.227595720D-13 0.743849426D-14 -0.291683132D+02 0.441129263D+01 0.357491814D-13 0.999200722D-15 -0.292129080D+02 0.410560648D+01 0.252020627D-13 0.301980663D-13 -0.292542993D+02 0.379947010D+01 0.267563749D-13 0.220268248D-12 -0.292924825D+02 0.349291707D+01 0.398570066D-13 0.120570220D-12 -0.293274534D+02 0.318598099D+01 0.339728246D-13 0.279776202D-13 -0.293592083D+02 0.287869554D+01 0.144328993D-14 0.111022302D-13 -0.293877436D+02 0.257109441D+01 0.248689958D-13 0.199840144D-13 -0.294130562D+02 0.226321133D+01 0.222044605D-15 0.510702591D-14 -0.294351433D+02 0.195508006D+01 0.315303339D-13 0.421884749D-14 -0.294540025D+02 0.164673440D+01 0.166533454D-14 0.168753900D-13 -0.294696318D+02 0.133820815D+01 0.389688282D-13 0.872302230D-12 -0.294820294D+02 0.102953515D+01 0.262012634D-13 0.528466160D-13 -0.294911939D+02 0.720749256D+00 0.195399252D-13 0.152211577D-12 -0.294971245D+02 0.411884320D+00 0.239808173D-13 0.137667655D-13 -0.294998203D+02 0.102974217D+00 0.148769885D-13 0.202060590D-13 MAXIMUM VALUE OF THE MODULUS OF THE CHECK = 9.1704421834038D-14 MAXIMUM VALUE OF THE PHASE OF THE CHECK = 5.0297299658553D-10 SHAR_EOF fi # end of overwriting check if test -f 'res2' then echo shar: will not over-write existing file "'res2'" else cat << "SHAR_EOF" > 'res2' TEST OF THE SCALED GI(Z) CHECK THE FOLLOWING RELATION: GI(Z+W)=EXP((2/3)*Z**(3/2))* EXP(-(2/3)*(Z+W)**(3/2))* SUM_K W**K/K!GI^(K)(Z) X Y MODUL PHASE 0.493941867D-01 0.869494930D-01 0.000000000D+00 0.444089210D-15 0.484809620D-01 0.874619707D-01 0.111022302D-15 0.777156117D-15 0.475624209D-01 0.879648573D-01 0.111022302D-15 0.444089210D-15 0.466386640D-01 0.884580975D-01 0.444089210D-15 0.222044605D-15 0.457097927D-01 0.889416373D-01 0.444089210D-15 0.222044605D-15 0.447759088D-01 0.894154237D-01 0.000000000D+00 0.444089210D-15 0.438371147D-01 0.898794046D-01 0.888178420D-15 0.111022302D-14 0.428935133D-01 0.903335293D-01 0.222044605D-15 0.777156117D-15 0.419452082D-01 0.907777479D-01 0.222044605D-15 0.777156117D-15 0.409923034D-01 0.912120116D-01 0.111022302D-15 0.222044605D-15 0.400349033D-01 0.916362730D-01 0.222044605D-15 0.444089210D-15 0.390731128D-01 0.920504853D-01 0.111022302D-15 0.222044605D-15 0.381070376D-01 0.924546034D-01 0.222044605D-15 0.222044605D-15 0.371367836D-01 0.928485827D-01 0.222044605D-15 0.666133815D-15 0.361624570D-01 0.932323801D-01 0.222044605D-15 0.666133815D-15 0.351841648D-01 0.936059536D-01 0.222044605D-15 0.444089210D-15 0.342020143D-01 0.939692621D-01 0.555111512D-15 0.222044605D-15 0.332161132D-01 0.943222658D-01 0.222044605D-15 0.555111512D-15 0.322265695D-01 0.946649260D-01 0.222044605D-15 0.222044605D-15 0.312334919D-01 0.949972052D-01 0.444089210D-15 0.555111512D-15 0.302369891D-01 0.953190668D-01 0.555111512D-15 0.666133815D-15 0.292371705D-01 0.956304756D-01 0.444089210D-15 0.666133815D-15 0.282341457D-01 0.959313975D-01 0.444089210D-15 0.333066907D-15 0.272280247D-01 0.962217994D-01 0.444089210D-15 0.999200722D-15 0.262189179D-01 0.965016494D-01 0.444089210D-15 0.000000000D+00 0.252069358D-01 0.967709170D-01 0.000000000D+00 0.444089210D-15 0.241921896D-01 0.970295726D-01 0.444089210D-15 0.666133815D-15 0.231747903D-01 0.972775878D-01 0.444089210D-15 0.666133815D-15 0.221548498D-01 0.975149354D-01 0.111022302D-15 0.666133815D-15 0.211324796D-01 0.977415894D-01 0.444089210D-15 0.666133815D-15 0.201077921D-01 0.979575250D-01 0.222044605D-15 0.666133815D-15 0.190808995D-01 0.981627183D-01 0.222044605D-15 0.555111512D-15 0.180519145D-01 0.983571471D-01 0.222044605D-15 0.555111512D-15 0.170209499D-01 0.985407898D-01 0.444089210D-15 0.666133815D-15 0.159881188D-01 0.987136265D-01 0.444089210D-15 0.222044605D-15 0.149535343D-01 0.988756381D-01 0.000000000D+00 0.000000000D+00 0.139173101D-01 0.990268069D-01 0.222044605D-15 0.222044605D-15 0.128795597D-01 0.991671162D-01 0.000000000D+00 0.333066907D-15 0.118403968D-01 0.992965508D-01 0.111022302D-15 0.333066907D-15 0.107999356D-01 0.994150964D-01 0.111022302D-15 0.000000000D+00 0.975828998D-02 0.995227400D-01 0.222044605D-15 0.888178420D-15 0.871557427D-02 0.996194698D-01 0.111022302D-15 0.222044605D-15 0.767190281D-02 0.997052752D-01 0.444089210D-15 0.444089210D-15 0.662739004D-02 0.997801468D-01 0.222044605D-15 0.222044605D-15 0.558215050D-02 0.998440764D-01 0.222044605D-15 0.222044605D-15 0.453629881D-02 0.998970570D-01 0.444089210D-15 0.444089210D-15 0.348994967D-02 0.999390827D-01 0.444089210D-15 0.555111512D-15 0.244321782D-02 0.999701490D-01 0.222044605D-15 0.333066907D-15 0.139621803D-02 0.999902524D-01 0.222044605D-15 0.666133815D-15 0.349065142D-03 0.999993908D-01 0.111022302D-15 0.333066907D-15 -0.698126030D-03 0.999975631D-01 0.222044605D-15 0.555111512D-15 -0.174524064D-02 0.999847695D-01 0.444089210D-15 0.333066907D-15 -0.279216387D-02 0.999610115D-01 0.222044605D-15 0.122124533D-14 -0.383878091D-02 0.999262916D-01 0.000000000D+00 0.222044605D-15 -0.488497698D-02 0.998806137D-01 0.000000000D+00 0.333066907D-15 -0.593063736D-02 0.998239828D-01 0.222044605D-15 0.333066907D-15 -0.697564737D-02 0.997564050D-01 0.000000000D+00 0.888178420D-15 -0.801989243D-02 0.996778878D-01 0.111022302D-15 0.222044605D-15 -0.906325802D-02 0.995884399D-01 0.111022302D-15 0.333066907D-15 -0.101056297D-01 0.994880709D-01 0.222044605D-15 0.133226763D-14 -0.111468932D-01 0.993767919D-01 0.000000000D+00 0.222044605D-15 -0.121869343D-01 0.992546152D-01 0.000000000D+00 0.444089210D-15 -0.132256390D-01 0.991215540D-01 0.222044605D-15 0.333066907D-15 -0.142628934D-01 0.989776231D-01 0.111022302D-15 0.333066907D-15 -0.152985836D-01 0.988228381D-01 0.444089210D-15 0.444089210D-15 -0.163325962D-01 0.986572162D-01 0.222044605D-15 0.222044605D-15 -0.173648178D-01 0.984807753D-01 0.222044605D-15 0.111022302D-14 -0.183951351D-01 0.982935349D-01 0.000000000D+00 0.000000000D+00 -0.194234351D-01 0.980955155D-01 0.888178420D-15 0.144328993D-14 -0.204496052D-01 0.978867389D-01 0.222044605D-15 0.222044605D-15 -0.214735327D-01 0.976672278D-01 0.444089210D-15 0.888178420D-15 -0.224951054D-01 0.974370065D-01 0.444089210D-15 0.222044605D-15 -0.235142113D-01 0.971961001D-01 0.333066907D-15 0.000000000D+00 -0.245307386D-01 0.969445350D-01 0.666133815D-15 0.333066907D-15 -0.255445758D-01 0.966823389D-01 0.111022302D-15 0.666133815D-15 -0.265556117D-01 0.964095404D-01 0.333066907D-15 0.000000000D+00 -0.275637356D-01 0.961261696D-01 0.000000000D+00 0.222044605D-15 -0.285688367D-01 0.958322574D-01 0.222044605D-15 0.000000000D+00 -0.295708050D-01 0.955278362D-01 0.666133815D-15 0.777156117D-15 -0.305695305D-01 0.952129393D-01 0.222044605D-15 0.000000000D+00 -0.315649037D-01 0.948876012D-01 0.333066907D-15 0.666133815D-15 -0.325568154D-01 0.945518576D-01 0.222044605D-15 0.444089210D-15 -0.335451570D-01 0.942057453D-01 0.444089210D-15 0.222044605D-15 -0.345298199D-01 0.938493023D-01 0.111022302D-15 0.444089210D-15 -0.355106962D-01 0.934825676D-01 0.111022302D-14 0.177635684D-14 -0.364876784D-01 0.931055816D-01 0.444089210D-15 0.111022302D-14 -0.374606593D-01 0.927183855D-01 0.222044605D-15 0.222044605D-15 -0.384295323D-01 0.923210217D-01 0.666133815D-15 0.222044605D-15 -0.393941910D-01 0.919135339D-01 0.555111512D-15 0.222044605D-15 -0.403545296D-01 0.914959668D-01 0.111022302D-15 0.444089210D-15 -0.413104430D-01 0.910683661D-01 0.111022302D-15 0.666133815D-15 -0.422618262D-01 0.906307787D-01 0.333066907D-15 0.666133815D-15 -0.432085749D-01 0.901832526D-01 0.222044605D-15 0.666133815D-15 -0.441505853D-01 0.897258370D-01 0.000000000D+00 0.666133815D-15 -0.450877541D-01 0.892585818D-01 0.222044605D-15 0.666133815D-15 -0.460199785D-01 0.887815385D-01 0.111022302D-15 0.666133815D-15 -0.469471563D-01 0.882947593D-01 0.222044605D-15 0.222044605D-15 -0.478691858D-01 0.877982975D-01 0.222044605D-15 0.444089210D-15 -0.487859659D-01 0.872922077D-01 0.222044605D-15 0.444089210D-15 -0.496973961D-01 0.867765453D-01 0.000000000D+00 0.444089210D-15 -0.506033764D-01 0.862513669D-01 0.222044605D-15 0.666133815D-15 -0.515038075D-01 0.857167301D-01 0.222044605D-15 0.999200722D-15 -0.523985906D-01 0.851726934D-01 0.222044605D-15 0.166533454D-14 -0.532876276D-01 0.846193166D-01 0.000000000D+00 0.555111512D-15 -0.541708210D-01 0.840566603D-01 0.222044605D-15 0.444089210D-15 -0.550480740D-01 0.834847863D-01 0.222044605D-15 0.155431223D-14 -0.559192903D-01 0.829037573D-01 0.222044605D-15 0.111022302D-15 -0.567843745D-01 0.823136369D-01 0.333066907D-15 0.133226763D-14 -0.576432316D-01 0.817144898D-01 0.666133815D-15 0.666133815D-15 -0.584957675D-01 0.811063819D-01 0.222044605D-15 0.222044605D-15 -0.593418887D-01 0.804893797D-01 0.333066907D-15 0.244249065D-14 -0.601815023D-01 0.798635510D-01 0.222044605D-15 0.555111512D-15 -0.610145164D-01 0.792289643D-01 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0.115265683D+02 0.111022302D-15 0.222044605D-15 -0.272741080D+02 0.112415761D+02 0.222044605D-15 0.777156117D-15 -0.273903319D+02 0.109553511D+02 0.000000000D+00 0.222044605D-15 -0.275035521D+02 0.106679248D+02 0.333066907D-15 0.555111512D-15 -0.276137563D+02 0.103793286D+02 0.111022302D-15 0.222044605D-15 -0.277209323D+02 0.100895942D+02 0.000000000D+00 0.222044605D-15 -0.278250684D+02 0.979875339D+01 0.444089210D-15 0.222044605D-15 -0.279261532D+02 0.950683801D+01 0.222044605D-15 0.222044605D-15 -0.280241755D+02 0.921388010D+01 0.666133815D-15 0.333066907D-15 -0.281191247D+02 0.891991178D+01 0.000000000D+00 0.222044605D-15 -0.282109903D+02 0.862496529D+01 0.222044605D-15 0.222044605D-15 -0.282997622D+02 0.832907298D+01 0.444089210D-15 0.222044605D-15 -0.283854308D+02 0.803226729D+01 0.222044605D-15 0.222044605D-15 -0.284679866D+02 0.773458077D+01 0.000000000D+00 0.555111512D-15 -0.285474205D+02 0.743604607D+01 0.222044605D-15 0.444089210D-15 -0.286237239D+02 0.713669592D+01 0.000000000D+00 0.222044605D-15 -0.286968884D+02 0.683656315D+01 0.000000000D+00 0.777156117D-15 -0.287669060D+02 0.653568068D+01 0.888178420D-15 0.555111512D-15 -0.288337689D+02 0.623408150D+01 0.222044605D-15 0.777156117D-15 -0.288974699D+02 0.593179867D+01 0.777156117D-15 0.666133815D-15 -0.289580019D+02 0.562886536D+01 0.000000000D+00 0.222044605D-15 -0.290153584D+02 0.532531478D+01 0.333066907D-15 0.444089210D-15 -0.290695330D+02 0.502118023D+01 0.000000000D+00 0.222044605D-15 -0.291205198D+02 0.471649504D+01 0.111022302D-15 0.000000000D+00 -0.291683132D+02 0.441129263D+01 0.111022302D-15 0.222044605D-15 -0.292129080D+02 0.410560648D+01 0.111022302D-15 0.444089210D-15 -0.292542993D+02 0.379947010D+01 0.000000000D+00 0.000000000D+00 -0.292924825D+02 0.349291707D+01 0.000000000D+00 0.222044605D-15 -0.293274534D+02 0.318598099D+01 0.000000000D+00 0.222044605D-15 -0.293592083D+02 0.287869554D+01 0.000000000D+00 0.666133815D-15 -0.293877436D+02 0.257109441D+01 0.333066907D-15 0.666133815D-15 -0.294130562D+02 0.226321133D+01 0.111022302D-15 0.444089210D-15 -0.294351433D+02 0.195508006D+01 0.000000000D+00 0.222044605D-15 -0.294540025D+02 0.164673440D+01 0.222044605D-15 0.444089210D-15 -0.294696318D+02 0.133820815D+01 0.666133815D-15 0.222044605D-15 -0.294820294D+02 0.102953515D+01 0.444089210D-15 0.444089210D-15 -0.294911939D+02 0.720749256D+00 0.000000000D+00 0.444089210D-15 -0.294971245D+02 0.411884320D+00 0.000000000D+00 0.666133815D-15 -0.294998203D+02 0.102974217D+00 0.766053887D-13 0.106581410D-12 MAXIMUM VALUE OF THE MODULUS OF THE CHECK = 7.6605388699136D-14 MAXIMUM VALUE OF THE PHASE OF THE CHECK = 1.3080647676134D-12 SHAR_EOF fi # end of overwriting check if test -f 'res3' then echo shar: will not over-write existing file "'res3'" else cat << "SHAR_EOF" > 'res3' TEST OF THE UNSCALED HI(Z) CHECK THE FOLLOWING RELATION: HI(Z+W)=SUM_K W**K/K!HI^(K)(Z) X Y MODUL PHASE 0.999847695D-01 0.174524064D-02 0.000000000D+00 0.000000000D+00 0.999610115D-01 0.279216387D-02 0.000000000D+00 0.222044605D-15 0.999262916D-01 0.383878091D-02 0.222044605D-15 0.444089210D-15 0.998806137D-01 0.488497698D-02 0.111022302D-15 0.222044605D-15 0.998239828D-01 0.593063736D-02 0.222044605D-15 0.222044605D-15 0.997564050D-01 0.697564737D-02 0.000000000D+00 0.000000000D+00 0.996778878D-01 0.801989243D-02 0.111022302D-15 0.222044605D-15 0.995884399D-01 0.906325802D-02 0.000000000D+00 0.333066907D-15 0.994880709D-01 0.101056297D-01 0.111022302D-15 0.444089210D-15 0.993767919D-01 0.111468932D-01 0.000000000D+00 0.000000000D+00 0.992546152D-01 0.121869343D-01 0.222044605D-15 0.000000000D+00 0.991215540D-01 0.132256390D-01 0.333066907D-15 0.000000000D+00 0.989776231D-01 0.142628934D-01 0.000000000D+00 0.111022302D-15 0.988228381D-01 0.152985836D-01 0.222044605D-15 0.111022302D-15 0.986572162D-01 0.163325962D-01 0.222044605D-15 0.222044605D-15 0.984807753D-01 0.173648178D-01 0.222044605D-15 0.666133815D-15 0.982935349D-01 0.183951351D-01 0.444089210D-15 0.444089210D-15 0.980955155D-01 0.194234351D-01 0.222044605D-15 0.555111512D-15 0.978867389D-01 0.204496052D-01 0.222044605D-15 0.000000000D+00 0.976672278D-01 0.214735327D-01 0.333066907D-15 0.444089210D-15 0.974370065D-01 0.224951054D-01 0.111022302D-15 0.444089210D-15 0.971961001D-01 0.235142113D-01 0.111022302D-15 0.222044605D-15 0.969445350D-01 0.245307386D-01 0.333066907D-15 0.444089210D-15 0.966823389D-01 0.255445758D-01 0.111022302D-15 0.000000000D+00 0.964095404D-01 0.265556117D-01 0.111022302D-15 0.333066907D-15 0.961261696D-01 0.275637356D-01 0.222044605D-15 0.222044605D-15 0.958322574D-01 0.285688367D-01 0.111022302D-15 0.333066907D-15 0.955278362D-01 0.295708050D-01 0.222044605D-15 0.444089210D-15 0.952129393D-01 0.305695305D-01 0.444089210D-15 0.222044605D-15 0.948876012D-01 0.315649037D-01 0.333066907D-15 0.666133815D-15 0.945518576D-01 0.325568154D-01 0.444089210D-15 0.444089210D-15 0.942057453D-01 0.335451570D-01 0.666133815D-15 0.122124533D-14 0.938493023D-01 0.345298199D-01 0.444089210D-15 0.777156117D-15 0.934825676D-01 0.355106962D-01 0.222044605D-15 0.666133815D-15 0.931055816D-01 0.364876784D-01 0.222044605D-15 0.333066907D-15 0.927183855D-01 0.374606593D-01 0.222044605D-15 0.555111512D-15 0.923210217D-01 0.384295323D-01 0.111022302D-15 0.444089210D-15 0.919135339D-01 0.393941910D-01 0.222044605D-15 0.000000000D+00 0.914959668D-01 0.403545296D-01 0.222044605D-15 0.222044605D-15 0.910683661D-01 0.413104430D-01 0.222044605D-15 0.666133815D-15 0.906307787D-01 0.422618262D-01 0.222044605D-15 0.222044605D-15 0.901832526D-01 0.432085749D-01 0.000000000D+00 0.222044605D-15 0.897258370D-01 0.441505853D-01 0.222044605D-15 0.222044605D-15 0.892585818D-01 0.450877541D-01 0.444089210D-15 0.555111512D-15 0.887815385D-01 0.460199785D-01 0.444089210D-15 0.222044605D-15 0.882947593D-01 0.469471563D-01 0.222044605D-15 0.444089210D-15 0.877982975D-01 0.478691858D-01 0.000000000D+00 0.222044605D-15 0.872922077D-01 0.487859659D-01 0.666133815D-15 0.777156117D-15 0.867765453D-01 0.496973961D-01 0.222044605D-15 0.222044605D-15 0.862513669D-01 0.506033764D-01 0.444089210D-15 0.333066907D-15 0.857167301D-01 0.515038075D-01 0.222044605D-15 0.555111512D-15 0.851726934D-01 0.523985906D-01 0.111022302D-15 0.666133815D-15 0.846193166D-01 0.532876276D-01 0.000000000D+00 0.000000000D+00 0.840566603D-01 0.541708210D-01 0.222044605D-15 0.111022302D-15 0.834847863D-01 0.550480740D-01 0.111022302D-15 0.222044605D-15 0.829037573D-01 0.559192903D-01 0.222044605D-15 0.333066907D-15 0.823136369D-01 0.567843745D-01 0.222044605D-15 0.222044605D-15 0.817144898D-01 0.576432316D-01 0.222044605D-15 0.222044605D-15 0.811063819D-01 0.584957675D-01 0.000000000D+00 0.333066907D-15 0.804893797D-01 0.593418887D-01 0.000000000D+00 0.000000000D+00 0.798635510D-01 0.601815023D-01 0.222044605D-15 0.777156117D-15 0.792289643D-01 0.610145164D-01 0.000000000D+00 0.222044605D-15 0.785856893D-01 0.618408395D-01 0.333066907D-15 0.222044605D-15 0.779337965D-01 0.626603811D-01 0.444089210D-15 0.000000000D+00 0.772733573D-01 0.634730513D-01 0.222044605D-15 0.222044605D-15 0.766044443D-01 0.642787610D-01 0.333066907D-15 0.222044605D-15 0.759271307D-01 0.650774217D-01 0.000000000D+00 0.444089210D-15 0.752414909D-01 0.658689460D-01 0.222044605D-15 0.111022302D-15 0.745476000D-01 0.666532470D-01 0.000000000D+00 0.111022302D-15 0.738455341D-01 0.674302388D-01 0.333066907D-15 0.222044605D-15 0.731353702D-01 0.681998360D-01 0.000000000D+00 0.222044605D-15 0.724171861D-01 0.689619544D-01 0.000000000D+00 0.222044605D-15 0.716910608D-01 0.697165103D-01 0.222044605D-15 0.222044605D-15 0.709570737D-01 0.704634210D-01 0.000000000D+00 0.777156117D-15 0.702153053D-01 0.712026046D-01 0.333066907D-15 0.444089210D-15 0.694658370D-01 0.719339800D-01 0.222044605D-15 0.222044605D-15 0.687087511D-01 0.726574671D-01 0.111022302D-15 0.666133815D-15 0.679441304D-01 0.733729865D-01 0.222044605D-15 0.333066907D-15 0.671720589D-01 0.740804596D-01 0.222044605D-15 0.222044605D-15 0.663926213D-01 0.747798090D-01 0.222044605D-15 0.333066907D-15 0.656059029D-01 0.754709580D-01 0.222044605D-15 0.555111512D-15 0.648119901D-01 0.761538308D-01 0.000000000D+00 0.000000000D+00 0.640109699D-01 0.768283524D-01 0.333066907D-15 0.222044605D-15 0.632029303D-01 0.774944489D-01 0.111022302D-15 0.222044605D-15 0.623879597D-01 0.781520472D-01 0.111022302D-15 0.222044605D-15 0.615661475D-01 0.788010754D-01 0.222044605D-15 0.222044605D-15 0.607375840D-01 0.794414621D-01 0.444089210D-15 0.444089210D-15 0.599023599D-01 0.800731371D-01 0.222044605D-15 0.111022302D-15 0.590605668D-01 0.806960312D-01 0.222044605D-15 0.222044605D-15 0.582122970D-01 0.813100761D-01 0.111022302D-15 0.666133815D-15 0.573576436D-01 0.819152044D-01 0.222044605D-15 0.222044605D-15 0.564967003D-01 0.825113498D-01 0.444089210D-15 0.222044605D-15 0.556295616D-01 0.830984469D-01 0.222044605D-15 0.222044605D-15 0.547563223D-01 0.836764313D-01 0.111022302D-15 0.000000000D+00 0.538770785D-01 0.842452397D-01 0.222044605D-15 0.444089210D-15 0.529919264D-01 0.848048096D-01 0.000000000D+00 0.222044605D-15 0.521009632D-01 0.853550797D-01 0.222044605D-15 0.222044605D-15 0.512042865D-01 0.858959897D-01 0.444089210D-15 0.222044605D-15 0.503019947D-01 0.864274802D-01 0.222044605D-15 0.222044605D-15 0.493941867D-01 0.869494930D-01 0.000000000D+00 0.000000000D+00 0.484809620D-01 0.874619707D-01 0.222044605D-15 0.777156117D-15 0.475624209D-01 0.879648573D-01 0.555111512D-15 0.444089210D-15 0.466386640D-01 0.884580975D-01 0.222044605D-15 0.000000000D+00 0.457097927D-01 0.889416373D-01 0.222044605D-15 0.111022302D-14 0.447759088D-01 0.894154237D-01 0.222044605D-15 0.222044605D-15 0.438371147D-01 0.898794046D-01 0.000000000D+00 0.888178420D-15 0.428935133D-01 0.903335293D-01 0.222044605D-15 0.222044605D-15 0.419452082D-01 0.907777479D-01 0.222044605D-15 0.222044605D-15 0.409923034D-01 0.912120116D-01 0.000000000D+00 0.444089210D-15 0.400349033D-01 0.916362730D-01 0.333066907D-15 0.444089210D-15 0.390731128D-01 0.920504853D-01 0.333066907D-15 0.222044605D-15 0.381070376D-01 0.924546034D-01 0.111022302D-15 0.222044605D-15 0.371367836D-01 0.928485827D-01 0.444089210D-15 0.444089210D-15 0.361624570D-01 0.932323801D-01 0.000000000D+00 0.222044605D-15 0.351841648D-01 0.936059536D-01 0.222044605D-15 0.222044605D-15 0.342020143D-01 0.939692621D-01 0.222044605D-15 0.555111512D-15 0.332161132D-01 0.943222658D-01 0.000000000D+00 0.000000000D+00 0.322265695D-01 0.946649260D-01 0.666133815D-15 0.777156117D-15 0.312334919D-01 0.949972052D-01 0.444089210D-15 0.555111512D-15 0.302369891D-01 0.953190668D-01 0.000000000D+00 0.000000000D+00 0.292371705D-01 0.956304756D-01 0.222044605D-15 0.222044605D-15 0.282341457D-01 0.959313975D-01 0.222044605D-15 0.444089210D-15 0.272280247D-01 0.962217994D-01 0.222044605D-15 0.222044605D-15 0.262189179D-01 0.965016494D-01 0.000000000D+00 0.444089210D-15 0.252069358D-01 0.967709170D-01 0.444089210D-15 0.222044605D-15 0.241921896D-01 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0.244566084D+02 0.222044605D-15 0.333066907D-15 -0.167513905D+02 0.242825229D+02 0.222044605D-15 0.222044605D-15 -0.170047533D+02 0.241057745D+02 0.222044605D-15 0.333066907D-15 -0.172562514D+02 0.239263827D+02 0.222044605D-15 0.111022302D-15 -0.175058572D+02 0.237443670D+02 0.000000000D+00 0.888178420D-15 -0.177535432D+02 0.235597475D+02 0.222044605D-15 0.111022302D-15 -0.179992823D+02 0.233725445D+02 0.000000000D+00 0.111022302D-14 -0.182430477D+02 0.231827783D+02 0.222044605D-15 0.222044605D-15 -0.184848124D+02 0.229904700D+02 0.000000000D+00 0.111022302D-14 -0.187245501D+02 0.227956404D+02 0.222044605D-15 0.444089210D-15 -0.189622345D+02 0.225983111D+02 0.111022302D-15 0.444089210D-15 -0.191978394D+02 0.223985036D+02 0.444089210D-15 0.444089210D-15 -0.194313391D+02 0.221962398D+02 0.000000000D+00 0.444089210D-15 -0.196627079D+02 0.219915420D+02 0.000000000D+00 0.000000000D+00 -0.198919204D+02 0.217844325D+02 0.111022302D-15 0.666133815D-15 -0.201189516D+02 0.215749342D+02 0.222044605D-15 0.222044605D-15 -0.203437765D+02 0.213630699D+02 0.444089210D-15 0.666133815D-15 -0.205663705D+02 0.211488629D+02 0.000000000D+00 0.444089210D-15 -0.207867092D+02 0.209323367D+02 0.000000000D+00 0.222044605D-15 -0.210047684D+02 0.207135151D+02 0.000000000D+00 0.999200722D-15 -0.212205241D+02 0.204924219D+02 0.111022302D-15 0.000000000D+00 -0.214339528D+02 0.202690816D+02 0.000000000D+00 0.000000000D+00 -0.216450310D+02 0.200435185D+02 0.222044605D-15 0.222044605D-15 -0.218537356D+02 0.198157574D+02 0.222044605D-15 0.444089210D-15 -0.220600437D+02 0.195858233D+02 0.222044605D-15 0.000000000D+00 -0.222639326D+02 0.193537414D+02 0.222044605D-15 0.000000000D+00 -0.224653801D+02 0.191195371D+02 0.222044605D-15 0.888178420D-15 -0.226643639D+02 0.188832361D+02 0.000000000D+00 0.444089210D-15 -0.228608624D+02 0.186448644D+02 0.444089210D-15 0.000000000D+00 -0.230548539D+02 0.184044481D+02 0.000000000D+00 0.000000000D+00 -0.232463172D+02 0.181620135D+02 0.000000000D+00 0.222044605D-15 -0.234352313D+02 0.179175873D+02 0.222044605D-15 0.111022302D-14 -0.236215754D+02 0.176711962D+02 0.222044605D-15 0.111022302D-14 -0.238053292D+02 0.174228672D+02 0.222044605D-15 0.222044605D-15 -0.239864725D+02 0.171726276D+02 0.222044605D-15 0.111022302D-15 -0.241649853D+02 0.169205049D+02 0.111022302D-15 0.111022302D-15 -0.243408482D+02 0.166665266D+02 0.222044605D-15 0.000000000D+00 -0.245140418D+02 0.164107207D+02 0.111022302D-15 0.222044605D-15 -0.246845472D+02 0.161531151D+02 0.111022302D-15 0.333066907D-15 -0.248523457D+02 0.158937382D+02 0.000000000D+00 0.111022302D-14 -0.250174188D+02 0.156326183D+02 0.444089210D-15 0.111022302D-14 -0.251797485D+02 0.153697841D+02 0.222044605D-15 0.444089210D-15 -0.253393170D+02 0.151052645D+02 0.444089210D-15 0.222044605D-15 -0.254961067D+02 0.148390884D+02 0.000000000D+00 0.888178420D-15 -0.256501004D+02 0.145712851D+02 0.000000000D+00 0.666133815D-15 -0.258012814D+02 0.143018838D+02 0.000000000D+00 0.666133815D-15 -0.259496329D+02 0.140309142D+02 0.222044605D-15 0.222044605D-15 -0.260951388D+02 0.137584059D+02 0.222044605D-15 0.222044605D-15 -0.262377830D+02 0.134843888D+02 0.222044605D-15 0.444089210D-15 -0.263775500D+02 0.132088931D+02 0.222044605D-15 0.444089210D-15 -0.265144244D+02 0.129319488D+02 0.000000000D+00 0.155431223D-14 -0.266483911D+02 0.126535864D+02 0.000000000D+00 0.111022302D-15 -0.267794356D+02 0.123738364D+02 0.222044605D-15 0.333066907D-15 -0.269075434D+02 0.120927295D+02 0.000000000D+00 0.000000000D+00 -0.270327005D+02 0.118102965D+02 0.222044605D-15 0.111022302D-15 -0.271548932D+02 0.115265683D+02 0.222044605D-15 0.444089210D-15 -0.272741080D+02 0.112415761D+02 0.444089210D-15 0.222044605D-15 -0.273903319D+02 0.109553511D+02 0.222044605D-15 0.666133815D-15 -0.275035521D+02 0.106679248D+02 0.222044605D-15 0.666133815D-15 -0.276137563D+02 0.103793286D+02 0.222044605D-15 0.222044605D-15 -0.277209323D+02 0.100895942D+02 0.444089210D-15 0.888178420D-15 -0.278250684D+02 0.979875339D+01 0.222044605D-15 0.666133815D-15 -0.279261532D+02 0.950683801D+01 0.222044605D-15 0.000000000D+00 -0.280241755D+02 0.921388010D+01 0.444089210D-15 0.444089210D-15 -0.281191247D+02 0.891991178D+01 0.222044605D-15 0.888178420D-15 -0.282109903D+02 0.862496529D+01 0.222044605D-15 0.222044605D-15 -0.282997622D+02 0.832907298D+01 0.222044605D-15 0.111022302D-14 -0.283854308D+02 0.803226729D+01 0.000000000D+00 0.222044605D-15 -0.284679866D+02 0.773458077D+01 0.000000000D+00 0.222044605D-15 -0.285474205D+02 0.743604607D+01 0.000000000D+00 0.000000000D+00 -0.286237239D+02 0.713669592D+01 0.666133815D-15 0.133226763D-14 -0.286968884D+02 0.683656315D+01 0.222044605D-15 0.666133815D-15 -0.287669060D+02 0.653568068D+01 0.222044605D-15 0.444089210D-15 -0.288337689D+02 0.623408150D+01 0.222044605D-15 0.444089210D-15 -0.288974699D+02 0.593179867D+01 0.000000000D+00 0.888178420D-15 -0.289580019D+02 0.562886536D+01 0.222044605D-15 0.333066907D-15 -0.290153584D+02 0.532531478D+01 0.222044605D-15 0.000000000D+00 -0.290695330D+02 0.502118023D+01 0.000000000D+00 0.133226763D-14 -0.291205198D+02 0.471649504D+01 0.444089210D-15 0.177635684D-14 -0.291683132D+02 0.441129263D+01 0.111022302D-15 0.444089210D-15 -0.292129080D+02 0.410560648D+01 0.000000000D+00 0.266453526D-14 -0.292542993D+02 0.379947010D+01 0.222044605D-15 0.444089210D-15 -0.292924825D+02 0.349291707D+01 0.222044605D-15 0.288657986D-14 -0.293274534D+02 0.318598099D+01 0.222044605D-15 0.222044605D-14 -0.293592083D+02 0.287869554D+01 0.222044605D-15 0.111022302D-15 -0.293877436D+02 0.257109441D+01 0.000000000D+00 0.177635684D-14 -0.294130562D+02 0.226321133D+01 0.000000000D+00 0.222044605D-15 -0.294351433D+02 0.195508006D+01 0.222044605D-15 0.399680289D-14 -0.294540025D+02 0.164673440D+01 0.000000000D+00 0.111022302D-15 -0.294696318D+02 0.133820815D+01 0.444089210D-15 0.532907052D-14 -0.294820294D+02 0.102953515D+01 0.666133815D-15 0.555111512D-14 -0.294911939D+02 0.720749256D+00 0.222044605D-15 0.111022302D-15 -0.294971245D+02 0.411884320D+00 0.222044605D-15 0.199840144D-13 -0.294998203D+02 0.102974217D+00 0.222044605D-15 0.164313008D-13 MAXIMUM VALUE OF THE MODULUS OF THE CHECK = 1.0502709812954D-13 MAXIMUM VALUE OF THE PHASE OF THE CHECK = 2.5517143953380D-11 SHAR_EOF fi # end of overwriting check if test -f 'res4' then echo shar: will not over-write existing file "'res4'" else cat << "SHAR_EOF" > 'res4' TEST OF THE SCALED HI(Z) CHECK THE FOLLOWING RELATION: HI(Z+W)=EXP((2/3)*Z**(3/2))* EXP(-(2/3)*(Z+W)**(3/2))* SUM_K W**K/K!HI^(K)(Z) X Y MODUL PHASE 0.999847695D-01 0.174524064D-02 0.111022302D-15 0.666133815D-15 0.999610115D-01 0.279216387D-02 0.222044605D-15 0.444089210D-15 0.999262916D-01 0.383878091D-02 0.222044605D-15 0.155431223D-14 0.998806137D-01 0.488497698D-02 0.000000000D+00 0.111022302D-15 0.998239828D-01 0.593063736D-02 0.222044605D-15 0.444089210D-15 0.997564050D-01 0.697564737D-02 0.222044605D-15 0.666133815D-15 0.996778878D-01 0.801989243D-02 0.111022302D-15 0.155431223D-14 0.995884399D-01 0.906325802D-02 0.222044605D-15 0.199840144D-14 0.994880709D-01 0.101056297D-01 0.222044605D-15 0.666133815D-15 0.993767919D-01 0.111468932D-01 0.222044605D-15 0.444089210D-15 0.992546152D-01 0.121869343D-01 0.222044605D-15 0.666133815D-15 0.991215540D-01 0.132256390D-01 0.333066907D-15 0.555111512D-15 0.989776231D-01 0.142628934D-01 0.222044605D-15 0.111022302D-14 0.988228381D-01 0.152985836D-01 0.666133815D-15 0.999200722D-15 0.986572162D-01 0.163325962D-01 0.222044605D-15 0.000000000D+00 0.984807753D-01 0.173648178D-01 0.222044605D-15 0.199840144D-14 0.982935349D-01 0.183951351D-01 0.444089210D-15 0.444089210D-15 0.980955155D-01 0.194234351D-01 0.222044605D-15 0.144328993D-14 0.978867389D-01 0.204496052D-01 0.222044605D-15 0.666133815D-15 0.976672278D-01 0.214735327D-01 0.222044605D-15 0.888178420D-15 0.974370065D-01 0.224951054D-01 0.444089210D-15 0.666133815D-15 0.971961001D-01 0.235142113D-01 0.222044605D-15 0.666133815D-15 0.969445350D-01 0.245307386D-01 0.222044605D-15 0.155431223D-14 0.966823389D-01 0.255445758D-01 0.444089210D-15 0.222044605D-15 0.964095404D-01 0.265556117D-01 0.222044605D-15 0.133226763D-14 0.961261696D-01 0.275637356D-01 0.444089210D-15 0.333066907D-15 0.958322574D-01 0.285688367D-01 0.222044605D-15 0.777156117D-15 0.955278362D-01 0.295708050D-01 0.333066907D-15 0.222044605D-15 0.952129393D-01 0.305695305D-01 0.444089210D-15 0.888178420D-15 0.948876012D-01 0.315649037D-01 0.444089210D-15 0.888178420D-15 0.945518576D-01 0.325568154D-01 0.222044605D-15 0.111022302D-14 0.942057453D-01 0.335451570D-01 0.444089210D-15 0.199840144D-14 0.938493023D-01 0.345298199D-01 0.000000000D+00 0.444089210D-15 0.934825676D-01 0.355106962D-01 0.000000000D+00 0.888178420D-15 0.931055816D-01 0.364876784D-01 0.000000000D+00 0.144328993D-14 0.927183855D-01 0.374606593D-01 0.222044605D-15 0.999200722D-15 0.923210217D-01 0.384295323D-01 0.222044605D-15 0.888178420D-15 0.919135339D-01 0.393941910D-01 0.000000000D+00 0.222044605D-15 0.914959668D-01 0.403545296D-01 0.222044605D-15 0.666133815D-15 0.910683661D-01 0.413104430D-01 0.000000000D+00 0.133226763D-14 0.906307787D-01 0.422618262D-01 0.000000000D+00 0.999200722D-15 0.901832526D-01 0.432085749D-01 0.000000000D+00 0.888178420D-15 0.897258370D-01 0.441505853D-01 0.222044605D-15 0.133226763D-14 0.892585818D-01 0.450877541D-01 0.666133815D-15 0.999200722D-15 0.887815385D-01 0.460199785D-01 0.222044605D-15 0.666133815D-15 0.882947593D-01 0.469471563D-01 0.444089210D-15 0.666133815D-15 0.877982975D-01 0.478691858D-01 0.222044605D-15 0.000000000D+00 0.872922077D-01 0.487859659D-01 0.444089210D-15 0.122124533D-14 0.867765453D-01 0.496973961D-01 0.222044605D-15 0.222044605D-15 0.862513669D-01 0.506033764D-01 0.666133815D-15 0.444089210D-15 0.857167301D-01 0.515038075D-01 0.000000000D+00 0.777156117D-15 0.851726934D-01 0.523985906D-01 0.444089210D-15 0.288657986D-14 0.846193166D-01 0.532876276D-01 0.000000000D+00 0.000000000D+00 0.840566603D-01 0.541708210D-01 0.111022302D-15 0.666133815D-15 0.834847863D-01 0.550480740D-01 0.222044605D-15 0.888178420D-15 0.829037573D-01 0.559192903D-01 0.444089210D-15 0.122124533D-14 0.823136369D-01 0.567843745D-01 0.222044605D-15 0.888178420D-15 0.817144898D-01 0.576432316D-01 0.111022302D-15 0.222044605D-15 0.811063819D-01 0.584957675D-01 0.000000000D+00 0.999200722D-15 0.804893797D-01 0.593418887D-01 0.111022302D-15 0.122124533D-14 0.798635510D-01 0.601815023D-01 0.444089210D-15 0.144328993D-14 0.792289643D-01 0.610145164D-01 0.222044605D-15 0.888178420D-15 0.785856893D-01 0.618408395D-01 0.333066907D-15 0.222044605D-15 0.779337965D-01 0.626603811D-01 0.444089210D-15 0.111022302D-15 0.772733573D-01 0.634730513D-01 0.000000000D+00 0.888178420D-15 0.766044443D-01 0.642787610D-01 0.222044605D-15 0.666133815D-15 0.759271307D-01 0.650774217D-01 0.222044605D-15 0.111022302D-14 0.752414909D-01 0.658689460D-01 0.000000000D+00 0.333066907D-15 0.745476000D-01 0.666532470D-01 0.444089210D-15 0.999200722D-15 0.738455341D-01 0.674302388D-01 0.333066907D-15 0.111022302D-14 0.731353702D-01 0.681998360D-01 0.222044605D-15 0.444089210D-15 0.724171861D-01 0.689619544D-01 0.111022302D-15 0.111022302D-15 0.716910608D-01 0.697165103D-01 0.222044605D-15 0.666133815D-15 0.709570737D-01 0.704634210D-01 0.222044605D-15 0.188737914D-14 0.702153053D-01 0.712026046D-01 0.333066907D-15 0.444089210D-15 0.694658370D-01 0.719339800D-01 0.000000000D+00 0.999200722D-15 0.687087511D-01 0.726574671D-01 0.222044605D-15 0.155431223D-14 0.679441304D-01 0.733729865D-01 0.222044605D-15 0.144328993D-14 0.671720589D-01 0.740804596D-01 0.111022302D-15 0.111022302D-15 0.663926213D-01 0.747798090D-01 0.222044605D-15 0.166533454D-14 0.656059029D-01 0.754709580D-01 0.222044605D-15 0.222044605D-15 0.648119901D-01 0.761538308D-01 0.222044605D-15 0.122124533D-14 0.640109699D-01 0.768283524D-01 0.444089210D-15 0.666133815D-15 0.632029303D-01 0.774944489D-01 0.222044605D-15 0.111022302D-15 0.623879597D-01 0.781520472D-01 0.444089210D-15 0.111022302D-15 0.615661475D-01 0.788010754D-01 0.111022302D-15 0.111022302D-15 0.607375840D-01 0.794414621D-01 0.000000000D+00 0.555111512D-15 0.599023599D-01 0.800731371D-01 0.000000000D+00 0.222044605D-15 0.590605668D-01 0.806960312D-01 0.222044605D-15 0.000000000D+00 0.582122970D-01 0.813100761D-01 0.222044605D-15 0.888178420D-15 0.573576436D-01 0.819152044D-01 0.222044605D-15 0.777156117D-15 0.564967003D-01 0.825113498D-01 0.000000000D+00 0.222044605D-15 0.556295616D-01 0.830984469D-01 0.333066907D-15 0.333066907D-15 0.547563223D-01 0.836764313D-01 0.000000000D+00 0.222044605D-15 0.538770785D-01 0.842452397D-01 0.222044605D-15 0.111022302D-14 0.529919264D-01 0.848048096D-01 0.444089210D-15 0.222044605D-15 0.521009632D-01 0.853550797D-01 0.000000000D+00 0.666133815D-15 0.512042865D-01 0.858959897D-01 0.222044605D-15 0.888178420D-15 0.503019947D-01 0.864274802D-01 0.000000000D+00 0.222044605D-15 0.699893387D+00 0.122166845D-01 0.444089210D-15 0.131006317D-13 0.699727081D+00 0.195451471D-01 0.444089210D-15 0.766053887D-14 0.699484041D+00 0.268714664D-01 0.333066907D-15 0.177635684D-14 0.699164296D+00 0.341948389D-01 0.333066907D-15 0.532907052D-14 0.698767880D+00 0.415144615D-01 0.777156117D-15 0.133226763D-14 0.698294835D+00 0.488295316D-01 0.000000000D+00 0.532907052D-14 0.697745215D+00 0.561392470D-01 0.222044605D-15 0.333066907D-14 0.697119079D+00 0.634428061D-01 0.222044605D-15 0.432986980D-14 0.696416496D+00 0.707394080D-01 0.444089210D-15 0.632827124D-14 0.695637543D+00 0.780282525D-01 0.122124533D-14 0.131006317D-13 0.694782306D+00 0.853085404D-01 0.111022302D-15 0.488498131D-14 0.693850878D+00 0.925794732D-01 0.111022302D-15 0.777156117D-14 0.692843362D+00 0.998402536D-01 0.222044605D-15 0.821565038D-14 0.691759867D+00 0.107090085D+00 0.222044605D-15 0.999200722D-15 0.690600513D+00 0.114328174D+00 0.000000000D+00 0.244249065D-14 0.689365427D+00 0.121553724D+00 0.111022302D-14 0.102140518D-13 0.688054744D+00 0.128765945D+00 0.000000000D+00 0.128785871D-13 0.686668609D+00 0.135964046D+00 0.000000000D+00 0.888178420D-15 0.685207172D+00 0.143147236D+00 0.888178420D-15 0.643929354D-14 0.683670595D+00 0.150314729D+00 0.222044605D-15 0.188737914D-13 0.682059045D+00 0.157465738D+00 0.222044605D-15 0.139888101D-13 0.680372700D+00 0.164599479D+00 0.444089210D-15 0.377475828D-14 0.678611745D+00 0.171715170D+00 0.000000000D+00 0.577315973D-14 0.676776372D+00 0.178812031D+00 0.000000000D+00 0.188737914D-14 0.674866783D+00 0.185889282D+00 0.222044605D-15 0.466293670D-14 0.672883187D+00 0.192946149D+00 0.222044605D-15 0.599520433D-14 0.670825802D+00 0.199981857D+00 0.444089210D-15 0.488498131D-14 0.668694853D+00 0.206995635D+00 0.444089210D-15 0.544009282D-14 0.666490575D+00 0.213986713D+00 0.000000000D+00 0.943689571D-14 0.664213208D+00 0.220954326D+00 0.222044605D-15 0.111022302D-13 0.661863003D+00 0.227897708D+00 0.000000000D+00 0.510702591D-14 0.659440217D+00 0.234816099D+00 0.444089210D-15 0.899280650D-14 0.656945116D+00 0.241708739D+00 0.444089210D-15 0.173194792D-13 0.654377973D+00 0.248574874D+00 0.444089210D-15 0.488498131D-14 0.651739071D+00 0.255413749D+00 0.222044605D-15 0.555111512D-14 0.649028698D+00 0.262224615D+00 0.444089210D-15 0.666133815D-15 0.646247152D+00 0.269006726D+00 0.222044605D-15 0.510702591D-14 0.643394737D+00 0.275759337D+00 0.000000000D+00 0.133226763D-14 0.640471767D+00 0.282481707D+00 0.666133815D-15 0.126565425D-13 0.637478563D+00 0.289173101D+00 0.000000000D+00 0.113242749D-13 0.634415451D+00 0.295832783D+00 0.222044605D-15 0.255351296D-14 0.631282768D+00 0.302460024D+00 0.222044605D-15 0.621724894D-14 0.628080859D+00 0.309054097D+00 0.666133815D-15 0.777156117D-14 0.624810073D+00 0.315614278D+00 0.222044605D-15 0.888178420D-15 0.621470770D+00 0.322139849D+00 0.444089210D-15 0.821565038D-14 0.618063315D+00 0.328630094D+00 0.222044605D-15 0.222044605D-15 0.614588083D+00 0.335084301D+00 0.666133815D-15 0.499600361D-14 0.611045454D+00 0.341501761D+00 0.444089210D-15 0.632827124D-14 0.607435817D+00 0.347881773D+00 0.000000000D+00 0.355271368D-14 0.603759568D+00 0.354223635D+00 0.222044605D-15 0.999200722D-14 0.600017110D+00 0.360526652D+00 0.222044605D-15 0.444089210D-15 0.596208854D+00 0.366790134D+00 0.222044605D-15 0.106581410D-13 0.592335216D+00 0.373013393D+00 0.000000000D+00 0.888178420D-15 0.588396622D+00 0.379195747D+00 0.000000000D+00 0.117683641D-13 0.584393504D+00 0.385336518D+00 0.222044605D-15 0.432986980D-14 0.580326301D+00 0.391435032D+00 0.000000000D+00 0.421884749D-14 0.576195458D+00 0.397490622D+00 0.444089210D-15 0.399680289D-14 0.572001429D+00 0.403502621D+00 0.222044605D-15 0.488498131D-14 0.567744673D+00 0.409470372D+00 0.000000000D+00 0.444089210D-15 0.563425658D+00 0.415393221D+00 0.222044605D-15 0.444089210D-15 0.559044857D+00 0.421270516D+00 0.000000000D+00 0.266453526D-14 0.554602750D+00 0.427101615D+00 0.666133815D-15 0.377475828D-14 0.550099825D+00 0.432885877D+00 0.222044605D-15 0.155431223D-14 0.545536575D+00 0.438622668D+00 0.444089210D-15 0.288657986D-14 0.540913501D+00 0.444311359D+00 0.444089210D-15 0.155431223D-14 0.536231110D+00 0.449951327D+00 0.222044605D-15 0.166533454D-14 0.531489915D+00 0.455541952D+00 0.000000000D+00 0.333066907D-15 0.526690436D+00 0.461082622D+00 0.444089210D-15 0.266453526D-14 0.521833200D+00 0.466572729D+00 0.222044605D-15 0.488498131D-14 0.516918738D+00 0.472011671D+00 0.444089210D-15 0.688338275D-14 0.511947591D+00 0.477398852D+00 0.000000000D+00 0.688338275D-14 0.506920303D+00 0.482733681D+00 0.222044605D-15 0.133226763D-14 0.501837425D+00 0.488015572D+00 0.222044605D-15 0.544009282D-14 0.496699516D+00 0.493243947D+00 0.666133815D-15 0.288657986D-14 0.491507137D+00 0.498418232D+00 0.000000000D+00 0.222044605D-15 0.486260859D+00 0.503537860D+00 0.444089210D-15 0.666133815D-15 0.480961258D+00 0.508602270D+00 0.000000000D+00 0.000000000D+00 0.475608913D+00 0.513610905D+00 0.222044605D-15 0.177635684D-14 0.470204413D+00 0.518563217D+00 0.222044605D-15 0.155431223D-14 0.464748349D+00 0.523458663D+00 0.666133815D-15 0.588418203D-14 0.459241320D+00 0.528296706D+00 0.000000000D+00 0.555111512D-14 0.453683931D+00 0.533076815D+00 0.444089210D-15 0.266453526D-14 0.448076790D+00 0.537798467D+00 0.222044605D-15 0.266453526D-14 0.442420512D+00 0.542461142D+00 0.222044605D-15 0.333066907D-14 0.436715718D+00 0.547064331D+00 0.222044605D-15 0.666133815D-15 0.430963033D+00 0.551607528D+00 0.000000000D+00 0.544009282D-14 0.425163088D+00 0.556090234D+00 0.444089210D-15 0.233146835D-14 0.419316519D+00 0.560511960D+00 0.000000000D+00 0.244249065D-14 0.413423967D+00 0.564872219D+00 0.000000000D+00 0.666133815D-15 0.407486079D+00 0.569170533D+00 0.222044605D-15 0.466293670D-14 0.401503505D+00 0.573406431D+00 0.666133815D-15 0.244249065D-14 0.395476902D+00 0.577579449D+00 0.222044605D-15 0.133226763D-14 0.389406931D+00 0.581689128D+00 0.000000000D+00 0.255351296D-14 0.383294256D+00 0.585735019D+00 0.000000000D+00 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0.442129067D+01 0.444089210D-15 0.421884749D-14 0.285119355D+02 0.472012031D+01 0.666133815D-15 0.310862447D-14 0.284609441D+02 0.501843233D+01 0.222044605D-15 0.155431223D-14 0.284068316D+02 0.531619403D+01 0.222044605D-15 0.199840144D-14 0.283496040D+02 0.561337275D+01 0.222044605D-15 0.377475828D-14 0.282892675D+02 0.590993590D+01 0.222044605D-15 0.000000000D+00 0.282258288D+02 0.620585096D+01 0.444089210D-15 0.222044605D-14 0.281592949D+02 0.650108547D+01 0.222044605D-15 0.177635684D-14 0.280896729D+02 0.679560707D+01 0.444089210D-15 0.222044605D-14 0.280169706D+02 0.708938345D+01 0.000000000D+00 0.177635684D-14 0.279411959D+02 0.738238240D+01 0.222044605D-15 0.666133815D-15 0.278623572D+02 0.767457180D+01 0.000000000D+00 0.266453526D-14 0.277804630D+02 0.796591958D+01 0.000000000D+00 0.133226763D-14 0.276955224D+02 0.825639382D+01 0.222044605D-15 0.444089210D-15 0.276075447D+02 0.854596265D+01 0.000000000D+00 0.244249065D-14 0.275165395D+02 0.883459431D+01 0.222044605D-15 0.000000000D+00 0.274225167D+02 0.912225717D+01 0.222044605D-15 0.888178420D-15 0.273254868D+02 0.940891966D+01 0.888178420D-15 0.177635684D-14 0.272254604D+02 0.969455037D+01 0.444089210D-15 0.222044605D-14 0.271224484D+02 0.997911795D+01 0.000000000D+00 0.222044605D-15 0.270164620D+02 0.102625912D+02 0.000000000D+00 0.222044605D-14 0.269075131D+02 0.105449391D+02 0.000000000D+00 0.199840144D-14 0.267956134D+02 0.108261305D+02 0.222044605D-15 0.666133815D-15 0.266807753D+02 0.111061348D+02 0.000000000D+00 0.000000000D+00 0.265630113D+02 0.113849212D+02 0.444089210D-15 0.888178420D-15 0.264423344D+02 0.116624591D+02 0.000000000D+00 0.888178420D-15 0.263187578D+02 0.119387180D+02 0.000000000D+00 0.155431223D-14 0.261922950D+02 0.122136678D+02 0.222044605D-15 0.222044605D-14 0.260629600D+02 0.124872781D+02 0.666133815D-15 0.199840144D-14 0.259307669D+02 0.127595191D+02 0.000000000D+00 0.222044605D-15 0.257957302D+02 0.130303609D+02 0.666133815D-15 0.111022302D-15 0.256578646D+02 0.132997738D+02 0.444089210D-15 0.111022302D-14 0.255171854D+02 0.135677282D+02 0.000000000D+00 0.222044605D-15 0.253737080D+02 0.138341947D+02 0.000000000D+00 0.888178420D-15 0.252274480D+02 0.140991441D+02 0.222044605D-15 0.888178420D-15 0.250784216D+02 0.143625475D+02 0.222044605D-15 0.155431223D-14 0.249266450D+02 0.146243758D+02 0.444089210D-15 0.444089210D-15 0.247721350D+02 0.148846004D+02 0.444089210D-15 0.222044605D-15 0.246149084D+02 0.151431927D+02 0.555111512D-15 0.155431223D-14 0.244549825D+02 0.154001244D+02 0.666133815D-15 0.111022302D-14 0.242923748D+02 0.156553673D+02 0.222044605D-15 0.222044605D-15 0.241271032D+02 0.159088934D+02 0.222044605D-15 0.666133815D-15 0.239591858D+02 0.161606749D+02 0.666133815D-15 0.133226763D-14 0.237886411D+02 0.164106842D+02 0.111022302D-14 0.888178420D-15 0.236154876D+02 0.166588939D+02 0.444089210D-15 0.133226763D-14 0.234397444D+02 0.169052768D+02 0.444089210D-15 0.444089210D-15 0.232614307D+02 0.171498058D+02 0.555111512D-15 0.222044605D-15 0.230805662D+02 0.173924542D+02 0.444089210D-15 0.155431223D-14 0.228971707D+02 0.176331952D+02 0.000000000D+00 0.444089210D-15 0.227112642D+02 0.178720026D+02 0.222044605D-15 0.000000000D+00 0.225228672D+02 0.181088501D+02 0.444089210D-15 0.133226763D-14 0.223320003D+02 0.183437118D+02 0.444089210D-15 0.888178420D-15 0.221386844D+02 0.185765619D+02 0.222044605D-15 0.222044605D-15 0.219429408D+02 0.188073749D+02 0.000000000D+00 0.444089210D-15 0.217447909D+02 0.190361254D+02 0.444089210D-15 0.333066907D-15 0.215442564D+02 0.192627884D+02 0.666133815D-15 0.333066907D-15 0.213413593D+02 0.194873390D+02 0.444089210D-15 0.111022302D-14 0.211361220D+02 0.197097526D+02 0.444089210D-15 0.111022302D-14 0.209285668D+02 0.199300048D+02 0.888178420D-15 0.666133815D-15 0.207187166D+02 0.201480715D+02 0.444089210D-15 0.666133815D-15 0.205065943D+02 0.203639287D+02 0.222044605D-15 0.111022302D-14 0.202922232D+02 0.205775527D+02 0.666133815D-15 0.222044605D-15 0.200756269D+02 0.207889202D+02 0.444089210D-15 0.133226763D-14 0.198568291D+02 0.209980080D+02 0.444089210D-15 0.222044605D-15 0.196358537D+02 0.212047931D+02 0.000000000D+00 0.444089210D-15 0.194127250D+02 0.214092528D+02 0.444089210D-15 0.222044605D-15 0.191874675D+02 0.216113648D+02 0.222044605D-15 0.111022302D-15 0.189601059D+02 0.218111069D+02 0.444089210D-15 0.444089210D-15 0.187306651D+02 0.220084571D+02 0.000000000D+00 0.888178420D-15 0.184991703D+02 0.222033938D+02 0.000000000D+00 0.666133815D-15 0.182656468D+02 0.223958957D+02 0.333066907D-15 0.666133815D-15 0.180301203D+02 0.225859417D+02 0.000000000D+00 0.888178420D-15 0.177926166D+02 0.227735108D+02 0.666133815D-15 0.666133815D-15 0.175531618D+02 0.229585825D+02 0.222044605D-15 0.111022302D-14 0.173117820D+02 0.231411366D+02 0.666133815D-15 0.222044605D-15 0.170685038D+02 0.233211530D+02 0.222044605D-15 0.444089210D-15 0.168233538D+02 0.234986120D+02 0.444089210D-15 0.444089210D-15 0.165763590D+02 0.236734941D+02 0.000000000D+00 0.111022302D-14 0.163275464D+02 0.238457801D+02 0.222044605D-15 0.888178420D-15 0.160769433D+02 0.240154512D+02 0.666133815D-15 0.888178420D-15 0.158245772D+02 0.241824887D+02 0.222044605D-15 0.222044605D-15 0.155704757D+02 0.243468743D+02 0.222044605D-15 0.222044605D-15 0.153146667D+02 0.245085900D+02 0.666133815D-15 0.666133815D-15 0.150571784D+02 0.246676180D+02 0.333066907D-15 0.222044605D-15 0.147980388D+02 0.248239410D+02 0.222044605D-15 0.888178420D-15 0.145372765D+02 0.249775418D+02 0.555111512D-15 0.177635684D-14 0.294955070D+02 0.514845990D+00 0.444089210D-15 0.122124533D-14 0.294884984D+02 0.823688342D+00 0.222044605D-15 0.666133815D-15 0.294782560D+02 0.113244037D+01 0.000000000D+00 0.159872116D-13 0.294647811D+02 0.144106821D+01 0.666133815D-15 0.170974346D-13 0.294480749D+02 0.174953802D+01 0.444089210D-15 0.577315973D-14 0.294281395D+02 0.205781598D+01 0.222044605D-15 0.732747196D-14 0.294049769D+02 0.236586827D+01 0.222044605D-15 0.366373598D-14 0.293785898D+02 0.267366112D+01 0.666133815D-15 0.222044605D-14 0.293489809D+02 0.298116077D+01 0.222044605D-15 0.155431223D-14 0.293161536D+02 0.328833350D+01 0.555111512D-15 0.688338275D-14 0.292801115D+02 0.359514563D+01 0.000000000D+00 0.288657986D-14 0.292408584D+02 0.390156351D+01 0.111022302D-15 0.355271368D-14 0.291983988D+02 0.420755354D+01 0.000000000D+00 0.222044605D-14 0.291527373D+02 0.451308217D+01 0.222044605D-15 0.133226763D-14 0.291038788D+02 0.481811589D+01 0.000000000D+00 0.244249065D-14 0.290518287D+02 0.512262124D+01 0.222044605D-15 0.888178420D-15 0.289965928D+02 0.542656484D+01 0.222044605D-15 0.888178420D-15 0.289381771D+02 0.572991336D+01 0.000000000D+00 0.377475828D-14 0.288765880D+02 0.603263353D+01 0.000000000D+00 0.288657986D-14 0.288118322D+02 0.633469215D+01 0.666133815D-15 0.288657986D-14 0.287439169D+02 0.663605610D+01 0.000000000D+00 0.133226763D-14 0.286728495D+02 0.693669234D+01 0.444089210D-15 0.310862447D-14 0.285986378D+02 0.723656788D+01 0.222044605D-15 0.310862447D-14 0.285212900D+02 0.753564986D+01 0.222044605D-15 0.155431223D-14 0.284408144D+02 0.783390547D+01 0.444089210D-15 0.355271368D-14 0.283572200D+02 0.813130200D+01 0.444089210D-15 0.288657986D-14 0.282705159D+02 0.842780684D+01 0.222044605D-15 0.888178420D-15 0.281807117D+02 0.872338748D+01 0.222044605D-15 0.199840144D-14 0.280878171D+02 0.901801150D+01 0.444089210D-15 0.266453526D-14 0.279918423D+02 0.931164659D+01 0.666133815D-15 0.666133815D-15 0.278927980D+02 0.960426056D+01 0.222044605D-15 0.111022302D-14 0.277906949D+02 0.989582131D+01 0.000000000D+00 0.133226763D-14 0.276855442D+02 0.101862969D+02 0.222044605D-15 0.222044605D-15 0.275773575D+02 0.104756554D+02 0.666133815D-15 0.133226763D-14 0.274661466D+02 0.107638651D+02 0.444089210D-15 0.666133815D-15 0.273519237D+02 0.110508945D+02 0.222044605D-15 0.111022302D-14 0.272347014D+02 0.113367120D+02 0.444089210D-15 0.555111512D-15 0.271144925D+02 0.116212863D+02 0.222044605D-15 0.888178420D-15 0.269913102D+02 0.119045862D+02 0.222044605D-15 0.888178420D-15 0.268651680D+02 0.121865807D+02 0.444089210D-15 0.000000000D+00 0.267360797D+02 0.124672387D+02 0.666133815D-15 0.888178420D-15 0.266040595D+02 0.127465296D+02 0.444089210D-15 0.333066907D-15 0.264691219D+02 0.130244227D+02 0.222044605D-15 0.888178420D-15 0.263312816D+02 0.133008875D+02 0.444089210D-15 0.111022302D-14 0.261905539D+02 0.135758937D+02 0.666133815D-15 0.133226763D-14 0.260469540D+02 0.138494111D+02 0.444089210D-15 0.133226763D-14 0.259004978D+02 0.141214098D+02 0.222044605D-15 0.133226763D-14 0.257512013D+02 0.143918599D+02 0.444089210D-15 0.444089210D-15 0.255990809D+02 0.146607319D+02 0.000000000D+00 0.222044605D-15 0.254441532D+02 0.149279960D+02 0.222044605D-15 0.155431223D-14 0.252864354D+02 0.151936232D+02 0.444089210D-15 0.222044605D-15 0.251259446D+02 0.154575842D+02 0.000000000D+00 0.111022302D-14 0.249626984D+02 0.157198501D+02 0.444089210D-15 0.444089210D-15 0.247967148D+02 0.159803922D+02 0.444089210D-15 0.111022302D-14 0.246280120D+02 0.162391818D+02 0.222044605D-15 0.444089210D-15 0.244566084D+02 0.164961907D+02 0.555111512D-15 0.222044605D-15 0.242825229D+02 0.167513905D+02 0.222044605D-15 0.666133815D-15 0.241057745D+02 0.170047533D+02 0.444089210D-15 0.888178420D-15 0.239263827D+02 0.172562514D+02 0.222044605D-15 0.666133815D-15 0.237443670D+02 0.175058572D+02 0.000000000D+00 0.155431223D-14 0.235597475D+02 0.177535432D+02 0.222044605D-15 0.111022302D-14 0.233725445D+02 0.179992823D+02 0.444089210D-15 0.666133815D-15 0.231827783D+02 0.182430477D+02 0.444089210D-15 0.888178420D-15 0.229904700D+02 0.184848124D+02 0.222044605D-15 0.222044605D-15 0.227956404D+02 0.187245501D+02 0.000000000D+00 0.222044605D-15 0.225983111D+02 0.189622345D+02 0.000000000D+00 0.111022302D-14 0.223985036D+02 0.191978394D+02 0.222044605D-15 0.155431223D-14 0.221962398D+02 0.194313391D+02 0.222044605D-15 0.133226763D-14 0.219915420D+02 0.196627079D+02 0.000000000D+00 0.888178420D-15 0.217844325D+02 0.198919204D+02 0.222044605D-15 0.666133815D-15 0.215749342D+02 0.201189516D+02 0.222044605D-15 0.666133815D-15 0.213630699D+02 0.203437765D+02 0.444089210D-15 0.333066907D-15 0.211488629D+02 0.205663705D+02 0.444089210D-15 0.000000000D+00 0.209323367D+02 0.207867092D+02 0.222044605D-15 0.444089210D-15 0.207135151D+02 0.210047684D+02 0.222044605D-15 0.222044605D-15 0.204924219D+02 0.212205241D+02 0.444089210D-15 0.133226763D-14 0.202690816D+02 0.214339528D+02 0.222044605D-15 0.888178420D-15 0.200435185D+02 0.216450310D+02 0.444089210D-15 0.222044605D-15 0.198157574D+02 0.218537356D+02 0.222044605D-15 0.888178420D-15 0.195858233D+02 0.220600437D+02 0.333066907D-15 0.222044605D-15 0.193537414D+02 0.222639326D+02 0.222044605D-15 0.444089210D-15 0.191195371D+02 0.224653801D+02 0.333066907D-15 0.111022302D-14 0.188832361D+02 0.226643639D+02 0.222044605D-15 0.222044605D-15 0.186448644D+02 0.228608624D+02 0.666133815D-15 0.444089210D-15 0.184044481D+02 0.230548539D+02 0.666133815D-15 0.666133815D-15 0.181620135D+02 0.232463172D+02 0.222044605D-15 0.888178420D-15 0.179175873D+02 0.234352313D+02 0.444089210D-15 0.666133815D-15 0.176711962D+02 0.236215754D+02 0.444089210D-15 0.111022302D-15 0.174228672D+02 0.238053292D+02 0.222044605D-15 0.222044605D-15 0.171726276D+02 0.239864725D+02 0.000000000D+00 0.444089210D-15 0.169205049D+02 0.241649853D+02 0.222044605D-15 0.888178420D-15 0.166665266D+02 0.243408482D+02 0.555111512D-15 0.666133815D-15 0.164107207D+02 0.245140418D+02 0.222044605D-15 0.666133815D-15 0.161531151D+02 0.246845472D+02 0.444089210D-15 0.222044605D-15 0.158937382D+02 0.248523457D+02 0.000000000D+00 0.888178420D-15 0.156326183D+02 0.250174188D+02 0.000000000D+00 0.888178420D-15 0.153697841D+02 0.251797485D+02 0.222044605D-15 0.000000000D+00 0.151052645D+02 0.253393170D+02 0.666133815D-15 0.444089210D-15 0.148390884D+02 0.254961067D+02 0.222044605D-15 0.444089210D-15 MAXIMUM VALUE OF THE MODULUS OF THE CHECK = 1.7652546091540D-14 MAXIMUM VALUE OF THE PHASE OF THE CHECK = 2.3736568266486D-13 SHAR_EOF fi # end of overwriting check cd .. cd .. if test ! -d 'Src' then mkdir 'Src' fi cd 'Src' if test ! -d 'Dp' then mkdir 'Dp' fi cd 'Dp' if test -f 'src.f' then echo shar: will not over-write existing file "'src.f'" else cat << "SHAR_EOF" > 'src.f' SUBROUTINE AIZ(IFUN,IFAC,X0,Y0,GAIR,GAII,IERRO) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C COMPUTATION OF THE AIRY FUNCTION AI(Z) OR ITS DERIVATIVE AI'(Z) C THE CODE USES: C 1. MACLAURIN SERIES FOR |Y|<3 AND -2.615. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C INPUTS: C IFUN: C * IFUN=1, THE CODE COMPUTES AI(Z) C * IFUN=2, THE CODE COMPUTES AI'(Z) C IFAC: C * IFAC=1, THE CODE COMPUTES AI(Z) OR AI'(Z) C * IFAC=2, THE CODE COMPUTES NORMALIZED AI(Z) OR AI'(Z) C X0: REAL PART OF THE ARGUMENT Z C Y0: IMAGINARY PART OF THE ARGUMENT Z C C OUTPUTS: C GAIR: REAL PART OF AI(Z) OR AI'(Z) C GAII: IMAGINARY PART OF AI(Z) OR AI'(Z) C C IERRO: ERROR FLAG C * IERRO=0, SUCCESSFUL COMPUTATION C * IERRO=1, COMPUTATION OUT OF RANGE CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C MACHINE DEPENDENT CONSTANTS: FUNCTION D1MACH CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C ACCURACY: C C 1) SCALED AIRY FUNCTIONS: C RELATIVE ACCURACY BETTER THAN 10**(-13) EXCEPT CLOSE TO C THE ZEROS, WHERE 10**(-13) IS THE ABSOLUTE PRECISION. C GRADUAL LOSS OF PRECISION TAKES PLACE FOR |Z|>1000 C (REACHING 10**(-8) ABSOLUTE ACCURACY FOR |Z| CLOSE C TO 10**(6)) IN THE CASE OF PHASE(Z) CLOSE TO PI OR -PI. C 2) UNSCALED AIRY FUNCTIONS: C THE FUNCTION OVERFLOWS/UNDERFLOWS FOR C 3/2*|Z|**(3/2)>LOG(OVER). C FOR |Z|<30: C A) RELATIVE ACCURACY FOR THE MODULUS (EXCEPT AT THE C ZEROS) BETTER THAN 10**(-13). C B) ABSOLUTE ACCURACY FOR MIN(R(Z),1/R(Z)) BETTER C THAN 10**(-13), WHERE R(Z)=REAL(AI)/IMAG(AI) C OR R(Z)=REAL(AI')/IMAG(AI'). C FOR |Z|>30, GRADUAL LOSS OF PRECISION TAKES PLACE C AS |Z| INCREASES. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C AUTHORS: C AMPARO GIL (U. AUTONOMA DE MADRID, MADRID, SPAIN). C E-MAIL: AMPARO.GIL@UAM.ES C JAVIER SEGURA (U. CARLOS III DE MADRID, MADRID, SPAIN). C E-MAIL: JSEGURA@MATH.UC3M.ES C NICO M. TEMME (CWI, AMSTERDAM, THE NETHERLANDS). C E-MAIL: NICO.TEMME@CWI.NL CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C REFERENCES: C COMPUTING AIRY FUNCTIONS BY NUMERICAL QUADRATURE. C NUMERICAL ALGORITHMS (2002). C A. GIL, J. SEGURA, N.M. TEMME CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X0,Y0,GAIR,GAII,X,W,XD,WD DOUBLE PRECISION OVER,UNDER,DL1,DL2,COVER,D1MACH DOUBLE PRECISION PI,PIHAL,PIH3,PISR,A,ALF,THET,R,TH15,S1,C1, * R32,FACTO,TH025,S3,C3,F23,PI23,SQRT3,XA,YA,F23R,DF1,DF2, * S11,C11,DEX,DRE,DIMA,GAR,GAI,C,S,U,V,V0,AR,AI,AR1,AI1, * RO,COE1,COE2,REX,DFR,DFI,AR11,AI11,PHASE INTEGER IFUN,IFAC,IERRO,IEXPF,IEXPF2,N DIMENSION X(25),W(25) DIMENSION XD(25),WD(25) COMMON/PARAM1/PI,PIHAL COMMON/PARAM2/PIH3,PISR,A,ALF COMMON/PARAM3/THET,R,TH15,S1,C1,R32 COMMON/PARAM4/FACTO,TH025,S3,C3 SAVE X,W SAVE XD,WD DATA X,W/.283891417994567679D-1,.170985378860034935D0, *.435871678341770460D0,.823518257913030858D0,1.33452543254227372D0, *1.96968293206435071D0,2.72998134002859938D0,3.61662161916100897D0, *4.63102611052654146D0,5.77485171830547694D0,7.05000568630218682D0, *8.45866437513237792D0,10.0032955242749393D0,11.6866845947722423D0, *13.5119659344693551D0,15.4826596959377140D0,17.6027156808069112D0, *19.8765656022785451D0,22.3091856773962780D0,24.9061720212974207D0, *27.6738320739497190D0,30.6192963295084111D0,33.7506560850239946D0, *37.0771349708391198D0,40.6093049694341322D0,.143720408803313866D0, *.230407559241880881D0,.242253045521327626D0,.203636639103440807D0, *.143760630622921410D0,.869128834706078120D-1,.4541750018329 * 15883D-1,.206118031206069497D-1,.814278821268606972D-2,.280266 *075663377634D-2,.840337441621719716D-3,.219303732907765020D-3, *.497401659009257760D-4,.978508095920717661D-5,.166542824603725 *563D-5,.244502736801316287D-6,.308537034236207072D-7,.3332960 *72940112245D-8,.306781892316295828D-9,.239331309885375719D-10, *.157294707710054952D-11,.864936011664392267D-13,.394819815 *638647111D-14,.148271173082850884D-15,.453390377327054458D-17/ DATA XD,WD/.435079659953445D-1,.205779160144678D0, *.489916161318751D0,.896390483211727D0,1.42582496737580D0, *2.07903190767599D0,2.85702335104978D0,3.76102058198275D0, *4.79246521225895D0,5.95303247470003D0,7.24464710774066D0, *8.66950223642504D0,10.2300817341775D0,11.9291866622602D0, *13.7699665302828D0,15.7559563095946D0,17.8911203751898D0, *20.1799048700978D0,22.6273004064466D0,25.2389175786164D0, *28.0210785229929D0,30.9809287996116D0,34.1265753192057D0, *37.4672580871163D0,41.0135664833476D0,.576354557898966D-1, *.139560003272262D0,.187792315011311D0,.187446935256946D0, *.150716717316301D0,.101069904453380D0,.575274105486025D-1, *.280625783448681D-1,.117972164134041D-1,.428701743297432D-2, *.134857915232883D-2,.367337337105948D-3,.865882267841931D-4, *.176391622890609D-4,.309929190938078D-5,.468479653648208D-6, *.607273267228907D-7,.672514812555074D-8,.633469931761606D-9, *.504938861248542D-10,.338602527895834D-11,.189738532450555D-12, *.881618802142698D-14,.336676636121976D-15,.104594827170761D-16/ CC CONSTANTS CCCCCCCCCCCCCCCCCCCCCCC PI=3.1415926535897932385D0 PIHAL=1.5707963267948966192D0 PIH3=4.71238898038469D0 F23=.6666666666666666D0 PI23=2.09439510239320D0 PISR=1.77245385090552D0 SQRT3=1.7320508075688772935D0 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC YA=Y0 XA=X0 IERRO=0 IEXPF=0 IEXPF2=0 IF (YA.LT.0.D0) YA=-YA R=SQRT(XA*XA+YA*YA) R32=R*SQRT(R) THET=PHASE(XA,YA) COVER=2.D0/3.D0*R32*ABS(COS(1.5D0*THET)) CCC MACHINE DEPENDENT CONSTANT (OVERFLOW NUMBER) OVER=D1MACH(2)*1.D-4 CCC MACHINE DEPENDENT CONSTANT (UNDERFLOW NUMBER) UNDER=D1MACH(1)*1.D+4 DL1=LOG(OVER) DL2=-LOG(UNDER) IF (DL1.GT.DL2) OVER=1/UNDER IF (IFAC.EQ.1) THEN IF (COVER.GE.LOG(OVER)) THEN CCC OVERFLOW/UNDERFLOW PROBLEMS. CCC CALCULATION ABORTED IERRO=1 GAIR=0 GAII=0 ENDIF IF (COVER.GE.(LOG(OVER)*0.2)) IEXPF2=1 ELSE IF (COVER.GE.(LOG(OVER)*0.2)) IEXPF=1 ENDIF IF (IERRO.EQ.0) THEN IF (IFUN.EQ.1) THEN CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CALCULATION OF AI(Z) CCCCCCCCCCCCCCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCCCCCCCCCC SERIES, INTEGRALS OR EXPANSIONS CCCCCCCCCCCCCCCCCCCCCCCC IF ((YA.LT.3.D0).AND.(XA.LT.1.3D0).AND.(XA.GT.-2.6D0)) THEN CCC SERIES CCC CALL SERAI(XA,YA,GAR,GAI) IF (IFAC.EQ.2) THEN THET=PHASE(XA,YA) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(DF1) DRE=DEX*C11 DIMA=DEX*S11 GAIR=DRE*GAR-DIMA*GAI GAII=DRE*GAI+DIMA*GAR ELSE GAIR=GAR GAII=GAI IF (Y0.EQ.0.) GAII=0.D0 ENDIF ELSE IF (R.GT.15.D0) THEN CCC ASYMPTOTIC EXPANSIONS CCC THET=PHASE(XA,YA) FACTO=0.5D0/PISR*R**(-0.25D0) IF (THET.GT.PI23) THEN CCCCCCCCCCC CONNECTION FORMULAE CCCCCCCCCCCCCCCCCCCCCCCCCC CCC N= 1: TRANSFORM Z TO W= U+IV=Z EXP( 2 PI I/3) N=1 C=-0.5D0 S=N*0.5*SQRT3 U=XA*C-YA*S V=XA*S+YA*C V0=V IF (V.LT.0.D0) V=-V THET=PHASE(U,V) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL EXPAI(AR1,AI1) IF (V0.LT.0.D0) AI1=-AI1 AR=-(C*AR1-S*AI1) AI=-(S*AR1+C*AI1) IF (IEXPF.EQ.0) THEN IF (IEXPF2.EQ.0) THEN CCC N=-1: TRANSFORM Z TO W= U+IV=Z EXP(-2 PI I/3) N=-1 C=-0.5D0 S=N*0.5*SQRT3 U=XA*C-YA*S V=XA*S+YA*C V0=V IF (V.LT.0.D0) V=-V THET=PHASE(U,V) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL EXPAI(AR1,AI1) IF (V0.LT.0.D0) AI1=-AI1 THET=PHASE(XA,YA) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) RO=1.333333333333333D0*R32 COE1=RO*C1 COE2=RO*S1 REX=EXP(COE1) DFR=REX*COS(COE2) DFI=REX*SIN(COE2) AR11=DFR*AR1-DFI*AI1 AI11=DFR*AI1+DFI*AR1 GAIR=AR-(C*AR11-S*AI11) GAII=AI-(S*AR11+C*AI11) ELSE THET=PHASE(XA,YA) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) GAIR=AR GAII=AI ENDIF ELSE GAIR=AR GAII=AI ENDIF ELSE CCCCCCC ASYMPTOTIC EXPANSION CCCCCCCCCCCCCCC THET=PHASE(XA,YA) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL EXPAI(GAIR,GAII) ENDIF ELSE CCC INTEGRALS A=0.1666666666666666D0 ALF=-A FACTO=0.280514117723058D0*R**(-0.25D0) THET=PHASE(XA,YA) IF (THET.LE.PIHAL) THEN TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL AIRY1(X,W,GAIR,GAII) ENDIF IF ((THET.GT.PIHAL).AND.(THET.LE.PI23)) THEN TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL AIRY2(X,W,GAIR,GAII) ENDIF IF (THET.GT.PI23) THEN N=1 C=-0.5D0 S=N*0.5*SQRT3 U=XA*C-YA*S V=XA*S+YA*C V0=V IF (V.LT.0.D0) V=-V THET=PHASE(U,V) IF (THET.LE.PIHAL) THEN TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL AIRY1(X,W,AR1,AI1) ENDIF IF ((THET.GT.PIHAL).AND.(THET.LE.PI23)) THEN TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL AIRY2(X,W,AR1,AI1) ENDIF IF (V0.LT.0.D0) AI1=-AI1 AR=-(C*AR1-S*AI1) AI=-(S*AR1+C*AI1) N=-1 C=-0.5D0 S=N*0.5*SQRT3 U=XA*C-YA*S V=XA*S+YA*C V0=V IF (V.LT.0.D0) V=-V THET=PHASE(U,V) IF (THET.LE.PIHAL) THEN TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL AIRY1(X,W,AR1,AI1) ENDIF IF ((THET.GT.PIHAL).AND.(THET.LE.PI23)) THEN TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL AIRY2(X,W,AR1,AI1) ENDIF IF (V0.LT.0.D0) AI1=-AI1 THET=PHASE(XA,YA) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) RO=1.333333333333333D0*R32 COE1=RO*C1 COE2=RO*S1 REX=EXP(COE1) DFR=REX*COS(COE2) DFI=REX*SIN(COE2) AR11=DFR*AR1-DFI*AI1 AI11=DFR*AI1+DFI*AR1 GAIR=AR-(C*AR11-S*AI11) GAII=AI-(S*AR11+C*AI11) ENDIF ENDIF IF (IFAC.EQ.1) THEN CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CALCULATION OF THE UNSCALED AI(Z) CCCCCCCCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(-DF1) DRE=DEX*C11 DIMA=-DEX*S11 GAR=DRE*GAIR-DIMA*GAII GAI=DRE*GAII+DIMA*GAIR GAIR=GAR GAII=GAI IF (Y0.EQ.0.) GAII=0.D0 ENDIF ENDIF ELSE CCCC CALCULATION OF AI´(Z) CCCCCCCCCCC ALF=0.1666666666666666D0 FACTO=-0.270898621247918D0*R**0.25D0 CCCCCCCCCCCCCCC SERIES OR INTEGRALS CCCCCCCCCCCCCCCCCCCCCCCCCC IF ((YA.LT.3.D0).AND.(XA.LT.1.3D0).AND.(XA.GT.-2.6D0)) THEN CCC SERIES CALL SERAID(XA,YA,GAR,GAI) IF (IFAC.EQ.2) THEN THET=PHASE(XA,YA) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(DF1) DRE=DEX*C11 DIMA=DEX*S11 GAIR=DRE*GAR-DIMA*GAI GAII=DRE*GAI+DIMA*GAR ELSE GAIR=GAR GAII=GAI IF (Y0.EQ.0.) GAII=0.D0 ENDIF ELSE IF (R.GT.15.D0) THEN CCC ASYMPTOTIC EXPANSIONS CCCCCCCCCCCCC THET=PHASE(XA,YA) FACTO=0.5D0/PISR*R**0.25D0 IF (THET.GT.PI23) THEN CCCCCCC CONNECTION FORMULAE CCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC N= 1: TRANSFORM Z TO W= U+IV=Z EXP( 2 PI I/3) N=1 C=-0.5D0 S=N*0.5*SQRT3 U=XA*C-YA*S V=XA*S+YA*C V0=V IF (V.LT.0.D0) V=-V THET=PHASE(U,V) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL EXPAID(AR1,AI1) IF (V0.LT.0.D0) AI1=-AI1 AR=-(C*AR1+S*AI1) AI=-(-S*AR1+C*AI1) IF (IEXPF.EQ.0) THEN IF (IEXPF2.EQ.0) THEN CCC N=-1: TRANSFORM Z TO W= U+IV=Z EXP(-2 PI I/3) N=-1 C=-0.5D0 S=N*0.5*SQRT3 U=XA*C-YA*S V=XA*S+YA*C V0=V IF (V.LT.0.D0) V=-V THET=PHASE(U,V) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL EXPAID(AR1,AI1) IF (V0.LT.0.D0) AI1=-AI1 THET=PHASE(XA,YA) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) RO=1.333333333333333D0*R32 COE1=RO*C1 COE2=RO*S1 REX=EXP(COE1) DFR=REX*COS(COE2) DFI=REX*SIN(COE2) AR11=DFR*AR1-DFI*AI1 AI11=DFR*AI1+DFI*AR1 GAIR=AR-(C*AR11+S*AI11) GAII=AI-(-S*AR11+C*AI11) ELSE THET=PHASE(XA,YA) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) GAIR=AR GAII=AI ENDIF ELSE GAIR=AR GAII=AI ENDIF ELSE TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL EXPAID(GAIR,GAII) ENDIF ELSE CCC INTEGRALS CCCCCCCCCCCCCCCC THET=PHASE(XA,YA) IF (THET.LE.PIHAL) THEN TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL AIRY1D(XD,WD,GAIR,GAII) ENDIF IF ((THET.GT.PIHAL).AND.(THET.LE.PI23)) THEN TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL AIRY2D(XD,WD,GAIR,GAII) ENDIF IF (THET.GT.PI23) THEN N=1 C=-0.5D0 S=N*0.5*SQRT3 U=XA*C-YA*S V=XA*S+YA*C V0=V IF (V.LT.0.D0) V=-V THET=PHASE(U,V) IF (THET.LE.PIHAL) THEN TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL AIRY1D(XD,WD,AR1,AI1) ENDIF IF ((THET.GT.PIHAL).AND.(THET.LE.PI23)) THEN TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL AIRY2D(XD,WD,AR1,AI1) ENDIF IF (V0.LT.0.D0) AI1=-AI1 AR=-(C*AR1+S*AI1) AI=-(-S*AR1+C*AI1) N=-1 C=-0.5D0 S=N*0.5*SQRT3 U=XA*C-YA*S V=XA*S+YA*C V0=V IF (V.LT.0.D0) V=-V THET=PHASE(U,V) IF (THET.LE.PIHAL) THEN TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL AIRY1D(XD,WD,AR1,AI1) ENDIF IF ((THET.GT.PIHAL).AND.(THET.LE.PI23)) THEN TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) TH025=THET*0.25D0 S3=SIN(TH025) C3=COS(TH025) CALL AIRY2D(XD,WD,AR1,AI1) ENDIF IF (V0.LT.0.D0) AI1=-AI1 THET=PHASE(XA,YA) TH15=1.5D0*THET S1=SIN(TH15) C1=COS(TH15) RO=1.333333333333333D0*R32 COE1=RO*C1 COE2=RO*S1 REX=EXP(COE1) DFR=REX*COS(COE2) DFI=REX*SIN(COE2) AR11=DFR*AR1-DFI*AI1 AI11=DFR*AI1+DFI*AR1 GAIR=AR-(C*AR11+S*AI11) GAII=AI-(-S*AR11+C*AI11) ENDIF ENDIF IF (IFAC.EQ.1) THEN CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CALCULATION OF THE UNSCALED AI'(z) CCCCCCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(-DF1) DRE=DEX*C11 DIMA=-DEX*S11 GAR=DRE*GAIR-DIMA*GAII GAI=DRE*GAII+DIMA*GAIR GAIR=GAR GAII=GAI IF (Y0.EQ.0) GAII=0.D0 ENDIF ENDIF ENDIF ENDIF IF (Y0.LT.0.D0) GAII=-GAII RETURN END SUBROUTINE AIRY1(X,W,GAIR,GAII) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC COMPUTES AI(Z) BY GAUSS-LAGUERRE QUADRATURE IN THE SECTOR C CCC 0 <= PHASE(Z) <= PI/2 C CCC C CCC INPUTS: C CCC X,W, NODES AND WEIGHTS FOR THE GAUSSIAN C CCC QUADRATURE C CCC OUTPUTS: C CCC GAIR, GAII, REAL AND IMAGINARY PARTS OF AI(Z) C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,W,GAIR,GAII DOUBLE PRECISION PIH3,PISR,A,ALF,THET,R,TH15,S1,C1, * R32,FACTO,TH025,S3,C3,SUMAR,SUMAI,DF1,DF1C1,PHI,PHI6, * S2,C2,DMODU,DMODU2,FUNR,FUNI,FAC1,FAC2,PHASE INTEGER I DIMENSION X(25),W(25) COMMON/PARAM2/PIH3,PISR,A,ALF COMMON/PARAM3/THET,R,TH15,S1,C1,R32 COMMON/PARAM4/FACTO,TH025,S3,C3 SUMAR=0.D0 SUMAI=0.D0 DO 1 I=1,25 DF1=1.5D0*X(I)/R32 DF1C1=DF1*C1 PHI=PHASE(2.D0+DF1C1,DF1*S1) PHI6=PHI/6.D0 S2=SIN(PHI6) C2=COS(PHI6) DMODU=SQRT(4.D0+DF1*DF1+4.D0*DF1C1) DMODU2=DMODU**ALF FUNR=DMODU2*C2 FUNI=DMODU2*S2 SUMAR=SUMAR+W(I)*FUNR SUMAI=SUMAI+W(I)*FUNI 1 CONTINUE FAC1=FACTO*C3 FAC2=FACTO*S3 GAIR=FAC1*SUMAR+FAC2*SUMAI GAII=FAC1*SUMAI-FAC2*SUMAR RETURN END SUBROUTINE AIRY2(X,W,GAIR,GAII) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC COMPUTES AI(Z) BY GAUSS-LAGUERRE QUADRATURE IN THE SECTOR C CCC PI/2 < PHASE(Z) <= 2PI/3 C CCC C CCC INPUTS: C CCC X,W, NODES AND WEIGHTS FOR THE GAUSSIAN C CCC QUADRATURE C CCC OUTPUTS: C CCC GAIR, GAII, REAL AND IMAGINARY PARTS OF AI(Z) C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,W,GAIR,GAII DOUBLE PRECISION PIH3,PISR,A,ALF,THET,R,TH15,S1,C1, * R32,FACTO,TH025,S3,C3,SUMAR,SUMAI,DF1,DF1C1,PHI,PHI6, * S2,C2,DMODU,DMODU2,FUNR,FUNI,FAC1,FAC2,PHASE DOUBLE PRECISION SQR2,SQR2I,TAU,TGTAU,B,ANG,CTAU,CFAC,CT,ST, * SUMR,SUMI,TTAU,BETA INTEGER I DIMENSION X(25),W(25) COMMON/PARAM2/PIH3,PISR,A,ALF COMMON/PARAM3/THET,R,TH15,S1,C1,R32 COMMON/PARAM4/FACTO,TH025,S3,C3 SQR2=1.41421356237310D0 SQR2I=0.707106781186548D0 TAU=TH15-PIH3*0.5D0 TGTAU=DTAN(TAU) B=5.D0*A ANG=TAU*B CTAU=COS(TAU) CFAC=CTAU**(-B) CT=COS(ANG) ST=SIN(ANG) SUMR=0.D0 SUMI=0.D0 DO 2 I=1,25 DF1=3.D0*X(I)/(CTAU*R32) DF1C1=DF1*SQR2I*0.5D0 PHI=PHASE(2.D0-DF1C1,DF1C1) PHI6=PHI/6.D0 TTAU=X(I)*TGTAU BETA=PHI6-TTAU S2=SIN(BETA) C2=COS(BETA) DMODU=SQRT(4.D0+DF1*DF1*0.25D0-SQR2*DF1) DMODU2=DMODU**ALF FUNR=DMODU2*C2 FUNI=DMODU2*S2 SUMR=SUMR+W(I)*FUNR SUMI=SUMI+W(I)*FUNI 2 CONTINUE SUMAR=CFAC*(CT*SUMR-ST*SUMI) SUMAI=CFAC*(CT*SUMI+ST*SUMR) FAC1=FACTO*C3 FAC2=FACTO*S3 GAIR=FAC1*SUMAR+FAC2*SUMAI GAII=FAC1*SUMAI-FAC2*SUMAR RETURN END SUBROUTINE AIRY1D(X,W,GAIR,GAII) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC COMPUTES AI'(Z) BY GAUSS-LAGUERRE QUADRATURE IN THE SECTOR C CCC 0 <= PHASE(Z) <= PI/2 C CCC C CCC INPUTS: C CCC X,W, NODES AND WEIGHTS FOR THE GAUSSIAN C CCC QUADRATURE C CCC OUTPUTS: C CCC GAIR,GAII, REAL AND IMAGINARY PARTS OF AI'(Z) C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,W,GAIR,GAII DOUBLE PRECISION PIH3,PISR,A,ALF,THET,R,TH15,S1,C1, * R32,FACTO,TH025,S3,C3,SUMAR,SUMAI,DF1,DF1C1,PHI,PHI6, * S2,C2,DMODU,DMODU2,FUNR,FUNI,FAC1,FAC2,PHASE INTEGER I DIMENSION X(25),W(25) COMMON/PARAM2/PIH3,PISR,A,ALF COMMON/PARAM3/THET,R,TH15,S1,C1,R32 COMMON/PARAM4/FACTO,TH025,S3,C3 SUMAR=0.D0 SUMAI=0.D0 DO 3 I=1,25 DF1=1.5D0*X(I)/R32 DF1C1=DF1*C1 PHI=PHASE(2.D0+DF1C1,DF1*S1) PHI6=-PHI*ALF S2=SIN(PHI6) C2=COS(PHI6) DMODU=SQRT(4.D0+DF1*DF1+4.D0*DF1C1) DMODU2=DMODU**ALF FUNR=DMODU2*C2 FUNI=DMODU2*S2 SUMAR=SUMAR+W(I)*FUNR SUMAI=SUMAI+W(I)*FUNI 3 CONTINUE FAC1=FACTO*C3 FAC2=FACTO*S3 GAIR=FAC1*SUMAR-FAC2*SUMAI GAII=FAC1*SUMAI+FAC2*SUMAR RETURN END SUBROUTINE AIRY2D(X,W,GAIR,GAII) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC COMPUTES AI'(Z) BY GAUSS-LAGUERRE QUADRATURE IN THE SECTOR C CCC PI/2 < PHASE(Z) <= 3PI/2 C CCC C CCC INPUTS: C CCC X,W, NODES AND WEIGHTS FOR THE GAUSSIAN C CCC QUADRATURE C CCC OUTPUTS: C CCC GAIR,GAII, REAL AND IMAGINARY PARTS OF AI'(Z) C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,W,GAIR,GAII DOUBLE PRECISION PIH3,PISR,A,ALF,THET,R,TH15,S1,C1, * R32,FACTO,TH025,S3,C3,SUMAR,SUMAI,DF1,DF1C1,PHI,PHI6, * S2,C2,DMODU,DMODU2,FUNR,FUNI,FAC1,FAC2,PHASE DOUBLE PRECISION SQR2,SQR2I,TAU,TGTAU,B,ANG,CTAU,CFAC,CT,ST, * SUMR,SUMI,TTAU,BETA INTEGER I DIMENSION X(25),W(25) COMMON/PARAM2/PIH3,PISR,A,ALF COMMON/PARAM3/THET,R,TH15,S1,C1,R32 COMMON/PARAM4/FACTO,TH025,S3,C3 SQR2=1.41421356237310D0 SQR2I=0.707106781186548D0 TAU=TH15-PIH3*0.5D0 TGTAU=DTAN(TAU) B=7.D0*ALF ANG=TAU*B CTAU=COS(TAU) CFAC=CTAU**(-B) CT=COS(ANG) ST=SIN(ANG) SUMR=0.D0 SUMI=0.D0 DO 4 I=1,25 DF1=3.D0*X(I)/(CTAU*R32) DF1C1=DF1*SQR2I*0.5D0 PHI=PHASE(2.D0-DF1C1,DF1C1) PHI6=-PHI/6.D0 TTAU=X(I)*TGTAU BETA=PHI6-TTAU S2=SIN(BETA) C2=COS(BETA) DMODU=SQRT(4.D0+DF1*DF1*0.25D0-SQR2*DF1) DMODU2=DMODU**ALF FUNR=DMODU2*C2 FUNI=DMODU2*S2 SUMR=SUMR+W(I)*FUNR SUMI=SUMI+W(I)*FUNI 4 CONTINUE SUMAR=CFAC*(CT*SUMR-ST*SUMI) SUMAI=CFAC*(CT*SUMI+ST*SUMR) FAC1=FACTO*C3 FAC2=FACTO*S3 GAIR=FAC1*SUMAR-FAC2*SUMAI GAII=FAC1*SUMAI+FAC2*SUMAR RETURN END DOUBLE PRECISION FUNCTION PHASE(X,Y) DOUBLE PRECISION PI,PIHAL,X,Y,AY,P CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC COMPUTES THE PHASE OF Z = X + IY, IN (-PI,PI] CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC COMMON/PARAM1/PI,PIHAL IF ((X.EQ.0).AND.(Y.EQ.0)) THEN P=0.D0 ELSE AY=ABS(Y) IF (X.GE.AY) THEN P=ATAN(AY/X) ELSEIF ((X+AY).GE.0.D0) THEN P=PIHAL-ATAN(X/AY) ELSE P=PI+ATAN(AY/X) ENDIF IF (Y.LT.0.D0) P=-P ENDIF PHASE=P END SUBROUTINE FGP(X,Y,EPS,FR,FI,GR,GI) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C COMPUTES THE FUNCTIONS F AND G FOR THE SERIES C C OF AI'(Z). C C THIS ROUTINE IS CALLED BY SERAID. C C C C INPUTS: C C X,Y, REAL AND IMAGINARY PARTS OF Z C C EPS, PRECISION FOR THE COMPUTATION OF C C THE SERIES C C OUTPUTS: C C FR,FI, REAL AND IMAGINARY PARTS OF F C C GR,GI, REAL AND IMAGINARY PARTS OF G C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,Y,EPS,FR,FI,GR,GI INTEGER A,B,K3 DOUBLE PRECISION X2,Y2,U,V,P,Q,CR,CI,DR,DI X2=X*X Y2=Y*Y K3=0 U=X*(X2-3*Y2) V=Y*(3*X2-Y2) CR=0.5D0 CI=0.D0 DR=1.D0 DI=0.D0 FR=0.5D0 FI=0.D0 GR=1.D0 GI=0.D0 70 A=(K3+5)*(K3+3) B=(K3+1)*(K3+3) P=(U*CR-V*CI)/A Q=(V*CR+U*CI)/A CR=P CI=Q P=(U*DR-V*DI)/B Q=(V*DR+U*DI)/B DR=P DI=Q FR=FR+CR FI=FI+CI GR=GR+DR GI=GI+DI K3=K3+3 IF ((ABS(CR)+ABS(DR)+ABS(CI)+ABS(DI)).GE.EPS) GOTO 70 U=X2-Y2 V=2.D0*X*Y P=U*FR-V*FI Q=U*FI+V*FR FR=P FI=Q RETURN END SUBROUTINE FG(X,Y,EPS,FR,FI,GR,GI) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C COMPUTES THE FUNCTIONS F AND G IN EXPRESSION C C 10.4.2 OF ABRAMOWITZ & STEGUN FOR THE SERIES C C OF AI(Z). C C THIS ROUTINE IS CALLED BY SERAI. C C C C INPUTS: C C X,Y, REAL AND IMAGINARY PARTS OF Z C C EPS, PRECISION FOR THE COMPUTATION C C OF THE SERIES. C C OUTPUTS: C C FR,FI, REAL AND IMAGINARY PARTS OF F C C GR,GI, REAL AND IMAGINARY PARTS OF G C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC INTEGER A,B,K3 DOUBLE PRECISION X2,Y2,U,V,P,Q,CR,CI,DR,DI DOUBLE PRECISION X,Y,EPS,FR,FI,GR,GI X2=X*X Y2=Y*Y K3=0 U=X*(X2-3.D0*Y2) V=Y*(3.D0*X2-Y2) CR=1.D0 CI=0.D0 DR=1.D0 DI=0.D0 FR=1.D0 FI=0.D0 GR=1.D0 GI=0.D0 71 A=(K3+2)*(K3+3) B=(K3+4)*(K3+3) P=(U*CR-V*CI)/A Q=(V*CR+U*CI)/A CR=P CI=Q P=(U*DR-V*DI)/B Q=(V*DR+U*DI)/B DR=P DI=Q FR=FR+CR FI=FI+CI GR=GR+DR GI=GI+DI K3=K3+3 IF ((ABS(CR)+ABS(DR)+ABS(CI)+ABS(DI)).GE.EPS) GOTO 71 P=X*GR-Y*GI Q=X*GI+Y*GR GR=P GI=Q RETURN END SUBROUTINE SERAI(X,Y,AIR,AII) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC AIRY AI(Z), TAYLOR, COMPLEX Z CCC CCC CCC CCC INPUTS: CCC CCC X,Y, REAL AND IMAGINARY CCC CCC PARTS OF Z CCC CCC OUTPUTS: CCC CCC AIR,AII, REAL AND IMAGINARY CCC CCC PARTS OF AI(Z) CCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,Y,EPS,AIR,AII DOUBLE PRECISION FZR,FZI,GZR,GZI,CONS1,CONS2 DOUBLE PRECISION D1MACH EPS=D1MACH(3) IF (EPS.LT.1.D-15) EPS=1.D-15 CONS1=0.355028053887817239260D0 CONS2=0.258819403792806798405D0 CALL FG(X,Y,EPS,FZR,FZI,GZR,GZI) AIR=CONS1*FZR-CONS2*GZR AII=CONS1*FZI-CONS2*GZI RETURN END SUBROUTINE SERAID(X,Y,AIR,AII) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC AIRY AI'(Z), TAYLOR, COMPLEX Z CCC CCC CCC CCC INPUTS: CCC CCC X,Y, REAL AND IMAGINARY CCC CCC PARTS OF Z CCC CCC OUTPUTS: CCC CCC AIR,AII, REAL AND IMAGINARY CCC CCC PARTS OF AI'(Z) CCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,Y,EPS,AIR,AII DOUBLE PRECISION FZR,FZI,GZR,GZI,CONS1,CONS2 DOUBLE PRECISION D1MACH EPS=D1MACH(3) IF (EPS.LT.1.D-15) EPS=1.D-15 CONS1=0.355028053887817239260D0 CONS2=0.258819403792806798405D0 CALL FGP(X,Y,EPS,FZR,FZI,GZR,GZI) AIR=CONS1*FZR-CONS2*GZR AII=CONS1*FZI-CONS2*GZI RETURN END SUBROUTINE EXPAI(GAIR,GAII) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC AIRY AI(Z), ASYMPTOTIC EXPANSION, COMPLEX Z CCC CCC CCC CCC OUTPUTS: CCC CCC GAIR, GAII, REAL AND IMAGINARY CCC CCC PARTS OF AI(Z) CCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION EPS,GAIR,GAII DOUBLE PRECISION THET,R,TH15,S1, * C1,R32,FACTO,TH025,S3,C3 DOUBLE PRECISION DF1,PSIIR,PSIII,CK,DFRR,DFII,SUMAR,SUMAI, * DFR,DFI,DELTAR,DELTAI,FAC1,FAC2 DOUBLE PRECISION CO,DF DOUBLE PRECISION D1MACH INTEGER K DIMENSION CO(20) COMMON/PARAM3/THET,R,TH15,S1,C1,R32 COMMON/PARAM4/FACTO,TH025,S3,C3 SAVE CO DATA CO/-6.944444444444445D-2,3.713348765432099D-2, * -3.799305912780064D-2,5.764919041266972D-2,-0.116099064025515D0, * 0.291591399230751D0,-0.877666969510017D0,3.07945303017317D0, * -12.3415733323452D0,55.6227853659171D0,-278.465080777603D0, * 1533.16943201280D0,-9207.20659972641D0,59892.5135658791D0, * -419524.875116551D0,3148257.41786683D0,-25198919.8716024D0, * 214288036.963680D0,-1929375549.18249D0,18335766937.8906D0/ EPS=D1MACH(3) IF (EPS.LT.1.D-15) EPS=1.D-15 DF1=1.5D0/R32 PSIIR=C1 PSIII=-S1 K=0 CK=1.D0 DF=1.D0 DFRR=1.D0 DFII=0.D0 SUMAR=1.D0 SUMAI=0.D0 80 DF=DF*DF1 CK=CO(K+1)*DF DFR=DFRR DFI=DFII DFRR=DFR*PSIIR-DFI*PSIII DFII=DFR*PSIII+DFI*PSIIR DELTAR=DFRR*CK DELTAI=DFII*CK SUMAR=SUMAR+DELTAR SUMAI=SUMAI+DELTAI K=K+1 IF (SUMAR.NE.0) THEN IF (ABS(DELTAR/SUMAR).GT.EPS) GOTO 80 ENDIF IF (SUMAI.NE.0) THEN IF (ABS(DELTAI/SUMAI).GT.EPS) GOTO 80 ENDIF FAC1=FACTO*C3 FAC2=FACTO*S3 GAIR=FAC1*SUMAR+FAC2*SUMAI GAII=FAC1*SUMAI-FAC2*SUMAR RETURN END SUBROUTINE EXPAID(GAIR,GAII) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC AIRY AI'(Z), ASYMPTOTIC EXPANSION, COMPLEX Z CCC CCC CCC CCC OUTPUTS: CCC CCC GAIR, GAII, REAL AND IMAGINARY CCC CCC PARTS OF AI'(Z) CCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION EPS,GAIR,GAII DOUBLE PRECISION THET,R,TH15,S1, * C1,R32,FACTO,TH025,S3,C3 DOUBLE PRECISION DF1,PSIIR,PSIII,VK,DFRR,DFII,SUMAR,SUMAI, * DFR,DFI,DELTAR,DELTAI,FAC1,FAC2 DOUBLE PRECISION CO,DF DOUBLE PRECISION D1MACH INTEGER K DIMENSION CO(20) COMMON/PARAM3/THET,R,TH15,S1,C1,R32 COMMON/PARAM4/FACTO,TH025,S3,C3 SAVE CO DATA CO/9.722222222222222D-2,-4.388503086419753D-2, * 4.246283078989484D-2,-6.266216349203230D-2, * 0.124105896027275D0,-0.308253764901079D0, * 0.920479992412945D0,-3.21049358464862D0, * 12.8072930807356D0,-57.5083035139143D0, * 287.033237109221D0,-1576.35730333710D0, * 9446.35482309593D0,-61335.7066638521D0, * 428952.400400069D0,-3214536.52140086D0, * 25697908.3839113D0,-218293420.832160D0, * 1963523788.99103D0,-18643931088.1072D0/ EPS=D1MACH(3) IF (EPS.LT.1.D-15) EPS=1.D-15 DF1=1.5D0/R32 PSIIR=C1 PSIII=-S1 K=0 DF=1.D0 DFRR=1.D0 DFII=0.D0 SUMAR=1.D0 SUMAI=0.D0 81 DF=DF*DF1 VK=CO(K+1)*DF DFR=DFRR DFI=DFII DFRR=DFR*PSIIR-DFI*PSIII DFII=DFR*PSIII+DFI*PSIIR DELTAR=DFRR*VK DELTAI=DFII*VK SUMAR=SUMAR+DELTAR SUMAI=SUMAI+DELTAI K=K+1 IF (SUMAR.NE.0) THEN IF (ABS(DELTAR/SUMAR).GT.EPS) GOTO 81 ENDIF IF (SUMAI.NE.0) THEN IF (ABS(DELTAI/SUMAI).GT.EPS) GOTO 81 ENDIF FAC1=FACTO*C3 FAC2=FACTO*S3 GAIR=-(FAC1*SUMAR-FAC2*SUMAI) GAII=-(FAC1*SUMAI+FAC2*SUMAR) RETURN END SUBROUTINE BIZ(IFUN,IFAC,X0,Y0,GBIR,GBII,IERRO) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C COMPUTATION OF THE AIRY FUNCTION BI(Z) OR ITS DERIVATIVE BI'(Z) C THE CODE USES THE CONNECTION OF BI(Z) WITH AI(Z). C BIZ CALLS THE ROUTINE AIZ CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C INPUTS: C IFUN: C * IFUN=1, THE CODE COMPUTES BI(Z) C * IFUN=2, THE CODE COMPUTES BI'(Z) C IFAC: C * IFAC=1, THE CODE COMPUTES BI(Z) OR BI'(Z) C * IFAC=2, THE CODE COMPUTES NORMALIZED BI(Z) OR BI'(Z) C X0: REAL PART OF THE ARGUMENT Z C Y0: IMAGINARY PART OF THE ARGUMENT Z C C OUTPUTS: C GBIR: REAL PART OF BI(Z) OR BI'(Z) C GBII: IMAGINARY PART OF BI(Z) OR BI'(Z) C C IERRO: ERROR FLAG C * IERRO=0, SUCCESSFUL COMPUTATION C * IERRO=1, COMPUTATION OUT OF RANGE CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C MACHINE DEPENDENT CONSTANTS: FUNCTION D1MACH CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C ACCURACY: C C 1) SCALED AIRY FUNCTIONS: C RELATIVE ACCURACY BETTER THAN 10**(-13) EXCEPT CLOSE TO C THE ZEROS, WHERE 10**(-13) IS THE ABSOLUTE PRECISION. C GRADUAL LOSS OF PRECISION TAKES PLACE FOR |Z|>1000 C IN THE CASE OF PHASE(Z) CLOSE TO +3*PI/2 OR -3*PI/2. C 2) UNSCALED AIRY FUNCTIONS: C THE FUNCTION OVERFLOWS/UNDERFLOWS FOR C 3/2*|Z|**(3/2)>LOG(OVER). C FOR |Z|<30: C A) RELATIVE ACCURACY FOR THE MODULUS (EXCEPT AT THE C ZEROS) BETTER THAN 10**(-13). C B) ABSOLUTE ACCURACY FOR MIN(R(Z),1/R(Z)) BETTER C THAN 10**(-13), WHERE R(Z)=REAL(BI)/IMAG(BI) C OR R(Z)=REAL(BI')/IMAG(BI'). C FOR |Z|>30, GRADUAL LOSS OF PRECISION TAKES PLACE C AS |Z| INCREASES. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C AUTHORS: C AMPARO GIL (U. AUTONOMA DE MADRID, MADRID, SPAIN). C E-MAIL: AMPARO.GIL@UAM.ES C JAVIER SEGURA (U. CARLOS III DE MADRID, MADRID, SPAIN). C E-MAIL: JSEGURA@MATH.UC3M.ES C NICO M. TEMME (CWI, AMSTERDAM, THE NETHERLANDS). C E-MAIL: NICO.TEMME@CWI.NL CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C REFERENCES: C COMPUTING AIRY FUNCTIONS BY NUMERICAL QUADRATURE. C NUMERICAL ALGORITHMS (2002). C A. GIL, J. SEGURA, N.M. TEMME CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X0,Y0,GBIR,GBII DOUBLE PRECISION OVER,UNDER,DL1,DL2,COVER,D1MACH DOUBLE PRECISION PI,PI3,PI23,SQRT3,C,S,C1,S1,U,V,X,Y,AR,AI, * APR,API,BR,BI,BPR,BPI,BBR,BBI,BBPR,BBPI,PHASE DOUBLE PRECISION THET,R,R32,THET32,A1,B1,DF1,EXPO,EXPOI, * ETAR,ETAI,ETAGR,ETAGI,PIHAL INTEGER IFUN,IFAC,IEXPF,IERR,IERRO COMMON/PARAM1/PI,PIHAL SQRT3=1.7320508075688772935D0 PI=3.1415926535897932385D0 PIHAL=1.5707963267948966192D0 PI3=PI/3.D0 PI23=2.D0*PI3 X=X0 C=0.5D0*SQRT3 S=0.5D0 IERRO=0 IEXPF=0 IF (Y0.LT.0.D0) THEN Y=-Y0 ELSE Y=Y0 ENDIF R=SQRT(X*X+Y*Y) R32=R*SQRT(R) THET=PHASE(X,Y) COVER=2.D0/3.D0*R32*ABS(COS(1.5D0*THET)) CCC MACHINE DEPENDENT CONSTANT (OVERFLOW NUMBER) OVER=D1MACH(2)*1.D-4 CCC MACHINE DEPENDENT CONSTANT (UNDERFLOW NUMBER) UNDER=D1MACH(1)*1.D+4 DL1=LOG(OVER) DL2=-LOG(UNDER) IF (DL1.GT.DL2) OVER=1/UNDER IF (IFAC.EQ.1) THEN IF (COVER.GE.LOG(OVER)) THEN CCC OVERFLOW/UNDERFLOW PROBLEMS. CCC CALCULATION ABORTED IERRO=1 GBIR=0 GBII=0 ENDIF ELSE IF (COVER.GE.(LOG(OVER)*0.2)) IEXPF=1 ENDIF IF (IERRO.EQ.0) THEN IF (IFAC.EQ.1) THEN IF (Y.EQ.0.D0) THEN CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC TAKE TWICE THE REAL PART OF EXP(-PI I/6) AI_(1)(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C1=-0.5D0 S1=-0.5D0*SQRT3 U=X*C1-Y*S1 V=X*S1+Y*C1 CALL AIZ(IFUN,IFAC,U,V,AR,AI,IERR) IF (IFUN.EQ.1) THEN BR=SQRT3*AR+AI BI=0.D0 ELSE U=AR*C1-AI*S1 V=AR*S1+AI*C1 APR=U API=V BPR=SQRT3*APR+API BPI=0.D0 ENDIF ELSE IF ((X.LT.0.D0).AND.(Y.LT.-X*SQRT3)) THEN CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC 2 PI/3 < PHASE(Z) < PI CCC BI(Z)=EXP(I PI/6) AI_(-1)(Z) + EXP(-I PI/6) AI_(1)(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C1=-0.5D0 S1=0.5D0*SQRT3 U=X*C1-Y*S1 V=X*S1+Y*C1 CALL AIZ(IFUN,IFAC,U,V,AR,AI,IERR) IF (IFUN.EQ.1) THEN BR=C*AR-S*AI BI=C*AI+S*AR ELSE U=AR*C1-AI*S1 V=AR*S1+AI*C1 APR=U API=V BPR=C*APR-S*API BPI=C*API+S*APR ENDIF CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC WE NEED ALSO AI_(1)(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C1=-0.5D0 S1=-0.5D0*SQRT3 U=X*C1-Y*S1 V=X*S1+Y*C1 CALL AIZ(IFUN,IFAC,U,V,AR,AI,IERR) IF (IFUN.EQ.1) THEN S=-S BR=BR+C*AR-S*AI BI=BI+C*AI+S*AR ELSE U=AR*C1-AI*S1 V=AR*S1+AI*C1 APR=U API=V S=-S BPR=BPR+C*APR-S*API BPI=BPI+C*API+S*APR ENDIF ELSE CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC BI(Z) = I AI(Z) + 2 EXP(-I PI/6) AI_(1)(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C1=-0.5D0 S1=-0.5D0*SQRT3 U=X*C1-Y*S1 V=X*S1+Y*C1 CALL AIZ(IFUN,IFAC,U,V,AR,AI,IERR) IF (IFUN.EQ.1) THEN BR=SQRT3*AR+AI BI=-AR+SQRT3*AI ELSE U=AR*C1-AI*S1 V=AR*S1+AI*C1 APR=U API=V BPR=SQRT3*APR+API BPI=-APR+SQRT3*API ENDIF CALL AIZ(IFUN,IFAC,X,Y,AR,AI,IERR) IF (IFUN.EQ.1) THEN BR=BR-AI BI=BI+AR ELSE BPR=BPR-AI BPI=BPI+AR ENDIF ENDIF ENDIF ELSE CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC SCALED BI AIRY FUNCTIONS C CCC WE USE THE FOLLOWING NORMALIZATION: C CCC LET ARGZ=ARG(Z), THEN: C CCC A) IF 0 <= ARGZ <= PI/3 C CCC BI=EXP(-2/3Z^3/2)BI C CCC B) IF PI/3 <= ARGZ <= PI C CCC BI=EXP(2/3Z^3/2)BI C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC THET=PHASE(X,Y) IF (THET.LE.PI3) THEN C1=-0.5D0 S1=-0.5D0*SQRT3 U=X*C1-Y*S1 V=X*S1+Y*C1 CALL AIZ(IFUN,IFAC,U,V,AR,AI,IERR) IF (IFUN.EQ.1) THEN BR=SQRT3*AR+AI BI=-AR+SQRT3*AI ELSE U=AR*C1-AI*S1 V=AR*S1+AI*C1 APR=U API=V BPR=SQRT3*APR+API BPI=-APR+SQRT3*API ENDIF IF (IEXPF.EQ.0) THEN R=SQRT(X*X+Y*Y) R32=R*SQRT(R) THET32=THET*1.5D0 A1=COS(THET32) B1=SIN(THET32) DF1=4.D0/3.D0*R32 EXPO=EXP(DF1*A1) EXPOI=1.D0/EXPO ETAR=EXPO*COS(DF1*B1) ETAI=EXPO*SIN(DF1*B1) ETAGR=EXPOI*COS(-DF1*B1) ETAGI=EXPOI*SIN(-DF1*B1) CALL AIZ(IFUN,IFAC,X,Y,AR,AI,IERR) IF (IFUN.EQ.1) THEN BR=BR-AR*ETAGI-ETAGR*AI BI=BI+AR*ETAGR-ETAGI*AI ELSE BPR=BPR-AR*ETAGI-ETAGR*AI BPI=BPI+AR*ETAGR-ETAGI*AI ENDIF ENDIF ENDIF IF ((THET.GT.PI3).AND.(THET.LE.PI23)) THEN IF (IEXPF.EQ.0) THEN R=SQRT(X*X+Y*Y) R32=R*SQRT(R) THET32=THET*1.5D0 A1=COS(THET32) B1=SIN(THET32) DF1=4.D0/3.D0*R32 EXPO=EXP(DF1*A1) EXPOI=1.D0/EXPO ETAR=EXPO*COS(DF1*B1) ETAI=EXPO*SIN(DF1*B1) ETAGR=EXPOI*COS(-DF1*B1) ETAGI=EXPOI*SIN(-DF1*B1) C1=-0.5D0 S1=-0.5D0*SQRT3 U=X*C1-Y*S1 V=X*S1+Y*C1 CALL AIZ(IFUN,IFAC,U,V,AR,AI,IERR) IF (IFUN.EQ.1) THEN BBR=SQRT3*AR+AI BBI=-AR+SQRT3*AI BR=BBR*ETAR-BBI*ETAI BI=BBI*ETAR+BBR*ETAI ELSE U=AR*C1-AI*S1 V=AR*S1+AI*C1 APR=U API=V BBPR=SQRT3*APR+API BBPI=-APR+SQRT3*API BPR=BBPR*ETAR-BBPI*ETAI BPI=BBPI*ETAR+BBPR*ETAI ENDIF ELSE IF (IFUN.EQ.1) THEN BR=0.D0 BI=0.D0 ELSE BPR=0.D0 BPI=0.D0 ENDIF ENDIF CALL AIZ(IFUN,IFAC,X,Y,AR,AI,IERR) IF (IFUN.EQ.1) THEN BR=BR-AI BI=BI+AR ELSE BPR=BPR-AI BPI=BPI+AR ENDIF ENDIF IF (THET.GT.PI23) THEN C1=-0.5D0 S1=0.5D0*SQRT3 U=X*C1-Y*S1 V=X*S1+Y*C1 CALL AIZ(IFUN,IFAC,U,V,AR,AI,IERR) IF (IFUN.EQ.1) THEN BR=C*AR-S*AI BI=C*AI+S*AR ELSE U=AR*C1-AI*S1 V=AR*S1+AI*C1 APR=U API=V BPR=C*APR-S*API BPI=C*API+S*APR ENDIF IF (IEXPF.EQ.0) THEN CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC WE NEED ALSO AI_(1)(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC R=SQRT(X*X+Y*Y) R32=R*SQRT(R) THET32=THET*1.5D0 A1=COS(THET32) B1=SIN(THET32) DF1=4.D0/3.D0*R32 EXPO=EXP(DF1*A1) EXPOI=1.D0/EXPO ETAR=EXPO*COS(DF1*B1) ETAI=EXPO*SIN(DF1*B1) ETAGR=EXPOI*COS(-DF1*B1) ETAGI=EXPOI*SIN(-DF1*B1) C1=-0.5D0 S1=-0.5D0*SQRT3 U=X*C1-Y*S1 V=X*S1+Y*C1 CALL AIZ(IFUN,IFAC,U,V,AR,AI,IERR) IF (IFUN.EQ.1) THEN S=-S BBR=C*AR-S*AI BBI=C*AI+S*AR BR=BR+ETAR*BBR-ETAI*BBI BI=BI+BBI*ETAR+ETAI*BBR ELSE U=AR*C1-AI*S1 V=AR*S1+AI*C1 APR=U API=V S=-S BBPR=C*APR-S*API BBPI=C*API+S*APR BPR=BPR+ETAR*BBPR-ETAI*BBPI BPI=BPI+BBPI*ETAR+ETAI*BBPR ENDIF ENDIF ENDIF ENDIF IF (Y0.LT.0) THEN BI=-BI BPI=-BPI ENDIF IF (IFUN.EQ.1) THEN GBIR=BR GBII=BI ELSE GBIR=BPR GBII=BPI ENDIF ENDIF RETURN END SHAR_EOF fi # end of overwriting check if test -f 'src_819.f' then echo shar: will not over-write existing file "'src_819.f'" else cat << "SHAR_EOF" > 'src_819.f' SUBROUTINE GIZ(IFACG,X,Y,REG,IMG,REGP,IMGP,IERROG) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCC CALCULATION OF GI(Z). WE USE: CCCC 1) SERIES, |Z|<1.5 CCCC 2) ASYMPTOTIC EXPANSION, |Z|>30 AND PHASE(Z)30 AND PHASE(Z)30) ARE CONSIDERED. CCCC THIS DEGRADATION IN ACCURACY IS ELIMINATED IN THE SECTORS CCCC WHERE SCALING IS POSSIBLE. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCC LIST OF VARIABLES CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCC AII : IMAGINARY PART OF AI(Z) CCCC AIR : REAL PART OF AI(Z) CCCC BII : IMAGINARY PART OF BI(Z) CCCC BIR : REAL PART OF BI(Z) CCCC C : COS(2*PI/3) CCCC C1 : COS(3*PHASE(Z)/2) CCCC C11 : COS( 2/3*|Z|**(3/2)*SIN(3*PHASE(Z)/2) ) CCCC COVER : 2/3*|Z|**(3/2)*|COS(PHASE(Z)*3/2)| CCCC D1MACH: PROVIDES THE MACHINE DEPENDENT CONSTANTS CCCC DEX : EXP(- 2/3*|Z|**(3/2)*COS(3*PHASE(Z)/2) ) CCCC DF1 : 2/3*|Z|**(3/2)*COS(3*PHASE(Z)/2) CCCC DF2 : 2/3*|Z|**(3/2)*SIN(3*PHASE(Z)/2) CCCC DIMA : -EXP(- 2/3*|Z|**(3/2)*COS(3*PHASE(Z)/2) )* CCCC SIN( 2/3*|Z|**(3/2)*SIN(3*PHASE(Z)/2) ) CCCC DL1 : LOGARITHM OF THE OVERFLOW NUMBER CCCC DL2 : - LOGARITHM OF THE UNDERFLOW NUMBER CCCC DRE : EXP(- 2/3*|Z|**(3/2)*COS(3*PHASE(Z)/2) )* CCCC COS( 2/3*|Z|**(3/2)*SIN(3*PHASE(Z)/2) ) CCCC F23 : 2/3 CCCC F23R : 2/3*|Z|**(3/2) CCCC IERRO : ERROR FLAG FOR THE COMPUTATION OF AI(Z) OR BI(Z) CCCC IERROG: ERROR FLAG FOR THE COMPUTATION OF GI(Z) CCCC IERROH: ERROR FLAG FOR THE COMPUTATION OF HI(Z) CCCC IEXPF : OVERFLOW PARAMETER CCCC IFAC : PARAMETER FOR THE COMPUTATION OF THE HOMOGENEOUS AIRY CCCC FUNCTIONS: CCCC * IF IFAC=1, COMPUTATION OF UNSCALED AIRY FUNCTIONS. CCCC * IF IFAC=2, COMPUTATION OF SCALED AIRY FUNCTIONS. CCCC IFACG : CCCC * IF IFACG=1, COMPUTATION OF UNSCALED GI(Z). CCCC * IF IFACG=2, COMPUTATION OF SCALED GI(Z). CCCC IFACGS: STORES THE VALUE OF IFACG USED AS INPUT CCCC IFACH : CCCC * IF IFACH=1, COMPUTATION OF UNSCALED HI(Z). CCCC * IF IFACH=2, COMPUTATION OF SCALED HI(Z). CCCC IFUN : PARAMETER FOR THE COMPUTATION OF THE HOMOGENEOUS AIRY CCCC FUNCTIONS: CCCC * IF IFUN=1, COMPUTATION OF AI(Z) OR BI(Z). CCCC * IF IFUN=2, COMPUTATION OF AI'(Z) OR BI'(Z). CCCC IMG : IMAGINARY PART OF THE FUNCTION GI(Z) CCCC IMG1 : CONTRIBUTION TO THE IMAGINARY PART OF GI(Z) CCCC IMGP : IMAGINARY PART OF THE FUNCTION GI'(Z) CCCC IMGP1 : CONTRIBUTION TO THE IMAGINARY PART OF GI'(Z) CCCC IMH : IMAGINARY PART OF -EXP(2/3*Z**(3/2))*EXP(2*PI*I/3)* CCCC HI(Z*EXP(2*PI*I/3)) CCCC IMH1 : IMAGINARY PART OF HI(Z*EXP(2*PI*I/3)) CCCC IMH2 : IMAGINARY PART OF -EXP(2*PI*I/3)*HI(Z*EXP(2*PI*I/3)) CCCC IMHP : IMAGINARY PART OF -EXP(2/3*Z**(3/2))*EXP(2*PI*I/3)* CCCC HI'(Z*EXP(2*PI*I/3)) CCCC IMHP1 : IMAGINARY PART OF HI'(Z*EXP(2*PI*I/3)) CCCC IMHP2 : IMAGINARY PART OF -EXP(2*PI*I/3)*HI'(Z*EXP(2*PI*I/3)) CCCC IZ : FLAG FOR THE PARTICULAR CASE Z=0 (IZ=1) CCCC OVER : OVERFLOW NUMBER CCCC PH : PHASE OF Z CCCC PHASE : FUNCTION FOR THE CALCULATION OF THE PHASE OF CCCC A COMPLEX NUMBER CCCC PI : 3.1415... CCCC PI13 : PI/3 CCCC PI23 : 2*PI/3 CCCC PIHAL : PI/2 CCCC R : |Z| CCCC R32 : |Z|**(3/2) CCCC REG : REAL PART OF THE FUNCTION GI(Z) CCCC REG1 : CONTRIBUTION TO THE REAL PART OF GI(Z) CCCC REGP : REAL PART OF THE FUNCTION GI'(Z) CCCC REGP1 : CONTRIBUTION TO THE REAL PART OF GI'(Z) CCCC REH : REAL PART OF -EXP(2/3*Z**(3/2))*EXP(2*PI*I/3)* CCCC HI(Z*EXP(2*PI*I/3)) CCCC REH1 : REAL PART OF HI(Z*EXP(2*PI*I/3)) CCCC REH2 : REAL PART OF -EXP(2*PI*I/3)*HI(Z*EXP(2*PI*I/3)) CCCC REHP : REAL PART OF -EXP(2/3*Z**(3/2))*EXP(2*PI*I/3)* CCCC HI'(Z*EXP(2*PI*I/3)) CCCC REHP1 : REAL PART OF HI'(Z*EXP(2*PI*I/3)) CCCC REHP2 : REAL PART OF -EXP(2*PI*I/3)*HI'(Z*EXP(2*PI*I/3)) CCCC S : SIN(2*PI/3) CCCC S1 : SIN(3*PHASE(Z)/2) CCCC S11 : SIN( 2/3*|Z|**(3/2)*SIN(3*PHASE(Z)/2) ) CCCC SQRT3 : 3**(1/2) CCCC TH15 : PHASE(Z)*3/2 CCCC U : REAL PART OF Z*EXP(2*PI*I/3) CCCC UNDER : UNDERFLOW NUMBER CCCC V : IMAGINARY PART OF Z*EXP(2*PI*I/3) CCCC Y : IMAGINARY PART OF Z CCCC YA : IMAGINARY PART OF Z CCCC X : REAL PART OF Z CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C AUTHORS: C AMPARO GIL (U. AUTONOMA DE MADRID, MADRID, SPAIN). C E-MAIL: AMPARO.GIL@UAM.ES C JAVIER SEGURA (U. CARLOS III DE MADRID, MADRID, SPAIN). C E-MAIL: JSEGURA@MATH.UC3M.ES C NICO M. TEMME (CWI, AMSTERDAM, THE NETHERLANDS). C E-MAIL: NICO.TEMME@CWI.NL CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C REFERENCES: C ON NON-OSCILLATING INTEGRALS FOR COMPUTING C INHOMOGENEOUS AIRY FUNCTIONS. C A. GIL, J. SEGURA, N.M. TEMME C MATH. COMPUT. 70 (2001) 1183-1194. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,Y,REG,IMG,REGP,IMGP DOUBLE PRECISION YA,REH,IMH,REHP,IMHP DOUBLE PRECISION PI,PIHAL,F23,PI13,PI23,SQRT3,R,R32,PHASE,PH, +COVER,OVER,UNDER,DL1,DL2,D1MACH,C,S,U,V DOUBLE PRECISION TH15,S1,C1,F23R,DF1,DF2,S11,C11,DEX,DRE,DIMA DOUBLE PRECISION AIR,AII,BIR,BII,REH1,IMH1,REHP1,IMHP1, +REH2,IMH2,REHP2,IMHP2,REG1,IMG1,REGP1,IMGP1 INTEGER N,IFUN,IFAC,IEXPF,IFACH,IFACG,IFACGS,IERRO,IERROH, +IERROG,IZ COMMON/PARAM1/PI,PIHAL YA=Y IFACGS=IFACG IF (YA.LT.0.D0) THEN Y=-Y ENDIF PI=ACOS(-1.D0) PIHAL=PI*0.5D0 PI23=2.D0*PI/3.D0 PI13=PI/3.D0 F23=.6666666666666667D0 SQRT3=1.7320508075688772935D0 R=SQRT(X*X+Y*Y) R32=R*SQRT(R) PH=PHASE(X,Y) IERROG=0 IFAC=1 IFACH=1 IEXPF=0 COVER=F23*R32*ABS(COS(1.5D0*PH)) CCC MACHINE DEPENDENT CONSTANT (OVERFLOW NUMBER) OVER=D1MACH(2)*1.D-3 CCC MACHINE DEPENDENT CONSTANT (UNDERFLOW NUMBER) UNDER=D1MACH(1)*1.D+3 DL1=LOG(OVER) DL2=-LOG(UNDER) IF (DL1.GT.DL2) OVER=1/UNDER IF (IFACG.EQ.2) THEN CCC IS Z INSIDE THE SECTOR FOR NORMALIZED FUNCTIONS? CCC IF NOT, NON NORMALIZED FUNCTIONS ARE COMPUTED IF (PH.LT.PI13) THEN IFACG=1 ENDIF ENDIF IF (IFACG.EQ.1) THEN IF (PH.GE.PI13) THEN IF (COVER.GE.LOG(OVER)) THEN CCC OVERFLOW/UNDERFLOW PROBLEMS. CCC CALCULATION ABORTED IERROG=1 REG=0 IMG=0 REGP=0 IMGP=0 ENDIF ENDIF ELSE IF (COVER.GE.(LOG(OVER)*0.2)) THEN IEXPF=1 IFAC=2 ENDIF ENDIF IZ=0 CCC PARTICULAR CASE: Z=0 IF ((ABS(X).LE.UNDER).AND.(ABS(Y).LE.UNDER)) THEN REG=.2049755424820002D0 IMG=0.D0 REGP=.149429452451275D0 IMGP=0.D0 IZ=1 ENDIF IF ((IERROG.EQ.0).AND.(IZ.EQ.0)) THEN IF (R.LT.1.5) THEN CCC USE OF SERIES CALL GIZSER(X,Y,REG1,IMG1,REGP1,IMGP1) IF ((IFACG.EQ.2).AND.(PH.GE.PI13)) THEN TH15=1.5D0*PH S1=SIN(TH15) C1=COS(TH15) F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(DF1) DRE=DEX*C11 DIMA=DEX*S11 REG=(DRE*REG1-DIMA*IMG1)/PI IMG=(DRE*IMG1+DIMA*REG1)/PI REGP=(DRE*REGP1-DIMA*IMGP1)/PI IMGP=(DRE*IMGP1+DIMA*REGP1)/PI ELSE REG=REG1/PI IMG=IMG1/PI REGP=REGP1/PI IMGP=IMGP1/PI ENDIF ELSE IF ((R.GT.30).AND.(PH.LT.(PI13-0.3D0))) THEN CCC USE OF ASYMPTOTIC EXPANSION CALL HIZEXP(X,Y,REG,IMG,REGP,IMGP) REG=REG/PI IMG=IMG/PI REGP=-REGP/PI IMGP=-IMGP/PI ELSE CCCCCCCCC CONNECTION FORMULAE IF (ABS(PH).LT.PI23) THEN CCCCCC CONNECTION FORMULA 1: CCC N= 1: TRANSFORM Z TO W= U+IV=Z EXP( 2 PI I/3) IF (IEXPF.EQ.0) THEN N=1 C=-0.5D0 S=N*0.5*SQRT3 U=X*C-Y*S V=X*S+Y*C CALL HIZ(IFACH,U,V,REH1,IMH1,REHP1,IMHP1,IERROH) REH2=-(C*REH1-S*IMH1) IMH2=-(S*REH1+C*IMH1) S=-S REHP2=-(C*REHP1-S*IMHP1) IMHP2=-(S*REHP1+C*IMHP1) IF (IFACG.EQ.2) THEN TH15=1.5D0*PH S1=SIN(TH15) C1=COS(TH15) F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(DF1) DRE=DEX*C11 DIMA=DEX*S11 REH=(DRE*REH2-DIMA*IMH2) IMH=(DRE*IMH2+DIMA*REH2) REHP=(DRE*REHP2-DIMA*IMHP2) IMHP=(DRE*IMHP2+DIMA*REHP2) IFAC=2 ELSE REH=REH2 IMH=IMH2 REHP=REHP2 IMHP=IMHP2 ENDIF ELSE REH=0 IMH=0 REHP=0 IMHP=0 IFAC=2 ENDIF IFUN=1 CALL AIZ(IFUN,IFAC,X,Y,AIR,AII,IERRO) REG=REH-AII IMG=IMH+AIR IFUN=2 CALL AIZ(IFUN,IFAC,X,Y,AIR,AII,IERRO) REGP=REHP-AII IMGP=IMHP+AIR ELSE CCCCCC CONNECTION FORMULA 2: IF (IEXPF.EQ.0) THEN CALL HIZ(IFACH,X,Y,REH1,IMH1,REHP1,IMHP1,IERROH) IF (IFACG.EQ.2) THEN TH15=1.5D0*PH S1=SIN(TH15) C1=COS(TH15) F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(DF1) DRE=DEX*C11 DIMA=DEX*S11 REH=(DRE*REH1-DIMA*IMH1) IMH=(DRE*IMH1+DIMA*REH1) REHP=(DRE*REHP1-DIMA*IMHP1) IMHP=(DRE*IMHP1+DIMA*REHP1) IFAC=2 ELSE REH=REH1 IMH=IMH1 REHP=REHP1 IMHP=IMHP1 ENDIF ELSE REH=0 IMH=0 REHP=0 IMHP=0 IFAC=2 ENDIF IFUN=1 CALL BIZ(IFUN,IFAC,X,Y,BIR,BII,IERRO) REG=BIR-REH IMG=BII-IMH IFUN=2 CALL BIZ(IFUN,IFAC,X,Y,BIR,BII,IERRO) REGP=BIR-REHP IMGP=BII-IMHP ENDIF ENDIF ENDIF ENDIF IF (YA.LT.0.D0) THEN Y=YA IMG=-IMG IMGP=-IMGP ENDIF IF ((YA.EQ.0.D0).AND.(IFACG.EQ.1)) THEN IMG=0.D0 IMGP=0.D0 ENDIF IFACG=IFACGS RETURN END SUBROUTINE GIZSER(X,Y,REG,IMG,REGP,IMGP) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC GI(Z), GI'(Z) SERIES, COMPLEX Z CCC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC LIST OF VARIABLES CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CK : SUCCESIVE COEFFICIENTS OF THE SERIES CCC CO : ARRAY OF THE COEFFICIENTS OF THE CCC SERIES CCC D1MACH : FUNCTION FOR THE COMPUTATION OF CCC MACHINE DEPENDENT CONSTANTS CCC DELTAI : CONTRIBUTION TO THE IMAGINARY PART OF CCC THE SERIES FOR GI(Z) CCC DELTAR : CONTRIBUTION TO THE REAL PART OF THE CCC SERIES FOR GI(Z) CCC DELTIP : CONTRIBUTION TO THE IMAGINARY PART OF CCC THE SERIES FOR GI'(Z) CCC DELTRP : CONTRIBUTION TO THE REAL PART OF THE CCC SERIES FOR GI'(Z) CCC DFI : ELEMENTARY CONTRIBUTION TO THE CCC IMAGINARY PART OF THE SERIES FOR GI(Z) CCC AND GI'(Z) CCC DFII : ELEMENTARY CONTRIBUTION TO THE CCC IMAGINARY PART OF THE SERIES FOR GI(Z) CCC AND GI'(Z) CCC DFR : ELEMENTARY CONTRIBUTION TO THE REAL CCC PART OF THE SERIES FOR GI(Z) AND GI'(Z) CCC DFRR : ELEMENTARY CONTRIBUTION TO THE REAL CCC PART OF THE SERIES FOR GI(Z) AND GI'(Z) CCC EPS : PRECISION CCC IMG : IMAGINARY PART OF GI(Z) CCC IMGP : IMAGINARY PART OF GI'(Z) CCC R2 : |Z|**2 CCC REG : REAL PART OF GI(Z) CCC REGP : REAL PART OF GI'(Z) CCC SUMAI : ACCUMULATES THE CONTRIBUTION TO THE IMAGINARY CCC PART OF GI(Z) CCC SUMAIP : ACCUMULATES THE CONTRIBUTION TO THE IMAGINARY CCC PART OF GI'(Z) CCC SUMAR : ACCUMULATES THE CONTRIBUTION TO THE REAL CCC PART OF GI(Z) CCC SUMARP : ACCUMULATES THE CONTRIBUTION TO THE REAL CCC PART OF GI'(Z) CCC Y : REAL PART OF Z CCC X : IMAGINARY PART OF Z CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,Y,EPS,D1MACH,REG,IMG,REGP,IMGP DOUBLE PRECISION CK,DFRR,DFII,SUMAR,SUMAI,DFR,DFI,DELTAR, +DELTAI DOUBLE PRECISION R2,SUMARP,SUMAIP,DELTRP,DELTIP DOUBLE PRECISION CO(0:40) INTEGER K SAVE CO DATA CO(0)/.64394965842703454362D0/ DATA CO(1)/.46944647005087228316D0/ DATA CO(2)/-.50000000000000000000D0/ DATA CO(3)/.10732494307117242394D0/ DATA CO(4)/ .39120539170906023596D-1/ DATA CO(5)/-.25000000000000000000D-1/ DATA CO(6)/.35774981023724141313D-2/ DATA CO(7)/.93144140883109579990D-3/ DATA CO(8)/-.44642857142857142857D-3/ DATA CO(9)/.49687473644061307378D-4/ DATA CO(10)/.10349348987012175554D-4/ DATA CO(11)/-.40584415584415584416D-5/ DATA CO(12)/.37642025487925232862D-6/ DATA CO(13)/.66341980685975484324D-7/ DATA CO(14)/-.22299129441986584844D-7/ DATA CO(15)/.17924774041869158506D-8/ DATA CO(16)/.27642491952489785135D-9/ DATA CO(17)/-.81982093536715385455D-10/ DATA CO(18)/.58577692947284831717D-11/ DATA CO(19)/.80825999861081243083D-12/ DATA CO(20)/-.21574235141240890909D-12/ DATA CO(21)/.13947069749353531362D-13/ DATA CO(22)/.17494805164736199802D-14/ DATA CO(23)/-.42636828342373302192D-15/ DATA CO(24)/.25266430705350600292D-16/ DATA CO(25)/.29158008607893666335D-17/ DATA CO(26)/-.65595120526728157219D-18/ DATA CO(27)/.35992066531838461956D-19/ DATA CO(28)/.38568794454885802032D-20/ DATA CO(29)/-.80782168136364725639D-21/ DATA CO(30)/.41370191415906278110D-22/ DATA CO(31)/.41471821994500862401D-23/ DATA CO(32)/-.81433637234238634716D-24/ DATA CO(33)/.39176317628699126998D-25/ DATA CO(34)/.36962408194742301605D-26/ DATA CO(35)/-.68431627927931625812D-27/ DATA CO(36)/.31092315578332640475D-28/ DATA CO(37)/.27749555701758484688D-29/ DATA CO(38)/-.48671143618728041118D-30/ DATA CO(39)/.20979970025865479402D-31/ DATA CO(40)/.17788176731896464543D-32/ EPS=D1MACH(3) IF (EPS.LT.1.D-15) EPS=1.D-15 R2=X*X+Y*Y K=0 CK=CO(0) DFRR=1.D0 DFII=0.D0 SUMAR=CK SUMAI=0.D0 SUMARP=0.D0 SUMAIP=0.D0 33 CK=CO(K+1) DFR=DFRR DFI=DFII DFRR=DFR*X-DFI*Y DFII=DFR*Y+DFI*X DELTAR=DFRR*CK DELTAI=DFII*CK DELTRP=DELTAR*(K+1) DELTIP=DELTAI*(K+1) SUMAR=SUMAR+DELTAR SUMAI=SUMAI+DELTAI SUMARP=SUMARP+DELTRP SUMAIP=SUMAIP+DELTIP K=K+1 IF (SUMAR.NE.0) THEN IF (ABS(DELTAR/SUMAR).GT.EPS) GOTO 33 ENDIF IF (SUMAI.NE.0) THEN IF (ABS(DELTAI/SUMAI).GT.EPS) GOTO 33 ENDIF IF (SUMARP.NE.0) THEN IF (ABS(DELTRP/SUMARP).GT.EPS) GOTO 33 ENDIF IF (SUMAIP.NE.0) THEN IF (ABS(DELTIP/SUMAIP).GT.EPS) GOTO 33 ENDIF REG=SUMAR IMG=SUMAI REGP=(X*SUMARP+Y*SUMAIP)/R2 IMGP=-(Y*SUMARP-X*SUMAIP)/R2 RETURN END SUBROUTINE HIZ(IFACH,X,Y,REH,IMH,REHP,IMHP,IERROH) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCC CALCULATION OF HI(Z) AND HI'(Z). WE USE: CCCC 1) SERIES, |Z|<1.5 CCCC 2) LET PH=PHASE(Z) CCCC 2.A) NUMERICAL QUADRATURE, 2PI/3<|PH|20 CCCC IFACH: CCCC * IFACH=1, THE CODE COMPUTES HI(Z) AND HI'(Z) IN CCCC THE COMPLEX PLANE CCCC * IFACH=2, THE CODE COMPUTES: CCCC A) NORMALIZED HI(Z) AND HI'(Z), |PH|30) ARE CONSIDERED. CCCC THIS DEGRADATION IN ACCURACY IS ELIMINATED IN THE SECTORS CCCC WHERE SCALING IS POSSIBLE. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCC LIST OF VARIABLES CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCC AII : IMAGINARY PART OF EXP(-PI*I/6)*AI(Z*EXP(-2*PI*I/3)) CCCC AII1 : IMAGINARY PART OF AI(Z*EXP(-2*PI*I/3)) CCCC AIR : REAL PART OF EXP(-PI*I/6)*AI(Z*EXP(-2*PI*I/3)) CCCC AIR1 : REAL PART OF AI(Z*EXP(-2*PI*I/3)) CCCC C : COS(2*PI/3) CCCC C1 : COS(3*PHASE(Z)/2) CCCC C11 : COS( 2/3*|Z|**(3/2)*SIN(3*PHASE(Z)/2) ) CCCC CC : COS(PI/6) CCCC COVER : 2/3*|Z|**(3/2)*|COS(PHASE(Z)*3/2)| CCCC DEX : EXP(- 2/3*|Z|**(3/2)*COS(3*PHASE(Z)/2) ) CCCC DF1 : 2/3*|Z|**(3/2)*COS(3*PHASE(Z)/2) CCCC DF2 : 2/3*|Z|**(3/2)*SIN(3*PHASE(Z)/2) CCCC DIMA : -EXP(- 2/3*|Z|**(3/2)*COS(3*PHASE(Z)/2) )* CCCC SIN( 2/3*|Z|**(3/2)*SIN(3*PHASE(Z)/2) ) CCCC DL1 : LOGARITHM OF THE OVERFLOW NUMBER CCCC DL2 : - LOGARITHM OF THE UNDERFLOW NUMBER CCCC DRE : EXP(- 2/3*|Z|**(3/2)*COS(3*PHASE(Z)/2) )* CCCC COS( 2/3*|Z|**(3/2)*SIN(3*PHASE(Z)/2) ) CCCC F23 : 2/3 CCCC F23R : 2/3*|Z|**(3/2) CCCC H : INTEGRATION STEP CCCC IERRO : ERROR FLAG FOR THE COMPUTATION OF AI(Z) OR BI(Z) CCCC IERROH: ERROR FLAG FOR THE COMPUTATION OF HI(Z) CCCC IEXPF : OVERFLOW PARAMETER CCCC IFAC : PARAMETER FOR THE COMPUTATION OF THE HOMOGENEOUS AIRY CCCC IFACH : CCCC * IF IFACH=1, COMPUTATION OF UNSCALED HI(Z). CCCC * IF IFACH=2, COMPUTATION OF SCALED HI(Z). CCCC IFACHS: STORES THE VALUE OF IFACH USED AS INPUT CCCC IFUN : PARAMETER FOR THE COMPUTATION OF THE HOMOGENEOUS AIRY CCCC FUNCTIONS: CCCC * IF IFUN=1, COMPUTATION OF AI(Z) OR BI(Z). CCCC * IF IFUN=2, COMPUTATION OF AI'(Z) OR BI'(Z). CCCC IMH : IMAGINARY PART OF THE FUNCTION HI(Z) CCCC IMH1 : CONTRIBUTION TO THE IMAGINARY PART OF HI(Z) CCCC IMH2 : IMAGINARY PART OF EXP(2*PI*I/3)*HI(2*PI*I/3) CCCC IMH3 : IMAGINARY PART OF EXP(-2/3*Z**(3/2))*EXP(2*PI*I/3)* CCCC HI(Z*EXP(2*PI*I/3)) CCCC IMHP : IMAGINARY PART OF THE FUNCTION HI'(Z) CCCC IMHP1 : CONTRIBUTION TO THE IMAGINARY PART OF HI'(Z) CCCC IMHP2 : IMAGINARY PART OF EXP(2*PI*I/3)*HI'(2*PI*I/3) CCCC IMHP3 : IMAGINARY PART OF EXP(-2/3*Z**(3/2))*EXP(2*PI*I/3)* CCCC HI'(Z*EXP(2*PI*I/3)) CCCC IZ : FLAG FOR THE PARTICULAR CASE Z=0 (IZ=1) CCCC OVER : OVERFLOW NUMBER CCCC PH : PHASE OF Z CCCC PHASE : FUNCTION FOR THE CALCULATION OF THE PHASE OF CCCC A COMPLEX NUMBER CCCC PI : 3.1415... CCCC PI13 : PI/3 CCCC PI23 : PI*2/3 CCCC PI56 : PI*5/6 CCCC PI6 : PI/6 CCCC PIHAL : PI/2 CCCC R : MODULUS OF Z CCCC R32 : |Z|**(3/2) CCCC REH : REAL PART OF THE FUNCTION HI(Z) CCCC REH1 : CONTRIBUTION TO THE REAL PART OF HI(Z) CCCC REH2 : REAL PART OF EXP(2*PI*I/3)*HI(2*PI*I/3) CCCC REH3 : REAL PART OF EXP(-2/3*Z**(3/2))*EXP(2*PI*I/3)* CCCC HI(Z*EXP(2*PI*I/3)) CCCC REHP : REAL PART OF THE FUNCTION HI'(Z) CCCC REHP1 : CONTRIBUTION TO THE REAL PART OF HI'(Z) CCCC REHP2 : REAL PART OF EXP(2*PI*I/3)*HI'(2*PI*I/3) CCCC REHP3 : REAL PART OF EXP(-2/3*Z**(3/2))*EXP(2*PI*I/3)* CCCC HI'(Z*EXP(2*PI*I/3)) CCCC S : SIN(+-2*PI/3) CCCC S1 : SIN(3*PHASE(Z)/2) CCCC S11 : SIN( 2/3*|Z|**(3/2)*SIN(3*PHASE(Z)/2) ) CCCC SQRT3 : 3**(1/2) CCCC SS : -SIN(PI/6) CCCC TH15 : PHASE(Z)*3/2 CCCC U : REAL PART OF Z*EXP(+-2*PI/3) CCCC UNDER : UNDERFLOW NUMBER CCCC V : IMAGINARY PART OF Z*EXP(+-2*PI/3) CCCC X : REAL PART OF Z CCCC Y : IMAGINARY PART OF Z CCCC YA : IMAGINARY PART OF Z CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C AUTHORS: C AMPARO GIL (U. AUTONOMA DE MADRID, MADRID, SPAIN). C E-MAIL: AMPARO.GIL@UAM.ES C JAVIER SEGURA (U. CARLOS III DE MADRID, MADRID, SPAIN). C E-MAIL: JSEGURA@MATH.UC3M.ES C NICO M. TEMME (CWI, AMSTERDAM, THE NETHERLANDS). C E-MAIL: NICO.TEMME@CWI.NL CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C REFERENCES: C ON NON-OSCILLATING INTEGRALS FOR COMPUTING C INHOMOGENEOUS AIRY FUNCTIONS. C A. GIL, J. SEGURA, N.M. TEMME C MATH. COMPUT. 70 (2001) 1183-1194. CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,Y,REH,IMH,REHP,IMHP DOUBLE PRECISION YA,F23,PI,PIHAL,PI13,PI23,PI6,PI56,SQRT3,R,H, *PHASE,PH,C,S,U,V,D1MACH,OVER,UNDER,DL1,DL2,COVER,R32 DOUBLE PRECISION TH15,S1,C1,F23R,DF1,DF2,S11,C11,DEX,DRE,DIMA DOUBLE PRECISION AIR1,AII1,AIR,AII,REH1,IMH1,REHP1,IMHP1 DOUBLE PRECISION REHP2,IMHP2,REH2,IMH2,SS,CC DOUBLE PRECISION REHP3,IMHP3,REH3,IMH3 INTEGER N,IFUN,IFAC,IERRO,IFACH,IFACHS,IERROH,IEXPF,IZ COMMON/PARAM1/PI,PIHAL YA=Y IFACHS=IFACH IF (YA.LT.0.D0) THEN Y=-Y ENDIF PI=ACOS(-1.D0) PIHAL=PI*0.5D0 PI13=PI/3.D0 PI23=2.D0*PI13 F23=.6666666666666667D0 SQRT3=1.7320508075688772935D0 R=SQRT(X*X+Y*Y) R32=R*SQRT(R) PH=PHASE(X,Y) H=0.1D0 IERROH=0 IFAC=1 IEXPF=0 COVER=F23*R32*ABS(COS(1.5D0*PH)) CCC MACHINE DEPENDENT CONSTANT (OVERFLOW NUMBER) OVER=D1MACH(2)*1.D-3 CCC MACHINE DEPENDENT CONSTANT (UNDERFLOW NUMBER) UNDER=D1MACH(1)*1.D+3 DL1=LOG(OVER) DL2=-LOG(UNDER) IF (DL1.GT.DL2) OVER=1/UNDER IF (IFACH.EQ.2) THEN CCC IS Z INSIDE THE SECTOR FOR NORMALIZED FUNCTIONS? CCC IF NOT, NON NORMALIZED FUNCTIONS ARE COMPUTED IF (PH.GT.PI13) THEN IFACH=1 ENDIF ENDIF IF (IFACH.EQ.1) THEN IF (PH.LE.PI13) THEN IF (COVER.GE.LOG(OVER)) THEN CCC OVERFLOW/UNDERFLOW PROBLEMS. CCC CALCULATION ABORTED IERROH=1 REH=0 IMH=0 REHP=0 IMHP=0 ENDIF ENDIF ELSE IF (COVER.GE.(LOG(OVER)*0.2)) THEN IEXPF=1 IFAC=2 ENDIF ENDIF IZ=0 CCC PARTICULAR CASE: Z=0 IF ((ABS(X).LE.UNDER).AND.(ABS(Y).LE.UNDER)) THEN REH=.4099510849640005D0 IMH=0.D0 REHP=.298858904902551D0 IMHP=0.D0 IZ=1 ENDIF IF ((IERROH.EQ.0).AND.(IZ.EQ.0)) THEN IF (R.LT.1.5) THEN CCC USE OF SERIES CALL HIZSER(X,Y,REH1,IMH1,REHP1,IMHP1) IF (IFACH.EQ.2) THEN TH15=1.5D0*PH S1=SIN(TH15) C1=COS(TH15) F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(-DF1) DRE=DEX*C11 DIMA=-DEX*S11 REH=(DRE*REH1-DIMA*IMH1)/PI IMH=(DRE*IMH1+DIMA*REH1)/PI REHP=(DRE*REHP1-DIMA*IMHP1)/PI IMHP=(DRE*IMHP1+DIMA*REHP1)/PI ELSE REH=REH1/PI IMH=IMH1/PI REHP=REHP1/PI IMHP=IMHP1/PI ENDIF ELSE IF ((R.GT.20).AND.(PH.GT.PI23)) THEN CCC USE OF ASYMPTOTIC EXPANSION CALL HIZEXP(X,Y,REH,IMH,REHP,IMHP) REH=-REH/PI IMH=-IMH/PI REHP=REHP/PI IMHP=IMHP/PI ELSE IF (PH.LT.PI23) THEN CCCCCCCCC CONNECTION FORMULAE CCC N= 1: TRANSFORM Z TO W= U+IV=Z EXP( 2 PI I/3) IF (IEXPF.EQ.0) THEN N=1 C=-0.5D0 S=N*0.5*SQRT3 U=X*C-Y*S V=X*S+Y*C IF (R.GT.20) THEN CALL HIZEXP(U,V,REH1,IMH1,REHP1,IMHP1) REH1=-REH1/PI IMH1=-IMH1/PI REHP1=REHP1/PI IMHP1=IMHP1/PI ELSE CALL HIZINT(U,V,H,REH1,IMH1,REHP1,IMHP1) ENDIF REH2=C*REH1-S*IMH1 IMH2=S*REH1+C*IMH1 S=-S REHP2=C*REHP1-S*IMHP1 IMHP2=S*REHP1+C*IMHP1 IF (IFACH.EQ.2) THEN TH15=1.5D0*PH S1=SIN(TH15) C1=COS(TH15) F23R=F23*R32 DF1=F23R*C1 DF2=F23R*S1 S11=SIN(DF2) C11=COS(DF2) DEX=EXP(-DF1) DRE=DEX*C11 DIMA=-DEX*S11 REH3=(DRE*REH2-DIMA*IMH2) IMH3=(DRE*IMH2+DIMA*REH2) REHP3=(DRE*REHP2-DIMA*IMHP2) IMHP3=(DRE*IMHP2+DIMA*REHP2) IFAC=2 ELSE REH3=REH2 IMH3=IMH2 REHP3=REHP2 IMHP3=IMHP2 ENDIF ELSE REH3=0 IMH3=0 REHP3=0 IMHP3=0 IFAC=2 ENDIF CCC N= -1: TRANSFORM Z TO W= U+IV=Z EXP( -2 PI I/3) N=-1 C=-0.5D0 S=N*0.5*SQRT3 U=X*C-Y*S V=X*S+Y*C IFUN=1 CALL AIZ(IFUN,IFAC,U,V,AIR1,AII1,IERRO) PI6=PI/6.D0 CC=COS(PI6) SS=-SIN(PI6) AIR=CC*AIR1-SS*AII1 AII=SS*AIR1+CC*AII1 REH=REH3+2.D0*AIR IMH=IMH3+2.D0*AII IFUN=2 CALL AIZ(IFUN,IFAC,U,V,AIR1,AII1,IERRO) PI56=5.D0*PI6 CC=COS(PI56) SS=-SIN(PI56) AIR=CC*AIR1-SS*AII1 AII=SS*AIR1+CC*AII1 REHP=REHP3+2.D0*AIR IMHP=IMHP3+2.D0*AII ELSE CCCCCCCCC NUMERICAL QUADRATURE (TRAPEZOIDAL) CALL HIZINT(X,Y,H,REH,IMH,REHP,IMHP) ENDIF ENDIF ENDIF ENDIF IF (YA.LT.0.D0) THEN Y=YA IMH=-IMH IMHP=-IMHP ENDIF IF (YA.EQ.0.D0) THEN IMH=0.D0 IMHP=0.D0 ENDIF IFACH=IFACHS RETURN END SUBROUTINE HIZINT(X,Y,H,REH,IMH,REHP,IMHP) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCC CALCULATION OF HI(Z) BY NUMERICAL QUADRATURE CCC CCC CCC INPUTS: CCC X,Y, REAL AND IMAGINARY PARTS OF Z CCC OUTPUTS: CCC REH,IMH, REAL AND IMAGINARY PARTS OF HI(Z) CCC REHP,IMHP, REAL AND IMAGINARY PARTS OF HI'(Z) CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCC LIST OF VARIABLES CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CCCC A : LOWER INTEGRATION LIMIT CCCC ABB : |RE(CONTRIBUTION TO HI(Z))|+ CCCC |IM(CONTRIBUTION TO HI(Z))|+ CCCC |RE(CONTRIBUTION TO HI'(Z))|+ CCCC |IM(CONTRIBUTION TO HI'(Z))| CCCC B : UPPER INTEGRATION LIMIT CCCC D1MACH: COMPUTES THE MACHINE DEPENDENT CONSTANTS CCCC EPS : PRECISION CCCC H : INTEGRATION STEP CCCC HS : INTEGRATION STEP/PI CCCC IMG : CONTRIBUTION TO THE IMAGINARY PART OF HI(Z) CCCC IMGP : CONTRIBUTION TO THE IMAGINARY PART OF HI'(Z) CCCC PI : 3.1415... CCCC REG : CONTRIBUTION TO THE REAL PART OF HI(Z) CCCC REGP : CONTRIBUTION TO THE REAL PART OF HI'(Z) CCCC RR : PARAMETER USED IN THE ROUTINE INTU TO DECIDE CCCC IF THE STEEPEST DESCENT CONTOUR IS USED OR CCCC THE MODIFIED CONTOUR CCCC SQRT3 : 3**(1/2) CCCC T : INTEGRATION ABSCISSA CCCC YA : IMAGINARY PART OF Z CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC DOUBLE PRECISION X,Y,H,REH,IMH,REHP,IMHP DOUBLE PRECISION YA,EPS,SQRT3,PI,RR,A,B,T,REG,IMG,REGP,IMGP, + ABB,HS,D1MACH COMMON/CONST/SQRT3,RR EPS=D1MACH(3) IF (EPS.LT.1.D-16) EPS=1.D-16 CCCCC CONSTANTS SQRT3=SQRT(3.D0) PI=ACOS(-1.D0) YA=Y IF (YA.LT.0.D0) THEN Y=-Y ENDIF CCCCC RR IS USED IN INTU TO DECIDE IF THE STEEPEST DESCENT CCCCC CONTOUR IS USED OR THE MODIFIED CONTOUR RR=0.8D0 CCCCC INTEGRATION LIMITS: A,B A=-4.38D0 B=-A T=A REH=0.D0 IMH=0.D0 REHP=0.D0 IMHP=0.D0 CCCCC DO WHILE T