#include "blaswrap.h" /* -- translated by f2c (version 19990503). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Common Block Declarations */ struct { integer infot, nunit; logical ok, lerr; } infoc_; #define infoc_1 infoc_ struct { char srnamt[6]; } srnamc_; #define srnamc_1 srnamc_ /* Table of constant values */ static integer c__2 = 2; static integer c__0 = 0; static integer c_n1 = -1; static integer c__1 = 1; static real c_b24 = 1.f; static real c_b25 = 0.f; static complex c_b62 = {0.f,0.f}; /* Subroutine */ int cdrvpt_(logical *dotype, integer *nn, integer *nval, integer *nrhs, real *thresh, logical *tsterr, complex *a, real *d__, complex *e, complex *b, complex *x, complex *xact, complex *work, real *rwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 0,0,0,1 }; /* Format strings */ static char fmt_9999[] = "(1x,a6,\002, N =\002,i5,\002, type \002,i2," "\002, test \002,i2,\002, ratio = \002,g12.5)"; static char fmt_9998[] = "(1x,a6,\002, FACT='\002,a1,\002', N =\002,i5" ",\002, type \002,i2,\002, test \002,i2,\002, ratio = \002,g12.5)"; /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; real r__1, r__2; /* Builtin functions Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); double c_abs(complex *); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Local variables */ static char fact[1]; static real cond; static integer mode; static real dmax__; static integer imat, info; static char path[3], dist[1], type__[1]; static integer nrun, i__, j, k, n, ifact; extern /* Subroutine */ int cget04_(integer *, integer *, complex *, integer *, complex *, integer *, real *, real *); static integer nfail, iseed[4]; static real z__[3], rcond; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); static integer nimat; extern doublereal sget06_(real *, real *); extern /* Subroutine */ int cptt01_(integer *, real *, complex *, real *, complex *, complex *, real *); static real anorm; extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, complex *, integer *), cptt02_(char *, integer *, integer *, real *, complex *, complex *, integer *, complex *, integer *, real *), cptt05_(integer *, integer *, real *, complex *, complex *, integer *, complex *, integer *, complex *, integer *, real *, real *, real *); static integer izero, nerrs, k1; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *), cptsv_(integer *, integer *, real *, complex *, complex *, integer *, integer *); static logical zerot; extern /* Subroutine */ int clatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, real *, integer *, real *, char * ); static integer ia; extern /* Subroutine */ int aladhd_(integer *, char *); static integer in, kl; extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); static integer ku, ix, nt; static real rcondc; extern doublereal clanht_(char *, integer *, real *, complex *); extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer *), clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), claset_(char *, integer *, integer *, complex *, complex *, complex *, integer *), claptm_( char *, integer *, integer *, real *, real *, complex *, complex * , integer *, real *, complex *, integer *); extern integer isamax_(integer *, real *, integer *); extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer *, integer *), clarnv_(integer *, integer *, integer *, complex *), clatms_(integer *, integer *, char *, integer *, char *, real *, integer *, real *, real *, integer *, integer *, char * , complex *, integer *, complex *, integer *); static real ainvnm; extern doublereal scasum_(integer *, complex *, integer *); extern /* Subroutine */ int cpttrf_(integer *, real *, complex *, integer *), slarnv_(integer *, integer *, integer *, real *), cerrvx_( char *, integer *); static real result[6]; extern /* Subroutine */ int cpttrs_(char *, integer *, integer *, real *, complex *, complex *, integer *, integer *), cptsvx_(char *, integer *, integer *, real *, complex *, real *, complex *, complex *, integer *, complex *, integer *, real *, real *, real * , complex *, real *, integer *); static integer lda; /* Fortran I/O blocks */ static cilist io___35 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___38 = { 0, 0, 0, fmt_9998, 0 }; /* -- LAPACK test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= CDRVPT tests CPTSV and -SVX. Arguments ========= DOTYPE (input) LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. NN (input) INTEGER The number of values of N contained in the vector NVAL. NVAL (input) INTEGER array, dimension (NN) The values of the matrix dimension N. NRHS (input) INTEGER The number of right hand side vectors to be generated for each linear system. THRESH (input) REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0. TSTERR (input) LOGICAL Flag that indicates whether error exits are to be tested. A (workspace) COMPLEX array, dimension (NMAX*2) D (workspace) REAL array, dimension (NMAX*2) E (workspace) COMPLEX array, dimension (NMAX*2) B (workspace) COMPLEX array, dimension (NMAX*NRHS) X (workspace) COMPLEX array, dimension (NMAX*NRHS) XACT (workspace) COMPLEX array, dimension (NMAX*NRHS) WORK (workspace) COMPLEX array, dimension (NMAX*max(3,NRHS)) RWORK (workspace) REAL array, dimension (NMAX+2*NRHS) NOUT (input) INTEGER The unit number for output. ===================================================================== Parameter adjustments */ --rwork; --work; --xact; --x; --b; --e; --d__; --a; --nval; --dotype; /* Function Body */ s_copy(path, "Complex precision", (ftnlen)1, (ftnlen)17); s_copy(path + 1, "PT", (ftnlen)2, (ftnlen)2); nrun = 0; nfail = 0; nerrs = 0; for (i__ = 1; i__ <= 4; ++i__) { iseed[i__ - 1] = iseedy[i__ - 1]; /* L10: */ } /* Test the error exits */ if (*tsterr) { cerrvx_(path, nout); } infoc_1.infot = 0; i__1 = *nn; for (in = 1; in <= i__1; ++in) { /* Do for each value of N in NVAL. */ n = nval[in]; lda = max(1,n); nimat = 12; if (n <= 0) { nimat = 1; } i__2 = nimat; for (imat = 1; imat <= i__2; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (n > 0 && ! dotype[imat]) { goto L110; } /* Set up parameters with CLATB4. */ clatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, & cond, dist); zerot = imat >= 8 && imat <= 10; if (imat <= 6) { /* Type 1-6: generate a symmetric tridiagonal matrix of known condition number in lower triangular band storage. */ s_copy(srnamc_1.srnamt, "CLATMS", (ftnlen)6, (ftnlen)6); clatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cond, &anorm, &kl, &ku, "B", &a[1], &c__2, &work[1], &info); /* Check the error code from CLATMS. */ if (info != 0) { alaerh_(path, "CLATMS", &info, &c__0, " ", &n, &n, &kl, & ku, &c_n1, &imat, &nfail, &nerrs, nout); goto L110; } izero = 0; /* Copy the matrix to D and E. */ ia = 1; i__3 = n - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__; i__5 = ia; d__[i__4] = a[i__5].r; i__4 = i__; i__5 = ia + 1; e[i__4].r = a[i__5].r, e[i__4].i = a[i__5].i; ia += 2; /* L20: */ } if (n > 0) { i__3 = n; i__4 = ia; d__[i__3] = a[i__4].r; } } else { /* Type 7-12: generate a diagonally dominant matrix with unknown condition number in the vectors D and E. */ if (! zerot || ! dotype[7]) { /* Let D and E have values from [-1,1]. */ slarnv_(&c__2, iseed, &n, &d__[1]); i__3 = n - 1; clarnv_(&c__2, iseed, &i__3, &e[1]); /* Make the tridiagonal matrix diagonally dominant. */ if (n == 1) { d__[1] = dabs(d__[1]); } else { d__[1] = dabs(d__[1]) + c_abs(&e[1]); d__[n] = (r__1 = d__[n], dabs(r__1)) + c_abs(&e[n - 1] ); i__3 = n - 1; for (i__ = 2; i__ <= i__3; ++i__) { d__[i__] = (r__1 = d__[i__], dabs(r__1)) + c_abs(& e[i__]) + c_abs(&e[i__ - 1]); /* L30: */ } } /* Scale D and E so the maximum element is ANORM. */ ix = isamax_(&n, &d__[1], &c__1); dmax__ = d__[ix]; r__1 = anorm / dmax__; sscal_(&n, &r__1, &d__[1], &c__1); if (n > 1) { i__3 = n - 1; r__1 = anorm / dmax__; csscal_(&i__3, &r__1, &e[1], &c__1); } } else if (izero > 0) { /* Reuse the last matrix by copying back the zeroed out elements. */ if (izero == 1) { d__[1] = z__[1]; if (n > 1) { e[1].r = z__[2], e[1].i = 0.f; } } else if (izero == n) { i__3 = n - 1; e[i__3].r = z__[0], e[i__3].i = 0.f; d__[n] = z__[1]; } else { i__3 = izero - 1; e[i__3].r = z__[0], e[i__3].i = 0.f; d__[izero] = z__[1]; i__3 = izero; e[i__3].r = z__[2], e[i__3].i = 0.f; } } /* For types 8-10, set one row and column of the matrix to zero. */ izero = 0; if (imat == 8) { izero = 1; z__[1] = d__[1]; d__[1] = 0.f; if (n > 1) { z__[2] = e[1].r; e[1].r = 0.f, e[1].i = 0.f; } } else if (imat == 9) { izero = n; if (n > 1) { i__3 = n - 1; z__[0] = e[i__3].r; i__3 = n - 1; e[i__3].r = 0.f, e[i__3].i = 0.f; } z__[1] = d__[n]; d__[n] = 0.f; } else if (imat == 10) { izero = (n + 1) / 2; if (izero > 1) { i__3 = izero - 1; z__[0] = e[i__3].r; i__3 = izero - 1; e[i__3].r = 0.f, e[i__3].i = 0.f; i__3 = izero; z__[2] = e[i__3].r; i__3 = izero; e[i__3].r = 0.f, e[i__3].i = 0.f; } z__[1] = d__[izero]; d__[izero] = 0.f; } } /* Generate NRHS random solution vectors. */ ix = 1; i__3 = *nrhs; for (j = 1; j <= i__3; ++j) { clarnv_(&c__2, iseed, &n, &xact[ix]); ix += lda; /* L40: */ } /* Set the right hand side. */ claptm_("Lower", &n, nrhs, &c_b24, &d__[1], &e[1], &xact[1], &lda, &c_b25, &b[1], &lda); for (ifact = 1; ifact <= 2; ++ifact) { if (ifact == 1) { *(unsigned char *)fact = 'F'; } else { *(unsigned char *)fact = 'N'; } /* Compute the condition number for comparison with the value returned by CPTSVX. */ if (zerot) { if (ifact == 1) { goto L100; } rcondc = 0.f; } else if (ifact == 1) { /* Compute the 1-norm of A. */ anorm = clanht_("1", &n, &d__[1], &e[1]); scopy_(&n, &d__[1], &c__1, &d__[n + 1], &c__1); if (n > 1) { i__3 = n - 1; ccopy_(&i__3, &e[1], &c__1, &e[n + 1], &c__1); } /* Factor the matrix A. */ cpttrf_(&n, &d__[n + 1], &e[n + 1], &info); /* Use CPTTRS to solve for one column at a time of inv(A), computing the maximum column sum as we go. */ ainvnm = 0.f; i__3 = n; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = n; for (j = 1; j <= i__4; ++j) { i__5 = j; x[i__5].r = 0.f, x[i__5].i = 0.f; /* L50: */ } i__4 = i__; x[i__4].r = 1.f, x[i__4].i = 0.f; cpttrs_("Lower", &n, &c__1, &d__[n + 1], &e[n + 1], & x[1], &lda, &info); /* Computing MAX */ r__1 = ainvnm, r__2 = scasum_(&n, &x[1], &c__1); ainvnm = dmax(r__1,r__2); /* L60: */ } /* Compute the 1-norm condition number of A. */ if (anorm <= 0.f || ainvnm <= 0.f) { rcondc = 1.f; } else { rcondc = 1.f / anorm / ainvnm; } } if (ifact == 2) { /* --- Test CPTSV -- */ scopy_(&n, &d__[1], &c__1, &d__[n + 1], &c__1); if (n > 1) { i__3 = n - 1; ccopy_(&i__3, &e[1], &c__1, &e[n + 1], &c__1); } clacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &lda); /* Factor A as L*D*L' and solve the system A*X = B. */ s_copy(srnamc_1.srnamt, "CPTSV ", (ftnlen)6, (ftnlen)6); cptsv_(&n, nrhs, &d__[n + 1], &e[n + 1], &x[1], &lda, & info); /* Check error code from CPTSV . */ if (info != izero) { alaerh_(path, "CPTSV ", &info, &izero, " ", &n, &n, & c__1, &c__1, nrhs, &imat, &nfail, &nerrs, nout); } nt = 0; if (izero == 0) { /* Check the factorization by computing the ratio norm(L*D*L' - A) / (n * norm(A) * EPS ) */ cptt01_(&n, &d__[1], &e[1], &d__[n + 1], &e[n + 1], & work[1], result); /* Compute the residual in the solution. */ clacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda); cptt02_("Lower", &n, nrhs, &d__[1], &e[1], &x[1], & lda, &work[1], &lda, &result[1]); /* Check solution from generated exact solution. */ cget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[2]); nt = 3; } /* Print information about the tests that did not pass the threshold. */ i__3 = nt; for (k = 1; k <= i__3; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } io___35.ciunit = *nout; s_wsfe(&io___35); do_fio(&c__1, "CPTSV ", (ftnlen)6); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&imat, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&result[k - 1], (ftnlen) sizeof(real)); e_wsfe(); ++nfail; } /* L70: */ } nrun += nt; } /* --- Test CPTSVX --- */ if (ifact > 1) { /* Initialize D( N+1:2*N ) and E( N+1:2*N ) to zero. */ i__3 = n - 1; for (i__ = 1; i__ <= i__3; ++i__) { d__[n + i__] = 0.f; i__4 = n + i__; e[i__4].r = 0.f, e[i__4].i = 0.f; /* L80: */ } if (n > 0) { d__[n + n] = 0.f; } } claset_("Full", &n, nrhs, &c_b62, &c_b62, &x[1], &lda); /* Solve the system and compute the condition number and error bounds using CPTSVX. */ s_copy(srnamc_1.srnamt, "CPTSVX", (ftnlen)6, (ftnlen)6); cptsvx_(fact, &n, nrhs, &d__[1], &e[1], &d__[n + 1], &e[n + 1] , &b[1], &lda, &x[1], &lda, &rcond, &rwork[1], &rwork[ *nrhs + 1], &work[1], &rwork[(*nrhs << 1) + 1], &info); /* Check the error code from CPTSVX. */ if (info != izero) { alaerh_(path, "CPTSVX", &info, &izero, fact, &n, &n, & c__1, &c__1, nrhs, &imat, &nfail, &nerrs, nout); } if (izero == 0) { if (ifact == 2) { /* Check the factorization by computing the ratio norm(L*D*L' - A) / (n * norm(A) * EPS ) */ k1 = 1; cptt01_(&n, &d__[1], &e[1], &d__[n + 1], &e[n + 1], & work[1], result); } else { k1 = 2; } /* Compute the residual in the solution. */ clacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda); cptt02_("Lower", &n, nrhs, &d__[1], &e[1], &x[1], &lda, & work[1], &lda, &result[1]); /* Check solution from generated exact solution. */ cget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, & result[2]); /* Check error bounds from iterative refinement. */ cptt05_(&n, nrhs, &d__[1], &e[1], &b[1], &lda, &x[1], & lda, &xact[1], &lda, &rwork[1], &rwork[*nrhs + 1], &result[3]); } else { k1 = 6; } /* Check the reciprocal of the condition number. */ result[5] = sget06_(&rcond, &rcondc); /* Print information about the tests that did not pass the threshold. */ for (k = k1; k <= 6; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } io___38.ciunit = *nout; s_wsfe(&io___38); do_fio(&c__1, "CPTSVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[k - 1], (ftnlen)sizeof( real)); e_wsfe(); ++nfail; } /* L90: */ } nrun = nrun + 7 - k1; L100: ; } L110: ; } /* L120: */ } /* Print a summary of the results. */ alasvm_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of CDRVPT */ } /* cdrvpt_ */