#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__1 = 1; static integer c__2 = 2; static integer c__0 = 0; static integer c_n1 = -1; static doublecomplex c_b50 = {0.,0.}; /* Subroutine */ int zdrvhe_(logical *dotype, integer *nn, integer *nval, integer *nrhs, doublereal *thresh, logical *tsterr, integer *nmax, doublecomplex *a, doublecomplex *afac, doublecomplex *ainv, doublecomplex *b, doublecomplex *x, doublecomplex *xact, doublecomplex *work, doublereal *rwork, integer *iwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; static char uplos[1*2] = "U" "L"; static char facts[1*2] = "F" "N"; /* Format strings */ static char fmt_9999[] = "(1x,a6,\002, UPLO='\002,a1,\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', UPLO='\002,a" "1,\002', N =\002,i5,\002, type \002,i2,\002, test \002,i2,\002, " "ratio =\002,g12.5)"; /* System generated locals */ address a__1[2]; integer i__1, i__2, i__3, i__4, i__5, i__6[2]; char ch__1[2]; /* Builtin functions Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ static char fact[1]; static integer ioff, mode, imat, info; static char path[3], dist[1], uplo[1], type__[1]; static integer nrun, i__, j, k, n, ifact, nfail, iseed[4]; extern doublereal dget06_(doublereal *, doublereal *); static integer nbmin; static doublereal rcond; static integer nimat; extern /* Subroutine */ int zhet01_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *); static doublereal anorm; extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal * ); static integer iuplo, izero, i1, i2, k1, lwork, nerrs; extern /* Subroutine */ int zhesv_(char *, integer *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *), zpot02_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal * ); static logical zerot; extern /* Subroutine */ int zpot05_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *); static char xtype[1]; extern /* Subroutine */ int zlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, char *), aladhd_(integer *, char *); static integer nb, in, kl; extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); static integer ku, nt; static doublereal rcondc; extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer *, integer *); static doublereal cndnum; extern /* Subroutine */ int zlaipd_(integer *, doublecomplex *, integer *, integer *); static doublereal ainvnm; extern /* Subroutine */ int xlaenv_(integer *, integer *), zhetrf_(char *, integer *, doublecomplex *, integer *, integer *, doublecomplex * , integer *, integer *), zhetri_(char *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer * , integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlatms_(integer *, integer *, char *, integer *, char *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, char *, doublecomplex *, integer *, doublecomplex *, integer *); static doublereal result[6]; extern /* Subroutine */ int zhesvx_(char *, char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, doublecomplex *, integer *, doublereal *, integer *), zerrvx_(char *, integer *); static integer lda; /* Fortran I/O blocks */ static cilist io___42 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___45 = { 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 ======= ZDRVHE tests the driver routines ZHESV 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) DOUBLE PRECISION 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. NMAX (input) INTEGER The maximum value permitted for N, used in dimensioning the work arrays. A (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) AFAC (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) AINV (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) B (workspace) COMPLEX*16 array, dimension (NMAX*NRHS) X (workspace) COMPLEX*16 array, dimension (NMAX*NRHS) XACT (workspace) COMPLEX*16 array, dimension (NMAX*NRHS) WORK (workspace) COMPLEX*16 array, dimension (NMAX*max(2,NRHS)) RWORK (workspace) DOUBLE PRECISION array, dimension (NMAX+2*NRHS) IWORK (workspace) INTEGER array, dimension (NMAX) NOUT (input) INTEGER The unit number for output. ===================================================================== Parameter adjustments */ --iwork; --rwork; --work; --xact; --x; --b; --ainv; --afac; --a; --nval; --dotype; /* Function Body Initialize constants and the random number seed. */ *(unsigned char *)path = 'Z'; s_copy(path + 1, "HE", (ftnlen)2, (ftnlen)2); nrun = 0; nfail = 0; nerrs = 0; for (i__ = 1; i__ <= 4; ++i__) { iseed[i__ - 1] = iseedy[i__ - 1]; /* L10: */ } /* Computing MAX */ i__1 = *nmax << 1, i__2 = *nmax * *nrhs; lwork = max(i__1,i__2); /* Test the error exits */ if (*tsterr) { zerrvx_(path, nout); } infoc_1.infot = 0; /* Set the block size and minimum block size for testing. */ nb = 1; nbmin = 2; xlaenv_(&c__1, &nb); xlaenv_(&c__2, &nbmin); /* Do for each value of N in NVAL */ i__1 = *nn; for (in = 1; in <= i__1; ++in) { n = nval[in]; lda = max(n,1); *(unsigned char *)xtype = 'N'; nimat = 10; 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 (! dotype[imat]) { goto L170; } /* Skip types 3, 4, 5, or 6 if the matrix size is too small. */ zerot = imat >= 3 && imat <= 6; if (zerot && n < imat - 2) { goto L170; } /* Do first for UPLO = 'U', then for UPLO = 'L' */ for (iuplo = 1; iuplo <= 2; ++iuplo) { *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1]; /* Set up parameters with ZLATB4 and generate a test matrix with ZLATMS. */ zlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)6, (ftnlen)6); zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, & cndnum, &anorm, &kl, &ku, uplo, &a[1], &lda, &work[1], &info); /* Check error code from ZLATMS. */ if (info != 0) { alaerh_(path, "ZLATMS", &info, &c__0, uplo, &n, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); goto L160; } /* For types 3-6, zero one or more rows and columns of the matrix to test that INFO is returned correctly. */ if (zerot) { if (imat == 3) { izero = 1; } else if (imat == 4) { izero = n; } else { izero = n / 2 + 1; } if (imat < 6) { /* Set row and column IZERO to zero. */ if (iuplo == 1) { ioff = (izero - 1) * lda; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = ioff + i__; a[i__4].r = 0., a[i__4].i = 0.; /* L20: */ } ioff += izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { i__4 = ioff; a[i__4].r = 0., a[i__4].i = 0.; ioff += lda; /* L30: */ } } else { ioff = izero; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = ioff; a[i__4].r = 0., a[i__4].i = 0.; ioff += lda; /* L40: */ } ioff -= izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { i__4 = ioff + i__; a[i__4].r = 0., a[i__4].i = 0.; /* L50: */ } } } else { ioff = 0; if (iuplo == 1) { /* Set the first IZERO rows and columns to zero. */ i__3 = n; for (j = 1; j <= i__3; ++j) { i2 = min(j,izero); i__4 = i2; for (i__ = 1; i__ <= i__4; ++i__) { i__5 = ioff + i__; a[i__5].r = 0., a[i__5].i = 0.; /* L60: */ } ioff += lda; /* L70: */ } } else { /* Set the last IZERO rows and columns to zero. */ i__3 = n; for (j = 1; j <= i__3; ++j) { i1 = max(j,izero); i__4 = n; for (i__ = i1; i__ <= i__4; ++i__) { i__5 = ioff + i__; a[i__5].r = 0., a[i__5].i = 0.; /* L80: */ } ioff += lda; /* L90: */ } } } } else { izero = 0; } /* Set the imaginary part of the diagonals. */ i__3 = lda + 1; zlaipd_(&n, &a[1], &i__3, &c__0); for (ifact = 1; ifact <= 2; ++ifact) { /* Do first for FACT = 'F', then for other values. */ *(unsigned char *)fact = *(unsigned char *)&facts[ifact - 1]; /* Compute the condition number for comparison with the value returned by ZHESVX. */ if (zerot) { if (ifact == 1) { goto L150; } rcondc = 0.; } else if (ifact == 1) { /* Compute the 1-norm of A. */ anorm = zlanhe_("1", uplo, &n, &a[1], &lda, &rwork[1]); /* Factor the matrix A. */ zlacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda); zhetrf_(uplo, &n, &afac[1], &lda, &iwork[1], &work[1], &lwork, &info); /* Compute inv(A) and take its norm. */ zlacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda); zhetri_(uplo, &n, &ainv[1], &lda, &iwork[1], &work[1], &info); ainvnm = zlanhe_("1", uplo, &n, &ainv[1], &lda, & rwork[1]); /* Compute the 1-norm condition number of A. */ if (anorm <= 0. || ainvnm <= 0.) { rcondc = 1.; } else { rcondc = 1. / anorm / ainvnm; } } /* Form an exact solution and set the right hand side. */ s_copy(srnamc_1.srnamt, "ZLARHS", (ftnlen)6, (ftnlen)6); zlarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, nrhs, & a[1], &lda, &xact[1], &lda, &b[1], &lda, iseed, & info); *(unsigned char *)xtype = 'C'; /* --- Test ZHESV --- */ if (ifact == 2) { zlacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda); zlacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &lda); /* Factor the matrix and solve the system using ZHESV. */ s_copy(srnamc_1.srnamt, "ZHESV ", (ftnlen)6, (ftnlen) 6); zhesv_(uplo, &n, nrhs, &afac[1], &lda, &iwork[1], &x[ 1], &lda, &work[1], &lwork, &info); /* Adjust the expected value of INFO to account for pivoting. */ k = izero; if (k > 0) { L100: if (iwork[k] < 0) { if (iwork[k] != -k) { k = -iwork[k]; goto L100; } } else if (iwork[k] != k) { k = iwork[k]; goto L100; } } /* Check error code from ZHESV . */ if (info != k) { alaerh_(path, "ZHESV ", &info, &k, uplo, &n, &n, & c_n1, &c_n1, nrhs, &imat, &nfail, &nerrs, nout); goto L120; } else if (info != 0) { goto L120; } /* Reconstruct matrix from factors and compute residual. */ zhet01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &iwork[ 1], &ainv[1], &lda, &rwork[1], result); /* Compute residual of the computed solution. */ zlacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda); zpot02_(uplo, &n, nrhs, &a[1], &lda, &x[1], &lda, & work[1], &lda, &rwork[1], &result[1]); /* Check solution from generated exact solution. */ zget04_(&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___42.ciunit = *nout; s_wsfe(&io___42); do_fio(&c__1, "ZHESV ", (ftnlen)6); do_fio(&c__1, uplo, (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(doublereal)); e_wsfe(); ++nfail; } /* L110: */ } nrun += nt; L120: ; } /* --- Test ZHESVX --- */ if (ifact == 2) { zlaset_(uplo, &n, &n, &c_b50, &c_b50, &afac[1], &lda); } zlaset_("Full", &n, nrhs, &c_b50, &c_b50, &x[1], &lda); /* Solve the system and compute the condition number and error bounds using ZHESVX. */ s_copy(srnamc_1.srnamt, "ZHESVX", (ftnlen)6, (ftnlen)6); zhesvx_(fact, uplo, &n, nrhs, &a[1], &lda, &afac[1], &lda, &iwork[1], &b[1], &lda, &x[1], &lda, &rcond, & rwork[1], &rwork[*nrhs + 1], &work[1], &lwork, & rwork[(*nrhs << 1) + 1], &info); /* Adjust the expected value of INFO to account for pivoting. */ k = izero; if (k > 0) { L130: if (iwork[k] < 0) { if (iwork[k] != -k) { k = -iwork[k]; goto L130; } } else if (iwork[k] != k) { k = iwork[k]; goto L130; } } /* Check the error code from ZHESVX. */ if (info != k) { /* Writing concatenation */ i__6[0] = 1, a__1[0] = fact; i__6[1] = 1, a__1[1] = uplo; s_cat(ch__1, a__1, i__6, &c__2, (ftnlen)2); alaerh_(path, "ZHESVX", &info, &k, ch__1, &n, &n, & c_n1, &c_n1, nrhs, &imat, &nfail, &nerrs, nout); goto L150; } if (info == 0) { if (ifact >= 2) { /* Reconstruct matrix from factors and compute residual. */ zhet01_(uplo, &n, &a[1], &lda, &afac[1], &lda, & iwork[1], &ainv[1], &lda, &rwork[(*nrhs << 1) + 1], result); k1 = 1; } else { k1 = 2; } /* Compute residual of the computed solution. */ zlacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda); zpot02_(uplo, &n, nrhs, &a[1], &lda, &x[1], &lda, & work[1], &lda, &rwork[(*nrhs << 1) + 1], & result[1]); /* Check solution from generated exact solution. */ zget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[2]); /* Check the error bounds from iterative refinement. */ zpot05_(uplo, &n, nrhs, &a[1], &lda, &b[1], &lda, &x[ 1], &lda, &xact[1], &lda, &rwork[1], &rwork[* nrhs + 1], &result[3]); } else { k1 = 6; } /* Compare RCOND from ZHESVX with the computed value in RCONDC. */ result[5] = dget06_(&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___45.ciunit = *nout; s_wsfe(&io___45); do_fio(&c__1, "ZHESVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, uplo, (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(doublereal)); e_wsfe(); ++nfail; } /* L140: */ } nrun = nrun + 7 - k1; L150: ; } L160: ; } L170: ; } /* L180: */ } /* Print a summary of the results. */ alasvm_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of ZDRVHE */ } /* zdrvhe_ */