#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__0 = 0; static integer c_n1 = -1; static integer c__1 = 1; static integer c__8 = 8; /* Subroutine */ int zchkhe_(logical *dotype, integer *nn, integer *nval, integer *nnb, integer *nbval, integer *nns, integer *nsval, 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"; /* Format strings */ static char fmt_9999[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, " "NB =\002,i4,\002, type \002,i2,\002, test \002,i2,\002, ratio " "=\002,g12.5)"; static char fmt_9998[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, " "NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g" "12.5)"; static char fmt_9997[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002" ",\002,10x,\002 type \002,i2,\002, test(\002,i2,\002) =\002,g12.5)" ; /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; /* Builtin functions Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Local variables */ static integer ioff, mode, imat, info; static char path[3], dist[1]; static integer irhs, nrhs; static char uplo[1], type__[1]; static integer nrun, i__, j, k; extern /* Subroutine */ int alahd_(integer *, char *); static integer n, nfail, iseed[4]; extern doublereal dget06_(doublereal *, doublereal *); 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, nerrs, lwork; extern /* Subroutine */ int zpot02_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *), zpot03_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *), zpot05_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex * , integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *); static logical zerot; static char xtype[1]; extern /* Subroutine */ int zlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, 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 alasum_(char *, integer *, integer *, integer *, integer *); static doublereal cndnum; extern /* Subroutine */ int zlaipd_(integer *, doublecomplex *, integer *, integer *), zhecon_(char *, integer *, doublecomplex *, integer * , integer *, doublereal *, doublereal *, doublecomplex *, integer *); static logical trfcon; extern /* Subroutine */ int xlaenv_(integer *, integer *), zerrhe_(char *, integer *), zherfs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zhetrf_(char *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zhetri_(char *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *), zlarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *), zlatms_(integer *, integer *, char *, integer *, char *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, char *, doublecomplex *, integer *, doublecomplex *, integer *); static doublereal result[8]; extern /* Subroutine */ int zhetrs_(char *, integer *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *); static integer lda, inb; /* Fortran I/O blocks */ static cilist io___39 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___42 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___44 = { 0, 0, 0, fmt_9997, 0 }; /* -- LAPACK test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 Purpose ======= ZCHKHE tests ZHETRF, -TRI, -TRS, -RFS, and -CON. 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. NNB (input) INTEGER The number of values of NB contained in the vector NBVAL. NBVAL (input) INTEGER array, dimension (NBVAL) The values of the blocksize NB. NNS (input) INTEGER The number of values of NRHS contained in the vector NSVAL. NSVAL (input) INTEGER array, dimension (NNS) The values of the number of right hand sides NRHS. 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*NSMAX) where NSMAX is the largest entry in NSVAL. X (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) XACT (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) WORK (workspace) COMPLEX*16 array, dimension (NMAX*max(3,NSMAX)) RWORK (workspace) DOUBLE PRECISION array, dimension (max(NMAX,2*NSMAX)) 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; --nsval; --nbval; --nval; --dotype; /* Function Body Initialize constants and the random number seed. */ s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17); 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: */ } /* Test the error exits */ if (*tsterr) { zerrhe_(path, nout); } infoc_1.infot = 0; /* 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; } izero = 0; 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); /* Do for each value of NB in NBVAL */ i__3 = *nnb; for (inb = 1; inb <= i__3; ++inb) { nb = nbval[inb]; xlaenv_(&c__1, &nb); /* Compute the L*D*L' or U*D*U' factorization of the matrix. */ zlacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda); lwork = max(2,nb) * lda; s_copy(srnamc_1.srnamt, "ZHETRF", (ftnlen)6, (ftnlen)6); zhetrf_(uplo, &n, &afac[1], &lda, &iwork[1], &ainv[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 ZHETRF. */ if (info != k) { alaerh_(path, "ZHETRF", &info, &k, uplo, &n, &n, & c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout); } if (info != 0) { trfcon = TRUE_; } else { trfcon = FALSE_; } /* + TEST 1 Reconstruct matrix from factors and compute residual. */ zhet01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &iwork[1], &ainv[1], &lda, &rwork[1], result); nt = 1; /* + TEST 2 Form the inverse and compute the residual. */ if (inb == 1 && ! trfcon) { zlacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda); s_copy(srnamc_1.srnamt, "ZHETRI", (ftnlen)6, (ftnlen) 6); zhetri_(uplo, &n, &ainv[1], &lda, &iwork[1], &work[1], &info); /* Check error code from ZHETRI. */ if (info != 0) { alaerh_(path, "ZHETRI", &info, &c_n1, uplo, &n, & n, &c_n1, &c_n1, &c_n1, &imat, &nfail, & nerrs, nout); } zpot03_(uplo, &n, &a[1], &lda, &ainv[1], &lda, &work[ 1], &lda, &rwork[1], &rcondc, &result[1]); nt = 2; } /* Print information about the tests that did not pass the threshold. */ i__4 = nt; for (k = 1; k <= i__4; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___39.ciunit = *nout; s_wsfe(&io___39); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&nb, (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; /* Skip the other tests if this is not the first block size. */ if (inb > 1) { goto L150; } /* Do only the condition estimate if INFO is not 0. */ if (trfcon) { rcondc = 0.; goto L140; } i__4 = *nns; for (irhs = 1; irhs <= i__4; ++irhs) { nrhs = nsval[irhs]; /* + TEST 3 Solve and compute residual for A * X = B. */ 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'; zlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda); s_copy(srnamc_1.srnamt, "ZHETRS", (ftnlen)6, (ftnlen) 6); zhetrs_(uplo, &n, &nrhs, &afac[1], &lda, &iwork[1], & x[1], &lda, &info); /* Check error code from ZHETRS. */ if (info != 0) { alaerh_(path, "ZHETRS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &nrhs, &imat, &nfail, & nerrs, nout); } 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[2]); /* + TEST 4 Check solution from generated exact solution. */ zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[3]); /* + TESTS 5, 6, and 7 Use iterative refinement to improve the solution. */ s_copy(srnamc_1.srnamt, "ZHERFS", (ftnlen)6, (ftnlen) 6); zherfs_(uplo, &n, &nrhs, &a[1], &lda, &afac[1], &lda, &iwork[1], &b[1], &lda, &x[1], &lda, &rwork[1] , &rwork[nrhs + 1], &work[1], &rwork[(nrhs << 1) + 1], &info); /* Check error code from ZHERFS. */ if (info != 0) { alaerh_(path, "ZHERFS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &nrhs, &imat, &nfail, & nerrs, nout); } zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[4]); zpot05_(uplo, &n, &nrhs, &a[1], &lda, &b[1], &lda, &x[ 1], &lda, &xact[1], &lda, &rwork[1], &rwork[ nrhs + 1], &result[5]); /* Print information about the tests that did not pass the threshold. */ for (k = 3; k <= 7; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___42.ciunit = *nout; s_wsfe(&io___42); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&nrhs, (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; } /* L120: */ } nrun += 5; /* L130: */ } /* + TEST 8 Get an estimate of RCOND = 1/CNDNUM. */ L140: anorm = zlanhe_("1", uplo, &n, &a[1], &lda, &rwork[1]); s_copy(srnamc_1.srnamt, "ZHECON", (ftnlen)6, (ftnlen)6); zhecon_(uplo, &n, &afac[1], &lda, &iwork[1], &anorm, & rcond, &work[1], &info); /* Check error code from ZHECON. */ if (info != 0) { alaerh_(path, "ZHECON", &info, &c__0, uplo, &n, &n, & c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } result[7] = dget06_(&rcond, &rcondc); /* Print information about the tests that did not pass the threshold. */ if (result[7] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___44.ciunit = *nout; s_wsfe(&io___44); 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 *)&c__8, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof( doublereal)); e_wsfe(); ++nfail; } ++nrun; L150: ; } L160: ; } L170: ; } /* L180: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of ZCHKHE */ } /* zchkhe_ */