#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 zchksp_(logical *dotype, integer *nn, integer *nval, 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, " "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)"; /* 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 *); extern logical lsame_(char *, char *); static doublereal rcond; static integer nimat; static doublereal anorm; extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal * ); static integer iuplo, izero, i1, i2, nerrs; extern /* Subroutine */ int zspt01_(char *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *); static logical zerot; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zppt05_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *), zspt02_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *), zspt03_(char *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *); static char xtype[1]; extern /* Subroutine */ int zlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, 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, nt; static doublereal rcondc; static char packit[1]; extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer *, integer *); static doublereal cndnum; static logical trfcon; extern /* Subroutine */ int 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 *); extern doublereal zlansp_(char *, char *, integer *, doublecomplex *, doublereal *); extern /* Subroutine */ int zlatms_(integer *, integer *, char *, integer *, char *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, char *, doublecomplex *, integer *, doublecomplex *, integer *), zspcon_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, integer *), zlatsp_(char *, integer *, doublecomplex *, integer *); static doublereal result[8]; extern /* Subroutine */ int zsprfs_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zsptrf_(char * , integer *, doublecomplex *, integer *, integer *), zsptri_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zerrsy_(char *, integer *), zsptrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *); static integer lda, npp; /* Fortran I/O blocks */ static cilist io___38 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___41 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___43 = { 0, 0, 0, fmt_9999, 0 }; /* -- LAPACK test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University December 7, 1999 Purpose ======= ZCHKSP tests ZSPTRF, -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. 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+1)/2) AFAC (workspace) COMPLEX*16 array, dimension (NMAX*(NMAX+1)/2) AINV (workspace) COMPLEX*16 array, dimension (NMAX*(NMAX+1)/2) 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(2,NSMAX)) RWORK (workspace) DOUBLE PRECISION array, dimension (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; --nval; --dotype; /* Function Body Initialize constants and the random number seed. */ s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17); s_copy(path + 1, "SP", (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) { zerrsy_(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 = 11; 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 L160; } /* 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 L160; } /* Do first for UPLO = 'U', then for UPLO = 'L' */ for (iuplo = 1; iuplo <= 2; ++iuplo) { *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1]; if (lsame_(uplo, "U")) { *(unsigned char *)packit = 'C'; } else { *(unsigned char *)packit = 'R'; } if (imat != 11) { /* 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, packit, &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 L150; } /* 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) * izero / 2; 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 += i__; /* 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 = ioff + n - i__; /* 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 { if (iuplo == 1) { /* Set the first IZERO rows and columns to zero. */ ioff = 0; 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 += j; /* L70: */ } } else { /* Set the last IZERO rows and columns to zero. */ ioff = 0; 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 = ioff + n - j; /* L90: */ } } } } else { izero = 0; } } else { /* Use a special block diagonal matrix to test alternate code for the 2 x 2 blocks. */ zlatsp_(uplo, &n, &a[1], iseed); } /* Compute the L*D*L' or U*D*U' factorization of the matrix. */ npp = n * (n + 1) / 2; zcopy_(&npp, &a[1], &c__1, &afac[1], &c__1); s_copy(srnamc_1.srnamt, "ZSPTRF", (ftnlen)6, (ftnlen)6); zsptrf_(uplo, &n, &afac[1], &iwork[1], &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 ZSPTRF. */ if (info != k) { alaerh_(path, "ZSPTRF", &info, &k, uplo, &n, &n, &c_n1, & c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } if (info != 0) { trfcon = TRUE_; } else { trfcon = FALSE_; } /* + TEST 1 Reconstruct matrix from factors and compute residual. */ zspt01_(uplo, &n, &a[1], &afac[1], &iwork[1], &ainv[1], &lda, &rwork[1], result); nt = 1; /* + TEST 2 Form the inverse and compute the residual. */ if (! trfcon) { zcopy_(&npp, &afac[1], &c__1, &ainv[1], &c__1); s_copy(srnamc_1.srnamt, "ZSPTRI", (ftnlen)6, (ftnlen)6); zsptri_(uplo, &n, &ainv[1], &iwork[1], &work[1], &info); /* Check error code from ZSPTRI. */ if (info != 0) { alaerh_(path, "ZSPTRI", &info, &c__0, uplo, &n, &n, & c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } zspt03_(uplo, &n, &a[1], &ainv[1], &work[1], &lda, &rwork[ 1], &rcondc, &result[1]); nt = 2; } /* 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) { alahd_(nout, path); } io___38.ciunit = *nout; s_wsfe(&io___38); 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; /* Do only the condition estimate if INFO is not 0. */ if (trfcon) { rcondc = 0.; goto L140; } i__3 = *nns; for (irhs = 1; irhs <= i__3; ++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); zlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda); s_copy(srnamc_1.srnamt, "ZSPTRS", (ftnlen)6, (ftnlen)6); zsptrs_(uplo, &n, &nrhs, &afac[1], &iwork[1], &x[1], &lda, &info); /* Check error code from ZSPTRS. */ if (info != 0) { alaerh_(path, "ZSPTRS", &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); zspt02_(uplo, &n, &nrhs, &a[1], &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, "ZSPRFS", (ftnlen)6, (ftnlen)6); zsprfs_(uplo, &n, &nrhs, &a[1], &afac[1], &iwork[1], &b[1] , &lda, &x[1], &lda, &rwork[1], &rwork[nrhs + 1], &work[1], &rwork[(nrhs << 1) + 1], &info); /* Check error code from ZSPRFS. */ if (info != 0) { alaerh_(path, "ZSPRFS", &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]); zppt05_(uplo, &n, &nrhs, &a[1], &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___41.ciunit = *nout; s_wsfe(&io___41); 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 = zlansp_("1", uplo, &n, &a[1], &rwork[1]); s_copy(srnamc_1.srnamt, "ZSPCON", (ftnlen)6, (ftnlen)6); zspcon_(uplo, &n, &afac[1], &iwork[1], &anorm, &rcond, &work[ 1], &info); /* Check error code from ZSPCON. */ if (info != 0) { alaerh_(path, "ZSPCON", &info, &c__0, uplo, &n, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } result[7] = dget06_(&rcond, &rcondc); /* Print the test ratio if it is .GE. THRESH. */ if (result[7] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___43.ciunit = *nout; s_wsfe(&io___43); 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: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of ZCHKSP */ } /* zchksp_ */