#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, iounit; 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__1 = 1; static integer c__0 = 0; static integer c_n1 = -1; static integer c__3 = 3; static integer c__7 = 7; static integer c__4 = 4; static real c_b101 = 1.f; static integer c__8 = 8; static integer c__9 = 9; /* Subroutine */ int schktr_(logical *dotype, integer *nn, integer *nval, integer *nnb, integer *nbval, integer *nns, integer *nsval, real * thresh, logical *tsterr, integer *nmax, real *a, real *ainv, real *b, real *x, real *xact, real *work, real *rwork, integer *iwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; static char uplos[1*2] = "U" "L"; static char transs[1*3] = "N" "T" "C"; /* Format strings */ static char fmt_9999[] = "(\002 UPLO='\002,a1,\002', DIAG='\002,a1,\002'" ", N=\002,i5,\002, NB=\002,i4,\002, type \002,i2,\002, test(\002," "i2,\002)= \002,g12.5)"; static char fmt_9998[] = "(\002 UPLO='\002,a1,\002', TRANS='\002,a1,\002" "', DIAG='\002,a1,\002', N=\002,i5,\002, NB=\002,i4,\002, type" " \002,i2,\002, test(\002,i2,\002)= \002,g12" ".5)"; static char fmt_9997[] = "(\002 NORM='\002,a1,\002', UPLO ='\002,a1,\002" "', N=\002,i5,\002,\002,11x,\002 type \002,i2,\002, test(\002,i2" ",\002)=\002,g12.5)"; static char fmt_9996[] = "(1x,a6,\002( '\002,a1,\002', '\002,a1,\002', " "'\002,a1,\002', '\002,a1,\002',\002,i5,\002, ... ), type \002,i2," "\002, test(\002,i2,\002)=\002,g12.5)"; /* System generated locals */ address a__1[2], a__2[3], a__3[4]; integer i__1, i__2, i__3[2], i__4, i__5[3], i__6[4]; char ch__1[2], ch__2[3], ch__3[4]; /* Builtin functions Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen), s_cat(char *, char **, integer *, integer *, ftnlen); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Local variables */ static char diag[1]; static integer imat, info; static char path[3]; static integer irhs, nrhs; static char norm[1], uplo[1]; static integer nrun, i__; extern /* Subroutine */ int alahd_(integer *, char *); static integer k, idiag, n; static real scale; static integer nfail, iseed[4]; extern logical lsame_(char *, char *); static real rcond; extern /* Subroutine */ int sget04_(integer *, integer *, real *, integer *, real *, integer *, real *, real *); static real anorm; static integer itran; static char trans[1]; static integer iuplo, nerrs; static real dummy; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *), strt01_(char *, char *, integer *, real *, integer *, real *, integer *, real *, real *, real *), strt02_(char *, char *, char *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, real *), strt03_(char *, char *, char *, integer * , integer *, real *, integer *, real *, real *, real *, real *, integer *, real *, integer *, real *, real *), strt05_(char *, char *, char *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, real *, real *), strt06_(real *, real *, char *, char *, integer *, real *, integer *, real *, real *); static char xtype[1]; static integer nb, in; extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); static real rcondc, rcondi; extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer *, integer *); static real rcondo, ainvnm; extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer * , integer *, integer *), xlaenv_( integer *, integer *); extern doublereal slantr_(char *, char *, char *, integer *, integer *, real *, integer *, real *); extern /* Subroutine */ int slatrs_(char *, char *, char *, char *, integer *, real *, integer *, real *, real *, real *, integer *), slattr_(integer *, char *, char * , char *, integer *, integer *, real *, integer *, real *, real *, integer *), strcon_(char *, char *, char *, integer *, real *, integer *, real *, real *, integer *, integer *); static real result[9]; extern /* Subroutine */ int serrtr_(char *, integer *), strrfs_( char *, char *, char *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, real *, real *, integer *, integer *), strtri_(char *, char *, integer *, real *, integer *, integer *), strtrs_(char *, char *, char *, integer *, integer *, real *, integer *, real *, integer *, integer *); static integer lda, inb; /* Fortran I/O blocks */ static cilist io___27 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___36 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___38 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___40 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___41 = { 0, 0, 0, fmt_9996, 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 ======= SCHKTR tests STRTRI, -TRS, -RFS, and -CON, and SLATRS 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 column dimension N. NNB (input) INTEGER The number of values of NB contained in the vector NBVAL. NBVAL (input) INTEGER array, dimension (NNB) 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) 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. NMAX (input) INTEGER The leading dimension of the work arrays. NMAX >= the maximum value of N in NVAL. A (workspace) REAL array, dimension (NMAX*NMAX) AINV (workspace) REAL array, dimension (NMAX*NMAX) B (workspace) REAL array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL. X (workspace) REAL array, dimension (NMAX*NSMAX) XACT (workspace) REAL array, dimension (NMAX*NSMAX) WORK (workspace) REAL array, dimension (NMAX*max(3,NSMAX)) RWORK (workspace) REAL 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; --a; --nsval; --nbval; --nval; --dotype; /* Function Body Initialize constants and the random number seed. */ s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "TR", (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) { serrtr_(path, nout); } infoc_1.infot = 0; xlaenv_(&c__2, &c__2); 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); *(unsigned char *)xtype = 'N'; for (imat = 1; imat <= 10; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L80; } for (iuplo = 1; iuplo <= 2; ++iuplo) { /* Do first for UPLO = 'U', then for UPLO = 'L' */ *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1]; /* Call SLATTR to generate a triangular test matrix. */ s_copy(srnamc_1.srnamt, "SLATTR", (ftnlen)6, (ftnlen)6); slattr_(&imat, uplo, "No transpose", diag, iseed, &n, &a[1], & lda, &x[1], &work[1], &info); /* Set IDIAG = 1 for non-unit matrices, 2 for unit. */ if (lsame_(diag, "N")) { idiag = 1; } else { idiag = 2; } i__2 = *nnb; for (inb = 1; inb <= i__2; ++inb) { /* Do for each blocksize in NBVAL */ nb = nbval[inb]; xlaenv_(&c__1, &nb); /* + TEST 1 Form the inverse of A. */ slacpy_(uplo, &n, &n, &a[1], &lda, &ainv[1], &lda); s_copy(srnamc_1.srnamt, "STRTRI", (ftnlen)6, (ftnlen)6); strtri_(uplo, diag, &n, &ainv[1], &lda, &info); /* Check error code from STRTRI. */ if (info != 0) { /* Writing concatenation */ i__3[0] = 1, a__1[0] = uplo; i__3[1] = 1, a__1[1] = diag; s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); alaerh_(path, "STRTRI", &info, &c__0, ch__1, &n, &n, & c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout); } /* Compute the infinity-norm condition number of A. */ anorm = slantr_("I", uplo, diag, &n, &n, &a[1], &lda, & rwork[1]); ainvnm = slantr_("I", uplo, diag, &n, &n, &ainv[1], &lda, &rwork[1]); if (anorm <= 0.f || ainvnm <= 0.f) { rcondi = 1.f; } else { rcondi = 1.f / anorm / ainvnm; } /* Compute the residual for the triangular matrix times its inverse. Also compute the 1-norm condition number of A. */ strt01_(uplo, diag, &n, &a[1], &lda, &ainv[1], &lda, & rcondo, &rwork[1], result); /* Print the test ratio if it is .GE. THRESH. */ if (result[0] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___27.ciunit = *nout; s_wsfe(&io___27); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, diag, (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 *)&c__1, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[0], (ftnlen)sizeof(real) ); e_wsfe(); ++nfail; } ++nrun; /* Skip remaining tests if not the first block size. */ if (inb != 1) { goto L60; } i__4 = *nns; for (irhs = 1; irhs <= i__4; ++irhs) { nrhs = nsval[irhs]; *(unsigned char *)xtype = 'N'; for (itran = 1; itran <= 3; ++itran) { /* Do for op(A) = A, A**T, or A**H. */ *(unsigned char *)trans = *(unsigned char *)& transs[itran - 1]; if (itran == 1) { *(unsigned char *)norm = 'O'; rcondc = rcondo; } else { *(unsigned char *)norm = 'I'; rcondc = rcondi; } /* + TEST 2 Solve and compute residual for op(A)*x = b. */ s_copy(srnamc_1.srnamt, "SLARHS", (ftnlen)6, ( ftnlen)6); slarhs_(path, xtype, uplo, trans, &n, &n, &c__0, & idiag, &nrhs, &a[1], &lda, &xact[1], &lda, &b[1], &lda, iseed, &info); *(unsigned char *)xtype = 'C'; slacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], & lda); s_copy(srnamc_1.srnamt, "STRTRS", (ftnlen)6, ( ftnlen)6); strtrs_(uplo, trans, diag, &n, &nrhs, &a[1], &lda, &x[1], &lda, &info); /* Check error code from STRTRS. */ if (info != 0) { /* Writing concatenation */ i__5[0] = 1, a__2[0] = uplo; i__5[1] = 1, a__2[1] = trans; i__5[2] = 1, a__2[2] = diag; s_cat(ch__2, a__2, i__5, &c__3, (ftnlen)3); alaerh_(path, "STRTRS", &info, &c__0, ch__2, & n, &n, &c_n1, &c_n1, &nrhs, &imat, & nfail, &nerrs, nout); } /* This line is needed on a Sun SPARCstation. */ if (n > 0) { dummy = a[1]; } strt02_(uplo, trans, diag, &n, &nrhs, &a[1], &lda, &x[1], &lda, &b[1], &lda, &work[1], & result[1]); /* + TEST 3 Check solution from generated exact solution. */ sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[2]); /* + TESTS 4, 5, and 6 Use iterative refinement to improve the solution and compute error bounds. */ s_copy(srnamc_1.srnamt, "STRRFS", (ftnlen)6, ( ftnlen)6); strrfs_(uplo, trans, diag, &n, &nrhs, &a[1], &lda, &b[1], &lda, &x[1], &lda, &rwork[1], & rwork[nrhs + 1], &work[1], &iwork[1], & info); /* Check error code from STRRFS. */ if (info != 0) { /* Writing concatenation */ i__5[0] = 1, a__2[0] = uplo; i__5[1] = 1, a__2[1] = trans; i__5[2] = 1, a__2[2] = diag; s_cat(ch__2, a__2, i__5, &c__3, (ftnlen)3); alaerh_(path, "STRRFS", &info, &c__0, ch__2, & n, &n, &c_n1, &c_n1, &nrhs, &imat, & nfail, &nerrs, nout); } sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[3]); strt05_(uplo, trans, diag, &n, &nrhs, &a[1], &lda, &b[1], &lda, &x[1], &lda, &xact[1], &lda, &rwork[1], &rwork[nrhs + 1], &result[4]); /* Print information about the tests that did not pass the threshold. */ for (k = 2; k <= 6; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___36.ciunit = *nout; s_wsfe(&io___36); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, diag, (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(real)); e_wsfe(); ++nfail; } /* L20: */ } nrun += 5; /* L30: */ } /* L40: */ } /* + TEST 7 Get an estimate of RCOND = 1/CNDNUM. */ for (itran = 1; itran <= 2; ++itran) { if (itran == 1) { *(unsigned char *)norm = 'O'; rcondc = rcondo; } else { *(unsigned char *)norm = 'I'; rcondc = rcondi; } s_copy(srnamc_1.srnamt, "STRCON", (ftnlen)6, (ftnlen) 6); strcon_(norm, uplo, diag, &n, &a[1], &lda, &rcond, & work[1], &iwork[1], &info); /* Check error code from STRCON. */ if (info != 0) { /* Writing concatenation */ i__5[0] = 1, a__2[0] = norm; i__5[1] = 1, a__2[1] = uplo; i__5[2] = 1, a__2[2] = diag; s_cat(ch__2, a__2, i__5, &c__3, (ftnlen)3); alaerh_(path, "STRCON", &info, &c__0, ch__2, &n, & n, &c_n1, &c_n1, &c_n1, &imat, &nfail, & nerrs, nout); } strt06_(&rcond, &rcondc, uplo, diag, &n, &a[1], &lda, &rwork[1], &result[6]); /* Print the test ratio if it is .GE. THRESH. */ if (result[6] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___38.ciunit = *nout; s_wsfe(&io___38); do_fio(&c__1, norm, (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 *)&c__7, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[6], (ftnlen)sizeof( real)); e_wsfe(); ++nfail; } ++nrun; /* L50: */ } L60: ; } /* L70: */ } L80: ; } /* Use pathological test matrices to test SLATRS. */ for (imat = 11; imat <= 18; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L110; } for (iuplo = 1; iuplo <= 2; ++iuplo) { /* Do first for UPLO = 'U', then for UPLO = 'L' */ *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1]; for (itran = 1; itran <= 3; ++itran) { /* Do for op(A) = A, A**T, and A**H. */ *(unsigned char *)trans = *(unsigned char *)&transs[itran - 1]; /* Call SLATTR to generate a triangular test matrix. */ s_copy(srnamc_1.srnamt, "SLATTR", (ftnlen)6, (ftnlen)6); slattr_(&imat, uplo, trans, diag, iseed, &n, &a[1], &lda, &x[1], &work[1], &info); /* + TEST 8 Solve the system op(A)*x = b. */ s_copy(srnamc_1.srnamt, "SLATRS", (ftnlen)6, (ftnlen)6); scopy_(&n, &x[1], &c__1, &b[1], &c__1); slatrs_(uplo, trans, diag, "N", &n, &a[1], &lda, &b[1], & scale, &rwork[1], &info); /* Check error code from SLATRS. */ if (info != 0) { /* Writing concatenation */ i__6[0] = 1, a__3[0] = uplo; i__6[1] = 1, a__3[1] = trans; i__6[2] = 1, a__3[2] = diag; i__6[3] = 1, a__3[3] = "N"; s_cat(ch__3, a__3, i__6, &c__4, (ftnlen)4); alaerh_(path, "SLATRS", &info, &c__0, ch__3, &n, &n, & c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } strt03_(uplo, trans, diag, &n, &c__1, &a[1], &lda, &scale, &rwork[1], &c_b101, &b[1], &lda, &x[1], &lda, & work[1], &result[7]); /* + TEST 9 Solve op(A)*X = b again with NORMIN = 'Y'. */ scopy_(&n, &x[1], &c__1, &b[n + 1], &c__1); slatrs_(uplo, trans, diag, "Y", &n, &a[1], &lda, &b[n + 1] , &scale, &rwork[1], &info); /* Check error code from SLATRS. */ if (info != 0) { /* Writing concatenation */ i__6[0] = 1, a__3[0] = uplo; i__6[1] = 1, a__3[1] = trans; i__6[2] = 1, a__3[2] = diag; i__6[3] = 1, a__3[3] = "Y"; s_cat(ch__3, a__3, i__6, &c__4, (ftnlen)4); alaerh_(path, "SLATRS", &info, &c__0, ch__3, &n, &n, & c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } strt03_(uplo, trans, diag, &n, &c__1, &a[1], &lda, &scale, &rwork[1], &c_b101, &b[n + 1], &lda, &x[1], &lda, &work[1], &result[8]); /* Print information about the tests that did not pass the threshold. */ if (result[7] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___40.ciunit = *nout; s_wsfe(&io___40); do_fio(&c__1, "SLATRS", (ftnlen)6); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, diag, (ftnlen)1); do_fio(&c__1, "N", (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(real) ); e_wsfe(); ++nfail; } if (result[8] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___41.ciunit = *nout; s_wsfe(&io___41); do_fio(&c__1, "SLATRS", (ftnlen)6); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, diag, (ftnlen)1); do_fio(&c__1, "Y", (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__9, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[8], (ftnlen)sizeof(real) ); e_wsfe(); ++nfail; } nrun += 2; /* L90: */ } /* L100: */ } L110: ; } /* L120: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of SCHKTR */ } /* schktr_ */