#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 real c_b21 = 0.f; static integer c__1 = 1; static integer c__8 = 8; /* Subroutine */ int schkge_(logical *dotype, integer *nm, integer *mval, integer *nn, integer *nval, integer *nnb, integer *nbval, integer * nns, integer *nsval, real *thresh, logical *tsterr, integer *nmax, real *a, real *afac, 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 transs[1*3] = "N" "T" "C"; /* Format strings */ static char fmt_9999[] = "(\002 M = \002,i5,\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 TRANS='\002,a1,\002', N =\002,i5,\002, N" "RHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g1" "2.5)"; static char fmt_9997[] = "(\002 NORM ='\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 norm[1], type__[1]; static integer nrun, i__; extern /* Subroutine */ int alahd_(integer *, char *); static integer k, m, n, nfail, iseed[4]; extern /* Subroutine */ int sget01_(integer *, integer *, real *, integer *, real *, integer *, integer *, real *, real *), sget02_(char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, real *); static real rcond; extern /* Subroutine */ int sget03_(integer *, real *, integer *, real *, integer *, real *, integer *, real *, real *, real *), sget04_( integer *, integer *, real *, integer *, real *, integer *, real * , real *); static integer nimat; extern doublereal sget06_(real *, real *); extern /* Subroutine */ int sget07_(char *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer * , real *, real *, real *); static real anorm; static integer itran; static char trans[1]; static integer izero, nerrs; static real dummy; static integer lwork; static logical zerot; static char xtype[1]; extern /* Subroutine */ int slatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, real *, integer *, real *, char * ); static integer nb, im, 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 real rcondc; extern doublereal slange_(char *, integer *, integer *, real *, integer *, real *); static real rcondi; extern /* Subroutine */ int sgecon_(char *, integer *, real *, integer *, real *, real *, real *, integer *, integer *), alasum_( char *, integer *, integer *, integer *, integer *); static real cndnum, anormi, rcondo; extern /* Subroutine */ int serrge_(char *, integer *); static real ainvnm; extern /* Subroutine */ int sgerfs_(char *, integer *, integer *, real *, integer *, real *, integer *, integer *, real *, integer *, real * , integer *, real *, real *, real *, integer *, integer *) , sgetrf_(integer *, integer *, real *, integer *, integer *, integer *); static logical trfcon; static real anormo; extern /* Subroutine */ int sgetri_(integer *, real *, integer *, integer *, real *, integer *, integer *), 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 *) , slaset_(char *, integer *, integer *, real *, real *, real *, integer *), xlaenv_(integer *, integer *), slatms_( integer *, integer *, char *, integer *, char *, real *, integer * , real *, real *, integer *, integer *, char *, real *, integer *, real *, integer *), sgetrs_(char *, integer *, integer *, real *, integer *, integer *, real *, integer *, integer *); static real result[8]; static integer lda, inb; /* Fortran I/O blocks */ static cilist io___41 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___46 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___50 = { 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 December 7, 1999 Purpose ======= SCHKGE tests SGETRF, -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. NM (input) INTEGER The number of values of M contained in the vector MVAL. MVAL (input) INTEGER array, dimension (NM) The values of the matrix row dimension M. 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 (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) 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 maximum value permitted for M or N, used in dimensioning the work arrays. A (workspace) REAL array, dimension (NMAX*NMAX) AFAC (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(2*NMAX,2*NSMAX+NWORK)) IWORK (workspace) INTEGER array, dimension (2*NMAX) NOUT (input) INTEGER The unit number for output. ===================================================================== Parameter adjustments */ --iwork; --rwork; --work; --xact; --x; --b; --ainv; --afac; --a; --nsval; --nbval; --nval; --mval; --dotype; /* Function Body Initialize constants and the random number seed. */ s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "GE", (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) { serrge_(path, nout); } infoc_1.infot = 0; xlaenv_(&c__2, &c__2); /* Do for each value of M in MVAL */ i__1 = *nm; for (im = 1; im <= i__1; ++im) { m = mval[im]; lda = max(1,m); /* Do for each value of N in NVAL */ i__2 = *nn; for (in = 1; in <= i__2; ++in) { n = nval[in]; *(unsigned char *)xtype = 'N'; nimat = 11; if (m <= 0 || n <= 0) { nimat = 1; } i__3 = nimat; for (imat = 1; imat <= i__3; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L100; } /* Skip types 5, 6, or 7 if the matrix size is too small. */ zerot = imat >= 5 && imat <= 7; if (zerot && n < imat - 4) { goto L100; } /* Set up parameters with SLATB4 and generate a test matrix with SLATMS. */ slatb4_(path, &imat, &m, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)6, (ftnlen)6); slatms_(&m, &n, dist, iseed, type__, &rwork[1], &mode, & cndnum, &anorm, &kl, &ku, "No packing", &a[1], &lda, & work[1], &info); /* Check error code from SLATMS. */ if (info != 0) { alaerh_(path, "SLATMS", &info, &c__0, " ", &m, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); goto L100; } /* For types 5-7, zero one or more columns of the matrix to test that INFO is returned correctly. */ if (zerot) { if (imat == 5) { izero = 1; } else if (imat == 6) { izero = min(m,n); } else { izero = min(m,n) / 2 + 1; } ioff = (izero - 1) * lda; if (imat < 7) { i__4 = m; for (i__ = 1; i__ <= i__4; ++i__) { a[ioff + i__] = 0.f; /* L20: */ } } else { i__4 = n - izero + 1; slaset_("Full", &m, &i__4, &c_b21, &c_b21, &a[ioff + 1], &lda); } } else { izero = 0; } /* These lines, if used in place of the calls in the DO 60 loop, cause the code to bomb on a Sun SPARCstation. ANORMO = SLANGE( 'O', M, N, A, LDA, RWORK ) ANORMI = SLANGE( 'I', M, N, A, LDA, RWORK ) Do for each blocksize in NBVAL */ i__4 = *nnb; for (inb = 1; inb <= i__4; ++inb) { nb = nbval[inb]; xlaenv_(&c__1, &nb); /* Compute the LU factorization of the matrix. */ slacpy_("Full", &m, &n, &a[1], &lda, &afac[1], &lda); s_copy(srnamc_1.srnamt, "SGETRF", (ftnlen)6, (ftnlen)6); sgetrf_(&m, &n, &afac[1], &lda, &iwork[1], &info); /* Check error code from SGETRF. */ if (info != izero) { alaerh_(path, "SGETRF", &info, &izero, " ", &m, &n, & c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout); } trfcon = FALSE_; /* + TEST 1 Reconstruct matrix from factors and compute residual. */ slacpy_("Full", &m, &n, &afac[1], &lda, &ainv[1], &lda); sget01_(&m, &n, &a[1], &lda, &ainv[1], &lda, &iwork[1], & rwork[1], result); nt = 1; /* + TEST 2 Form the inverse if the factorization was successful and compute the residual. */ if (m == n && info == 0) { slacpy_("Full", &n, &n, &afac[1], &lda, &ainv[1], & lda); s_copy(srnamc_1.srnamt, "SGETRI", (ftnlen)6, (ftnlen) 6); nrhs = nsval[1]; lwork = *nmax * max(3,nrhs); sgetri_(&n, &ainv[1], &lda, &iwork[1], &work[1], & lwork, &info); /* Check error code from SGETRI. */ if (info != 0) { alaerh_(path, "SGETRI", &info, &c__0, " ", &n, &n, &c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout); } /* Compute the residual for the matrix times its inverse. Also compute the 1-norm condition number of A. */ sget03_(&n, &a[1], &lda, &ainv[1], &lda, &work[1], & lda, &rwork[1], &rcondo, &result[1]); anormo = slange_("O", &m, &n, &a[1], &lda, &rwork[1]); /* Compute the infinity-norm condition number of A. */ anormi = slange_("I", &m, &n, &a[1], &lda, &rwork[1]); ainvnm = slange_("I", &n, &n, &ainv[1], &lda, &rwork[ 1]); if (anormi <= 0.f || ainvnm <= 0.f) { rcondi = 1.f; } else { rcondi = 1.f / anormi / ainvnm; } nt = 2; } else { /* Do only the condition estimate if INFO > 0. */ trfcon = TRUE_; anormo = slange_("O", &m, &n, &a[1], &lda, &rwork[1]); anormi = slange_("I", &m, &n, &a[1], &lda, &rwork[1]); rcondo = 0.f; rcondi = 0.f; } /* Print information about the tests so far that did not pass the threshold. */ i__5 = nt; for (k = 1; k <= i__5; ++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, (char *)&m, (ftnlen)sizeof(integer)) ; 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(real)); e_wsfe(); ++nfail; } /* L30: */ } nrun += nt; /* Skip the remaining tests if this is not the first block size or if M .ne. N. Skip the solve tests if the matrix is singular. */ if (inb > 1 || m != n) { goto L90; } if (trfcon) { goto L70; } i__5 = *nns; for (irhs = 1; irhs <= i__5; ++irhs) { nrhs = nsval[irhs]; *(unsigned char *)xtype = 'N'; for (itran = 1; itran <= 3; ++itran) { *(unsigned char *)trans = *(unsigned char *)& transs[itran - 1]; if (itran == 1) { rcondc = rcondo; } else { rcondc = rcondi; } /* + TEST 3 Solve and compute residual for A * X = B. */ s_copy(srnamc_1.srnamt, "SLARHS", (ftnlen)6, ( ftnlen)6); slarhs_(path, xtype, " ", trans, &n, &n, &kl, &ku, &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, "SGETRS", (ftnlen)6, ( ftnlen)6); sgetrs_(trans, &n, &nrhs, &afac[1], &lda, &iwork[ 1], &x[1], &lda, &info); /* Check error code from SGETRS. */ if (info != 0) { alaerh_(path, "SGETRS", &info, &c__0, trans, & n, &n, &c_n1, &c_n1, &nrhs, &imat, & nfail, &nerrs, nout); } slacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &lda); sget02_(trans, &n, &n, &nrhs, &a[1], &lda, &x[1], &lda, &work[1], &lda, &rwork[1], &result[ 2]); /* + TEST 4 Check solution from generated exact solution. */ sget04_(&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, "SGERFS", (ftnlen)6, ( ftnlen)6); sgerfs_(trans, &n, &nrhs, &a[1], &lda, &afac[1], & lda, &iwork[1], &b[1], &lda, &x[1], &lda, &rwork[1], &rwork[nrhs + 1], &work[1], & iwork[n + 1], &info); /* Check error code from SGERFS. */ if (info != 0) { alaerh_(path, "SGERFS", &info, &c__0, trans, & n, &n, &c_n1, &c_n1, &nrhs, &imat, & nfail, &nerrs, nout); } sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[4]); sget07_(trans, &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___46.ciunit = *nout; s_wsfe(&io___46); do_fio(&c__1, trans, (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; } /* L40: */ } nrun += 5; /* L50: */ } /* L60: */ } /* + TEST 8 Get an estimate of RCOND = 1/CNDNUM. */ L70: for (itran = 1; itran <= 2; ++itran) { if (itran == 1) { anorm = anormo; rcondc = rcondo; *(unsigned char *)norm = 'O'; } else { anorm = anormi; rcondc = rcondi; *(unsigned char *)norm = 'I'; } s_copy(srnamc_1.srnamt, "SGECON", (ftnlen)6, (ftnlen) 6); sgecon_(norm, &n, &afac[1], &lda, &anorm, &rcond, & work[1], &iwork[n + 1], &info); /* Check error code from SGECON. */ if (info != 0) { alaerh_(path, "SGECON", &info, &c__0, norm, &n, & n, &c_n1, &c_n1, &c_n1, &imat, &nfail, & nerrs, nout); } /* This line is needed on a Sun SPARCstation. */ dummy = rcond; result[7] = sget06_(&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___50.ciunit = *nout; s_wsfe(&io___50); do_fio(&c__1, norm, (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; } ++nrun; /* L80: */ } L90: ; } L100: ; } /* L110: */ } /* L120: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of SCHKGE */ } /* schkge_ */