#include "f2c.h" #include "blaswrap.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 real c_b23 = 0.f; 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 */ integer i__, k, m, n, nb, im, in, kl, ku, nt, lda, inb, ioff, mode, imat, info; char path[3], dist[1]; integer irhs, nrhs; char norm[1], type__[1]; integer nrun; extern /* Subroutine */ int alahd_(integer *, char *); integer 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 *); 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 *); 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 *); real anorm; integer itran; char trans[1]; integer izero, nerrs; real dummy; integer lwork; logical zerot; char xtype[1]; extern /* Subroutine */ int slatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, real *, integer *, real *, char * ), alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); real rcondc; extern doublereal slange_(char *, integer *, integer *, real *, integer *, real *); real rcondi; extern /* Subroutine */ int sgecon_(char *, integer *, real *, integer *, real *, real *, real *, integer *, integer *), alasum_( char *, integer *, integer *, integer *, integer *); real cndnum, anormi, rcondo; extern /* Subroutine */ int serrge_(char *, integer *); 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 *); logical trfcon; 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 *); real result[8]; /* 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 3.1.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* January 2007 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* 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. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Data statements .. */ /* Parameter adjustments */ --iwork; --rwork; --work; --xact; --x; --b; --ainv; --afac; --a; --nsval; --nbval; --nval; --mval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* 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 */ xlaenv_(&c__1, &c__1); 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_b23, &c_b23, &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_ */