#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__1 = 1; static integer c__2 = 2; static integer c__0 = 0; static integer c_n1 = -1; static real c_b50 = 0.f; /* Subroutine */ int sdrvpo_(logical *dotype, integer *nn, integer *nval, integer *nrhs, real *thresh, logical *tsterr, integer *nmax, real *a, real *afac, real *asav, real *b, real *bsav, real *x, real *xact, real *s, 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 facts[1*3] = "F" "N" "E"; static char equeds[1*2] = "N" "Y"; /* Format strings */ static char fmt_9999[] = "(1x,a6,\002, UPLO='\002,a1,\002', N =\002,i5" ",\002, type \002,i1,\002, test(\002,i1,\002)=\002,g12.5)"; static char fmt_9997[] = "(1x,a6,\002, FACT='\002,a1,\002', UPLO='\002,a" "1,\002', N=\002,i5,\002, EQUED='\002,a1,\002', type \002,i1,\002" ", test(\002,i1,\002) =\002,g12.5)"; static char fmt_9998[] = "(1x,a6,\002, FACT='\002,a1,\002', UPLO='\002,a" "1,\002', N=\002,i5,\002, type \002,i1,\002, test(\002,i1,\002)" "=\002,g12.5)"; /* System generated locals */ address a__1[2]; integer i__1, i__2, i__3, i__4, i__5[2]; char ch__1[2]; /* Builtin functions Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ static char fact[1]; static integer ioff, mode; static real amax; static char path[3]; static integer imat, info; static char dist[1], uplo[1], type__[1]; static integer nrun, i__, k, n, ifact, nfail, iseed[4], nfact; extern logical lsame_(char *, char *); static char equed[1]; static integer nbmin; static real rcond, roldc, scond; static integer nimat; extern doublereal sget06_(real *, real *); extern /* Subroutine */ int sget04_(integer *, integer *, real *, integer *, real *, integer *, real *, real *); static real anorm; static logical equil; extern /* Subroutine */ int spot01_(char *, integer *, real *, integer *, real *, integer *, real *, real *), spot02_(char *, integer *, integer *, real *, integer *, real *, integer *, real * , integer *, real *, real *); static integer iuplo, izero, nerrs, k1; extern /* Subroutine */ int spot05_(char *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer * , real *, real *, real *); static logical zerot; static char xtype[1]; extern /* Subroutine */ int sposv_(char *, integer *, integer *, real *, integer *, real *, integer *, integer *), slatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, real *, integer *, real *, char *), aladhd_(integer *, 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 logical prefac; static integer ku, nt; static real rcondc; static logical nofact; static integer iequed; extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer *, integer *); static real cndnum, 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 *), 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 *); extern doublereal slansy_(char *, char *, integer *, real *, integer *, real *); extern /* Subroutine */ int slaqsy_(char *, integer *, real *, integer *, real *, real *, real *, char *); static real result[6]; extern /* Subroutine */ int spoequ_(integer *, real *, integer *, real *, real *, real *, integer *), spotrf_(char *, integer *, real *, integer *, integer *), spotri_(char *, integer *, real *, integer *, integer *), serrvx_(char *, integer *), sposvx_(char *, char *, integer *, integer *, real *, integer *, real *, integer *, char *, real *, real *, integer *, real *, integer *, real *, real *, real *, real *, integer *, integer *); static integer lda; /* Fortran I/O blocks */ static cilist io___48 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___51 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___52 = { 0, 0, 0, fmt_9998, 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 ======= SDRVPO tests the driver routines SPOSV and -SVX. 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. NRHS (input) INTEGER The number of right hand side vectors to be generated for each linear system. 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 N, used in dimensioning the work arrays. A (workspace) REAL array, dimension (NMAX*NMAX) AFAC (workspace) REAL array, dimension (NMAX*NMAX) ASAV (workspace) REAL array, dimension (NMAX*NMAX) B (workspace) REAL array, dimension (NMAX*NRHS) BSAV (workspace) REAL array, dimension (NMAX*NRHS) X (workspace) REAL array, dimension (NMAX*NRHS) XACT (workspace) REAL array, dimension (NMAX*NRHS) S (workspace) REAL array, dimension (NMAX) WORK (workspace) REAL array, dimension (NMAX*max(3,NRHS)) RWORK (workspace) REAL array, dimension (NMAX+2*NRHS) IWORK (workspace) INTEGER array, dimension (NMAX) NOUT (input) INTEGER The unit number for output. ===================================================================== Parameter adjustments */ --iwork; --rwork; --work; --s; --xact; --x; --bsav; --b; --asav; --afac; --a; --nval; --dotype; /* Function Body Initialize constants and the random number seed. */ s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "PO", (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) { serrvx_(path, nout); } infoc_1.infot = 0; /* Set the block size and minimum block size for testing. */ nb = 1; nbmin = 2; xlaenv_(&c__1, &nb); xlaenv_(&c__2, &nbmin); /* 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 = 9; 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 L120; } /* Skip types 3, 4, or 5 if the matrix size is too small. */ zerot = imat >= 3 && imat <= 5; if (zerot && n < imat - 2) { goto L120; } /* 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 SLATB4 and generate a test matrix with SLATMS. */ slatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)6, (ftnlen)6); slatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, & cndnum, &anorm, &kl, &ku, uplo, &a[1], &lda, &work[1], &info); /* Check error code from SLATMS. */ if (info != 0) { alaerh_(path, "SLATMS", &info, &c__0, uplo, &n, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); goto L110; } /* For types 3-5, zero one row and column 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; } ioff = (izero - 1) * lda; /* Set row and column IZERO of A to 0. */ if (iuplo == 1) { i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { a[ioff + i__] = 0.f; /* L20: */ } ioff += izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { a[ioff] = 0.f; ioff += lda; /* L30: */ } } else { ioff = izero; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { a[ioff] = 0.f; ioff += lda; /* L40: */ } ioff -= izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { a[ioff + i__] = 0.f; /* L50: */ } } } else { izero = 0; } /* Save a copy of the matrix A in ASAV. */ slacpy_(uplo, &n, &n, &a[1], &lda, &asav[1], &lda); for (iequed = 1; iequed <= 2; ++iequed) { *(unsigned char *)equed = *(unsigned char *)&equeds[ iequed - 1]; if (iequed == 1) { nfact = 3; } else { nfact = 1; } i__3 = nfact; for (ifact = 1; ifact <= i__3; ++ifact) { *(unsigned char *)fact = *(unsigned char *)&facts[ ifact - 1]; prefac = lsame_(fact, "F"); nofact = lsame_(fact, "N"); equil = lsame_(fact, "E"); if (zerot) { if (prefac) { goto L90; } rcondc = 0.f; } else if (! lsame_(fact, "N")) { /* Compute the condition number for comparison with the value returned by SPOSVX (FACT = 'N' reuses the condition number from the previous iteration with FACT = 'F'). */ slacpy_(uplo, &n, &n, &asav[1], &lda, &afac[1], & lda); if (equil || iequed > 1) { /* Compute row and column scale factors to equilibrate the matrix A. */ spoequ_(&n, &afac[1], &lda, &s[1], &scond, & amax, &info); if (info == 0 && n > 0) { if (iequed > 1) { scond = 0.f; } /* Equilibrate the matrix. */ slaqsy_(uplo, &n, &afac[1], &lda, &s[1], & scond, &amax, equed); } } /* Save the condition number of the non-equilibrated system for use in SGET04. */ if (equil) { roldc = rcondc; } /* Compute the 1-norm of A. */ anorm = slansy_("1", uplo, &n, &afac[1], &lda, & rwork[1]); /* Factor the matrix A. */ spotrf_(uplo, &n, &afac[1], &lda, &info); /* Form the inverse of A. */ slacpy_(uplo, &n, &n, &afac[1], &lda, &a[1], &lda); spotri_(uplo, &n, &a[1], &lda, &info); /* Compute the 1-norm condition number of A. */ ainvnm = slansy_("1", uplo, &n, &a[1], &lda, & rwork[1]); if (anorm <= 0.f || ainvnm <= 0.f) { rcondc = 1.f; } else { rcondc = 1.f / anorm / ainvnm; } } /* Restore the matrix A. */ slacpy_(uplo, &n, &n, &asav[1], &lda, &a[1], &lda); /* Form an exact solution and set the right hand side. */ s_copy(srnamc_1.srnamt, "SLARHS", (ftnlen)6, (ftnlen) 6); slarhs_(path, xtype, uplo, " ", &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, &bsav[1], &lda); if (nofact) { /* --- Test SPOSV --- Compute the L*L' or U'*U factorization of the matrix and solve the system. */ slacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda); slacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], & lda); s_copy(srnamc_1.srnamt, "SPOSV ", (ftnlen)6, ( ftnlen)6); sposv_(uplo, &n, nrhs, &afac[1], &lda, &x[1], & lda, &info); /* Check error code from SPOSV . */ if (info != izero) { alaerh_(path, "SPOSV ", &info, &izero, uplo, & n, &n, &c_n1, &c_n1, nrhs, &imat, & nfail, &nerrs, nout); goto L70; } else if (info != 0) { goto L70; } /* Reconstruct matrix from factors and compute residual. */ spot01_(uplo, &n, &a[1], &lda, &afac[1], &lda, & rwork[1], result); /* Compute residual of the computed solution. */ slacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], & lda); spot02_(uplo, &n, nrhs, &a[1], &lda, &x[1], &lda, &work[1], &lda, &rwork[1], &result[1]); /* Check solution from generated exact solution. */ sget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[2]); nt = 3; /* 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) { aladhd_(nout, path); } io___48.ciunit = *nout; s_wsfe(&io___48); do_fio(&c__1, "SPOSV ", (ftnlen)6); 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(real)); e_wsfe(); ++nfail; } /* L60: */ } nrun += nt; L70: ; } /* --- Test SPOSVX --- */ if (! prefac) { slaset_(uplo, &n, &n, &c_b50, &c_b50, &afac[1], & lda); } slaset_("Full", &n, nrhs, &c_b50, &c_b50, &x[1], &lda); if (iequed > 1 && n > 0) { /* Equilibrate the matrix if FACT='F' and EQUED='Y'. */ slaqsy_(uplo, &n, &a[1], &lda, &s[1], &scond, & amax, equed); } /* Solve the system and compute the condition number and error bounds using SPOSVX. */ s_copy(srnamc_1.srnamt, "SPOSVX", (ftnlen)6, (ftnlen) 6); sposvx_(fact, uplo, &n, nrhs, &a[1], &lda, &afac[1], & lda, equed, &s[1], &b[1], &lda, &x[1], &lda, & rcond, &rwork[1], &rwork[*nrhs + 1], &work[1], &iwork[1], &info); /* Check the error code from SPOSVX. */ if (info != izero) { /* Writing concatenation */ i__5[0] = 1, a__1[0] = fact; i__5[1] = 1, a__1[1] = uplo; s_cat(ch__1, a__1, i__5, &c__2, (ftnlen)2); alaerh_(path, "SPOSVX", &info, &izero, ch__1, &n, &n, &c_n1, &c_n1, nrhs, &imat, &nfail, & nerrs, nout); goto L90; } if (info == 0) { if (! prefac) { /* Reconstruct matrix from factors and compute residual. */ spot01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &rwork[(*nrhs << 1) + 1], result); k1 = 1; } else { k1 = 2; } /* Compute residual of the computed solution. */ slacpy_("Full", &n, nrhs, &bsav[1], &lda, &work[1] , &lda); spot02_(uplo, &n, nrhs, &asav[1], &lda, &x[1], & lda, &work[1], &lda, &rwork[(*nrhs << 1) + 1], &result[1]); /* Check solution from generated exact solution. */ if (nofact || prefac && lsame_(equed, "N")) { sget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &result[2]); } else { sget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &roldc, &result[2]); } /* Check the error bounds from iterative refinement. */ spot05_(uplo, &n, nrhs, &asav[1], &lda, &b[1], & lda, &x[1], &lda, &xact[1], &lda, &rwork[ 1], &rwork[*nrhs + 1], &result[3]); } else { k1 = 6; } /* Compare RCOND from SPOSVX with the computed value in RCONDC. */ result[5] = sget06_(&rcond, &rcondc); /* Print information about the tests that did not pass the threshold. */ for (k = k1; k <= 6; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } if (prefac) { io___51.ciunit = *nout; s_wsfe(&io___51); do_fio(&c__1, "SPOSVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, equed, (ftnlen)1); 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(); } else { io___52.ciunit = *nout; s_wsfe(&io___52); do_fio(&c__1, "SPOSVX", (ftnlen)6); do_fio(&c__1, fact, (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 *)&k, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[k - 1], ( ftnlen)sizeof(real)); e_wsfe(); } ++nfail; } /* L80: */ } nrun = nrun + 7 - k1; L90: ; } /* L100: */ } L110: ; } L120: ; } /* L130: */ } /* Print a summary of the results. */ alasvm_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of SDRVPO */ } /* sdrvpo_ */