#include "blaswrap.h" /* ddrvpb.f -- translated by f2c (version 20061008). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #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 doublereal c_b45 = 0.; static doublereal c_b46 = 1.; /* Subroutine */ int ddrvpb_(logical *dotype, integer *nn, integer *nval, integer *nrhs, doublereal *thresh, logical *tsterr, integer *nmax, doublereal *a, doublereal *afac, doublereal *asav, doublereal *b, doublereal *bsav, doublereal *x, doublereal *xact, doublereal *s, doublereal *work, doublereal *rwork, integer *iwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; 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, KD =\002,i5,\002, type \002,i1,\002, test(\002,i1,\002)" "=\002,g12.5)"; static char fmt_9997[] = "(1x,a6,\002( '\002,a1,\002', '\002,a1,\002'," " \002,i5,\002, \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( '\002,a1,\002', '\002,a1,\002'," " \002,i5,\002, \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, i__6, i__7[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 integer i__, k, n, i1, i2, k1, kd, nb, in, kl, iw, ku, nt, lda, ikd, nkd, ldab; static char fact[1]; static integer ioff, mode, koff; static doublereal amax; static char path[3]; static integer imat, info; static char dist[1], uplo[1], type__[1]; static integer nrun, ifact; extern /* Subroutine */ int dget04_(integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *); static integer nfail, iseed[4], nfact; extern doublereal dget06_(doublereal *, doublereal *); extern /* Subroutine */ int dpbt01_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *), dpbt02_(char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *), dpbt05_(char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *); static integer kdval[4]; extern logical lsame_(char *, char *); static char equed[1]; static integer nbmin; static doublereal rcond, roldc, scond; static integer nimat; static doublereal anorm; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); static logical equil; extern /* Subroutine */ int dpbsv_(char *, integer *, integer *, integer * , doublereal *, integer *, doublereal *, integer *, integer *), dswap_(integer *, doublereal *, integer *, doublereal *, integer *); static integer iuplo, izero, nerrs; static logical zerot; static char xtype[1]; extern /* Subroutine */ int dlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, char *), aladhd_(integer *, char *); extern doublereal dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); static logical prefac; extern doublereal dlansb_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ int dlaqsb_(char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, char *); static doublereal rcondc; static logical nofact; static char packit[1]; static integer iequed; extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), dlarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, integer *), dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *), dpbequ_(char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *), alasvm_(char *, integer *, integer *, integer *, integer *); static doublereal cndnum; extern /* Subroutine */ int dlatms_(integer *, integer *, char *, integer *, char *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, char *, doublereal *, integer *, doublereal *, integer *), dpbtrf_(char *, integer *, integer *, doublereal *, integer *, integer *); static doublereal ainvnm; extern /* Subroutine */ int dpbtrs_(char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *), xlaenv_(integer *, integer *), dpbsvx_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, char *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *), derrvx_(char *, integer *); static doublereal result[6]; /* Fortran I/O blocks */ static cilist io___57 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___60 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___61 = { 0, 0, 0, fmt_9998, 0 }; /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DDRVPB tests the driver routines DPBSV 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) 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) DOUBLE PRECISION array, dimension (NMAX*NMAX) AFAC (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) ASAV (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) B (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) BSAV (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) X (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) XACT (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) S (workspace) DOUBLE PRECISION array, dimension (NMAX) WORK (workspace) DOUBLE PRECISION array, dimension (NMAX*max(3,NRHS)) RWORK (workspace) DOUBLE PRECISION 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, "Double precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "PB", (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) { derrvx_(path, nout); } infoc_1.infot = 0; kdval[0] = 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'; /* Set limits on the number of loop iterations. Computing MAX */ i__2 = 1, i__3 = min(n,4); nkd = max(i__2,i__3); nimat = 8; if (n == 0) { nimat = 1; } kdval[1] = n + (n + 1) / 4; kdval[2] = (n * 3 - 1) / 4; kdval[3] = (n + 1) / 4; i__2 = nkd; for (ikd = 1; ikd <= i__2; ++ikd) { /* Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order makes it easier to skip redundant values for small values of N. */ kd = kdval[ikd - 1]; ldab = kd + 1; /* Do first for UPLO = 'U', then for UPLO = 'L' */ for (iuplo = 1; iuplo <= 2; ++iuplo) { koff = 1; if (iuplo == 1) { *(unsigned char *)uplo = 'U'; *(unsigned char *)packit = 'Q'; /* Computing MAX */ i__3 = 1, i__4 = kd + 2 - n; koff = max(i__3,i__4); } else { *(unsigned char *)uplo = 'L'; *(unsigned char *)packit = 'B'; } i__3 = nimat; for (imat = 1; imat <= i__3; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L80; } /* Skip types 2, 3, or 4 if the matrix size is too small. */ zerot = imat >= 2 && imat <= 4; if (zerot && n < imat - 1) { goto L80; } if (! zerot || ! dotype[1]) { /* Set up parameters with DLATB4 and generate a test matrix with DLATMS. */ dlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "DLATMS", (ftnlen)6, (ftnlen) 6); dlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cndnum, &anorm, &kd, &kd, packit, &a[koff], &ldab, &work[1], &info); /* Check error code from DLATMS. */ if (info != 0) { alaerh_(path, "DLATMS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &c_n1, &imat, &nfail, & nerrs, nout); goto L80; } } else if (izero > 0) { /* Use the same matrix for types 3 and 4 as for type 2 by copying back the zeroed out column, */ iw = (lda << 1) + 1; if (iuplo == 1) { ioff = (izero - 1) * ldab + kd + 1; i__4 = izero - i1; dcopy_(&i__4, &work[iw], &c__1, &a[ioff - izero + i1], &c__1); iw = iw + izero - i1; i__4 = i2 - izero + 1; /* Computing MAX */ i__6 = ldab - 1; i__5 = max(i__6,1); dcopy_(&i__4, &work[iw], &c__1, &a[ioff], &i__5); } else { ioff = (i1 - 1) * ldab + 1; i__4 = izero - i1; /* Computing MAX */ i__6 = ldab - 1; i__5 = max(i__6,1); dcopy_(&i__4, &work[iw], &c__1, &a[ioff + izero - i1], &i__5); ioff = (izero - 1) * ldab + 1; iw = iw + izero - i1; i__4 = i2 - izero + 1; dcopy_(&i__4, &work[iw], &c__1, &a[ioff], &c__1); } } /* For types 2-4, zero one row and column of the matrix to test that INFO is returned correctly. */ izero = 0; if (zerot) { if (imat == 2) { izero = 1; } else if (imat == 3) { izero = n; } else { izero = n / 2 + 1; } /* Save the zeroed out row and column in WORK(*,3) */ iw = lda << 1; /* Computing MIN */ i__5 = (kd << 1) + 1; i__4 = min(i__5,n); for (i__ = 1; i__ <= i__4; ++i__) { work[iw + i__] = 0.; /* L20: */ } ++iw; /* Computing MAX */ i__4 = izero - kd; i1 = max(i__4,1); /* Computing MIN */ i__4 = izero + kd; i2 = min(i__4,n); if (iuplo == 1) { ioff = (izero - 1) * ldab + kd + 1; i__4 = izero - i1; dswap_(&i__4, &a[ioff - izero + i1], &c__1, &work[ iw], &c__1); iw = iw + izero - i1; i__4 = i2 - izero + 1; /* Computing MAX */ i__6 = ldab - 1; i__5 = max(i__6,1); dswap_(&i__4, &a[ioff], &i__5, &work[iw], &c__1); } else { ioff = (i1 - 1) * ldab + 1; i__4 = izero - i1; /* Computing MAX */ i__6 = ldab - 1; i__5 = max(i__6,1); dswap_(&i__4, &a[ioff + izero - i1], &i__5, &work[ iw], &c__1); ioff = (izero - 1) * ldab + 1; iw = iw + izero - i1; i__4 = i2 - izero + 1; dswap_(&i__4, &a[ioff], &c__1, &work[iw], &c__1); } } /* Save a copy of the matrix A in ASAV. */ i__4 = kd + 1; dlacpy_("Full", &i__4, &n, &a[1], &ldab, &asav[1], &ldab); for (iequed = 1; iequed <= 2; ++iequed) { *(unsigned char *)equed = *(unsigned char *)&equeds[ iequed - 1]; if (iequed == 1) { nfact = 3; } else { nfact = 1; } i__4 = nfact; for (ifact = 1; ifact <= i__4; ++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 L60; } rcondc = 0.; } else if (! lsame_(fact, "N")) { /* Compute the condition number for comparison with the value returned by DPBSVX (FACT = 'N' reuses the condition number from the previous iteration with FACT = 'F'). */ i__5 = kd + 1; dlacpy_("Full", &i__5, &n, &asav[1], &ldab, & afac[1], &ldab); if (equil || iequed > 1) { /* Compute row and column scale factors to equilibrate the matrix A. */ dpbequ_(uplo, &n, &kd, &afac[1], &ldab, & s[1], &scond, &amax, &info); if (info == 0 && n > 0) { if (iequed > 1) { scond = 0.; } /* Equilibrate the matrix. */ dlaqsb_(uplo, &n, &kd, &afac[1], & ldab, &s[1], &scond, &amax, equed); } } /* Save the condition number of the non-equilibrated system for use in DGET04. */ if (equil) { roldc = rcondc; } /* Compute the 1-norm of A. */ anorm = dlansb_("1", uplo, &n, &kd, &afac[1], &ldab, &rwork[1]); /* Factor the matrix A. */ dpbtrf_(uplo, &n, &kd, &afac[1], &ldab, &info); /* Form the inverse of A. */ dlaset_("Full", &n, &n, &c_b45, &c_b46, &a[1], &lda); s_copy(srnamc_1.srnamt, "DPBTRS", (ftnlen)6, ( ftnlen)6); dpbtrs_(uplo, &n, &kd, &n, &afac[1], &ldab, & a[1], &lda, &info); /* Compute the 1-norm condition number of A. */ ainvnm = dlange_("1", &n, &n, &a[1], &lda, & rwork[1]); if (anorm <= 0. || ainvnm <= 0.) { rcondc = 1.; } else { rcondc = 1. / anorm / ainvnm; } } /* Restore the matrix A. */ i__5 = kd + 1; dlacpy_("Full", &i__5, &n, &asav[1], &ldab, &a[1], &ldab); /* Form an exact solution and set the right hand side. */ s_copy(srnamc_1.srnamt, "DLARHS", (ftnlen)6, ( ftnlen)6); dlarhs_(path, xtype, uplo, " ", &n, &n, &kd, &kd, nrhs, &a[1], &ldab, &xact[1], &lda, &b[1], &lda, iseed, &info); *(unsigned char *)xtype = 'C'; dlacpy_("Full", &n, nrhs, &b[1], &lda, &bsav[1], & lda); if (nofact) { /* --- Test DPBSV --- Compute the L*L' or U'*U factorization of the matrix and solve the system. */ i__5 = kd + 1; dlacpy_("Full", &i__5, &n, &a[1], &ldab, & afac[1], &ldab); dlacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &lda); s_copy(srnamc_1.srnamt, "DPBSV ", (ftnlen)6, ( ftnlen)6); dpbsv_(uplo, &n, &kd, nrhs, &afac[1], &ldab, & x[1], &lda, &info); /* Check error code from DPBSV . */ if (info != izero) { alaerh_(path, "DPBSV ", &info, &izero, uplo, &n, &n, &kd, &kd, nrhs, & imat, &nfail, &nerrs, nout); goto L40; } else if (info != 0) { goto L40; } /* Reconstruct matrix from factors and compute residual. */ dpbt01_(uplo, &n, &kd, &a[1], &ldab, &afac[1], &ldab, &rwork[1], result); /* Compute residual of the computed solution. */ dlacpy_("Full", &n, nrhs, &b[1], &lda, &work[ 1], &lda); dpbt02_(uplo, &n, &kd, nrhs, &a[1], &ldab, &x[ 1], &lda, &work[1], &lda, &rwork[1], & result[1]); /* Check solution from generated exact solution. */ dget04_(&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__5 = nt; for (k = 1; k <= i__5; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } io___57.ciunit = *nout; s_wsfe(&io___57); do_fio(&c__1, "DPBSV ", (ftnlen)6); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&kd, (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; } /* L30: */ } nrun += nt; L40: ; } /* --- Test DPBSVX --- */ if (! prefac) { i__5 = kd + 1; dlaset_("Full", &i__5, &n, &c_b45, &c_b45, & afac[1], &ldab); } dlaset_("Full", &n, nrhs, &c_b45, &c_b45, &x[1], & lda); if (iequed > 1 && n > 0) { /* Equilibrate the matrix if FACT='F' and EQUED='Y' */ dlaqsb_(uplo, &n, &kd, &a[1], &ldab, &s[1], & scond, &amax, equed); } /* Solve the system and compute the condition number and error bounds using DPBSVX. */ s_copy(srnamc_1.srnamt, "DPBSVX", (ftnlen)6, ( ftnlen)6); dpbsvx_(fact, uplo, &n, &kd, nrhs, &a[1], &ldab, & afac[1], &ldab, 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 DPBSVX. */ if (info != izero) { /* Writing concatenation */ i__7[0] = 1, a__1[0] = fact; i__7[1] = 1, a__1[1] = uplo; s_cat(ch__1, a__1, i__7, &c__2, (ftnlen)2); alaerh_(path, "DPBSVX", &info, &izero, ch__1, &n, &n, &kd, &kd, nrhs, &imat, &nfail, &nerrs, nout); goto L60; } if (info == 0) { if (! prefac) { /* Reconstruct matrix from factors and compute residual. */ dpbt01_(uplo, &n, &kd, &a[1], &ldab, & afac[1], &ldab, &rwork[(*nrhs << 1) + 1], result); k1 = 1; } else { k1 = 2; } /* Compute residual of the computed solution. */ dlacpy_("Full", &n, nrhs, &bsav[1], &lda, & work[1], &lda); dpbt02_(uplo, &n, &kd, nrhs, &asav[1], &ldab, &x[1], &lda, &work[1], &lda, &rwork[(* nrhs << 1) + 1], &result[1]); /* Check solution from generated exact solution. */ if (nofact || prefac && lsame_(equed, "N")) { dget04_(&n, nrhs, &x[1], &lda, &xact[1], & lda, &rcondc, &result[2]); } else { dget04_(&n, nrhs, &x[1], &lda, &xact[1], & lda, &roldc, &result[2]); } /* Check the error bounds from iterative refinement. */ dpbt05_(uplo, &n, &kd, nrhs, &asav[1], &ldab, &b[1], &lda, &x[1], &lda, &xact[1], & lda, &rwork[1], &rwork[*nrhs + 1], & result[3]); } else { k1 = 6; } /* Compare RCOND from DPBSVX with the computed value in RCONDC. */ result[5] = dget06_(&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___60.ciunit = *nout; s_wsfe(&io___60); do_fio(&c__1, "DPBSVX", (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 *)&kd, (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(doublereal)); e_wsfe(); } else { io___61.ciunit = *nout; s_wsfe(&io___61); do_fio(&c__1, "DPBSVX", (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 *)&kd, (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; } /* L50: */ } nrun = nrun + 7 - k1; L60: ; } /* L70: */ } L80: ; } /* L90: */ } /* L100: */ } /* L110: */ } /* Print a summary of the results. */ alasvm_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of DDRVPB */ } /* ddrvpb_ */