#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 integer c__1 = 1; static doublereal c_b50 = 0.; static doublereal c_b51 = 1.; static integer c__7 = 7; /* Subroutine */ int dchkpb_(logical *dotype, integer *nn, integer *nval, integer *nnb, integer *nbval, integer *nns, integer *nsval, doublereal *thresh, logical *tsterr, integer *nmax, doublereal *a, doublereal *afac, doublereal *ainv, doublereal *b, doublereal *x, doublereal *xact, doublereal *work, doublereal *rwork, integer *iwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; /* Format strings */ static char fmt_9999[] = "(\002 UPLO='\002,a1,\002', N=\002,i5,\002, KD" "=\002,i5,\002, NB=\002,i4,\002, type \002,i2,\002, test \002,i2" ",\002, ratio= \002,g12.5)"; static char fmt_9998[] = "(\002 UPLO='\002,a1,\002', N=\002,i5,\002, KD" "=\002,i5,\002, NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i" "2,\002) = \002,g12.5)"; static char fmt_9997[] = "(\002 UPLO='\002,a1,\002', N=\002,i5,\002, KD" "=\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, i__6; /* 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 ldab, ioff, mode, koff, imat, info; static char path[3], dist[1]; static integer irhs, nrhs; static char uplo[1], type__[1]; static integer nrun, i__; extern /* Subroutine */ int alahd_(integer *, char *); static integer k, n; extern /* Subroutine */ int dget04_(integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *); static integer nfail, iseed[4]; 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]; static doublereal rcond; static integer nimat; static doublereal anorm; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), dswap_(integer *, doublereal *, integer *, doublereal *, integer *); static integer iuplo, izero, i1, i2, nerrs; static logical zerot; static char xtype[1]; extern /* Subroutine */ int dlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, char *); static integer kd, nb, in, kl; 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 integer iw, ku; extern doublereal dlansb_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ int dpbcon_(char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *); static doublereal rcondc; static char packit[1]; 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 *), dpbrfs_(char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dpbtrf_(char *, integer *, integer *, doublereal *, integer *, integer *), alasum_(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 *); static doublereal ainvnm; extern /* Subroutine */ int derrpo_(char *, integer *), dpbtrs_( char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *), xlaenv_(integer *, integer *); static doublereal result[7]; static integer lda, ikd, inb, nkd; /* Fortran I/O blocks */ static cilist io___40 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___46 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___48 = { 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 ======= DCHKPB tests DPBTRF, -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. 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. 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) 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) AINV (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) B (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX) where NSMAX is the largest entry in NSVAL. X (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX) XACT (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX) WORK (workspace) DOUBLE PRECISION array, dimension (NMAX*max(3,NSMAX)) RWORK (workspace) DOUBLE PRECISION 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; --afac; --a; --nsval; --nbval; --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) { derrpo_(path, nout); } infoc_1.infot = 0; xlaenv_(&c__2, &c__2); kdval[0] = 0; /* 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'; /* Computing MAX */ i__3 = 1, i__4 = kd + 2 - n; koff = max(i__3,i__4); *(unsigned char *)packit = 'Q'; } 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 L60; } /* Skip types 2, 3, or 4 if the matrix size is too small. */ zerot = imat >= 2 && imat <= 4; if (zerot && n < imat - 1) { goto L60; } 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, &kd, &kd, &c_n1, &imat, &nfail, &nerrs, nout); goto L60; } } 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); } } /* Do for each value of NB in NBVAL */ i__4 = *nnb; for (inb = 1; inb <= i__4; ++inb) { nb = nbval[inb]; xlaenv_(&c__1, &nb); /* Compute the L*L' or U'*U factorization of the band matrix. */ i__5 = kd + 1; dlacpy_("Full", &i__5, &n, &a[1], &ldab, &afac[1], & ldab); s_copy(srnamc_1.srnamt, "DPBTRF", (ftnlen)6, (ftnlen) 6); dpbtrf_(uplo, &n, &kd, &afac[1], &ldab, &info); /* Check error code from DPBTRF. */ if (info != izero) { alaerh_(path, "DPBTRF", &info, &izero, uplo, &n, & n, &kd, &kd, &nb, &imat, &nfail, &nerrs, nout); goto L50; } /* Skip the tests if INFO is not 0. */ if (info != 0) { goto L50; } /* + TEST 1 Reconstruct matrix from factors and compute residual. */ i__5 = kd + 1; dlacpy_("Full", &i__5, &n, &afac[1], &ldab, &ainv[1], &ldab); dpbt01_(uplo, &n, &kd, &a[1], &ldab, &ainv[1], &ldab, &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___40.ciunit = *nout; s_wsfe(&io___40); 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 *)&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( doublereal)); e_wsfe(); ++nfail; } ++nrun; /* Only do other tests if this is the first blocksize. */ if (inb > 1) { goto L50; } /* Form the inverse of A so we can get a good estimate of RCONDC = 1/(norm(A) * norm(inv(A))). */ dlaset_("Full", &n, &n, &c_b50, &c_b51, &ainv[1], & lda); s_copy(srnamc_1.srnamt, "DPBTRS", (ftnlen)6, (ftnlen) 6); dpbtrs_(uplo, &n, &kd, &n, &afac[1], &ldab, &ainv[1], &lda, &info); /* Compute RCONDC = 1/(norm(A) * norm(inv(A))). */ anorm = dlansb_("1", uplo, &n, &kd, &a[1], &ldab, & rwork[1]); ainvnm = dlange_("1", &n, &n, &ainv[1], &lda, &rwork[ 1]); if (anorm <= 0. || ainvnm <= 0.) { rcondc = 1.; } else { rcondc = 1. / anorm / ainvnm; } i__5 = *nns; for (irhs = 1; irhs <= i__5; ++irhs) { nrhs = nsval[irhs]; /* + TEST 2 Solve and compute residual for A * X = B. */ 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); dlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], & lda); s_copy(srnamc_1.srnamt, "DPBTRS", (ftnlen)6, ( ftnlen)6); dpbtrs_(uplo, &n, &kd, &nrhs, &afac[1], &ldab, &x[ 1], &lda, &info); /* Check error code from DPBTRS. */ if (info != 0) { alaerh_(path, "DPBTRS", &info, &c__0, uplo, & n, &n, &kd, &kd, &nrhs, &imat, &nfail, &nerrs, nout); } 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]); /* + TEST 3 Check solution from generated exact solution. */ dget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[2]); /* + TESTS 4, 5, and 6 Use iterative refinement to improve the solution. */ s_copy(srnamc_1.srnamt, "DPBRFS", (ftnlen)6, ( ftnlen)6); dpbrfs_(uplo, &n, &kd, &nrhs, &a[1], &ldab, &afac[ 1], &ldab, &b[1], &lda, &x[1], &lda, & rwork[1], &rwork[nrhs + 1], &work[1], & iwork[1], &info); /* Check error code from DPBRFS. */ if (info != 0) { alaerh_(path, "DPBRFS", &info, &c__0, uplo, & n, &n, &kd, &kd, &nrhs, &imat, &nfail, &nerrs, nout); } dget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[3]); dpbt05_(uplo, &n, &kd, &nrhs, &a[1], &ldab, &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___46.ciunit = *nout; s_wsfe(&io___46); 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 *)&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(doublereal)); e_wsfe(); ++nfail; } /* L30: */ } nrun += 5; /* L40: */ } /* + TEST 7 Get an estimate of RCOND = 1/CNDNUM. */ s_copy(srnamc_1.srnamt, "DPBCON", (ftnlen)6, (ftnlen) 6); dpbcon_(uplo, &n, &kd, &afac[1], &ldab, &anorm, & rcond, &work[1], &iwork[1], &info); /* Check error code from DPBCON. */ if (info != 0) { alaerh_(path, "DPBCON", &info, &c__0, uplo, &n, & n, &kd, &kd, &c_n1, &imat, &nfail, &nerrs, nout); } result[6] = dget06_(&rcond, &rcondc); /* Print the test ratio if it is .GE. THRESH. */ if (result[6] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___48.ciunit = *nout; s_wsfe(&io___48); 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 *)&c__7, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[6], (ftnlen)sizeof( doublereal)); e_wsfe(); ++nfail; } ++nrun; L50: ; } L60: ; } /* L70: */ } /* L80: */ } /* L90: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of DCHKPB */ } /* dchkpb_ */