#include "blaswrap.h" /* zchkpb.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__0 = 0; static integer c_n1 = -1; static integer c__1 = 1; static doublecomplex c_b50 = {0.,0.}; static doublecomplex c_b51 = {1.,0.}; static integer c__7 = 7; /* Subroutine */ int zchkpb_(logical *dotype, integer *nn, integer *nval, integer *nnb, integer *nbval, integer *nns, integer *nsval, doublereal *thresh, logical *tsterr, integer *nmax, doublecomplex *a, doublecomplex *afac, doublecomplex *ainv, doublecomplex *b, doublecomplex *x, doublecomplex *xact, doublecomplex *work, doublereal *rwork, 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 i__, k, n, i1, i2, kd, nb, in, kl, iw, ku, lda, ikd, inb, nkd, 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; extern /* Subroutine */ int alahd_(integer *, char *); static integer nfail, iseed[4]; extern doublereal dget06_(doublereal *, doublereal *); static integer kdval[4]; static doublereal rcond; static integer nimat; static doublereal anorm; extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal * ), zpbt01_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *) , zpbt02_(char *, integer *, integer *, integer *, doublecomplex * , integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *), zpbt05_(char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex * , integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *); static integer iuplo, izero, nerrs; static logical zerot; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); static char xtype[1]; extern /* Subroutine */ int zlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, char *), alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); static doublereal rcondc; static char packit[1]; extern doublereal zlanhb_(char *, char *, integer *, integer *, doublecomplex *, integer *, doublereal *), zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer *, integer *); static doublereal cndnum; extern /* Subroutine */ int zlaipd_(integer *, doublecomplex *, integer *, integer *); static doublereal ainvnm; extern /* Subroutine */ int zpbcon_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), xlaenv_( integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *), zpbrfs_(char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer * , doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpbtrf_(char *, integer *, integer *, doublecomplex *, integer *, integer *), zlatms_(integer *, integer *, char *, integer *, char *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, char *, doublecomplex *, integer *, doublecomplex *, integer *); static doublereal result[7]; extern /* Subroutine */ int zerrpo_(char *, integer *), zpbtrs_( char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *); /* 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 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZCHKPB tests ZPBTRF, -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)) NOUT (input) INTEGER The unit number for output. ===================================================================== Parameter adjustments */ --rwork; --work; --xact; --x; --b; --ainv; --afac; --a; --nsval; --nbval; --nval; --dotype; /* Function Body Initialize constants and the random number seed. */ s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17); 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) { zerrpo_(path, nout); } infoc_1.infot = 0; 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 ZLATB4 and generate a test matrix with ZLATMS. */ zlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)6, (ftnlen) 6); zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cndnum, &anorm, &kd, &kd, packit, &a[koff], &ldab, &work[1], &info); /* Check error code from ZLATMS. */ if (info != 0) { alaerh_(path, "ZLATMS", &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; zcopy_(&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); zcopy_(&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); zcopy_(&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; zcopy_(&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__) { i__5 = iw + i__; work[i__5].r = 0., work[i__5].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; zswap_(&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); zswap_(&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); zswap_(&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; zswap_(&i__4, &a[ioff], &c__1, &work[iw], &c__1); } } /* Set the imaginary part of the diagonals. */ if (iuplo == 1) { zlaipd_(&n, &a[kd + 1], &ldab, &c__0); } else { zlaipd_(&n, &a[1], &ldab, &c__0); } /* 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; zlacpy_("Full", &i__5, &n, &a[1], &ldab, &afac[1], & ldab); s_copy(srnamc_1.srnamt, "ZPBTRF", (ftnlen)6, (ftnlen) 6); zpbtrf_(uplo, &n, &kd, &afac[1], &ldab, &info); /* Check error code from ZPBTRF. */ if (info != izero) { alaerh_(path, "ZPBTRF", &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; zlacpy_("Full", &i__5, &n, &afac[1], &ldab, &ainv[1], &ldab); zpbt01_(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))). */ zlaset_("Full", &n, &n, &c_b50, &c_b51, &ainv[1], & lda); s_copy(srnamc_1.srnamt, "ZPBTRS", (ftnlen)6, (ftnlen) 6); zpbtrs_(uplo, &n, &kd, &n, &afac[1], &ldab, &ainv[1], &lda, &info); /* Compute RCONDC = 1/(norm(A) * norm(inv(A))). */ anorm = zlanhb_("1", uplo, &n, &kd, &a[1], &ldab, & rwork[1]); ainvnm = zlange_("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, "ZLARHS", (ftnlen)6, ( ftnlen)6); zlarhs_(path, xtype, uplo, " ", &n, &n, &kd, &kd, &nrhs, &a[1], &ldab, &xact[1], &lda, &b[1] , &lda, iseed, &info); zlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], & lda); s_copy(srnamc_1.srnamt, "ZPBTRS", (ftnlen)6, ( ftnlen)6); zpbtrs_(uplo, &n, &kd, &nrhs, &afac[1], &ldab, &x[ 1], &lda, &info); /* Check error code from ZPBTRS. */ if (info != 0) { alaerh_(path, "ZPBTRS", &info, &c__0, uplo, & n, &n, &kd, &kd, &nrhs, &imat, &nfail, &nerrs, nout); } zlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &lda); zpbt02_(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. */ zget04_(&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, "ZPBRFS", (ftnlen)6, ( ftnlen)6); zpbrfs_(uplo, &n, &kd, &nrhs, &a[1], &ldab, &afac[ 1], &ldab, &b[1], &lda, &x[1], &lda, & rwork[1], &rwork[nrhs + 1], &work[1], & rwork[(nrhs << 1) + 1], &info); /* Check error code from ZPBRFS. */ if (info != 0) { alaerh_(path, "ZPBRFS", &info, &c__0, uplo, & n, &n, &kd, &kd, &nrhs, &imat, &nfail, &nerrs, nout); } zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[3]); zpbt05_(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, "ZPBCON", (ftnlen)6, (ftnlen) 6); zpbcon_(uplo, &n, &kd, &afac[1], &ldab, &anorm, & rcond, &work[1], &rwork[1], &info); /* Check error code from ZPBCON. */ if (info != 0) { alaerh_(path, "ZPBCON", &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 ZCHKPB */ } /* zchkpb_ */