int main(void) { /* Local scalars */ char uplo, uplo_i; lapack_int n, n_i; lapack_int lda, lda_i; lapack_int lda_r; double anorm, anorm_i; double rcond, rcond_i; lapack_int info, info_i; lapack_int i; int failed; /* Local arrays */ lapack_complex_double *a = NULL, *a_i = NULL; lapack_complex_double *work = NULL, *work_i = NULL; double *rwork = NULL, *rwork_i = NULL; lapack_complex_double *a_r = NULL; /* Iniitialize the scalar parameters */ init_scalars_zpocon( &uplo, &n, &lda, &anorm ); lda_r = n+2; uplo_i = uplo; n_i = n; lda_i = lda; anorm_i = anorm; /* Allocate memory for the LAPACK routine arrays */ a = (lapack_complex_double *) LAPACKE_malloc( lda*n * sizeof(lapack_complex_double) ); work = (lapack_complex_double *) LAPACKE_malloc( 2*n * sizeof(lapack_complex_double) ); rwork = (double *)LAPACKE_malloc( n * sizeof(double) ); /* Allocate memory for the C interface function arrays */ a_i = (lapack_complex_double *) LAPACKE_malloc( lda*n * sizeof(lapack_complex_double) ); work_i = (lapack_complex_double *) LAPACKE_malloc( 2*n * sizeof(lapack_complex_double) ); rwork_i = (double *)LAPACKE_malloc( n * sizeof(double) ); /* Allocate memory for the row-major arrays */ a_r = (lapack_complex_double *) LAPACKE_malloc( n*(n+2) * sizeof(lapack_complex_double) ); /* Initialize input arrays */ init_a( lda*n, a ); init_work( 2*n, work ); init_rwork( n, rwork ); /* Call the LAPACK routine */ zpocon_( &uplo, &n, a, &lda, &anorm, &rcond, work, rwork, &info ); /* Initialize input data, call the column-major middle-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a[i]; } for( i = 0; i < 2*n; i++ ) { work_i[i] = work[i]; } for( i = 0; i < n; i++ ) { rwork_i[i] = rwork[i]; } info_i = LAPACKE_zpocon_work( LAPACK_COL_MAJOR, uplo_i, n_i, a_i, lda_i, anorm_i, &rcond_i, work_i, rwork_i ); failed = compare_zpocon( rcond, rcond_i, info, info_i ); if( failed == 0 ) { printf( "PASSED: column-major middle-level interface to zpocon\n" ); } else { printf( "FAILED: column-major middle-level interface to zpocon\n" ); } /* Initialize input data, call the column-major high-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a[i]; } for( i = 0; i < 2*n; i++ ) { work_i[i] = work[i]; } for( i = 0; i < n; i++ ) { rwork_i[i] = rwork[i]; } info_i = LAPACKE_zpocon( LAPACK_COL_MAJOR, uplo_i, n_i, a_i, lda_i, anorm_i, &rcond_i ); failed = compare_zpocon( rcond, rcond_i, info, info_i ); if( failed == 0 ) { printf( "PASSED: column-major high-level interface to zpocon\n" ); } else { printf( "FAILED: column-major high-level interface to zpocon\n" ); } /* Initialize input data, call the row-major middle-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a[i]; } for( i = 0; i < 2*n; i++ ) { work_i[i] = work[i]; } for( i = 0; i < n; i++ ) { rwork_i[i] = rwork[i]; } LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 ); info_i = LAPACKE_zpocon_work( LAPACK_ROW_MAJOR, uplo_i, n_i, a_r, lda_r, anorm_i, &rcond_i, work_i, rwork_i ); failed = compare_zpocon( rcond, rcond_i, info, info_i ); if( failed == 0 ) { printf( "PASSED: row-major middle-level interface to zpocon\n" ); } else { printf( "FAILED: row-major middle-level interface to zpocon\n" ); } /* Initialize input data, call the row-major high-level * interface to LAPACK routine and check the results */ for( i = 0; i < lda*n; i++ ) { a_i[i] = a[i]; } for( i = 0; i < 2*n; i++ ) { work_i[i] = work[i]; } for( i = 0; i < n; i++ ) { rwork_i[i] = rwork[i]; } /* Init row_major arrays */ LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 ); info_i = LAPACKE_zpocon( LAPACK_ROW_MAJOR, uplo_i, n_i, a_r, lda_r, anorm_i, &rcond_i ); failed = compare_zpocon( rcond, rcond_i, info, info_i ); if( failed == 0 ) { printf( "PASSED: row-major high-level interface to zpocon\n" ); } else { printf( "FAILED: row-major high-level interface to zpocon\n" ); } /* Release memory */ if( a != NULL ) { LAPACKE_free( a ); } if( a_i != NULL ) { LAPACKE_free( a_i ); } if( a_r != NULL ) { LAPACKE_free( a_r ); } if( work != NULL ) { LAPACKE_free( work ); } if( work_i != NULL ) { LAPACKE_free( work_i ); } if( rwork != NULL ) { LAPACKE_free( rwork ); } if( rwork_i != NULL ) { LAPACKE_free( rwork_i ); } return 0; }
/* Subroutine */ int zposvx_(char *fact, char *uplo, integer *n, integer * nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * ldaf, char *equed, doublereal *s, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal *rwork, integer * info) { /* System generated locals */ integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5; doublereal d__1, d__2; doublecomplex z__1; /* Local variables */ integer i__, j; doublereal amax, smin, smax; extern logical lsame_(char *, char *); doublereal scond, anorm; logical equil, rcequ; extern doublereal dlamch_(char *); logical nofact; extern /* Subroutine */ int xerbla_(char *, integer *); doublereal bignum; extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int zlaqhe_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, char *); integer infequ; extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zpocon_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *) ; doublereal smlnum; extern /* Subroutine */ int zpoequ_(integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, integer *), zporfs_( char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpotrf_(char *, integer *, doublecomplex *, integer *, integer *), zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *); /* -- LAPACK driver routine (version 3.4.1) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* April 2012 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; af_dim1 = *ldaf; af_offset = 1 + af_dim1; af -= af_offset; --s; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; --ferr; --berr; --work; --rwork; /* Function Body */ *info = 0; nofact = lsame_(fact, "N"); equil = lsame_(fact, "E"); if (nofact || equil) { *(unsigned char *)equed = 'N'; rcequ = FALSE_; } else { rcequ = lsame_(equed, "Y"); smlnum = dlamch_("Safe minimum"); bignum = 1. / smlnum; } /* Test the input parameters. */ if (! nofact && ! equil && ! lsame_(fact, "F")) { *info = -1; } else if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*nrhs < 0) { *info = -4; } else if (*lda < max(1,*n)) { *info = -6; } else if (*ldaf < max(1,*n)) { *info = -8; } else if (lsame_(fact, "F") && ! (rcequ || lsame_( equed, "N"))) { *info = -9; } else { if (rcequ) { smin = bignum; smax = 0.; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ d__1 = smin; d__2 = s[j]; // , expr subst smin = min(d__1,d__2); /* Computing MAX */ d__1 = smax; d__2 = s[j]; // , expr subst smax = max(d__1,d__2); /* L10: */ } if (smin <= 0.) { *info = -10; } else if (*n > 0) { scond = max(smin,smlnum) / min(smax,bignum); } else { scond = 1.; } } if (*info == 0) { if (*ldb < max(1,*n)) { *info = -12; } else if (*ldx < max(1,*n)) { *info = -14; } } } if (*info != 0) { i__1 = -(*info); xerbla_("ZPOSVX", &i__1); return 0; } if (equil) { /* Compute row and column scalings to equilibrate the matrix A. */ zpoequ_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ); if (infequ == 0) { /* Equilibrate the matrix. */ zlaqhe_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed); rcequ = lsame_(equed, "Y"); } } /* Scale the right hand side. */ if (rcequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__; i__5 = i__ + j * b_dim1; z__1.r = s[i__4] * b[i__5].r; z__1.i = s[i__4] * b[i__5].i; // , expr subst b[i__3].r = z__1.r; b[i__3].i = z__1.i; // , expr subst /* L20: */ } /* L30: */ } } if (nofact || equil) { /* Compute the Cholesky factorization A = U**H *U or A = L*L**H. */ zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf); zpotrf_(uplo, n, &af[af_offset], ldaf, info); /* Return if INFO is non-zero. */ if (*info > 0) { *rcond = 0.; return 0; } } /* Compute the norm of the matrix A. */ anorm = zlanhe_("1", uplo, n, &a[a_offset], lda, &rwork[1]); /* Compute the reciprocal of the condition number of A. */ zpocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1], info); /* Compute the solution matrix X. */ zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); zpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info); /* Use iterative refinement to improve the computed solution and */ /* compute error bounds and backward error estimates for it. */ zporfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &b[ b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1], & rwork[1], info); /* Transform the solution matrix X to a solution of the original */ /* system. */ if (rcequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * x_dim1; i__4 = i__; i__5 = i__ + j * x_dim1; z__1.r = s[i__4] * x[i__5].r; z__1.i = s[i__4] * x[i__5].i; // , expr subst x[i__3].r = z__1.r; x[i__3].i = z__1.i; // , expr subst /* L40: */ } /* L50: */ } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] /= scond; /* L60: */ } } /* Set INFO = N+1 if the matrix is singular to working precision. */ if (*rcond < dlamch_("Epsilon")) { *info = *n + 1; } return 0; /* End of ZPOSVX */ }
/* Subroutine */ int zerrpo_(char *path, integer *nunit) { /* System generated locals */ integer i__1; doublereal d__1, d__2; doublecomplex z__1; /* Builtin functions */ integer s_wsle(cilist *), e_wsle(void); /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); /* Local variables */ doublecomplex a[16] /* was [4][4] */, b[4]; integer i__, j; doublereal r__[4]; doublecomplex w[8], x[4]; char c2[2]; doublereal r1[4], r2[4]; doublecomplex af[16] /* was [4][4] */; integer info; doublereal anrm, rcond; extern /* Subroutine */ int zpbtf2_(char *, integer *, integer *, doublecomplex *, integer *, integer *), zpotf2_(char *, integer *, doublecomplex *, integer *, integer *), alaesm_(char *, logical *, integer *); extern logical lsamen_(integer *, char *, char *); extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical *, logical *), zpbcon_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpbequ_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, 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 *), zpocon_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zppcon_(char *, integer *, doublecomplex *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpoequ_(integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, integer *), zpbtrs_( char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *), zporfs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex * , integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpotrf_(char *, integer *, doublecomplex *, integer *, integer *), zpotri_(char *, integer *, doublecomplex *, integer *, integer *), zppequ_(char *, integer *, doublecomplex *, doublereal *, doublereal *, doublereal *, integer *), zpprfs_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpptrf_(char * , integer *, doublecomplex *, integer *), zpptri_(char *, integer *, doublecomplex *, integer *), zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *), zpptrs_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___1 = { 0, 0, 0, 0, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZERRPO tests the error exits for the COMPLEX*16 routines */ /* for Hermitian positive definite matrices. */ /* Arguments */ /* ========= */ /* PATH (input) CHARACTER*3 */ /* The LAPACK path name for the routines to be tested. */ /* NUNIT (input) INTEGER */ /* The unit number for output. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ infoc_1.nout = *nunit; io___1.ciunit = infoc_1.nout; s_wsle(&io___1); e_wsle(); s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2); /* Set the variables to innocuous values. */ for (j = 1; j <= 4; ++j) { for (i__ = 1; i__ <= 4; ++i__) { i__1 = i__ + (j << 2) - 5; d__1 = 1. / (doublereal) (i__ + j); d__2 = -1. / (doublereal) (i__ + j); z__1.r = d__1, z__1.i = d__2; a[i__1].r = z__1.r, a[i__1].i = z__1.i; i__1 = i__ + (j << 2) - 5; d__1 = 1. / (doublereal) (i__ + j); d__2 = -1. / (doublereal) (i__ + j); z__1.r = d__1, z__1.i = d__2; af[i__1].r = z__1.r, af[i__1].i = z__1.i; /* L10: */ } i__1 = j - 1; b[i__1].r = 0., b[i__1].i = 0.; r1[j - 1] = 0.; r2[j - 1] = 0.; i__1 = j - 1; w[i__1].r = 0., w[i__1].i = 0.; i__1 = j - 1; x[i__1].r = 0., x[i__1].i = 0.; /* L20: */ } anrm = 1.; infoc_1.ok = TRUE_; /* Test error exits of the routines that use the Cholesky */ /* decomposition of a Hermitian positive definite matrix. */ if (lsamen_(&c__2, c2, "PO")) { /* ZPOTRF */ s_copy(srnamc_1.srnamt, "ZPOTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotrf_("/", &c__0, a, &c__1, &info); chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotrf_("U", &c_n1, a, &c__1, &info); chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpotrf_("U", &c__2, a, &c__1, &info); chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOTF2 */ s_copy(srnamc_1.srnamt, "ZPOTF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotf2_("/", &c__0, a, &c__1, &info); chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotf2_("U", &c_n1, a, &c__1, &info); chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpotf2_("U", &c__2, a, &c__1, &info); chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOTRI */ s_copy(srnamc_1.srnamt, "ZPOTRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotri_("/", &c__0, a, &c__1, &info); chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotri_("U", &c_n1, a, &c__1, &info); chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpotri_("U", &c__2, a, &c__1, &info); chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOTRS */ s_copy(srnamc_1.srnamt, "ZPOTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotrs_("/", &c__0, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotrs_("U", &c_n1, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpotrs_("U", &c__0, &c_n1, a, &c__1, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpotrs_("U", &c__2, &c__1, a, &c__1, b, &c__2, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zpotrs_("U", &c__2, &c__1, a, &c__2, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPORFS */ s_copy(srnamc_1.srnamt, "ZPORFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zporfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zporfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zporfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zporfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 9; zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__1, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 11; zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__2, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOCON */ s_copy(srnamc_1.srnamt, "ZPOCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpocon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpocon_("U", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpocon_("U", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; d__1 = -anrm; zpocon_("U", &c__1, a, &c__1, &d__1, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOEQU */ s_copy(srnamc_1.srnamt, "ZPOEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpoequ_(&c_n1, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpoequ_(&c__2, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* Test error exits of the routines that use the Cholesky */ /* decomposition of a Hermitian positive definite packed matrix. */ } else if (lsamen_(&c__2, c2, "PP")) { /* ZPPTRF */ s_copy(srnamc_1.srnamt, "ZPPTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpptrf_("/", &c__0, a, &info); chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpptrf_("U", &c_n1, a, &info); chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPTRI */ s_copy(srnamc_1.srnamt, "ZPPTRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpptri_("/", &c__0, a, &info); chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpptri_("U", &c_n1, a, &info); chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPTRS */ s_copy(srnamc_1.srnamt, "ZPPTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpptrs_("/", &c__0, &c__0, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpptrs_("U", &c_n1, &c__0, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpptrs_("U", &c__0, &c_n1, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zpptrs_("U", &c__2, &c__1, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPRFS */ s_copy(srnamc_1.srnamt, "ZPPRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpprfs_("/", &c__0, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpprfs_("U", &c_n1, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpprfs_("U", &c__0, &c_n1, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zpprfs_("U", &c__2, &c__1, a, af, b, &c__1, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 9; zpprfs_("U", &c__2, &c__1, a, af, b, &c__2, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPCON */ s_copy(srnamc_1.srnamt, "ZPPCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zppcon_("/", &c__0, a, &anrm, &rcond, w, r__, &info); chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zppcon_("U", &c_n1, a, &anrm, &rcond, w, r__, &info); chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; d__1 = -anrm; zppcon_("U", &c__1, a, &d__1, &rcond, w, r__, &info); chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPEQU */ s_copy(srnamc_1.srnamt, "ZPPEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zppequ_("/", &c__0, a, r1, &rcond, &anrm, &info); chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zppequ_("U", &c_n1, a, r1, &rcond, &anrm, &info); chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* Test error exits of the routines that use the Cholesky */ /* decomposition of a Hermitian positive definite band matrix. */ } else if (lsamen_(&c__2, c2, "PB")) { /* ZPBTRF */ s_copy(srnamc_1.srnamt, "ZPBTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbtrf_("/", &c__0, &c__0, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbtrf_("U", &c_n1, &c__0, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbtrf_("U", &c__1, &c_n1, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbtrf_("U", &c__2, &c__1, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBTF2 */ s_copy(srnamc_1.srnamt, "ZPBTF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbtf2_("/", &c__0, &c__0, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbtf2_("U", &c_n1, &c__0, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbtf2_("U", &c__1, &c_n1, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbtf2_("U", &c__2, &c__1, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBTRS */ s_copy(srnamc_1.srnamt, "ZPBTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbtrs_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbtrs_("U", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbtrs_("U", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpbtrs_("U", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zpbtrs_("U", &c__2, &c__1, &c__1, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; zpbtrs_("U", &c__2, &c__0, &c__1, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBRFS */ s_copy(srnamc_1.srnamt, "ZPBRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbrfs_("/", &c__0, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbrfs_("U", &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbrfs_("U", &c__1, &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpbrfs_("U", &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zpbrfs_("U", &c__2, &c__1, &c__1, a, &c__1, af, &c__2, b, &c__2, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; zpbrfs_("U", &c__2, &c__1, &c__1, a, &c__2, af, &c__1, b, &c__2, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; zpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__1, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 12; zpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__2, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBCON */ s_copy(srnamc_1.srnamt, "ZPBCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbcon_("/", &c__0, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbcon_("U", &c_n1, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbcon_("U", &c__1, &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbcon_("U", &c__2, &c__1, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; d__1 = -anrm; zpbcon_("U", &c__1, &c__0, a, &c__1, &d__1, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBEQU */ s_copy(srnamc_1.srnamt, "ZPBEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbequ_("/", &c__0, &c__0, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbequ_("U", &c_n1, &c__0, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbequ_("U", &c__1, &c_n1, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbequ_("U", &c__2, &c__1, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); } /* Print a summary line. */ alaesm_(path, &infoc_1.ok, &infoc_1.nout); return 0; /* End of ZERRPO */ } /* zerrpo_ */
/* Subroutine */ int zposvx_(char *fact, char *uplo, integer *n, integer * nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * ldaf, char *equed, doublereal *s, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal *rwork, integer * info, ftnlen fact_len, ftnlen uplo_len, ftnlen equed_len) { /* System generated locals */ integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5; doublereal d__1, d__2; doublecomplex z__1; /* Local variables */ static integer i__, j; static doublereal amax, smin, smax; extern logical lsame_(char *, char *, ftnlen, ftnlen); static doublereal scond, anorm; static logical equil, rcequ; extern doublereal dlamch_(char *, ftnlen); static logical nofact; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); static doublereal bignum; extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *, ftnlen, ftnlen); extern /* Subroutine */ int zlaqhe_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, char *, ftnlen, ftnlen); static integer infequ; extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, ftnlen), zpocon_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *, ftnlen) ; static doublereal smlnum; extern /* Subroutine */ int zpoequ_(integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, integer *), zporfs_( char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *, ftnlen), zpotrf_(char *, integer *, doublecomplex *, integer *, integer *, ftnlen), zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, ftnlen); /* -- LAPACK driver routine (version 3.0) -- */ /* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */ /* Courant Institute, Argonne National Lab, and Rice University */ /* June 30, 1999 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZPOSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to */ /* compute the solution to a complex system of linear equations */ /* A * X = B, */ /* where A is an N-by-N Hermitian positive definite matrix and X and B */ /* are N-by-NRHS matrices. */ /* Error bounds on the solution and a condition estimate are also */ /* provided. */ /* Description */ /* =========== */ /* The following steps are performed: */ /* 1. If FACT = 'E', real scaling factors are computed to equilibrate */ /* the system: */ /* diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B */ /* Whether or not the system will be equilibrated depends on the */ /* scaling of the matrix A, but if equilibration is used, A is */ /* overwritten by diag(S)*A*diag(S) and B by diag(S)*B. */ /* 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to */ /* factor the matrix A (after equilibration if FACT = 'E') as */ /* A = U**H* U, if UPLO = 'U', or */ /* A = L * L**H, if UPLO = 'L', */ /* where U is an upper triangular matrix and L is a lower triangular */ /* matrix. */ /* 3. If the leading i-by-i principal minor is not positive definite, */ /* then the routine returns with INFO = i. Otherwise, the factored */ /* form of A is used to estimate the condition number of the matrix */ /* A. If the reciprocal of the condition number is less than machine */ /* precision, INFO = N+1 is returned as a warning, but the routine */ /* still goes on to solve for X and compute error bounds as */ /* described below. */ /* 4. The system of equations is solved for X using the factored form */ /* of A. */ /* 5. Iterative refinement is applied to improve the computed solution */ /* matrix and calculate error bounds and backward error estimates */ /* for it. */ /* 6. If equilibration was used, the matrix X is premultiplied by */ /* diag(S) so that it solves the original system before */ /* equilibration. */ /* Arguments */ /* ========= */ /* FACT (input) CHARACTER*1 */ /* Specifies whether or not the factored form of the matrix A is */ /* supplied on entry, and if not, whether the matrix A should be */ /* equilibrated before it is factored. */ /* = 'F': On entry, AF contains the factored form of A. */ /* If EQUED = 'Y', the matrix A has been equilibrated */ /* with scaling factors given by S. A and AF will not */ /* be modified. */ /* = 'N': The matrix A will be copied to AF and factored. */ /* = 'E': The matrix A will be equilibrated if necessary, then */ /* copied to AF and factored. */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangle of A is stored; */ /* = 'L': Lower triangle of A is stored. */ /* N (input) INTEGER */ /* The number of linear equations, i.e., the order of the */ /* matrix A. N >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrices B and X. NRHS >= 0. */ /* A (input/output) COMPLEX*16 array, dimension (LDA,N) */ /* On entry, the Hermitian matrix A, except if FACT = 'F' and */ /* EQUED = 'Y', then A must contain the equilibrated matrix */ /* diag(S)*A*diag(S). If UPLO = 'U', the leading */ /* N-by-N upper triangular part of A contains the upper */ /* triangular part of the matrix A, and the strictly lower */ /* triangular part of A is not referenced. If UPLO = 'L', the */ /* leading N-by-N lower triangular part of A contains the lower */ /* triangular part of the matrix A, and the strictly upper */ /* triangular part of A is not referenced. A is not modified if */ /* FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. */ /* On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by */ /* diag(S)*A*diag(S). */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* AF (input or output) COMPLEX*16 array, dimension (LDAF,N) */ /* If FACT = 'F', then AF is an input argument and on entry */ /* contains the triangular factor U or L from the Cholesky */ /* factorization A = U**H*U or A = L*L**H, in the same storage */ /* format as A. If EQUED .ne. 'N', then AF is the factored form */ /* of the equilibrated matrix diag(S)*A*diag(S). */ /* If FACT = 'N', then AF is an output argument and on exit */ /* returns the triangular factor U or L from the Cholesky */ /* factorization A = U**H*U or A = L*L**H of the original */ /* matrix A. */ /* If FACT = 'E', then AF is an output argument and on exit */ /* returns the triangular factor U or L from the Cholesky */ /* factorization A = U**H*U or A = L*L**H of the equilibrated */ /* matrix A (see the description of A for the form of the */ /* equilibrated matrix). */ /* LDAF (input) INTEGER */ /* The leading dimension of the array AF. LDAF >= max(1,N). */ /* EQUED (input or output) CHARACTER*1 */ /* Specifies the form of equilibration that was done. */ /* = 'N': No equilibration (always true if FACT = 'N'). */ /* = 'Y': Equilibration was done, i.e., A has been replaced by */ /* diag(S) * A * diag(S). */ /* EQUED is an input argument if FACT = 'F'; otherwise, it is an */ /* output argument. */ /* S (input or output) DOUBLE PRECISION array, dimension (N) */ /* The scale factors for A; not accessed if EQUED = 'N'. S is */ /* an input argument if FACT = 'F'; otherwise, S is an output */ /* argument. If FACT = 'F' and EQUED = 'Y', each element of S */ /* must be positive. */ /* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) */ /* On entry, the N-by-NRHS righthand side matrix B. */ /* On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y', */ /* B is overwritten by diag(S) * B. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= max(1,N). */ /* X (output) COMPLEX*16 array, dimension (LDX,NRHS) */ /* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X to */ /* the original system of equations. Note that if EQUED = 'Y', */ /* A and B are modified on exit, and the solution to the */ /* equilibrated system is inv(diag(S))*X. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. LDX >= max(1,N). */ /* RCOND (output) DOUBLE PRECISION */ /* The estimate of the reciprocal condition number of the matrix */ /* A after equilibration (if done). If RCOND is less than the */ /* machine precision (in particular, if RCOND = 0), the matrix */ /* is singular to working precision. This condition is */ /* indicated by a return code of INFO > 0. */ /* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */ /* The estimated forward error bound for each solution vector */ /* X(j) (the j-th column of the solution matrix X). */ /* If XTRUE is the true solution corresponding to X(j), FERR(j) */ /* is an estimated upper bound for the magnitude of the largest */ /* element in (X(j) - XTRUE) divided by the magnitude of the */ /* largest element in X(j). The estimate is as reliable as */ /* the estimate for RCOND, and is almost always a slight */ /* overestimate of the true error. */ /* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */ /* The componentwise relative backward error of each solution */ /* vector X(j) (i.e., the smallest relative change in */ /* any element of A or B that makes X(j) an exact solution). */ /* WORK (workspace) COMPLEX*16 array, dimension (2*N) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = i, and i is */ /* <= N: the leading minor of order i of A is */ /* not positive definite, so the factorization */ /* could not be completed, and the solution has not */ /* been computed. RCOND = 0 is returned. */ /* = N+1: U is nonsingular, but RCOND is less than machine */ /* precision, meaning that the matrix is singular */ /* to working precision. Nevertheless, the */ /* solution and error bounds are computed because */ /* there are a number of situations where the */ /* computed solution can be more accurate than the */ /* value of RCOND would suggest. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; af_dim1 = *ldaf; af_offset = 1 + af_dim1; af -= af_offset; --s; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; --ferr; --berr; --work; --rwork; /* Function Body */ *info = 0; nofact = lsame_(fact, "N", (ftnlen)1, (ftnlen)1); equil = lsame_(fact, "E", (ftnlen)1, (ftnlen)1); if (nofact || equil) { *(unsigned char *)equed = 'N'; rcequ = FALSE_; } else { rcequ = lsame_(equed, "Y", (ftnlen)1, (ftnlen)1); smlnum = dlamch_("Safe minimum", (ftnlen)12); bignum = 1. / smlnum; } /* Test the input parameters. */ if (! nofact && ! equil && ! lsame_(fact, "F", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*nrhs < 0) { *info = -4; } else if (*lda < max(1,*n)) { *info = -6; } else if (*ldaf < max(1,*n)) { *info = -8; } else if (lsame_(fact, "F", (ftnlen)1, (ftnlen)1) && ! (rcequ || lsame_( equed, "N", (ftnlen)1, (ftnlen)1))) { *info = -9; } else { if (rcequ) { smin = bignum; smax = 0.; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ d__1 = smin, d__2 = s[j]; smin = min(d__1,d__2); /* Computing MAX */ d__1 = smax, d__2 = s[j]; smax = max(d__1,d__2); /* L10: */ } if (smin <= 0.) { *info = -10; } else if (*n > 0) { scond = max(smin,smlnum) / min(smax,bignum); } else { scond = 1.; } } if (*info == 0) { if (*ldb < max(1,*n)) { *info = -12; } else if (*ldx < max(1,*n)) { *info = -14; } } } if (*info != 0) { i__1 = -(*info); xerbla_("ZPOSVX", &i__1, (ftnlen)6); return 0; } if (equil) { /* Compute row and column scalings to equilibrate the matrix A. */ zpoequ_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ); if (infequ == 0) { /* Equilibrate the matrix. */ zlaqhe_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed, ( ftnlen)1, (ftnlen)1); rcequ = lsame_(equed, "Y", (ftnlen)1, (ftnlen)1); } } /* Scale the right hand side. */ if (rcequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__; i__5 = i__ + j * b_dim1; z__1.r = s[i__4] * b[i__5].r, z__1.i = s[i__4] * b[i__5].i; b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L20: */ } /* L30: */ } } if (nofact || equil) { /* Compute the Cholesky factorization A = U'*U or A = L*L'. */ zlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf, (ftnlen) 1); zpotrf_(uplo, n, &af[af_offset], ldaf, info, (ftnlen)1); /* Return if INFO is non-zero. */ if (*info != 0) { if (*info > 0) { *rcond = 0.; } return 0; } } /* Compute the norm of the matrix A. */ anorm = zlanhe_("1", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, ( ftnlen)1); /* Compute the reciprocal of the condition number of A. */ zpocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1], info, (ftnlen)1); /* Set INFO = N+1 if the matrix is singular to working precision. */ if (*rcond < dlamch_("Epsilon", (ftnlen)7)) { *info = *n + 1; } /* Compute the solution matrix X. */ zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx, (ftnlen)4); zpotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info, ( ftnlen)1); /* Use iterative refinement to improve the computed solution and */ /* compute error bounds and backward error estimates for it. */ zporfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &b[ b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1], & rwork[1], info, (ftnlen)1); /* Transform the solution matrix X to a solution of the original */ /* system. */ if (rcequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * x_dim1; i__4 = i__; i__5 = i__ + j * x_dim1; z__1.r = s[i__4] * x[i__5].r, z__1.i = s[i__4] * x[i__5].i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; /* L40: */ } /* L50: */ } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] /= scond; /* L60: */ } } return 0; /* End of ZPOSVX */ } /* zposvx_ */
/* Subroutine */ int zporfsx_(char *uplo, char *equed, integer *n, integer * nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * ldaf, doublereal *s, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *berr, integer * n_err_bnds__, doublereal *err_bnds_norm__, doublereal * err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex * work, doublereal *rwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, err_bnds_comp_dim1, err_bnds_comp_offset, i__1; doublereal d__1, d__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ doublereal illrcond_thresh__, unstable_thresh__, err_lbnd__; integer ref_type__, j; doublereal rcond_tmp__; integer prec_type__; doublereal cwise_wrong__; extern /* Subroutine */ int zla_porfsx_extended_(integer *, char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, logical *, doublereal *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, doublecomplex *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, logical *, integer *); char norm[1]; logical ignore_cwise__; extern logical lsame_(char *, char *); doublereal anorm; logical rcequ; extern doublereal zla_porcond_c_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, logical *, integer *, doublecomplex *, doublereal *), zla_porcond_x_(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublereal *), dlamch_(char *); extern /* Subroutine */ int xerbla_(char *, integer *); extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int zpocon_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *); extern integer ilaprec_(char *); integer ithresh, n_norms__; doublereal rthresh; /* -- LAPACK computational routine (version 3.4.1) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* April 2012 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* ================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Check the input parameters. */ /* Parameter adjustments */ err_bnds_comp_dim1 = *nrhs; err_bnds_comp_offset = 1 + err_bnds_comp_dim1; err_bnds_comp__ -= err_bnds_comp_offset; err_bnds_norm_dim1 = *nrhs; err_bnds_norm_offset = 1 + err_bnds_norm_dim1; err_bnds_norm__ -= err_bnds_norm_offset; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; af_dim1 = *ldaf; af_offset = 1 + af_dim1; af -= af_offset; --s; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; --berr; --params; --work; --rwork; /* Function Body */ *info = 0; ref_type__ = 1; if (*nparams >= 1) { if (params[1] < 0.) { params[1] = 1.; } else { ref_type__ = (integer) params[1]; } } /* Set default parameters. */ illrcond_thresh__ = (doublereal) (*n) * dlamch_("Epsilon"); ithresh = 10; rthresh = .5; unstable_thresh__ = .25; ignore_cwise__ = FALSE_; if (*nparams >= 2) { if (params[2] < 0.) { params[2] = (doublereal) ithresh; } else { ithresh = (integer) params[2]; } } if (*nparams >= 3) { if (params[3] < 0.) { if (ignore_cwise__) { params[3] = 0.; } else { params[3] = 1.; } } else { ignore_cwise__ = params[3] == 0.; } } if (ref_type__ == 0 || *n_err_bnds__ == 0) { n_norms__ = 0; } else if (ignore_cwise__) { n_norms__ = 1; } else { n_norms__ = 2; } rcequ = lsame_(equed, "Y"); /* Test input parameters. */ if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { *info = -1; } else if (! rcequ && ! lsame_(equed, "N")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*nrhs < 0) { *info = -4; } else if (*lda < max(1,*n)) { *info = -6; } else if (*ldaf < max(1,*n)) { *info = -8; } else if (*ldb < max(1,*n)) { *info = -11; } else if (*ldx < max(1,*n)) { *info = -13; } if (*info != 0) { i__1 = -(*info); xerbla_("ZPORFSX", &i__1); return 0; } /* Quick return if possible. */ if (*n == 0 || *nrhs == 0) { *rcond = 1.; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { berr[j] = 0.; if (*n_err_bnds__ >= 1) { err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; } if (*n_err_bnds__ >= 2) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.; err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.; } if (*n_err_bnds__ >= 3) { err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.; } } return 0; } /* Default to failure. */ *rcond = 0.; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { berr[j] = 1.; if (*n_err_bnds__ >= 1) { err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; } if (*n_err_bnds__ >= 2) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; } if (*n_err_bnds__ >= 3) { err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.; err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.; } } /* Compute the norm of A and the reciprocal of the condition */ /* number of A. */ *(unsigned char *)norm = 'I'; anorm = zlanhe_(norm, uplo, n, &a[a_offset], lda, &rwork[1]); zpocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1], info); /* Perform refinement on each right-hand side */ if (ref_type__ != 0) { prec_type__ = ilaprec_("E"); zla_porfsx_extended_(&prec_type__, uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &rcequ, &s[1], &b[b_offset], ldb, &x[ x_offset], ldx, &berr[1], &n_norms__, &err_bnds_norm__[ err_bnds_norm_offset], &err_bnds_comp__[err_bnds_comp_offset], &work[1], &rwork[1], &work[*n + 1], &rwork[1], rcond, & ithresh, &rthresh, &unstable_thresh__, &ignore_cwise__, info); } /* Computing MAX */ d__1 = 10.; d__2 = sqrt((doublereal) (*n)); // , expr subst err_lbnd__ = max(d__1,d__2) * dlamch_("Epsilon"); if (*n_err_bnds__ >= 1 && n_norms__ >= 1) { /* Compute scaled normwise condition number cond(A*C). */ if (rcequ) { rcond_tmp__ = zla_porcond_c_(uplo, n, &a[a_offset], lda, &af[ af_offset], ldaf, &s[1], &c_true, info, &work[1], &rwork[ 1]); } else { rcond_tmp__ = zla_porcond_c_(uplo, n, &a[a_offset], lda, &af[ af_offset], ldaf, &s[1], &c_false, info, &work[1], &rwork[ 1]); } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { /* Cap the error at 1.0. */ if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] > 1.) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; } /* Threshold the error (see LAWN). */ if (rcond_tmp__ < illrcond_thresh__) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; err_bnds_norm__[j + err_bnds_norm_dim1] = 0.; if (*info <= *n) { *info = *n + j; } } else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < err_lbnd__) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__; err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; } /* Save the condition number. */ if (*n_err_bnds__ >= 3) { err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__; } } } if (*n_err_bnds__ >= 1 && n_norms__ >= 2) { /* Compute componentwise condition number cond(A*diag(Y(:,J))) for */ /* each right-hand side using the current solution as an estimate of */ /* the true solution. If the componentwise error estimate is too */ /* large, then the solution is a lousy estimate of truth and the */ /* estimated RCOND may be too optimistic. To avoid misleading users, */ /* the inverse condition number is set to 0.0 when the estimated */ /* cwise error is at least CWISE_WRONG. */ cwise_wrong__ = sqrt(dlamch_("Epsilon")); i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < cwise_wrong__) { rcond_tmp__ = zla_porcond_x_(uplo, n, &a[a_offset], lda, &af[ af_offset], ldaf, &x[j * x_dim1 + 1], info, &work[1], &rwork[1]); } else { rcond_tmp__ = 0.; } /* Cap the error at 1.0. */ if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] > 1.) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; } /* Threshold the error (see LAWN). */ if (rcond_tmp__ < illrcond_thresh__) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1] = 0.; if (params[3] == 1. && *info < *n + j) { *info = *n + j; } } else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < err_lbnd__) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__; err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; } /* Save the condition number. */ if (*n_err_bnds__ >= 3) { err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__; } } } return 0; /* End of ZPORFSX */ }
/* Subroutine */ int zerrpo_(char *path, integer *nunit) { /* System generated locals */ integer i__1; doublereal d__1, d__2; doublecomplex z__1; /* Builtin functions */ integer s_wsle(cilist *), e_wsle(void); /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); /* Local variables */ static integer info; static doublereal anrm; static doublecomplex a[16] /* was [4][4] */, b[4]; static integer i__, j; static doublereal r__[4]; static doublecomplex w[8], x[4]; static doublereal rcond; static char c2[2]; static doublereal r1[4], r2[4]; static doublecomplex af[16] /* was [4][4] */; extern /* Subroutine */ int zpbtf2_(char *, integer *, integer *, doublecomplex *, integer *, integer *), zpotf2_(char *, integer *, doublecomplex *, integer *, integer *), alaesm_(char *, logical *, integer *); extern logical lsamen_(integer *, char *, char *); extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical *, logical *), zpbcon_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpbequ_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, 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 *), zpocon_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zppcon_(char *, integer *, doublecomplex *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpoequ_(integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, integer *), zpbtrs_( char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *), zporfs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex * , integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpotrf_(char *, integer *, doublecomplex *, integer *, integer *), zpotri_(char *, integer *, doublecomplex *, integer *, integer *), zppequ_(char *, integer *, doublecomplex *, doublereal *, doublereal *, doublereal *, integer *), zpprfs_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zpptrf_(char * , integer *, doublecomplex *, integer *), zpptri_(char *, integer *, doublecomplex *, integer *), zpotrs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *), zpptrs_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___1 = { 0, 0, 0, 0, 0 }; #define a_subscr(a_1,a_2) (a_2)*4 + a_1 - 5 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] #define af_subscr(a_1,a_2) (a_2)*4 + a_1 - 5 #define af_ref(a_1,a_2) af[af_subscr(a_1,a_2)] /* -- LAPACK test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University February 29, 1992 Purpose ======= ZERRPO tests the error exits for the COMPLEX*16 routines for Hermitian positive definite matrices. Arguments ========= PATH (input) CHARACTER*3 The LAPACK path name for the routines to be tested. NUNIT (input) INTEGER The unit number for output. ===================================================================== */ infoc_1.nout = *nunit; io___1.ciunit = infoc_1.nout; s_wsle(&io___1); e_wsle(); s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2); /* Set the variables to innocuous values. */ for (j = 1; j <= 4; ++j) { for (i__ = 1; i__ <= 4; ++i__) { i__1 = a_subscr(i__, j); d__1 = 1. / (doublereal) (i__ + j); d__2 = -1. / (doublereal) (i__ + j); z__1.r = d__1, z__1.i = d__2; a[i__1].r = z__1.r, a[i__1].i = z__1.i; i__1 = af_subscr(i__, j); d__1 = 1. / (doublereal) (i__ + j); d__2 = -1. / (doublereal) (i__ + j); z__1.r = d__1, z__1.i = d__2; af[i__1].r = z__1.r, af[i__1].i = z__1.i; /* L10: */ } i__1 = j - 1; b[i__1].r = 0., b[i__1].i = 0.; r1[j - 1] = 0.; r2[j - 1] = 0.; i__1 = j - 1; w[i__1].r = 0., w[i__1].i = 0.; i__1 = j - 1; x[i__1].r = 0., x[i__1].i = 0.; /* L20: */ } anrm = 1.; infoc_1.ok = TRUE_; /* Test error exits of the routines that use the Cholesky decomposition of a Hermitian positive definite matrix. */ if (lsamen_(&c__2, c2, "PO")) { /* ZPOTRF */ s_copy(srnamc_1.srnamt, "ZPOTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotrf_("/", &c__0, a, &c__1, &info); chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotrf_("U", &c_n1, a, &c__1, &info); chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpotrf_("U", &c__2, a, &c__1, &info); chkxer_("ZPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOTF2 */ s_copy(srnamc_1.srnamt, "ZPOTF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotf2_("/", &c__0, a, &c__1, &info); chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotf2_("U", &c_n1, a, &c__1, &info); chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpotf2_("U", &c__2, a, &c__1, &info); chkxer_("ZPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOTRI */ s_copy(srnamc_1.srnamt, "ZPOTRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotri_("/", &c__0, a, &c__1, &info); chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotri_("U", &c_n1, a, &c__1, &info); chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpotri_("U", &c__2, a, &c__1, &info); chkxer_("ZPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOTRS */ s_copy(srnamc_1.srnamt, "ZPOTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpotrs_("/", &c__0, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpotrs_("U", &c_n1, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpotrs_("U", &c__0, &c_n1, a, &c__1, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpotrs_("U", &c__2, &c__1, a, &c__1, b, &c__2, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zpotrs_("U", &c__2, &c__1, a, &c__2, b, &c__1, &info); chkxer_("ZPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPORFS */ s_copy(srnamc_1.srnamt, "ZPORFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zporfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zporfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zporfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zporfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 9; zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__1, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 11; zporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__2, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOCON */ s_copy(srnamc_1.srnamt, "ZPOCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpocon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpocon_("U", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpocon_("U", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; d__1 = -anrm; zpocon_("U", &c__1, a, &c__1, &d__1, &rcond, w, r__, &info) ; chkxer_("ZPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPOEQU */ s_copy(srnamc_1.srnamt, "ZPOEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpoequ_(&c_n1, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpoequ_(&c__2, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* Test error exits of the routines that use the Cholesky decomposition of a Hermitian positive definite packed matrix. */ } else if (lsamen_(&c__2, c2, "PP")) { /* ZPPTRF */ s_copy(srnamc_1.srnamt, "ZPPTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpptrf_("/", &c__0, a, &info); chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpptrf_("U", &c_n1, a, &info); chkxer_("ZPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPTRI */ s_copy(srnamc_1.srnamt, "ZPPTRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpptri_("/", &c__0, a, &info); chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpptri_("U", &c_n1, a, &info); chkxer_("ZPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPTRS */ s_copy(srnamc_1.srnamt, "ZPPTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpptrs_("/", &c__0, &c__0, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpptrs_("U", &c_n1, &c__0, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpptrs_("U", &c__0, &c_n1, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zpptrs_("U", &c__2, &c__1, a, b, &c__1, &info); chkxer_("ZPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPRFS */ s_copy(srnamc_1.srnamt, "ZPPRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpprfs_("/", &c__0, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpprfs_("U", &c_n1, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpprfs_("U", &c__0, &c_n1, a, af, b, &c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zpprfs_("U", &c__2, &c__1, a, af, b, &c__1, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 9; zpprfs_("U", &c__2, &c__1, a, af, b, &c__2, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPCON */ s_copy(srnamc_1.srnamt, "ZPPCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zppcon_("/", &c__0, a, &anrm, &rcond, w, r__, &info); chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zppcon_("U", &c_n1, a, &anrm, &rcond, w, r__, &info); chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; d__1 = -anrm; zppcon_("U", &c__1, a, &d__1, &rcond, w, r__, &info); chkxer_("ZPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPPEQU */ s_copy(srnamc_1.srnamt, "ZPPEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zppequ_("/", &c__0, a, r1, &rcond, &anrm, &info); chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zppequ_("U", &c_n1, a, r1, &rcond, &anrm, &info); chkxer_("ZPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* Test error exits of the routines that use the Cholesky decomposition of a Hermitian positive definite band matrix. */ } else if (lsamen_(&c__2, c2, "PB")) { /* ZPBTRF */ s_copy(srnamc_1.srnamt, "ZPBTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbtrf_("/", &c__0, &c__0, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbtrf_("U", &c_n1, &c__0, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbtrf_("U", &c__1, &c_n1, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbtrf_("U", &c__2, &c__1, a, &c__1, &info); chkxer_("ZPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBTF2 */ s_copy(srnamc_1.srnamt, "ZPBTF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbtf2_("/", &c__0, &c__0, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbtf2_("U", &c_n1, &c__0, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbtf2_("U", &c__1, &c_n1, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbtf2_("U", &c__2, &c__1, a, &c__1, &info); chkxer_("ZPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBTRS */ s_copy(srnamc_1.srnamt, "ZPBTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbtrs_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbtrs_("U", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbtrs_("U", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpbtrs_("U", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zpbtrs_("U", &c__2, &c__1, &c__1, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; zpbtrs_("U", &c__2, &c__0, &c__1, a, &c__1, b, &c__1, &info); chkxer_("ZPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBRFS */ s_copy(srnamc_1.srnamt, "ZPBRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbrfs_("/", &c__0, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbrfs_("U", &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbrfs_("U", &c__1, &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zpbrfs_("U", &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zpbrfs_("U", &c__2, &c__1, &c__1, a, &c__1, af, &c__2, b, &c__2, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; zpbrfs_("U", &c__2, &c__1, &c__1, a, &c__2, af, &c__1, b, &c__2, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; zpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__1, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 12; zpbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__2, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBCON */ s_copy(srnamc_1.srnamt, "ZPBCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbcon_("/", &c__0, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbcon_("U", &c_n1, &c__0, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbcon_("U", &c__1, &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbcon_("U", &c__2, &c__1, a, &c__1, &anrm, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; d__1 = -anrm; zpbcon_("U", &c__1, &c__0, a, &c__1, &d__1, &rcond, w, r__, &info); chkxer_("ZPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZPBEQU */ s_copy(srnamc_1.srnamt, "ZPBEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zpbequ_("/", &c__0, &c__0, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zpbequ_("U", &c_n1, &c__0, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zpbequ_("U", &c__1, &c_n1, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zpbequ_("U", &c__2, &c__1, a, &c__1, r1, &rcond, &anrm, &info); chkxer_("ZPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); } /* Print a summary line. */ alaesm_(path, &infoc_1.ok, &infoc_1.nout); return 0; /* End of ZERRPO */ } /* zerrpo_ */
/* Subroutine */ int zporfsx_(char *uplo, char *equed, integer *n, integer * nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer * ldaf, doublereal *s, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *berr, integer * n_err_bnds__, doublereal *err_bnds_norm__, doublereal * err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex * work, doublereal *rwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, err_bnds_comp_dim1, err_bnds_comp_offset, i__1; doublereal d__1, d__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ doublereal illrcond_thresh__, unstable_thresh__, err_lbnd__; integer ref_type__; integer j; doublereal rcond_tmp__; integer prec_type__; doublereal cwise_wrong__; extern /* Subroutine */ int zla_porfsx_extended__(integer *, char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, logical *, doublereal *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, doublecomplex *, doublecomplex *, doublereal *, integer *, doublereal *, doublereal *, logical *, integer *, ftnlen); char norm[1]; logical ignore_cwise__; extern logical lsame_(char *, char *); doublereal anorm; logical rcequ; extern doublereal zla_porcond_c__(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, logical *, integer *, doublecomplex *, doublereal *, ftnlen), zla_porcond_x__(char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublereal *, ftnlen), dlamch_(char *); extern /* Subroutine */ int xerbla_(char *, integer *); extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int zpocon_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *); extern integer ilaprec_(char *); integer ithresh, n_norms__; doublereal rthresh; /* -- LAPACK routine (version 3.2.1) -- */ /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ /* -- Jason Riedy of Univ. of California Berkeley. -- */ /* -- April 2009 -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley and NAG Ltd. -- */ /* .. */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZPORFSX improves the computed solution to a system of linear */ /* equations when the coefficient matrix is symmetric positive */ /* definite, and provides error bounds and backward error estimates */ /* for the solution. In addition to normwise error bound, the code */ /* provides maximum componentwise error bound if possible. See */ /* comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the */ /* error bounds. */ /* The original system of linear equations may have been equilibrated */ /* before calling this routine, as described by arguments EQUED and S */ /* below. In this case, the solution and error bounds returned are */ /* for the original unequilibrated system. */ /* Arguments */ /* ========= */ /* Some optional parameters are bundled in the PARAMS array. These */ /* settings determine how refinement is performed, but often the */ /* defaults are acceptable. If the defaults are acceptable, users */ /* can pass NPARAMS = 0 which prevents the source code from accessing */ /* the PARAMS argument. */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangle of A is stored; */ /* = 'L': Lower triangle of A is stored. */ /* EQUED (input) CHARACTER*1 */ /* Specifies the form of equilibration that was done to A */ /* before calling this routine. This is needed to compute */ /* the solution and error bounds correctly. */ /* = 'N': No equilibration */ /* = 'Y': Both row and column equilibration, i.e., A has been */ /* replaced by diag(S) * A * diag(S). */ /* The right hand side B has been changed accordingly. */ /* N (input) INTEGER */ /* The order of the matrix A. N >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrices B and X. NRHS >= 0. */ /* A (input) COMPLEX*16 array, dimension (LDA,N) */ /* The symmetric matrix A. If UPLO = 'U', the leading N-by-N */ /* upper triangular part of A contains the upper triangular part */ /* of the matrix A, and the strictly lower triangular part of A */ /* is not referenced. If UPLO = 'L', the leading N-by-N lower */ /* triangular part of A contains the lower triangular part of */ /* the matrix A, and the strictly upper triangular part of A is */ /* not referenced. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* AF (input) COMPLEX*16 array, dimension (LDAF,N) */ /* The triangular factor U or L from the Cholesky factorization */ /* A = U**T*U or A = L*L**T, as computed by DPOTRF. */ /* LDAF (input) INTEGER */ /* The leading dimension of the array AF. LDAF >= max(1,N). */ /* S (input or output) DOUBLE PRECISION array, dimension (N) */ /* The row scale factors for A. If EQUED = 'Y', A is multiplied on */ /* the left and right by diag(S). S is an input argument if FACT = */ /* 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED */ /* = 'Y', each element of S must be positive. If S is output, each */ /* element of S is a power of the radix. If S is input, each element */ /* of S should be a power of the radix to ensure a reliable solution */ /* and error estimates. Scaling by powers of the radix does not cause */ /* rounding errors unless the result underflows or overflows. */ /* Rounding errors during scaling lead to refining with a matrix that */ /* is not equivalent to the input matrix, producing error estimates */ /* that may not be reliable. */ /* B (input) COMPLEX*16 array, dimension (LDB,NRHS) */ /* The right hand side matrix B. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= max(1,N). */ /* X (input/output) COMPLEX*16 array, dimension (LDX,NRHS) */ /* On entry, the solution matrix X, as computed by DGETRS. */ /* On exit, the improved solution matrix X. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. LDX >= max(1,N). */ /* RCOND (output) DOUBLE PRECISION */ /* Reciprocal scaled condition number. This is an estimate of the */ /* reciprocal Skeel condition number of the matrix A after */ /* equilibration (if done). If this is less than the machine */ /* precision (in particular, if it is zero), the matrix is singular */ /* to working precision. Note that the error may still be small even */ /* if this number is very small and the matrix appears ill- */ /* conditioned. */ /* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */ /* Componentwise relative backward error. This is the */ /* componentwise relative backward error of each solution vector X(j) */ /* (i.e., the smallest relative change in any element of A or B that */ /* makes X(j) an exact solution). */ /* N_ERR_BNDS (input) INTEGER */ /* Number of error bounds to return for each right hand side */ /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ /* ERR_BNDS_COMP below. */ /* ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */ /* For each right-hand side, this array contains information about */ /* various error bounds and condition numbers corresponding to the */ /* normwise relative error, which is defined as follows: */ /* Normwise relative error in the ith solution vector: */ /* max_j (abs(XTRUE(j,i) - X(j,i))) */ /* ------------------------------ */ /* max_j abs(X(j,i)) */ /* The array is indexed by the type of error information as described */ /* below. There currently are up to three pieces of information */ /* returned. */ /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ /* right-hand side. */ /* The second index in ERR_BNDS_NORM(:,err) contains the following */ /* three fields: */ /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ /* reciprocal condition number is less than the threshold */ /* sqrt(n) * dlamch('Epsilon'). */ /* err = 2 "Guaranteed" error bound: The estimated forward error, */ /* almost certainly within a factor of 10 of the true error */ /* so long as the next entry is greater than the threshold */ /* sqrt(n) * dlamch('Epsilon'). This error bound should only */ /* be trusted if the previous boolean is true. */ /* err = 3 Reciprocal condition number: Estimated normwise */ /* reciprocal condition number. Compared with the threshold */ /* sqrt(n) * dlamch('Epsilon') to determine if the error */ /* estimate is "guaranteed". These reciprocal condition */ /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ /* appropriately scaled matrix Z. */ /* Let Z = S*A, where S scales each row by a power of the */ /* radix so all absolute row sums of Z are approximately 1. */ /* See Lapack Working Note 165 for further details and extra */ /* cautions. */ /* ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */ /* For each right-hand side, this array contains information about */ /* various error bounds and condition numbers corresponding to the */ /* componentwise relative error, which is defined as follows: */ /* Componentwise relative error in the ith solution vector: */ /* abs(XTRUE(j,i) - X(j,i)) */ /* max_j ---------------------- */ /* abs(X(j,i)) */ /* The array is indexed by the right-hand side i (on which the */ /* componentwise relative error depends), and the type of error */ /* information as described below. There currently are up to three */ /* pieces of information returned for each right-hand side. If */ /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ /* the first (:,N_ERR_BNDS) entries are returned. */ /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ /* right-hand side. */ /* The second index in ERR_BNDS_COMP(:,err) contains the following */ /* three fields: */ /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ /* reciprocal condition number is less than the threshold */ /* sqrt(n) * dlamch('Epsilon'). */ /* err = 2 "Guaranteed" error bound: The estimated forward error, */ /* almost certainly within a factor of 10 of the true error */ /* so long as the next entry is greater than the threshold */ /* sqrt(n) * dlamch('Epsilon'). This error bound should only */ /* be trusted if the previous boolean is true. */ /* err = 3 Reciprocal condition number: Estimated componentwise */ /* reciprocal condition number. Compared with the threshold */ /* sqrt(n) * dlamch('Epsilon') to determine if the error */ /* estimate is "guaranteed". These reciprocal condition */ /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ /* appropriately scaled matrix Z. */ /* Let Z = S*(A*diag(x)), where x is the solution for the */ /* current right-hand side and S scales each row of */ /* A*diag(x) by a power of the radix so all absolute row */ /* sums of Z are approximately 1. */ /* See Lapack Working Note 165 for further details and extra */ /* cautions. */ /* NPARAMS (input) INTEGER */ /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ /* PARAMS array is never referenced and default values are used. */ /* PARAMS (input / output) DOUBLE PRECISION array, dimension NPARAMS */ /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ /* that entry will be filled with default value used for that */ /* parameter. Only positions up to NPARAMS are accessed; defaults */ /* are used for higher-numbered parameters. */ /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ /* refinement or not. */ /* Default: 1.0D+0 */ /* = 0.0 : No refinement is performed, and no error bounds are */ /* computed. */ /* = 1.0 : Use the double-precision refinement algorithm, */ /* possibly with doubled-single computations if the */ /* compilation environment does not support DOUBLE */ /* PRECISION. */ /* (other values are reserved for future use) */ /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ /* computations allowed for refinement. */ /* Default: 10 */ /* Aggressive: Set to 100 to permit convergence using approximate */ /* factorizations or factorizations other than LU. If */ /* the factorization uses a technique other than */ /* Gaussian elimination, the guarantees in */ /* err_bnds_norm and err_bnds_comp may no longer be */ /* trustworthy. */ /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ /* will attempt to find a solution with small componentwise */ /* relative error in the double-precision algorithm. Positive */ /* is true, 0.0 is false. */ /* Default: 1.0 (attempt componentwise convergence) */ /* WORK (workspace) COMPLEX*16 array, dimension (2*N) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) */ /* INFO (output) INTEGER */ /* = 0: Successful exit. The solution to every right-hand side is */ /* guaranteed. */ /* < 0: If INFO = -i, the i-th argument had an illegal value */ /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ /* has been completed, but the factor U is exactly singular, so */ /* the solution and error bounds could not be computed. RCOND = 0 */ /* is returned. */ /* = N+J: The solution corresponding to the Jth right-hand side is */ /* not guaranteed. The solutions corresponding to other right- */ /* hand sides K with K > J may not be guaranteed as well, but */ /* only the first such right-hand side is reported. If a small */ /* componentwise error is not requested (PARAMS(3) = 0.0) then */ /* the Jth right-hand side is the first with a normwise error */ /* bound that is not guaranteed (the smallest J such */ /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ /* the Jth right-hand side is the first with either a normwise or */ /* componentwise error bound that is not guaranteed (the smallest */ /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ /* about all of the right-hand sides check ERR_BNDS_NORM or */ /* ERR_BNDS_COMP. */ /* ================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Check the input parameters. */ /* Parameter adjustments */ err_bnds_comp_dim1 = *nrhs; err_bnds_comp_offset = 1 + err_bnds_comp_dim1; err_bnds_comp__ -= err_bnds_comp_offset; err_bnds_norm_dim1 = *nrhs; err_bnds_norm_offset = 1 + err_bnds_norm_dim1; err_bnds_norm__ -= err_bnds_norm_offset; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; af_dim1 = *ldaf; af_offset = 1 + af_dim1; af -= af_offset; --s; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; --berr; --params; --work; --rwork; /* Function Body */ *info = 0; ref_type__ = 1; if (*nparams >= 1) { if (params[1] < 0.) { params[1] = 1.; } else { ref_type__ = (integer) params[1]; } } /* Set default parameters. */ illrcond_thresh__ = (doublereal) (*n) * dlamch_("Epsilon"); ithresh = 10; rthresh = .5; unstable_thresh__ = .25; ignore_cwise__ = FALSE_; if (*nparams >= 2) { if (params[2] < 0.) { params[2] = (doublereal) ithresh; } else { ithresh = (integer) params[2]; } } if (*nparams >= 3) { if (params[3] < 0.) { if (ignore_cwise__) { params[3] = 0.; } else { params[3] = 1.; } } else { ignore_cwise__ = params[3] == 0.; } } if (ref_type__ == 0 || *n_err_bnds__ == 0) { n_norms__ = 0; } else if (ignore_cwise__) { n_norms__ = 1; } else { n_norms__ = 2; } rcequ = lsame_(equed, "Y"); /* Test input parameters. */ if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { *info = -1; } else if (! rcequ && ! lsame_(equed, "N")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*nrhs < 0) { *info = -4; } else if (*lda < max(1,*n)) { *info = -6; } else if (*ldaf < max(1,*n)) { *info = -8; } else if (*ldb < max(1,*n)) { *info = -11; } else if (*ldx < max(1,*n)) { *info = -13; } if (*info != 0) { i__1 = -(*info); xerbla_("ZPORFSX", &i__1); return 0; } /* Quick return if possible. */ if (*n == 0 || *nrhs == 0) { *rcond = 1.; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { berr[j] = 0.; if (*n_err_bnds__ >= 1) { err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; } else if (*n_err_bnds__ >= 2) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.; err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.; } else if (*n_err_bnds__ >= 3) { err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.; } } return 0; } /* Default to failure. */ *rcond = 0.; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { berr[j] = 1.; if (*n_err_bnds__ >= 1) { err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; } else if (*n_err_bnds__ >= 2) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; } else if (*n_err_bnds__ >= 3) { err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.; err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.; } } /* Compute the norm of A and the reciprocal of the condition */ /* number of A. */ *(unsigned char *)norm = 'I'; anorm = zlanhe_(norm, uplo, n, &a[a_offset], lda, &rwork[1]); zpocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1], info); /* Perform refinement on each right-hand side */ if (ref_type__ != 0) { prec_type__ = ilaprec_("E"); zla_porfsx_extended__(&prec_type__, uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &rcequ, &s[1], &b[b_offset], ldb, &x[ x_offset], ldx, &berr[1], &n_norms__, &err_bnds_norm__[ err_bnds_norm_offset], &err_bnds_comp__[err_bnds_comp_offset], &work[1], &rwork[1], &work[*n + 1], (doublecomplex *)(&rwork[1]), rcond, &ithresh, & rthresh, &unstable_thresh__, &ignore_cwise__, info, (ftnlen)1) ; } /* Computing MAX */ d__1 = 10., d__2 = sqrt((doublereal) (*n)); err_lbnd__ = max(d__1,d__2) * dlamch_("Epsilon"); if (*n_err_bnds__ >= 1 && n_norms__ >= 1) { /* Compute scaled normwise condition number cond(A*C). */ if (rcequ) { rcond_tmp__ = zla_porcond_c__(uplo, n, &a[a_offset], lda, &af[ af_offset], ldaf, &s[1], &c_true, info, &work[1], &rwork[ 1], (ftnlen)1); } else { rcond_tmp__ = zla_porcond_c__(uplo, n, &a[a_offset], lda, &af[ af_offset], ldaf, &s[1], &c_false, info, &work[1], &rwork[ 1], (ftnlen)1); } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { /* Cap the error at 1.0. */ if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] > 1.) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; } /* Threshold the error (see LAWN). */ if (rcond_tmp__ < illrcond_thresh__) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; err_bnds_norm__[j + err_bnds_norm_dim1] = 0.; if (*info <= *n) { *info = *n + j; } } else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < err_lbnd__) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__; err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; } /* Save the condition number. */ if (*n_err_bnds__ >= 3) { err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__; } } } if (*n_err_bnds__ >= 1 && n_norms__ >= 2) { /* Compute componentwise condition number cond(A*diag(Y(:,J))) for */ /* each right-hand side using the current solution as an estimate of */ /* the true solution. If the componentwise error estimate is too */ /* large, then the solution is a lousy estimate of truth and the */ /* estimated RCOND may be too optimistic. To avoid misleading users, */ /* the inverse condition number is set to 0.0 when the estimated */ /* cwise error is at least CWISE_WRONG. */ cwise_wrong__ = sqrt(dlamch_("Epsilon")); i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < cwise_wrong__) { rcond_tmp__ = zla_porcond_x__(uplo, n, &a[a_offset], lda, &af[ af_offset], ldaf, &x[j * x_dim1 + 1], info, &work[1], &rwork[1], (ftnlen)1); } else { rcond_tmp__ = 0.; } /* Cap the error at 1.0. */ if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] > 1.) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; } /* Threshold the error (see LAWN). */ if (rcond_tmp__ < illrcond_thresh__) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1] = 0.; if (params[3] == 1. && *info < *n + j) { *info = *n + j; } } else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < err_lbnd__) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__; err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; } /* Save the condition number. */ if (*n_err_bnds__ >= 3) { err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__; } } } return 0; /* End of ZPORFSX */ } /* zporfsx_ */
/* Subroutine */ int zchkpo_(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 }; static char uplos[1*2] = "U" "L"; /* Format strings */ static char fmt_9999[] = "(\002 UPLO = '\002,a1,\002', N =\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, " "NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g" "12.5)"; static char fmt_9997[] = "(\002 UPLO = '\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; /* Local variables */ integer i__, k, n, nb, in, kl, ku, lda, inb, ioff, mode, imat, info; char path[3], dist[1]; integer irhs, nrhs; char uplo[1], type__[1]; integer nrun; integer nfail, iseed[4]; doublereal rcond; integer nimat; doublereal anorm; integer iuplo, izero, nerrs; logical zerot; char xtype[1]; doublereal rcondc; doublereal cndnum; doublereal result[8]; /* Fortran I/O blocks */ static cilist io___33 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___36 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___38 = { 0, 0, 0, fmt_9997, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZCHKPO tests ZPOTRF, -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. */ /* 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) COMPLEX*16 array, dimension (NMAX*NMAX) */ /* AFAC (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */ /* AINV (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */ /* B (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* where NSMAX is the largest entry in NSVAL. */ /* X (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* XACT (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* WORK (workspace) COMPLEX*16 array, dimension */ /* (NMAX*max(3,NSMAX)) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension */ /* (NMAX+2*NSMAX) */ /* NOUT (input) INTEGER */ /* The unit number for output. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Data statements .. */ /* Parameter adjustments */ --rwork; --work; --xact; --x; --b; --ainv; --afac; --a; --nsval; --nbval; --nval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* Initialize constants and the random number seed. */ s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17); 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) { zerrpo_(path, nout); } infoc_1.infot = 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'; nimat = 9; if (n <= 0) { nimat = 1; } izero = 0; i__2 = nimat; for (imat = 1; imat <= i__2; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L110; } /* Skip types 3, 4, or 5 if the matrix size is too small. */ zerot = imat >= 3 && imat <= 5; if (zerot && n < imat - 2) { goto L110; } /* 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 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)32, (ftnlen)6); zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, & cndnum, &anorm, &kl, &ku, uplo, &a[1], &lda, &work[1], &info); /* Check error code from ZLATMS. */ if (info != 0) { alaerh_(path, "ZLATMS", &info, &c__0, uplo, &n, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); goto L100; } /* 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__) { i__4 = ioff + i__; a[i__4].r = 0., a[i__4].i = 0.; /* L20: */ } ioff += izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { i__4 = ioff; a[i__4].r = 0., a[i__4].i = 0.; ioff += lda; /* L30: */ } } else { ioff = izero; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = ioff; a[i__4].r = 0., a[i__4].i = 0.; ioff += lda; /* L40: */ } ioff -= izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { i__4 = ioff + i__; a[i__4].r = 0., a[i__4].i = 0.; /* L50: */ } } } else { izero = 0; } /* Set the imaginary part of the diagonals. */ i__3 = lda + 1; zlaipd_(&n, &a[1], &i__3, &c__0); /* Do for each value of NB in NBVAL */ i__3 = *nnb; for (inb = 1; inb <= i__3; ++inb) { nb = nbval[inb]; xlaenv_(&c__1, &nb); /* Compute the L*L' or U'*U factorization of the matrix. */ zlacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda); s_copy(srnamc_1.srnamt, "ZPOTRF", (ftnlen)32, (ftnlen)6); zpotrf_(uplo, &n, &afac[1], &lda, &info); /* Check error code from ZPOTRF. */ if (info != izero) { alaerh_(path, "ZPOTRF", &info, &izero, uplo, &n, &n, & c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout); goto L90; } /* Skip the tests if INFO is not 0. */ if (info != 0) { goto L90; } /* + TEST 1 */ /* Reconstruct matrix from factors and compute residual. */ zlacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda); zpot01_(uplo, &n, &a[1], &lda, &ainv[1], &lda, &rwork[1], result); /* + TEST 2 */ /* Form the inverse and compute the residual. */ zlacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda); s_copy(srnamc_1.srnamt, "ZPOTRI", (ftnlen)32, (ftnlen)6); zpotri_(uplo, &n, &ainv[1], &lda, &info); /* Check error code from ZPOTRI. */ if (info != 0) { alaerh_(path, "ZPOTRI", &info, &c__0, uplo, &n, &n, & c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } zpot03_(uplo, &n, &a[1], &lda, &ainv[1], &lda, &work[1], & lda, &rwork[1], &rcondc, &result[1]); /* Print information about the tests that did not pass */ /* the threshold. */ for (k = 1; k <= 2; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___33.ciunit = *nout; s_wsfe(&io___33); do_fio(&c__1, uplo, (ftnlen)1); 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(doublereal)); e_wsfe(); ++nfail; } /* L60: */ } nrun += 2; /* Skip the rest of the tests unless this is the first */ /* blocksize. */ if (inb != 1) { goto L90; } i__4 = *nns; for (irhs = 1; irhs <= i__4; ++irhs) { nrhs = nsval[irhs]; /* + TEST 3 */ /* Solve and compute residual for A * X = B . */ s_copy(srnamc_1.srnamt, "ZLARHS", (ftnlen)32, (ftnlen) 6); zlarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, & nrhs, &a[1], &lda, &xact[1], &lda, &b[1], & lda, iseed, &info); zlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda); s_copy(srnamc_1.srnamt, "ZPOTRS", (ftnlen)32, (ftnlen) 6); zpotrs_(uplo, &n, &nrhs, &afac[1], &lda, &x[1], &lda, &info); /* Check error code from ZPOTRS. */ if (info != 0) { alaerh_(path, "ZPOTRS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &nrhs, &imat, &nfail, & nerrs, nout); } zlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], & lda); zpot02_(uplo, &n, &nrhs, &a[1], &lda, &x[1], &lda, & work[1], &lda, &rwork[1], &result[2]); /* + TEST 4 */ /* Check solution from generated exact solution. */ zget04_(&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, "ZPORFS", (ftnlen)32, (ftnlen) 6); zporfs_(uplo, &n, &nrhs, &a[1], &lda, &afac[1], &lda, &b[1], &lda, &x[1], &lda, &rwork[1], &rwork[ nrhs + 1], &work[1], &rwork[(nrhs << 1) + 1], &info); /* Check error code from ZPORFS. */ if (info != 0) { alaerh_(path, "ZPORFS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &nrhs, &imat, &nfail, & nerrs, nout); } zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[4]); zpot05_(uplo, &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___36.ciunit = *nout; s_wsfe(&io___36); do_fio(&c__1, uplo, (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(doublereal)); e_wsfe(); ++nfail; } /* L70: */ } nrun += 5; /* L80: */ } /* + TEST 8 */ /* Get an estimate of RCOND = 1/CNDNUM. */ anorm = zlanhe_("1", uplo, &n, &a[1], &lda, &rwork[1]); s_copy(srnamc_1.srnamt, "ZPOCON", (ftnlen)32, (ftnlen)6); zpocon_(uplo, &n, &afac[1], &lda, &anorm, &rcond, &work[1] , &rwork[1], &info); /* Check error code from ZPOCON. */ if (info != 0) { alaerh_(path, "ZPOCON", &info, &c__0, uplo, &n, &n, & c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } result[7] = dget06_(&rcond, &rcondc); /* Print the test ratio if it is .GE. THRESH. */ if (result[7] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___38.ciunit = *nout; s_wsfe(&io___38); 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 *)&c__8, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof( doublereal)); e_wsfe(); ++nfail; } ++nrun; L90: ; } L100: ; } L110: ; } /* L120: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of ZCHKPO */ } /* zchkpo_ */