/* Subroutine */ int dptsvx_(char *fact, integer *n, integer *nrhs, doublereal *d__, doublereal *e, doublereal *df, doublereal *ef, doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal * rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer * info) { /* System generated locals */ integer b_dim1, b_offset, x_dim1, x_offset, i__1; /* Local variables */ extern logical lsame_(char *, char *); doublereal anorm; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); extern doublereal dlamch_(char *); logical nofact; extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *); extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *); extern /* Subroutine */ int dptcon_(integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *), dptrfs_( integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *), dpttrf_( integer *, doublereal *, doublereal *, integer *), dpttrs_( integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *); /* -- LAPACK routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DPTSVX uses the factorization A = L*D*L**T to compute the solution */ /* to a real system of linear equations A*X = B, where A is an N-by-N */ /* symmetric positive definite tridiagonal 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 = 'N', the matrix A is factored as A = L*D*L**T, where L */ /* is a unit lower bidiagonal matrix and D is diagonal. The */ /* factorization can also be regarded as having the form */ /* A = U**T*D*U. */ /* 2. 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. */ /* 3. The system of equations is solved for X using the factored form */ /* of A. */ /* 4. Iterative refinement is applied to improve the computed solution */ /* matrix and calculate error bounds and backward error estimates */ /* for it. */ /* Arguments */ /* ========= */ /* FACT (input) CHARACTER*1 */ /* Specifies whether or not the factored form of A has been */ /* supplied on entry. */ /* = 'F': On entry, DF and EF contain the factored form of A. */ /* D, E, DF, and EF will not be modified. */ /* = 'N': The matrix A will be copied to DF and EF and */ /* factored. */ /* 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. */ /* D (input) DOUBLE PRECISION array, dimension (N) */ /* The n diagonal elements of the tridiagonal matrix A. */ /* E (input) DOUBLE PRECISION array, dimension (N-1) */ /* The (n-1) subdiagonal elements of the tridiagonal matrix A. */ /* DF (input or output) DOUBLE PRECISION array, dimension (N) */ /* If FACT = 'F', then DF is an input argument and on entry */ /* contains the n diagonal elements of the diagonal matrix D */ /* from the L*D*L**T factorization of A. */ /* If FACT = 'N', then DF is an output argument and on exit */ /* contains the n diagonal elements of the diagonal matrix D */ /* from the L*D*L**T factorization of A. */ /* EF (input or output) DOUBLE PRECISION array, dimension (N-1) */ /* If FACT = 'F', then EF is an input argument and on entry */ /* contains the (n-1) subdiagonal elements of the unit */ /* bidiagonal factor L from the L*D*L**T factorization of A. */ /* If FACT = 'N', then EF is an output argument and on exit */ /* contains the (n-1) subdiagonal elements of the unit */ /* bidiagonal factor L from the L*D*L**T factorization of A. */ /* B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) */ /* The N-by-NRHS right hand side matrix B. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= max(1,N). */ /* X (output) DOUBLE PRECISION array, dimension (LDX,NRHS) */ /* If INFO = 0 of INFO = N+1, the N-by-NRHS solution matrix X. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. LDX >= max(1,N). */ /* RCOND (output) DOUBLE PRECISION */ /* The reciprocal condition number of the matrix A. 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 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). */ /* 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) DOUBLE PRECISION array, dimension (2*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 .. */ /* Test the input parameters. */ /* Parameter adjustments */ --d__; --e; --df; --ef; 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; /* Function Body */ *info = 0; nofact = lsame_(fact, "N"); if (! nofact && ! lsame_(fact, "F")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; } else if (*ldb < max(1,*n)) { *info = -9; } else if (*ldx < max(1,*n)) { *info = -11; } if (*info != 0) { i__1 = -(*info); xerbla_("DPTSVX", &i__1); return 0; } if (nofact) { /* Compute the L*D*L' (or U'*D*U) factorization of A. */ dcopy_(n, &d__[1], &c__1, &df[1], &c__1); if (*n > 1) { i__1 = *n - 1; dcopy_(&i__1, &e[1], &c__1, &ef[1], &c__1); } dpttrf_(n, &df[1], &ef[1], info); /* Return if INFO is non-zero. */ if (*info > 0) { *rcond = 0.; return 0; } } /* Compute the norm of the matrix A. */ anorm = dlanst_("1", n, &d__[1], &e[1]); /* Compute the reciprocal of the condition number of A. */ dptcon_(n, &df[1], &ef[1], &anorm, rcond, &work[1], info); /* Compute the solution vectors X. */ dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); dpttrs_(n, nrhs, &df[1], &ef[1], &x[x_offset], ldx, info); /* Use iterative refinement to improve the computed solutions and */ /* compute error bounds and backward error estimates for them. */ dptrfs_(n, nrhs, &d__[1], &e[1], &df[1], &ef[1], &b[b_offset], ldb, &x[ x_offset], ldx, &ferr[1], &berr[1], &work[1], info); /* Set INFO = N+1 if the matrix is singular to working precision. */ if (*rcond < dlamch_("Epsilon")) { *info = *n + 1; } return 0; /* End of DPTSVX */ } /* dptsvx_ */
/* Subroutine */ int derrgt_(char *path, integer *nunit) { /* System generated locals */ doublereal d__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 b[2], c__[2], d__[2], e[2], f[2], w[2], x[2], rcond, anorm; static char c2[2]; static doublereal r1[2], r2[2], cf[2], df[2], ef[2]; static integer ip[2], iw[2]; extern /* Subroutine */ int alaesm_(char *, logical *, integer *), dgtcon_(char *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *); extern logical lsamen_(integer *, char *, char *); extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical *, logical *), dptcon_(integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *) , dgtrfs_(char *, integer *, integer *, doublereal *, doublereal * , doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dgttrf_(integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *), dptrfs_( integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *), dpttrf_( integer *, doublereal *, doublereal *, integer *), dgttrs_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *), dpttrs_(integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___1 = { 0, 0, 0, 0, 0 }; /* -- 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 ======= DERRGT tests the error exits for the DOUBLE PRECISION tridiagonal routines. 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); d__[0] = 1.; d__[1] = 2.; df[0] = 1.; df[1] = 2.; e[0] = 3.; e[1] = 4.; ef[0] = 3.; ef[1] = 4.; anorm = 1.; infoc_1.ok = TRUE_; if (lsamen_(&c__2, c2, "GT")) { /* Test error exits for the general tridiagonal routines. DGTTRF */ s_copy(srnamc_1.srnamt, "DGTTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgttrf_(&c_n1, c__, d__, e, f, ip, &info); chkxer_("DGTTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGTTRS */ s_copy(srnamc_1.srnamt, "DGTTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgttrs_("/", &c__0, &c__0, c__, d__, e, f, ip, x, &c__1, &info); chkxer_("DGTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgttrs_("N", &c_n1, &c__0, c__, d__, e, f, ip, x, &c__1, &info); chkxer_("DGTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgttrs_("N", &c__0, &c_n1, c__, d__, e, f, ip, x, &c__1, &info); chkxer_("DGTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; dgttrs_("N", &c__2, &c__1, c__, d__, e, f, ip, x, &c__1, &info); chkxer_("DGTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGTRFS */ s_copy(srnamc_1.srnamt, "DGTRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgtrfs_("/", &c__0, &c__0, c__, d__, e, cf, df, ef, f, ip, b, &c__1, x, &c__1, r1, r2, w, iw, &info); chkxer_("DGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgtrfs_("N", &c_n1, &c__0, c__, d__, e, cf, df, ef, f, ip, b, &c__1, x, &c__1, r1, r2, w, iw, &info); chkxer_("DGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgtrfs_("N", &c__0, &c_n1, c__, d__, e, cf, df, ef, f, ip, b, &c__1, x, &c__1, r1, r2, w, iw, &info); chkxer_("DGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 13; dgtrfs_("N", &c__2, &c__1, c__, d__, e, cf, df, ef, f, ip, b, &c__1, x, &c__2, r1, r2, w, iw, &info); chkxer_("DGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 15; dgtrfs_("N", &c__2, &c__1, c__, d__, e, cf, df, ef, f, ip, b, &c__2, x, &c__1, r1, r2, w, iw, &info); chkxer_("DGTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGTCON */ s_copy(srnamc_1.srnamt, "DGTCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgtcon_("/", &c__0, c__, d__, e, f, ip, &anorm, &rcond, w, iw, &info); chkxer_("DGTCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgtcon_("I", &c_n1, c__, d__, e, f, ip, &anorm, &rcond, w, iw, &info); chkxer_("DGTCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; d__1 = -anorm; dgtcon_("I", &c__0, c__, d__, e, f, ip, &d__1, &rcond, w, iw, &info); chkxer_("DGTCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); } else if (lsamen_(&c__2, c2, "PT")) { /* Test error exits for the positive definite tridiagonal routines. DPTTRF */ s_copy(srnamc_1.srnamt, "DPTTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dpttrf_(&c_n1, d__, e, &info); chkxer_("DPTTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DPTTRS */ s_copy(srnamc_1.srnamt, "DPTTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dpttrs_(&c_n1, &c__0, d__, e, x, &c__1, &info); chkxer_("DPTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dpttrs_(&c__0, &c_n1, d__, e, x, &c__1, &info); chkxer_("DPTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; dpttrs_(&c__2, &c__1, d__, e, x, &c__1, &info); chkxer_("DPTTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DPTRFS */ s_copy(srnamc_1.srnamt, "DPTRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dptrfs_(&c_n1, &c__0, d__, e, df, ef, b, &c__1, x, &c__1, r1, r2, w, & info); chkxer_("DPTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dptrfs_(&c__0, &c_n1, d__, e, df, ef, b, &c__1, x, &c__1, r1, r2, w, & info); chkxer_("DPTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; dptrfs_(&c__2, &c__1, d__, e, df, ef, b, &c__1, x, &c__2, r1, r2, w, & info); chkxer_("DPTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; dptrfs_(&c__2, &c__1, d__, e, df, ef, b, &c__2, x, &c__1, r1, r2, w, & info); chkxer_("DPTRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DPTCON */ s_copy(srnamc_1.srnamt, "DPTCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dptcon_(&c_n1, d__, e, &anorm, &rcond, w, &info); chkxer_("DPTCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; d__1 = -anorm; dptcon_(&c__0, d__, e, &d__1, &rcond, w, &info); chkxer_("DPTCON", &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 DERRGT */ } /* derrgt_ */