Пример #1
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/* Subroutine */ int dgesvxx_(char *fact, char *trans, integer *n, integer *
                              nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf,
                              integer *ipiv, char *equed, doublereal *r__, doublereal *c__,
                              doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
                              rcond, doublereal *rpvgrw, doublereal *berr, integer *n_err_bnds__,
                              doublereal *err_bnds_norm__, doublereal *err_bnds_comp__, integer *
                              nparams, doublereal *params, doublereal *work, integer *iwork,
                              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;

    /* Local variables */
    integer j;
    doublereal amax;
    doublereal rcmin, rcmax;
    logical equil;
    doublereal colcnd;
    logical nofact;
    doublereal bignum;
    integer infequ;
    logical colequ;
    doublereal rowcnd;
    logical notran;
    doublereal smlnum;
    logical rowequ;

    /*     -- LAPACK driver routine (version 3.2)                          -- */
    /*     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
    /*     -- Jason Riedy of Univ. of California Berkeley.                 -- */
    /*     -- November 2008                                                -- */

    /*     -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /*     -- Univ. of California Berkeley and NAG Ltd.                    -- */

    /*     Purpose */
    /*     ======= */

    /*     DGESVXX uses the LU factorization to compute the solution to a */
    /*     double precision system of linear equations  A * X = B,  where A is an */
    /*     N-by-N matrix and X and B are N-by-NRHS matrices. */

    /*     If requested, both normwise and maximum componentwise error bounds */
    /*     are returned. DGESVXX will return a solution with a tiny */
    /*     guaranteed error (O(eps) where eps is the working machine */
    /*     precision) unless the matrix is very ill-conditioned, in which */
    /*     case a warning is returned. Relevant condition numbers also are */
    /*     calculated and returned. */

    /*     DGESVXX accepts user-provided factorizations and equilibration */
    /*     factors; see the definitions of the FACT and EQUED options. */
    /*     Solving with refinement and using a factorization from a previous */
    /*     DGESVXX call will also produce a solution with either O(eps) */
    /*     errors or warnings, but we cannot make that claim for general */
    /*     user-provided factorizations and equilibration factors if they */
    /*     differ from what DGESVXX would itself produce. */

    /*     Description */
    /*     =========== */

    /*     The following steps are performed: */

    /*     1. If FACT = 'E', double precision scaling factors are computed to equilibrate */
    /*     the system: */

    /*       TRANS = 'N':  diag(R)*A*diag(C)     *inv(diag(C))*X = diag(R)*B */
    /*       TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */
    /*       TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*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(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */
    /*     or diag(C)*B (if TRANS = 'T' or 'C'). */

    /*     2. If FACT = 'N' or 'E', the LU decomposition is used to factor */
    /*     the matrix A (after equilibration if FACT = 'E') as */

    /*       A = P * L * U, */

    /*     where P is a permutation matrix, L is a unit lower triangular */
    /*     matrix, and U is upper triangular. */

    /*     3. If some U(i,i)=0, so that U is exactly singular, then the */
    /*     routine returns with INFO = i. Otherwise, the factored form of A */
    /*     is used to estimate the condition number of the matrix A (see */
    /*     argument RCOND). If the reciprocal of the condition number is less */
    /*     than machine precision, 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. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero), */
    /*     the routine will use iterative refinement to try to get a small */
    /*     error and error bounds.  Refinement calculates the residual to at */
    /*     least twice the working precision. */

    /*     6. If equilibration was used, the matrix X is premultiplied by */
    /*     diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */
    /*     that it solves the original system before equilibration. */

    /*     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. */

    /*     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 and IPIV contain the factored form of A. */
    /*               If EQUED is not 'N', the matrix A has been */
    /*               equilibrated with scaling factors given by R and C. */
    /*               A, AF, and IPIV are not 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. */

    /*     TRANS   (input) CHARACTER*1 */
    /*     Specifies the form of the system of equations: */
    /*       = 'N':  A * X = B     (No transpose) */
    /*       = 'T':  A**T * X = B  (Transpose) */
    /*       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose) */

    /*     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) DOUBLE PRECISION array, dimension (LDA,N) */
    /*     On entry, the N-by-N matrix A.  If FACT = 'F' and EQUED is */
    /*     not 'N', then A must have been equilibrated by the scaling */
    /*     factors in R and/or C.  A is not modified if FACT = 'F' or */
    /*     'N', or if FACT = 'E' and EQUED = 'N' on exit. */

    /*     On exit, if EQUED .ne. 'N', A is scaled as follows: */
    /*     EQUED = 'R':  A := diag(R) * A */
    /*     EQUED = 'C':  A := A * diag(C) */
    /*     EQUED = 'B':  A := diag(R) * A * diag(C). */

    /*     LDA     (input) INTEGER */
    /*     The leading dimension of the array A.  LDA >= max(1,N). */

    /*     AF      (input or output) DOUBLE PRECISION array, dimension (LDAF,N) */
    /*     If FACT = 'F', then AF is an input argument and on entry */
    /*     contains the factors L and U from the factorization */
    /*     A = P*L*U as computed by DGETRF.  If EQUED .ne. 'N', then */
    /*     AF is the factored form of the equilibrated matrix A. */

    /*     If FACT = 'N', then AF is an output argument and on exit */
    /*     returns the factors L and U from the factorization A = P*L*U */
    /*     of the original matrix A. */

    /*     If FACT = 'E', then AF is an output argument and on exit */
    /*     returns the factors L and U from the factorization A = P*L*U */
    /*     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). */

    /*     IPIV    (input or output) INTEGER array, dimension (N) */
    /*     If FACT = 'F', then IPIV is an input argument and on entry */
    /*     contains the pivot indices from the factorization A = P*L*U */
    /*     as computed by DGETRF; row i of the matrix was interchanged */
    /*     with row IPIV(i). */

    /*     If FACT = 'N', then IPIV is an output argument and on exit */
    /*     contains the pivot indices from the factorization A = P*L*U */
    /*     of the original matrix A. */

    /*     If FACT = 'E', then IPIV is an output argument and on exit */
    /*     contains the pivot indices from the factorization A = P*L*U */
    /*     of the equilibrated matrix A. */

    /*     EQUED   (input or output) CHARACTER*1 */
    /*     Specifies the form of equilibration that was done. */
    /*       = 'N':  No equilibration (always true if FACT = 'N'). */
    /*       = 'R':  Row equilibration, i.e., A has been premultiplied by */
    /*               diag(R). */
    /*       = 'C':  Column equilibration, i.e., A has been postmultiplied */
    /*               by diag(C). */
    /*       = 'B':  Both row and column equilibration, i.e., A has been */
    /*               replaced by diag(R) * A * diag(C). */
    /*     EQUED is an input argument if FACT = 'F'; otherwise, it is an */
    /*     output argument. */

    /*     R       (input or output) DOUBLE PRECISION array, dimension (N) */
    /*     The row scale factors for A.  If EQUED = 'R' or 'B', A is */
    /*     multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */
    /*     is not accessed.  R is an input argument if FACT = 'F'; */
    /*     otherwise, R is an output argument.  If FACT = 'F' and */
    /*     EQUED = 'R' or 'B', each element of R must be positive. */
    /*     If R is output, each element of R is a power of the radix. */
    /*     If R is input, each element of R 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. */

    /*     C       (input or output) DOUBLE PRECISION array, dimension (N) */
    /*     The column scale factors for A.  If EQUED = 'C' or 'B', A is */
    /*     multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */
    /*     is not accessed.  C is an input argument if FACT = 'F'; */
    /*     otherwise, C is an output argument.  If FACT = 'F' and */
    /*     EQUED = 'C' or 'B', each element of C must be positive. */
    /*     If C is output, each element of C is a power of the radix. */
    /*     If C is input, each element of C 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/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */
    /*     On entry, the N-by-NRHS right hand side matrix B. */
    /*     On exit, */
    /*     if EQUED = 'N', B is not modified; */
    /*     if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */
    /*        diag(R)*B; */
    /*     if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */
    /*        overwritten by diag(C)*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, the N-by-NRHS solution matrix X to the original */
    /*     system of equations.  Note that A and B are modified on exit */
    /*     if EQUED .ne. 'N', and the solution to the equilibrated system is */
    /*     inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or 'B', or */
    /*     inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R' or 'B'. */

    /*     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. */

    /*     RPVGRW  (output) DOUBLE PRECISION */
    /*     Reciprocal pivot growth.  On exit, this contains the reciprocal */
    /*     pivot growth factor norm(A)/norm(U). The "max absolute element" */
    /*     norm is used.  If this is much less than 1, then the stability of */
    /*     the LU factorization of the (equilibrated) matrix A could be poor. */
    /*     This also means that the solution X, estimated condition numbers, */
    /*     and error bounds could be unreliable. If factorization fails with */
    /*     0<INFO<=N, then this contains the reciprocal pivot growth factor */
    /*     for the leading INFO columns of A.  In DGESVX, this quantity is */
    /*     returned in WORK(1). */

    /*     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 extra-precise refinement algorithm. */
    /*              (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) DOUBLE PRECISION array, dimension (4*N) */

    /*     IWORK   (workspace) INTEGER array, dimension (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. */

    /*     ================================================================== */

    /* 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;
    --ipiv;
    --r__;
    --c__;
    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;
    --iwork;

    /* Function Body */
    *info = 0;
    nofact = lsame_(fact, "N");
    equil = lsame_(fact, "E");
    notran = lsame_(trans, "N");
    smlnum = dlamch_("Safe minimum");
    bignum = 1. / smlnum;
    if (nofact || equil) {
        *(unsigned char *)equed = 'N';
        rowequ = FALSE_;
        colequ = FALSE_;
    } else {
        rowequ = lsame_(equed, "R") || lsame_(equed,
                                              "B");
        colequ = lsame_(equed, "C") || lsame_(equed,
                                              "B");
    }

    /*     Default is failure.  If an input parameter is wrong or */
    /*     factorization fails, make everything look horrible.  Only the */
    /*     pivot growth is set here, the rest is initialized in DGERFSX. */

    *rpvgrw = 0.;

    /*     Test the input parameters.  PARAMS is not tested until DGERFSX. */

    if (! nofact && ! equil && ! lsame_(fact, "F")) {
        *info = -1;
    } else if (! notran && ! lsame_(trans, "T") && !
               lsame_(trans, "C")) {
        *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") && ! (rowequ || colequ
                                       || lsame_(equed, "N"))) {
        *info = -10;
    } else {
        if (rowequ) {
            rcmin = bignum;
            rcmax = 0.;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                /* Computing MIN */
                d__1 = rcmin, d__2 = r__[j];
                rcmin = min(d__1,d__2);
                /* Computing MAX */
                d__1 = rcmax, d__2 = r__[j];
                rcmax = max(d__1,d__2);
            }
            if (rcmin <= 0.) {
                *info = -11;
            } else if (*n > 0) {
                rowcnd = max(rcmin,smlnum) / min(rcmax,bignum);
            } else {
                rowcnd = 1.;
            }
        }
        if (colequ && *info == 0) {
            rcmin = bignum;
            rcmax = 0.;
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                /* Computing MIN */
                d__1 = rcmin, d__2 = c__[j];
                rcmin = min(d__1,d__2);
                /* Computing MAX */
                d__1 = rcmax, d__2 = c__[j];
                rcmax = max(d__1,d__2);
            }
            if (rcmin <= 0.) {
                *info = -12;
            } else if (*n > 0) {
                colcnd = max(rcmin,smlnum) / min(rcmax,bignum);
            } else {
                colcnd = 1.;
            }
        }
        if (*info == 0) {
            if (*ldb < max(1,*n)) {
                *info = -14;
            } else if (*ldx < max(1,*n)) {
                *info = -16;
            }
        }
    }

    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DGESVXX", &i__1);
        return 0;
    }

    if (equil) {

        /*     Compute row and column scalings to equilibrate the matrix A. */

        dgeequb_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd,
                 &amax, &infequ);
        if (infequ == 0) {

            /*     Equilibrate the matrix. */

            dlaqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &
                    colcnd, &amax, equed);
            rowequ = lsame_(equed, "R") || lsame_(equed,
                                                  "B");
            colequ = lsame_(equed, "C") || lsame_(equed,
                                                  "B");
        }

        /*     If the scaling factors are not applied, set them to 1.0. */

        if (! rowequ) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                r__[j] = 1.;
            }
        }
        if (! colequ) {
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                c__[j] = 1.;
            }
        }
    }

    /*     Scale the right-hand side. */

    if (notran) {
        if (rowequ) {
            dlascl2_(n, nrhs, &r__[1], &b[b_offset], ldb);
        }
    } else {
        if (colequ) {
            dlascl2_(n, nrhs, &c__[1], &b[b_offset], ldb);
        }
    }

    if (nofact || equil) {

        /*        Compute the LU factorization of A. */

        dlacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf);
        dgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info);

        /*        Return if INFO is non-zero. */

        if (*info > 0) {

            /*           Pivot in column INFO is exactly 0 */
            /*           Compute the reciprocal pivot growth factor of the */
            /*           leading rank-deficient INFO columns of A. */

            *rpvgrw = dla_rpvgrw__(n, info, &a[a_offset], lda, &af[af_offset],
                                   ldaf);
            return 0;
        }
    }

    /*     Compute the reciprocal pivot growth factor RPVGRW. */

    *rpvgrw = dla_rpvgrw__(n, n, &a[a_offset], lda, &af[af_offset], ldaf);

    /*     Compute the solution matrix X. */

    dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    dgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx,
            info);

    /*     Use iterative refinement to improve the computed solution and */
    /*     compute error bounds and backward error estimates for it. */

    dgerfsx_(trans, equed, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &
             ipiv[1], &r__[1], &c__[1], &b[b_offset], ldb, &x[x_offset], ldx,
             rcond, &berr[1], n_err_bnds__, &err_bnds_norm__[
                 err_bnds_norm_offset], &err_bnds_comp__[err_bnds_comp_offset],
             nparams, &params[1], &work[1], &iwork[1], info);

    /*     Scale solutions. */

    if (colequ && notran) {
        dlascl2_(n, nrhs, &c__[1], &x[x_offset], ldx);
    } else if (rowequ && ! notran) {
        dlascl2_(n, nrhs, &r__[1], &x[x_offset], ldx);
    }

    return 0;

    /*     End of DGESVXX */
} /* dgesvxx_ */
Пример #2
0
/* Subroutine */
int dsysvxx_(char *fact, char *uplo, integer *n, integer * nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, integer *ipiv, char *equed, doublereal *s, doublereal *b, integer * ldb, doublereal *x, integer *ldx, doublereal *rcond, doublereal * rpvgrw, doublereal *berr, integer *n_err_bnds__, doublereal * err_bnds_norm__, doublereal *err_bnds_comp__, integer *nparams, doublereal *params, doublereal *work, integer *iwork, 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;
    /* Local variables */
    integer j;
    doublereal amax, smin, smax;
    extern doublereal dla_syrpvgrw_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *);
    extern logical lsame_(char *, char *);
    doublereal scond;
    logical equil, rcequ;
    extern doublereal dlamch_(char *);
    logical nofact;
    extern /* Subroutine */
    int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *);
    doublereal bignum;
    integer infequ;
    extern /* Subroutine */
    int dlaqsy_(char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, char *);
    doublereal smlnum;
    extern /* Subroutine */
    int dsytrf_(char *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dlascl2_(integer *, integer *, doublereal *, doublereal *, integer *), dsytrs_(char *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dsyequb_(char *, integer *, doublereal *, integer *, doublereal * , doublereal *, doublereal *, doublereal *, integer *), dsyrfsx_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *);
    /* -- LAPACK driver routine (version 3.4.2) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* September 2012 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ================================================================== */
    /* .. Parameters .. */
    /* .. */
    /* .. Local Scalars .. */
    /* .. */
    /* .. External Functions .. */
    /* .. */
    /* .. External Subroutines .. */
    /* .. */
    /* .. Intrinsic Functions .. */
    /* .. */
    /* .. Executable Statements .. */
    /* 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;
    --ipiv;
    --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;
    --iwork;
    /* Function Body */
    *info = 0;
    nofact = lsame_(fact, "N");
    equil = lsame_(fact, "E");
    smlnum = dlamch_("Safe minimum");
    bignum = 1. / smlnum;
    if (nofact || equil)
    {
        *(unsigned char *)equed = 'N';
        rcequ = FALSE_;
    }
    else
    {
        rcequ = lsame_(equed, "Y");
    }
    /* Default is failure. If an input parameter is wrong or */
    /* factorization fails, make everything look horrible. Only the */
    /* pivot growth is set here, the rest is initialized in DSYRFSX. */
    *rpvgrw = 0.;
    /* Test the input parameters. PARAMS is not tested until DSYRFSX. */
    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_("DSYSVXX", &i__1);
        return 0;
    }
    if (equil)
    {
        /* Compute row and column scalings to equilibrate the matrix A. */
        dsyequb_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, &work[1], & infequ);
        if (infequ == 0)
        {
            /* Equilibrate the matrix. */
            dlaqsy_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed);
            rcequ = lsame_(equed, "Y");
        }
    }
    /* Scale the right-hand side. */
    if (rcequ)
    {
        dlascl2_(n, nrhs, &s[1], &b[b_offset], ldb);
    }
    if (nofact || equil)
    {
        /* Compute the LDL^T or UDU^T factorization of A. */
        dlacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
        i__1 = max(1,*n) * 5;
        dsytrf_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &work[1], &i__1, info);
        /* Return if INFO is non-zero. */
        if (*info > 0)
        {
            /* Pivot in column INFO is exactly 0 */
            /* Compute the reciprocal pivot growth factor of the */
            /* leading rank-deficient INFO columns of A. */
            if (*n > 0)
            {
                *rpvgrw = dla_syrpvgrw_(uplo, n, info, &a[a_offset], lda, & af[af_offset], ldaf, &ipiv[1], &work[1]);
            }
            return 0;
        }
    }
    /* Compute the reciprocal pivot growth factor RPVGRW. */
    if (*n > 0)
    {
        *rpvgrw = dla_syrpvgrw_(uplo, n, info, &a[a_offset], lda, &af[ af_offset], ldaf, &ipiv[1], &work[1]);
    }
    /* Compute the solution matrix X. */
    dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    dsytrs_(uplo, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx, info);
    /* Use iterative refinement to improve the computed solution and */
    /* compute error bounds and backward error estimates for it. */
    dsyrfsx_(uplo, equed, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, & ipiv[1], &s[1], &b[b_offset], ldb, &x[x_offset], ldx, rcond, & berr[1], n_err_bnds__, &err_bnds_norm__[err_bnds_norm_offset], & err_bnds_comp__[err_bnds_comp_offset], nparams, &params[1], &work[ 1], &iwork[1], info);
    /* Scale solutions. */
    if (rcequ)
    {
        dlascl2_(n, nrhs, &s[1], &x[x_offset], ldx);
    }
    return 0;
    /* End of DSYSVXX */
}