dsposv.c

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/* dsposv.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static doublereal c_b10 = -1.;
static doublereal c_b11 = 1.;
static integer c__1 = 1;

/* Subroutine */ int dsposv_(char *uplo, integer *n, integer *nrhs, 
        doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
        x, integer *ldx, doublereal *work, real *swork, integer *iter, 
        integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, work_dim1, work_offset, 
            x_dim1, x_offset, i__1;
    doublereal d__1;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    integer i__;
    doublereal cte, eps, anrm;
    integer ptsa;
    doublereal rnrm, xnrm;
    integer ptsx;
    extern logical lsame_(char *, char *);
    integer iiter;
    extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, 
            integer *, doublereal *, integer *), dsymm_(char *, char *, 
            integer *, integer *, doublereal *, doublereal *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *), dlag2s_(integer *, integer *, doublereal *, 
            integer *, real *, integer *, integer *), slag2d_(integer *, 
            integer *, real *, integer *, doublereal *, integer *, integer *),
             dlat2s_(char *, integer *, doublereal *, integer *, real *, 
            integer *, integer *);
    extern doublereal dlamch_(char *);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
            doublereal *, integer *, doublereal *, integer *), 
            xerbla_(char *, integer *);
    extern doublereal dlansy_(char *, char *, integer *, doublereal *, 
            integer *, doublereal *);
    extern /* Subroutine */ int dpotrf_(char *, integer *, doublereal *, 
            integer *, integer *), dpotrs_(char *, integer *, integer 
            *, doublereal *, integer *, doublereal *, integer *, integer *), spotrf_(char *, integer *, real *, integer *, integer *), spotrs_(char *, integer *, integer *, real *, integer *, 
            real *, integer *, integer *);


/*  -- LAPACK PROTOTYPE driver routine (version 3.1.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. */
/*     May 2007 */

/*     .. */
/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

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

/*  DSPOSV computes the solution to a real system of linear equations */
/*     A * X = B, */
/*  where A is an N-by-N symmetric positive definite matrix and X and B */
/*  are N-by-NRHS matrices. */

/*  DSPOSV first attempts to factorize the matrix in SINGLE PRECISION */
/*  and use this factorization within an iterative refinement procedure */
/*  to produce a solution with DOUBLE PRECISION normwise backward error */
/*  quality (see below). If the approach fails the method switches to a */
/*  DOUBLE PRECISION factorization and solve. */

/*  The iterative refinement is not going to be a winning strategy if */
/*  the ratio SINGLE PRECISION performance over DOUBLE PRECISION */
/*  performance is too small. A reasonable strategy should take the */
/*  number of right-hand sides and the size of the matrix into account. */
/*  This might be done with a call to ILAENV in the future. Up to now, we */
/*  always try iterative refinement. */

/*  The iterative refinement process is stopped if */
/*      ITER > ITERMAX */
/*  or for all the RHS we have: */
/*      RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX */
/*  where */
/*      o ITER is the number of the current iteration in the iterative */
/*        refinement process */
/*      o RNRM is the infinity-norm of the residual */
/*      o XNRM is the infinity-norm of the solution */
/*      o ANRM is the infinity-operator-norm of the matrix A */
/*      o EPS is the machine epsilon returned by DLAMCH('Epsilon') */
/*  The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 */
/*  respectively. */

/*  Arguments */
/*  ========= */

/*  UPLO    (input) CHARACTER */
/*          = '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 matrix B.  NRHS >= 0. */

/*  A       (input or input/ouptut) DOUBLE PRECISION array, */
/*          dimension (LDA,N) */
/*          On entry, 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. */
/*          On exit, if iterative refinement has been successfully used */
/*          (INFO.EQ.0 and ITER.GE.0, see description below), then A is */
/*          unchanged, if double precision factorization has been used */
/*          (INFO.EQ.0 and ITER.LT.0, see description below), then the */
/*          array A contains the factor U or L from the Cholesky */
/*          factorization A = U**T*U or A = L*L**T. */


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

/*  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, the N-by-NRHS solution matrix X. */

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

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (N*NRHS) */
/*          This array is used to hold the residual vectors. */

/*  SWORK   (workspace) REAL array, dimension (N*(N+NRHS)) */
/*          This array is used to use the single precision matrix and the */
/*          right-hand sides or solutions in single precision. */

/*  ITER    (output) INTEGER */
/*          < 0: iterative refinement has failed, double precision */
/*               factorization has been performed */
/*               -1 : the routine fell back to full precision for */
/*                    implementation- or machine-specific reasons */
/*               -2 : narrowing the precision induced an overflow, */
/*                    the routine fell back to full precision */
/*               -3 : failure of SPOTRF */
/*               -31: stop the iterative refinement after the 30th */
/*                    iterations */
/*          > 0: iterative refinement has been sucessfully used. */
/*               Returns the number of iterations */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = i, the leading minor of order i of (DOUBLE */
/*                PRECISION) A is not positive definite, so the */
/*                factorization could not be completed, and the solution */
/*                has not been computed. */

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

/*     .. Parameters .. */




/*     .. Local Scalars .. */

/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

    /* Parameter adjustments */
    work_dim1 = *n;
    work_offset = 1 + work_dim1;
    work -= work_offset;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1;
    x -= x_offset;
    --swork;

    /* Function Body */
    *info = 0;
    *iter = 0;

/*     Test the input parameters. */

    if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*nrhs < 0) {
        *info = -3;
    } else if (*lda < max(1,*n)) {
        *info = -5;
    } else if (*ldb < max(1,*n)) {
        *info = -7;
    } else if (*ldx < max(1,*n)) {
        *info = -9;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DSPOSV", &i__1);
        return 0;
    }

/*     Quick return if (N.EQ.0). */

    if (*n == 0) {
        return 0;
    }

/*     Skip single precision iterative refinement if a priori slower */
/*     than double precision factorization. */

    if (FALSE_) {
        *iter = -1;
        goto L40;
    }

/*     Compute some constants. */

    anrm = dlansy_("I", uplo, n, &a[a_offset], lda, &work[work_offset]);
    eps = dlamch_("Epsilon");
    cte = anrm * eps * sqrt((doublereal) (*n)) * 1.;

/*     Set the indices PTSA, PTSX for referencing SA and SX in SWORK. */

    ptsa = 1;
    ptsx = ptsa + *n * *n;

/*     Convert B from double precision to single precision and store the */
/*     result in SX. */

    dlag2s_(n, nrhs, &b[b_offset], ldb, &swork[ptsx], n, info);

    if (*info != 0) {
        *iter = -2;
        goto L40;
    }

/*     Convert A from double precision to single precision and store the */
/*     result in SA. */

    dlat2s_(uplo, n, &a[a_offset], lda, &swork[ptsa], n, info);

    if (*info != 0) {
        *iter = -2;
        goto L40;
    }

/*     Compute the Cholesky factorization of SA. */

    spotrf_(uplo, n, &swork[ptsa], n, info);

    if (*info != 0) {
        *iter = -3;
        goto L40;
    }

/*     Solve the system SA*SX = SB. */

    spotrs_(uplo, n, nrhs, &swork[ptsa], n, &swork[ptsx], n, info);

/*     Convert SX back to double precision */

    slag2d_(n, nrhs, &swork[ptsx], n, &x[x_offset], ldx, info);

/*     Compute R = B - AX (R is WORK). */

    dlacpy_("All", n, nrhs, &b[b_offset], ldb, &work[work_offset], n);

    dsymm_("Left", uplo, n, nrhs, &c_b10, &a[a_offset], lda, &x[x_offset], 
            ldx, &c_b11, &work[work_offset], n);

/*     Check whether the NRHS normwise backward errors satisfy the */
/*     stopping criterion. If yes, set ITER=0 and return. */

    i__1 = *nrhs;
    for (i__ = 1; i__ <= i__1; ++i__) {
        xnrm = (d__1 = x[idamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ * 
                x_dim1], abs(d__1));
        rnrm = (d__1 = work[idamax_(n, &work[i__ * work_dim1 + 1], &c__1) + 
                i__ * work_dim1], abs(d__1));
        if (rnrm > xnrm * cte) {
            goto L10;
        }
    }

/*     If we are here, the NRHS normwise backward errors satisfy the */
/*     stopping criterion. We are good to exit. */

    *iter = 0;
    return 0;

L10:

    for (iiter = 1; iiter <= 30; ++iiter) {

/*        Convert R (in WORK) from double precision to single precision */
/*        and store the result in SX. */

        dlag2s_(n, nrhs, &work[work_offset], n, &swork[ptsx], n, info);

        if (*info != 0) {
            *iter = -2;
            goto L40;
        }

/*        Solve the system SA*SX = SR. */

        spotrs_(uplo, n, nrhs, &swork[ptsa], n, &swork[ptsx], n, info);

/*        Convert SX back to double precision and update the current */
/*        iterate. */

        slag2d_(n, nrhs, &swork[ptsx], n, &work[work_offset], n, info);

        i__1 = *nrhs;
        for (i__ = 1; i__ <= i__1; ++i__) {
            daxpy_(n, &c_b11, &work[i__ * work_dim1 + 1], &c__1, &x[i__ * 
                    x_dim1 + 1], &c__1);
        }

/*        Compute R = B - AX (R is WORK). */

        dlacpy_("All", n, nrhs, &b[b_offset], ldb, &work[work_offset], n);

        dsymm_("L", uplo, n, nrhs, &c_b10, &a[a_offset], lda, &x[x_offset], 
                ldx, &c_b11, &work[work_offset], n);

/*        Check whether the NRHS normwise backward errors satisfy the */
/*        stopping criterion. If yes, set ITER=IITER>0 and return. */

        i__1 = *nrhs;
        for (i__ = 1; i__ <= i__1; ++i__) {
            xnrm = (d__1 = x[idamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ * 
                    x_dim1], abs(d__1));
            rnrm = (d__1 = work[idamax_(n, &work[i__ * work_dim1 + 1], &c__1) 
                    + i__ * work_dim1], abs(d__1));
            if (rnrm > xnrm * cte) {
                goto L20;
            }
        }

/*        If we are here, the NRHS normwise backward errors satisfy the */
/*        stopping criterion, we are good to exit. */

        *iter = iiter;

        return 0;

L20:

/* L30: */
        ;
    }

/*     If we are at this place of the code, this is because we have */
/*     performed ITER=ITERMAX iterations and never satisified the */
/*     stopping criterion, set up the ITER flag accordingly and follow */
/*     up on double precision routine. */

    *iter = -31;

L40:

/*     Single-precision iterative refinement failed to converge to a */
/*     satisfactory solution, so we resort to double precision. */

    dpotrf_(uplo, n, &a[a_offset], lda, info);

    if (*info != 0) {
        return 0;
    }

    dlacpy_("All", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
    dpotrs_(uplo, n, nrhs, &a[a_offset], lda, &x[x_offset], ldx, info);

    return 0;

/*     End of DSPOSV. */

} /* dsposv_ */