zcposv.c

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/* zcposv.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 doublecomplex c_b1 = {-1.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;

/* Subroutine */ int zcposv_(char *uplo, integer *n, integer *nrhs, 
        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
        doublecomplex *x, integer *ldx, doublecomplex *work, complex *swork, 
        doublereal *rwork, 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, i__2;
    doublereal d__1, d__2;

    /* Builtin functions */
    double sqrt(doublereal), d_imag(doublecomplex *);

    /* 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 zhemm_(char *, char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, doublecomplex *, 
            integer *, doublecomplex *, integer *), zlag2c_(integer *, 
            integer *, doublecomplex *, integer *, complex *, integer *, 
            integer *), clag2z_(integer *, integer *, complex *, integer *, 
            doublecomplex *, integer *, integer *), zlat2c_(char *, integer *, 
             doublecomplex *, integer *, complex *, integer *, integer *);
    extern doublereal dlamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, 
            integer *, doublereal *);
    extern integer izamax_(integer *, doublecomplex *, integer *);
    extern /* Subroutine */ int cpotrf_(char *, integer *, complex *, integer 
            *, integer *), zlacpy_(char *, integer *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *), 
            cpotrs_(char *, integer *, integer *, complex *, integer *, 
            complex *, integer *, integer *), zpotrf_(char *, integer 
            *, doublecomplex *, integer *, integer *), zpotrs_(char *, 
             integer *, integer *, doublecomplex *, integer *, doublecomplex *
, integer *, integer *);


/*  -- LAPACK PROTOTYPE driver routine (version 3.2.1)                 -- */

/*  -- April 2009                                                      -- */

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

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

/*  ZCPOSV computes 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. */

/*  ZCPOSV first attempts to factorize the matrix in COMPLEX and use this */
/*  factorization within an iterative refinement procedure to produce a */
/*  solution with COMPLEX*16 normwise backward error quality (see below). */
/*  If the approach fails the method switches to a COMPLEX*16 */
/*  factorization and solve. */

/*  The iterative refinement is not going to be a winning strategy if */
/*  the ratio COMPLEX performance over COMPLEX*16 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) COMPLEX*16 array, */
/*          dimension (LDA,N) */
/*          On entry, the Hermitian 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. */

/*          Note that the imaginary parts of the diagonal */
/*          elements need not be set and are assumed to be zero. */

/*          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**H*U or A = L*L**H. */

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

/*  B       (input) COMPLEX*16 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) COMPLEX*16 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) COMPLEX*16 array, dimension (N*NRHS) */
/*          This array is used to hold the residual vectors. */

/*  SWORK   (workspace) COMPLEX 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. */

/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N) */

/*  ITER    (output) INTEGER */
/*          < 0: iterative refinement has failed, COMPLEX*16 */
/*               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 CPOTRF */
/*               -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 */
/*                (COMPLEX*16) 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 .. */
/*     .. Statement Functions .. */
/*     .. */
/*     .. Statement Function definitions .. */
/*     .. */
/*     .. 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;
    --rwork;

    /* 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_("ZCPOSV", &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 = zlanhe_("I", uplo, n, &a[a_offset], lda, &rwork[1]);
    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. */

    zlag2c_(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. */

    zlat2c_(uplo, n, &a[a_offset], lda, &swork[ptsa], n, info);

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

/*     Compute the Cholesky factorization of SA. */

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

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

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

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

/*     Convert SX back to COMPLEX*16 */

    clag2z_(n, nrhs, &swork[ptsx], n, &x[x_offset], ldx, info);

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

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

    zhemm_("Left", uplo, n, nrhs, &c_b1, &a[a_offset], lda, &x[x_offset], ldx, 
             &c_b2, &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__) {
        i__2 = izamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ * x_dim1;
        xnrm = (d__1 = x[i__2].r, abs(d__1)) + (d__2 = d_imag(&x[izamax_(n, &
                x[i__ * x_dim1 + 1], &c__1) + i__ * x_dim1]), abs(d__2));
        i__2 = izamax_(n, &work[i__ * work_dim1 + 1], &c__1) + i__ * 
                work_dim1;
        rnrm = (d__1 = work[i__2].r, abs(d__1)) + (d__2 = d_imag(&work[
                izamax_(n, &work[i__ * work_dim1 + 1], &c__1) + i__ * 
                work_dim1]), abs(d__2));
        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. */

        zlag2c_(n, nrhs, &work[work_offset], n, &swork[ptsx], n, info);

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

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

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

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

        clag2z_(n, nrhs, &swork[ptsx], n, &work[work_offset], n, info);

        i__1 = *nrhs;
        for (i__ = 1; i__ <= i__1; ++i__) {
            zaxpy_(n, &c_b2, &work[i__ * work_dim1 + 1], &c__1, &x[i__ * 
                    x_dim1 + 1], &c__1);
        }

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

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

        zhemm_("L", uplo, n, nrhs, &c_b1, &a[a_offset], lda, &x[x_offset], 
                ldx, &c_b2, &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__) {
            i__2 = izamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ * x_dim1;
            xnrm = (d__1 = x[i__2].r, abs(d__1)) + (d__2 = d_imag(&x[izamax_(
                    n, &x[i__ * x_dim1 + 1], &c__1) + i__ * x_dim1]), abs(
                    d__2));
            i__2 = izamax_(n, &work[i__ * work_dim1 + 1], &c__1) + i__ * 
                    work_dim1;
            rnrm = (d__1 = work[i__2].r, abs(d__1)) + (d__2 = d_imag(&work[
                    izamax_(n, &work[i__ * work_dim1 + 1], &c__1) + i__ * 
                    work_dim1]), abs(d__2));
            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. */

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

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

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

    return 0;

/*     End of ZCPOSV. */

} /* zcposv_ */