dpstrf.c

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/* dpstrf.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 integer c__1 = 1;
static integer c_n1 = -1;
static doublereal c_b22 = -1.;
static doublereal c_b24 = 1.;

/* Subroutine */ int dpstrf_(char *uplo, integer *n, doublereal *a, integer *
        lda, integer *piv, integer *rank, doublereal *tol, doublereal *work, 
        integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
    doublereal d__1;

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

    /* Local variables */
    integer i__, j, k, maxlocvar, jb, nb;
    doublereal ajj;
    integer pvt;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
            integer *);
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, doublereal *, integer *, 
            doublereal *, doublereal *, integer *);
    doublereal dtemp;
    integer itemp;
    extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, 
            doublereal *, integer *);
    doublereal dstop;
    logical upper;
    extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, doublereal *, doublereal *, 
             integer *), dpstf2_(char *, integer *, 
            doublereal *, integer *, integer *, integer *, doublereal *, 
            doublereal *, integer *);
    extern doublereal dlamch_(char *);
    extern logical disnan_(doublereal *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern integer dmaxloc_(doublereal *, integer *);


/*  -- LAPACK routine (version 3.2) -- */
/*     Craig Lucas, University of Manchester / NAG Ltd. */
/*     October, 2008 */

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

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

/*  DPSTRF computes the Cholesky factorization with complete */
/*  pivoting of a real symmetric positive semidefinite matrix A. */

/*  The factorization has the form */
/*     P' * A * P = U' * U ,  if UPLO = 'U', */
/*     P' * A * P = L  * L',  if UPLO = 'L', */
/*  where U is an upper triangular matrix and L is lower triangular, and */
/*  P is stored as vector PIV. */

/*  This algorithm does not attempt to check that A is positive */
/*  semidefinite. This version of the algorithm calls level 3 BLAS. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the upper or lower triangular part of the */
/*          symmetric matrix A is stored. */
/*          = 'U':  Upper triangular */
/*          = 'L':  Lower triangular */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  A       (input/output) 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 INFO = 0, the factor U or L from the Cholesky */
/*          factorization as above. */

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

/*  PIV     (output) INTEGER array, dimension (N) */
/*          PIV is such that the nonzero entries are P( PIV(K), K ) = 1. */

/*  RANK    (output) INTEGER */
/*          The rank of A given by the number of steps the algorithm */
/*          completed. */

/*  TOL     (input) DOUBLE PRECISION */
/*          User defined tolerance. If TOL < 0, then N*U*MAX( A(K,K) ) */
/*          will be used. The algorithm terminates at the (K-1)st step */
/*          if the pivot <= TOL. */

/*  WORK    DOUBLE PRECISION array, dimension (2*N) */
/*          Work space. */

/*  INFO    (output) INTEGER */
/*          < 0: If INFO = -K, the K-th argument had an illegal value, */
/*          = 0: algorithm completed successfully, and */
/*          > 0: the matrix A is either rank deficient with computed rank */
/*               as returned in RANK, or is indefinite.  See Section 7 of */
/*               LAPACK Working Note #161 for further information. */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    --work;
    --piv;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L")) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*lda < max(1,*n)) {
        *info = -4;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DPSTRF", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

/*     Get block size */

    nb = ilaenv_(&c__1, "DPOTRF", uplo, n, &c_n1, &c_n1, &c_n1);
    if (nb <= 1 || nb >= *n) {

/*        Use unblocked code */

        dpstf2_(uplo, n, &a[a_dim1 + 1], lda, &piv[1], rank, tol, &work[1], 
                info);
        goto L200;

    } else {

/*     Initialize PIV */

        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            piv[i__] = i__;
/* L100: */
        }

/*     Compute stopping value */

        pvt = 1;
        ajj = a[pvt + pvt * a_dim1];
        i__1 = *n;
        for (i__ = 2; i__ <= i__1; ++i__) {
            if (a[i__ + i__ * a_dim1] > ajj) {
                pvt = i__;
                ajj = a[pvt + pvt * a_dim1];
            }
        }
        if (ajj == 0. || disnan_(&ajj)) {
            *rank = 0;
            *info = 1;
            goto L200;
        }

/*     Compute stopping value if not supplied */

        if (*tol < 0.) {
            dstop = *n * dlamch_("Epsilon") * ajj;
        } else {
            dstop = *tol;
        }


        if (upper) {

/*           Compute the Cholesky factorization P' * A * P = U' * U */

            i__1 = *n;
            i__2 = nb;
            for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {

/*              Account for last block not being NB wide */

/* Computing MIN */
                i__3 = nb, i__4 = *n - k + 1;
                jb = min(i__3,i__4);

/*              Set relevant part of first half of WORK to zero, */
/*              holds dot products */

                i__3 = *n;
                for (i__ = k; i__ <= i__3; ++i__) {
                    work[i__] = 0.;
/* L110: */
                }

                i__3 = k + jb - 1;
                for (j = k; j <= i__3; ++j) {

/*              Find pivot, test for exit, else swap rows and columns */
/*              Update dot products, compute possible pivots which are */
/*              stored in the second half of WORK */

                    i__4 = *n;
                    for (i__ = j; i__ <= i__4; ++i__) {

                        if (j > k) {
/* Computing 2nd power */
                            d__1 = a[j - 1 + i__ * a_dim1];
                            work[i__] += d__1 * d__1;
                        }
                        work[*n + i__] = a[i__ + i__ * a_dim1] - work[i__];

/* L120: */
                    }

                    if (j > 1) {
                        maxlocvar = (*n << 1) - (*n + j) + 1;
                        itemp = dmaxloc_(&work[*n + j], &maxlocvar);
                        pvt = itemp + j - 1;
                        ajj = work[*n + pvt];
                        if (ajj <= dstop || disnan_(&ajj)) {
                            a[j + j * a_dim1] = ajj;
                            goto L190;
                        }
                    }

                    if (j != pvt) {

/*                    Pivot OK, so can now swap pivot rows and columns */

                        a[pvt + pvt * a_dim1] = a[j + j * a_dim1];
                        i__4 = j - 1;
                        dswap_(&i__4, &a[j * a_dim1 + 1], &c__1, &a[pvt * 
                                a_dim1 + 1], &c__1);
                        if (pvt < *n) {
                            i__4 = *n - pvt;
                            dswap_(&i__4, &a[j + (pvt + 1) * a_dim1], lda, &a[
                                    pvt + (pvt + 1) * a_dim1], lda);
                        }
                        i__4 = pvt - j - 1;
                        dswap_(&i__4, &a[j + (j + 1) * a_dim1], lda, &a[j + 1 
                                + pvt * a_dim1], &c__1);

/*                    Swap dot products and PIV */

                        dtemp = work[j];
                        work[j] = work[pvt];
                        work[pvt] = dtemp;
                        itemp = piv[pvt];
                        piv[pvt] = piv[j];
                        piv[j] = itemp;
                    }

                    ajj = sqrt(ajj);
                    a[j + j * a_dim1] = ajj;

/*                 Compute elements J+1:N of row J. */

                    if (j < *n) {
                        i__4 = j - k;
                        i__5 = *n - j;
                        dgemv_("Trans", &i__4, &i__5, &c_b22, &a[k + (j + 1) *
                                 a_dim1], lda, &a[k + j * a_dim1], &c__1, &
                                c_b24, &a[j + (j + 1) * a_dim1], lda);
                        i__4 = *n - j;
                        d__1 = 1. / ajj;
                        dscal_(&i__4, &d__1, &a[j + (j + 1) * a_dim1], lda);
                    }

/* L130: */
                }

/*              Update trailing matrix, J already incremented */

                if (k + jb <= *n) {
                    i__3 = *n - j + 1;
                    dsyrk_("Upper", "Trans", &i__3, &jb, &c_b22, &a[k + j * 
                            a_dim1], lda, &c_b24, &a[j + j * a_dim1], lda);
                }

/* L140: */
            }

        } else {

/*        Compute the Cholesky factorization P' * A * P = L * L' */

            i__2 = *n;
            i__1 = nb;
            for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {

/*              Account for last block not being NB wide */

/* Computing MIN */
                i__3 = nb, i__4 = *n - k + 1;
                jb = min(i__3,i__4);

/*              Set relevant part of first half of WORK to zero, */
/*              holds dot products */

                i__3 = *n;
                for (i__ = k; i__ <= i__3; ++i__) {
                    work[i__] = 0.;
/* L150: */
                }

                i__3 = k + jb - 1;
                for (j = k; j <= i__3; ++j) {

/*              Find pivot, test for exit, else swap rows and columns */
/*              Update dot products, compute possible pivots which are */
/*              stored in the second half of WORK */

                    i__4 = *n;
                    for (i__ = j; i__ <= i__4; ++i__) {

                        if (j > k) {
/* Computing 2nd power */
                            d__1 = a[i__ + (j - 1) * a_dim1];
                            work[i__] += d__1 * d__1;
                        }
                        work[*n + i__] = a[i__ + i__ * a_dim1] - work[i__];

/* L160: */
                    }

                    if (j > 1) {
                        maxlocvar = (*n << 1) - (*n + j) + 1;
                        itemp = dmaxloc_(&work[*n + j], &maxlocvar);
                        pvt = itemp + j - 1;
                        ajj = work[*n + pvt];
                        if (ajj <= dstop || disnan_(&ajj)) {
                            a[j + j * a_dim1] = ajj;
                            goto L190;
                        }
                    }

                    if (j != pvt) {

/*                    Pivot OK, so can now swap pivot rows and columns */

                        a[pvt + pvt * a_dim1] = a[j + j * a_dim1];
                        i__4 = j - 1;
                        dswap_(&i__4, &a[j + a_dim1], lda, &a[pvt + a_dim1], 
                                lda);
                        if (pvt < *n) {
                            i__4 = *n - pvt;
                            dswap_(&i__4, &a[pvt + 1 + j * a_dim1], &c__1, &a[
                                    pvt + 1 + pvt * a_dim1], &c__1);
                        }
                        i__4 = pvt - j - 1;
                        dswap_(&i__4, &a[j + 1 + j * a_dim1], &c__1, &a[pvt + 
                                (j + 1) * a_dim1], lda);

/*                    Swap dot products and PIV */

                        dtemp = work[j];
                        work[j] = work[pvt];
                        work[pvt] = dtemp;
                        itemp = piv[pvt];
                        piv[pvt] = piv[j];
                        piv[j] = itemp;
                    }

                    ajj = sqrt(ajj);
                    a[j + j * a_dim1] = ajj;

/*                 Compute elements J+1:N of column J. */

                    if (j < *n) {
                        i__4 = *n - j;
                        i__5 = j - k;
                        dgemv_("No Trans", &i__4, &i__5, &c_b22, &a[j + 1 + k 
                                * a_dim1], lda, &a[j + k * a_dim1], lda, &
                                c_b24, &a[j + 1 + j * a_dim1], &c__1);
                        i__4 = *n - j;
                        d__1 = 1. / ajj;
                        dscal_(&i__4, &d__1, &a[j + 1 + j * a_dim1], &c__1);
                    }

/* L170: */
                }

/*              Update trailing matrix, J already incremented */

                if (k + jb <= *n) {
                    i__3 = *n - j + 1;
                    dsyrk_("Lower", "No Trans", &i__3, &jb, &c_b22, &a[j + k *
                             a_dim1], lda, &c_b24, &a[j + j * a_dim1], lda);
                }

/* L180: */
            }

        }
    }

/*     Ran to completion, A has full rank */

    *rank = *n;

    goto L200;
L190:

/*     Rank is the number of steps completed.  Set INFO = 1 to signal */
/*     that the factorization cannot be used to solve a system. */

    *rank = j - 1;
    *info = 1;

L200:
    return 0;

/*     End of DPSTRF */

} /* dpstrf_ */