dpotf2.c

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/* dpotf2.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 doublereal c_b10 = -1.;
static doublereal c_b12 = 1.;

/* Subroutine */ int dpotf2_(char *uplo, integer *n, doublereal *a, integer *
        lda, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    doublereal d__1;

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

    /* Local variables */
    integer j;
    doublereal ajj;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
            integer *);
    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 *);
    logical upper;
    extern logical disnan_(doublereal *);
    extern /* Subroutine */ int xerbla_(char *, integer *);


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  DPOTF2 computes the Cholesky factorization of a real symmetric */
/*  positive definite matrix A. */

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

/*  This is the unblocked version of the algorithm, calling Level 2 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 A = U'*U  or A = L*L'. */

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

/*  INFO    (output) INTEGER */
/*          = 0: successful exit */
/*          < 0: if INFO = -k, the k-th argument had an illegal value */
/*          > 0: if INFO = k, the leading minor of order k is not */
/*               positive definite, and the factorization could not be */
/*               completed. */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    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_("DPOTF2", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

    if (upper) {

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

        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {

/*           Compute U(J,J) and test for non-positive-definiteness. */

            i__2 = j - 1;
            ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j * a_dim1 + 1], &c__1, 
                    &a[j * a_dim1 + 1], &c__1);
            if (ajj <= 0. || disnan_(&ajj)) {
                a[j + j * a_dim1] = ajj;
                goto L30;
            }
            ajj = sqrt(ajj);
            a[j + j * a_dim1] = ajj;

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

            if (j < *n) {
                i__2 = j - 1;
                i__3 = *n - j;
                dgemv_("Transpose", &i__2, &i__3, &c_b10, &a[(j + 1) * a_dim1 
                        + 1], lda, &a[j * a_dim1 + 1], &c__1, &c_b12, &a[j + (
                        j + 1) * a_dim1], lda);
                i__2 = *n - j;
                d__1 = 1. / ajj;
                dscal_(&i__2, &d__1, &a[j + (j + 1) * a_dim1], lda);
            }
/* L10: */
        }
    } else {

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

        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {

/*           Compute L(J,J) and test for non-positive-definiteness. */

            i__2 = j - 1;
            ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j + a_dim1], lda, &a[j 
                    + a_dim1], lda);
            if (ajj <= 0. || disnan_(&ajj)) {
                a[j + j * a_dim1] = ajj;
                goto L30;
            }
            ajj = sqrt(ajj);
            a[j + j * a_dim1] = ajj;

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

            if (j < *n) {
                i__2 = *n - j;
                i__3 = j - 1;
                dgemv_("No transpose", &i__2, &i__3, &c_b10, &a[j + 1 + 
                        a_dim1], lda, &a[j + a_dim1], lda, &c_b12, &a[j + 1 + 
                        j * a_dim1], &c__1);
                i__2 = *n - j;
                d__1 = 1. / ajj;
                dscal_(&i__2, &d__1, &a[j + 1 + j * a_dim1], &c__1);
            }
/* L20: */
        }
    }
    goto L40;

L30:
    *info = j;

L40:
    return 0;

/*     End of DPOTF2 */

} /* dpotf2_ */