starpu-max/min-dgels/base/SRC/dpbstf.c

/* dpbstf.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_b9 = -1.;

/* Subroutine */ int dpbstf_(char *uplo, integer *n, integer *kd, doublereal *
	ab, integer *ldab, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1, i__2, i__3;
    doublereal d__1;

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

    /* Local variables */
    integer j, m, km;
    doublereal ajj;
    integer kld;
    extern /* Subroutine */ int dsyr_(char *, integer *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *), dscal_(
	    integer *, doublereal *, doublereal *, integer *);
    extern logical lsame_(char *, char *);
    logical upper;
    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 */
/*  ======= */

/*  DPBSTF computes a split Cholesky factorization of a real */
/*  symmetric positive definite band matrix A. */

/*  This routine is designed to be used in conjunction with DSBGST. */

/*  The factorization has the form  A = S**T*S  where S is a band matrix */
/*  of the same bandwidth as A and the following structure: */

/*    S = ( U    ) */
/*        ( M  L ) */

/*  where U is upper triangular of order m = (n+kd)/2, and L is lower */
/*  triangular of order n-m. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangle of A is stored; */
/*          = 'L':  Lower triangle of A is stored. */

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

/*  KD      (input) INTEGER */
/*          The number of superdiagonals of the matrix A if UPLO = 'U', */
/*          or the number of subdiagonals if UPLO = 'L'.  KD >= 0. */

/*  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N) */
/*          On entry, the upper or lower triangle of the symmetric band */
/*          matrix A, stored in the first kd+1 rows of the array.  The */
/*          j-th column of A is stored in the j-th column of the array AB */
/*          as follows: */
/*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd). */

/*          On exit, if INFO = 0, the factor S from the split Cholesky */
/*          factorization A = S**T*S. See Further Details. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= KD+1. */

/*  INFO    (output) INTEGER */
/*          = 0: successful exit */
/*          < 0: if INFO = -i, the i-th argument had an illegal value */
/*          > 0: if INFO = i, the factorization could not be completed, */
/*               because the updated element a(i,i) was negative; the */
/*               matrix A is not positive definite. */

/*  Further Details */
/*  =============== */

/*  The band storage scheme is illustrated by the following example, when */
/*  N = 7, KD = 2: */

/*  S = ( s11  s12  s13                     ) */
/*      (      s22  s23  s24                ) */
/*      (           s33  s34                ) */
/*      (                s44                ) */
/*      (           s53  s54  s55           ) */
/*      (                s64  s65  s66      ) */
/*      (                     s75  s76  s77 ) */

/*  If UPLO = 'U', the array AB holds: */

/*  on entry:                          on exit: */

/*   *    *   a13  a24  a35  a46  a57   *    *   s13  s24  s53  s64  s75 */
/*   *   a12  a23  a34  a45  a56  a67   *   s12  s23  s34  s54  s65  s76 */
/*  a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55  s66  s77 */

/*  If UPLO = 'L', the array AB holds: */

/*  on entry:                          on exit: */

/*  a11  a22  a33  a44  a55  a66  a77  s11  s22  s33  s44  s55  s66  s77 */
/*  a21  a32  a43  a54  a65  a76   *   s12  s23  s34  s54  s65  s76   * */
/*  a31  a42  a53  a64  a64   *    *   s13  s24  s53  s64  s75   *    * */

/*  Array elements marked * are not used by the routine. */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*kd < 0) {
	*info = -3;
    } else if (*ldab < *kd + 1) {
	*info = -5;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DPBSTF", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

/* Computing MAX */
    i__1 = 1, i__2 = *ldab - 1;
    kld = max(i__1,i__2);

/*     Set the splitting point m. */

    m = (*n + *kd) / 2;

    if (upper) {

/*        Factorize A(m+1:n,m+1:n) as L**T*L, and update A(1:m,1:m). */

	i__1 = m + 1;
	for (j = *n; j >= i__1; --j) {

/*           Compute s(j,j) and test for non-positive-definiteness. */

	    ajj = ab[*kd + 1 + j * ab_dim1];
	    if (ajj <= 0.) {
		goto L50;
	    }
	    ajj = sqrt(ajj);
	    ab[*kd + 1 + j * ab_dim1] = ajj;
/* Computing MIN */
	    i__2 = j - 1;
	    km = min(i__2,*kd);

/*           Compute elements j-km:j-1 of the j-th column and update the */
/*           the leading submatrix within the band. */

	    d__1 = 1. / ajj;
	    dscal_(&km, &d__1, &ab[*kd + 1 - km + j * ab_dim1], &c__1);
	    dsyr_("Upper", &km, &c_b9, &ab[*kd + 1 - km + j * ab_dim1], &c__1, 
		     &ab[*kd + 1 + (j - km) * ab_dim1], &kld);
/* L10: */
	}

/*        Factorize the updated submatrix A(1:m,1:m) as U**T*U. */

	i__1 = m;
	for (j = 1; j <= i__1; ++j) {

/*           Compute s(j,j) and test for non-positive-definiteness. */

	    ajj = ab[*kd + 1 + j * ab_dim1];
	    if (ajj <= 0.) {
		goto L50;
	    }
	    ajj = sqrt(ajj);
	    ab[*kd + 1 + j * ab_dim1] = ajj;
/* Computing MIN */
	    i__2 = *kd, i__3 = m - j;
	    km = min(i__2,i__3);

/*           Compute elements j+1:j+km of the j-th row and update the */
/*           trailing submatrix within the band. */

	    if (km > 0) {
		d__1 = 1. / ajj;
		dscal_(&km, &d__1, &ab[*kd + (j + 1) * ab_dim1], &kld);
		dsyr_("Upper", &km, &c_b9, &ab[*kd + (j + 1) * ab_dim1], &kld, 
			 &ab[*kd + 1 + (j + 1) * ab_dim1], &kld);
	    }
/* L20: */
	}
    } else {

/*        Factorize A(m+1:n,m+1:n) as L**T*L, and update A(1:m,1:m). */

	i__1 = m + 1;
	for (j = *n; j >= i__1; --j) {

/*           Compute s(j,j) and test for non-positive-definiteness. */

	    ajj = ab[j * ab_dim1 + 1];
	    if (ajj <= 0.) {
		goto L50;
	    }
	    ajj = sqrt(ajj);
	    ab[j * ab_dim1 + 1] = ajj;
/* Computing MIN */
	    i__2 = j - 1;
	    km = min(i__2,*kd);

/*           Compute elements j-km:j-1 of the j-th row and update the */
/*           trailing submatrix within the band. */

	    d__1 = 1. / ajj;
	    dscal_(&km, &d__1, &ab[km + 1 + (j - km) * ab_dim1], &kld);
	    dsyr_("Lower", &km, &c_b9, &ab[km + 1 + (j - km) * ab_dim1], &kld, 
		     &ab[(j - km) * ab_dim1 + 1], &kld);
/* L30: */
	}

/*        Factorize the updated submatrix A(1:m,1:m) as U**T*U. */

	i__1 = m;
	for (j = 1; j <= i__1; ++j) {

/*           Compute s(j,j) and test for non-positive-definiteness. */

	    ajj = ab[j * ab_dim1 + 1];
	    if (ajj <= 0.) {
		goto L50;
	    }
	    ajj = sqrt(ajj);
	    ab[j * ab_dim1 + 1] = ajj;
/* Computing MIN */
	    i__2 = *kd, i__3 = m - j;
	    km = min(i__2,i__3);

/*           Compute elements j+1:j+km of the j-th column and update the */
/*           trailing submatrix within the band. */

	    if (km > 0) {
		d__1 = 1. / ajj;
		dscal_(&km, &d__1, &ab[j * ab_dim1 + 2], &c__1);
		dsyr_("Lower", &km, &c_b9, &ab[j * ab_dim1 + 2], &c__1, &ab[(
			j + 1) * ab_dim1 + 1], &kld);
	    }
/* L40: */
	}
    }
    return 0;

L50:
    *info = j;
    return 0;

/*     End of DPBSTF */

} /* dpbstf_ */