dsytrf.c

/* dsytrf.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 "clapack.h"


/* Table of constant values */

static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__2 = 2;

/* Subroutine */ int dsytrf_(char *uplo, integer *n, doublereal *a, integer *
	lda, integer *ipiv, doublereal *work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;

    /* Local variables */
    integer j, k, kb, nb, iws;
    extern logical lsame_(char *, char *);
    integer nbmin, iinfo;
    logical upper;
    extern /* Subroutine */ int dsytf2_(char *, integer *, doublereal *, 
	    integer *, integer *, integer *), xerbla_(char *, integer 
	    *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *);
    extern /* Subroutine */ int dlasyf_(char *, integer *, integer *, integer 
	    *, doublereal *, integer *, integer *, doublereal *, integer *, 
	    integer *);
    integer ldwork, lwkopt;
    logical lquery;


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

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

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

/*  DSYTRF computes the factorization of a real symmetric matrix A using */
/*  the Bunch-Kaufman diagonal pivoting method.  The form of the */
/*  factorization is */

/*     A = U*D*U**T  or  A = L*D*L**T */

/*  where U (or L) is a product of permutation and unit upper (lower) */
/*  triangular matrices, and D is symmetric and block diagonal with */
/*  1-by-1 and 2-by-2 diagonal blocks. */

/*  This is the blocked version of the algorithm, calling Level 3 BLAS. */

/*  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. */

/*  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, the block diagonal matrix D and the multipliers used */
/*          to obtain the factor U or L (see below for further details). */

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

/*  IPIV    (output) INTEGER array, dimension (N) */
/*          Details of the interchanges and the block structure of D. */
/*          If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
/*          interchanged and D(k,k) is a 1-by-1 diagonal block. */
/*          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */
/*          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */
/*          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) = */
/*          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */
/*          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */

/*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

/*  LWORK   (input) INTEGER */
/*          The length of WORK.  LWORK >=1.  For best performance */
/*          LWORK >= N*NB, where NB is the block size returned by ILAENV. */

/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates the optimal size of the WORK array, returns */
/*          this value as the first entry of the WORK array, and no error */
/*          message related to LWORK is issued by XERBLA. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
/*          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization */
/*                has been completed, but the block diagonal matrix D is */
/*                exactly singular, and division by zero will occur if it */
/*                is used to solve a system of equations. */

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

/*  If UPLO = 'U', then A = U*D*U', where */
/*     U = P(n)*U(n)* ... *P(k)U(k)* ..., */
/*  i.e., U is a product of terms P(k)*U(k), where k decreases from n to */
/*  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */
/*  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as */
/*  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such */
/*  that if the diagonal block D(k) is of order s (s = 1 or 2), then */

/*             (   I    v    0   )   k-s */
/*     U(k) =  (   0    I    0   )   s */
/*             (   0    0    I   )   n-k */
/*                k-s   s   n-k */

/*  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). */
/*  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), */
/*  and A(k,k), and v overwrites A(1:k-2,k-1:k). */

/*  If UPLO = 'L', then A = L*D*L', where */
/*     L = P(1)*L(1)* ... *P(k)*L(k)* ..., */
/*  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to */
/*  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */
/*  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as */
/*  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such */
/*  that if the diagonal block D(k) is of order s (s = 1 or 2), then */

/*             (   I    0     0   )  k-1 */
/*     L(k) =  (   0    I     0   )  s */
/*             (   0    v     I   )  n-k-s+1 */
/*                k-1   s  n-k-s+1 */

/*  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). */
/*  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), */
/*  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). */

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

/*     .. 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;
    --ipiv;
    --work;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    lquery = *lwork == -1;
    if (! upper && ! lsame_(uplo, "L")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < max(1,*n)) {
	*info = -4;
    } else if (*lwork < 1 && ! lquery) {
	*info = -7;
    }

    if (*info == 0) {

/*        Determine the block size */

	nb = ilaenv_(&c__1, "DSYTRF", uplo, n, &c_n1, &c_n1, &c_n1);
	lwkopt = *n * nb;
	work[1] = (doublereal) lwkopt;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DSYTRF", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

    nbmin = 2;
    ldwork = *n;
    if (nb > 1 && nb < *n) {
	iws = ldwork * nb;
	if (*lwork < iws) {
/* Computing MAX */
	    i__1 = *lwork / ldwork;
	    nb = max(i__1,1);
/* Computing MAX */
	    i__1 = 2, i__2 = ilaenv_(&c__2, "DSYTRF", uplo, n, &c_n1, &c_n1, &
		    c_n1);
	    nbmin = max(i__1,i__2);
	}
    } else {
	iws = 1;
    }
    if (nb < nbmin) {
	nb = *n;
    }

    if (upper) {

/*        Factorize A as U*D*U' using the upper triangle of A */

/*        K is the main loop index, decreasing from N to 1 in steps of */
/*        KB, where KB is the number of columns factorized by DLASYF; */
/*        KB is either NB or NB-1, or K for the last block */

	k = *n;
L10:

/*        If K < 1, exit from loop */

	if (k < 1) {
	    goto L40;
	}

	if (k > nb) {

/*           Factorize columns k-kb+1:k of A and use blocked code to */
/*           update columns 1:k-kb */

	    dlasyf_(uplo, &k, &nb, &kb, &a[a_offset], lda, &ipiv[1], &work[1], 
		     &ldwork, &iinfo);
	} else {

/*           Use unblocked code to factorize columns 1:k of A */

	    dsytf2_(uplo, &k, &a[a_offset], lda, &ipiv[1], &iinfo);
	    kb = k;
	}

/*        Set INFO on the first occurrence of a zero pivot */

	if (*info == 0 && iinfo > 0) {
	    *info = iinfo;
	}

/*        Decrease K and return to the start of the main loop */

	k -= kb;
	goto L10;

    } else {

/*        Factorize A as L*D*L' using the lower triangle of A */

/*        K is the main loop index, increasing from 1 to N in steps of */
/*        KB, where KB is the number of columns factorized by DLASYF; */
/*        KB is either NB or NB-1, or N-K+1 for the last block */

	k = 1;
L20:

/*        If K > N, exit from loop */

	if (k > *n) {
	    goto L40;
	}

	if (k <= *n - nb) {

/*           Factorize columns k:k+kb-1 of A and use blocked code to */
/*           update columns k+kb:n */

	    i__1 = *n - k + 1;
	    dlasyf_(uplo, &i__1, &nb, &kb, &a[k + k * a_dim1], lda, &ipiv[k], 
		    &work[1], &ldwork, &iinfo);
	} else {

/*           Use unblocked code to factorize columns k:n of A */

	    i__1 = *n - k + 1;
	    dsytf2_(uplo, &i__1, &a[k + k * a_dim1], lda, &ipiv[k], &iinfo);
	    kb = *n - k + 1;
	}

/*        Set INFO on the first occurrence of a zero pivot */

	if (*info == 0 && iinfo > 0) {
	    *info = iinfo + k - 1;
	}

/*        Adjust IPIV */

	i__1 = k + kb - 1;
	for (j = k; j <= i__1; ++j) {
	    if (ipiv[j] > 0) {
		ipiv[j] = ipiv[j] + k - 1;
	    } else {
		ipiv[j] = ipiv[j] - k + 1;
	    }
/* L30: */
	}

/*        Increase K and return to the start of the main loop */

	k += kb;
	goto L20;

    }

L40:
    work[1] = (doublereal) lwkopt;
    return 0;

/*     End of DSYTRF */

} /* dsytrf_ */