/* spstrf.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 real c_b22 = -1.f;
static real c_b24 = 1.f;

/* Subroutine */ int spstrf_(char *uplo, integer *n, real *a, integer *lda, 
	integer *piv, integer *rank, real *tol, real *work, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
    real r__1;

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

    /* Local variables */
    integer i__, j, k, maxlocval, jb, nb;
    real ajj;
    integer pvt;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    integer itemp;
    extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, 
	    real *, integer *, real *, integer *, real *, real *, integer *);
    real stemp;
    logical upper;
    extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *, 
	    integer *);
    real sstop;
    extern /* Subroutine */ int ssyrk_(char *, char *, integer *, integer *, 
	    real *, real *, integer *, real *, real *, integer *), spstf2_(char *, integer *, real *, integer *, integer *, 
	    integer *, real *, real *, integer *);
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *);
    extern logical sisnan_(real *);
    extern integer smaxloc_(real *, integer *);


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

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

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

/*  SPSTRF 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) REAL 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) REAL */
/*          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    REAL 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_("SPSTRF", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

/*     Get block size */

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

/*        Use unblocked code */

	spstf2_(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.f || sisnan_(&ajj)) {
	    *rank = 0;
	    *info = 1;
	    goto L200;
	}

/*     Compute stopping value if not supplied */

	if (*tol < 0.f) {
	    sstop = *n * slamch_("Epsilon") * ajj;
	} else {
	    sstop = *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.f;
/* 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 */
			    r__1 = a[j - 1 + i__ * a_dim1];
			    work[i__] += r__1 * r__1;
			}
			work[*n + i__] = a[i__ + i__ * a_dim1] - work[i__];

/* L120: */
		    }

		    if (j > 1) {
			maxlocval = (*n << 1) - (*n + j) + 1;
			itemp = smaxloc_(&work[*n + j], &maxlocval);
			pvt = itemp + j - 1;
			ajj = work[*n + pvt];
			if (ajj <= sstop || sisnan_(&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;
			sswap_(&i__4, &a[j * a_dim1 + 1], &c__1, &a[pvt * 
				a_dim1 + 1], &c__1);
			if (pvt < *n) {
			    i__4 = *n - pvt;
			    sswap_(&i__4, &a[j + (pvt + 1) * a_dim1], lda, &a[
				    pvt + (pvt + 1) * a_dim1], lda);
			}
			i__4 = pvt - j - 1;
			sswap_(&i__4, &a[j + (j + 1) * a_dim1], lda, &a[j + 1 
				+ pvt * a_dim1], &c__1);

/*                    Swap dot products and PIV */

			stemp = work[j];
			work[j] = work[pvt];
			work[pvt] = stemp;
			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;
			sgemv_("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;
			r__1 = 1.f / ajj;
			sscal_(&i__4, &r__1, &a[j + (j + 1) * a_dim1], lda);
		    }

/* L130: */
		}

/*              Update trailing matrix, J already incremented */

		if (k + jb <= *n) {
		    i__3 = *n - j + 1;
		    ssyrk_("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.f;
/* 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 */
			    r__1 = a[i__ + (j - 1) * a_dim1];
			    work[i__] += r__1 * r__1;
			}
			work[*n + i__] = a[i__ + i__ * a_dim1] - work[i__];

/* L160: */
		    }

		    if (j > 1) {
			maxlocval = (*n << 1) - (*n + j) + 1;
			itemp = smaxloc_(&work[*n + j], &maxlocval);
			pvt = itemp + j - 1;
			ajj = work[*n + pvt];
			if (ajj <= sstop || sisnan_(&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;
			sswap_(&i__4, &a[j + a_dim1], lda, &a[pvt + a_dim1], 
				lda);
			if (pvt < *n) {
			    i__4 = *n - pvt;
			    sswap_(&i__4, &a[pvt + 1 + j * a_dim1], &c__1, &a[
				    pvt + 1 + pvt * a_dim1], &c__1);
			}
			i__4 = pvt - j - 1;
			sswap_(&i__4, &a[j + 1 + j * a_dim1], &c__1, &a[pvt + 
				(j + 1) * a_dim1], lda);

/*                    Swap dot products and PIV */

			stemp = work[j];
			work[j] = work[pvt];
			work[pvt] = stemp;
			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;
			sgemv_("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;
			r__1 = 1.f / ajj;
			sscal_(&i__4, &r__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;
		    ssyrk_("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 SPSTRF */

} /* spstrf_ */