/* 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_ */