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/* 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 "f2c.h"
#include "blaswrap.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_ */
|
