Added a needed function
This commit is contained in:
Harry Moffat
parent
ac660e53c0
commit
198ab18640
4 changed files with 394 additions and 0 deletions
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@ -100,6 +100,7 @@ dormbr.o \
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dorml2.o \
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dormlq.o \
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dormqr.o \
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dpotf2.o \
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dpotrf.o \
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dpotrs.o \
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drscl.o \
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224
ext/f2c_lapack/dpotf2.c
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224
ext/f2c_lapack/dpotf2.c
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@ -0,0 +1,224 @@
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/* dpotf2.f -- translated by f2c (version 20031025).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "f2c.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static doublereal c_b10 = -1.;
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static doublereal c_b12 = 1.;
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/* Subroutine */ int dpotf2_(char *uplo, integer *n, doublereal *a, integer *
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lda, integer *info, ftnlen uplo_len)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3;
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doublereal d__1;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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static integer j;
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static doublereal ajj;
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extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
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integer *);
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extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
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integer *);
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
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doublereal *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *, ftnlen);
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static logical upper;
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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/* -- LAPACK routine (version 3.0) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
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/* Courant Institute, Argonne National Lab, and Rice University */
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/* February 29, 1992 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* DPOTF2 computes the Cholesky factorization of a real symmetric */
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/* positive definite matrix A. */
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/* The factorization has the form */
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/* A = U' * U , if UPLO = 'U', or */
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/* A = L * L', if UPLO = 'L', */
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/* where U is an upper triangular matrix and L is lower triangular. */
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/* This is the unblocked version of the algorithm, calling Level 2 BLAS. */
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/* Arguments */
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/* ========= */
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/* UPLO (input) CHARACTER*1 */
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/* Specifies whether the upper or lower triangular part of the */
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/* symmetric matrix A is stored. */
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/* = 'U': Upper triangular */
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/* = 'L': Lower triangular */
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/* N (input) INTEGER */
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/* The order of the matrix A. N >= 0. */
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/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
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/* On entry, the symmetric matrix A. If UPLO = 'U', the leading */
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/* n by n upper triangular part of A contains the upper */
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/* triangular part of the matrix A, and the strictly lower */
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/* triangular part of A is not referenced. If UPLO = 'L', the */
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/* leading n by n lower triangular part of A contains the lower */
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/* triangular part of the matrix A, and the strictly upper */
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/* triangular part of A is not referenced. */
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/* On exit, if INFO = 0, the factor U or L from the Cholesky */
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/* factorization A = U'*U or A = L*L'. */
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/* LDA (input) INTEGER */
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/* The leading dimension of the array A. LDA >= max(1,N). */
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/* INFO (output) INTEGER */
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/* = 0: successful exit */
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/* < 0: if INFO = -k, the k-th argument had an illegal value */
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/* > 0: if INFO = k, the leading minor of order k is not */
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/* positive definite, and the factorization could not be */
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/* completed. */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters. */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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/* Function Body */
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*info = 0;
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upper = lsame_(uplo, "U", (ftnlen)1, (ftnlen)1);
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if (! upper && ! lsame_(uplo, "L", (ftnlen)1, (ftnlen)1)) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*lda < max(1,*n)) {
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*info = -4;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DPOTF2", &i__1, (ftnlen)6);
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return 0;
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}
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/* Quick return if possible */
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if (*n == 0) {
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return 0;
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}
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if (upper) {
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/* Compute the Cholesky factorization A = U'*U. */
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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/* Compute U(J,J) and test for non-positive-definiteness. */
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i__2 = j - 1;
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ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j * a_dim1 + 1], &c__1,
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&a[j * a_dim1 + 1], &c__1);
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if (ajj <= 0.) {
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a[j + j * a_dim1] = ajj;
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goto L30;
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}
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ajj = sqrt(ajj);
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a[j + j * a_dim1] = ajj;
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/* Compute elements J+1:N of row J. */
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if (j < *n) {
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i__2 = j - 1;
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i__3 = *n - j;
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dgemv_("Transpose", &i__2, &i__3, &c_b10, &a[(j + 1) * a_dim1
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+ 1], lda, &a[j * a_dim1 + 1], &c__1, &c_b12, &a[j + (
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j + 1) * a_dim1], lda, (ftnlen)9);
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i__2 = *n - j;
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d__1 = 1. / ajj;
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dscal_(&i__2, &d__1, &a[j + (j + 1) * a_dim1], lda);
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}
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/* L10: */
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}
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} else {
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/* Compute the Cholesky factorization A = L*L'. */
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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/* Compute L(J,J) and test for non-positive-definiteness. */
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i__2 = j - 1;
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ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j + a_dim1], lda, &a[j
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+ a_dim1], lda);
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if (ajj <= 0.) {
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a[j + j * a_dim1] = ajj;
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goto L30;
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}
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ajj = sqrt(ajj);
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a[j + j * a_dim1] = ajj;
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/* Compute elements J+1:N of column J. */
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if (j < *n) {
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i__2 = *n - j;
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i__3 = j - 1;
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dgemv_("No transpose", &i__2, &i__3, &c_b10, &a[j + 1 +
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a_dim1], lda, &a[j + a_dim1], lda, &c_b12, &a[j + 1 +
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j * a_dim1], &c__1, (ftnlen)12);
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i__2 = *n - j;
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d__1 = 1. / ajj;
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dscal_(&i__2, &d__1, &a[j + 1 + j * a_dim1], &c__1);
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}
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/* L20: */
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}
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}
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goto L40;
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L30:
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*info = j;
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L40:
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return 0;
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/* End of DPOTF2 */
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} /* dpotf2_ */
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@ -71,6 +71,7 @@ dormlq.o \
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dormqr.o \
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dpotrf.o \
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dpotrs.o \
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dpotf2.o \
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drscl.o \
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dtrcon.o \
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dtrtrs.o \
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168
ext/lapack/dpotf2.f
Normal file
168
ext/lapack/dpotf2.f
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@ -0,0 +1,168 @@
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SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
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*
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* -- LAPACK routine (version 3.0) --
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* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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* Courant Institute, Argonne National Lab, and Rice University
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* February 29, 1992
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER INFO, LDA, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * )
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* ..
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*
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* Purpose
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* =======
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*
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* DPOTF2 computes the Cholesky factorization of a real symmetric
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* positive definite matrix A.
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*
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* The factorization has the form
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* A = U' * U , if UPLO = 'U', or
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* A = L * L', if UPLO = 'L',
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* where U is an upper triangular matrix and L is lower triangular.
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*
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* This is the unblocked version of the algorithm, calling Level 2 BLAS.
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*
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* Arguments
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* =========
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*
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* UPLO (input) CHARACTER*1
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* Specifies whether the upper or lower triangular part of the
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* symmetric matrix A is stored.
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* = 'U': Upper triangular
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* = 'L': Lower triangular
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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0.
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*
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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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* On entry, the symmetric matrix A. If UPLO = 'U', the leading
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* n by n upper triangular part of A contains the upper
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* triangular part of the matrix A, and the strictly lower
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* triangular part of A is not referenced. If UPLO = 'L', the
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* leading n by n lower triangular part of A contains the lower
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* triangular part of the matrix A, and the strictly upper
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* triangular part of A is not referenced.
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*
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* On exit, if INFO = 0, the factor U or L from the Cholesky
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* factorization A = U'*U or A = L*L'.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,N).
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -k, the k-th argument had an illegal value
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* > 0: if INFO = k, the leading minor of order k is not
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* positive definite, and the factorization could not be
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* completed.
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL UPPER
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INTEGER J
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DOUBLE PRECISION AJJ
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DDOT
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EXTERNAL LSAME, DDOT
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* ..
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* .. External Subroutines ..
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EXTERNAL DGEMV, DSCAL, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, SQRT
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DPOTF2', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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IF( UPPER ) THEN
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*
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* Compute the Cholesky factorization A = U'*U.
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*
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DO 10 J = 1, N
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*
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* Compute U(J,J) and test for non-positive-definiteness.
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*
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AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
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IF( AJJ.LE.ZERO ) THEN
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A( J, J ) = AJJ
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GO TO 30
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END IF
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AJJ = SQRT( AJJ )
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A( J, J ) = AJJ
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*
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* Compute elements J+1:N of row J.
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*
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IF( J.LT.N ) THEN
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CALL DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
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$ LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
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CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
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END IF
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10 CONTINUE
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ELSE
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*
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* Compute the Cholesky factorization A = L*L'.
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*
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DO 20 J = 1, N
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*
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* Compute L(J,J) and test for non-positive-definiteness.
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*
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AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
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$ LDA )
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IF( AJJ.LE.ZERO ) THEN
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A( J, J ) = AJJ
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GO TO 30
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END IF
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AJJ = SQRT( AJJ )
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A( J, J ) = AJJ
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*
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* Compute elements J+1:N of column J.
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*
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IF( J.LT.N ) THEN
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CALL DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
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$ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
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CALL DSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
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END IF
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20 CONTINUE
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END IF
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GO TO 40
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*
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30 CONTINUE
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INFO = J
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*
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40 CONTINUE
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RETURN
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*
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* End of DPOTF2
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*
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END
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