--- /dev/null
+#include "clapack.h"
+
+/* Subroutine */ int dsytrf_(char *uplo, integer *n, doublereal *a, integer *
+ lda, integer *ipiv, doublereal *work, integer *lwork, integer *info)
+{
+/* -- LAPACK routine (version 3.0) --
+ Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
+ Courant Institute, Argonne National Lab, and Rice University
+ June 30, 1999
+
+
+ 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 (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).
+
+ =====================================================================
+
+
+ Test the input parameters.
+
+ Parameter adjustments */
+ /* Table of constant values */
+ static integer c__1 = 1;
+ static integer c_n1 = -1;
+ static integer c__2 = 2;
+
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2;
+ /* Local variables */
+ static integer j, k;
+ extern logical lsame_(char *, char *);
+ static integer nbmin, iinfo;
+ static logical upper;
+ extern /* Subroutine */ int dsytf2_(char *, integer *, doublereal *,
+ integer *, integer *, integer *);
+ static integer kb, nb;
+ extern /* Subroutine */ int xerbla_(char *, integer *);
+ extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
+ integer *, integer *, ftnlen, ftnlen);
+ extern /* Subroutine */ int dlasyf_(char *, integer *, integer *, integer
+ *, doublereal *, integer *, integer *, doublereal *, integer *,
+ integer *);
+ static integer ldwork, lwkopt;
+ static logical lquery;
+ static integer iws;
+#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
+
+
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1 * 1;
+ 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, (ftnlen)6,
+ (ftnlen)1);
+ 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, (ftnlen)6, (ftnlen)1);
+ 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_ref(k, k), 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_ref(k, k), 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_ */
+
+#undef a_ref
+
+
projects / opencv / blobdiff