--- /dev/null
+#include "clapack.h"
+
+/* Subroutine */ int dsytrs_(char *uplo, integer *n, integer *nrhs,
+ doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer *
+ ldb, integer *info)
+{
+/* -- LAPACK routine (version 3.0) --
+ Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
+ Courant Institute, Argonne National Lab, and Rice University
+ March 31, 1993
+
+
+ Purpose
+ =======
+
+ DSYTRS solves a system of linear equations A*X = B with a real
+ symmetric matrix A using the factorization A = U*D*U**T or
+ A = L*D*L**T computed by DSYTRF.
+
+ Arguments
+ =========
+
+ UPLO (input) CHARACTER*1
+ Specifies whether the details of the factorization are stored
+ as an upper or lower triangular matrix.
+ = 'U': Upper triangular, form is A = U*D*U**T;
+ = 'L': Lower triangular, form is A = L*D*L**T.
+
+ N (input) INTEGER
+ The order of the matrix A. N >= 0.
+
+ NRHS (input) INTEGER
+ The number of right hand sides, i.e., the number of columns
+ of the matrix B. NRHS >= 0.
+
+ A (input) DOUBLE PRECISION array, dimension (LDA,N)
+ The block diagonal matrix D and the multipliers used to
+ obtain the factor U or L as computed by DSYTRF.
+
+ LDA (input) INTEGER
+ The leading dimension of the array A. LDA >= max(1,N).
+
+ IPIV (input) INTEGER array, dimension (N)
+ Details of the interchanges and the block structure of D
+ as determined by DSYTRF.
+
+ B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
+ On entry, the right hand side matrix B.
+ On exit, the solution matrix X.
+
+ LDB (input) INTEGER
+ The leading dimension of the array B. LDB >= max(1,N).
+
+ INFO (output) INTEGER
+ = 0: successful exit
+ < 0: if INFO = -i, the i-th argument had an illegal value
+
+ =====================================================================
+
+
+ Parameter adjustments */
+ /* Table of constant values */
+ static doublereal c_b7 = -1.;
+ static integer c__1 = 1;
+ static doublereal c_b19 = 1.;
+
+ /* System generated locals */
+ integer a_dim1, a_offset, b_dim1, b_offset, i__1;
+ doublereal d__1;
+ /* Local variables */
+ extern /* Subroutine */ int dger_(integer *, integer *, doublereal *,
+ doublereal *, integer *, doublereal *, integer *, doublereal *,
+ integer *);
+ static doublereal akm1k;
+ static integer j, k;
+ extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
+ integer *);
+ extern logical lsame_(char *, char *);
+ static doublereal denom;
+ extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
+ doublereal *, doublereal *, integer *, doublereal *, integer *,
+ doublereal *, doublereal *, integer *), dswap_(integer *,
+ doublereal *, integer *, doublereal *, integer *);
+ static logical upper;
+ static doublereal ak, bk;
+ static integer kp;
+ extern /* Subroutine */ int xerbla_(char *, integer *);
+ static doublereal akm1, bkm1;
+#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
+#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
+
+
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1 * 1;
+ a -= a_offset;
+ --ipiv;
+ b_dim1 = *ldb;
+ b_offset = 1 + b_dim1 * 1;
+ b -= b_offset;
+
+ /* Function Body */
+ *info = 0;
+ upper = lsame_(uplo, "U");
+ if (! upper && ! lsame_(uplo, "L")) {
+ *info = -1;
+ } else if (*n < 0) {
+ *info = -2;
+ } else if (*nrhs < 0) {
+ *info = -3;
+ } else if (*lda < max(1,*n)) {
+ *info = -5;
+ } else if (*ldb < max(1,*n)) {
+ *info = -8;
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("DSYTRS", &i__1);
+ return 0;
+ }
+
+/* Quick return if possible */
+
+ if (*n == 0 || *nrhs == 0) {
+ return 0;
+ }
+
+ if (upper) {
+
+/* Solve A*X = B, where A = U*D*U'.
+
+ First solve U*D*X = B, overwriting B with X.
+
+ K is the main loop index, decreasing from N to 1 in steps of
+ 1 or 2, depending on the size of the diagonal blocks. */
+
+ k = *n;
+L10:
+
+/* If K < 1, exit from loop. */
+
+ if (k < 1) {
+ goto L30;
+ }
+
+ if (ipiv[k] > 0) {
+
+/* 1 x 1 diagonal block
+
+ Interchange rows K and IPIV(K). */
+
+ kp = ipiv[k];
+ if (kp != k) {
+ dswap_(nrhs, &b_ref(k, 1), ldb, &b_ref(kp, 1), ldb);
+ }
+
+/* Multiply by inv(U(K)), where U(K) is the transformation
+ stored in column K of A. */
+
+ i__1 = k - 1;
+ dger_(&i__1, nrhs, &c_b7, &a_ref(1, k), &c__1, &b_ref(k, 1), ldb,
+ &b_ref(1, 1), ldb);
+
+/* Multiply by the inverse of the diagonal block. */
+
+ d__1 = 1. / a_ref(k, k);
+ dscal_(nrhs, &d__1, &b_ref(k, 1), ldb);
+ --k;
+ } else {
+
+/* 2 x 2 diagonal block
+
+ Interchange rows K-1 and -IPIV(K). */
+
+ kp = -ipiv[k];
+ if (kp != k - 1) {
+ dswap_(nrhs, &b_ref(k - 1, 1), ldb, &b_ref(kp, 1), ldb);
+ }
+
+/* Multiply by inv(U(K)), where U(K) is the transformation
+ stored in columns K-1 and K of A. */
+
+ i__1 = k - 2;
+ dger_(&i__1, nrhs, &c_b7, &a_ref(1, k), &c__1, &b_ref(k, 1), ldb,
+ &b_ref(1, 1), ldb);
+ i__1 = k - 2;
+ dger_(&i__1, nrhs, &c_b7, &a_ref(1, k - 1), &c__1, &b_ref(k - 1,
+ 1), ldb, &b_ref(1, 1), ldb);
+
+/* Multiply by the inverse of the diagonal block. */
+
+ akm1k = a_ref(k - 1, k);
+ akm1 = a_ref(k - 1, k - 1) / akm1k;
+ ak = a_ref(k, k) / akm1k;
+ denom = akm1 * ak - 1.;
+ i__1 = *nrhs;
+ for (j = 1; j <= i__1; ++j) {
+ bkm1 = b_ref(k - 1, j) / akm1k;
+ bk = b_ref(k, j) / akm1k;
+ b_ref(k - 1, j) = (ak * bkm1 - bk) / denom;
+ b_ref(k, j) = (akm1 * bk - bkm1) / denom;
+/* L20: */
+ }
+ k += -2;
+ }
+
+ goto L10;
+L30:
+
+/* Next solve U'*X = B, overwriting B with X.
+
+ K is the main loop index, increasing from 1 to N in steps of
+ 1 or 2, depending on the size of the diagonal blocks. */
+
+ k = 1;
+L40:
+
+/* If K > N, exit from loop. */
+
+ if (k > *n) {
+ goto L50;
+ }
+
+ if (ipiv[k] > 0) {
+
+/* 1 x 1 diagonal block
+
+ Multiply by inv(U'(K)), where U(K) is the transformation
+ stored in column K of A. */
+
+ i__1 = k - 1;
+ dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[b_offset], ldb, &a_ref(
+ 1, k), &c__1, &c_b19, &b_ref(k, 1), ldb);
+
+/* Interchange rows K and IPIV(K). */
+
+ kp = ipiv[k];
+ if (kp != k) {
+ dswap_(nrhs, &b_ref(k, 1), ldb, &b_ref(kp, 1), ldb);
+ }
+ ++k;
+ } else {
+
+/* 2 x 2 diagonal block
+
+ Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+ stored in columns K and K+1 of A. */
+
+ i__1 = k - 1;
+ dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[b_offset], ldb, &a_ref(
+ 1, k), &c__1, &c_b19, &b_ref(k, 1), ldb);
+ i__1 = k - 1;
+ dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[b_offset], ldb, &a_ref(
+ 1, k + 1), &c__1, &c_b19, &b_ref(k + 1, 1), ldb);
+
+/* Interchange rows K and -IPIV(K). */
+
+ kp = -ipiv[k];
+ if (kp != k) {
+ dswap_(nrhs, &b_ref(k, 1), ldb, &b_ref(kp, 1), ldb);
+ }
+ k += 2;
+ }
+
+ goto L40;
+L50:
+
+ ;
+ } else {
+
+/* Solve A*X = B, where A = L*D*L'.
+
+ First solve L*D*X = B, overwriting B with X.
+
+ K is the main loop index, increasing from 1 to N in steps of
+ 1 or 2, depending on the size of the diagonal blocks. */
+
+ k = 1;
+L60:
+
+/* If K > N, exit from loop. */
+
+ if (k > *n) {
+ goto L80;
+ }
+
+ if (ipiv[k] > 0) {
+
+/* 1 x 1 diagonal block
+
+ Interchange rows K and IPIV(K). */
+
+ kp = ipiv[k];
+ if (kp != k) {
+ dswap_(nrhs, &b_ref(k, 1), ldb, &b_ref(kp, 1), ldb);
+ }
+
+/* Multiply by inv(L(K)), where L(K) is the transformation
+ stored in column K of A. */
+
+ if (k < *n) {
+ i__1 = *n - k;
+ dger_(&i__1, nrhs, &c_b7, &a_ref(k + 1, k), &c__1, &b_ref(k,
+ 1), ldb, &b_ref(k + 1, 1), ldb);
+ }
+
+/* Multiply by the inverse of the diagonal block. */
+
+ d__1 = 1. / a_ref(k, k);
+ dscal_(nrhs, &d__1, &b_ref(k, 1), ldb);
+ ++k;
+ } else {
+
+/* 2 x 2 diagonal block
+
+ Interchange rows K+1 and -IPIV(K). */
+
+ kp = -ipiv[k];
+ if (kp != k + 1) {
+ dswap_(nrhs, &b_ref(k + 1, 1), ldb, &b_ref(kp, 1), ldb);
+ }
+
+/* Multiply by inv(L(K)), where L(K) is the transformation
+ stored in columns K and K+1 of A. */
+
+ if (k < *n - 1) {
+ i__1 = *n - k - 1;
+ dger_(&i__1, nrhs, &c_b7, &a_ref(k + 2, k), &c__1, &b_ref(k,
+ 1), ldb, &b_ref(k + 2, 1), ldb);
+ i__1 = *n - k - 1;
+ dger_(&i__1, nrhs, &c_b7, &a_ref(k + 2, k + 1), &c__1, &b_ref(
+ k + 1, 1), ldb, &b_ref(k + 2, 1), ldb);
+ }
+
+/* Multiply by the inverse of the diagonal block. */
+
+ akm1k = a_ref(k + 1, k);
+ akm1 = a_ref(k, k) / akm1k;
+ ak = a_ref(k + 1, k + 1) / akm1k;
+ denom = akm1 * ak - 1.;
+ i__1 = *nrhs;
+ for (j = 1; j <= i__1; ++j) {
+ bkm1 = b_ref(k, j) / akm1k;
+ bk = b_ref(k + 1, j) / akm1k;
+ b_ref(k, j) = (ak * bkm1 - bk) / denom;
+ b_ref(k + 1, j) = (akm1 * bk - bkm1) / denom;
+/* L70: */
+ }
+ k += 2;
+ }
+
+ goto L60;
+L80:
+
+/* Next solve L'*X = B, overwriting B with X.
+
+ K is the main loop index, decreasing from N to 1 in steps of
+ 1 or 2, depending on the size of the diagonal blocks. */
+
+ k = *n;
+L90:
+
+/* If K < 1, exit from loop. */
+
+ if (k < 1) {
+ goto L100;
+ }
+
+ if (ipiv[k] > 0) {
+
+/* 1 x 1 diagonal block
+
+ Multiply by inv(L'(K)), where L(K) is the transformation
+ stored in column K of A. */
+
+ if (k < *n) {
+ i__1 = *n - k;
+ dgemv_("Transpose", &i__1, nrhs, &c_b7, &b_ref(k + 1, 1), ldb,
+ &a_ref(k + 1, k), &c__1, &c_b19, &b_ref(k, 1), ldb);
+ }
+
+/* Interchange rows K and IPIV(K). */
+
+ kp = ipiv[k];
+ if (kp != k) {
+ dswap_(nrhs, &b_ref(k, 1), ldb, &b_ref(kp, 1), ldb);
+ }
+ --k;
+ } else {
+
+/* 2 x 2 diagonal block
+
+ Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+ stored in columns K-1 and K of A. */
+
+ if (k < *n) {
+ i__1 = *n - k;
+ dgemv_("Transpose", &i__1, nrhs, &c_b7, &b_ref(k + 1, 1), ldb,
+ &a_ref(k + 1, k), &c__1, &c_b19, &b_ref(k, 1), ldb);
+ i__1 = *n - k;
+ dgemv_("Transpose", &i__1, nrhs, &c_b7, &b_ref(k + 1, 1), ldb,
+ &a_ref(k + 1, k - 1), &c__1, &c_b19, &b_ref(k - 1, 1)
+ , ldb);
+ }
+
+/* Interchange rows K and -IPIV(K). */
+
+ kp = -ipiv[k];
+ if (kp != k) {
+ dswap_(nrhs, &b_ref(k, 1), ldb, &b_ref(kp, 1), ldb);
+ }
+ k += -2;
+ }
+
+ goto L90;
+L100:
+ ;
+ }
+
+ return 0;
+
+/* End of DSYTRS */
+
+} /* dsytrs_ */
+
+#undef b_ref
+#undef a_ref
+
+
projects / opencv / blobdiff