--- /dev/null
+#include "clapack.h"
+
+/* Subroutine */ int dsytri_(char *uplo, integer *n, doublereal *a, integer *
+ lda, integer *ipiv, doublereal *work, 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
+ =======
+
+ DSYTRI computes the inverse of a real symmetric indefinite 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.
+
+ A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
+ On entry, the block diagonal matrix D and the multipliers
+ used to obtain the factor U or L as computed by DSYTRF.
+
+ On exit, if INFO = 0, the (symmetric) inverse of the original
+ matrix. If UPLO = 'U', the upper triangular part of the
+ inverse is formed and the part of A below the diagonal is not
+ referenced; if UPLO = 'L' the lower triangular part of the
+ inverse is formed and the part of A above the diagonal is
+ not referenced.
+
+ 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.
+
+ WORK (workspace) DOUBLE PRECISION array, dimension (N)
+
+ 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) = 0; the matrix is singular and its
+ inverse could not be computed.
+
+ =====================================================================
+
+
+ Test the input parameters.
+
+ Parameter adjustments */
+ /* Table of constant values */
+ static integer c__1 = 1;
+ static doublereal c_b11 = -1.;
+ static doublereal c_b13 = 0.;
+
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1;
+ doublereal d__1;
+ /* Local variables */
+ extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
+ integer *);
+ static doublereal temp, akkp1, d__;
+ static integer k;
+ static doublereal t;
+ extern logical lsame_(char *, char *);
+ extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
+ doublereal *, integer *), dswap_(integer *, doublereal *, integer
+ *, doublereal *, integer *);
+ static integer kstep;
+ static logical upper;
+ extern /* Subroutine */ int dsymv_(char *, integer *, doublereal *,
+ doublereal *, integer *, doublereal *, integer *, doublereal *,
+ doublereal *, integer *);
+ static doublereal ak;
+ static integer kp;
+ extern /* Subroutine */ int xerbla_(char *, integer *);
+ static doublereal akp1;
+#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");
+ 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_("DSYTRI", &i__1);
+ return 0;
+ }
+
+/* Quick return if possible */
+
+ if (*n == 0) {
+ return 0;
+ }
+
+/* Check that the diagonal matrix D is nonsingular. */
+
+ if (upper) {
+
+/* Upper triangular storage: examine D from bottom to top */
+
+ for (*info = *n; *info >= 1; --(*info)) {
+ if (ipiv[*info] > 0 && a_ref(*info, *info) == 0.) {
+ return 0;
+ }
+/* L10: */
+ }
+ } else {
+
+/* Lower triangular storage: examine D from top to bottom. */
+
+ i__1 = *n;
+ for (*info = 1; *info <= i__1; ++(*info)) {
+ if (ipiv[*info] > 0 && a_ref(*info, *info) == 0.) {
+ return 0;
+ }
+/* L20: */
+ }
+ }
+ *info = 0;
+
+ if (upper) {
+
+/* Compute inv(A) from the factorization A = U*D*U'.
+
+ 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;
+L30:
+
+/* If K > N, exit from loop. */
+
+ if (k > *n) {
+ goto L40;
+ }
+
+ if (ipiv[k] > 0) {
+
+/* 1 x 1 diagonal block
+
+ Invert the diagonal block. */
+
+ a_ref(k, k) = 1. / a_ref(k, k);
+
+/* Compute column K of the inverse. */
+
+ if (k > 1) {
+ i__1 = k - 1;
+ dcopy_(&i__1, &a_ref(1, k), &c__1, &work[1], &c__1);
+ i__1 = k - 1;
+ dsymv_(uplo, &i__1, &c_b11, &a[a_offset], lda, &work[1], &
+ c__1, &c_b13, &a_ref(1, k), &c__1);
+ i__1 = k - 1;
+ a_ref(k, k) = a_ref(k, k) - ddot_(&i__1, &work[1], &c__1, &
+ a_ref(1, k), &c__1);
+ }
+ kstep = 1;
+ } else {
+
+/* 2 x 2 diagonal block
+
+ Invert the diagonal block. */
+
+ t = (d__1 = a_ref(k, k + 1), abs(d__1));
+ ak = a_ref(k, k) / t;
+ akp1 = a_ref(k + 1, k + 1) / t;
+ akkp1 = a_ref(k, k + 1) / t;
+ d__ = t * (ak * akp1 - 1.);
+ a_ref(k, k) = akp1 / d__;
+ a_ref(k + 1, k + 1) = ak / d__;
+ a_ref(k, k + 1) = -akkp1 / d__;
+
+/* Compute columns K and K+1 of the inverse. */
+
+ if (k > 1) {
+ i__1 = k - 1;
+ dcopy_(&i__1, &a_ref(1, k), &c__1, &work[1], &c__1);
+ i__1 = k - 1;
+ dsymv_(uplo, &i__1, &c_b11, &a[a_offset], lda, &work[1], &
+ c__1, &c_b13, &a_ref(1, k), &c__1);
+ i__1 = k - 1;
+ a_ref(k, k) = a_ref(k, k) - ddot_(&i__1, &work[1], &c__1, &
+ a_ref(1, k), &c__1);
+ i__1 = k - 1;
+ a_ref(k, k + 1) = a_ref(k, k + 1) - ddot_(&i__1, &a_ref(1, k),
+ &c__1, &a_ref(1, k + 1), &c__1);
+ i__1 = k - 1;
+ dcopy_(&i__1, &a_ref(1, k + 1), &c__1, &work[1], &c__1);
+ i__1 = k - 1;
+ dsymv_(uplo, &i__1, &c_b11, &a[a_offset], lda, &work[1], &
+ c__1, &c_b13, &a_ref(1, k + 1), &c__1);
+ i__1 = k - 1;
+ a_ref(k + 1, k + 1) = a_ref(k + 1, k + 1) - ddot_(&i__1, &
+ work[1], &c__1, &a_ref(1, k + 1), &c__1);
+ }
+ kstep = 2;
+ }
+
+ kp = (i__1 = ipiv[k], abs(i__1));
+ if (kp != k) {
+
+/* Interchange rows and columns K and KP in the leading
+ submatrix A(1:k+1,1:k+1) */
+
+ i__1 = kp - 1;
+ dswap_(&i__1, &a_ref(1, k), &c__1, &a_ref(1, kp), &c__1);
+ i__1 = k - kp - 1;
+ dswap_(&i__1, &a_ref(kp + 1, k), &c__1, &a_ref(kp, kp + 1), lda);
+ temp = a_ref(k, k);
+ a_ref(k, k) = a_ref(kp, kp);
+ a_ref(kp, kp) = temp;
+ if (kstep == 2) {
+ temp = a_ref(k, k + 1);
+ a_ref(k, k + 1) = a_ref(kp, k + 1);
+ a_ref(kp, k + 1) = temp;
+ }
+ }
+
+ k += kstep;
+ goto L30;
+L40:
+
+ ;
+ } else {
+
+/* Compute inv(A) from the factorization A = L*D*L'.
+
+ 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 = *n;
+L50:
+
+/* If K < 1, exit from loop. */
+
+ if (k < 1) {
+ goto L60;
+ }
+
+ if (ipiv[k] > 0) {
+
+/* 1 x 1 diagonal block
+
+ Invert the diagonal block. */
+
+ a_ref(k, k) = 1. / a_ref(k, k);
+
+/* Compute column K of the inverse. */
+
+ if (k < *n) {
+ i__1 = *n - k;
+ dcopy_(&i__1, &a_ref(k + 1, k), &c__1, &work[1], &c__1);
+ i__1 = *n - k;
+ dsymv_(uplo, &i__1, &c_b11, &a_ref(k + 1, k + 1), lda, &work[
+ 1], &c__1, &c_b13, &a_ref(k + 1, k), &c__1)
+ ;
+ i__1 = *n - k;
+ a_ref(k, k) = a_ref(k, k) - ddot_(&i__1, &work[1], &c__1, &
+ a_ref(k + 1, k), &c__1);
+ }
+ kstep = 1;
+ } else {
+
+/* 2 x 2 diagonal block
+
+ Invert the diagonal block. */
+
+ t = (d__1 = a_ref(k, k - 1), abs(d__1));
+ ak = a_ref(k - 1, k - 1) / t;
+ akp1 = a_ref(k, k) / t;
+ akkp1 = a_ref(k, k - 1) / t;
+ d__ = t * (ak * akp1 - 1.);
+ a_ref(k - 1, k - 1) = akp1 / d__;
+ a_ref(k, k) = ak / d__;
+ a_ref(k, k - 1) = -akkp1 / d__;
+
+/* Compute columns K-1 and K of the inverse. */
+
+ if (k < *n) {
+ i__1 = *n - k;
+ dcopy_(&i__1, &a_ref(k + 1, k), &c__1, &work[1], &c__1);
+ i__1 = *n - k;
+ dsymv_(uplo, &i__1, &c_b11, &a_ref(k + 1, k + 1), lda, &work[
+ 1], &c__1, &c_b13, &a_ref(k + 1, k), &c__1)
+ ;
+ i__1 = *n - k;
+ a_ref(k, k) = a_ref(k, k) - ddot_(&i__1, &work[1], &c__1, &
+ a_ref(k + 1, k), &c__1);
+ i__1 = *n - k;
+ a_ref(k, k - 1) = a_ref(k, k - 1) - ddot_(&i__1, &a_ref(k + 1,
+ k), &c__1, &a_ref(k + 1, k - 1), &c__1);
+ i__1 = *n - k;
+ dcopy_(&i__1, &a_ref(k + 1, k - 1), &c__1, &work[1], &c__1);
+ i__1 = *n - k;
+ dsymv_(uplo, &i__1, &c_b11, &a_ref(k + 1, k + 1), lda, &work[
+ 1], &c__1, &c_b13, &a_ref(k + 1, k - 1), &c__1);
+ i__1 = *n - k;
+ a_ref(k - 1, k - 1) = a_ref(k - 1, k - 1) - ddot_(&i__1, &
+ work[1], &c__1, &a_ref(k + 1, k - 1), &c__1);
+ }
+ kstep = 2;
+ }
+
+ kp = (i__1 = ipiv[k], abs(i__1));
+ if (kp != k) {
+
+/* Interchange rows and columns K and KP in the trailing
+ submatrix A(k-1:n,k-1:n) */
+
+ if (kp < *n) {
+ i__1 = *n - kp;
+ dswap_(&i__1, &a_ref(kp + 1, k), &c__1, &a_ref(kp + 1, kp), &
+ c__1);
+ }
+ i__1 = kp - k - 1;
+ dswap_(&i__1, &a_ref(k + 1, k), &c__1, &a_ref(kp, k + 1), lda);
+ temp = a_ref(k, k);
+ a_ref(k, k) = a_ref(kp, kp);
+ a_ref(kp, kp) = temp;
+ if (kstep == 2) {
+ temp = a_ref(k, k - 1);
+ a_ref(k, k - 1) = a_ref(kp, k - 1);
+ a_ref(kp, k - 1) = temp;
+ }
+ }
+
+ k -= kstep;
+ goto L50;
+L60:
+ ;
+ }
+
+ return 0;
+
+/* End of DSYTRI */
+
+} /* dsytri_ */
+
+#undef a_ref
+
+
projects / opencv / blobdiff