368 lines
9.6 KiB
C
368 lines
9.6 KiB
C
#include "clapack.h"
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/* Subroutine */ int dsytri_(char *uplo, integer *n, doublereal *a, integer *
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lda, integer *ipiv, doublereal *work, integer *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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March 31, 1993
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Purpose
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=======
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DSYTRI computes the inverse of a real symmetric indefinite matrix
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A using the factorization A = U*D*U**T or A = L*D*L**T computed by
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DSYTRF.
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Arguments
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=========
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UPLO (input) CHARACTER*1
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Specifies whether the details of the factorization are stored
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as an upper or lower triangular matrix.
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= 'U': Upper triangular, form is A = U*D*U**T;
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= 'L': Lower triangular, form is A = L*D*L**T.
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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 block diagonal matrix D and the multipliers
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used to obtain the factor U or L as computed by DSYTRF.
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On exit, if INFO = 0, the (symmetric) inverse of the original
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matrix. If UPLO = 'U', the upper triangular part of the
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inverse is formed and the part of A below the diagonal is not
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referenced; if UPLO = 'L' the lower triangular part of the
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inverse is formed and the part of A above the diagonal is
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not referenced.
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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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IPIV (input) INTEGER array, dimension (N)
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Details of the interchanges and the block structure of D
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as determined by DSYTRF.
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WORK (workspace) DOUBLE PRECISION array, dimension (N)
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INFO (output) INTEGER
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= 0: successful exit
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< 0: if INFO = -i, the i-th argument had an illegal value
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> 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
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inverse could not be computed.
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=====================================================================
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Test the input parameters.
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Parameter adjustments */
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/* Table of constant values */
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static integer c__1 = 1;
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static doublereal c_b11 = -1.;
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static doublereal c_b13 = 0.;
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/* System generated locals */
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integer a_dim1, a_offset, i__1;
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doublereal d__1;
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/* Local variables */
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extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
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integer *);
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static doublereal temp, akkp1, d__;
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static integer k;
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static doublereal t;
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extern logical lsame_(char *, char *);
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extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
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doublereal *, integer *), dswap_(integer *, doublereal *, integer
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*, doublereal *, integer *);
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static integer kstep;
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static logical upper;
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extern /* Subroutine */ int dsymv_(char *, integer *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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doublereal *, integer *);
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static doublereal ak;
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static integer kp;
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extern /* Subroutine */ int xerbla_(char *, integer *);
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static doublereal akp1;
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#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
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a_dim1 = *lda;
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a_offset = 1 + a_dim1 * 1;
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a -= a_offset;
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--ipiv;
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--work;
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/* Function Body */
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*info = 0;
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upper = lsame_(uplo, "U");
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if (! upper && ! lsame_(uplo, "L")) {
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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_("DSYTRI", &i__1);
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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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/* Check that the diagonal matrix D is nonsingular. */
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if (upper) {
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/* Upper triangular storage: examine D from bottom to top */
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for (*info = *n; *info >= 1; --(*info)) {
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if (ipiv[*info] > 0 && a_ref(*info, *info) == 0.) {
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return 0;
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}
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/* L10: */
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}
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} else {
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/* Lower triangular storage: examine D from top to bottom. */
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i__1 = *n;
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for (*info = 1; *info <= i__1; ++(*info)) {
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if (ipiv[*info] > 0 && a_ref(*info, *info) == 0.) {
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return 0;
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}
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/* L20: */
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}
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}
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*info = 0;
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if (upper) {
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/* Compute inv(A) from the factorization A = U*D*U'.
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K is the main loop index, increasing from 1 to N in steps of
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1 or 2, depending on the size of the diagonal blocks. */
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k = 1;
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L30:
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/* If K > N, exit from loop. */
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if (k > *n) {
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goto L40;
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}
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if (ipiv[k] > 0) {
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/* 1 x 1 diagonal block
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Invert the diagonal block. */
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a_ref(k, k) = 1. / a_ref(k, k);
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/* Compute column K of the inverse. */
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if (k > 1) {
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i__1 = k - 1;
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dcopy_(&i__1, &a_ref(1, k), &c__1, &work[1], &c__1);
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i__1 = k - 1;
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dsymv_(uplo, &i__1, &c_b11, &a[a_offset], lda, &work[1], &
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c__1, &c_b13, &a_ref(1, k), &c__1);
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i__1 = k - 1;
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a_ref(k, k) = a_ref(k, k) - ddot_(&i__1, &work[1], &c__1, &
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a_ref(1, k), &c__1);
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}
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kstep = 1;
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} else {
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/* 2 x 2 diagonal block
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Invert the diagonal block. */
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t = (d__1 = a_ref(k, k + 1), abs(d__1));
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ak = a_ref(k, k) / t;
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akp1 = a_ref(k + 1, k + 1) / t;
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akkp1 = a_ref(k, k + 1) / t;
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d__ = t * (ak * akp1 - 1.);
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a_ref(k, k) = akp1 / d__;
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a_ref(k + 1, k + 1) = ak / d__;
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a_ref(k, k + 1) = -akkp1 / d__;
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/* Compute columns K and K+1 of the inverse. */
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if (k > 1) {
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i__1 = k - 1;
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dcopy_(&i__1, &a_ref(1, k), &c__1, &work[1], &c__1);
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i__1 = k - 1;
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dsymv_(uplo, &i__1, &c_b11, &a[a_offset], lda, &work[1], &
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c__1, &c_b13, &a_ref(1, k), &c__1);
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i__1 = k - 1;
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a_ref(k, k) = a_ref(k, k) - ddot_(&i__1, &work[1], &c__1, &
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a_ref(1, k), &c__1);
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i__1 = k - 1;
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a_ref(k, k + 1) = a_ref(k, k + 1) - ddot_(&i__1, &a_ref(1, k),
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&c__1, &a_ref(1, k + 1), &c__1);
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i__1 = k - 1;
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dcopy_(&i__1, &a_ref(1, k + 1), &c__1, &work[1], &c__1);
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i__1 = k - 1;
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dsymv_(uplo, &i__1, &c_b11, &a[a_offset], lda, &work[1], &
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c__1, &c_b13, &a_ref(1, k + 1), &c__1);
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i__1 = k - 1;
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a_ref(k + 1, k + 1) = a_ref(k + 1, k + 1) - ddot_(&i__1, &
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work[1], &c__1, &a_ref(1, k + 1), &c__1);
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}
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kstep = 2;
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}
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kp = (i__1 = ipiv[k], abs(i__1));
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if (kp != k) {
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/* Interchange rows and columns K and KP in the leading
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submatrix A(1:k+1,1:k+1) */
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i__1 = kp - 1;
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dswap_(&i__1, &a_ref(1, k), &c__1, &a_ref(1, kp), &c__1);
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i__1 = k - kp - 1;
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dswap_(&i__1, &a_ref(kp + 1, k), &c__1, &a_ref(kp, kp + 1), lda);
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temp = a_ref(k, k);
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a_ref(k, k) = a_ref(kp, kp);
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a_ref(kp, kp) = temp;
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if (kstep == 2) {
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temp = a_ref(k, k + 1);
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a_ref(k, k + 1) = a_ref(kp, k + 1);
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a_ref(kp, k + 1) = temp;
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}
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}
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k += kstep;
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goto L30;
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L40:
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;
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} else {
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/* Compute inv(A) from the factorization A = L*D*L'.
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K is the main loop index, increasing from 1 to N in steps of
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1 or 2, depending on the size of the diagonal blocks. */
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k = *n;
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L50:
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/* If K < 1, exit from loop. */
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if (k < 1) {
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goto L60;
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}
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if (ipiv[k] > 0) {
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/* 1 x 1 diagonal block
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Invert the diagonal block. */
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a_ref(k, k) = 1. / a_ref(k, k);
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/* Compute column K of the inverse. */
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if (k < *n) {
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i__1 = *n - k;
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dcopy_(&i__1, &a_ref(k + 1, k), &c__1, &work[1], &c__1);
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i__1 = *n - k;
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dsymv_(uplo, &i__1, &c_b11, &a_ref(k + 1, k + 1), lda, &work[
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1], &c__1, &c_b13, &a_ref(k + 1, k), &c__1)
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;
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i__1 = *n - k;
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a_ref(k, k) = a_ref(k, k) - ddot_(&i__1, &work[1], &c__1, &
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a_ref(k + 1, k), &c__1);
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}
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kstep = 1;
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} else {
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/* 2 x 2 diagonal block
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Invert the diagonal block. */
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t = (d__1 = a_ref(k, k - 1), abs(d__1));
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ak = a_ref(k - 1, k - 1) / t;
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akp1 = a_ref(k, k) / t;
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akkp1 = a_ref(k, k - 1) / t;
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d__ = t * (ak * akp1 - 1.);
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a_ref(k - 1, k - 1) = akp1 / d__;
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a_ref(k, k) = ak / d__;
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a_ref(k, k - 1) = -akkp1 / d__;
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/* Compute columns K-1 and K of the inverse. */
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if (k < *n) {
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i__1 = *n - k;
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dcopy_(&i__1, &a_ref(k + 1, k), &c__1, &work[1], &c__1);
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i__1 = *n - k;
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dsymv_(uplo, &i__1, &c_b11, &a_ref(k + 1, k + 1), lda, &work[
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1], &c__1, &c_b13, &a_ref(k + 1, k), &c__1)
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;
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i__1 = *n - k;
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a_ref(k, k) = a_ref(k, k) - ddot_(&i__1, &work[1], &c__1, &
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a_ref(k + 1, k), &c__1);
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i__1 = *n - k;
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a_ref(k, k - 1) = a_ref(k, k - 1) - ddot_(&i__1, &a_ref(k + 1,
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k), &c__1, &a_ref(k + 1, k - 1), &c__1);
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i__1 = *n - k;
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dcopy_(&i__1, &a_ref(k + 1, k - 1), &c__1, &work[1], &c__1);
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i__1 = *n - k;
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dsymv_(uplo, &i__1, &c_b11, &a_ref(k + 1, k + 1), lda, &work[
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1], &c__1, &c_b13, &a_ref(k + 1, k - 1), &c__1);
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i__1 = *n - k;
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a_ref(k - 1, k - 1) = a_ref(k - 1, k - 1) - ddot_(&i__1, &
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work[1], &c__1, &a_ref(k + 1, k - 1), &c__1);
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}
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kstep = 2;
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}
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kp = (i__1 = ipiv[k], abs(i__1));
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if (kp != k) {
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/* Interchange rows and columns K and KP in the trailing
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submatrix A(k-1:n,k-1:n) */
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if (kp < *n) {
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i__1 = *n - kp;
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dswap_(&i__1, &a_ref(kp + 1, k), &c__1, &a_ref(kp + 1, kp), &
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c__1);
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}
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i__1 = kp - k - 1;
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dswap_(&i__1, &a_ref(k + 1, k), &c__1, &a_ref(kp, k + 1), lda);
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temp = a_ref(k, k);
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a_ref(k, k) = a_ref(kp, kp);
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a_ref(kp, kp) = temp;
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if (kstep == 2) {
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temp = a_ref(k, k - 1);
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a_ref(k, k - 1) = a_ref(kp, k - 1);
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a_ref(kp, k - 1) = temp;
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}
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}
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k -= kstep;
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goto L50;
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L60:
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;
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}
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return 0;
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/* End of DSYTRI */
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} /* dsytri_ */
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#undef a_ref
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