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367 lines
9.6 KiB
367 lines
9.6 KiB
#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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