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396 lines
11 KiB
396 lines
11 KiB
/* dsytri.f -- translated by f2c (version 20061008). |
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You must link the resulting object file with libf2c: |
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on Microsoft Windows system, link with libf2c.lib; |
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
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or, if you install libf2c.a in a standard place, with -lf2c -lm |
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-- in that order, at the end of the command line, as in |
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cc *.o -lf2c -lm |
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
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http://www.netlib.org/f2c/libf2c.zip |
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*/ |
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#include "clapack.h" |
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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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/* 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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/* 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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doublereal d__; |
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integer k; |
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doublereal t, ak; |
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integer kp; |
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doublereal akp1; |
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extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, |
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integer *); |
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doublereal temp, akkp1; |
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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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integer kstep; |
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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 *), xerbla_(char *, integer *); |
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/* -- LAPACK routine (version 3.2) -- */ |
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
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/* November 2006 */ |
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/* .. Scalar Arguments .. */ |
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/* .. */ |
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/* .. Array Arguments .. */ |
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/* .. */ |
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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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/* .. Parameters .. */ |
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/* .. */ |
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/* .. Local Scalars .. */ |
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/* .. */ |
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/* .. External Functions .. */ |
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/* .. */ |
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/* .. External Subroutines .. */ |
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/* .. */ |
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/* .. Intrinsic Functions .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Test the input parameters. */ |
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/* Parameter adjustments */ |
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a_dim1 = *lda; |
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a_offset = 1 + a_dim1; |
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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[*info + *info * a_dim1] == 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[*info + *info * a_dim1] == 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[k + k * a_dim1] = 1. / a[k + k * a_dim1]; |
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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[k * a_dim1 + 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[k * a_dim1 + 1], &c__1); |
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i__1 = k - 1; |
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a[k + k * a_dim1] -= ddot_(&i__1, &work[1], &c__1, &a[k * |
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a_dim1 + 1], &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[k + (k + 1) * a_dim1], abs(d__1)); |
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ak = a[k + k * a_dim1] / t; |
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akp1 = a[k + 1 + (k + 1) * a_dim1] / t; |
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akkp1 = a[k + (k + 1) * a_dim1] / t; |
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d__ = t * (ak * akp1 - 1.); |
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a[k + k * a_dim1] = akp1 / d__; |
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a[k + 1 + (k + 1) * a_dim1] = ak / d__; |
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a[k + (k + 1) * a_dim1] = -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[k * a_dim1 + 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[k * a_dim1 + 1], &c__1); |
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i__1 = k - 1; |
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a[k + k * a_dim1] -= ddot_(&i__1, &work[1], &c__1, &a[k * |
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a_dim1 + 1], &c__1); |
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i__1 = k - 1; |
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a[k + (k + 1) * a_dim1] -= ddot_(&i__1, &a[k * a_dim1 + 1], & |
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c__1, &a[(k + 1) * a_dim1 + 1], &c__1); |
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i__1 = k - 1; |
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dcopy_(&i__1, &a[(k + 1) * a_dim1 + 1], &c__1, &work[1], & |
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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[(k + 1) * a_dim1 + 1], &c__1); |
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i__1 = k - 1; |
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a[k + 1 + (k + 1) * a_dim1] -= ddot_(&i__1, &work[1], &c__1, & |
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a[(k + 1) * a_dim1 + 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[k * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], & |
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c__1); |
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i__1 = k - kp - 1; |
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dswap_(&i__1, &a[kp + 1 + k * a_dim1], &c__1, &a[kp + (kp + 1) * |
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a_dim1], lda); |
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temp = a[k + k * a_dim1]; |
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a[k + k * a_dim1] = a[kp + kp * a_dim1]; |
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a[kp + kp * a_dim1] = temp; |
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if (kstep == 2) { |
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temp = a[k + (k + 1) * a_dim1]; |
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a[k + (k + 1) * a_dim1] = a[kp + (k + 1) * a_dim1]; |
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a[kp + (k + 1) * a_dim1] = 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[k + k * a_dim1] = 1. / a[k + k * a_dim1]; |
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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[k + 1 + k * a_dim1], &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[k + 1 + (k + 1) * a_dim1], lda, |
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&work[1], &c__1, &c_b13, &a[k + 1 + k * a_dim1], & |
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c__1); |
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i__1 = *n - k; |
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a[k + k * a_dim1] -= ddot_(&i__1, &work[1], &c__1, &a[k + 1 + |
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k * a_dim1], &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[k + (k - 1) * a_dim1], abs(d__1)); |
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ak = a[k - 1 + (k - 1) * a_dim1] / t; |
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akp1 = a[k + k * a_dim1] / t; |
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akkp1 = a[k + (k - 1) * a_dim1] / t; |
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d__ = t * (ak * akp1 - 1.); |
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a[k - 1 + (k - 1) * a_dim1] = akp1 / d__; |
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a[k + k * a_dim1] = ak / d__; |
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a[k + (k - 1) * a_dim1] = -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[k + 1 + k * a_dim1], &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[k + 1 + (k + 1) * a_dim1], lda, |
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&work[1], &c__1, &c_b13, &a[k + 1 + k * a_dim1], & |
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c__1); |
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i__1 = *n - k; |
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a[k + k * a_dim1] -= ddot_(&i__1, &work[1], &c__1, &a[k + 1 + |
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k * a_dim1], &c__1); |
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i__1 = *n - k; |
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a[k + (k - 1) * a_dim1] -= ddot_(&i__1, &a[k + 1 + k * a_dim1] |
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, &c__1, &a[k + 1 + (k - 1) * a_dim1], &c__1); |
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i__1 = *n - k; |
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dcopy_(&i__1, &a[k + 1 + (k - 1) * a_dim1], &c__1, &work[1], & |
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c__1); |
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i__1 = *n - k; |
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dsymv_(uplo, &i__1, &c_b11, &a[k + 1 + (k + 1) * a_dim1], lda, |
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&work[1], &c__1, &c_b13, &a[k + 1 + (k - 1) * a_dim1] |
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, &c__1); |
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i__1 = *n - k; |
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a[k - 1 + (k - 1) * a_dim1] -= ddot_(&i__1, &work[1], &c__1, & |
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a[k + 1 + (k - 1) * a_dim1], &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[kp + 1 + k * a_dim1], &c__1, &a[kp + 1 + kp * |
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a_dim1], &c__1); |
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} |
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i__1 = kp - k - 1; |
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dswap_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[kp + (k + 1) * |
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a_dim1], lda); |
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temp = a[k + k * a_dim1]; |
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a[k + k * a_dim1] = a[kp + kp * a_dim1]; |
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a[kp + kp * a_dim1] = temp; |
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if (kstep == 2) { |
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temp = a[k + (k - 1) * a_dim1]; |
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a[k + (k - 1) * a_dim1] = a[kp + (k - 1) * a_dim1]; |
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a[kp + (k - 1) * a_dim1] = 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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