230 lines
6.3 KiB
C
230 lines
6.3 KiB
C
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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 integer c_n1 = -1;
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static integer c__2 = 2;
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static doublereal c_b18 = 1.;
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static doublereal c_b22 = -1.;
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/* Subroutine */ int dtrtri_(char *uplo, char *diag, integer *n, doublereal *
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a, integer *lda, integer *info)
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{
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/* System generated locals */
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address a__1[2];
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integer a_dim1, a_offset, i__1, i__2[2], i__3, i__4, i__5;
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char ch__1[2];
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/* Builtin functions */
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/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
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/* Local variables */
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integer j, jb, nb, nn;
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extern logical lsame_(char *, char *);
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extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *,
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integer *, integer *, doublereal *, doublereal *, integer *,
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doublereal *, integer *), dtrsm_(
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char *, char *, char *, char *, integer *, integer *, doublereal *
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, doublereal *, integer *, doublereal *, integer *);
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logical upper;
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extern /* Subroutine */ int dtrti2_(char *, char *, integer *, doublereal
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*, integer *, integer *), xerbla_(char *, integer
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*);
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *);
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logical nounit;
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/* -- LAPACK routine (version 3.1) -- */
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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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/* DTRTRI computes the inverse of a real upper or lower triangular */
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/* matrix A. */
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/* This is the Level 3 BLAS version of the algorithm. */
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/* Arguments */
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/* ========= */
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/* UPLO (input) CHARACTER*1 */
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/* = 'U': A is upper triangular; */
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/* = 'L': A is lower triangular. */
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/* DIAG (input) CHARACTER*1 */
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/* = 'N': A is non-unit triangular; */
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/* = 'U': A is unit triangular. */
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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 triangular matrix A. If UPLO = 'U', the */
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/* leading N-by-N upper triangular part of the array A contains */
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/* the upper triangular matrix, and the strictly lower */
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/* triangular part of A is not referenced. If UPLO = 'L', the */
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/* leading N-by-N lower triangular part of the array A contains */
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/* the lower triangular matrix, and the strictly upper */
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/* triangular part of A is not referenced. If DIAG = 'U', the */
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/* diagonal elements of A are also not referenced and are */
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/* assumed to be 1. */
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/* On exit, the (triangular) inverse of the original matrix, in */
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/* the same storage format. */
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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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/* 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, A(i,i) is exactly zero. The triangular */
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/* matrix is singular and its inverse can 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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/* Function Body */
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*info = 0;
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upper = lsame_(uplo, "U");
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nounit = lsame_(diag, "N");
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if (! upper && ! lsame_(uplo, "L")) {
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*info = -1;
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} else if (! nounit && ! lsame_(diag, "U")) {
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*info = -2;
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} else if (*n < 0) {
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*info = -3;
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} else if (*lda < max(1,*n)) {
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*info = -5;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DTRTRI", &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 for singularity if non-unit. */
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if (nounit) {
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i__1 = *n;
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for (*info = 1; *info <= i__1; ++(*info)) {
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if (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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*info = 0;
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}
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/* Determine the block size for this environment. */
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/* Writing concatenation */
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i__2[0] = 1, a__1[0] = uplo;
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i__2[1] = 1, a__1[1] = diag;
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s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2);
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nb = ilaenv_(&c__1, "DTRTRI", ch__1, n, &c_n1, &c_n1, &c_n1);
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if (nb <= 1 || nb >= *n) {
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/* Use unblocked code */
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dtrti2_(uplo, diag, n, &a[a_offset], lda, info);
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} else {
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/* Use blocked code */
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if (upper) {
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/* Compute inverse of upper triangular matrix */
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i__1 = *n;
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i__3 = nb;
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for (j = 1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) {
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/* Computing MIN */
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i__4 = nb, i__5 = *n - j + 1;
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jb = min(i__4,i__5);
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/* Compute rows 1:j-1 of current block column */
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i__4 = j - 1;
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dtrmm_("Left", "Upper", "No transpose", diag, &i__4, &jb, &
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c_b18, &a[a_offset], lda, &a[j * a_dim1 + 1], lda);
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i__4 = j - 1;
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dtrsm_("Right", "Upper", "No transpose", diag, &i__4, &jb, &
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c_b22, &a[j + j * a_dim1], lda, &a[j * a_dim1 + 1],
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lda);
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/* Compute inverse of current diagonal block */
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dtrti2_("Upper", diag, &jb, &a[j + j * a_dim1], lda, info);
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/* L20: */
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}
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} else {
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/* Compute inverse of lower triangular matrix */
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nn = (*n - 1) / nb * nb + 1;
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i__3 = -nb;
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for (j = nn; i__3 < 0 ? j >= 1 : j <= 1; j += i__3) {
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/* Computing MIN */
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i__1 = nb, i__4 = *n - j + 1;
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jb = min(i__1,i__4);
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if (j + jb <= *n) {
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/* Compute rows j+jb:n of current block column */
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i__1 = *n - j - jb + 1;
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dtrmm_("Left", "Lower", "No transpose", diag, &i__1, &jb,
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&c_b18, &a[j + jb + (j + jb) * a_dim1], lda, &a[j
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+ jb + j * a_dim1], lda);
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i__1 = *n - j - jb + 1;
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dtrsm_("Right", "Lower", "No transpose", diag, &i__1, &jb,
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&c_b22, &a[j + j * a_dim1], lda, &a[j + jb + j *
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a_dim1], lda);
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}
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/* Compute inverse of current diagonal block */
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dtrti2_("Lower", diag, &jb, &a[j + j * a_dim1], lda, info);
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/* L30: */
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}
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}
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}
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return 0;
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/* End of DTRTRI */
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} /* dtrtri_ */
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