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428 lines
11 KiB
428 lines
11 KiB
#include "clapack.h" |
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/* Subroutine */ int dsytrs_(char *uplo, integer *n, integer *nrhs, |
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doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer * |
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ldb, 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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DSYTRS solves a system of linear equations A*X = B with a real |
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symmetric matrix A using the factorization A = U*D*U**T or |
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A = L*D*L**T computed by 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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NRHS (input) INTEGER |
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The number of right hand sides, i.e., the number of columns |
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of the matrix B. NRHS >= 0. |
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A (input) DOUBLE PRECISION array, dimension (LDA,N) |
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The block diagonal matrix D and the multipliers used to |
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obtain the factor U or L as computed by DSYTRF. |
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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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B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) |
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On entry, the right hand side matrix B. |
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On exit, the solution matrix X. |
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LDB (input) INTEGER |
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The leading dimension of the array B. LDB >= 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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===================================================================== |
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Parameter adjustments */ |
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/* Table of constant values */ |
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static doublereal c_b7 = -1.; |
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static integer c__1 = 1; |
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static doublereal c_b19 = 1.; |
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/* System generated locals */ |
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integer a_dim1, a_offset, b_dim1, b_offset, i__1; |
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doublereal d__1; |
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/* Local variables */ |
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extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, |
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doublereal *, integer *, doublereal *, integer *, doublereal *, |
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integer *); |
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static doublereal akm1k; |
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static integer j, k; |
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extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, |
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integer *); |
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extern logical lsame_(char *, char *); |
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static doublereal denom; |
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extern /* Subroutine */ int dgemv_(char *, integer *, integer *, |
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doublereal *, doublereal *, integer *, doublereal *, integer *, |
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doublereal *, doublereal *, integer *), dswap_(integer *, |
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doublereal *, integer *, doublereal *, integer *); |
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static logical upper; |
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static doublereal ak, bk; |
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static integer kp; |
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extern /* Subroutine */ int xerbla_(char *, integer *); |
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static doublereal akm1, bkm1; |
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#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] |
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#define b_ref(a_1,a_2) b[(a_2)*b_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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b_dim1 = *ldb; |
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b_offset = 1 + b_dim1 * 1; |
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b -= b_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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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 (*nrhs < 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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} else if (*ldb < max(1,*n)) { |
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*info = -8; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("DSYTRS", &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 || *nrhs == 0) { |
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return 0; |
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} |
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if (upper) { |
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/* Solve A*X = B, where A = U*D*U'. |
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First solve U*D*X = B, overwriting B with X. |
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K is the main loop index, decreasing from N to 1 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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L10: |
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/* If K < 1, exit from loop. */ |
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if (k < 1) { |
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goto L30; |
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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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Interchange rows K and IPIV(K). */ |
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kp = ipiv[k]; |
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if (kp != k) { |
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dswap_(nrhs, &b_ref(k, 1), ldb, &b_ref(kp, 1), ldb); |
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} |
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/* Multiply by inv(U(K)), where U(K) is the transformation |
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stored in column K of A. */ |
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i__1 = k - 1; |
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dger_(&i__1, nrhs, &c_b7, &a_ref(1, k), &c__1, &b_ref(k, 1), ldb, |
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&b_ref(1, 1), ldb); |
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/* Multiply by the inverse of the diagonal block. */ |
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d__1 = 1. / a_ref(k, k); |
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dscal_(nrhs, &d__1, &b_ref(k, 1), ldb); |
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--k; |
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} else { |
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/* 2 x 2 diagonal block |
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Interchange rows K-1 and -IPIV(K). */ |
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kp = -ipiv[k]; |
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if (kp != k - 1) { |
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dswap_(nrhs, &b_ref(k - 1, 1), ldb, &b_ref(kp, 1), ldb); |
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} |
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/* Multiply by inv(U(K)), where U(K) is the transformation |
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stored in columns K-1 and K of A. */ |
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i__1 = k - 2; |
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dger_(&i__1, nrhs, &c_b7, &a_ref(1, k), &c__1, &b_ref(k, 1), ldb, |
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&b_ref(1, 1), ldb); |
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i__1 = k - 2; |
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dger_(&i__1, nrhs, &c_b7, &a_ref(1, k - 1), &c__1, &b_ref(k - 1, |
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1), ldb, &b_ref(1, 1), ldb); |
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/* Multiply by the inverse of the diagonal block. */ |
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akm1k = a_ref(k - 1, k); |
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akm1 = a_ref(k - 1, k - 1) / akm1k; |
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ak = a_ref(k, k) / akm1k; |
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denom = akm1 * ak - 1.; |
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i__1 = *nrhs; |
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for (j = 1; j <= i__1; ++j) { |
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bkm1 = b_ref(k - 1, j) / akm1k; |
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bk = b_ref(k, j) / akm1k; |
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b_ref(k - 1, j) = (ak * bkm1 - bk) / denom; |
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b_ref(k, j) = (akm1 * bk - bkm1) / denom; |
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/* L20: */ |
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} |
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k += -2; |
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} |
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goto L10; |
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L30: |
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/* Next solve U'*X = B, overwriting B with X. |
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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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L40: |
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/* If K > N, exit from loop. */ |
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if (k > *n) { |
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goto L50; |
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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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Multiply by inv(U'(K)), where U(K) is the transformation |
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stored in column K of A. */ |
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i__1 = k - 1; |
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dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[b_offset], ldb, &a_ref( |
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1, k), &c__1, &c_b19, &b_ref(k, 1), ldb); |
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/* Interchange rows K and IPIV(K). */ |
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kp = ipiv[k]; |
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if (kp != k) { |
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dswap_(nrhs, &b_ref(k, 1), ldb, &b_ref(kp, 1), ldb); |
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} |
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++k; |
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} else { |
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/* 2 x 2 diagonal block |
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Multiply by inv(U'(K+1)), where U(K+1) is the transformation |
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stored in columns K and K+1 of A. */ |
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i__1 = k - 1; |
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dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[b_offset], ldb, &a_ref( |
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1, k), &c__1, &c_b19, &b_ref(k, 1), ldb); |
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i__1 = k - 1; |
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dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[b_offset], ldb, &a_ref( |
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1, k + 1), &c__1, &c_b19, &b_ref(k + 1, 1), ldb); |
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/* Interchange rows K and -IPIV(K). */ |
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kp = -ipiv[k]; |
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if (kp != k) { |
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dswap_(nrhs, &b_ref(k, 1), ldb, &b_ref(kp, 1), ldb); |
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} |
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k += 2; |
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} |
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goto L40; |
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L50: |
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; |
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} else { |
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/* Solve A*X = B, where A = L*D*L'. |
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First solve L*D*X = B, overwriting B with X. |
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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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L60: |
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/* If K > N, exit from loop. */ |
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if (k > *n) { |
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goto L80; |
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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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Interchange rows K and IPIV(K). */ |
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kp = ipiv[k]; |
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if (kp != k) { |
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dswap_(nrhs, &b_ref(k, 1), ldb, &b_ref(kp, 1), ldb); |
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} |
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/* Multiply by inv(L(K)), where L(K) is the transformation |
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stored in column K of A. */ |
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if (k < *n) { |
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i__1 = *n - k; |
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dger_(&i__1, nrhs, &c_b7, &a_ref(k + 1, k), &c__1, &b_ref(k, |
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1), ldb, &b_ref(k + 1, 1), ldb); |
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} |
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/* Multiply by the inverse of the diagonal block. */ |
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d__1 = 1. / a_ref(k, k); |
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dscal_(nrhs, &d__1, &b_ref(k, 1), ldb); |
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++k; |
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} else { |
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/* 2 x 2 diagonal block |
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Interchange rows K+1 and -IPIV(K). */ |
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kp = -ipiv[k]; |
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if (kp != k + 1) { |
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dswap_(nrhs, &b_ref(k + 1, 1), ldb, &b_ref(kp, 1), ldb); |
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} |
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/* Multiply by inv(L(K)), where L(K) is the transformation |
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stored in columns K and K+1 of A. */ |
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if (k < *n - 1) { |
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i__1 = *n - k - 1; |
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dger_(&i__1, nrhs, &c_b7, &a_ref(k + 2, k), &c__1, &b_ref(k, |
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1), ldb, &b_ref(k + 2, 1), ldb); |
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i__1 = *n - k - 1; |
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dger_(&i__1, nrhs, &c_b7, &a_ref(k + 2, k + 1), &c__1, &b_ref( |
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k + 1, 1), ldb, &b_ref(k + 2, 1), ldb); |
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} |
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/* Multiply by the inverse of the diagonal block. */ |
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akm1k = a_ref(k + 1, k); |
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akm1 = a_ref(k, k) / akm1k; |
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ak = a_ref(k + 1, k + 1) / akm1k; |
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denom = akm1 * ak - 1.; |
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i__1 = *nrhs; |
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for (j = 1; j <= i__1; ++j) { |
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bkm1 = b_ref(k, j) / akm1k; |
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bk = b_ref(k + 1, j) / akm1k; |
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b_ref(k, j) = (ak * bkm1 - bk) / denom; |
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b_ref(k + 1, j) = (akm1 * bk - bkm1) / denom; |
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/* L70: */ |
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} |
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k += 2; |
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} |
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goto L60; |
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L80: |
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/* Next solve L'*X = B, overwriting B with X. |
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K is the main loop index, decreasing from N to 1 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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L90: |
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/* If K < 1, exit from loop. */ |
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if (k < 1) { |
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goto L100; |
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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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Multiply by inv(L'(K)), where L(K) is the transformation |
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stored in column K of A. */ |
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if (k < *n) { |
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i__1 = *n - k; |
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dgemv_("Transpose", &i__1, nrhs, &c_b7, &b_ref(k + 1, 1), ldb, |
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&a_ref(k + 1, k), &c__1, &c_b19, &b_ref(k, 1), ldb); |
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} |
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/* Interchange rows K and IPIV(K). */ |
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kp = ipiv[k]; |
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if (kp != k) { |
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dswap_(nrhs, &b_ref(k, 1), ldb, &b_ref(kp, 1), ldb); |
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} |
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--k; |
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} else { |
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/* 2 x 2 diagonal block |
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Multiply by inv(L'(K-1)), where L(K-1) is the transformation |
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stored in columns K-1 and K of A. */ |
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if (k < *n) { |
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i__1 = *n - k; |
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dgemv_("Transpose", &i__1, nrhs, &c_b7, &b_ref(k + 1, 1), ldb, |
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&a_ref(k + 1, k), &c__1, &c_b19, &b_ref(k, 1), ldb); |
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i__1 = *n - k; |
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dgemv_("Transpose", &i__1, nrhs, &c_b7, &b_ref(k + 1, 1), ldb, |
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&a_ref(k + 1, k - 1), &c__1, &c_b19, &b_ref(k - 1, 1) |
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, ldb); |
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} |
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/* Interchange rows K and -IPIV(K). */ |
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kp = -ipiv[k]; |
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if (kp != k) { |
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dswap_(nrhs, &b_ref(k, 1), ldb, &b_ref(kp, 1), ldb); |
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} |
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k += -2; |
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} |
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goto L90; |
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L100: |
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; |
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} |
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return 0; |
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/* End of DSYTRS */ |
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} /* dsytrs_ */ |
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#undef b_ref |
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#undef a_ref |
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