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453 lines
12 KiB
453 lines
12 KiB
/* dsytrs.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 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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/* 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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/* 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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integer j, k; |
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doublereal ak, bk; |
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integer kp; |
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doublereal akm1, bkm1; |
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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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doublereal akm1k; |
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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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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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logical upper; |
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extern /* Subroutine */ int 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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/* 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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/* .. 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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/* 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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b_dim1 = *ldb; |
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b_offset = 1 + b_dim1; |
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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[k + b_dim1], ldb, &b[kp + b_dim1], 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[k * a_dim1 + 1], &c__1, &b[k + |
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b_dim1], ldb, &b[b_dim1 + 1], ldb); |
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/* Multiply by the inverse of the diagonal block. */ |
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d__1 = 1. / a[k + k * a_dim1]; |
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dscal_(nrhs, &d__1, &b[k + b_dim1], 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[k - 1 + b_dim1], ldb, &b[kp + b_dim1], 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[k * a_dim1 + 1], &c__1, &b[k + |
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b_dim1], ldb, &b[b_dim1 + 1], ldb); |
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i__1 = k - 2; |
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dger_(&i__1, nrhs, &c_b7, &a[(k - 1) * a_dim1 + 1], &c__1, &b[k - |
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1 + b_dim1], ldb, &b[b_dim1 + 1], ldb); |
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/* Multiply by the inverse of the diagonal block. */ |
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akm1k = a[k - 1 + k * a_dim1]; |
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akm1 = a[k - 1 + (k - 1) * a_dim1] / akm1k; |
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ak = a[k + k * a_dim1] / 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[k - 1 + j * b_dim1] / akm1k; |
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bk = b[k + j * b_dim1] / akm1k; |
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b[k - 1 + j * b_dim1] = (ak * bkm1 - bk) / denom; |
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b[k + j * b_dim1] = (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[k * |
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a_dim1 + 1], &c__1, &c_b19, &b[k + b_dim1], 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[k + b_dim1], ldb, &b[kp + b_dim1], 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[k * |
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a_dim1 + 1], &c__1, &c_b19, &b[k + b_dim1], 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[(k |
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+ 1) * a_dim1 + 1], &c__1, &c_b19, &b[k + 1 + b_dim1], |
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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[k + b_dim1], ldb, &b[kp + b_dim1], 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[k + b_dim1], ldb, &b[kp + b_dim1], 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[k + 1 + k * a_dim1], &c__1, &b[k |
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+ b_dim1], ldb, &b[k + 1 + b_dim1], 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[k + k * a_dim1]; |
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dscal_(nrhs, &d__1, &b[k + b_dim1], 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[k + 1 + b_dim1], ldb, &b[kp + b_dim1], 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[k + 2 + k * a_dim1], &c__1, &b[k |
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+ b_dim1], ldb, &b[k + 2 + b_dim1], ldb); |
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i__1 = *n - k - 1; |
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dger_(&i__1, nrhs, &c_b7, &a[k + 2 + (k + 1) * a_dim1], &c__1, |
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&b[k + 1 + b_dim1], ldb, &b[k + 2 + b_dim1], ldb); |
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} |
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/* Multiply by the inverse of the diagonal block. */ |
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akm1k = a[k + 1 + k * a_dim1]; |
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akm1 = a[k + k * a_dim1] / akm1k; |
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ak = a[k + 1 + (k + 1) * a_dim1] / 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[k + j * b_dim1] / akm1k; |
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bk = b[k + 1 + j * b_dim1] / akm1k; |
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b[k + j * b_dim1] = (ak * bkm1 - bk) / denom; |
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b[k + 1 + j * b_dim1] = (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[k + 1 + b_dim1], |
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ldb, &a[k + 1 + k * a_dim1], &c__1, &c_b19, &b[k + |
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b_dim1], 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[k + b_dim1], ldb, &b[kp + b_dim1], 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[k + 1 + b_dim1], |
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ldb, &a[k + 1 + k * a_dim1], &c__1, &c_b19, &b[k + |
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b_dim1], ldb); |
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i__1 = *n - k; |
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dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[k + 1 + b_dim1], |
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ldb, &a[k + 1 + (k - 1) * a_dim1], &c__1, &c_b19, &b[ |
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k - 1 + b_dim1], 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[k + b_dim1], ldb, &b[kp + b_dim1], 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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