--- rpl/lapack/lapack/dsytrs.f 2010/08/06 15:32:36 1.4 +++ rpl/lapack/lapack/dsytrs.f 2017/06/17 11:06:36 1.16 @@ -1,9 +1,129 @@ +*> \brief \b DSYTRS +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DSYTRS + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, LDA, LDB, N, NRHS +* .. +* .. Array Arguments .. +* INTEGER IPIV( * ) +* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DSYTRS solves a system of linear equations A*X = B with a real +*> symmetric matrix A using the factorization A = U*D*U**T or +*> A = L*D*L**T computed by DSYTRF. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> Specifies whether the details of the factorization are stored +*> as an upper or lower triangular matrix. +*> = 'U': Upper triangular, form is A = U*D*U**T; +*> = 'L': Lower triangular, form is A = L*D*L**T. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The number of right hand sides, i.e., the number of columns +*> of the matrix B. NRHS >= 0. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> The block diagonal matrix D and the multipliers used to +*> obtain the factor U or L as computed by DSYTRF. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> \endverbatim +*> +*> \param[in] IPIV +*> \verbatim +*> IPIV is INTEGER array, dimension (N) +*> Details of the interchanges and the block structure of D +*> as determined by DSYTRF. +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) +*> On entry, the right hand side matrix B. +*> On exit, the solution matrix X. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= max(1,N). +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date December 2016 +* +*> \ingroup doubleSYcomputational +* +* ===================================================================== SUBROUTINE DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * -* -- LAPACK routine (version 3.2) -- +* -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* December 2016 * * .. Scalar Arguments .. CHARACTER UPLO @@ -14,51 +134,6 @@ DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * -* Purpose -* ======= -* -* DSYTRS solves a system of linear equations A*X = B with a real -* symmetric matrix A using the factorization A = U*D*U**T or -* A = L*D*L**T computed by DSYTRF. -* -* Arguments -* ========= -* -* UPLO (input) CHARACTER*1 -* Specifies whether the details of the factorization are stored -* as an upper or lower triangular matrix. -* = 'U': Upper triangular, form is A = U*D*U**T; -* = 'L': Lower triangular, form is A = L*D*L**T. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* NRHS (input) INTEGER -* The number of right hand sides, i.e., the number of columns -* of the matrix B. NRHS >= 0. -* -* A (input) DOUBLE PRECISION array, dimension (LDA,N) -* The block diagonal matrix D and the multipliers used to -* obtain the factor U or L as computed by DSYTRF. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,N). -* -* IPIV (input) INTEGER array, dimension (N) -* Details of the interchanges and the block structure of D -* as determined by DSYTRF. -* -* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) -* On entry, the right hand side matrix B. -* On exit, the solution matrix X. -* -* LDB (input) INTEGER -* The leading dimension of the array B. LDB >= max(1,N). -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* * ===================================================================== * * .. Parameters .. @@ -107,7 +182,7 @@ * IF( UPPER ) THEN * -* Solve A*X = B, where A = U*D*U'. +* Solve A*X = B, where A = U*D*U**T. * * First solve U*D*X = B, overwriting B with X. * @@ -178,7 +253,7 @@ GO TO 10 30 CONTINUE * -* Next solve U'*X = B, overwriting B with X. +* Next solve U**T *X = B, overwriting B with X. * * K is the main loop index, increasing from 1 to N in steps of * 1 or 2, depending on the size of the diagonal blocks. @@ -195,7 +270,7 @@ * * 1 x 1 diagonal block * -* Multiply by inv(U'(K)), where U(K) is the transformation +* Multiply by inv(U**T(K)), where U(K) is the transformation * stored in column K of A. * CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ), @@ -211,7 +286,7 @@ * * 2 x 2 diagonal block * -* Multiply by inv(U'(K+1)), where U(K+1) is the transformation +* Multiply by inv(U**T(K+1)), where U(K+1) is the transformation * stored in columns K and K+1 of A. * CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ), @@ -232,7 +307,7 @@ * ELSE * -* Solve A*X = B, where A = L*D*L'. +* Solve A*X = B, where A = L*D*L**T. * * First solve L*D*X = B, overwriting B with X. * @@ -306,7 +381,7 @@ GO TO 60 80 CONTINUE * -* Next solve L'*X = B, overwriting B with X. +* Next solve L**T *X = B, overwriting B with X. * * K is the main loop index, decreasing from N to 1 in steps of * 1 or 2, depending on the size of the diagonal blocks. @@ -323,7 +398,7 @@ * * 1 x 1 diagonal block * -* Multiply by inv(L'(K)), where L(K) is the transformation +* Multiply by inv(L**T(K)), where L(K) is the transformation * stored in column K of A. * IF( K.LT.N ) @@ -340,7 +415,7 @@ * * 2 x 2 diagonal block * -* Multiply by inv(L'(K-1)), where L(K-1) is the transformation +* Multiply by inv(L**T(K-1)), where L(K-1) is the transformation * stored in columns K-1 and K of A. * IF( K.LT.N ) THEN