--- rpl/lapack/lapack/dtrsyl.f 2011/07/22 07:38:13 1.8 +++ rpl/lapack/lapack/dtrsyl.f 2011/11/21 20:43:06 1.9 @@ -1,10 +1,173 @@ +*> \brief \b DTRSYL +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DTRSYL + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, +* LDC, SCALE, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER TRANA, TRANB +* INTEGER INFO, ISGN, LDA, LDB, LDC, M, N +* DOUBLE PRECISION SCALE +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DTRSYL solves the real Sylvester matrix equation: +*> +*> op(A)*X + X*op(B) = scale*C or +*> op(A)*X - X*op(B) = scale*C, +*> +*> where op(A) = A or A**T, and A and B are both upper quasi- +*> triangular. A is M-by-M and B is N-by-N; the right hand side C and +*> the solution X are M-by-N; and scale is an output scale factor, set +*> <= 1 to avoid overflow in X. +*> +*> A and B must be in Schur canonical form (as returned by DHSEQR), that +*> is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; +*> each 2-by-2 diagonal block has its diagonal elements equal and its +*> off-diagonal elements of opposite sign. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] TRANA +*> \verbatim +*> TRANA is CHARACTER*1 +*> Specifies the option op(A): +*> = 'N': op(A) = A (No transpose) +*> = 'T': op(A) = A**T (Transpose) +*> = 'C': op(A) = A**H (Conjugate transpose = Transpose) +*> \endverbatim +*> +*> \param[in] TRANB +*> \verbatim +*> TRANB is CHARACTER*1 +*> Specifies the option op(B): +*> = 'N': op(B) = B (No transpose) +*> = 'T': op(B) = B**T (Transpose) +*> = 'C': op(B) = B**H (Conjugate transpose = Transpose) +*> \endverbatim +*> +*> \param[in] ISGN +*> \verbatim +*> ISGN is INTEGER +*> Specifies the sign in the equation: +*> = +1: solve op(A)*X + X*op(B) = scale*C +*> = -1: solve op(A)*X - X*op(B) = scale*C +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The order of the matrix A, and the number of rows in the +*> matrices X and C. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix B, and the number of columns in the +*> matrices X and C. N >= 0. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,M) +*> The upper quasi-triangular matrix A, in Schur canonical form. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is DOUBLE PRECISION array, dimension (LDB,N) +*> The upper quasi-triangular matrix B, in Schur canonical form. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= max(1,N). +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is DOUBLE PRECISION array, dimension (LDC,N) +*> On entry, the M-by-N right hand side matrix C. +*> On exit, C is overwritten by the solution matrix X. +*> \endverbatim +*> +*> \param[in] LDC +*> \verbatim +*> LDC is INTEGER +*> The leading dimension of the array C. LDC >= max(1,M) +*> \endverbatim +*> +*> \param[out] SCALE +*> \verbatim +*> SCALE is DOUBLE PRECISION +*> The scale factor, scale, set <= 1 to avoid overflow in X. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> = 1: A and B have common or very close eigenvalues; perturbed +*> values were used to solve the equation (but the matrices +*> A and B are unchanged). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleSYcomputational +* +* ===================================================================== SUBROUTINE DTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, $ LDC, SCALE, INFO ) * -* -- LAPACK routine (version 3.3.1) -- +* -- LAPACK computational routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -- April 2011 -- +* November 2011 * * .. Scalar Arguments .. CHARACTER TRANA, TRANB @@ -15,81 +178,6 @@ DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ) * .. * -* Purpose -* ======= -* -* DTRSYL solves the real Sylvester matrix equation: -* -* op(A)*X + X*op(B) = scale*C or -* op(A)*X - X*op(B) = scale*C, -* -* where op(A) = A or A**T, and A and B are both upper quasi- -* triangular. A is M-by-M and B is N-by-N; the right hand side C and -* the solution X are M-by-N; and scale is an output scale factor, set -* <= 1 to avoid overflow in X. -* -* A and B must be in Schur canonical form (as returned by DHSEQR), that -* is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; -* each 2-by-2 diagonal block has its diagonal elements equal and its -* off-diagonal elements of opposite sign. -* -* Arguments -* ========= -* -* TRANA (input) CHARACTER*1 -* Specifies the option op(A): -* = 'N': op(A) = A (No transpose) -* = 'T': op(A) = A**T (Transpose) -* = 'C': op(A) = A**H (Conjugate transpose = Transpose) -* -* TRANB (input) CHARACTER*1 -* Specifies the option op(B): -* = 'N': op(B) = B (No transpose) -* = 'T': op(B) = B**T (Transpose) -* = 'C': op(B) = B**H (Conjugate transpose = Transpose) -* -* ISGN (input) INTEGER -* Specifies the sign in the equation: -* = +1: solve op(A)*X + X*op(B) = scale*C -* = -1: solve op(A)*X - X*op(B) = scale*C -* -* M (input) INTEGER -* The order of the matrix A, and the number of rows in the -* matrices X and C. M >= 0. -* -* N (input) INTEGER -* The order of the matrix B, and the number of columns in the -* matrices X and C. N >= 0. -* -* A (input) DOUBLE PRECISION array, dimension (LDA,M) -* The upper quasi-triangular matrix A, in Schur canonical form. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). -* -* B (input) DOUBLE PRECISION array, dimension (LDB,N) -* The upper quasi-triangular matrix B, in Schur canonical form. -* -* LDB (input) INTEGER -* The leading dimension of the array B. LDB >= max(1,N). -* -* C (input/output) DOUBLE PRECISION array, dimension (LDC,N) -* On entry, the M-by-N right hand side matrix C. -* On exit, C is overwritten by the solution matrix X. -* -* LDC (input) INTEGER -* The leading dimension of the array C. LDC >= max(1,M) -* -* SCALE (output) DOUBLE PRECISION -* The scale factor, scale, set <= 1 to avoid overflow in X. -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* = 1: A and B have common or very close eigenvalues; perturbed -* values were used to solve the equation (but the matrices -* A and B are unchanged). -* * ===================================================================== * * .. Parameters .. @@ -363,7 +451,7 @@ * A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L) * * Where -* K-1 L-1 +* K-1 T L-1 * R(K,L) = SUM [A(I,K)**T*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)] * I=1 J=1 *