[BACK]Return to dtrsyl.f CVS log [TXT] [DIR] Up to [local] / rpl / lapack / lapack

Diff for /rpl/lapack/lapack/dtrsyl.f between versions 1.8 and 1.9

version 1.8, 2011/07/22 07:38:13 version 1.9, 2011/11/21 20:43:06
Line 1 Line 1
   *> \brief \b DTRSYL
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DTRSYL + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrsyl.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrsyl.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrsyl.f"> 
   *> [TXT]</a>
   *> \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,        SUBROUTINE DTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
      $                   LDC, SCALE, INFO )       $                   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,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          TRANA, TRANB        CHARACTER          TRANA, TRANB
Line 15 Line 178
       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), C( LDC, * )        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 ..  *     .. Parameters ..
Line 363 Line 451
 *          A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)  *          A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
 *  *
 *        Where  *        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)]  *          R(K,L) = SUM [A(I,K)**T*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)]
 *                   I=1                          J=1  *                   I=1                          J=1
 *  *
Removed from v.1.8  
changed lines
  Added in v.1.9

CVSweb interface <joel.bertrand@systella.fr>