version 1.6, 2010/08/13 21:04:00
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version 1.13, 2014/01/27 09:28:30
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*> \brief \b DTRSYL |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download DTRSYL + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrsyl.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrsyl.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrsyl.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE DTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, |
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* LDC, SCALE, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER TRANA, TRANB |
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* INTEGER INFO, ISGN, LDA, LDB, LDC, M, N |
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* DOUBLE PRECISION SCALE |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DTRSYL solves the real Sylvester matrix equation: |
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*> |
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*> op(A)*X + X*op(B) = scale*C or |
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*> op(A)*X - X*op(B) = scale*C, |
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*> |
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*> where op(A) = A or A**T, and A and B are both upper quasi- |
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*> triangular. A is M-by-M and B is N-by-N; the right hand side C and |
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*> the solution X are M-by-N; and scale is an output scale factor, set |
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*> <= 1 to avoid overflow in X. |
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*> |
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*> A and B must be in Schur canonical form (as returned by DHSEQR), that |
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*> is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; |
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*> each 2-by-2 diagonal block has its diagonal elements equal and its |
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*> off-diagonal elements of opposite sign. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] TRANA |
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*> \verbatim |
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*> TRANA is CHARACTER*1 |
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*> Specifies the option op(A): |
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*> = 'N': op(A) = A (No transpose) |
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*> = 'T': op(A) = A**T (Transpose) |
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*> = 'C': op(A) = A**H (Conjugate transpose = Transpose) |
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*> \endverbatim |
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*> |
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*> \param[in] TRANB |
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*> \verbatim |
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*> TRANB is CHARACTER*1 |
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*> Specifies the option op(B): |
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*> = 'N': op(B) = B (No transpose) |
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*> = 'T': op(B) = B**T (Transpose) |
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*> = 'C': op(B) = B**H (Conjugate transpose = Transpose) |
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*> \endverbatim |
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*> |
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*> \param[in] ISGN |
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*> \verbatim |
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*> ISGN is INTEGER |
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*> Specifies the sign in the equation: |
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*> = +1: solve op(A)*X + X*op(B) = scale*C |
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*> = -1: solve op(A)*X - X*op(B) = scale*C |
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*> \endverbatim |
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*> |
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*> \param[in] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The order of the matrix A, and the number of rows in the |
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*> matrices X and C. M >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the matrix B, and the number of columns in the |
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*> matrices X and C. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] A |
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*> \verbatim |
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*> A is DOUBLE PRECISION array, dimension (LDA,M) |
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*> The upper quasi-triangular matrix A, in Schur canonical form. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(1,M). |
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*> \endverbatim |
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*> |
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*> \param[in] B |
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*> \verbatim |
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*> B is DOUBLE PRECISION array, dimension (LDB,N) |
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*> The upper quasi-triangular matrix B, in Schur canonical form. |
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*> \endverbatim |
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*> |
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*> \param[in] LDB |
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*> \verbatim |
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*> LDB is INTEGER |
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*> The leading dimension of the array B. LDB >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[in,out] C |
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*> \verbatim |
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*> C is DOUBLE PRECISION array, dimension (LDC,N) |
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*> On entry, the M-by-N right hand side matrix C. |
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*> On exit, C is overwritten by the solution matrix X. |
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*> \endverbatim |
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*> |
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*> \param[in] LDC |
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*> \verbatim |
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*> LDC is INTEGER |
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*> The leading dimension of the array C. LDC >= max(1,M) |
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*> \endverbatim |
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*> |
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*> \param[out] SCALE |
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*> \verbatim |
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*> SCALE is DOUBLE PRECISION |
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*> The scale factor, scale, set <= 1 to avoid overflow in X. |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is 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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*> = 1: A and B have common or very close eigenvalues; perturbed |
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*> values were used to solve the equation (but the matrices |
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*> A and B are unchanged). |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup doubleSYcomputational |
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* |
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* ===================================================================== |
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 3.2) -- |
* -- 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..-- |
* November 2006 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER TRANA, TRANB |
CHARACTER TRANA, TRANB |
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DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ) |
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DTRSYL solves the real Sylvester matrix equation: |
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* |
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* op(A)*X + X*op(B) = scale*C or |
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* op(A)*X - X*op(B) = scale*C, |
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* |
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* where op(A) = A or A**T, and A and B are both upper quasi- |
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* triangular. A is M-by-M and B is N-by-N; the right hand side C and |
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* the solution X are M-by-N; and scale is an output scale factor, set |
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* <= 1 to avoid overflow in X. |
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* |
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* A and B must be in Schur canonical form (as returned by DHSEQR), that |
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* is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; |
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* each 2-by-2 diagonal block has its diagonal elements equal and its |
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* off-diagonal elements of opposite sign. |
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* |
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* Arguments |
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* ========= |
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* |
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* TRANA (input) CHARACTER*1 |
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* Specifies the option op(A): |
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* = 'N': op(A) = A (No transpose) |
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* = 'T': op(A) = A**T (Transpose) |
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* = 'C': op(A) = A**H (Conjugate transpose = Transpose) |
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* |
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* TRANB (input) CHARACTER*1 |
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* Specifies the option op(B): |
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* = 'N': op(B) = B (No transpose) |
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* = 'T': op(B) = B**T (Transpose) |
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* = 'C': op(B) = B**H (Conjugate transpose = Transpose) |
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* |
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* ISGN (input) INTEGER |
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* Specifies the sign in the equation: |
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* = +1: solve op(A)*X + X*op(B) = scale*C |
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* = -1: solve op(A)*X - X*op(B) = scale*C |
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* |
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* M (input) INTEGER |
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* The order of the matrix A, and the number of rows in the |
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* matrices X and C. M >= 0. |
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* |
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* N (input) INTEGER |
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* The order of the matrix B, and the number of columns in the |
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* matrices X and C. N >= 0. |
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* |
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* A (input) DOUBLE PRECISION array, dimension (LDA,M) |
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* The upper quasi-triangular matrix A, in Schur canonical form. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,M). |
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* |
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* B (input) DOUBLE PRECISION array, dimension (LDB,N) |
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* The upper quasi-triangular matrix B, in Schur canonical form. |
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* |
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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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* |
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* C (input/output) DOUBLE PRECISION array, dimension (LDC,N) |
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* On entry, the M-by-N right hand side matrix C. |
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* On exit, C is overwritten by the solution matrix X. |
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* |
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* LDC (input) INTEGER |
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* The leading dimension of the array C. LDC >= max(1,M) |
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* |
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* SCALE (output) DOUBLE PRECISION |
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* The scale factor, scale, set <= 1 to avoid overflow in X. |
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* |
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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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* = 1: A and B have common or very close eigenvalues; perturbed |
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* values were used to solve the equation (but the matrices |
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* A and B are unchanged). |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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* |
* |
ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN |
ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN |
* |
* |
* Solve A' *X + ISGN*X*B = scale*C. |
* Solve A**T *X + ISGN*X*B = scale*C. |
* |
* |
* The (K,L)th block of X is determined starting from |
* The (K,L)th block of X is determined starting from |
* upper-left corner column by column by |
* upper-left corner column by column by |
* |
* |
* A(K,K)'*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)'*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 |
* |
* |
* Start column loop (index = L) |
* Start column loop (index = L) |
* L1 (L2): column index of the first (last) row of X(K,L) |
* L1 (L2): column index of the first (last) row of X(K,L) |
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* |
* |
ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN |
ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN |
* |
* |
* Solve A'*X + ISGN*X*B' = scale*C. |
* Solve A**T*X + ISGN*X*B**T = scale*C. |
* |
* |
* The (K,L)th block of X is determined starting from |
* The (K,L)th block of X is determined starting from |
* top-right corner column by column by |
* top-right corner column by column by |
* |
* |
* A(K,K)'*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)**T = C(K,L) - R(K,L) |
* |
* |
* Where |
* Where |
* K-1 N |
* K-1 N |
* R(K,L) = SUM [A(I,K)'*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)']. |
* R(K,L) = SUM [A(I,K)**T*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)**T]. |
* I=1 J=L+1 |
* I=1 J=L+1 |
* |
* |
* Start column loop (index = L) |
* Start column loop (index = L) |
* L1 (L2): column index of the first (last) row of X(K,L) |
* L1 (L2): column index of the first (last) row of X(K,L) |
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* |
* |
ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN |
ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN |
* |
* |
* Solve A*X + ISGN*X*B' = scale*C. |
* Solve A*X + ISGN*X*B**T = scale*C. |
* |
* |
* The (K,L)th block of X is determined starting from |
* The (K,L)th block of X is determined starting from |
* bottom-right corner column by column by |
* bottom-right corner column by column by |
* |
* |
* A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L)' = C(K,L) - R(K,L) |
* A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L)**T = C(K,L) - R(K,L) |
* |
* |
* Where |
* Where |
* M N |
* M N |
* R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)']. |
* R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)**T]. |
* I=K+1 J=L+1 |
* I=K+1 J=L+1 |
* |
* |
* Start column loop (index = L) |
* Start column loop (index = L) |