--- rpl/lapack/lapack/dtgsy2.f 2011/07/22 07:38:12 1.9
+++ rpl/lapack/lapack/dtgsy2.f 2011/11/21 20:43:06 1.10
@@ -1,11 +1,283 @@
+*> \brief \b DTGSY2
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DTGSY2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
+* LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL,
+* IWORK, PQ, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER TRANS
+* INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, M, N,
+* $ PQ
+* DOUBLE PRECISION RDSCAL, RDSUM, SCALE
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ),
+* $ D( LDD, * ), E( LDE, * ), F( LDF, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DTGSY2 solves the generalized Sylvester equation:
+*>
+*> A * R - L * B = scale * C (1)
+*> D * R - L * E = scale * F,
+*>
+*> using Level 1 and 2 BLAS. where R and L are unknown M-by-N matrices,
+*> (A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M,
+*> N-by-N and M-by-N, respectively, with real entries. (A, D) and (B, E)
+*> must be in generalized Schur canonical form, i.e. A, B are upper
+*> quasi triangular and D, E are upper triangular. The solution (R, L)
+*> overwrites (C, F). 0 <= SCALE <= 1 is an output scaling factor
+*> chosen to avoid overflow.
+*>
+*> In matrix notation solving equation (1) corresponds to solve
+*> Z*x = scale*b, where Z is defined as
+*>
+*> Z = [ kron(In, A) -kron(B**T, Im) ] (2)
+*> [ kron(In, D) -kron(E**T, Im) ],
+*>
+*> Ik is the identity matrix of size k and X**T is the transpose of X.
+*> kron(X, Y) is the Kronecker product between the matrices X and Y.
+*> In the process of solving (1), we solve a number of such systems
+*> where Dim(In), Dim(In) = 1 or 2.
+*>
+*> If TRANS = 'T', solve the transposed system Z**T*y = scale*b for y,
+*> which is equivalent to solve for R and L in
+*>
+*> A**T * R + D**T * L = scale * C (3)
+*> R * B**T + L * E**T = scale * -F
+*>
+*> This case is used to compute an estimate of Dif[(A, D), (B, E)] =
+*> sigma_min(Z) using reverse communicaton with DLACON.
+*>
+*> DTGSY2 also (IJOB >= 1) contributes to the computation in DTGSYL
+*> of an upper bound on the separation between to matrix pairs. Then
+*> the input (A, D), (B, E) are sub-pencils of the matrix pair in
+*> DTGSYL. See DTGSYL for details.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] TRANS
+*> \verbatim
+*> TRANS is CHARACTER*1
+*> = 'N', solve the generalized Sylvester equation (1).
+*> = 'T': solve the 'transposed' system (3).
+*> \endverbatim
+*>
+*> \param[in] IJOB
+*> \verbatim
+*> IJOB is INTEGER
+*> Specifies what kind of functionality to be performed.
+*> = 0: solve (1) only.
+*> = 1: A contribution from this subsystem to a Frobenius
+*> norm-based estimate of the separation between two matrix
+*> pairs is computed. (look ahead strategy is used).
+*> = 2: A contribution from this subsystem to a Frobenius
+*> norm-based estimate of the separation between two matrix
+*> pairs is computed. (DGECON on sub-systems is used.)
+*> Not referenced if TRANS = 'T'.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> On entry, M specifies the order of A and D, and the row
+*> dimension of C, F, R and L.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> On entry, N specifies the order of B and E, and the column
+*> dimension of C, F, R and L.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA, M)
+*> On entry, A contains an upper quasi triangular matrix.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the matrix A. LDA >= max(1, M).
+*> \endverbatim
+*>
+*> \param[in] B
+*> \verbatim
+*> B is DOUBLE PRECISION array, dimension (LDB, N)
+*> On entry, B contains an upper quasi triangular matrix.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the matrix B. LDB >= max(1, N).
+*> \endverbatim
+*>
+*> \param[in,out] C
+*> \verbatim
+*> C is DOUBLE PRECISION array, dimension (LDC, N)
+*> On entry, C contains the right-hand-side of the first matrix
+*> equation in (1).
+*> On exit, if IJOB = 0, C has been overwritten by the
+*> solution R.
+*> \endverbatim
+*>
+*> \param[in] LDC
+*> \verbatim
+*> LDC is INTEGER
+*> The leading dimension of the matrix C. LDC >= max(1, M).
+*> \endverbatim
+*>
+*> \param[in] D
+*> \verbatim
+*> D is DOUBLE PRECISION array, dimension (LDD, M)
+*> On entry, D contains an upper triangular matrix.
+*> \endverbatim
+*>
+*> \param[in] LDD
+*> \verbatim
+*> LDD is INTEGER
+*> The leading dimension of the matrix D. LDD >= max(1, M).
+*> \endverbatim
+*>
+*> \param[in] E
+*> \verbatim
+*> E is DOUBLE PRECISION array, dimension (LDE, N)
+*> On entry, E contains an upper triangular matrix.
+*> \endverbatim
+*>
+*> \param[in] LDE
+*> \verbatim
+*> LDE is INTEGER
+*> The leading dimension of the matrix E. LDE >= max(1, N).
+*> \endverbatim
+*>
+*> \param[in,out] F
+*> \verbatim
+*> F is DOUBLE PRECISION array, dimension (LDF, N)
+*> On entry, F contains the right-hand-side of the second matrix
+*> equation in (1).
+*> On exit, if IJOB = 0, F has been overwritten by the
+*> solution L.
+*> \endverbatim
+*>
+*> \param[in] LDF
+*> \verbatim
+*> LDF is INTEGER
+*> The leading dimension of the matrix F. LDF >= max(1, M).
+*> \endverbatim
+*>
+*> \param[out] SCALE
+*> \verbatim
+*> SCALE is DOUBLE PRECISION
+*> On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions
+*> R and L (C and F on entry) will hold the solutions to a
+*> slightly perturbed system but the input matrices A, B, D and
+*> E have not been changed. If SCALE = 0, R and L will hold the
+*> solutions to the homogeneous system with C = F = 0. Normally,
+*> SCALE = 1.
+*> \endverbatim
+*>
+*> \param[in,out] RDSUM
+*> \verbatim
+*> RDSUM is DOUBLE PRECISION
+*> On entry, the sum of squares of computed contributions to
+*> the Dif-estimate under computation by DTGSYL, where the
+*> scaling factor RDSCAL (see below) has been factored out.
+*> On exit, the corresponding sum of squares updated with the
+*> contributions from the current sub-system.
+*> If TRANS = 'T' RDSUM is not touched.
+*> NOTE: RDSUM only makes sense when DTGSY2 is called by DTGSYL.
+*> \endverbatim
+*>
+*> \param[in,out] RDSCAL
+*> \verbatim
+*> RDSCAL is DOUBLE PRECISION
+*> On entry, scaling factor used to prevent overflow in RDSUM.
+*> On exit, RDSCAL is updated w.r.t. the current contributions
+*> in RDSUM.
+*> If TRANS = 'T', RDSCAL is not touched.
+*> NOTE: RDSCAL only makes sense when DTGSY2 is called by
+*> DTGSYL.
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (M+N+2)
+*> \endverbatim
+*>
+*> \param[out] PQ
+*> \verbatim
+*> PQ is INTEGER
+*> On exit, the number of subsystems (of size 2-by-2, 4-by-4 and
+*> 8-by-8) solved by this routine.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> On exit, if INFO is set to
+*> =0: Successful exit
+*> <0: If INFO = -i, the i-th argument had an illegal value.
+*> >0: The matrix pairs (A, D) and (B, E) have common or very
+*> close eigenvalues.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup doubleSYauxiliary
+*
+*> \par Contributors:
+* ==================
+*>
+*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
+*> Umea University, S-901 87 Umea, Sweden.
+*
+* =====================================================================
SUBROUTINE DTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
$ LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL,
$ IWORK, PQ, INFO )
*
-* -- LAPACK auxiliary routine (version 3.3.1) --
+* -- LAPACK auxiliary 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 TRANS
@@ -19,160 +291,6 @@
$ D( LDD, * ), E( LDE, * ), F( LDF, * )
* ..
*
-* Purpose
-* =======
-*
-* DTGSY2 solves the generalized Sylvester equation:
-*
-* A * R - L * B = scale * C (1)
-* D * R - L * E = scale * F,
-*
-* using Level 1 and 2 BLAS. where R and L are unknown M-by-N matrices,
-* (A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M,
-* N-by-N and M-by-N, respectively, with real entries. (A, D) and (B, E)
-* must be in generalized Schur canonical form, i.e. A, B are upper
-* quasi triangular and D, E are upper triangular. The solution (R, L)
-* overwrites (C, F). 0 <= SCALE <= 1 is an output scaling factor
-* chosen to avoid overflow.
-*
-* In matrix notation solving equation (1) corresponds to solve
-* Z*x = scale*b, where Z is defined as
-*
-* Z = [ kron(In, A) -kron(B**T, Im) ] (2)
-* [ kron(In, D) -kron(E**T, Im) ],
-*
-* Ik is the identity matrix of size k and X**T is the transpose of X.
-* kron(X, Y) is the Kronecker product between the matrices X and Y.
-* In the process of solving (1), we solve a number of such systems
-* where Dim(In), Dim(In) = 1 or 2.
-*
-* If TRANS = 'T', solve the transposed system Z**T*y = scale*b for y,
-* which is equivalent to solve for R and L in
-*
-* A**T * R + D**T * L = scale * C (3)
-* R * B**T + L * E**T = scale * -F
-*
-* This case is used to compute an estimate of Dif[(A, D), (B, E)] =
-* sigma_min(Z) using reverse communicaton with DLACON.
-*
-* DTGSY2 also (IJOB >= 1) contributes to the computation in DTGSYL
-* of an upper bound on the separation between to matrix pairs. Then
-* the input (A, D), (B, E) are sub-pencils of the matrix pair in
-* DTGSYL. See DTGSYL for details.
-*
-* Arguments
-* =========
-*
-* TRANS (input) CHARACTER*1
-* = 'N', solve the generalized Sylvester equation (1).
-* = 'T': solve the 'transposed' system (3).
-*
-* IJOB (input) INTEGER
-* Specifies what kind of functionality to be performed.
-* = 0: solve (1) only.
-* = 1: A contribution from this subsystem to a Frobenius
-* norm-based estimate of the separation between two matrix
-* pairs is computed. (look ahead strategy is used).
-* = 2: A contribution from this subsystem to a Frobenius
-* norm-based estimate of the separation between two matrix
-* pairs is computed. (DGECON on sub-systems is used.)
-* Not referenced if TRANS = 'T'.
-*
-* M (input) INTEGER
-* On entry, M specifies the order of A and D, and the row
-* dimension of C, F, R and L.
-*
-* N (input) INTEGER
-* On entry, N specifies the order of B and E, and the column
-* dimension of C, F, R and L.
-*
-* A (input) DOUBLE PRECISION array, dimension (LDA, M)
-* On entry, A contains an upper quasi triangular matrix.
-*
-* LDA (input) INTEGER
-* The leading dimension of the matrix A. LDA >= max(1, M).
-*
-* B (input) DOUBLE PRECISION array, dimension (LDB, N)
-* On entry, B contains an upper quasi triangular matrix.
-*
-* LDB (input) INTEGER
-* The leading dimension of the matrix B. LDB >= max(1, N).
-*
-* C (input/output) DOUBLE PRECISION array, dimension (LDC, N)
-* On entry, C contains the right-hand-side of the first matrix
-* equation in (1).
-* On exit, if IJOB = 0, C has been overwritten by the
-* solution R.
-*
-* LDC (input) INTEGER
-* The leading dimension of the matrix C. LDC >= max(1, M).
-*
-* D (input) DOUBLE PRECISION array, dimension (LDD, M)
-* On entry, D contains an upper triangular matrix.
-*
-* LDD (input) INTEGER
-* The leading dimension of the matrix D. LDD >= max(1, M).
-*
-* E (input) DOUBLE PRECISION array, dimension (LDE, N)
-* On entry, E contains an upper triangular matrix.
-*
-* LDE (input) INTEGER
-* The leading dimension of the matrix E. LDE >= max(1, N).
-*
-* F (input/output) DOUBLE PRECISION array, dimension (LDF, N)
-* On entry, F contains the right-hand-side of the second matrix
-* equation in (1).
-* On exit, if IJOB = 0, F has been overwritten by the
-* solution L.
-*
-* LDF (input) INTEGER
-* The leading dimension of the matrix F. LDF >= max(1, M).
-*
-* SCALE (output) DOUBLE PRECISION
-* On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions
-* R and L (C and F on entry) will hold the solutions to a
-* slightly perturbed system but the input matrices A, B, D and
-* E have not been changed. If SCALE = 0, R and L will hold the
-* solutions to the homogeneous system with C = F = 0. Normally,
-* SCALE = 1.
-*
-* RDSUM (input/output) DOUBLE PRECISION
-* On entry, the sum of squares of computed contributions to
-* the Dif-estimate under computation by DTGSYL, where the
-* scaling factor RDSCAL (see below) has been factored out.
-* On exit, the corresponding sum of squares updated with the
-* contributions from the current sub-system.
-* If TRANS = 'T' RDSUM is not touched.
-* NOTE: RDSUM only makes sense when DTGSY2 is called by DTGSYL.
-*
-* RDSCAL (input/output) DOUBLE PRECISION
-* On entry, scaling factor used to prevent overflow in RDSUM.
-* On exit, RDSCAL is updated w.r.t. the current contributions
-* in RDSUM.
-* If TRANS = 'T', RDSCAL is not touched.
-* NOTE: RDSCAL only makes sense when DTGSY2 is called by
-* DTGSYL.
-*
-* IWORK (workspace) INTEGER array, dimension (M+N+2)
-*
-* PQ (output) INTEGER
-* On exit, the number of subsystems (of size 2-by-2, 4-by-4 and
-* 8-by-8) solved by this routine.
-*
-* INFO (output) INTEGER
-* On exit, if INFO is set to
-* =0: Successful exit
-* <0: If INFO = -i, the i-th argument had an illegal value.
-* >0: The matrix pairs (A, D) and (B, E) have common or very
-* close eigenvalues.
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Bo Kagstrom and Peter Poromaa, Department of Computing Science,
-* Umea University, S-901 87 Umea, Sweden.
-*
* =====================================================================
* Replaced various illegal calls to DCOPY by calls to DLASET.
* Sven Hammarling, 27/5/02.