698 lines
23 KiB
Fortran
698 lines
23 KiB
Fortran
*> \brief \b ZTGSYL
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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 ZTGSYL + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgsyl.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/ztgsyl.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/ztgsyl.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 ZTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
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* LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
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* IWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER TRANS
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* INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF,
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* $ LWORK, M, N
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* DOUBLE PRECISION DIF, SCALE
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* ..
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* .. Array Arguments ..
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* INTEGER IWORK( * )
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* COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * ),
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* $ D( LDD, * ), E( LDE, * ), F( LDF, * ),
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* $ WORK( * )
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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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*> ZTGSYL solves the generalized Sylvester equation:
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*>
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*> A * R - L * B = scale * C (1)
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*> D * R - L * E = scale * F
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*>
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*> where R and L are unknown m-by-n matrices, (A, D), (B, E) and
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*> (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n,
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*> respectively, with complex entries. A, B, D and E are upper
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*> triangular (i.e., (A,D) and (B,E) in generalized Schur form).
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*>
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*> The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1
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*> is an output scaling factor chosen to avoid overflow.
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*>
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*> In matrix notation (1) is equivalent to solve Zx = scale*b, where Z
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*> is defined as
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*>
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*> Z = [ kron(In, A) -kron(B**H, Im) ] (2)
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*> [ kron(In, D) -kron(E**H, Im) ],
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*>
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*> Here Ix is the identity matrix of size x and X**H is the conjugate
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*> transpose of X. Kron(X, Y) is the Kronecker product between the
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*> matrices X and Y.
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*>
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*> If TRANS = 'C', y in the conjugate transposed system Z**H *y = scale*b
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*> is solved for, which is equivalent to solve for R and L in
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*>
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*> A**H * R + D**H * L = scale * C (3)
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*> R * B**H + L * E**H = scale * -F
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*>
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*> This case (TRANS = 'C') is used to compute an one-norm-based estimate
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*> of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
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*> and (B,E), using ZLACON.
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*>
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*> If IJOB >= 1, ZTGSYL computes a Frobenius norm-based estimate of
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*> Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the
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*> reciprocal of the smallest singular value of Z.
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*>
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*> This is a level-3 BLAS algorithm.
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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] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> = 'N': solve the generalized sylvester equation (1).
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*> = 'C': solve the "conjugate transposed" system (3).
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*> \endverbatim
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*>
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*> \param[in] IJOB
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*> \verbatim
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*> IJOB is INTEGER
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*> Specifies what kind of functionality to be performed.
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*> =0: solve (1) only.
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*> =1: The functionality of 0 and 3.
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*> =2: The functionality of 0 and 4.
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*> =3: Only an estimate of Dif[(A,D), (B,E)] is computed.
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*> (look ahead strategy is used).
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*> =4: Only an estimate of Dif[(A,D), (B,E)] is computed.
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*> (ZGECON on sub-systems is used).
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*> Not referenced if TRANS = '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 matrices A and D, and the row dimension of
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*> the matrices C, F, R and L.
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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 matrices B and E, and the column dimension
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*> of the matrices C, F, R and L.
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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 COMPLEX*16 array, dimension (LDA, M)
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*> The upper triangular matrix A.
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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 COMPLEX*16 array, dimension (LDB, N)
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*> The upper triangular matrix B.
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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 COMPLEX*16 array, dimension (LDC, N)
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*> On entry, C contains the right-hand-side of the first matrix
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*> equation in (1) or (3).
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*> On exit, if IJOB = 0, 1 or 2, C has been overwritten by
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*> the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R,
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*> the solution achieved during the computation of the
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*> Dif-estimate.
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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[in] D
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*> \verbatim
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*> D is COMPLEX*16 array, dimension (LDD, M)
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*> The upper triangular matrix D.
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*> \endverbatim
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*>
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*> \param[in] LDD
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*> \verbatim
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*> LDD is INTEGER
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*> The leading dimension of the array D. LDD >= max(1, M).
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*> \endverbatim
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*>
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*> \param[in] E
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*> \verbatim
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*> E is COMPLEX*16 array, dimension (LDE, N)
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*> The upper triangular matrix E.
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*> \endverbatim
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*>
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*> \param[in] LDE
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*> \verbatim
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*> LDE is INTEGER
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*> The leading dimension of the array E. LDE >= max(1, N).
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*> \endverbatim
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*>
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*> \param[in,out] F
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*> \verbatim
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*> F is COMPLEX*16 array, dimension (LDF, N)
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*> On entry, F contains the right-hand-side of the second matrix
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*> equation in (1) or (3).
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*> On exit, if IJOB = 0, 1 or 2, F has been overwritten by
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*> the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L,
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*> the solution achieved during the computation of the
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*> Dif-estimate.
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*> \endverbatim
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*>
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*> \param[in] LDF
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*> \verbatim
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*> LDF is INTEGER
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*> The leading dimension of the array F. LDF >= max(1, M).
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*> \endverbatim
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*>
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*> \param[out] DIF
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*> \verbatim
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*> DIF is DOUBLE PRECISION
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*> On exit DIF is the reciprocal of a lower bound of the
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*> reciprocal of the Dif-function, i.e. DIF is an upper bound of
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*> Dif[(A,D), (B,E)] = sigma-min(Z), where Z as in (2).
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*> IF IJOB = 0 or TRANS = 'C', DIF is not referenced.
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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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*> On exit SCALE is the scaling factor in (1) or (3).
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*> If 0 < SCALE < 1, C and F hold the solutions R and L, resp.,
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*> to a slightly perturbed system but the input matrices A, B,
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*> D and E have not been changed. If SCALE = 0, R and L will
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*> hold the solutions to the homogenious system with C = F = 0.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK. LWORK > = 1.
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*> If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N).
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*>
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*> If LWORK = -1, then a workspace query is assumed; the routine
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*> only calculates the optimal size of the WORK array, returns
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*> this value as the first entry of the WORK array, and no error
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*> message related to LWORK is issued by XERBLA.
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (M+N+2)
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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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*> >0: (A, D) and (B, E) have common or very close
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*> eigenvalues.
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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 December 2016
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*
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*> \ingroup complex16SYcomputational
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*
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*> \par Contributors:
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* ==================
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*>
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*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
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*> Umea University, S-901 87 Umea, Sweden.
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*
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*> \par References:
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* ================
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*>
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*> [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
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*> for Solving the Generalized Sylvester Equation and Estimating the
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*> Separation between Regular Matrix Pairs, Report UMINF - 93.23,
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*> Department of Computing Science, Umea University, S-901 87 Umea,
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*> Sweden, December 1993, Revised April 1994, Also as LAPACK Working
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*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22,
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*> No 1, 1996.
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*> \n
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*> [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester
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*> Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal.
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*> Appl., 15(4):1045-1060, 1994.
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*> \n
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*> [3] B. Kagstrom and L. Westin, Generalized Schur Methods with
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*> Condition Estimators for Solving the Generalized Sylvester
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*> Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,
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*> July 1989, pp 745-751.
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*>
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* =====================================================================
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SUBROUTINE ZTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,
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$ LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK,
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$ IWORK, INFO )
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*
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* -- LAPACK computational routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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CHARACTER TRANS
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INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF,
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$ LWORK, M, N
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DOUBLE PRECISION DIF, SCALE
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * )
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COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * ),
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$ D( LDD, * ), E( LDE, * ), F( LDF, * ),
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$ WORK( * )
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* ..
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*
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* =====================================================================
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* Replaced various illegal calls to CCOPY by calls to CLASET.
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* Sven Hammarling, 1/5/02.
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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COMPLEX*16 CZERO
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PARAMETER ( CZERO = (0.0D+0, 0.0D+0) )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY, NOTRAN
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INTEGER I, IE, IFUNC, IROUND, IS, ISOLVE, J, JE, JS, K,
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$ LINFO, LWMIN, MB, NB, P, PQ, Q
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DOUBLE PRECISION DSCALE, DSUM, SCALE2, SCALOC
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAENV
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EXTERNAL LSAME, ILAENV
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZGEMM, ZLACPY, ZLASET, ZSCAL, ZTGSY2
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE, DCMPLX, MAX, SQRT
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* ..
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* .. Executable Statements ..
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*
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* Decode and test input parameters
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*
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INFO = 0
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NOTRAN = LSAME( TRANS, 'N' )
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LQUERY = ( LWORK.EQ.-1 )
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*
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IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
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INFO = -1
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ELSE IF( NOTRAN ) THEN
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IF( ( IJOB.LT.0 ) .OR. ( IJOB.GT.4 ) ) THEN
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INFO = -2
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END IF
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END IF
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IF( INFO.EQ.0 ) THEN
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IF( M.LE.0 ) THEN
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INFO = -3
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ELSE IF( N.LE.0 ) THEN
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INFO = -4
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -6
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -8
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ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
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INFO = -10
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ELSE IF( LDD.LT.MAX( 1, M ) ) THEN
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INFO = -12
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ELSE IF( LDE.LT.MAX( 1, N ) ) THEN
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INFO = -14
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ELSE IF( LDF.LT.MAX( 1, M ) ) THEN
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INFO = -16
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END IF
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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IF( NOTRAN ) THEN
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IF( IJOB.EQ.1 .OR. IJOB.EQ.2 ) THEN
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LWMIN = MAX( 1, 2*M*N )
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ELSE
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LWMIN = 1
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END IF
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ELSE
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LWMIN = 1
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END IF
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WORK( 1 ) = LWMIN
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*
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IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -20
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END IF
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZTGSYL', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( M.EQ.0 .OR. N.EQ.0 ) THEN
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SCALE = 1
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IF( NOTRAN ) THEN
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IF( IJOB.NE.0 ) THEN
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DIF = 0
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END IF
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END IF
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RETURN
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END IF
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*
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* Determine optimal block sizes MB and NB
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*
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MB = ILAENV( 2, 'ZTGSYL', TRANS, M, N, -1, -1 )
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NB = ILAENV( 5, 'ZTGSYL', TRANS, M, N, -1, -1 )
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*
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ISOLVE = 1
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IFUNC = 0
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IF( NOTRAN ) THEN
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IF( IJOB.GE.3 ) THEN
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IFUNC = IJOB - 2
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CALL ZLASET( 'F', M, N, CZERO, CZERO, C, LDC )
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CALL ZLASET( 'F', M, N, CZERO, CZERO, F, LDF )
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ELSE IF( IJOB.GE.1 .AND. NOTRAN ) THEN
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ISOLVE = 2
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END IF
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END IF
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*
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IF( ( MB.LE.1 .AND. NB.LE.1 ) .OR. ( MB.GE.M .AND. NB.GE.N ) )
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$ THEN
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*
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* Use unblocked Level 2 solver
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*
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DO 30 IROUND = 1, ISOLVE
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*
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SCALE = ONE
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DSCALE = ZERO
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DSUM = ONE
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PQ = M*N
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CALL ZTGSY2( TRANS, IFUNC, M, N, A, LDA, B, LDB, C, LDC, D,
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$ LDD, E, LDE, F, LDF, SCALE, DSUM, DSCALE,
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$ INFO )
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IF( DSCALE.NE.ZERO ) THEN
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IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN
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DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) )
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ELSE
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DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) )
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END IF
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END IF
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IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN
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IF( NOTRAN ) THEN
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IFUNC = IJOB
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END IF
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SCALE2 = SCALE
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CALL ZLACPY( 'F', M, N, C, LDC, WORK, M )
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CALL ZLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M )
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CALL ZLASET( 'F', M, N, CZERO, CZERO, C, LDC )
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CALL ZLASET( 'F', M, N, CZERO, CZERO, F, LDF )
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ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN
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CALL ZLACPY( 'F', M, N, WORK, M, C, LDC )
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CALL ZLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF )
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SCALE = SCALE2
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END IF
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30 CONTINUE
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*
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RETURN
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*
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END IF
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*
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* Determine block structure of A
|
|
*
|
|
P = 0
|
|
I = 1
|
|
40 CONTINUE
|
|
IF( I.GT.M )
|
|
$ GO TO 50
|
|
P = P + 1
|
|
IWORK( P ) = I
|
|
I = I + MB
|
|
IF( I.GE.M )
|
|
$ GO TO 50
|
|
GO TO 40
|
|
50 CONTINUE
|
|
IWORK( P+1 ) = M + 1
|
|
IF( IWORK( P ).EQ.IWORK( P+1 ) )
|
|
$ P = P - 1
|
|
*
|
|
* Determine block structure of B
|
|
*
|
|
Q = P + 1
|
|
J = 1
|
|
60 CONTINUE
|
|
IF( J.GT.N )
|
|
$ GO TO 70
|
|
*
|
|
Q = Q + 1
|
|
IWORK( Q ) = J
|
|
J = J + NB
|
|
IF( J.GE.N )
|
|
$ GO TO 70
|
|
GO TO 60
|
|
*
|
|
70 CONTINUE
|
|
IWORK( Q+1 ) = N + 1
|
|
IF( IWORK( Q ).EQ.IWORK( Q+1 ) )
|
|
$ Q = Q - 1
|
|
*
|
|
IF( NOTRAN ) THEN
|
|
DO 150 IROUND = 1, ISOLVE
|
|
*
|
|
* Solve (I, J) - subsystem
|
|
* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J)
|
|
* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J)
|
|
* for I = P, P - 1, ..., 1; J = 1, 2, ..., Q
|
|
*
|
|
PQ = 0
|
|
SCALE = ONE
|
|
DSCALE = ZERO
|
|
DSUM = ONE
|
|
DO 130 J = P + 2, Q
|
|
JS = IWORK( J )
|
|
JE = IWORK( J+1 ) - 1
|
|
NB = JE - JS + 1
|
|
DO 120 I = P, 1, -1
|
|
IS = IWORK( I )
|
|
IE = IWORK( I+1 ) - 1
|
|
MB = IE - IS + 1
|
|
CALL ZTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA,
|
|
$ B( JS, JS ), LDB, C( IS, JS ), LDC,
|
|
$ D( IS, IS ), LDD, E( JS, JS ), LDE,
|
|
$ F( IS, JS ), LDF, SCALOC, DSUM, DSCALE,
|
|
$ LINFO )
|
|
IF( LINFO.GT.0 )
|
|
$ INFO = LINFO
|
|
PQ = PQ + MB*NB
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 80 K = 1, JS - 1
|
|
CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ),
|
|
$ C( 1, K ), 1 )
|
|
CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ),
|
|
$ F( 1, K ), 1 )
|
|
80 CONTINUE
|
|
DO 90 K = JS, JE
|
|
CALL ZSCAL( IS-1, DCMPLX( SCALOC, ZERO ),
|
|
$ C( 1, K ), 1 )
|
|
CALL ZSCAL( IS-1, DCMPLX( SCALOC, ZERO ),
|
|
$ F( 1, K ), 1 )
|
|
90 CONTINUE
|
|
DO 100 K = JS, JE
|
|
CALL ZSCAL( M-IE, DCMPLX( SCALOC, ZERO ),
|
|
$ C( IE+1, K ), 1 )
|
|
CALL ZSCAL( M-IE, DCMPLX( SCALOC, ZERO ),
|
|
$ F( IE+1, K ), 1 )
|
|
100 CONTINUE
|
|
DO 110 K = JE + 1, N
|
|
CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ),
|
|
$ C( 1, K ), 1 )
|
|
CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ),
|
|
$ F( 1, K ), 1 )
|
|
110 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
*
|
|
* Substitute R(I,J) and L(I,J) into remaining equation.
|
|
*
|
|
IF( I.GT.1 ) THEN
|
|
CALL ZGEMM( 'N', 'N', IS-1, NB, MB,
|
|
$ DCMPLX( -ONE, ZERO ), A( 1, IS ), LDA,
|
|
$ C( IS, JS ), LDC, DCMPLX( ONE, ZERO ),
|
|
$ C( 1, JS ), LDC )
|
|
CALL ZGEMM( 'N', 'N', IS-1, NB, MB,
|
|
$ DCMPLX( -ONE, ZERO ), D( 1, IS ), LDD,
|
|
$ C( IS, JS ), LDC, DCMPLX( ONE, ZERO ),
|
|
$ F( 1, JS ), LDF )
|
|
END IF
|
|
IF( J.LT.Q ) THEN
|
|
CALL ZGEMM( 'N', 'N', MB, N-JE, NB,
|
|
$ DCMPLX( ONE, ZERO ), F( IS, JS ), LDF,
|
|
$ B( JS, JE+1 ), LDB,
|
|
$ DCMPLX( ONE, ZERO ), C( IS, JE+1 ),
|
|
$ LDC )
|
|
CALL ZGEMM( 'N', 'N', MB, N-JE, NB,
|
|
$ DCMPLX( ONE, ZERO ), F( IS, JS ), LDF,
|
|
$ E( JS, JE+1 ), LDE,
|
|
$ DCMPLX( ONE, ZERO ), F( IS, JE+1 ),
|
|
$ LDF )
|
|
END IF
|
|
120 CONTINUE
|
|
130 CONTINUE
|
|
IF( DSCALE.NE.ZERO ) THEN
|
|
IF( IJOB.EQ.1 .OR. IJOB.EQ.3 ) THEN
|
|
DIF = SQRT( DBLE( 2*M*N ) ) / ( DSCALE*SQRT( DSUM ) )
|
|
ELSE
|
|
DIF = SQRT( DBLE( PQ ) ) / ( DSCALE*SQRT( DSUM ) )
|
|
END IF
|
|
END IF
|
|
IF( ISOLVE.EQ.2 .AND. IROUND.EQ.1 ) THEN
|
|
IF( NOTRAN ) THEN
|
|
IFUNC = IJOB
|
|
END IF
|
|
SCALE2 = SCALE
|
|
CALL ZLACPY( 'F', M, N, C, LDC, WORK, M )
|
|
CALL ZLACPY( 'F', M, N, F, LDF, WORK( M*N+1 ), M )
|
|
CALL ZLASET( 'F', M, N, CZERO, CZERO, C, LDC )
|
|
CALL ZLASET( 'F', M, N, CZERO, CZERO, F, LDF )
|
|
ELSE IF( ISOLVE.EQ.2 .AND. IROUND.EQ.2 ) THEN
|
|
CALL ZLACPY( 'F', M, N, WORK, M, C, LDC )
|
|
CALL ZLACPY( 'F', M, N, WORK( M*N+1 ), M, F, LDF )
|
|
SCALE = SCALE2
|
|
END IF
|
|
150 CONTINUE
|
|
ELSE
|
|
*
|
|
* Solve transposed (I, J)-subsystem
|
|
* A(I, I)**H * R(I, J) + D(I, I)**H * L(I, J) = C(I, J)
|
|
* R(I, J) * B(J, J) + L(I, J) * E(J, J) = -F(I, J)
|
|
* for I = 1,2,..., P; J = Q, Q-1,..., 1
|
|
*
|
|
SCALE = ONE
|
|
DO 210 I = 1, P
|
|
IS = IWORK( I )
|
|
IE = IWORK( I+1 ) - 1
|
|
MB = IE - IS + 1
|
|
DO 200 J = Q, P + 2, -1
|
|
JS = IWORK( J )
|
|
JE = IWORK( J+1 ) - 1
|
|
NB = JE - JS + 1
|
|
CALL ZTGSY2( TRANS, IFUNC, MB, NB, A( IS, IS ), LDA,
|
|
$ B( JS, JS ), LDB, C( IS, JS ), LDC,
|
|
$ D( IS, IS ), LDD, E( JS, JS ), LDE,
|
|
$ F( IS, JS ), LDF, SCALOC, DSUM, DSCALE,
|
|
$ LINFO )
|
|
IF( LINFO.GT.0 )
|
|
$ INFO = LINFO
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 160 K = 1, JS - 1
|
|
CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ), C( 1, K ),
|
|
$ 1 )
|
|
CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ), F( 1, K ),
|
|
$ 1 )
|
|
160 CONTINUE
|
|
DO 170 K = JS, JE
|
|
CALL ZSCAL( IS-1, DCMPLX( SCALOC, ZERO ),
|
|
$ C( 1, K ), 1 )
|
|
CALL ZSCAL( IS-1, DCMPLX( SCALOC, ZERO ),
|
|
$ F( 1, K ), 1 )
|
|
170 CONTINUE
|
|
DO 180 K = JS, JE
|
|
CALL ZSCAL( M-IE, DCMPLX( SCALOC, ZERO ),
|
|
$ C( IE+1, K ), 1 )
|
|
CALL ZSCAL( M-IE, DCMPLX( SCALOC, ZERO ),
|
|
$ F( IE+1, K ), 1 )
|
|
180 CONTINUE
|
|
DO 190 K = JE + 1, N
|
|
CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ), C( 1, K ),
|
|
$ 1 )
|
|
CALL ZSCAL( M, DCMPLX( SCALOC, ZERO ), F( 1, K ),
|
|
$ 1 )
|
|
190 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
*
|
|
* Substitute R(I,J) and L(I,J) into remaining equation.
|
|
*
|
|
IF( J.GT.P+2 ) THEN
|
|
CALL ZGEMM( 'N', 'C', MB, JS-1, NB,
|
|
$ DCMPLX( ONE, ZERO ), C( IS, JS ), LDC,
|
|
$ B( 1, JS ), LDB, DCMPLX( ONE, ZERO ),
|
|
$ F( IS, 1 ), LDF )
|
|
CALL ZGEMM( 'N', 'C', MB, JS-1, NB,
|
|
$ DCMPLX( ONE, ZERO ), F( IS, JS ), LDF,
|
|
$ E( 1, JS ), LDE, DCMPLX( ONE, ZERO ),
|
|
$ F( IS, 1 ), LDF )
|
|
END IF
|
|
IF( I.LT.P ) THEN
|
|
CALL ZGEMM( 'C', 'N', M-IE, NB, MB,
|
|
$ DCMPLX( -ONE, ZERO ), A( IS, IE+1 ), LDA,
|
|
$ C( IS, JS ), LDC, DCMPLX( ONE, ZERO ),
|
|
$ C( IE+1, JS ), LDC )
|
|
CALL ZGEMM( 'C', 'N', M-IE, NB, MB,
|
|
$ DCMPLX( -ONE, ZERO ), D( IS, IE+1 ), LDD,
|
|
$ F( IS, JS ), LDF, DCMPLX( ONE, ZERO ),
|
|
$ C( IE+1, JS ), LDC )
|
|
END IF
|
|
200 CONTINUE
|
|
210 CONTINUE
|
|
END IF
|
|
*
|
|
WORK( 1 ) = LWMIN
|
|
*
|
|
RETURN
|
|
*
|
|
* End of ZTGSYL
|
|
*
|
|
END
|