1003 lines
35 KiB
Fortran
1003 lines
35 KiB
Fortran
*> \brief \b STRSYL
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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 STRSYL + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/strsyl.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/strsyl.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/strsyl.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 STRSYL( 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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* REAL SCALE
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* ..
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* .. Array Arguments ..
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* REAL 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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*> STRSYL 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 SHSEQR), 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 REAL 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 REAL 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 REAL 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 REAL
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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 December 2016
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*
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*> \ingroup realSYcomputational
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*
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* =====================================================================
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SUBROUTINE STRSYL( 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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* -- 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 TRANA, TRANB
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INTEGER INFO, ISGN, LDA, LDB, LDC, M, N
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REAL SCALE
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), B( LDB, * ), C( LDC, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL NOTRNA, NOTRNB
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INTEGER IERR, J, K, K1, K2, KNEXT, L, L1, L2, LNEXT
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REAL A11, BIGNUM, DA11, DB, EPS, SCALOC, SGN, SMIN,
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$ SMLNUM, SUML, SUMR, XNORM
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* ..
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* .. Local Arrays ..
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REAL DUM( 1 ), VEC( 2, 2 ), X( 2, 2 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL SDOT, SLAMCH, SLANGE
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EXTERNAL LSAME, SDOT, SLAMCH, SLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL SLABAD, SLALN2, SLASY2, SSCAL, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN, REAL
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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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NOTRNA = LSAME( TRANA, 'N' )
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NOTRNB = LSAME( TRANB, 'N' )
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*
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INFO = 0
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IF( .NOT.NOTRNA .AND. .NOT.LSAME( TRANA, 'T' ) .AND. .NOT.
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$ LSAME( TRANA, 'C' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.NOTRNB .AND. .NOT.LSAME( TRANB, 'T' ) .AND. .NOT.
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$ LSAME( TRANB, 'C' ) ) THEN
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INFO = -2
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ELSE IF( ISGN.NE.1 .AND. ISGN.NE.-1 ) THEN
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INFO = -3
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ELSE IF( M.LT.0 ) THEN
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INFO = -4
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ELSE IF( N.LT.0 ) THEN
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INFO = -5
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -7
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -9
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ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
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INFO = -11
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'STRSYL', -INFO )
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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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SCALE = ONE
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IF( M.EQ.0 .OR. N.EQ.0 )
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$ RETURN
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*
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* Set constants to control overflow
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*
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EPS = SLAMCH( 'P' )
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SMLNUM = SLAMCH( 'S' )
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BIGNUM = ONE / SMLNUM
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CALL SLABAD( SMLNUM, BIGNUM )
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SMLNUM = SMLNUM*REAL( M*N ) / EPS
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BIGNUM = ONE / SMLNUM
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*
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SMIN = MAX( SMLNUM, EPS*SLANGE( 'M', M, M, A, LDA, DUM ),
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$ EPS*SLANGE( 'M', N, N, B, LDB, DUM ) )
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*
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SGN = ISGN
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*
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IF( NOTRNA .AND. NOTRNB ) THEN
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*
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* Solve A*X + ISGN*X*B = scale*C.
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*
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* The (K,L)th block of X is determined starting from
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* bottom-left corner column by column by
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*
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* A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
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*
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* Where
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* M L-1
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* R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)].
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* I=K+1 J=1
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*
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* Start column loop (index = L)
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* L1 (L2) : column index of the first (first) row of X(K,L).
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*
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LNEXT = 1
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DO 70 L = 1, N
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IF( L.LT.LNEXT )
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$ GO TO 70
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IF( L.EQ.N ) THEN
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L1 = L
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L2 = L
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ELSE
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IF( B( L+1, L ).NE.ZERO ) THEN
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L1 = L
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L2 = L + 1
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LNEXT = L + 2
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ELSE
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L1 = L
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L2 = L
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LNEXT = L + 1
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END IF
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END IF
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*
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* Start row loop (index = K)
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* K1 (K2): row index of the first (last) row of X(K,L).
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*
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KNEXT = M
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DO 60 K = M, 1, -1
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IF( K.GT.KNEXT )
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$ GO TO 60
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IF( K.EQ.1 ) THEN
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K1 = K
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K2 = K
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ELSE
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IF( A( K, K-1 ).NE.ZERO ) THEN
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K1 = K - 1
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K2 = K
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KNEXT = K - 2
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ELSE
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K1 = K
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K2 = K
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KNEXT = K - 1
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END IF
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END IF
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*
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IF( L1.EQ.L2 .AND. K1.EQ.K2 ) THEN
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SUML = SDOT( M-K1, A( K1, MIN( K1+1, M ) ), LDA,
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$ C( MIN( K1+1, M ), L1 ), 1 )
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SUMR = SDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
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VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
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SCALOC = ONE
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*
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A11 = A( K1, K1 ) + SGN*B( L1, L1 )
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DA11 = ABS( A11 )
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IF( DA11.LE.SMIN ) THEN
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A11 = SMIN
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DA11 = SMIN
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INFO = 1
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END IF
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DB = ABS( VEC( 1, 1 ) )
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IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
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IF( DB.GT.BIGNUM*DA11 )
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$ SCALOC = ONE / DB
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END IF
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X( 1, 1 ) = ( VEC( 1, 1 )*SCALOC ) / A11
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*
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IF( SCALOC.NE.ONE ) THEN
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DO 10 J = 1, N
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CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
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10 CONTINUE
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SCALE = SCALE*SCALOC
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END IF
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C( K1, L1 ) = X( 1, 1 )
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*
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ELSE IF( L1.EQ.L2 .AND. K1.NE.K2 ) THEN
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*
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SUML = SDOT( M-K2, A( K1, MIN( K2+1, M ) ), LDA,
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$ C( MIN( K2+1, M ), L1 ), 1 )
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SUMR = SDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
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VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
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*
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SUML = SDOT( M-K2, A( K2, MIN( K2+1, M ) ), LDA,
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$ C( MIN( K2+1, M ), L1 ), 1 )
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SUMR = SDOT( L1-1, C( K2, 1 ), LDC, B( 1, L1 ), 1 )
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VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )
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*
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CALL SLALN2( .FALSE., 2, 1, SMIN, ONE, A( K1, K1 ),
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$ LDA, ONE, ONE, VEC, 2, -SGN*B( L1, L1 ),
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$ ZERO, X, 2, SCALOC, XNORM, IERR )
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IF( IERR.NE.0 )
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$ INFO = 1
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*
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IF( SCALOC.NE.ONE ) THEN
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DO 20 J = 1, N
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CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
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20 CONTINUE
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SCALE = SCALE*SCALOC
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END IF
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C( K1, L1 ) = X( 1, 1 )
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C( K2, L1 ) = X( 2, 1 )
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*
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ELSE IF( L1.NE.L2 .AND. K1.EQ.K2 ) THEN
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*
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SUML = SDOT( M-K1, A( K1, MIN( K1+1, M ) ), LDA,
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$ C( MIN( K1+1, M ), L1 ), 1 )
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SUMR = SDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
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VEC( 1, 1 ) = SGN*( C( K1, L1 )-( SUML+SGN*SUMR ) )
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*
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SUML = SDOT( M-K1, A( K1, MIN( K1+1, M ) ), LDA,
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$ C( MIN( K1+1, M ), L2 ), 1 )
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SUMR = SDOT( L1-1, C( K1, 1 ), LDC, B( 1, L2 ), 1 )
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VEC( 2, 1 ) = SGN*( C( K1, L2 )-( SUML+SGN*SUMR ) )
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*
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CALL SLALN2( .TRUE., 2, 1, SMIN, ONE, B( L1, L1 ),
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$ LDB, ONE, ONE, VEC, 2, -SGN*A( K1, K1 ),
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$ ZERO, X, 2, SCALOC, XNORM, IERR )
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IF( IERR.NE.0 )
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$ INFO = 1
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*
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IF( SCALOC.NE.ONE ) THEN
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DO 40 J = 1, N
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CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
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40 CONTINUE
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SCALE = SCALE*SCALOC
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END IF
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C( K1, L1 ) = X( 1, 1 )
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C( K1, L2 ) = X( 2, 1 )
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*
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ELSE IF( L1.NE.L2 .AND. K1.NE.K2 ) THEN
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*
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SUML = SDOT( M-K2, A( K1, MIN( K2+1, M ) ), LDA,
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$ C( MIN( K2+1, M ), L1 ), 1 )
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SUMR = SDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
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VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
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*
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SUML = SDOT( M-K2, A( K1, MIN( K2+1, M ) ), LDA,
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$ C( MIN( K2+1, M ), L2 ), 1 )
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SUMR = SDOT( L1-1, C( K1, 1 ), LDC, B( 1, L2 ), 1 )
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VEC( 1, 2 ) = C( K1, L2 ) - ( SUML+SGN*SUMR )
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*
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SUML = SDOT( M-K2, A( K2, MIN( K2+1, M ) ), LDA,
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$ C( MIN( K2+1, M ), L1 ), 1 )
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SUMR = SDOT( L1-1, C( K2, 1 ), LDC, B( 1, L1 ), 1 )
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VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )
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*
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SUML = SDOT( M-K2, A( K2, MIN( K2+1, M ) ), LDA,
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$ C( MIN( K2+1, M ), L2 ), 1 )
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SUMR = SDOT( L1-1, C( K2, 1 ), LDC, B( 1, L2 ), 1 )
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VEC( 2, 2 ) = C( K2, L2 ) - ( SUML+SGN*SUMR )
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*
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CALL SLASY2( .FALSE., .FALSE., ISGN, 2, 2,
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$ A( K1, K1 ), LDA, B( L1, L1 ), LDB, VEC,
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$ 2, SCALOC, X, 2, XNORM, IERR )
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IF( IERR.NE.0 )
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$ INFO = 1
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*
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IF( SCALOC.NE.ONE ) THEN
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DO 50 J = 1, N
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CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
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50 CONTINUE
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SCALE = SCALE*SCALOC
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END IF
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C( K1, L1 ) = X( 1, 1 )
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C( K1, L2 ) = X( 1, 2 )
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C( K2, L1 ) = X( 2, 1 )
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C( K2, L2 ) = X( 2, 2 )
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END IF
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*
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60 CONTINUE
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*
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70 CONTINUE
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*
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ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN
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*
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* Solve A**T *X + ISGN*X*B = scale*C.
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*
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* The (K,L)th block of X is determined starting from
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* upper-left corner column by column by
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*
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* A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
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*
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* Where
|
|
* K-1 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
|
|
*
|
|
* Start column loop (index = L)
|
|
* L1 (L2): column index of the first (last) row of X(K,L)
|
|
*
|
|
LNEXT = 1
|
|
DO 130 L = 1, N
|
|
IF( L.LT.LNEXT )
|
|
$ GO TO 130
|
|
IF( L.EQ.N ) THEN
|
|
L1 = L
|
|
L2 = L
|
|
ELSE
|
|
IF( B( L+1, L ).NE.ZERO ) THEN
|
|
L1 = L
|
|
L2 = L + 1
|
|
LNEXT = L + 2
|
|
ELSE
|
|
L1 = L
|
|
L2 = L
|
|
LNEXT = L + 1
|
|
END IF
|
|
END IF
|
|
*
|
|
* Start row loop (index = K)
|
|
* K1 (K2): row index of the first (last) row of X(K,L)
|
|
*
|
|
KNEXT = 1
|
|
DO 120 K = 1, M
|
|
IF( K.LT.KNEXT )
|
|
$ GO TO 120
|
|
IF( K.EQ.M ) THEN
|
|
K1 = K
|
|
K2 = K
|
|
ELSE
|
|
IF( A( K+1, K ).NE.ZERO ) THEN
|
|
K1 = K
|
|
K2 = K + 1
|
|
KNEXT = K + 2
|
|
ELSE
|
|
K1 = K
|
|
K2 = K
|
|
KNEXT = K + 1
|
|
END IF
|
|
END IF
|
|
*
|
|
IF( L1.EQ.L2 .AND. K1.EQ.K2 ) THEN
|
|
SUML = SDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )
|
|
SUMR = SDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
|
|
VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
|
|
SCALOC = ONE
|
|
*
|
|
A11 = A( K1, K1 ) + SGN*B( L1, L1 )
|
|
DA11 = ABS( A11 )
|
|
IF( DA11.LE.SMIN ) THEN
|
|
A11 = SMIN
|
|
DA11 = SMIN
|
|
INFO = 1
|
|
END IF
|
|
DB = ABS( VEC( 1, 1 ) )
|
|
IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
|
|
IF( DB.GT.BIGNUM*DA11 )
|
|
$ SCALOC = ONE / DB
|
|
END IF
|
|
X( 1, 1 ) = ( VEC( 1, 1 )*SCALOC ) / A11
|
|
*
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 80 J = 1, N
|
|
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
|
|
80 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
C( K1, L1 ) = X( 1, 1 )
|
|
*
|
|
ELSE IF( L1.EQ.L2 .AND. K1.NE.K2 ) THEN
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )
|
|
SUMR = SDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
|
|
VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K2 ), 1, C( 1, L1 ), 1 )
|
|
SUMR = SDOT( L1-1, C( K2, 1 ), LDC, B( 1, L1 ), 1 )
|
|
VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
CALL SLALN2( .TRUE., 2, 1, SMIN, ONE, A( K1, K1 ),
|
|
$ LDA, ONE, ONE, VEC, 2, -SGN*B( L1, L1 ),
|
|
$ ZERO, X, 2, SCALOC, XNORM, IERR )
|
|
IF( IERR.NE.0 )
|
|
$ INFO = 1
|
|
*
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 90 J = 1, N
|
|
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
|
|
90 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
C( K1, L1 ) = X( 1, 1 )
|
|
C( K2, L1 ) = X( 2, 1 )
|
|
*
|
|
ELSE IF( L1.NE.L2 .AND. K1.EQ.K2 ) THEN
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )
|
|
SUMR = SDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
|
|
VEC( 1, 1 ) = SGN*( C( K1, L1 )-( SUML+SGN*SUMR ) )
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K1 ), 1, C( 1, L2 ), 1 )
|
|
SUMR = SDOT( L1-1, C( K1, 1 ), LDC, B( 1, L2 ), 1 )
|
|
VEC( 2, 1 ) = SGN*( C( K1, L2 )-( SUML+SGN*SUMR ) )
|
|
*
|
|
CALL SLALN2( .TRUE., 2, 1, SMIN, ONE, B( L1, L1 ),
|
|
$ LDB, ONE, ONE, VEC, 2, -SGN*A( K1, K1 ),
|
|
$ ZERO, X, 2, SCALOC, XNORM, IERR )
|
|
IF( IERR.NE.0 )
|
|
$ INFO = 1
|
|
*
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 100 J = 1, N
|
|
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
|
|
100 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
C( K1, L1 ) = X( 1, 1 )
|
|
C( K1, L2 ) = X( 2, 1 )
|
|
*
|
|
ELSE IF( L1.NE.L2 .AND. K1.NE.K2 ) THEN
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )
|
|
SUMR = SDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
|
|
VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K1 ), 1, C( 1, L2 ), 1 )
|
|
SUMR = SDOT( L1-1, C( K1, 1 ), LDC, B( 1, L2 ), 1 )
|
|
VEC( 1, 2 ) = C( K1, L2 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K2 ), 1, C( 1, L1 ), 1 )
|
|
SUMR = SDOT( L1-1, C( K2, 1 ), LDC, B( 1, L1 ), 1 )
|
|
VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K2 ), 1, C( 1, L2 ), 1 )
|
|
SUMR = SDOT( L1-1, C( K2, 1 ), LDC, B( 1, L2 ), 1 )
|
|
VEC( 2, 2 ) = C( K2, L2 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
CALL SLASY2( .TRUE., .FALSE., ISGN, 2, 2, A( K1, K1 ),
|
|
$ LDA, B( L1, L1 ), LDB, VEC, 2, SCALOC, X,
|
|
$ 2, XNORM, IERR )
|
|
IF( IERR.NE.0 )
|
|
$ INFO = 1
|
|
*
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 110 J = 1, N
|
|
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
|
|
110 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
C( K1, L1 ) = X( 1, 1 )
|
|
C( K1, L2 ) = X( 1, 2 )
|
|
C( K2, L1 ) = X( 2, 1 )
|
|
C( K2, L2 ) = X( 2, 2 )
|
|
END IF
|
|
*
|
|
120 CONTINUE
|
|
130 CONTINUE
|
|
*
|
|
ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN
|
|
*
|
|
* Solve A**T*X + ISGN*X*B**T = scale*C.
|
|
*
|
|
* The (K,L)th block of X is determined starting from
|
|
* top-right corner column by column by
|
|
*
|
|
* A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L)**T = C(K,L) - R(K,L)
|
|
*
|
|
* Where
|
|
* K-1 N
|
|
* 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
|
|
*
|
|
* Start column loop (index = L)
|
|
* L1 (L2): column index of the first (last) row of X(K,L)
|
|
*
|
|
LNEXT = N
|
|
DO 190 L = N, 1, -1
|
|
IF( L.GT.LNEXT )
|
|
$ GO TO 190
|
|
IF( L.EQ.1 ) THEN
|
|
L1 = L
|
|
L2 = L
|
|
ELSE
|
|
IF( B( L, L-1 ).NE.ZERO ) THEN
|
|
L1 = L - 1
|
|
L2 = L
|
|
LNEXT = L - 2
|
|
ELSE
|
|
L1 = L
|
|
L2 = L
|
|
LNEXT = L - 1
|
|
END IF
|
|
END IF
|
|
*
|
|
* Start row loop (index = K)
|
|
* K1 (K2): row index of the first (last) row of X(K,L)
|
|
*
|
|
KNEXT = 1
|
|
DO 180 K = 1, M
|
|
IF( K.LT.KNEXT )
|
|
$ GO TO 180
|
|
IF( K.EQ.M ) THEN
|
|
K1 = K
|
|
K2 = K
|
|
ELSE
|
|
IF( A( K+1, K ).NE.ZERO ) THEN
|
|
K1 = K
|
|
K2 = K + 1
|
|
KNEXT = K + 2
|
|
ELSE
|
|
K1 = K
|
|
K2 = K
|
|
KNEXT = K + 1
|
|
END IF
|
|
END IF
|
|
*
|
|
IF( L1.EQ.L2 .AND. K1.EQ.K2 ) THEN
|
|
SUML = SDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )
|
|
SUMR = SDOT( N-L1, C( K1, MIN( L1+1, N ) ), LDC,
|
|
$ B( L1, MIN( L1+1, N ) ), LDB )
|
|
VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
|
|
SCALOC = ONE
|
|
*
|
|
A11 = A( K1, K1 ) + SGN*B( L1, L1 )
|
|
DA11 = ABS( A11 )
|
|
IF( DA11.LE.SMIN ) THEN
|
|
A11 = SMIN
|
|
DA11 = SMIN
|
|
INFO = 1
|
|
END IF
|
|
DB = ABS( VEC( 1, 1 ) )
|
|
IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
|
|
IF( DB.GT.BIGNUM*DA11 )
|
|
$ SCALOC = ONE / DB
|
|
END IF
|
|
X( 1, 1 ) = ( VEC( 1, 1 )*SCALOC ) / A11
|
|
*
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 140 J = 1, N
|
|
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
|
|
140 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
C( K1, L1 ) = X( 1, 1 )
|
|
*
|
|
ELSE IF( L1.EQ.L2 .AND. K1.NE.K2 ) THEN
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
|
|
$ B( L1, MIN( L2+1, N ) ), LDB )
|
|
VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K2 ), 1, C( 1, L1 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K2, MIN( L2+1, N ) ), LDC,
|
|
$ B( L1, MIN( L2+1, N ) ), LDB )
|
|
VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
CALL SLALN2( .TRUE., 2, 1, SMIN, ONE, A( K1, K1 ),
|
|
$ LDA, ONE, ONE, VEC, 2, -SGN*B( L1, L1 ),
|
|
$ ZERO, X, 2, SCALOC, XNORM, IERR )
|
|
IF( IERR.NE.0 )
|
|
$ INFO = 1
|
|
*
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 150 J = 1, N
|
|
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
|
|
150 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
C( K1, L1 ) = X( 1, 1 )
|
|
C( K2, L1 ) = X( 2, 1 )
|
|
*
|
|
ELSE IF( L1.NE.L2 .AND. K1.EQ.K2 ) THEN
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
|
|
$ B( L1, MIN( L2+1, N ) ), LDB )
|
|
VEC( 1, 1 ) = SGN*( C( K1, L1 )-( SUML+SGN*SUMR ) )
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K1 ), 1, C( 1, L2 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
|
|
$ B( L2, MIN( L2+1, N ) ), LDB )
|
|
VEC( 2, 1 ) = SGN*( C( K1, L2 )-( SUML+SGN*SUMR ) )
|
|
*
|
|
CALL SLALN2( .FALSE., 2, 1, SMIN, ONE, B( L1, L1 ),
|
|
$ LDB, ONE, ONE, VEC, 2, -SGN*A( K1, K1 ),
|
|
$ ZERO, X, 2, SCALOC, XNORM, IERR )
|
|
IF( IERR.NE.0 )
|
|
$ INFO = 1
|
|
*
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 160 J = 1, N
|
|
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
|
|
160 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
C( K1, L1 ) = X( 1, 1 )
|
|
C( K1, L2 ) = X( 2, 1 )
|
|
*
|
|
ELSE IF( L1.NE.L2 .AND. K1.NE.K2 ) THEN
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
|
|
$ B( L1, MIN( L2+1, N ) ), LDB )
|
|
VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K1 ), 1, C( 1, L2 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
|
|
$ B( L2, MIN( L2+1, N ) ), LDB )
|
|
VEC( 1, 2 ) = C( K1, L2 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K2 ), 1, C( 1, L1 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K2, MIN( L2+1, N ) ), LDC,
|
|
$ B( L1, MIN( L2+1, N ) ), LDB )
|
|
VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
SUML = SDOT( K1-1, A( 1, K2 ), 1, C( 1, L2 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K2, MIN( L2+1, N ) ), LDC,
|
|
$ B( L2, MIN(L2+1, N ) ), LDB )
|
|
VEC( 2, 2 ) = C( K2, L2 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
CALL SLASY2( .TRUE., .TRUE., ISGN, 2, 2, A( K1, K1 ),
|
|
$ LDA, B( L1, L1 ), LDB, VEC, 2, SCALOC, X,
|
|
$ 2, XNORM, IERR )
|
|
IF( IERR.NE.0 )
|
|
$ INFO = 1
|
|
*
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 170 J = 1, N
|
|
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
|
|
170 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
C( K1, L1 ) = X( 1, 1 )
|
|
C( K1, L2 ) = X( 1, 2 )
|
|
C( K2, L1 ) = X( 2, 1 )
|
|
C( K2, L2 ) = X( 2, 2 )
|
|
END IF
|
|
*
|
|
180 CONTINUE
|
|
190 CONTINUE
|
|
*
|
|
ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN
|
|
*
|
|
* Solve A*X + ISGN*X*B**T = scale*C.
|
|
*
|
|
* The (K,L)th block of X is determined starting from
|
|
* bottom-right corner column by column by
|
|
*
|
|
* A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L)**T = C(K,L) - R(K,L)
|
|
*
|
|
* Where
|
|
* M N
|
|
* 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
|
|
*
|
|
* Start column loop (index = L)
|
|
* L1 (L2): column index of the first (last) row of X(K,L)
|
|
*
|
|
LNEXT = N
|
|
DO 250 L = N, 1, -1
|
|
IF( L.GT.LNEXT )
|
|
$ GO TO 250
|
|
IF( L.EQ.1 ) THEN
|
|
L1 = L
|
|
L2 = L
|
|
ELSE
|
|
IF( B( L, L-1 ).NE.ZERO ) THEN
|
|
L1 = L - 1
|
|
L2 = L
|
|
LNEXT = L - 2
|
|
ELSE
|
|
L1 = L
|
|
L2 = L
|
|
LNEXT = L - 1
|
|
END IF
|
|
END IF
|
|
*
|
|
* Start row loop (index = K)
|
|
* K1 (K2): row index of the first (last) row of X(K,L)
|
|
*
|
|
KNEXT = M
|
|
DO 240 K = M, 1, -1
|
|
IF( K.GT.KNEXT )
|
|
$ GO TO 240
|
|
IF( K.EQ.1 ) THEN
|
|
K1 = K
|
|
K2 = K
|
|
ELSE
|
|
IF( A( K, K-1 ).NE.ZERO ) THEN
|
|
K1 = K - 1
|
|
K2 = K
|
|
KNEXT = K - 2
|
|
ELSE
|
|
K1 = K
|
|
K2 = K
|
|
KNEXT = K - 1
|
|
END IF
|
|
END IF
|
|
*
|
|
IF( L1.EQ.L2 .AND. K1.EQ.K2 ) THEN
|
|
SUML = SDOT( M-K1, A( K1, MIN(K1+1, M ) ), LDA,
|
|
$ C( MIN( K1+1, M ), L1 ), 1 )
|
|
SUMR = SDOT( N-L1, C( K1, MIN( L1+1, N ) ), LDC,
|
|
$ B( L1, MIN( L1+1, N ) ), LDB )
|
|
VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
|
|
SCALOC = ONE
|
|
*
|
|
A11 = A( K1, K1 ) + SGN*B( L1, L1 )
|
|
DA11 = ABS( A11 )
|
|
IF( DA11.LE.SMIN ) THEN
|
|
A11 = SMIN
|
|
DA11 = SMIN
|
|
INFO = 1
|
|
END IF
|
|
DB = ABS( VEC( 1, 1 ) )
|
|
IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
|
|
IF( DB.GT.BIGNUM*DA11 )
|
|
$ SCALOC = ONE / DB
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|
END IF
|
|
X( 1, 1 ) = ( VEC( 1, 1 )*SCALOC ) / A11
|
|
*
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 200 J = 1, N
|
|
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
|
|
200 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
C( K1, L1 ) = X( 1, 1 )
|
|
*
|
|
ELSE IF( L1.EQ.L2 .AND. K1.NE.K2 ) THEN
|
|
*
|
|
SUML = SDOT( M-K2, A( K1, MIN( K2+1, M ) ), LDA,
|
|
$ C( MIN( K2+1, M ), L1 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
|
|
$ B( L1, MIN( L2+1, N ) ), LDB )
|
|
VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
SUML = SDOT( M-K2, A( K2, MIN( K2+1, M ) ), LDA,
|
|
$ C( MIN( K2+1, M ), L1 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K2, MIN( L2+1, N ) ), LDC,
|
|
$ B( L1, MIN( L2+1, N ) ), LDB )
|
|
VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
CALL SLALN2( .FALSE., 2, 1, SMIN, ONE, A( K1, K1 ),
|
|
$ LDA, ONE, ONE, VEC, 2, -SGN*B( L1, L1 ),
|
|
$ ZERO, X, 2, SCALOC, XNORM, IERR )
|
|
IF( IERR.NE.0 )
|
|
$ INFO = 1
|
|
*
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 210 J = 1, N
|
|
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
|
|
210 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
C( K1, L1 ) = X( 1, 1 )
|
|
C( K2, L1 ) = X( 2, 1 )
|
|
*
|
|
ELSE IF( L1.NE.L2 .AND. K1.EQ.K2 ) THEN
|
|
*
|
|
SUML = SDOT( M-K1, A( K1, MIN( K1+1, M ) ), LDA,
|
|
$ C( MIN( K1+1, M ), L1 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
|
|
$ B( L1, MIN( L2+1, N ) ), LDB )
|
|
VEC( 1, 1 ) = SGN*( C( K1, L1 )-( SUML+SGN*SUMR ) )
|
|
*
|
|
SUML = SDOT( M-K1, A( K1, MIN( K1+1, M ) ), LDA,
|
|
$ C( MIN( K1+1, M ), L2 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
|
|
$ B( L2, MIN( L2+1, N ) ), LDB )
|
|
VEC( 2, 1 ) = SGN*( C( K1, L2 )-( SUML+SGN*SUMR ) )
|
|
*
|
|
CALL SLALN2( .FALSE., 2, 1, SMIN, ONE, B( L1, L1 ),
|
|
$ LDB, ONE, ONE, VEC, 2, -SGN*A( K1, K1 ),
|
|
$ ZERO, X, 2, SCALOC, XNORM, IERR )
|
|
IF( IERR.NE.0 )
|
|
$ INFO = 1
|
|
*
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 220 J = 1, N
|
|
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
|
|
220 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
C( K1, L1 ) = X( 1, 1 )
|
|
C( K1, L2 ) = X( 2, 1 )
|
|
*
|
|
ELSE IF( L1.NE.L2 .AND. K1.NE.K2 ) THEN
|
|
*
|
|
SUML = SDOT( M-K2, A( K1, MIN( K2+1, M ) ), LDA,
|
|
$ C( MIN( K2+1, M ), L1 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
|
|
$ B( L1, MIN( L2+1, N ) ), LDB )
|
|
VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
SUML = SDOT( M-K2, A( K1, MIN( K2+1, M ) ), LDA,
|
|
$ C( MIN( K2+1, M ), L2 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
|
|
$ B( L2, MIN( L2+1, N ) ), LDB )
|
|
VEC( 1, 2 ) = C( K1, L2 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
SUML = SDOT( M-K2, A( K2, MIN( K2+1, M ) ), LDA,
|
|
$ C( MIN( K2+1, M ), L1 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K2, MIN( L2+1, N ) ), LDC,
|
|
$ B( L1, MIN( L2+1, N ) ), LDB )
|
|
VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
SUML = SDOT( M-K2, A( K2, MIN( K2+1, M ) ), LDA,
|
|
$ C( MIN( K2+1, M ), L2 ), 1 )
|
|
SUMR = SDOT( N-L2, C( K2, MIN( L2+1, N ) ), LDC,
|
|
$ B( L2, MIN( L2+1, N ) ), LDB )
|
|
VEC( 2, 2 ) = C( K2, L2 ) - ( SUML+SGN*SUMR )
|
|
*
|
|
CALL SLASY2( .FALSE., .TRUE., ISGN, 2, 2, A( K1, K1 ),
|
|
$ LDA, B( L1, L1 ), LDB, VEC, 2, SCALOC, X,
|
|
$ 2, XNORM, IERR )
|
|
IF( IERR.NE.0 )
|
|
$ INFO = 1
|
|
*
|
|
IF( SCALOC.NE.ONE ) THEN
|
|
DO 230 J = 1, N
|
|
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
|
|
230 CONTINUE
|
|
SCALE = SCALE*SCALOC
|
|
END IF
|
|
C( K1, L1 ) = X( 1, 1 )
|
|
C( K1, L2 ) = X( 1, 2 )
|
|
C( K2, L1 ) = X( 2, 1 )
|
|
C( K2, L2 ) = X( 2, 2 )
|
|
END IF
|
|
*
|
|
240 CONTINUE
|
|
250 CONTINUE
|
|
*
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of STRSYL
|
|
*
|
|
END
|