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|
*> \brief \b STRSYL
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download STRSYL + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/strsyl.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/strsyl.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/strsyl.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE STRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
* LDC, SCALE, INFO )
*
* .. Scalar Arguments ..
* CHARACTER TRANA, TRANB
* INTEGER INFO, ISGN, LDA, LDB, LDC, M, N
* REAL SCALE
* ..
* .. Array Arguments ..
* REAL A( LDA, * ), B( LDB, * ), C( LDC, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> STRSYL solves the real Sylvester matrix equation:
*>
*> op(A)*X + X*op(B) = scale*C or
*> op(A)*X - X*op(B) = scale*C,
*>
*> where op(A) = A or A**T, and A and B are both upper quasi-
*> triangular. A is M-by-M and B is N-by-N; the right hand side C and
*> the solution X are M-by-N; and scale is an output scale factor, set
*> <= 1 to avoid overflow in X.
*>
*> A and B must be in Schur canonical form (as returned by SHSEQR), that
*> is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks;
*> each 2-by-2 diagonal block has its diagonal elements equal and its
*> off-diagonal elements of opposite sign.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANA
*> \verbatim
*> TRANA is CHARACTER*1
*> Specifies the option op(A):
*> = 'N': op(A) = A (No transpose)
*> = 'T': op(A) = A**T (Transpose)
*> = 'C': op(A) = A**H (Conjugate transpose = Transpose)
*> \endverbatim
*>
*> \param[in] TRANB
*> \verbatim
*> TRANB is CHARACTER*1
*> Specifies the option op(B):
*> = 'N': op(B) = B (No transpose)
*> = 'T': op(B) = B**T (Transpose)
*> = 'C': op(B) = B**H (Conjugate transpose = Transpose)
*> \endverbatim
*>
*> \param[in] ISGN
*> \verbatim
*> ISGN is INTEGER
*> Specifies the sign in the equation:
*> = +1: solve op(A)*X + X*op(B) = scale*C
*> = -1: solve op(A)*X - X*op(B) = scale*C
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The order of the matrix A, and the number of rows in the
*> matrices X and C. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix B, and the number of columns in the
*> matrices X and C. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is REAL array, dimension (LDA,M)
*> The upper quasi-triangular matrix A, in Schur canonical form.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is REAL array, dimension (LDB,N)
*> The upper quasi-triangular matrix B, in Schur canonical form.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*> C is REAL array, dimension (LDC,N)
*> On entry, the M-by-N right hand side matrix C.
*> On exit, C is overwritten by the solution matrix X.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is INTEGER
*> The leading dimension of the array C. LDC >= max(1,M)
*> \endverbatim
*>
*> \param[out] SCALE
*> \verbatim
*> SCALE is REAL
*> The scale factor, scale, set <= 1 to avoid overflow in X.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> = 1: A and B have common or very close eigenvalues; perturbed
*> values were used to solve the equation (but the matrices
*> A and B are unchanged).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup realSYcomputational
*
* =====================================================================
SUBROUTINE STRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
$ LDC, SCALE, INFO )
*
* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER TRANA, TRANB
INTEGER INFO, ISGN, LDA, LDB, LDC, M, N
REAL SCALE
* ..
* .. Array Arguments ..
REAL A( LDA, * ), B( LDB, * ), C( LDC, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL NOTRNA, NOTRNB
INTEGER IERR, J, K, K1, K2, KNEXT, L, L1, L2, LNEXT
REAL A11, BIGNUM, DA11, DB, EPS, SCALOC, SGN, SMIN,
$ SMLNUM, SUML, SUMR, XNORM
* ..
* .. Local Arrays ..
REAL DUM( 1 ), VEC( 2, 2 ), X( 2, 2 )
* ..
* .. External Functions ..
LOGICAL LSAME
REAL SDOT, SLAMCH, SLANGE
EXTERNAL LSAME, SDOT, SLAMCH, SLANGE
* ..
* .. External Subroutines ..
EXTERNAL SLABAD, SLALN2, SLASY2, SSCAL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, REAL
* ..
* .. Executable Statements ..
*
* Decode and Test input parameters
*
NOTRNA = LSAME( TRANA, 'N' )
NOTRNB = LSAME( TRANB, 'N' )
*
INFO = 0
IF( .NOT.NOTRNA .AND. .NOT.LSAME( TRANA, 'T' ) .AND. .NOT.
$ LSAME( TRANA, 'C' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOTRNB .AND. .NOT.LSAME( TRANB, 'T' ) .AND. .NOT.
$ LSAME( TRANB, 'C' ) ) THEN
INFO = -2
ELSE IF( ISGN.NE.1 .AND. ISGN.NE.-1 ) THEN
INFO = -3
ELSE IF( M.LT.0 ) THEN
INFO = -4
ELSE IF( N.LT.0 ) THEN
INFO = -5
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -7
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -9
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -11
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'STRSYL', -INFO )
RETURN
END IF
*
* Quick return if possible
*
SCALE = ONE
IF( M.EQ.0 .OR. N.EQ.0 )
$ RETURN
*
* Set constants to control overflow
*
EPS = SLAMCH( 'P' )
SMLNUM = SLAMCH( 'S' )
BIGNUM = ONE / SMLNUM
CALL SLABAD( SMLNUM, BIGNUM )
SMLNUM = SMLNUM*REAL( M*N ) / EPS
BIGNUM = ONE / SMLNUM
*
SMIN = MAX( SMLNUM, EPS*SLANGE( 'M', M, M, A, LDA, DUM ),
$ EPS*SLANGE( 'M', N, N, B, LDB, DUM ) )
*
SGN = ISGN
*
IF( NOTRNA .AND. NOTRNB ) THEN
*
* Solve A*X + ISGN*X*B = scale*C.
*
* The (K,L)th block of X is determined starting from
* bottom-left corner column by column by
*
* A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
*
* Where
* M L-1
* R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)].
* I=K+1 J=1
*
* Start column loop (index = L)
* L1 (L2) : column index of the first (first) row of X(K,L).
*
LNEXT = 1
DO 70 L = 1, N
IF( L.LT.LNEXT )
$ GO TO 70
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 = M
DO 60 K = M, 1, -1
IF( K.GT.KNEXT )
$ GO TO 60
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( 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 10 J = 1, N
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
10 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( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
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( L1-1, C( K2, 1 ), LDC, B( 1, L1 ), 1 )
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 20 J = 1, N
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
20 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( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
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( 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 40 J = 1, N
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
40 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( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
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( L1-1, C( K1, 1 ), LDC, B( 1, L2 ), 1 )
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( L1-1, C( K2, 1 ), LDC, B( 1, L1 ), 1 )
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( L1-1, C( K2, 1 ), LDC, B( 1, L2 ), 1 )
VEC( 2, 2 ) = C( K2, L2 ) - ( SUML+SGN*SUMR )
*
CALL SLASY2( .FALSE., .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 50 J = 1, N
CALL SSCAL( M, SCALOC, C( 1, J ), 1 )
50 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
*
60 CONTINUE
*
70 CONTINUE
*
ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN
*
* Solve A**T *X + ISGN*X*B = scale*C.
*
* The (K,L)th block of X is determined starting from
* upper-left corner column by column by
*
* A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
*
* 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
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
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