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SUBROUTINE CTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
$ LDC, SCALE, INFO )
*
* -- LAPACK routine (version 3.3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* -- April 2011 --
*
* .. Scalar Arguments ..
CHARACTER TRANA, TRANB
INTEGER INFO, ISGN, LDA, LDB, LDC, M, N
REAL SCALE
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * )
* ..
*
* Purpose
* =======
*
* CTRSYL solves the complex 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**H, and A and B are both upper 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.
*
* Arguments
* =========
*
* TRANA (input) CHARACTER*1
* Specifies the option op(A):
* = 'N': op(A) = A (No transpose)
* = 'C': op(A) = A**H (Conjugate transpose)
*
* TRANB (input) CHARACTER*1
* Specifies the option op(B):
* = 'N': op(B) = B (No transpose)
* = 'C': op(B) = B**H (Conjugate transpose)
*
* ISGN (input) 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
*
* M (input) INTEGER
* The order of the matrix A, and the number of rows in the
* matrices X and C. M >= 0.
*
* N (input) INTEGER
* The order of the matrix B, and the number of columns in the
* matrices X and C. N >= 0.
*
* A (input) COMPLEX array, dimension (LDA,M)
* The upper triangular matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,M).
*
* B (input) COMPLEX array, dimension (LDB,N)
* The upper triangular matrix B.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* C (input/output) COMPLEX 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.
*
* LDC (input) INTEGER
* The leading dimension of the array C. LDC >= max(1,M)
*
* SCALE (output) REAL
* The scale factor, scale, set <= 1 to avoid overflow in X.
*
* INFO (output) 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).
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL NOTRNA, NOTRNB
INTEGER J, K, L
REAL BIGNUM, DA11, DB, EPS, SCALOC, SGN, SMIN,
$ SMLNUM
COMPLEX A11, SUML, SUMR, VEC, X11
* ..
* .. Local Arrays ..
REAL DUM( 1 )
* ..
* .. External Functions ..
LOGICAL LSAME
REAL CLANGE, SLAMCH
COMPLEX CDOTC, CDOTU, CLADIV
EXTERNAL LSAME, CLANGE, SLAMCH, CDOTC, CDOTU, CLADIV
* ..
* .. External Subroutines ..
EXTERNAL CSSCAL, SLABAD, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, AIMAG, CMPLX, CONJG, 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, 'C' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOTRNB .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( 'CTRSYL', -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*CLANGE( 'M', M, M, A, LDA, DUM ),
$ EPS*CLANGE( '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
*
DO 30 L = 1, N
DO 20 K = M, 1, -1
*
SUML = CDOTU( M-K, A( K, MIN( K+1, M ) ), LDA,
$ C( MIN( K+1, M ), L ), 1 )
SUMR = CDOTU( L-1, C( K, 1 ), LDC, B( 1, L ), 1 )
VEC = C( K, L ) - ( SUML+SGN*SUMR )
*
SCALOC = ONE
A11 = A( K, K ) + SGN*B( L, L )
DA11 = ABS( REAL( A11 ) ) + ABS( AIMAG( A11 ) )
IF( DA11.LE.SMIN ) THEN
A11 = SMIN
DA11 = SMIN
INFO = 1
END IF
DB = ABS( REAL( VEC ) ) + ABS( AIMAG( VEC ) )
IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
IF( DB.GT.BIGNUM*DA11 )
$ SCALOC = ONE / DB
END IF
X11 = CLADIV( VEC*CMPLX( SCALOC ), A11 )
*
IF( SCALOC.NE.ONE ) THEN
DO 10 J = 1, N
CALL CSSCAL( M, SCALOC, C( 1, J ), 1 )
10 CONTINUE
SCALE = SCALE*SCALOC
END IF
C( K, L ) = X11
*
20 CONTINUE
30 CONTINUE
*
ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN
*
* Solve A**H *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**H(K,K)*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**H(I,K)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]
* I=1 J=1
*
DO 60 L = 1, N
DO 50 K = 1, M
*
SUML = CDOTC( K-1, A( 1, K ), 1, C( 1, L ), 1 )
SUMR = CDOTU( L-1, C( K, 1 ), LDC, B( 1, L ), 1 )
VEC = C( K, L ) - ( SUML+SGN*SUMR )
*
SCALOC = ONE
A11 = CONJG( A( K, K ) ) + SGN*B( L, L )
DA11 = ABS( REAL( A11 ) ) + ABS( AIMAG( A11 ) )
IF( DA11.LE.SMIN ) THEN
A11 = SMIN
DA11 = SMIN
INFO = 1
END IF
DB = ABS( REAL( VEC ) ) + ABS( AIMAG( VEC ) )
IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
IF( DB.GT.BIGNUM*DA11 )
$ SCALOC = ONE / DB
END IF
*
X11 = CLADIV( VEC*CMPLX( SCALOC ), A11 )
*
IF( SCALOC.NE.ONE ) THEN
DO 40 J = 1, N
CALL CSSCAL( M, SCALOC, C( 1, J ), 1 )
40 CONTINUE
SCALE = SCALE*SCALOC
END IF
C( K, L ) = X11
*
50 CONTINUE
60 CONTINUE
*
ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN
*
* Solve A**H*X + ISGN*X*B**H = C.
*
* The (K,L)th block of X is determined starting from
* upper-right corner column by column by
*
* A**H(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
*
* Where
* K-1
* R(K,L) = SUM [A**H(I,K)*X(I,L)] +
* I=1
* N
* ISGN*SUM [X(K,J)*B**H(L,J)].
* J=L+1
*
DO 90 L = N, 1, -1
DO 80 K = 1, M
*
SUML = CDOTC( K-1, A( 1, K ), 1, C( 1, L ), 1 )
SUMR = CDOTC( N-L, C( K, MIN( L+1, N ) ), LDC,
$ B( L, MIN( L+1, N ) ), LDB )
VEC = C( K, L ) - ( SUML+SGN*CONJG( SUMR ) )
*
SCALOC = ONE
A11 = CONJG( A( K, K )+SGN*B( L, L ) )
DA11 = ABS( REAL( A11 ) ) + ABS( AIMAG( A11 ) )
IF( DA11.LE.SMIN ) THEN
A11 = SMIN
DA11 = SMIN
INFO = 1
END IF
DB = ABS( REAL( VEC ) ) + ABS( AIMAG( VEC ) )
IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
IF( DB.GT.BIGNUM*DA11 )
$ SCALOC = ONE / DB
END IF
*
X11 = CLADIV( VEC*CMPLX( SCALOC ), A11 )
*
IF( SCALOC.NE.ONE ) THEN
DO 70 J = 1, N
CALL CSSCAL( M, SCALOC, C( 1, J ), 1 )
70 CONTINUE
SCALE = SCALE*SCALOC
END IF
C( K, L ) = X11
*
80 CONTINUE
90 CONTINUE
*
ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN
*
* Solve A*X + ISGN*X*B**H = 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**H(L,L) = 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**H(L,J)]
* I=K+1 J=L+1
*
DO 120 L = N, 1, -1
DO 110 K = M, 1, -1
*
SUML = CDOTU( M-K, A( K, MIN( K+1, M ) ), LDA,
$ C( MIN( K+1, M ), L ), 1 )
SUMR = CDOTC( N-L, C( K, MIN( L+1, N ) ), LDC,
$ B( L, MIN( L+1, N ) ), LDB )
VEC = C( K, L ) - ( SUML+SGN*CONJG( SUMR ) )
*
SCALOC = ONE
A11 = A( K, K ) + SGN*CONJG( B( L, L ) )
DA11 = ABS( REAL( A11 ) ) + ABS( AIMAG( A11 ) )
IF( DA11.LE.SMIN ) THEN
A11 = SMIN
DA11 = SMIN
INFO = 1
END IF
DB = ABS( REAL( VEC ) ) + ABS( AIMAG( VEC ) )
IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
IF( DB.GT.BIGNUM*DA11 )
$ SCALOC = ONE / DB
END IF
*
X11 = CLADIV( VEC*CMPLX( SCALOC ), A11 )
*
IF( SCALOC.NE.ONE ) THEN
DO 100 J = 1, N
CALL CSSCAL( M, SCALOC, C( 1, J ), 1 )
100 CONTINUE
SCALE = SCALE*SCALOC
END IF
C( K, L ) = X11
*
110 CONTINUE
120 CONTINUE
*
END IF
*
RETURN
*
* End of CTRSYL
*
END
|
