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DTRSYL(3F)							    DTRSYL(3F)


NAME    [Toc]    [Back]

     DTRSYL - solve the	real Sylvester matrix equation

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DTRSYL(	TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC,
			SCALE, INFO )

	 CHARACTER	TRANA, TRANB

	 INTEGER	INFO, ISGN, LDA, LDB, LDC, M, N

	 DOUBLE		PRECISION SCALE

	 DOUBLE		PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )

PURPOSE    [Toc]    [Back]

     DTRSYL 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 DHSEQR), 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.

ARGUMENTS    [Toc]    [Back]

     TRANA   (input) 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)

     TRANB   (input) 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)

     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






									Page 1






DTRSYL(3F)							    DTRSYL(3F)



     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) DOUBLE PRECISION array, dimension (LDA,M)
	     The upper quasi-triangular	matrix A, in Schur canonical form.

     LDA     (input) INTEGER
	     The leading dimension of the array	A. LDA >= max(1,M).

     B	     (input) DOUBLE PRECISION array, dimension (LDB,N)
	     The upper quasi-triangular	matrix B, in Schur canonical form.

     LDB     (input) INTEGER
	     The leading dimension of the array	B. LDB >= max(1,N).

     C	     (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION
	     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).
DTRSYL(3F)							    DTRSYL(3F)


NAME    [Toc]    [Back]

     DTRSYL - solve the	real Sylvester matrix equation

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DTRSYL(	TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC,
			SCALE, INFO )

	 CHARACTER	TRANA, TRANB

	 INTEGER	INFO, ISGN, LDA, LDB, LDC, M, N

	 DOUBLE		PRECISION SCALE

	 DOUBLE		PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )

PURPOSE    [Toc]    [Back]

     DTRSYL 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 DHSEQR), 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.

ARGUMENTS    [Toc]    [Back]

     TRANA   (input) 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)

     TRANB   (input) 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)

     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






									Page 1






DTRSYL(3F)							    DTRSYL(3F)



     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) DOUBLE PRECISION array, dimension (LDA,M)
	     The upper quasi-triangular	matrix A, in Schur canonical form.

     LDA     (input) INTEGER
	     The leading dimension of the array	A. LDA >= max(1,M).

     B	     (input) DOUBLE PRECISION array, dimension (LDB,N)
	     The upper quasi-triangular	matrix B, in Schur canonical form.

     LDB     (input) INTEGER
	     The leading dimension of the array	B. LDB >= max(1,N).

     C	     (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION
	     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).


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