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RedHat 9 (Linux i386) - man page for ztgsy2 (redhat section l)

ZTGSY2(l)					)					ZTGSY2(l)

NAME
       ZTGSY2 - solve the generalized Sylvester equation  A * R - L * B = scale * C (1) D * R - L
       * E = scale * F	using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices,

SYNOPSIS
       SUBROUTINE ZTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D,  LDD,  E,  LDE,  F,  LDF,
			  SCALE, RDSUM, RDSCAL, INFO )

	   CHARACTER	  TRANS

	   INTEGER	  IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, M, N

	   DOUBLE	  PRECISION RDSCAL, RDSUM, SCALE

	   COMPLEX*16	  A(  LDA,  *  ),  B( LDB, * ), C( LDC, * ), D( LDD, * ), E( LDE, * ), F(
			  LDF, * )

PURPOSE
       ZTGSY2 solves the generalized Sylvester equation A * R - L * B = scale * C (1) D * R - L *
       E = scale * F using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices, (A, D),
       (B, E) and (C, F) are given matrix pairs of size M-by-M, N-by-N and M-by-N,  respectively.
       A, B, D and E are upper triangular (i.e., (A,D) and (B,E) in generalized Schur form).

       The  solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output scaling factor chosen
       to avoid overflow.

       In matrix notation solving equation (1) corresponds to solve Zx = scale * b,  where  Z  is
       defined as

	      Z = [ kron(In, A)  -kron(B', Im) ]	     (2)
		  [ kron(In, D)  -kron(E', Im) ],

       Ik  is the identity matrix of size k and X' is the transpose of X.  kron(X, Y) is the Kro-
       necker product between the matrices X and Y.

       If TRANS = 'C', y in the conjugate transposed system Z'y = scale*b is solved for, which is
       equivalent to solve for R and L in

		   A' * R  + D' * L   = scale *  C	     (3)
		   R  * B' + L	* E'  = scale * -F

       This  case  is  used  to compute an estimate of Dif[(A, D), (B, E)] = = sigma_min(Z) using
       reverse communicaton with ZLACON.

       ZTGSY2 also (IJOB >= 1) contributes to the computation in ZTGSYL of an upper bound on  the
       separation  between  to matrix pairs. Then the input (A, D), (B, E) are sub-pencils of two
       matrix pairs in ZTGSYL.

ARGUMENTS
       TRANS   (input) CHARACTER
	       = 'N', solve the generalized Sylvester equation (1).  =	'T':  solve  the  'trans-
	       posed' system (3).

       IJOB    (input) INTEGER
	       Specifies what kind of functionality to be performed.  =0: solve (1) only.
	       =1:  A  contribution from this subsystem to a Frobenius norm-based estimate of the
	       separation between two matrix pairs is computed. (look ahead  strategy  is  used).
	       =2:  A  contribution from this subsystem to a Frobenius norm-based estimate of the
	       separation between two matrix pairs is computed. (DGECON on sub-systems is  used.)
	       Not referenced if TRANS = 'T'.

       M       (input) INTEGER
	       On  entry,  M specifies the order of A and D, and the row dimension of C, F, R and
	       L.

       N       (input) INTEGER
	       On entry, N specifies the order of B and E, and the column dimension of	C,  F,	R
	       and L.

       A       (input) COMPLEX*16 array, dimension (LDA, M)
	       On entry, A contains an upper triangular matrix.

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

       B       (input) COMPLEX*16 array, dimension (LDB, N)
	       On entry, B contains an upper triangular matrix.

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

       C       (input/ output) COMPLEX*16 array, dimension (LDC, N)
	       On  entry, C contains the right-hand-side of the first matrix equation in (1).  On
	       exit, if IJOB = 0, C has been overwritten by the solution R.

       LDC     (input) INTEGER
	       The leading dimension of the matrix C. LDC >= max(1, M).

       D       (input) COMPLEX*16 array, dimension (LDD, M)
	       On entry, D contains an upper triangular matrix.

       LDD     (input) INTEGER
	       The leading dimension of the matrix D. LDD >= max(1, M).

       E       (input) COMPLEX*16 array, dimension (LDE, N)
	       On entry, E contains an upper triangular matrix.

       LDE     (input) INTEGER
	       The leading dimension of the matrix E. LDE >= max(1, N).

       F       (input/ output) COMPLEX*16 array, dimension (LDF, N)
	       On entry, F contains the right-hand-side of the second matrix equation in (1).  On
	       exit, if IJOB = 0, F has been overwritten by the solution L.

       LDF     (input) INTEGER
	       The leading dimension of the matrix F. LDF >= max(1, M).

       SCALE   (output) DOUBLE PRECISION
	       On  exit,  0  <=  SCALE	<= 1. If 0 < SCALE < 1, the solutions R and L (C and F on
	       entry) will hold the solutions to a slightly perturbed system but the input matri-
	       ces A, B, D and E have not been changed. If SCALE = 0, R and L will hold the solu-
	       tions to the homogeneous system with C = F = 0.	Normally, SCALE = 1.

       RDSUM   (input/output) DOUBLE PRECISION
	       On entry, the sum of squares of computed contributions to the  Dif-estimate  under
	       computation  by	ZTGSYL, where the scaling factor RDSCAL (see below) has been fac-
	       tored out.  On exit, the corresponding sum of squares updated with  the	contribu-
	       tions  from  the  current sub-system.  If TRANS = 'T' RDSUM is not touched.  NOTE:
	       RDSUM only makes sense when ZTGSY2 is called by ZTGSYL.

       RDSCAL  (input/output) DOUBLE PRECISION
	       On entry, scaling factor used to prevent overflow in RDSUM.  On	exit,  RDSCAL  is
	       updated	w.r.t. the current contributions in RDSUM.  If TRANS = 'T', RDSCAL is not
	       touched.  NOTE: RDSCAL only makes sense when ZTGSY2 is called by ZTGSYL.

       INFO    (output) INTEGER
	       On exit, if INFO is set to =0: Successful exit
	       <0: If INFO = -i, input argument number i is illegal.
	       >0: The matrix pairs (A, D) and (B, E) have common or very close eigenvalues.

FURTHER DETAILS
       Based on contributions by
	  Bo Kagstrom and Peter Poromaa, Department of Computing Science,
	  Umea University, S-901 87 Umea, Sweden.

LAPACK version 3.0			   15 June 2000 				ZTGSY2(l)


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