DTGSY2 man page on Oracle

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dtgsy2.f(3)			    LAPACK			   dtgsy2.f(3)

NAME
       dtgsy2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dtgsy2 (TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, LDD,
	   E, LDE, F, LDF, SCALE, RDSUM, RDSCAL, IWORK, PQ, INFO)
	   DTGSY2 solves the generalized Sylvester equation (unblocked
	   algorithm).

Function/Subroutine Documentation
   subroutine dtgsy2 (characterTRANS, integerIJOB, integerM, integerN, double
       precision, dimension( lda, * )A, integerLDA, double precision,
       dimension( ldb, * )B, integerLDB, double precision, dimension( ldc, *
       )C, integerLDC, double precision, dimension( ldd, * )D, integerLDD,
       double precision, dimension( lde, * )E, integerLDE, double precision,
       dimension( ldf, * )F, integerLDF, double precisionSCALE, double
       precisionRDSUM, double precisionRDSCAL, integer, dimension( * )IWORK,
       integerPQ, integerINFO)
       DTGSY2 solves the generalized Sylvester equation (unblocked algorithm).

       Purpose:

	    DTGSY2 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, with real entries. (A, D) and (B, E)
	    must be in generalized Schur canonical form, i.e. A, B are upper
	    quasi triangular and D, E are upper triangular. 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
	    Z*x = scale*b, where Z is defined as

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

	    Ik is the identity matrix of size k and X**T is the transpose of X.
	    kron(X, Y) is the Kronecker product between the matrices X and Y.
	    In the process of solving (1), we solve a number of such systems
	    where Dim(In), Dim(In) = 1 or 2.

	    If TRANS = 'T', solve the transposed system Z**T*y = scale*b for y,
	    which is equivalent to solve for R and L in

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

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

	    DTGSY2 also (IJOB >= 1) contributes to the computation in DTGSYL
	    of an upper bound on the separation between to matrix pairs. Then
	    the input (A, D), (B, E) are sub-pencils of the matrix pair in
	    DTGSYL. See DTGSYL for details.

       Parameters:
	   TRANS

		     TRANS is CHARACTER*1
		     = 'N', solve the generalized Sylvester equation (1).
		     = 'T': solve the 'transposed' system (3).

	   IJOB

		     IJOB is 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

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

	   N

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

	   A

		     A is DOUBLE PRECISION array, dimension (LDA, M)
		     On entry, A contains an upper quasi triangular matrix.

	   LDA

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

	   B

		     B is DOUBLE PRECISION array, dimension (LDB, N)
		     On entry, B contains an upper quasi triangular matrix.

	   LDB

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

	   C

		     C is DOUBLE PRECISION 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

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

	   D

		     D is DOUBLE PRECISION array, dimension (LDD, M)
		     On entry, D contains an upper triangular matrix.

	   LDD

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

	   E

		     E is DOUBLE PRECISION array, dimension (LDE, N)
		     On entry, E contains an upper triangular matrix.

	   LDE

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

	   F

		     F is DOUBLE PRECISION 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

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

	   SCALE

		     SCALE is 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 matrices A, B, D and
		     E have not been changed. If SCALE = 0, R and L will hold the
		     solutions to the homogeneous system with C = F = 0. Normally,
		     SCALE = 1.

	   RDSUM

		     RDSUM is DOUBLE PRECISION
		     On entry, the sum of squares of computed contributions to
		     the Dif-estimate under computation by DTGSYL, where the
		     scaling factor RDSCAL (see below) has been factored out.
		     On exit, the corresponding sum of squares updated with the
		     contributions from the current sub-system.
		     If TRANS = 'T' RDSUM is not touched.
		     NOTE: RDSUM only makes sense when DTGSY2 is called by DTGSYL.

	   RDSCAL

		     RDSCAL is 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 DTGSY2 is called by
			   DTGSYL.

	   IWORK

		     IWORK is INTEGER array, dimension (M+N+2)

	   PQ

		     PQ is INTEGER
		     On exit, the number of subsystems (of size 2-by-2, 4-by-4 and
		     8-by-8) solved by this routine.

	   INFO

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Bo Kagstrom and Peter Poromaa, Department of Computing Science,
	   Umea University, S-901 87 Umea, Sweden.

       Definition at line 273 of file dtgsy2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2			Tue Sep 25 2012			   dtgsy2.f(3)
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