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

SLATDF(l)					)					SLATDF(l)

NAME
       SLATDF - use the LU factorization of the n-by-n matrix Z computed by SGETC2 and computes a
       contribution to the reciprocal Dif-estimate by solving Z * x = b for x, and  choosing  the
       r.h.s

SYNOPSIS
       SUBROUTINE SLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV )

	   INTEGER	  IJOB, LDZ, N

	   REAL 	  RDSCAL, RDSUM

	   INTEGER	  IPIV( * ), JPIV( * )

	   REAL 	  RHS( * ), Z( LDZ, * )

PURPOSE
       SLATDF  uses the LU factorization of the n-by-n matrix Z computed by SGETC2 and computes a
       contribution to the reciprocal Dif-estimate by solving Z * x = b for x, and  choosing  the
       r.h.s.  b such that the norm of x is as large as possible. On entry RHS = b holds the con-
       tribution from earlier solved sub-systems, and on return RHS = x.

       The factorization of Z returned by SGETC2 has the form Z = P*L*U*Q, where P and Q are per-
       mutation matrices. L is lower triangular with unit diagonal elements and U is upper trian-
       gular.

ARGUMENTS
       IJOB    (input) INTEGER
	       IJOB = 2: First compute an approximative null-vector e of Z  using  SGECON,  e  is
	       normalized  and	solve  for Zx = +-e - f with the sign giving the greater value of
	       2-norm(x). About 5 times as expensive as Default.  IJOB .ne. 2: Local  look  ahead
	       strategy  where	all  entries  of  the  r.h.s.  b  is  choosen  as either +1 or -1
	       (Default).

       N       (input) INTEGER
	       The number of columns of the matrix Z.

       Z       (input) REAL array, dimension (LDZ, N)
	       On entry, the LU part of the factorization of the  n-by-n  matrix  Z  computed  by
	       SGETC2:	Z = P * L * U * Q

       LDZ     (input) INTEGER
	       The leading dimension of the array Z.  LDA >= max(1, N).

       RHS     (input/output) REAL array, dimension N.
	       On entry, RHS contains contributions from other subsystems.  On exit, RHS contains
	       the solution of the subsystem with entries acoording to the  value  of  IJOB  (see
	       above).

       RDSUM   (input/output) REAL
	       On  entry,  the sum of squares of computed contributions to the Dif-estimate under
	       computation by STGSYL, 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 STGSY2 is called by STGSYL.

       RDSCAL  (input/output) REAL
	       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 STGSY2 is called by STGSYL.

       IPIV    (input) INTEGER array, dimension (N).
	       The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with
	       row IPIV(i).

       JPIV    (input) INTEGER array, dimension (N).
	       The pivot indices; for 1 <= j <= N, column j of the matrix has  been  interchanged
	       with column JPIV(j).

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

       This  routine  is a further developed implementation of algorithm BSOLVE in [1] using com-
       plete pivoting in the LU factorization.

       [1] Bo Kagstrom and Lars Westin,
	   Generalized Schur Methods with Condition Estimators for
	   Solving the Generalized Sylvester Equation, IEEE Transactions
	   on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.

       [2] Peter Poromaa,
	   On Efficient and Robust Estimators for the Separation
	   between two Regular Matrix Pairs with Applications in
	   Condition Estimation. Report IMINF-95.05, Departement of
	   Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.

LAPACK version 3.0			   15 June 2000 				SLATDF(l)


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