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DLATDF(3S)							    DLATDF(3S)

NAME
     DLATDF - use the LU factorization of the n-by-n matrix Z computed by
     DGETC2 and computes a contribution to the reciprocal Dif-estimate by
     solving Z * x = b for x, and choosing the r.h.s

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

	 INTEGER	IJOB, LDZ, N

	 DOUBLE		PRECISION RDSCAL, RDSUM

	 INTEGER	IPIV( * ), JPIV( * )

	 DOUBLE		PRECISION RHS( * ), Z( LDZ, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     DLATDF uses the LU factorization of the n-by-n matrix Z computed by
     DGETC2 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 contribution from
     earlier solved sub-systems, and on return RHS = x.

     The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q, where
     P and Q are permutation matrices. L is lower triangular with unit
     diagonal elements and U is upper triangular.

ARGUMENTS
     IJOB    (input) INTEGER
	     IJOB = 2: First compute an approximative null-vector e of Z using
	     DGECON, 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.

									Page 1

DLATDF(3S)							    DLATDF(3S)

     Z	     (input) DOUBLE PRECISION array, dimension (LDZ, N)
	     On entry, the LU part of the factorization of the n-by-n matrix Z
	     computed by DGETC2:  Z = P * L * U * Q

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

     RHS     (input/output) DOUBLE PRECISION 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) 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 STGSYL.

     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 DTGSY2 is called by DTGSYL.

     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 complete 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.

									Page 2

DLATDF(3S)							    DLATDF(3S)

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.

									Page 3

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