zlatdf()

subroutine zlatdf	(	integer	ijob,
		integer	n,
		complex*16, dimension( ldz, * )	z,
		integer	ldz,
		complex*16, dimension( * )	rhs,
		double precision	rdsum,
		double precision	rdscal,
		integer, dimension( * )	ipiv,
		integer, dimension( * )	jpiv )

ZLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

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Purpose:

!>
!> ZLATDF computes the contribution to the reciprocal Dif-estimate
!> by solving for x in Z * x = b, where b is chosen such that the norm
!> of x is as large as possible. It is assumed that LU decomposition
!> of Z has been computed by ZGETC2. On entry RHS = f holds the
!> contribution from earlier solved sub-systems, and on return RHS = x.
!>
!> The factorization of Z returned by ZGETC2 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.
!> 

Parameters

[in]	IJOB	!> IJOB is INTEGER !> IJOB = 2: First compute an approximative null-vector e !> of Z using ZGECON, 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 chosen as either +1 or !> -1. Default. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrix Z. !>
[in]	Z	!> Z is COMPLEX*16 array, dimension (LDZ, N) !> On entry, the LU part of the factorization of the n-by-n !> matrix Z computed by ZGETC2: Z = P * L * U * Q !>
[in]	LDZ	!> LDZ is INTEGER !> The leading dimension of the array Z. LDA >= max(1, N). !>
[in,out]	RHS	!> RHS is COMPLEX*16 array, dimension (N). !> On entry, RHS contains contributions from other subsystems. !> On exit, RHS contains the solution of the subsystem with !> entries according to the value of IJOB (see above). !>
[in,out]	RDSUM	!> RDSUM is 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 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 ZTGSY2 is called by CTGSYL. !>
[in,out]	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 ZTGSY2 is called by !> ZTGSYL. !>
[in]	IPIV	!> IPIV is INTEGER array, dimension (N). !> The pivot indices; for 1 <= i <= N, row i of the !> matrix has been interchanged with row IPIV(i). !>
[in]	JPIV	!> JPIV is INTEGER array, dimension (N). !> The pivot indices; for 1 <= j <= N, column j of the !> matrix has been interchanged with column JPIV(j). !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

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

Contributors:

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

References:

[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 UMINF-95.05, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.