# slatdf (l) - Linux Manuals

## 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

## NAME

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## 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 contribution 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 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 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 factored out. On exit, the corresponding sum of squares updated with the contributions from the current sub-system. If TRANS = aqTaq 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 = aqTaq, 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 byBo 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,