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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: solves a system of linear equations A * X = scale* RHS with a general N-by-N matrix A using the LU factorization with

```NAME
LAPACK-3  -  solves  a  system of linear equations   A * X = scale* RHS
with a general N-by-N matrix A using the LU factorization with complete
pivoting computed by ZGETC2

SYNOPSIS
SUBROUTINE ZGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )

INTEGER        LDA, N

DOUBLE         PRECISION SCALE

INTEGER        IPIV( * ), JPIV( * )

COMPLEX*16     A( LDA, * ), RHS( * )

PURPOSE
ZGESC2 solves a system of linear equations

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

A       (input) COMPLEX*16 array, dimension (LDA, N)
On entry, the  LU part of the factorization of the n-by-n
matrix A computed by ZGETC2:  A = P * L * U * Q

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

RHS     (input/output) COMPLEX*16 array, dimension N.
On entry, the right hand side vector b.
On exit, the solution vector X.

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).

SCALE    (output) DOUBLE PRECISION
On exit, SCALE contains the scale factor. SCALE is chosen
0 <= SCALE <= 1 to prevent owerflow in the solution.

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

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
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