?gesc2

Solves a system of linear equations using the LU factorization with complete pivoting computed by ?getc2.

Syntax

call sgesc2( n, a, lda, rhs, ipiv, jpiv, scale )

call dgesc2( n, a, lda, rhs, ipiv, jpiv, scale )

call cgesc2( n, a, lda, rhs, ipiv, jpiv, scale )

call zgesc2( n, a, lda, rhs, ipiv, jpiv, scale )

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).

Description

The routine 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 ?getc2.

Input Parameters

n

INTEGER. The order of the matrix A.

a, rhs

REAL for sgesc2

DOUBLE PRECISION for dgesc2

COMPLEX for cgesc2

DOUBLE COMPLEX for zgesc2.

Arrays:

a(lda,*) contains the LU part of the factorization of the n-by-n matrix A computed by ?getc2:

A = P*L*U*Q.

The second dimension of a must be at least max(1, n);

rhs(n) contains on entry the right hand side vector for the system of equations.

lda

INTEGER. The leading dimension of a; at least max(1, n).

ipiv

INTEGER.

Array, DIMENSION at least max(1,n).

The pivot indices: for 1 ≤ i ≤ n, row i of the matrix has been interchanged with row ipiv(i).

jpiv

INTEGER.

Array, DIMENSION at least max(1,n).

The pivot indices: for 1 ≤ j ≤ n, column j of the matrix has been interchanged with column jpiv(j).

Output Parameters

rhs

On exit, overwritten with the solution vector X.

scale

REAL for sgesc2/cgesc2

DOUBLE PRECISION for dgesc2/zgesc2

Contains the scale factor. scale is chosen in the range 0 ≤ scale ≤ 1 to prevent overflow in the solution.