sgetri(3F)

NAME
     SGETRI - compute the inverse of a matrix using the LU factorization
     computed by SGETRF

SYNOPSIS
     SUBROUTINE SGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )

         INTEGER        INFO, LDA, LWORK, N

         INTEGER        IPIV( * )

         REAL           A( LDA, * ), WORK( LWORK )

PURPOSE
     SGETRI computes the inverse of a matrix using the LU factorization
     computed by SGETRF.

     This method inverts U and then computes inv(A) by solving the system
     inv(A)*L = inv(U) for inv(A).


ARGUMENTS
     N       (input) INTEGER
             The order of the matrix A.  N >= 0.

     A       (input/output) REAL array, dimension (LDA,N)
             On entry, the factors L and U from the factorization A = P*L*U as
             computed by SGETRF.  On exit, if INFO = 0, the inverse of the
             original matrix A.

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

     IPIV    (input) INTEGER array, dimension (N)
             The pivot indices from SGETRF; for 1<=i<=N, row i of the matrix
             was interchanged with row IPIV(i).

     WORK    (workspace/output) REAL array, dimension (LWORK)
             On exit, if INFO=0, then WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
             The dimension of the array WORK.  LWORK >= max(1,N).  For optimal
             performance LWORK >= N*NB, where NB is the optimal blocksize
             returned by ILAENV.

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value
             > 0:  if INFO = i, U(i,i) is exactly zero; the matrix is singular
             and its inverse could not be computed.