cgetri man page on Scientific

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```CGETRI(1)		 LAPACK routine (version 3.2)		     CGETRI(1)

NAME
CGETRI  -  computes  the inverse of a matrix using the LU factorization
computed by CGETRF

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

INTEGER	  INFO, LDA, LWORK, N

INTEGER	  IPIV( * )

COMPLEX	  A( LDA, * ), WORK( * )

PURPOSE
CGETRI computes the inverse of a matrix using the LU factorization com‐
puted  by  CGETRF.   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) COMPLEX array, dimension (LDA,N)
On entry, the factors L and U from the factorization A =	 P*L*U
as  computed  by	 CGETRF.  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 CGETRF; for 1<=i<=N, row i of the matrix
was interchanged with row IPIV(i).

WORK    (workspace/output) COMPLEX array, dimension (MAX(1,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 opti‐
mal performance LWORK >= N*NB, where NB is the  optimal	block‐
size returned by ILAENV.	 If LWORK = -1, then a workspace query
is assumed; the routine only calculates the optimal size of the
WORK  array,  returns this value as the first entry of the WORK
array, and no error message  related  to	 LWORK	is  issued  by
XERBLA.

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 singu‐
lar and its inverse could not be computed.

LAPACK routine (version 3.2)	 November 2008			     CGETRI(1)
```
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