WOLFRAM SYSTEM MODELER

# dgetri

Compute the inverse of a matrix using the LU factorization from dgetrf

# Wolfram Language

In[1]:=
`SystemModel["Modelica.Math.Matrices.LAPACK.dgetri"]`
Out[1]:=

# Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

```Lapack documentation
Purpose
=======

DGETRI computes the inverse of a matrix using the LU factorization
computed by DGETRF.

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) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the factors L and U from the factorization
A = P*L*U as computed by DGETRF.
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 DGETRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIV(i).

WORK    (workspace/output) DOUBLE PRECISION 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 optimal performance LWORK >= N*NB, where NB is
the optimal blocksize 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
singular and its inverse could not be computed.```

# Syntax

(inv, info) = dgetri(LU, pivots)

# Inputs (2)

LU Type: Real[:,size(LU, 1)] Description: LU factorization of dgetrf of a square matrix Type: Integer[size(LU, 1)] Description: Pivot vector of dgetrf

# Outputs (2)

inv Default Value: LU Type: Real[size(LU, 1),size(LU, 2)] Description: Inverse of matrix P*L*U Type: Integer