WOLFRAM SYSTEM MODELER

# dgetrf

Compute LU factorization of square or rectangular matrix A (A = P*L*U) # Wolfram Language

In:= `SystemModel["Modelica.Math.Matrices.LAPACK.dgetrf"]`
Out:= # Information

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

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

DGETRF computes an LU factorization of a general M-by-N matrix A
using partial pivoting with row interchanges.

The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.

Arguments
=========

M       (input) INTEGER
The number of rows of the matrix A.  M >= 0.

N       (input) INTEGER
The number of columns of the matrix A.  N >= 0.

A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix to be factored.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.

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

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

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 factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.```

# Syntax

(LU, pivots, info) = dgetrf(A)

# Inputs (1)

A Type: Real[:,:] Description: Square or rectangular matrix

# Outputs (3)

LU Default Value: A Type: Real[size(A, 1),size(A, 2)] Type: Integer[min(size(A, 1), size(A, 2))] Description: Pivot vector Type: Integer Description: Information