WOLFRAM SYSTEM MODELER

# dgetrs

Solve a system of linear equations with the LU decomposition from dgetrf

# Wolfram Language

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

# Information

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

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

DGETRS solves a system of linear equations
A * X = B  or  A' * X = B
with a general N-by-N matrix A using the LU factorization computed
by DGETRF.

Arguments
=========

TRANS   (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N':  A * X = B  (No transpose)
= 'T':  A'* X = B  (Transpose)
= 'C':  A'* X = B  (Conjugate transpose = Transpose)

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

NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 0.

A       (input) DOUBLE PRECISION array, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U
as computed by DGETRF.

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).

B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

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

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```

# Syntax

(X, info) = dgetrs(LU, pivots, B)

# Inputs (3)

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 Type: Real[size(LU, 1),:] Description: Right hand side matrix B

# Outputs (2)

X Default Value: B Type: Real[size(B, 1),size(B, 2)] Description: Solution matrix X Type: Integer