WOLFRAM SYSTEM MODELER

# dgesv

Solve real system of linear equations A*X=B with a B matrix

# Wolfram Language

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

# Information

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

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

DGESV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is
used to factor A as
A = P * L * U,
where P is a permutation matrix, L is unit lower triangular, and U is
upper triangular.  The factored form of A is then used to solve the
system of equations A * X = B.

Arguments
=========

N       (input) INTEGER
The number of linear equations, i.e., 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/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the N-by-N coefficient matrix A.
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,N).

IPIV    (output) INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).

B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the N-by-NRHS matrix of right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS 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
> 0:  if INFO = i, U(i,i) is exactly zero.  The factorization
has been completed, but the factor U is exactly
singular, so the solution could not be computed.```

# Syntax

(X, info) = dgesv(A, B)

# Inputs (2)

A Type: Real[:,size(A, 1)] Type: Real[size(A, 1),:]

# Outputs (2)

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