WOLFRAM SYSTEM MODELER

# solve

Solve real system of linear equations A*x=b with a b vector (Gaussian elimination with partial pivoting) # Wolfram Language

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

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

#### Syntax

```Matrices.solve(A,b);
```

#### Description

This function call returns the solution x of the linear system of equations

A*x = b

If a unique solution x does not exist (since A is singular), an assertion is triggered. If this is not desired, use instead Matrices.leastSquares and inquire the singularity of the solution with the return argument rank (a unique solution is computed if rank = size(A,1)).

Note, the solution is computed with the LAPACK function "dgesv", i.e., by Gaussian elimination with partial pivoting.

#### Example

```  Real A[3,3] = [1,2,3;
3,4,5;
2,1,4];
Real b = {10,22,12};
Real x;
algorithm
x := Matrices.solve(A,b);  // x = {3,2,1}
```

Matrices.LU, Matrices.LU_solve, Matrices.leastSquares.

x = solve(A, b)

# Inputs (2)

A Type: Real[:,size(A, 1)] Description: Matrix A of A*x = b Type: Real[size(A, 1)] Description: Vector b of A*x = b

# Outputs (1)

x Type: Real[size(b, 1)] Description: Vector x such that A*x = b