# solve_linsys

Computes the solution to a real system of linear equations.

## Prototype

function solve_linsys ( A [*][*] : numeric, B : numeric ) return_val [dimsizes(B)] : float or double

## Arguments

*A*

A two-dimensional (*N*, *N*) coefficient matrix.

*B*

A one- or two-dimensional array containing the right hand side
matrix. If *B* is one-dimensional, it must be of length
*N*. If it is two-dimensional, it must be
*B*(*NRHS*, *N*) where *NRHS* is the number of
right hand sides.

## Return value

Returns an array dimensioned the same as *B*.

The return type is floating point if the input is floating point, and double if the input is of type double.

## Description

This function computes the solution to a real system of linear
equations * A * x = B* where

*B*may have multiple right-hand-sides. An LU decomposition with partial pivoting and row interchange is used to factor

*A*as

*A*= P * L * U where P is a permutation matrix, L is the unit lower tridiagonalar matrix, and U is the upper triangular matrix. The factored form is then used to solve the system of equations.

## Examples

**Example 1:**

Solve the system A * x = B where B is one-dimensional:

3 2 -1 2 0 A = 1 4 0 2 B = 0 2 1 2 -1 1 1 1 -1 3 0In NCL:

A = (/ (/3.0, 2.0, -1.0, 2.0/), \ (/1.0, 4.0, 0.0, 2.0/), \ (/2.0, 1.0, 2.0,-1.0/), \ (/1.0, 1.0, -1.0, 3.0/) /) B = (/0.0, 0.0, 1.0, 0.0/) ; this is treated as a one-dimensional ; column vector (special case) x =Note: the following would also work:solve_linsys(A, B) ; x will be one-dimensional [x(N)]

NRHS = 1 N = 4 B = new ((/NRHS,N/), "float") ; "double" also B(0, 0) = 0.0 B(0, 1) = 0.0 B(0, 2) = 1.0 B(0, 3) = 0.0

**Example 2:**

The same as Example 1, but with multiple right hand sides:

nrhs = 3 n = 4 b = new ((/nrhs,n/), "float") ; "double" also b(0,:) = (/0.0, 0.0, 1.0, 0.0/) b(1,:) = (/-2.0, 1.0, 3.0, 4.0/) b(2,:) = (/2.0, 2.0, 0.0, 0.0/) x =solve_linsys(A, B) ; x will be 2D: x(3, 4)

## Errors

**info**- = 0 : successful exit
- < 0: the
*i*-th argument had an illegal value - > 0: 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.