Solving linear systems

Enumerations
enum	af_solve_t {   af_solve_none = 0, af_solve_posdef = 1, af_solve_nonposdef = 2, af_solve_gaussian = 3,   af_solve_pseudo = 4, af_solve_ctrans = 256, af_solve_trans = 512, af_solve_uppertri = 1024,   af_solve_lowertri = 2048, af_solve_tridiag = 4096, af_solve_blkdiag = 8192 }

Functions
array	solve (const array &A, const array &b, af_solve_t options=af_solve_none)
	Solve linear system. More...

Detailed Description

Enumeration Type Documentation

enum af_solve_t

Enumerator
af_solve_none	Default.
af_solve_posdef	A is positive definite.
af_solve_nonposdef	A is not positive definite.
af_solve_gaussian	Use Gaussian elimination (fast, cannot be combined with other options)
af_solve_pseudo	Use pseudo inverse (fast, cannot be combined with other options)
af_solve_ctrans	Solve A.H() (conjugate transpose)
af_solve_trans	Solve A.T() (non-conjugate transpose)
af_solve_uppertri	Solve uppertri(A) (upper triangular system)
af_solve_lowertri	Solve lowertri(A) (lower triangular system)
af_solve_tridiag
af_solve_blkdiag

Function Documentation

array af::solve	(	const array &	A,
		const array &	b,
		af_solve_t	options = af_solve_none
	)

Solve linear system.

Uses lu or cholesky for square systems and qr for non-square systems. Sparse matrices are not currently supported.

Double-precision or complex input requires ArrayFire Pro.

#include<stdio.h>
#include <arrayfire.h>
using namespace af;

int main(void)
{
    try {

    // create a coefficient matrix A
    float h_buffer[] = {2, 3, 6, -4, -3, -1, 2, -4, 5};   // A = 2  -4   2
    array A(3, 3, h_buffer);                              //     3  -3  -4
    print(A);                                             //     6  -1   5

    // create a solution vector x
    float h_sol[] = {-20, 32, 4.22};                      // x = -20.00
    array x(3, 1, h_sol);                                 //      32.00
    print(x);                                             //       4.22

    // create a right hand side vector b = Ax             // b =  -159.5600
    array b = matmul(A, x);                               //      -172.8800
    print(b);                                             //      -130.9000

    // solve for x using A and b
    x = solve(A, b);
    print(x);

    } catch(af::exception &ae) {
        std::cout << ae.what() << std::endl;
    }

    return 0;
}

Parameters

[in]	A	system matrix
[in]	b	residual vector or matrix
[in]	options	bitwise combination (see af_solve_t)

Returns

x from the linear system A * x = b.

Examples:

examples/getting_started/lin_algebra.cpp.