solve

Solve a system of equations. More...

Functions
AFAPI array	solve (const array &a, const array &b, const matProp options=AF_MAT_NONE)
	C++ Interface to solve a system of equations. More...
AFAPI af_err	af_solve (af_array *x, const af_array a, const af_array b, const af_mat_prop options)
	C Interface to solve a system of equations. More...

Detailed Description

Solve a system of equations.

This function takes a co-efficient matrix \(A\) and an output matrix \(B\) as inputs to solve the following equation for \(X\), \(A * X = B\).

This operation can be done in ArrayFire using the following code snippet.

    af::array X1 = af::solve(A, B0);

The results can be verified by reconstructing the output matrix using af::matmul in the following manner,

    af::array B1 = af::matmul(A, X1);

The sample output can be seen below.

A [3 3 1 1]
    0.1000     3.1000     6.1000
    1.1000     4.1000     7.0000
    2.0000     5.0000     8.0000
 
B0 [3 1 1 1]
   21.9000
   30.7000
   39.0000
 
X1 [3 1 1 1]
    4.0000
    3.0000
    2.0000
 
B1 [3 1 1 1]
   21.9000
   30.7000
   39.0000

If the coefficient matrix is known to be a triangular matrix, AF_MAT_LOWER or AF_MAT_UPPER can be passed to make solve faster.

The sample code snippets for solving a lower triangular matrix can be seen below.

        af::array X = af::solve(AT, B0, AF_MAT_LOWER);

Similarily, the code snippet for solving an upper triangular matrix can be seen below.

        af::array X = af::solve(AT, B0, AF_MAT_UPPER);

See also: af::solveLU

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Function Documentation

af_solve()

AFAPI af_err af_solve	(	af_array *	x,
		const af_array	a,
		const af_array	b,
		const af_mat_prop	options
	)

C Interface to solve a system of equations.

The options parameter must be one of AF_MAT_NONE, AF_MAT_LOWER or AF_MAT_UPPER.

This function is not supported in GFOR.

Parameters

[out]	x	matrix of unknown variables
[in]	a	coefficient matrix
[in]	b	measured values
[in]	options	determines various properties of matrix a

Returns

AF_SUCCESS, if function returns successfully, else an af_err code is given

solve()

AFAPI array solve	(	const array &	a,
		const array &	b,
		const matProp	options = AF_MAT_NONE
	)

C++ Interface to solve a system of equations.

The options parameter must be one of AF_MAT_NONE, AF_MAT_LOWER or AF_MAT_UPPER.

This function is not supported in GFOR.

Parameters

[in]	a	coefficient matrix
[in]	b	measured values
[in]	options	determines various properties of matrix a

Returns

x, the matrix of unknown variables