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ArrayFire: cholesky

Perform Cholesky decomposition. More...

Perform Cholesky decomposition.

This function decomposes a positive definite matrix \(A\) into two triangular matrices such that, \(A = L * U\) and \(L = U^T\).

Only one of \(L\) and \(U\) is stored to conserve space when solving linear equations.

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

array out;

cholesky(out, in, is_upper);

When memory is a concern, users can perform Cholesky decomposition in place as shown below.

array in2 = in.copy();

choleskyInPlace(in2, is_upper);

C Interface to perform Cholesky decomposition.

Multiplying out with its conjugate transpose reproduces the input in.

The input must be positive definite.

Parameters

[out] out triangular matrix; [out] info 0 if cholesky decomposition passes; if not, it returns the rank at which the decomposition fails [in] in input matrix [in] is_upper boolean determining if out is upper or lower triangular

Returns

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

C Interface to perform in-place Cholesky decomposition.

The input must be positive definite.

Parameters

[out] info 0 if cholesky decomposition passes; if not, it returns the rank at which the decomposition fails [in,out] in input matrix on entry; triangular matrix on exit [in] is_upper boolean determining if in is upper or lower triangular

Returns

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

C++ Interface to perform Cholesky decomposition.

Multiplying out with its conjugate transpose reproduces the input in.

The input must be positive definite.

This function is not supported in GFOR.

Parameters

[out] out triangular matrix; [in] in input matrix [in] is_upper boolean determining if out is upper or lower triangular

Returns

0 if cholesky decomposition passes; if not, it returns the rank at which the decomposition fails

C++ Interface to perform in-place Cholesky decomposition.

The input must be positive definite.

This function is not supported in GFOR.

Parameters

[in,out] in input matrix on entry; triangular matrix on exit [in] is_upper boolean determining if in is upper or lower triangular

Returns

0 if cholesky decomposition passes; if not, it returns the rank at which the decomposition fails

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