A high-performance general-purpose compute library

Perform Cholesky decomposition. More...

## Functions

AFAPI int cholesky (array &out, const array &in, const bool is_upper=true)
C++ Interface to perform Cholesky decomposition. More...

AFAPI int choleskyInPlace (array &in, const bool is_upper=true)
C++ Interface to perform in-place Cholesky decomposition. More...

AFAPI af_err af_cholesky (af_array *out, int *info, const af_array in, const bool is_upper)
C Interface to perform Cholesky decomposition. More...

AFAPI af_err af_cholesky_inplace (int *info, af_array in, const bool is_upper)
C Interface to perform in-place Cholesky decomposition. More...

## Detailed Description

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);

## ◆ af_cholesky()

 AFAPI af_err af_cholesky ( af_array * out, int * info, const af_array in, const bool 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

## ◆ af_cholesky_inplace()

 AFAPI af_err af_cholesky_inplace ( int * info, af_array in, const bool is_upper )

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

## ◆ cholesky()

 AFAPI int cholesky ( array & out, const array & in, const bool is_upper = true )

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

## ◆ choleskyInPlace()

 AFAPI int choleskyInPlace ( array & in, const bool is_upper = true )

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