la_cholesky::chol Interface Reference

Computes the Cholesky factorization $A = L \cdot L^T$, or $A = U^T \cdot U$. More...

Public Member Functions
pure real(sp) function, dimension(size(a, 1), size(a, 2))	la_s_cholesky_fun (a, lower, other_zeroed)
pure real(dp) function, dimension(size(a, 1), size(a, 2))	la_d_cholesky_fun (a, lower, other_zeroed)
pure real(qp) function, dimension(size(a, 1), size(a, 2))	la_q_cholesky_fun (a, lower, other_zeroed)
pure complex(sp) function, dimension(size(a, 1), size(a, 2))	la_c_cholesky_fun (a, lower, other_zeroed)
pure complex(dp) function, dimension(size(a, 1), size(a, 2))	la_z_cholesky_fun (a, lower, other_zeroed)
pure complex(qp) function, dimension(size(a, 1), size(a, 2))	la_w_cholesky_fun (a, lower, other_zeroed)

Detailed Description

Computes the Cholesky factorization $A = L \cdot L^T$, or $A = U^T \cdot U$.

Summary

Pure function interface for computing the Cholesky triangular factors.

Description

This interface provides methods for computing the lower- or upper-triangular matrix from the Cholesky factorization of a real symmetric or complex Hermitian matrix. Supported data types include real and complex.
The function returns the Cholesky factor as a separate matrix. The lower logical flag allows selection between upper or lower factorization, and the other_zeroed optional logical flag determines whether the unused part of the triangular matrix should be zeroed.

Note

The solution is based on LAPACK's POTRF methods.

Parameters

[in]	a	The input matrix of size $[n, n]$.
[in]	lower	(Optional) Logical flag indicating whether the lower or upper triangular factor is required. Default: lower triangular factor.
[in]	other_zeroed	(Optional) Logical flag indicating whether the unused half of the matrix should be zeroed. Default: true.

Returns

c The output matrix of size $[n, n]$, containing the Cholesky factor.

Member Function/Subroutine Documentation

la_c_cholesky_fun()

pure complex(sp) function, dimension(size(a,1),size(a,2)) la_cholesky::chol::la_c_cholesky_fun	(	complex(sp), dimension(:,:), intent(in)	a,
		logical(lk), intent(in), optional	lower,
		logical(lk), intent(in), optional	other_zeroed )

Parameters

[in]

a

Input matrix a[n,n]

Returns

Output matrix with Cholesky factors c[n,n]

Parameters

[in]	lower	[optional] is the lower or upper triangular factor required? Default = lower
[in]	other_zeroed	[optional] should the unused half of the return matrix be zeroed out? Default: yes

la_d_cholesky_fun()

pure real(dp) function, dimension(size(a,1),size(a,2)) la_cholesky::chol::la_d_cholesky_fun	(	real(dp), dimension(:,:), intent(in)	a,
		logical(lk), intent(in), optional	lower,
		logical(lk), intent(in), optional	other_zeroed )

Parameters

[in]

a

Input matrix a[n,n]

Returns

Output matrix with Cholesky factors c[n,n]

Parameters

[in]	lower	[optional] is the lower or upper triangular factor required? Default = lower
[in]	other_zeroed	[optional] should the unused half of the return matrix be zeroed out? Default: yes

la_q_cholesky_fun()

pure real(qp) function, dimension(size(a,1),size(a,2)) la_cholesky::chol::la_q_cholesky_fun	(	real(qp), dimension(:,:), intent(in)	a,
		logical(lk), intent(in), optional	lower,
		logical(lk), intent(in), optional	other_zeroed )

Parameters

[in]

a

Input matrix a[n,n]

Returns

Output matrix with Cholesky factors c[n,n]

Parameters

[in]	lower	[optional] is the lower or upper triangular factor required? Default = lower
[in]	other_zeroed	[optional] should the unused half of the return matrix be zeroed out? Default: yes

la_s_cholesky_fun()

pure real(sp) function, dimension(size(a,1),size(a,2)) la_cholesky::chol::la_s_cholesky_fun	(	real(sp), dimension(:,:), intent(in)	a,
		logical(lk), intent(in), optional	lower,
		logical(lk), intent(in), optional	other_zeroed )

Parameters

[in]

a

Input matrix a[n,n]

Returns

Output matrix with Cholesky factors c[n,n]

Parameters

[in]	lower	[optional] is the lower or upper triangular factor required? Default = lower
[in]	other_zeroed	[optional] should the unused half of the return matrix be zeroed out? Default: yes

la_w_cholesky_fun()

pure complex(qp) function, dimension(size(a,1),size(a,2)) la_cholesky::chol::la_w_cholesky_fun	(	complex(qp), dimension(:,:), intent(in)	a,
		logical(lk), intent(in), optional	lower,
		logical(lk), intent(in), optional	other_zeroed )

Parameters

[in]

a

Input matrix a[n,n]

Returns

Output matrix with Cholesky factors c[n,n]

Parameters

[in]	lower	[optional] is the lower or upper triangular factor required? Default = lower
[in]	other_zeroed	[optional] should the unused half of the return matrix be zeroed out? Default: yes

la_z_cholesky_fun()

pure complex(dp) function, dimension(size(a,1),size(a,2)) la_cholesky::chol::la_z_cholesky_fun	(	complex(dp), dimension(:,:), intent(in)	a,
		logical(lk), intent(in), optional	lower,
		logical(lk), intent(in), optional	other_zeroed )

Parameters

[in]

a

Input matrix a[n,n]

Returns

Output matrix with Cholesky factors c[n,n]

Parameters

[in]	lower	[optional] is the lower or upper triangular factor required? Default = lower
[in]	other_zeroed	[optional] should the unused half of the return matrix be zeroed out? Default: yes

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The documentation for this interface was generated from the following file:

• la_cholesky.f90