Cheng S H and Higham N J (1998) A modified Cholesky algorithm based on a symmetric indefinite factorization SIAM J. Matrix Anal. Appl. 19(4) 1097–1110

5 Arguments

1: $uplo$ – Nag_UploType Input

On entry: indicates whether the upper or lower triangular part of

A

was stored and how it was factorized.

$uplo = Nag_Upper$: The upper triangular part of $A$ was stored and we compute $A + E$ such that $P^{T} (A + E) P = U D U^{T}$ .
$uplo = Nag_Lower$: The lower triangular part of $A$ was stored and we compute $A + E$ such that $P^{T} (A + E) P = L D L^{T}$ .

Constraint:

uplo = Nag_Upper

Nag_Lower

2: $n$ – Integer Input

On entry:

n

, the order of the matrix

A

Constraint:

n > 0

3: $a [\dim]$ – double Input/Output

Note: the dimension, dim, of the array a must be at least

\max (1, pda \times n)

On entry: the modified Cholesky factor of

A

, as returned by f01mdc.

On exit:

If $uplo = Nag_Upper$ , the upper triangular part of $A + E$ is returned and the elements of the array below the diagonal are not referenced.
If $uplo = Nag_Lower$ , the lower triangular part of $A + E$ is returned and the elements of the array above the diagonal are not referenced.

4: $pda$ – Integer Input

On entry: the stride separating row elements of the matrix

A

in the array a.

Constraint:

pda \geq n

5: $offdiag [n]$ – const double Input

On entry: the array offdiag as returned by f01mdc.

6: $ipiv [n]$ – const Integer Input

On entry: the array ipiv as returned by f01mdc.

7: $fail$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $⟨ value ⟩$ had an illegal value.
NE_INT: On entry, $n = ⟨ value ⟩$ .
Constraint: $n > 0$ .
NE_INT_2: On entry, $pda = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $pda \geq n$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

See Section 7 in f01mdc for an indication of the accuracy of the computed factors

L

U

, and

D

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

f01mec is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

f01mec makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.