Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
1: – Nag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by . See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
2: – Nag_UploTypeInput
On entry: specifies whether the upper or lower triangular part of is stored and how is to be factorized.
The upper triangular part of is stored and is factorized as , where is upper triangular.
The lower triangular part of is stored and is factorized as , where is lower triangular.
3: – IntegerInput
On entry: , the order of the matrix .
4: – ComplexInput/Output
Note: the dimension, dim, of the array a
must be at least
On entry: the Hermitian positive definite matrix .
If , is stored in .
If , is stored in .
If , the upper triangular part of must be stored and the elements of the array below the diagonal are not referenced.
If , the lower triangular part of must be stored and the elements of the array above the diagonal are not referenced.
On exit: the upper or lower triangle of is overwritten by the Cholesky factor or as specified by uplo.
5: – IntegerInput
On entry: the stride separating row or column elements (depending on the value of order) of the matrix in the array
6: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, .
On entry, . Constraint: .
On entry, and .
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.
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.
The leading minor of order is not positive definite
and the factorization could not be completed. Hence itself
is not positive definite. This may indicate an error in forming the
matrix . To factorize a Hermitian matrix which is not
positive definite, call f07mrc instead.
If , the computed factor is the exact factor of a perturbed matrix , where
is a modest linear function of , and is the machine precision. If , a similar statement holds for the computed factor . It follows that .
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
f07frc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f07frc 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.
The total number of real floating-point operations is approximately .
A call to f07frc may be followed by calls to the functions: