Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
1: – Character(1)Input
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.
2: – IntegerInput
On entry: , the order of the matrix .
3: – Complex (Kind=nag_wp) arrayInput/Output
Note: the second dimension of the array a
must be at least
On entry: the Hermitian positive definite matrix .
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.
4: – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f07frf is called.
5: – IntegerOutput
On exit: unless the routine detects an error (see Section 6).
6Error Indicators and Warnings
If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
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 f07mrf 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.
f07frf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f07frf 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 routine. 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 f07frf may be followed by calls to the routines: