NAG Library Routine Document
F07GRF (ZPPTRF) computes the Cholesky factorization of a complex Hermitian positive definite matrix, using packed storage.
The routine may be called by its
F07GRF (ZPPTRF) forms the Cholesky factorization of a complex Hermitian positive definite matrix either as if or if , where is an upper triangular matrix and is lower triangular, using packed storage.
Demmel J W (1989) On floating-point errors in Cholesky LAPACK Working Note No. 14 University of Tennessee, Knoxville
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
- 1: UPLO – CHARACTER(1)Input
: 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: N – INTEGERInput
On entry: , the order of the matrix .
- 3: AP() – COMPLEX (KIND=nag_wp) arrayInput/Output
the dimension of the array AP
must be at least
, packed by columns.
- if , the upper triangle of must be stored with element in for ;
- if , the lower triangle of must be stored with element in for .
On exit: if , the factor or from the Cholesky factorization or , in the same storage format as .
- 4: INFO – INTEGEROutput
unless the routine detects an error (see Section 6
6 Error Indicators and Warnings
Errors or warnings detected by the routine:
If , the th parameter 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
matrix which is not positive definite, call
, the computed factor
is the exact factor of a perturbed matrix
is a modest linear function of
is the machine precision
If , a similar statement holds for the computed factor . It follows that .
The total number of real floating point operations is approximately .
A call to F07GRF (ZPPTRF) may be followed by calls to the routines:
The real analogue of this routine is F07GDF (DPPTRF)
This example computes the Cholesky factorization of the matrix
using packed storage.
9.1 Program Text
Program Text (f07grfe.f90)
9.2 Program Data
Program Data (f07grfe.d)
9.3 Program Results
Program Results (f07grfe.r)