F07FRF (ZPOTRF) (PDF version)
F07 Chapter Contents
F07 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F07FRF (ZPOTRF)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

F07FRF (ZPOTRF) computes the Cholesky factorization of a complex Hermitian positive definite matrix.

2  Specification

SUBROUTINE F07FRF ( UPLO, N, A, LDA, INFO)
INTEGER  N, LDA, INFO
COMPLEX (KIND=nag_wp)  A(LDA,*)
CHARACTER(1)  UPLO
The routine may be called by its LAPACK name zpotrf.

3  Description

F07FRF (ZPOTRF) forms the Cholesky factorization of a complex Hermitian positive definite matrix A either as A=UHU if UPLO='U' or A=LLH if UPLO='L', where U is an upper triangular matrix and L is lower triangular.

4  References

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

5  Parameters

1:     UPLO – CHARACTER(1)Input
2:     N – INTEGERInput
On entry: n, the order of the matrix A.
Constraint: N0.
3:     A(LDA,*) – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array A must be at least max1,N.
On entry: the n by n Hermitian symmetric indefinite matrix A.
  • If UPLO='U', the upper triangular part of A must be stored and the elements of the array below the diagonal are not referenced.
  • If UPLO='L', the lower triangular part of A must be stored and the elements of the array above the diagonal are not referenced.
On exit: the upper or lower triangle of A is overwritten by details of the block diagonal matrix D and the multipliers used to obtain the factor U or L as specified by UPLO.
4:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F07FRF (ZPOTRF) is called.
Constraint: LDAmax1,N.
5:     INFO – INTEGEROutput

6  Error Indicators and Warnings

Errors or warnings detected by the routine:
INFO<0
If INFO=-i, the ith parameter had an illegal value. An explanatory message is output, and execution of the program is terminated.
INFO>0

7  Accuracy

If UPLO='U', the computed factor U is the exact factor of a perturbed matrix A+E, where
EcnεUHU ,
cn is a modest linear function of n, and ε is the machine precision. If UPLO='L', a similar statement holds for the computed factor L. It follows that eijcnεaiiajj.

8  Further Comments

The total number of real floating point operations is approximately 43n3.
A call to F07FRF (ZPOTRF) may be followed by calls to the routines:
The real analogue of this routine is F07FDF (DPOTRF).

9  Example

This example computes the Cholesky factorization of the matrix A, where
A= 3.23+0.00i 1.51-1.92i 1.90+0.84i 0.42+2.50i 1.51+1.92i 3.58+0.00i -0.23+1.11i -1.18+1.37i 1.90-0.84i -0.23-1.11i 4.09+0.00i 2.33-0.14i 0.42-2.50i -1.18-1.37i 2.33+0.14i 4.29+0.00i .

9.1  Program Text

Program Text (f07frfe.f90)

9.2  Program Data

Program Data (f07frfe.d)

9.3  Program Results

Program Results (f07frfe.r)


F07FRF (ZPOTRF) (PDF version)
F07 Chapter Contents
F07 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2011