F07FDF (DPOTRF) (PDF version)
F07 Chapter Contents
F07 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F07FDF (DPOTRF)

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

F07FDF (DPOTRF) computes the Cholesky factorization of a real symmetric positive definite matrix.

2  Specification

SUBROUTINE F07FDF ( UPLO, N, A, LDA, INFO)
INTEGER  N, LDA, INFO
REAL (KIND=nag_wp)  A(LDA,*)
CHARACTER(1)  UPLO
The routine may be called by its LAPACK name dpotrf.

3  Description

F07FDF (DPOTRF) forms the Cholesky factorization of a real symmetric positive definite matrix A either as A=UTU if UPLO='U' or A=LLT 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,*) – REAL (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 symmetric positive definite 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 F07FDF (DPOTRF) 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
EcnεUTU ,
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 floating point operations is approximately 13n3.
A call to F07FDF (DPOTRF) may be followed by calls to the routines:
The complex analogue of this routine is F07FRF (ZPOTRF).

9  Example

This example computes the Cholesky factorization of the matrix A, where
A= 4.16 -3.12 0.56 -0.10 -3.12 5.03 -0.83 1.18 0.56 -0.83 0.76 0.34 -0.10 1.18 0.34 1.18 .

9.1  Program Text

Program Text (f07fdfe.f90)

9.2  Program Data

Program Data (f07fdfe.d)

9.3  Program Results

Program Results (f07fdfe.r)


F07FDF (DPOTRF) (PDF version)
F07 Chapter Contents
F07 Chapter Introduction
NAG Library Manual

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