F07MJF (DSYTRI) (PDF version)
F07 Chapter Contents
F07 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F07MJF (DSYTRI)

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

F07MJF (DSYTRI) computes the inverse of a real symmetric indefinite matrix A, where A has been factorized by F07MDF (DSYTRF).

2  Specification

SUBROUTINE F07MJF ( UPLO, N, A, LDA, IPIV, WORK, INFO)
INTEGER  N, LDA, IPIV(*), INFO
REAL (KIND=nag_wp)  A(LDA,*), WORK(N)
CHARACTER(1)  UPLO
The routine may be called by its LAPACK name dsytri.

3  Description

F07MJF (DSYTRI) is used to compute the inverse of a real symmetric indefinite matrix A, the routine must be preceded by a call to F07MDF (DSYTRF), which computes the Bunch–Kaufman factorization of A.
If UPLO='U', A=PUDUTPT and A-1 is computed by solving UTPTXPU=D-1 for X.
If UPLO='L', A=PLDLTPT and A-1 is computed by solving LTPTXPL=D-1 for X.

4  References

Du Croz J J and Higham N J (1992) Stability of methods for matrix inversion IMA J. Numer. Anal. 12 1–19

5  Parameters

1:     UPLO – CHARACTER(1)Input
On entry: specifies how A has been factorized.
UPLO='U'
A=PUDUTPT, where U is upper triangular.
UPLO='L'
A=PLDLTPT, where L is lower triangular.
Constraint: UPLO='U' or 'L'.
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: details of the factorization of A, as returned by F07MDF (DSYTRF).
On exit: the factorization is overwritten by the n by n symmetric matrix A-1.
If UPLO='U', the upper triangle of A-1 is stored in the upper triangular part of the array.
If UPLO='L', the lower triangle of A-1 is stored in the lower triangular part of the array.
4:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F07MJF (DSYTRI) is called.
Constraint: LDAmax1,N.
5:     IPIV(*) – INTEGER arrayInput
Note: the dimension of the array IPIV must be at least max1,N.
On entry: details of the interchanges and the block structure of D, as returned by F07MDF (DSYTRF).
6:     WORK(N) – REAL (KIND=nag_wp) arrayWorkspace
7:     INFO – INTEGEROutput
On exit: INFO=0 unless the routine detects an error (see Section 6).

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
If INFO=i, di,i is exactly zero; D is singular and the inverse of A cannot be computed.

7  Accuracy

The computed inverse X satisfies a bound of the form cn is a modest linear function of n, and ε is the machine precision.

8  Further Comments

The total number of floating point operations is approximately 23n3.
The complex analogues of this routine are F07MWF (ZHETRI) for Hermitian matrices and F07NWF (ZSYTRI) for symmetric matrices.

9  Example

This example computes the inverse of the matrix A, where
A= 2.07 3.87 4.20 -1.15 3.87 -0.21 1.87 0.63 4.20 1.87 1.15 2.06 -1.15 0.63 2.06 -1.81 .
Here A is symmetric indefinite and must first be factorized by F07MDF (DSYTRF).

9.1  Program Text

Program Text (f07mjfe.f90)

9.2  Program Data

Program Data (f07mjfe.d)

9.3  Program Results

Program Results (f07mjfe.r)


F07MJF (DSYTRI) (PDF version)
F07 Chapter Contents
F07 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012