nag_dsytri (f07mjc) (PDF version)
f07 Chapter Contents
f07 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_dsytri (f07mjc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_dsytri (f07mjc) computes the inverse of a real symmetric indefinite matrix A, where A has been factorized by nag_dsytrf (f07mdc).

2  Specification

#include <nag.h>
#include <nagf07.h>
void  nag_dsytri (Nag_OrderType order, Nag_UploType uplo, Integer n, double a[], Integer pda, const Integer ipiv[], NagError *fail)

3  Description

nag_dsytri (f07mjc) is used to compute the inverse of a real symmetric indefinite matrix A, the function must be preceded by a call to nag_dsytrf (f07mdc), which computes the Bunch–Kaufman factorization of A.
If uplo=Nag_Upper, A=PUDUTPT and A-1 is computed by solving UTPTXPU=D-1 for X.
If uplo=Nag_Lower, 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  Arguments

1:     orderNag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     uploNag_UploTypeInput
On entry: specifies how A has been factorized.
uplo=Nag_Upper
A=PUDUTPT, where U is upper triangular.
uplo=Nag_Lower
A=PLDLTPT, where L is lower triangular.
Constraint: uplo=Nag_Upper or Nag_Lower.
3:     nIntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
4:     a[dim]doubleInput/Output
Note: the dimension, dim, of the array a must be at least max1,pda×n.
On entry: details of the factorization of A, as returned by nag_dsytrf (f07mdc).
On exit: the factorization is overwritten by the n by n symmetric matrix A-1.
If uplo=Nag_Upper, the upper triangle of A-1 is stored in the upper triangular part of the array.
If uplo=Nag_Lower, the lower triangle of A-1 is stored in the lower triangular part of the array.
5:     pdaIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) of the matrix in the array a.
Constraint: pdamax1,n.
6:     ipiv[dim]const IntegerInput
Note: the dimension, dim, 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 nag_dsytrf (f07mdc).
7:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, n=value.
Constraint: n0.
On entry, pda=value.
Constraint: pda>0.
NE_INT_2
On entry, pda=value and n=value.
Constraint: pdamax1,n.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_SINGULAR
dvalue,value 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 function are nag_zhetri (f07mwc) for Hermitian matrices and nag_zsytri (f07nwc) 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 nag_dsytrf (f07mdc).

9.1  Program Text

Program Text (f07mjce.c)

9.2  Program Data

Program Data (f07mjce.d)

9.3  Program Results

Program Results (f07mjce.r)


nag_dsytri (f07mjc) (PDF version)
f07 Chapter Contents
f07 Chapter Introduction
NAG C Library Manual

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