nag_zsytri (f07nwc) (PDF version)
f07 Chapter Contents
f07 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_zsytri (f07nwc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_zsytri (f07nwc) computes the inverse of a complex symmetric matrix A, where A has been factorized by nag_zsytrf (f07nrc).

2  Specification

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

3  Description

nag_zsytri (f07nwc) is used to compute the inverse of a complex symmetric matrix A, the function must be preceded by a call to nag_zsytrf (f07nrc), 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]ComplexInput/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_zsytrf (f07nrc).
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_zsytrf (f07nrc).
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  Parallelism and Performance

nag_zsytri (f07nwc) is not threaded by NAG in any implementation.
nag_zsytri (f07nwc) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the Users' Note for your implementation for any additional implementation-specific information.

9  Further Comments

The total number of real floating-point operations is approximately 83n3.
The real analogue of this function is nag_dsytri (f07mjc).

10  Example

This example computes the inverse of the matrix A, where
A= -0.39-0.71i 5.14-0.64i -7.86-2.96i 3.80+0.92i 5.14-0.64i 8.86+1.81i -3.52+0.58i 5.32-1.59i -7.86-2.96i -3.52+0.58i -2.83-0.03i -1.54-2.86i 3.80+0.92i 5.32-1.59i -1.54-2.86i -0.56+0.12i .
Here A is symmetric and must first be factorized by nag_zsytrf (f07nrc).

10.1  Program Text

Program Text (f07nwce.c)

10.2  Program Data

Program Data (f07nwce.d)

10.3  Program Results

Program Results (f07nwce.r)


nag_zsytri (f07nwc) (PDF version)
f07 Chapter Contents
f07 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014