nag_dgetri (f07ajc) (PDF version)
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f07 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_dgetri (f07ajc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_dgetri (f07ajc) computes the inverse of a real matrix A, where A has been factorized by nag_dgetrf (f07adc).

2  Specification

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

3  Description

nag_dgetri (f07ajc) is used to compute the inverse of a real matrix A, the function must be preceded by a call to nag_dgetrf (f07adc), which computes the LU factorization of A as A=PLU. The inverse of A is computed by forming U-1 and then solving the equation XPL=U-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 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     nIntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
3:     a[dim]doubleInput/Output
Note: the dimension, dim, of the array a must be at least max1,pda×n.
The i,jth element of the matrix A is stored in
  • a[j-1×pda+i-1] when order=Nag_ColMajor;
  • a[i-1×pda+j-1] when order=Nag_RowMajor.
On entry: the LU factorization of A, as returned by nag_dgetrf (f07adc).
On exit: the factorization is overwritten by the n by n matrix A-1.
4:     pdaIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
Constraint: pdamax1,n.
5:     ipiv[dim]const IntegerInput
Note: the dimension, dim, of the array ipiv must be at least max1,n.
On entry: the pivot indices, as returned by nag_dgetrf (f07adc).
6:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n0.
On entry, pda=value.
Constraint: pda>0.
On entry, pda=value and n=value.
Constraint: pdamax1,n.
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.
Element value of the diagonal is zero. U is singular, and the inverse of A cannot be computed.

7  Accuracy

The computed inverse X satisfies a bound of the form:
where cn is a modest linear function of n, and ε is the machine precision.
Note that a similar bound for AX-I cannot be guaranteed, although it is almost always satisfied. See Du Croz and Higham (1992).

8  Further Comments

The total number of floating point operations is approximately 43n3.
The complex analogue of this function is nag_zgetri (f07awc).

9  Example

This example computes the inverse of the matrix A, where
A= 1.80 2.88 2.05 -0.89 5.25 -2.95 -0.95 -3.80 1.58 -2.69 -2.90 -1.04 -1.11 -0.66 -0.59 0.80 .
Here A is nonsymmetric and must first be factorized by nag_dgetrf (f07adc).

9.1  Program Text

Program Text (f07ajce.c)

9.2  Program Data

Program Data (f07ajce.d)

9.3  Program Results

Program Results (f07ajce.r)

nag_dgetri (f07ajc) (PDF version)
f07 Chapter Contents
f07 Chapter Introduction
NAG C Library Manual

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