nag_dgetri (f07ajc) (PDF version)
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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 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:     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

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
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:
XA-IcnεXPLU ,
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