nag_dtrtri (f07tjc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_dtrtri (f07tjc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_dtrtri (f07tjc) computes the inverse of a real triangular matrix.

2  Specification

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

3  Description

nag_dtrtri (f07tjc) forms the inverse of a real triangular matrix A. Note that the inverse of an upper (lower) triangular matrix is also upper (lower) triangular.

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:     uploNag_UploTypeInput
On entry: specifies whether A is upper or lower triangular.
A is upper triangular.
A is lower triangular.
Constraint: uplo=Nag_Upper or Nag_Lower.
3:     diagNag_DiagTypeInput
On entry: indicates whether A is a nonunit or unit triangular matrix.
A is a nonunit triangular matrix.
A is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be 1.
Constraint: diag=Nag_NonUnitDiag or Nag_UnitDiag.
4:     nIntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
5:     a[dim]doubleInput/Output
Note: the dimension, dim, of the array a must be at least max1,pda×n.
On entry: the n by n triangular matrix A.
If order=Nag_ColMajor, Aij is stored in a[j-1×pda+i-1].
If order=Nag_RowMajor, Aij is stored in a[i-1×pda+j-1].
If uplo=Nag_Upper, the upper triangular part of A must be stored and the elements of the array below the diagonal are not referenced.
If uplo=Nag_Lower, the lower triangular part of A must be stored and the elements of the array above the diagonal are not referenced.
If diag=Nag_UnitDiag, the diagonal elements of A are assumed to be 1, and are not referenced.
On exit: A is overwritten by A-1, using the same storage format as described above.
6:     pdaIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) of the matrix A in the array a.
Constraint: pdamax1,n.
7:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

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.
avalue,value is exactly zero. A is singular its inverse cannot be computed.

7  Accuracy

The computed inverse X satisfies
XA-IcnεXA ,
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.
The computed inverse satisfies the forward error bound
X-A-1cnεA-1AX .
See Du Croz and Higham (1992).

8  Further Comments

The total number of floating point operations is approximately 13n3.
The complex analogue of this function is nag_ztrtri (f07twc).

9  Example

This example computes the inverse of the matrix A, where
A= 4.30 0.00 0.00 0.00 -3.96 -4.87 0.00 0.00 0.40 0.31 -8.02 0.00 -0.27 0.07 -5.95 0.12 .

9.1  Program Text

Program Text (f07tjce.c)

9.2  Program Data

Program Data (f07tjce.d)

9.3  Program Results

Program Results (f07tjce.r)

nag_dtrtri (f07tjc) (PDF version)
f07 Chapter Contents
f07 Chapter Introduction
NAG C Library Manual

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