F07TJF (DTRTRI) (PDF version)
F07 Chapter Contents
F07 Chapter Introduction
NAG Library Manual

NAG Library Routine Document


Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

F07TJF (DTRTRI) computes the inverse of a real triangular matrix.

2  Specification

REAL (KIND=nag_wp)  A(LDA,*)
The routine may be called by its LAPACK name dtrtri.

3  Description

F07TJF (DTRTRI) 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  Parameters

1:     UPLO – CHARACTER(1)Input
On entry: specifies whether A is upper or lower triangular.
A is upper triangular.
A is lower triangular.
Constraint: UPLO='U' or 'L'.
2:     DIAG – CHARACTER(1)Input
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='N' or 'U'.
3:     N – INTEGERInput
On entry: n, the order of the matrix A.
Constraint: N0.
4:     A(LDA,*) – REAL (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array A must be at least max1,N.
On entry: the n by n triangular matrix A.
  • If UPLO='U', A is upper triangular and the elements of the array below the diagonal are not referenced.
  • If UPLO='L', A is lower triangular and the elements of the array above the diagonal are not referenced.
  • If DIAG='U', 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.
5:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F07TJF (DTRTRI) is called.
Constraint: LDAmax1,N.
6:     INFO – INTEGEROutput
On exit: INFO=0 unless the routine detects an error (see Section 6).

6  Error Indicators and Warnings

Errors or warnings detected by the routine:
If INFO=-i, the ith parameter had an illegal value. An explanatory message is output, and execution of the program is terminated.
If INFO=i, ai,i is exactly zero; A is singular and 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 routine is F07TWF (ZTRTRI).

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 (f07tjfe.f90)

9.2  Program Data

Program Data (f07tjfe.d)

9.3  Program Results

Program Results (f07tjfe.r)

F07TJF (DTRTRI) (PDF version)
F07 Chapter Contents
F07 Chapter Introduction
NAG Library Manual

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