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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_lapack_dtptri (f07uj)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_lapack_dtptri (f07uj) computes the inverse of a real triangular matrix, using packed storage.


[ap, info] = f07uj(uplo, diag, n, ap)
[ap, info] = nag_lapack_dtptri(uplo, diag, n, ap)


nag_lapack_dtptri (f07uj) forms the inverse of a real triangular matrix A, using packed storage. Note that the inverse of an upper (lower) triangular matrix is also upper (lower) triangular.


Du Croz J J and Higham N J (1992) Stability of methods for matrix inversion IMA J. Numer. Anal. 12 1–19


Compulsory Input Parameters

1:     uplo – string (length ≥ 1)
Specifies whether A is upper or lower triangular.
A is upper triangular.
A is lower triangular.
Constraint: uplo='U' or 'L'.
2:     diag – string (length ≥ 1)
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 int64int32nag_int scalar
n, the order of the matrix A.
Constraint: n0.
4:     ap: – double array
The dimension of the array ap must be at least max1,n×n+1/2
The n by n triangular matrix A, packed by columns.
More precisely,
  • if uplo='U', the upper triangle of A must be stored with element Aij in api+jj-1/2 for ij;
  • if uplo='L', the lower triangle of A must be stored with element Aij in api+2n-jj-1/2 for ij.
If diag='U', the diagonal elements of A are assumed to be 1, and are not referenced; the same storage scheme is used whether diag='N' or ‘U’.

Optional Input Parameters


Output Parameters

1:     ap: – double array
The dimension of the array ap will be max1,n×n+1/2
A stores A-1, using the same storage format as described above.
2:     info int64int32nag_int scalar
info=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

If info=-i, argument i had an illegal value. An explanatory message is output, and execution of the program is terminated.
W  info>0
Element _ of the diagonal is exactly zero. A is singular its inverse cannot be computed.


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).

Further Comments

The total number of floating-point operations is approximately 13n3.
The complex analogue of this function is nag_lapack_ztptri (f07uw).


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 ,  
using packed storage.
function f07uj_example

fprintf('f07uj example results\n\n');

% Invert A, where A is Lower triangular and packed
n = int64(4);
ap = [ 4.30; -3.96;  0.40; -0.27;
             -4.87;  0.31;  0.07;
                    -8.02; -5.95;
uplo = 'L';
diag = 'N';

% Invert
[ainv, info] = f07uj(uplo, diag, n, ap);

[ifail] = x04cc( ...
                 uplo, 'Non-unit', n, ainv, 'Inverse');

f07uj example results

             1          2          3          4
 1      0.2326
 2     -0.1891    -0.2053
 3      0.0043    -0.0079    -0.1247
 4      0.8463    -0.2738    -6.1825     8.3333

PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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