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NAG Toolbox: nag_lapack_dsytri (f07mj)

Purpose

nag_lapack_dsytri (f07mj) computes the inverse of a real symmetric indefinite matrix AA, where AA has been factorized by nag_lapack_dsytrf (f07md).

Syntax

[a, info] = f07mj(uplo, a, ipiv, 'n', n)
[a, info] = nag_lapack_dsytri(uplo, a, ipiv, 'n', n)

Description

nag_lapack_dsytri (f07mj) is used to compute the inverse of a real symmetric indefinite matrix AA, the function must be preceded by a call to nag_lapack_dsytrf (f07md), which computes the Bunch–Kaufman factorization of AA.
If uplo = 'U'uplo='U', A = PUDUTPTA=PUDUTPT and A1A-1 is computed by solving UTPTXPU = D1UTPTXPU=D-1 for XX.
If uplo = 'L'uplo='L', A = PLDLTPTA=PLDLTPT and A1A-1 is computed by solving LTPTXPL = D1LTPTXPL=D-1 for XX.

References

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

Parameters

Compulsory Input Parameters

1:     uplo – string (length ≥ 1)
Specifies how AA has been factorized.
uplo = 'U'uplo='U'
A = PUDUTPTA=PUDUTPT, where UU is upper triangular.
uplo = 'L'uplo='L'
A = PLDLTPTA=PLDLTPT, where LL is lower triangular.
Constraint: uplo = 'U'uplo='U' or 'L''L'.
2:     a(lda, : :) – double array
The first dimension of the array a must be at least max (1,n)max(1,n)
The second dimension of the array must be at least max (1,n)max(1,n)
Details of the factorization of AA, as returned by nag_lapack_dsytrf (f07md).
3:     ipiv( : :) – int64int32nag_int array
Note: the dimension of the array ipiv must be at least max (1,n)max(1,n).
Details of the interchanges and the block structure of DD, as returned by nag_lapack_dsytrf (f07md).

Optional Input Parameters

1:     n – int64int32nag_int scalar
Default: The first dimension of the array a The second dimension of the arrays a, ipiv.
nn, the order of the matrix AA.
Constraint: n0n0.

Input Parameters Omitted from the MATLAB Interface

lda work

Output Parameters

1:     a(lda, : :) – double array
The first dimension of the array a will be max (1,n)max(1,n)
The second dimension of the array will be max (1,n)max(1,n)
ldamax (1,n)ldamax(1,n).
The factorization stores the nn by nn symmetric matrix A1A-1.
If uplo = 'U'uplo='U', the upper triangle of A1A-1 is stored in the upper triangular part of the array.
If uplo = 'L'uplo='L', the lower triangle of A1A-1 is stored in the lower triangular part of the array.
2:     info – int64int32nag_int scalar
info = 0info=0 unless the function detects an error (see Section [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.

  info = iinfo=-i
If info = iinfo=-i, parameter ii had an illegal value on entry. The parameters are numbered as follows:
1: uplo, 2: n, 3: a, 4: lda, 5: ipiv, 6: work, 7: info.
It is possible that info refers to a parameter that is omitted from the MATLAB interface. This usually indicates that an error in one of the other input parameters has caused an incorrect value to be inferred.
W INFO > 0INFO>0
If info = iinfo=i, d(i,i)d(i,i) is exactly zero; DD is singular and the inverse of AA cannot be computed.

Accuracy

The computed inverse XX satisfies a bound of the form c(n)c(n) is a modest linear function of nn, and εε is the machine precision

Further Comments

The total number of floating point operations is approximately (2/3)n323n3.
The complex analogues of this function are nag_lapack_zhetri (f07mw) for Hermitian matrices and nag_lapack_zsytri (f07nw) for symmetric matrices.

Example

function nag_lapack_dsytri_example
uplo = 'L';
a = [2.07, 0, 0, 0;
     3.87, -0.21, 0, 0;
     4.2, 1.87, 1.15, 0;
     -1.15, 0.63, 2.06, -1.81];
[a, ipiv, info] = nag_lapack_dsytrf(uplo, a);
[aOut, info] = nag_lapack_dsytri(uplo, a, ipiv)
 

aOut =

    0.7485         0         0         0
    0.5221   -0.1605         0         0
   -1.0058   -0.3131    1.3501         0
   -1.4386   -0.7440    2.0667    2.4547


info =

                    0


function f07mj_example
uplo = 'L';
a = [2.07, 0, 0, 0;
     3.87, -0.21, 0, 0;
     4.2, 1.87, 1.15, 0;
     -1.15, 0.63, 2.06, -1.81];
[a, ipiv, info] = f07md(uplo, a);
[aOut, info] = f07mj(uplo, a, ipiv)
 

aOut =

    0.7485         0         0         0
    0.5221   -0.1605         0         0
   -1.0058   -0.3131    1.3501         0
   -1.4386   -0.7440    2.0667    2.4547


info =

                    0



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