?sptri

Computes the inverse of a symmetric matrix using packed storage.

Syntax

FORTRAN 77:

call ssptri( uplo, n, ap, ipiv, work, info )

call dsptri( uplo, n, ap, ipiv, work, info )

call csptri( uplo, n, ap, ipiv, work, info )

call zsptri( uplo, n, ap, ipiv, work, info )

Fortran 95:

call sptri( ap, ipiv [,uplo] [,info] )

Description

This routine is declared in mkl_lapack.fi for FORTRAN 77 interface, in mkl_lapack.f90 for Fortran 95 interface, and in mkl_lapack.h for C interface.

The routine computes the inverse inv(A) of a packed symmetric matrix A. Before calling this routine, call ?sptrf to factorize A.

Input Parameters

uplo

CHARACTER*1. Must be 'U' or 'L'.

Indicates how the input matrix A has been factored:

If uplo = 'U', the array ap stores the Bunch-Kaufman factorization A = P*U*D*U^T*P^T.

If uplo = 'L', the array ap stores the Bunch-Kaufman factorization A = P*L*D*L^T*P^T.

n

INTEGER. The order of the matrix A; n ≥ 0.

ap, work

REAL for ssptri

DOUBLE PRECISION for dsptri

COMPLEX for csptri

DOUBLE COMPLEX for zsptri.

Arrays:

ap(*) contains the factorization of the matrix A, as returned by ?sptrf.

The dimension of ap must be at least max(1,n(n+1)/2).

work(*) is a workspace array.

The dimension of work must be at least max(1,n).

ipiv

INTEGER.

Array, DIMENSION at least max(1, n). The ipiv array, as returned by ?sptrf.

Output Parameters

ap

Overwritten by the n-by-n matrix inv(A) in packed form.

info

INTEGER.

If info = 0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

If info = i, the i-th diagonal element of D is zero, D is singular, and the inversion could not be completed.

Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.

Specific details for the routine sptri interface are as follows:

ap: Holds the array A of size (n*(n+1)/2).
ipiv: Holds the vector of length n.
uplo: Must be 'U' or 'L'. The default value is 'U'.

Application Notes

The computed inverse X satisfies the following error bounds:

|D*U^T*P^T*X*P*U - I| ≤ c(n)ε(|D||U^T|P^T|X|P|U| + |D||D^-1|)

for uplo = 'U', and

|D*L^T*P^T*X*P*L - I| ≤ c(n)ε(|D||L^T|P^T|X|P|L| + |D||D^-1|)

for uplo = 'L'. Here c(n) is a modest linear function of n, and ε is the machine precision; I denotes the identity matrix.

The total number of floating-point operations is approximately (2/3)n³ for real flavors and (8/3)n³ for complex flavors.