?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] )

lapack_int LAPACKE_<?>sptri( int matrix_order, char uplo, lapack_int n, <datatype>* ap, const lapack_int* ipiv );

Include Files

Fortran: mkl_lapack.fi and mkl_lapack.h
Fortran 95: lapack.f90
C: mkl_lapacke.h

Description

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

Input Parameters

The data types are given for the Fortran interface. A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.

uplo	CHARACTER1. 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 = PUDU^TP^T`. If `uplo = 'L'`, the array `ap` stores the Bunch-Kaufman factorization `A = PLDL^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

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.