?pftri

Computes the inverse of a symmetric (Hermitian) positive-definite matrix in RFP format using the Cholesky factorization.

Syntax

FORTRAN 77:

call spftri( transr, uplo, n, a, info )

call dpftri( transr, uplo, n, a, info )

call cpftri( transr, uplo, n, a, info )

call zpftri( transr, uplo, n, a, info )

lapack_int LAPACKE_<?>pftri( int matrix_order, char transr, char uplo, lapack_int n, <datatype>* a );

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 symmetric positive definite or, for complex data, Hermitian positive-definite matrix A using the Cholesky factorization:

`A = U^TU` for real data, `A = U^HU` for complex data	if `uplo='U'`
`A = LL^T` for real data, `A = LL^H` for complex data	if `uplo='L'`

Before calling this routine, call ?pftrf to factorize A.

The matrix A is in the Rectangular Full Packed (RFP) format. For the description of the RFP format, see Matrix Storage Schemes.

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.

transr	CHARACTER*1. Must be 'N', 'T' (for real data) or 'C' (for complex data). If transr = 'N', the Normal transr of RFP `A` is stored. If transr = 'T', the Transpose transr of RFP `A` is stored. If transr = 'C', the Conjugate-Transpose transr of RFP `A` is stored.
uplo	CHARACTER*1. Must be 'U' or 'L'. Indicates whether the upper or lower triangular part of the RFP matrix `A` is stored: If uplo = 'U', the array a stores the upper triangular part of the matrix `A`. If uplo = 'L', the array a stores the lower triangular part of the matrix `A`.
n	INTEGER. The order of the matrix `A`; n ≥ 0.
a	REAL for spftri DOUBLE PRECISION for dpftri COMPLEX for cpftri DOUBLE COMPLEX for zpftri. Array, DIMENSION `(n*(n+1)/2)`. The array a contains the matrix `A` in the RFP format.

Output Parameters

The symmetric/Hermitian inverse of the original matrix in the same storage format.

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,i) element of the factor U or L is zero, and the inverse could not be computed.