?pftri

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?pftri

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

Syntax

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 )

Include Files

mkl.fi, lapack.f90

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

transr	CHARACTER*1. Must be 'N', 'T' (for real data) or 'C' (for complex data). If transr = 'N', the Normal transr of RFP `U` (if uplo = 'U') or `L` (if uplo = 'L') is stored. If transr = 'T', the Transpose transr of RFP `U` (if uplo = 'U') or `L` (if uplo = 'L' is stored. If transr = 'C', the Conjugate-Transpose transr of RFP `U` (if uplo = 'U') or `L` (if uplo = 'L' is stored.
uplo	CHARACTER1. Must be 'U' or 'L'. Indicates how the input matrix `A` has been factored: If uplo = 'U', `A` = `U`^T`U` for real data or `A` = `U`^H`U` for complex data, and `U` is stored. If uplo = 'L', `A` = `L``L`^T for real data or `A` = `L`*`L`^H for complex data, and `L` is stored.
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, size `(n*(n+1)/2)`. The array a contains the factor `U` or `L` 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.

Parent topic: Matrix Inversion: LAPACK Computational Routines

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?pftri

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