?hptri

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?hptri

Computes the inverse of a complex Hermitian matrix using U*D*U^H or L*D*L^H Bunch-Kaufman factorization of matrix in packed storage.

Syntax

lapack_int LAPACKE_chptri (int matrix_layout , char uplo , lapack_int n , lapack_complex_float * ap , const lapack_int * ipiv );

lapack_int LAPACKE_zhptri (int matrix_layout , char uplo , lapack_int n , lapack_complex_double * ap , const lapack_int * ipiv );

Include Files

mkl.h

Description

The routine computes the inverse inv(A) of a complex Hermitian matrix A using packed storage. Before calling this routine, call ?hptrf to factorize A.

Input Parameters

matrix_layout	Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
uplo	Must be 'U' or 'L'. Indicates how the input matrix `A` has been factored: If `uplo = 'U'`, the array `ap` stores the packed Bunch-Kaufman factorization `A = UDU^H`. If `uplo = 'L'`, the array `ap` stores the packed Bunch-Kaufman factorization `A = LDL^H`.
n	The order of the matrix `A`; `n≥ 0`.
ap	Array `ap` (size max(1,`n`(`n`+1)/2)) contains the factorization of the matrix `A`, as returned by ?hptrf.
ipiv	Array, size at least `max(1, n)`. The `ipiv` array, as returned by ?hptrf.

Output Parameters

ap	Overwritten by the matrix `inv(A)`.

Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info = -i, parameter i 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.

Application Notes

The computed inverse X satisfies the following error bounds:

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

for uplo = 'U', and

|D*L^H*P^T*X*PL - I| ≤ c(n)ε(|D||L^H|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 (8/3)n³.

The real counterpart of this routine is ?sptri.

Parent topic: Matrix Inversion: LAPACK Computational Routines

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?hptri

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