Visible to Intel only — GUID: GUID-9A2DE6CA-69B8-4B9C-9709-C4AD0E167725
Visible to Intel only — GUID: GUID-9A2DE6CA-69B8-4B9C-9709-C4AD0E167725
?hptri
Computes the inverse of a complex Hermitian matrix using U*D*UH or L*D*LH Bunch-Kaufman factorization of matrix in packed storage.
Syntax
call chptri( uplo, n, ap, ipiv, work, info )
call zhptri( uplo, n, ap, ipiv, work, info )
call hptri( ap, ipiv [,uplo] [,info] )
Include Files
- mkl.fi, lapack.f90
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
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 packed Bunch-Kaufman factorization A = U*D*UH. If uplo = 'L', the array ap stores the packed Bunch-Kaufman factorization A = L*D*LH. |
n |
INTEGER. The order of the matrix A; n≥ 0. |
ap, work |
COMPLEX for chptri DOUBLE COMPLEX for zhptri. Arrays: ap(*) contains the factorization of the matrix A, as returned by ?hptrf. 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, size at least max(1, n). The ipiv array, as returned by ?hptrf. |
Output Parameters
ap |
Overwritten by the matrix inv(A). |
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. |
LAPACK 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 LAPACK 95 Interface Conventions.
Specific details for the routine hptri 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*UH*PT*X*P*U - I| ≤ c(n)ε(|D||UH|PT|X|P|U| + |D||D-1|)
for uplo = 'U', and
|D*LH*PT*X*PL - I| ≤ c(n)ε(|D||LH|PT|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.