Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 7/13/2023
Public

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?sytri_rook

Computes the inverse of a symmetric matrix using U*D*UT or L*D*LT bounded Bunch-Kaufman factorization.

Syntax

call ssytri_rook( uplo, n, a, lda, ipiv, work, info )

call dsytri_rook( uplo, n, a, lda, ipiv, work, info )

call csytri_rook( uplo, n, a, lda, ipiv, work, info )

call zsytri_rook( uplo, n, a, lda, ipiv, work, info )

call sytri_rook( a, ipiv [,uplo] [,info] )

Include Files

  • mkl.fi, lapack.f90

Description

The routine computes the inverse inv(A) of a symmetric matrix A. Before calling this routine, call ?sytrf_rook 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 a stores the factorization A = U*D*UT.

If uplo = 'L', the array a stores the factorization A = L*D*LT.

n

INTEGER. The order of the matrix A; n 0.

a, work

REAL for ssytri_rook

DOUBLE PRECISION for dsytri_rook

COMPLEX for csytri_rook

DOUBLE COMPLEX for zsytri_rook.

Arrays:

a(size lda by *) contains the factorization of the matrix A, as returned by ?sytrf_rook.

The second dimension of a must be at least max(1,n).

work(*) is a workspace array. The dimension of work must be at least max(1,n).

lda

INTEGER. The leading dimension of a; lda max(1, n).

ipiv

INTEGER.

Array, size at least max(1, n).

The ipiv array, as returned by ?sytrf_rook.

Output Parameters

a

Overwritten by the n-by-n matrix inv(A). If uplo = 'U', the upper triangular part of the inverse is formed and the part of a below the diagonal is not referenced; if uplo = 'L' the lower triangular part of the inverse is formed and the part of a above the diagonal is not referenced."

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 sytri_rook interface are as follows:

a

Holds the matrix A of size (n,n).

ipiv

Holds the vector of length n.

uplo

Must be 'U' or 'L'. The default value is 'U'.

Application Notes

The total number of floating-point operations is approximately (2/3)n3 for real flavors and (8/3)n3 for complex flavors.