?sytri_rook

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?sytri_rook

Computes the inverse of a symmetric matrix using U*D*U^T or L*D*L^T 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	CHARACTER1. Must be 'U' or 'L'. Indicates how the input matrix `A` has been factored: If `uplo = 'U'`, the array `a` stores the factorization `A = UDU^T`. If `uplo = 'L'`, the array `a` stores the factorization `A = LD*L^T`.
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

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.

Parent topic: Matrix Inversion: LAPACK Computational Routines

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?sytri_rook

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