?sytri

Developer Reference for Intel® oneAPI Math Kernel Library for C

Download PDF

ID 766684

Date 4/28/2026

Version

Public

?sytri

Computes the inverse of a symmetric matrix using U * D * U^T or L * D * L^T Bunch-Kaufman factorization.

Syntax

lapack_intLAPACKE_ssytri ( intmatrix_layout , charuplo , lapack_intn , float*a , lapack_intlda , constlapack_int*ipiv );

lapack_intLAPACKE_dsytri ( intmatrix_layout , charuplo , lapack_intn , double*a , lapack_intlda , constlapack_int*ipiv );

lapack_intLAPACKE_csytri ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_float*a , lapack_intlda , constlapack_int*ipiv );

lapack_intLAPACKE_zsytri ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_double*a , lapack_intlda , constlapack_int*ipiv );

Include Files

mkl.h

Description

ssytri dsytri csytri zsytri sytri

The routine computes the inverse inv(A) of a symmetric matrix A . Before calling this routine, call ?sytrf (Computes the Bunch-Kaufman factorization of a symmetric matrix.) 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 a stores the Bunch-Kaufman factorization A = U*D*U^{T} .

If uplo = 'L' , the array a stores the Bunch-Kaufman factorization A = L*D*L^{T} .

n

The order of the matrix A ; n≥ 0 .

a , work

a (size max(1, lda * n )) contains the factorization of the matrix A , as returned by GUID-E63FFF60-72A7-44E2-8DEE-4331872FF8D5.xml#GUID-E63FFF60-72A7-44E2-8DEE-4331872FF8D5 .

lda

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

ipiv

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

The ipiv array, as returned by ?sytrf (Computes the Bunch-Kaufman factorization of a symmetric matrix.) .

Output Parameters

a

Overwritten by the n -by- n 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.

LAPACK 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

Application Notes

The computed inverse \(X\) satisfies the following error bounds:

\[|D U^{T} P^{T} X P U - I| \leq c(n)\varepsilon(|D||U^{T}|P^{T}|X|P|U| + |D||D^{-1}|)\]

for uplo = ‘U’ , and

\[|D L^{T} P^{T} X P L - I| \leq c(n)\varepsilon(|D||L^{T}|P^{T}|X|P|L| + |D||D^{-1}|)\]

for uplo = 'L' . Here c(n) is a modest linear function of n , and \(\varepsilon\) is the machine precision; \(I\) denotes the identity matrix.

The total number of floating-point operations is approximately \((2/3)n^{3}\) for real flavors and \((8/3)n^{3}\) for complex flavors.

NOTE:

Matrix Storage Schemes

Select Your Language

Using Intel.com Search

Quick Links

Recent Searches

Advanced Search

Only search in

Developer Reference for Intel® oneAPI Math Kernel Library for C

?sytri

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes