?sytri

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

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

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

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

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

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

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

Include Files

mkl.fi , mkl_lapack.f90

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

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 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

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

a , work

REAL for ssytri

DOUBLE PRECISION for dsytri

COMPLEX for csytri

DOUBLE COMPLEX for zsytri .

Arrays:

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

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(1,2*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 (Computes the Bunch-Kaufman factorization of a symmetric matrix.) .

Output Parameters

a

Overwritten by the n -by- n 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.

Return Values

No return value, info is an Output Parameter.

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 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 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

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?sytri

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes