?sptri

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?sptri

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

Syntax

call ssptri ( uplo , n , ap , ipiv , work , info )

call dsptri ( uplo , n , ap , ipiv , work , info )

call csptri ( uplo , n , ap , ipiv , work , info )

call zsptri ( uplo , n , ap , ipiv , work , info )

call sptri ( ap , ipiv [ , uplo ] [ , info ] )

Include Files

mkl.fi , mkl_lapack.f90

Description

ssptri dsptri csptri zsptri sptri

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

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

n

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

ap , work

REAL for ssptri

DOUBLE PRECISION for dsptri

COMPLEX for csptri

DOUBLE COMPLEX for zsptri .

Arrays:

ap(*) contains the factorization of the matrix A , as returned by ?sptrf (Computes the Bunch-Kaufman factorization of a symmetric matrix using packed storage.) .

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) .

ap

Arrays ap (size max(1, n(n+1)/2)) contains the factorization of the matrix A , as returned by ?sptrf (Computes the Bunch-Kaufman factorization of a symmetric matrix using packed storage.) .

ipiv

INTEGER .

Array, size at least max(1, n) . The ipiv array, as returned by ?sptrf (Computes the Bunch-Kaufman factorization of a symmetric matrix using packed storage.) .

Output Parameters

ap

Overwritten by the matrix inv(A) in packed form.

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 sptri 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:

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

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

?sptri

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes