?potri

Developer Reference for Intel® oneAPI Math Kernel Library for C

Download PDF

ID 766684

Date 4/28/2026

Version

Public

?potri

Computes the inverse of a symmetric (Hermitian) positive-definite matrix using the Cholesky factorization.

Syntax

lapack_intLAPACKE_spotri ( intmatrix_layout , charuplo , lapack_intn , float*a , lapack_intlda );

lapack_intLAPACKE_dpotri ( intmatrix_layout , charuplo , lapack_intn , double*a , lapack_intlda );

lapack_intLAPACKE_cpotri ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_float*a , lapack_intlda );

lapack_intLAPACKE_zpotri ( intmatrix_layout , charuplo , lapack_intn , lapack_complex_double*a , lapack_intlda );

Include Files

mkl.h

Description

spotri dpotri cpotri zpotri potri

The routine computes the inverse inv(A) of a symmetric positive definite or, for complex flavors, Hermitian positive-definite matrix A . Before calling this routine, call ?potrf (Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite 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 upper triangle of A is stored.

If uplo = 'L' , the lower triangle of A is stored.

n

The order of the matrix A ; n≥ 0 .

a

Array a (size max(1, lda * n )). Contains the factorization of the matrix A , as returned by GUID-15A9E907-2600-430B-BF11-DFA0A375711B.xml#GUID-15A9E907-2600-430B-BF11-DFA0A375711B .

lda

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

Output Parameters

a

Overwritten by the upper or lower triangle of the inverse of 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 the Cholesky factor (and therefore the factor itself) is zero, 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:

\[||XA - I||_{2} \leq c(n)\varepsilon\kappa_{2}(A), ||AX - I||_{2} \leq c(n)\varepsilon\kappa_{2}(A),\]

where c(n) is a modest linear function of n , and \(\varepsilon\) is the machine precision; \(I\) denotes the identity matrix.

The 2-norm \(||A||_{2}\) of a matrix \(A\) is defined by \(||A||_{2} = max_{x \cdot x=1}(Ax \cdot Ax)^{1/2}\) , and the condition number \(\kappa_{2}(A)\) is defined by \(\kappa_{2}(A) = ||A||_{2} ||A^{-1}||_{2}\) .

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

?potri

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes