?pftri

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?pftri

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

Syntax

lapack_intLAPACKE_spftri ( intmatrix_layout , chartransr , charuplo , lapack_intn , float*a );

lapack_intLAPACKE_dpftri ( intmatrix_layout , chartransr , charuplo , lapack_intn , double*a );

lapack_intLAPACKE_cpftri ( intmatrix_layout , chartransr , charuplo , lapack_intn , lapack_complex_float*a );

lapack_intLAPACKE_zpftri ( intmatrix_layout , chartransr , charuplo , lapack_intn , lapack_complex_double*a );

Include Files

mkl.h

Description

spftri dpftri cpftri zpftri

The routine computes the inverse inv(A) of a symmetric positive definite or, for complex data, Hermitian positive-definite matrix A using the Cholesky factorization:

`A = U^{T}U` for real data, `A = U^{H}U` for complex data	if `uplo='U'`
`A = LL^{T}` for real data, `A = LL^{H}` for complex data	if `uplo='L'`

Before calling this routine, call ?pftrf (Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix using the Rectangular Full Packed (RFP) format .) to factorize A .

The matrix A is in the Rectangular Full Packed (RFP) format. For the description of the RFP format, see Matrix Storage Schemes .

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).

transr

Must be ‘N’ , ‘T’ (for real data) or ‘C’ (for complex data).

If transr = ‘N’ , the Normal transr of RFP U (if uplo = ‘U’ ) or L (if uplo = ‘L’ ) is stored.

If transr = ‘T’ , the Transpose transr of RFP U (if uplo = ‘U’ ) or L (if uplo = ‘L’ is stored.

If transr = ‘C’ , the Conjugate-Transpose transr of RFP U (if uplo = ‘U’ ) or L (if uplo = ‘L’ is stored.

uplo

Must be ‘U’ or ‘L’ .

Indicates how the input matrix A has been factored:

If uplo = ‘U’ , A = U^T * U for real data or A = U^H * U for complex data, and U is stored.

If uplo = ‘L’ , A = L * L^T for real data or A = L * L^H for complex data, and L is stored.

n

The order of the matrix A ; n ≥ 0.

a

Array, size (n*(n+1)/2) . The array a contains the factor U or L matrix A in the RFP format.

Output Parameters

a

The symmetric/Hermitian inverse of the original matrix in the same storage format.

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,i) element of the factor U or L is zero, and the inverse could not be computed.

NOTE:

Matrix Storage Schemes

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?pftri

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values