?pftri

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?pftri

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

Syntax

call spftri(transr, uplo, n, a, info)
call dpftri(transr, uplo, n, a, info)
call cpftri(transr, uplo, n, a, info)
call zpftri(transr, uplo, n, a, info)

Include Files

mkl.fi , mkl_lapack.f90

Description

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

transr

CHARACTER*1 . 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

CHARACTER*1 . 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: INTEGER. Specifies the order of the matrix A. The value of n must be at least zero.

a

REAL for spftri

DOUBLE PRECISION for dpftri

COMPLEX for cpftri

DOUBLE COMPLEX for zpftri .

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.

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

Return Values

No return value, info is an Output Parameter.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?pftri

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values