?pftrs

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?pftrs

Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix using the Rectangular Full Packed (RFP) format.

Syntax

call spftrs ( transr , uplo , n , nrhs , a , b , ldb , info )

call dpftrs ( transr , uplo , n , nrhs , a , b , ldb , info )

call cpftrs ( transr , uplo , n , nrhs , a , b , ldb , info )

call zpftrs ( transr , uplo , n , nrhs , a , b , ldb , info )

Include Files

mkl.fi , mkl_lapack.f90

Description

spftrs dpftrs cpftrs zpftrs

The routine solves a system of linear equations A*X = B with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix A using the Cholesky factorization of A :

`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 ?pftrs , you must call ?pftrf (Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix using the Rectangular Full Packed (RFP) format .) to compute the Cholesky factorization of A . L stands for a lower triangular matrix and U for an upper triangular matrix.

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 untransposed factor of A is stored in RFP format.

If transr = ‘T’ , the transposed factor of A is stored in RFP format.

If transr = ‘C’ , the conjugate-transposed factor of A is stored in RFP format.

uplo

CHARACTER*1 . Must be ‘U’ or ‘L’ .

Indicates how the input matrix A has been factored:

If uplo = 'U' , U is stored, where A = U^T * U for real data, A = U^H * U for complex data.

If uplo = 'L' , L is stored, where A = L * L^T for real data, A = L * L^H for complex data

n

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

nrhs

INTEGER . The number of right-hand sides, that is, the number of columns of the matrix B ; nrhs ≥ 0.

a , b

REAL for spftrs

DOUBLE PRECISION for dpftrs

COMPLEX for cpftrs

DOUBLE COMPLEX for zpftrs .

Arrays: a(n*(n + 1)/2) , b(ldb,nrhs) .

The array a contains, in the RFP format, the factor U or L obtained by factorization of matrix A .

The array b contains the matrix B whose columns are the right-hand sides for the systems of equations.

b

The array b of size max(1, ldb * nrhs ) for column major layout and max(1, ldb * n ) for row major layout contains the matrix B whose columns are the right-hand sides for the systems of equations.

ldb

INTEGER . The leading dimension of b ; ldb≥ max(1, n) .

Output Parameters

b

The solution matrix X .

info

INTEGER .

If info=0 , the execution is successful.
If info = -i , the i -th parameter had an illegal value.

Return Values

No return value, info is an Output Parameter.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?pftrs

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values