?pftrs

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

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

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. Specifies the order of the matrix A. The value of n must be at least zero.

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