?pftrs

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

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

lapack_int LAPACKE_spftrs(int matrix_layout, char transr, char uplo, lapack_int n,
                          lapack_int nrhs, const float *a, float *b, lapack_int ldb);

lapack_int LAPACKE_dpftrs(int matrix_layout, char transr, char uplo, lapack_int n,
                          lapack_int nrhs, const double *a, double *b, lapack_int ldb);

lapack_int LAPACKE_cpftrs(int matrix_layout, char transr, char uplo, lapack_int n,
                          lapack_int nrhs, const lapack_complex_float *a,
                          lapack_complex_float *b, lapack_int ldb);

lapack_int LAPACKE_zpftrs(int matrix_layout, char transr, char uplo, lapack_int n,
                          lapack_int nrhs, const lapack_complex_double *a,
                          lapack_complex_double *b, lapack_int ldb);

Include Files

mkl.h

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

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 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

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

nrhs

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

a , b

Array a of size max(1, n *( n + 1)/2).

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

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

The leading dimension of b ; ldb≥ max(1, n)ldb ≥ max(1, n ) for column major layout and ldb ≥ nrhs for row major layout .

Output Parameters

b

The solution matrix X .

Return Values

This function returns a value info .

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

NOTE:

Matrix Storage Schemes

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?pftrs

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values