?pftrs

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?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^TU` for real data, `A = U^HU` 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 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	The order of the matrix `A`; n≥ 0.
nrhs	The number of right-hand sides, that is, the number of columns of the matrix `B`; `nrhs`≥ 0.
a	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, ldbnrhs) for column major layout and max(1,ldbn) 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) 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.

Parent topic: Solving Systems of Linear Equations: LAPACK Computational Routines

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