?pftrs

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

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

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, 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^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

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	CHARACTER1. 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.
ldb	INTEGER. The leading dimension of b; `ldb≥ max(1, n)`.

Output Parameters

The solution matrix X.

info

INTEGER. If info=0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

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

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