?pttrs

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?pttrs

Solves a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal coefficient matrix using the factorization computed by ?pttrf.

Syntax

call spttrs( n, nrhs, d, e, b, ldb, info )

call dpttrs( n, nrhs, d, e, b, ldb, info )

call cpttrs( uplo, n, nrhs, d, e, b, ldb, info )

call zpttrs( uplo, n, nrhs, d, e, b, ldb, info )

call pttrs( d, e, b [,info] )

call pttrs( d, e, b [,uplo] [,info] )

Include Files

mkl.fi, lapack.f90

Description

The routine solves for X a system of linear equations A*X = B with a symmetric (Hermitian) positive-definite tridiagonal matrix A. Before calling this routine, call ?pttrf to compute the L*D*L^T or U^T*D*Ufor real data and the L*D*L^H or U^H*D*Ufactorization of A for complex data.

Input Parameters

uplo	CHARACTER1. Used for cpttrs/zpttrs only. Must be 'U' or 'L'. Specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix `A` is stored and how `A` is factored: If `uplo = 'U'`, the array `e` stores the conjugated values of the superdiagonal of `U`, and `A` is factored as `U^HDU`. If `uplo = 'L'`, the array `e` stores the subdiagonal of `L`, and `A` is factored as `LD*L^H`.
n	INTEGER. The order of `A`; `n`≥ 0.
nrhs	INTEGER. The number of right-hand sides, that is, the number of columns of the matrix `B`; `nrhs`≥ 0.
d	REAL for spttrs, cpttrs DOUBLE PRECISION for dpttrs, zpttrs. Array, dimension (`n`). Contains the diagonal elements of the diagonal matrix `D` from the factorization computed by ?pttrf.
e, b	REAL for spttrs DOUBLE PRECISION for dpttrs COMPLEX for cpttrs DOUBLE COMPLEX for zpttrs. Arrays: `e`(`n` -1), `b`(`ldb`, `nrhs`). The array `e` contains the (`n` - 1) sub-diagonal elements of the unit bidiagonal factor `L` or the conjugated values of the superdiagonal of `U` from the factorization computed by ?pttrf (see `uplo`). 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

Overwritten by the solution matrix X.

info

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

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

LAPACK 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.

Specific details for the routine pttrs interface are as follows:

d	Holds the vector of length `n`.
e	Holds the vector of length (`n`-1).
b	Holds the matrix `B` of size (`n`, `nrhs`).
uplo	Used in complex flavors only. Must be 'U' or 'L'. The default value is 'U'.

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

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?pttrs

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