?ptts2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?ptts2

Solves a tridiagonal system of the form A*X=B using the L*D*L^H/L*D*L^H factorization computed by ?pttrf.

Syntax

call sptts2( n, nrhs, d, e, b, ldb )

call dptts2( n, nrhs, d, e, b, ldb )

call cptts2( iuplo, n, nrhs, d, e, b, ldb )

call zptts2( iuplo, n, nrhs, d, e, b, ldb )

Include Files

mkl.fi

Description

The routine ?ptts2 solves a tridiagonal system of the form

A*X = B

Real flavors sptts2/dptts2 use the L*D*L^T factorization of A computed by spttrf/dpttrf, and complex flavors cptts2/zptts2 use the U^H*D*U or L*D*L^H factorization of A computed by cpttrf/zpttrf.

D is a diagonal matrix specified in the vector d, U (or L) is a unit bidiagonal matrix whose superdiagonal (subdiagonal) is specified in the vector e, and X and B are n-by-nrhs matrices.

Input Parameters

iuplo

INTEGER. Used with complex flavors only.

Specifies the form of the factorization, and whether the vector e is the superdiagonal of the upper bidiagonal factor U or the subdiagonal of the lower bidiagonal factor L.

= 1: A = U^H*D*U, e is the superdiagonal of U;

= 0: A = L*D*L^H, e is the subdiagonal of L

n

INTEGER. The order of the tridiagonal matrix 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 sptts2/cptts2

DOUBLE PRECISION for dptts2/zptts2.

Array, DIMENSION (n).

The n diagonal elements of the diagonal matrix D from the factorization of A.

e

REAL for sptts2

DOUBLE PRECISION for dptts2

COMPLEX for cptts2

DOUBLE COMPLEX for zptts2.

Array, DIMENSION (n-1).

Contains the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L^T (for real flavors) or L*D*L^H (for complex flavors when iuplo = 0) factorization of A.

For complex flavors when iuplo = 1, e contains the (n-1) superdiagonal elements of the unit bidiagonal factor U from the factorization A = U^H*D*U.

B

REAL for sptts2/cptts2

DOUBLE PRECISION for dptts2/zptts2.

Array, DIMENSION (ldb, nrhs).

On entry, the right hand side vectors B for the system of linear equations.

ldb

INTEGER. The leading dimension of the array B. ldb≥ max(1,n).

Output Parameters

b: On exit, the solution vectors, X.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?ptts2