?ptts2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?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 (Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.) / dpttrf (Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.) , and complex flavors cptts2 / zptts2 use the U^{H}*D*U or L*D*L^{H} factorization of A computed by cpttrf (Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.) / zpttrf (Computes the factorization of a symmetric (Hermitian) positive-definite tridiagonal matrix.) .

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

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 .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?ptts2

Syntax

Include Files

Description

Input Parameters

Output Parameters