?ptts2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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 . 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 .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?ptts2

Syntax

Include Files

Description

Input Parameters

Output Parameters