?gtts2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?gtts2

Solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by ?gttrf.

Syntax

call sgtts2( itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb )

call dgtts2( itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb )

call cgtts2( itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb )

call zgtts2( itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb )

Include Files

mkl.fi

Description

The routine solves for X one of the following systems of linear equations with multiple right hand sides:

A*X = B, A^T*X = B, or A^H*X = B (for complex matrices only), with a tridiagonal matrix A using the LU factorization computed by ?gttrf.

Input Parameters

itrans

INTEGER. Must be 0, 1, or 2.

Indicates the form of the equations to be solved:

If itrans = 0, then A*X = B (no transpose).

If itrans = 1, then A^T*X = B (transpose).

If itrans = 2, then A^H*X = B (conjugate transpose).

n

INTEGER. The order of the matrix A (n≥ 0).

nrhs

INTEGER. The number of right-hand sides, i.e., the number of columns in B (nrhs≥ 0).

dl,d,du,du2,b

REAL for sgtts2

DOUBLE PRECISION for dgtts2

COMPLEX for cgtts2

DOUBLE COMPLEX for zgtts2.

Arrays: dl(n - 1), d(n ), du(n - 1), du2(n - 2), b(ldb,nrhs).

The array dl contains the (n - 1) multipliers that define the matrix L from the LU factorization of A.

The array d contains the n diagonal elements of the upper triangular matrix U from the LU factorization of A.

The array du contains the (n - 1) elements of the first super-diagonal of U.

The array du2 contains the (n - 2) elements of the second super-diagonal of U.

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; must be ldb≥ max(1, n).

ipiv

INTEGER.

Array, DIMENSION (n).

The pivot indices array, as returned by ?gttrf.

Output Parameters

b: Overwritten by the solution matrix X.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?gtts2