?dttrsb

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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Solves a system of linear equations with a diagonally dominant tridiagonal coefficient matrix using the LU factorization computed by ?dttrfb.

Syntax

call sdttrsb( trans, n, nrhs, dl, d, du, b, ldb, info )

call ddttrsb( trans, n, nrhs, dl, d, du, b, ldb, info )

call cdttrsb( trans, n, nrhs, dl, d, du, b, ldb, info )

call zdttrsb( trans, n, nrhs, dl, d, du, b, ldb, info )

call dttrsb( dl, d, du, b [, trans] [, info] )

Include Files

Description

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

`A`*`X` = `B`	if trans='N',
`A`^T*`X` = `B`	if trans='T',
`A`^H*`X` = `B`	if trans='C' (for complex matrices only).

Before calling this routine, call ?dttrfb to compute the factorization of A.

Input Parameters

trans	CHARACTER1. Must be 'N' or 'T' or 'C'. Indicates the form of the equations solved for `X`: If `trans = 'N'`, then `AX = B`. If `trans = 'T'`, then `A`^T`X` = `B`. If `trans = 'C'`, then `A`^H`X` = `B`.
n	INTEGER. The order of `A`; n≥ 0.
nrhs	INTEGER. The number of right-hand sides, that is, the number of columns in `B`; nrhs≥ 0.
dl, d, du, b	REAL for sdttrsb DOUBLE PRECISION for ddttrsb COMPLEX for cdttrsb DOUBLE COMPLEX for zdttrsb. Arrays: `dl(n -1)`, `d(n)`, `du(n -1)`, `b(ldb,nrhs)`. The array dl contains the `(n - 1)` multipliers that define the matrices `L`₁, `L`₂ from the factorization of `A`. The array d contains the n diagonal elements of the upper triangular matrix `U` from the factorization of `A`. The array du contains the (n - 1) elements of the superdiagonal 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; `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.

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