TRISOL

The TRISOL function solves tridiagonal systems of linear equations that have the form: A^TU = R

Note
Because IDL subscripts are in column-row order, the equation above is written A^TU = R rather than AU = R. The result U is a vector of length n whose type is identical to A.

TRISOL is based on the routine tridag described in section 2.4 of Numerical Recipes in C: The Art of Scientific Computing (Second Edition), published by Cambridge University Press, and is used by permission.

Note
If you are working with complex inputs, use the LA_TRISOL procedure instead.

Syntax

Result = TRISOL( A, B, C, R [, /DOUBLE] )

Return Value

Returns a vector containing the solutions.

Arguments

A

A vector of length n containing the n-1 sub-diagonal elements of A^T. The first element of A, A₀, is ignored.

B

An n-element vector containing the main diagonal elements of A^T.

C

An n-element vector containing the n-1 super-diagonal elements of A^T. The last element of C, C_n-1, is ignored.

R

An n-element vector containing the right hand side of the linear system
A^TU = R.

Keywords

DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

Example

To solve a tridiagonal linear system, begin with an array representing a real tridiagonal linear system. (Note that only three vectors need be specified; there is no need to enter the entire array shown.)

; Define a vector A containing the sub-diagonal elements with a
; leading 0.0 element:
A = [0.0, 2.0, 2.0, 2.0]

; Define B containing the main diagonal elements:
B = [-4.0, -4.0, -4.0, -4.0]

; Define C containing the super-diagonal elements with a trailing
; 0.0 element:
C = [1.0, 1.0, 1.0, 0.0]

; Define the right-hand side vector:
R = [6.0, -8.0, -5.0, 8.0]

; Compute the solution and print:
result = TRISOL(A, B, C, R)
PRINT, result

IDL prints:

  -1.00000  2.00000  2.00000  -1.00000

The exact solution vector is [-1.0, 2.0, 2.0, -1.0].

Version History


4.0	Introduced