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IDL Reference Guide: Procedures and Functions |
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The TRISOL function solves tridiagonal systems of linear equations that have the form: ATU = R
| Note Because IDL subscripts are in column-row order, the equation above is written ATU = 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. |
Result = TRISOL( A, B, C, R [, /DOUBLE] )
Returns a vector containing the solutions.
A vector of length n containing the n-1 sub-diagonal elements of AT. The first element of A, A0, is ignored.
An n-element vector containing the main diagonal elements of AT.
An n-element vector containing the n-1 super-diagonal elements of AT. The last element of C, Cn-1, is ignored.
An n-element vector containing the right hand side of the linear system
ATU = R.
Set this keyword to force the computation to be done in double-precision arithmetic.
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].
CRAMER, GS_ITER, LA_TRISOL, LU_COMPLEX, CHOLSOL, LUSOL, SVSOL, TRISOL
IDL Online Help (March 06, 2007)