## TRISOL

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

Note: because IDL subscripts are in column-row order, the equation above is written A T U = 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.

### Calling Sequence

Result = TRISOL( A, B, C, R )

### Arguments

#### A

A vector of length n containing the n -1 sub-diagonal elements of A T . The first element of A , A 0 , 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 T U = 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].