# TridiagonalSystemSolver

engine/Source/Core/TridiagonalSystemSolver.js 5
Uses the Tridiagonal Matrix Algorithm, also known as the Thomas Algorithm, to solve a system of linear equations where the coefficient matrix is a tridiagonal matrix.

### Methods

#### static Cesium.TridiagonalSystemSolver.solve(diagonal, lower, upper, right) → Array.<Cartesian3>
engine/Source/Core/TridiagonalSystemSolver.js 43

Solves a tridiagonal system of linear equations.

##### Performance:

Linear time.

Name | Type | Description
--- | --- | ---
`diagonal` | Array.<number> | An array with length `n` that contains the diagonal of the coefficient matrix.
`lower` | Array.<number> | An array with length `n - 1` that contains the lower diagonal of the coefficient matrix.
`upper` | Array.<number> | An array with length `n - 1` that contains the upper diagonal of the coefficient matrix.
`right` | Array.<Cartesian3> | An array of Cartesians with length `n` that is the right side of the system of equations.

##### Returns:

An array of Cartesians with length `n` that is the solution to the tridiagonal system of equations.

##### Throws:

- DeveloperError : diagonal and right must have the same lengths.
- DeveloperError : lower and upper must have the same lengths.
- DeveloperError : lower and upper must be one less than the length of diagonal.

##### Example:

    const lowerDiagonal = [1.0, 1.0, 1.0, 1.0];
    const diagonal = [2.0, 4.0, 4.0, 4.0, 2.0];
    const upperDiagonal = [1.0, 1.0, 1.0, 1.0];
    const rightHandSide = [
        new Cesium.Cartesian3(410757.0, -1595711.0, 1375302.0),
        new Cesium.Cartesian3(-5986705.0, -2190640.0, 1099600.0),
        new Cesium.Cartesian3(-12593180.0, 288588.0, -1755549.0),
        new Cesium.Cartesian3(-5349898.0, 2457005.0, -2685438.0),
        new Cesium.Cartesian3(845820.0, 1573488.0, -1205591.0)
    ];

    const solution = Cesium.TridiagonalSystemSolver.solve(lowerDiagonal, diagonal, upperDiagonal, rightHandSide);

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