//============================================================================
//
// Listing 16.6
//
// Mathematics for 3D Game Programming and Computer Graphics, 3rd ed.
// By Eric Lengyel
//
// The code in this file may be freely used in any software. It is provided
// as-is, with no warranty of any kind.
//
//============================================================================


void SolveTridiagonalSystem(int n, const float *a, const float *b,
		const float *c, const float *r, float *x)
{
	// Allocate temporary storage for c[i]/beta[i].
	float *t = new float[n - 1];
	
	float recipBeta = 1.0F / b[0];
	x[0] = r[0] * recipBeta;
	
	for (int i = 1; i < n; i++)
	{
		t[i - 1] = c[i - 1] * recipBeta; 
		recipBeta = 1.0F / (b[i] - a[i] * t[i - 1]);
		x[i] = (r[i] - a[i] * x[i - 1]) * recipBeta;
	}
	
	for (int i = n - 2; i >= 0; i--) x[i] -= t[i] * x[i + 1];
	
	delete[] t;
}