/*	Imhf.c
	
	Implicit heat flow equation, finite differenced.
	From Claerbout (1985) p. 98.

	Usage:		imhf >output

	Compile:	cc imhf.c rtris.c -fswitch -o imhf
									*/
/* The usual includes */
#include <stdio.h>
#include <math.h>

main()
	{
	int nx, it, ix;
	float alpha, a, q[12], d[12], e[12], f[12];

	nx = 12;
	a = 8;
	printf("a = %4.2f\n", a);
	alpha = 0.5*a;

	/* Initial temperature step */
	for (ix=0; ix<6; ix++)
		q[ix] = 0;
	for (ix=6; ix<12; ix++)
		q[ix] = 1;

	/* Iterate in time */
	for (it=0; it<4; it++)
		{
		/* Print current state of array */
		for (ix=0; ix<nx; ix++)
			printf("%6.2f", q[ix]);
		printf("\n");

		/* Set sides of implicit array */
		d[0] = 0;
		d[nx-1] = 0;

		/* Apply differencing star to array */
		for (ix=1; ix<nx-1; ix++)
			d[ix] = q[ix] + alpha*(q[ix-1] - 2*q[ix] + q[ix+1]);
			
		/* Solve the tridiagonal system */
		rtris(nx, alpha, -alpha, 1.0+2.0*alpha, -alpha, alpha,
			d, q, e, f);
		}
	exit(0);
	}