Trap.c

From Education

#include <stdio.h>

// This is intended to be a straightforward implementation of area under a curve
//
// Suggested modifications to scalar code:
// 	- actually use a trapezoidal approximation
// 	- calculate upper and lower rectangles for each segment and thus upper and lower bounds 
//           and thus error estimate
// 	- release restriction that function be monotonic increasing
//
// Suggested modifications to parallel code:
// 	- modify to be run under parallel method du jour: OpenMP/MPI/Cuda or hybrid combination of these
// 	- what happens when number of processes does not evenly divide number of segments
// 	- what happens to accuracy of solution as you increase the number of segments (any anomalies?)
// 	- what happens if you derive number of segments from a desired error bound
//

// (monotonic increasing) function to integrate
float func(float x){
	return x*x;
}

int main() {

	// constraints
	int num_seg=1000;               	// number of segments 
	float start_x=0.0, end_x=1.0;		// start and end of overall area 

  	// variables
	int i;							// loop counter
	float seg_width;              	// segment width
	float low_x, low_y;				// low endpoint of segment
	float high_x, high_y;			// low endpoint of segment
	float area;						// area of segment

	printf("Hello\n");

	// calculate the segment width

	seg_width = (end_x-start_x)/num_seg;
	printf("seg_width= %f\n", seg_width); 

	for (i=0; i<num_seg; ++i) {
		low_x = (start_x + i * seg_width);
		high_x = (start_x + (i+1) * seg_width);
		low_y = func(low_x);
		high_y = func(high_x);

		area += seg_width * (low_y + high_y) * 0.5;

		printf("i = %d, low_x = %f, high_x = %f, low_y = %f, high_y = %f, area = %f \n", i, 
                        low_x, high_x, low_y, high_y, area);
	}
}