int main(int argc, char *argv[]) {
iParams p;
int i;
/* set defaults for parameters */
p.a = 0.0;
p.b = 1.0;
p.n = 10;
parse_arguments(argc, argv, &p);
fprintf(stdout,"Initializing integration of f(x) = sqrt(x) + sin(x^(3/2)), from %f to %f with %d segments\n",p.a, p.b, p.n);
p.h = (double)(p.b - p.a)/(double)p.n;
double trapezoid_sum = 0;
for (i = 0; i < p.n; ++i) {
trapezoid_sum += trapezoid(p.a + (double)i * p.h, p.a + (double)(i+1) * p.h);
}
fprintf(stdout, "Integrated value: %20.15f\n",trapezoid_sum);
return 0;
}
static typename function_traits<F>::result_t integrate(const F &f, double a, double b) {
using T = typename function_traits<F>::result_t;
if (a >= b)
return T(0);
T t;
std::array<T, N> Tk;
Tk.fill(T(0));
Tk[0] = .5 * (b - a) * (f(a) + f(b));
for (std::uint64_t n = 1; n < N; ++n) {
std::uint64_t k = static_cast<std::uint64_t>(1) << n;
double h = (b - a) / static_cast<double>(k);
t = .5 * Tk[0] + h * trapezoid(f, h, a, b, k);
for (std::uint64_t m = 1; m <= n; ++m) {
T s = t + (t - Tk[m - 1]) / static_cast<double>((1 << 2 * m) - 1);
Tk[m - 1] = t;
t = s;
}
Tk[n] = t;
}
return Tk[N - 1];
}
int testTrapezoid(acc sample1, acc sample2, CAWAX_TIME_MSM time1, CAWAX_TIME_MSM time2, sample_th order1, sample_th order2) {
printf("Testing trapezoid \n");
printf("Sample 1: %.6f / %li / %li\n", sample1, time1, order1);
printf("Sample 2: %.6f / %li / %li\n", sample2, time2, order2);
printf("Trapezoid = %.6f\n", trapezoid(sample1, sample2, time1, time2, order1, order2, UNIT_MILLISEC_TO_MICRO));
}
/* Ex 8.04 -- compute the area of a polygon */
double
area(poly_t P) {
int i;
double area=0.0;
/* step through the edges, adding up the areas of the
trapezoidal regions indicated by pairs of consecutive
points. Assumes that polygon is well-behaved.
*/
for (i=0; i<P.npts-1; i++) {
area += trapezoid(P.pts[i], P.pts[i+1]);
}
/* plus the last closing edge */
area += trapezoid(P.pts[P.npts-1], P.pts[0]);
/* area is always positive, but summation may have ended
up with a negative value */
if (area<0) {
area = -area;
}
return area;
}
void calcarea(double start, double stop, int steps)
{
double totarea = 0.0, x1, x2, fx1, fx2, dx, sum_y;
x1 = start;
fx1 = f(x1);
for(int i =1; i<= steps; i++)
{
x2 = x1 + (double)i*(stop-start)/steps;
fx2 = f(x2);
dx = x2 - x1;
sum_y = fx1 + fx2;
totarea = totarea + trapezoid(dx, sum_y);
}
printf("\nThE total area is: %f\n", totarea );
}
/* Main function */
int main(int argc, char* argv[]) {
double j = 0.0;
integral fun = &f1;
/* Print the integrals of the first function using all of the available
* methods including trapezoidal, rectangle, Simpson and Gauss
*/
printf("\nIntegrals of x^2 on [0,1]:\n\n");
j = trapezoid(10, 0, 1, fun);
printf("Trapezoidal \t= %G\n", j);
j = rect(10, 0, 1, fun);
printf("Rectangle \t= %G\n", j);
j = simpson(10, 0, 1, fun);
printf("Simpson \t= %G\n", j);
j = gauss(10, 0, 1, fun);
printf("Gauss \t\t= %G\n", j);
fun = &f2;
/* Print the integrals of the second function using all of the available
* methods including trapezoidal, rectangle, Simpson and Gauss
*/
printf("\nIntegrals of x^3 on [0,1]:\n\n");
j = trapezoid(10, 0, 1, fun);
printf("Trapezoidal \t= %G\n", j);
j = rect(10, 0, 1, fun);
printf("Rectangle \t= %G\n", j);
j = simpson(10, 0, 1, fun);
printf("Simpson \t= %G\n", j);
j = gauss(10, 0, 1, fun);
printf("Gauss \t\t= %G\n", j);
fun = &f3;
/* Print the integrals of the third function using all of the available
* methods including trapezoidal, rectangle, Simpson and Gauss
*/
printf("\nIntegrals of x^5 on [0,1]:\n\n");
j = trapezoid(10, 0, 1, fun);
printf("Trapezoidal \t= %G\n", j);
j = rect(10, 0, 1, fun);
printf("Rectangle \t= %G\n", j);
j = simpson(10, 0, 1, fun);
printf("Simpson \t= %G\n", j);
j = gauss(10, 0, 1, fun);
printf("Gauss \t\t= %G\n", j);
fun = &f4;
/* Print the integrals of the fourth function using all of the available
* methods including trapezoidal, rectangle, Simpson and Gauss
*/
printf("\nIntegrals of e^-x on [0,1]:\n\n");
j = trapezoid(10, 0, 1, fun);
printf("Trapezoidal \t= %G\n", j);
j = rect(10, 0, 1, fun);
printf("Rectangle \t= %G\n", j);
j = simpson(10, 0, 1, fun);
printf("Simpson \t= %G\n", j);
j = gauss(10, 0, 1, fun);
printf("Gauss \t\t= %G\n", j);
fun = &f5;
/* Print the integrals of the fifth function using all of the available
* methods including trapezoidal, rectangle, Simpson and Gauss
*/
printf("\nIntegrals of xe^-x on [0,2]:\n\n");
j = trapezoid(10, 0, 2, fun);
printf("Trapezoidal \t= %G\n", j);
j = rect(10, 0, 2, fun);
printf("Rectangle \t= %G\n", j);
j = simpson(10, 0, 2, fun);
printf("Simpson \t= %G\n", j);
j = gauss(10, 0, 2, fun);
printf("Gauss \t\t= %G\n", j);
fun = &f6;
/* Print the integrals of the sixth function using all of the available
* methods including trapezoidal, rectangle, Simpson and Gauss
*/
printf("\nIntegrals of x^-0.5 on [0,2]:\n\n");
j = trapezoid(10, 0, 2, fun);
printf("Trapezoidal \t= %G\n", j);
j = rect(10, 0, 2, fun);
printf("Rectangle \t= %G\n", j);
j = simpson(10, 0, 2, fun);
printf("Simpson \t= %G\n", j);
j = gauss(10, 0, 2, fun);
printf("Gauss \t\t= %G\n", j);
return 1;
}
int main(int argc, char** argv) {
int rank; /* process rank */
int nprocs; /* number of processes */
int source; /* rank of sender */
int dest = MASTER; /* all procs send to master */
int tag = 0; /* message tag */
MPI_Status status; /* struct to hold message status */
int local_n; /* number of trapezoids evaluated by each process */
double integral; /* where we'll store the result of the integration */
double local_sum; /* local portion of the integration summation */
double a = 0.0; /* left endpoint of definite integration */
double b = 1.0; /* right endpoint of definite integration */
double local_a; /* left endpoint for local chunk */
double local_b; /* right endpoint for local chunk */
double width; /* width of each trapezoid - same for all proceses*/
double PI25DT = 3.141592653589793238462643;
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
/* width is the same for all trapezoids, on all procs */
width = (b - a)/(double)N;
/* how many trapezoids per process? */
local_n = N/nprocs;
printf("rank %d:\tlocal_n %d\n", rank, local_n);
/* calculate local interals to work on */
local_a = a + (rank * (local_n * width)); /* since each local interval is (local_n * width) */
local_b = local_a + (local_n * width);
printf("rank %d:\tlocal_a %f, local_b %f\n", rank, local_a, local_b);
/* local trapezoid calculations are bundled into a function */
local_sum = trapezoid(local_a,local_b, local_n, width);
printf("rank %d:\tlocal_sum %f\n", rank, local_sum);
/* message passing and totalling of local sums */
if (rank == MASTER) {
integral = local_sum;
for (source =1; source < nprocs; source++) {
MPI_Recv(&local_sum, 1, MPI_DOUBLE, source, tag, MPI_COMM_WORLD, &status);
integral += local_sum;
}
}
else {
MPI_Send(&local_sum, 1, MPI_DOUBLE, dest, tag, MPI_COMM_WORLD);
}
/* print the result */
if (rank == MASTER) {
printf("\n");
printf("Definite integral from %f to %f estimated as %f (using %d trapezoids)\n",
a, b, integral, N);
printf("(error: %.16f)\n",fabs(integral - PI25DT));
}
MPI_Finalize();
return EXIT_SUCCESS;
}
