int main(){
double (*f)(double x)=&f3;
double (*d)(double x)=&d3;
double start=3;
//double end=1.5;
int decimal_accuracy=5;
double error=pow(10,-decimal_accuracy);
double answer;
printf("The root of the function is: %.10lf\n", answer=newton_raphson(f,d,start,error));
printf("The value of the function is: %.10lf\n", (*f)(answer));
// printf("Bisection : %.10lf\n",iterative_bisection(f,3,start,error));
return 0;
}
void newtonMain()
{
clock_t start, finish;
double root, value, estimate, tolerance, time_taken;
int iterations, max_iterations, error;
char err_string[80];
get_conditions(estimate, tolerance, max_iterations);
start = clock();
// Do the calculation 50000 times so that the time taken is a few
// seconds, rather than a few milliseconds.
for (unsigned long i = 0 ; i < 50000; i++)
{
error = newton_raphson(estimate, tolerance, max_iterations,
iterations, root, value, err_string);
}
finish = clock();
time_taken = (finish - start) / double(CLOCKS_PER_SEC);
// Print out the number of iterations, or an error message }
if (error)
{
cout << "ERROR : " << err_string << endl;
}
else
{
cout << "Successful calculation, " << iterations
<< " iterations." << endl
<< "The root is " << root << endl
<< "The value of the function at this point is "
<< setiosflags(ios::fixed) << setprecision(2)
<< value << endl
<< "Time for 1000 Newton-Raphson calculations was "
<< time_taken << " seconds." << endl;
}
return 0;
}
/**************************** EX10 ****************************/
void EX10(void)
{
double fluxo[2][ANOS] = {{0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0},
{-1000.0, 100.0, 200.0, 100.0, 200.0, 100.0, 200.0, 100.0, 200.0, 100.0, 200.0}};
double r = 0.0;
int iter = 0;
if (bisseccao(fluxo, 0.0, 1.0, r, iter)==0){
cout << "[EX10 out] Bissecção: TIR = " << r * 100.0 << "%" << endl;
cout << "[EX10 out] Bissecção: Número de iterações = " << iter << endl;
}
if (newton_raphson(fluxo, 0.0, r, iter)==0){
cout << "[EX10 out] Newton-Raphson: TIR = " << r * 100.0 << "%" << endl;
cout << "[EX10 out] Newton-Raphson: Número de iterações = " << iter << endl;
}
}
// Find zero points according to chapter (2.4.1)
// Also stores wave numbers (zero-point / R)
void find_zero_points(int l_max, double x_max, double x_min, double epsilon, double R)
{
int i, l;
// Intervallgrenzen
double width = fabs(x_max - x_min);
// Anzahl Nullstellen von j_0 ( = sin(x)/x ) ist floor(width / pi):
int N = floor(width / PI);
// initialize zero points
double zeros[N];
FILE *file_zp = fopen("results/zero-points/0.txt", "w+"),
*file_wn = fopen("results/wave-numbers/0.txt", "w+");
for (i = 0; i < N; i++)
{
zeros[i] = (i+1) * PI; // i+1 = n
fprintf(file_zp, "%f %e\n", zeros[i], 0.0);
fprintf(file_wn, "%f %e\n", zeros[i]/R, 0.0);
}
fclose(file_zp);
fclose(file_wn);
bessel j;
char fp_zp[100], fp_wn[100];
for (l = 1; l <= l_max; l++)
{
// open zero-point file
snprintf(fp_zp, sizeof(fp_zp), "results/zero-points/%i.txt", l);
printf("Opening file %s...\n", fp_zp);
file_zp = fopen(fp_zp, "w+");
if (!file_zp)
printf("ERROR: Cannot open file %s.", fp_zp);
// open wave-numbers file
snprintf(fp_wn, sizeof(fp_wn), "results/wave-numbers/%i.txt", l);
printf("Opening file %s...\n", fp_wn);
file_wn = fopen(fp_wn, "w+");
if (!file_wn)
printf("ERROR: Cannot open file %s.", fp_wn);
for (i = 0; i < N-1; i++) // only go up to N-1 !
{
// start newton raphson at position x_start = (zeros[i] + zeros[i+1]) / 2
j = newton_raphson(epsilon, j_l(l, (zeros[i] + zeros[i+1])/2.0));
if (j.x < zeros[i+1] && j.x <= x_max)
{
fprintf(file_zp, "%f %e\n", j.x, j.val);
fprintf(file_wn, "%f %e\n", j.x/R, j.val);
zeros[i] = j.x;
}
else
{
printf("ERROR: Invalid value, j_%i(%f) = %f\n", j.l, j.x, j.val);
}
}
// find last zero point
if (N > 0)
{
// find approx. width of interval between two zero points
double dN;
if (N > 2)
dN = zeros[N-1] - zeros[N-2];
else
dN = x_max - zeros[N-1]; // use x_max as highest value instead
// start at z_N + 1/2 dN
j = newton_raphson(epsilon, j_l(l, zeros[N-1] + dN/2.0));
if (zeros[N-1] < j.x && j.x < x_max)
{
fprintf(file_zp, "%f %e\n", j.x, j.val);
fprintf(file_wn, "%f %e\n", j.x/R, j.val);
zeros[N-1] = j.x;
}
else
{
N--; // "drop" the last zero point
}
}
fclose(file_zp);
fclose(file_wn);
}
}
int main(void) {
double temperature, init_pressure, final_pressure, num_increments,
a, b, max_iterations, converg_criteria;
char gas_type, output_filename[101];
int i = 0;
double abs_pressure, press_single_incr, results[2], ideal;
// get inputs
get_double("Temperature (K)", &temperature);
get_double("initial pressure (atm)", &init_pressure);
get_double("final pressure (atm)", &final_pressure);
get_double("number of pressure increments", &num_increments);
get_char("gas type", &gas_type);
if(gas_type == 'c') {
a = 3.59200;
b = 0.04267;
}
else if(gas_type == 'o') {
a = 1.36000;
b = 0.03183;
}
else {
get_double("a (for a gas, if not carbon dioxide or oxygen)", &a);
get_double("b (for a gas, if not carbon dioxide or oxygen)", &b);
}
get_double("maximum number of iterations", &max_iterations);
get_double("convergence criteria", &converg_criteria);
for(i = 0; i < 5; i++) {
get_string("Output file name", output_filename);
output = fopen(output_filename, "r");
if(output != NULL) {
printf("Silly goose! '%s' already exists!\n", output_filename);
fclose(output);
}
else {
output = fopen(output_filename, "w");
break;
}
// the user has inputted 5 files that exist
if(i == 4) {
printf("Unable to make \"new\" output file after 5 attempts! Exiting!\n");
return 1;
}
}
// output known data
DBL_PRINT("\n\ninitial pressure (atm) = %lf\n", init_pressure);
DBL_PRINT("final pressure (atm) = %lf\n", final_pressure);
DBL_PRINT("number of pressure increments = %lf\n", num_increments);
DBL_PRINT("\na = %lf\n", a);
DBL_PRINT("b = %lf\n\n", b);
DBL_PRINT("gas type = %c\n", gas_type);
DBL_PRINT("maximum number of iterations = %lf\n", max_iterations);
DBL_PRINT("convergence criteria = %lf\n", converg_criteria);
DBL_PRINT("\n\n");
DBL_PRINT("Temperature (K)\t\tPressure (atm)\t\tMolal Volume,");
DBL_PRINT("\t\tNumber Iterations\t\tMolal Volume,\n");
DBL_PRINT("\t\t\t\t\t\t L/mol (vdW)\t\t\t\t\t\t L/mol (IGL)\n");
press_single_incr = (final_pressure - init_pressure) / num_increments;
for(abs_pressure = init_pressure
; abs_pressure <= final_pressure
; abs_pressure += press_single_incr) {
ideal = ideal_gas_law(abs_pressure, temperature);
newton_raphson(results, ideal, abs_pressure, temperature, a, b,
max_iterations, converg_criteria);
DBL_PRINT(" %lf\t\t %10lf\t\t %10lf\t\t %10lf\t\t\t%10lf\n", temperature,
abs_pressure, results[0], results[1], ideal);
}
fclose(output);
return 0;
}
double revised_temperature(double f(double,double,double), double epsilon_kl, double rho_kl,
double theta_kl)
{
double theta1= newton_raphson(f,epsilon_kl,rho_kl,theta_kl);
return theta1;
}
double test_(double x)
{
return newton_raphson(0.001, parabola, parabola_, x);
}
