Subversion Repositories programming

#include <iostream>

#include <iomanip>

#include <cmath>

using namespace std;

enum {IDX0, IDX1, IDX5, IDX10, IDX15, IDX19, IDX20};

#define ARRAY_SIZE 21

float x1_const[7] = { 1.266065978,     5.651591040E-01, 2.714631560E-04,

                      2.752948040E-10, 2.370463051E-17, 1.587678369E-23,

                      3.966835986E-25 };

float x2_const[7] = { 2.279585302,     1.590636855,     9.825679323E-03,

                      3.016963879E-07, 8.139432531E-13, 8.641603385E-18,

                      4.310560576E-19 };

float x5_const[7] = { 2.723987182E+01, 2.433564214E+01, 2.157974547,

                      4.580044419E-03, 1.047977675E-6 , 4.078415017E-10,

                      5.024239358E-11 };

/* Copied from the Project #2 Handout.

 *

 * FOR TESTING ONLY

 */

float Bessel_Recursive_BU (int n, float x, float base0, float base1)

{

    if (n == 0)

        return base0;

    else if (n == 1)

        return base1;

    return Bessel_Recursive_BU (n-2, x, base0, base1)

           + 2.0F * (float)(n-1) * Bessel_Recursive_BU (n-1, x, base0, base1) / x;

}

float Bessel_Recursive_TD (int n, float x, float base19, float base20)

{

    if (n == 19)

        return base19;

    else if (n == 20)

        return base20;

    return (2.0F * (float)(n+1) / x) * Bessel_Recursive_TD (n+1, x, base19, base20)

           + Bessel_Recursive_TD (n+2, x, base19, base20);

}

/* Find the Bessel Function.

 * Algorithm: I[n+1](x) = I[n-1](x) - (2*n/x) * I[n](x)

 * Which is equvalent to: I[n](x) = I[n-2](x) - (2 * (n-1)/x) * I[n-1](x)

 * by simple substitution.

 *

 * This is the recurrence relation for PART #1.

 */

float Bessel_BottomUp (int n, float x, float *constants)

{

    int i = 0;

    float  answer;

    float *storage = new float[ARRAY_SIZE];

    // Prime the array

    storage[0] = constants[IDX0];

    storage[1] = constants[IDX1];

    // Calculate each value in turn

    for (i=2; i<=20; i++)

        storage[i] = storage[i-2] - (2.0 * (n-1) / x) * storage[i-1];

    // Store the answer, delete the memory

    answer = storage[n];

    delete[] storage;

    // Return the result

    return answer;

}

/* Find the Bessel Function, from the Top -> Down.

 * Algorithm: I[n-1](x) = (2*n/x)*I[n](x) + I[n+1](x)

 * Which is equivalent to: I[n](x) = (2 * (n+1) / x) * I[n+1](x) + I[n+2](x)

 * by simple substitution.

 *

 * This is the recurrence relation for PART #2.

 */

float Bessel_TopDown (int n, float x, float *constants)

{

    int i = 18;

    float answer;

    float *storage = new float[ARRAY_SIZE];

    // Prime the array

    storage[20] = constants[IDX20];

    storage[19] = constants[IDX19];

    // Calculate each value in turn

    for (i=18; i>=0; i--)

        storage[i] = (2.0 * (n+1) / x) * storage[i+1] + storage[i+2];

    // Store the answer, free the memory

    answer = storage[n];

    delete[] storage;

    // Return the result

    return answer;

}

/* Print out a table for a given x value, and function.

 * Call like this: print_table (1.0, &BesselFunc);

 *

 * It chooses the correct constants appropriately.

 */

void print_table (float x, float (*bessel_func)(int, float, float*))

{

    int n;

    float true_val, calc_val, abs_err, rel_err;

    float *constants;

    if (x == 1.0) constants = x1_const;

    if (x == 2.0) constants = x2_const;

    if (x == 5.0) constants = x5_const;

    // Set the output flags

    cout << setiosflags (ios_base::scientific | ios_base::showpoint);

    // A line of equal signs

    for (n=0; n<(20+20+20+20+10); n++)

        cout << "=";

    cout << endl;

    // Print the x value we're using

    cout << "Using x = " << x << endl;

    // Print the table header

    cout << setw(10) << "n Val."

         << setw(20) << "TRUE"

         << setw(20) << "COMPUTED"

         << setw(20) << "ABS ERROR"

         << setw(20) << "REL ERROR"

         << endl;

    // A line of equal signs

    for (n=0; n<(20+20+20+20+10); n++)

        cout << "=";

    cout << endl;

    // Run once for n = 5,10,15,20

    for (n=5; n<=20; n+=5)

    {

        if (n==5 ) true_val = constants[IDX5];

        if (n==10) true_val = constants[IDX10];

        if (n==15) true_val = constants[IDX15];

        if (n==20) true_val = constants[IDX20];

        calc_val = bessel_func(n, x, constants);

        abs_err  = abs (true_val - calc_val);

        rel_err  = abs_err / abs (true_val);

        cout << setw(10) << n

             << setw(20) << true_val

             << setw(20) << calc_val

             << setw(20) << abs_err

             << setw(20) << rel_err

             << endl;

    }

}

int main (void)

{

    print_table (1.0, &Bessel_BottomUp);

    cout << endl;

    print_table (2.0, &Bessel_BottomUp);

    cout << endl;

    print_table (5.0, &Bessel_BottomUp);

    cout << endl;

    return 0;

}