d12r7.cpp

使用VC++编写的大量数学算法的源代码

#include <iostream.h>
#include <math.h>
#include <iomanip.h>
#include <stdlib.h>
#include <fstream.h>
#include <string>
#include <process.h>
#include<stdio.h>

void four1(double data[65], int nn, int isign)
{
	int n,j,i,m,mmax,istep;
	double tempr,tempi,theta,wpr,wpi,wr,wi,wtemp;
    n = 2 * nn;
    j = 1;
    for (i = 1; i<=n ; i=i+2)
	{
        if( j > i)
		{
            tempr = data[j];
            tempi = data[j + 1];
            data[j] = data[i];
            data[j + 1] = data[i + 1];
            data[i] = tempr;
            data[i + 1] = tempi;
        }
        m = n / 2;
        while (m >= 2 && j > m)
		{
            j = j - m;
            m = m / 2;
        }
        j = j + m;
    }
    mmax = 2;
    while( n > mmax )
	{
        istep = 2 * mmax;
        theta = 6.28318530717959 / (isign * mmax);
        wpr = -2.0 * sin(0.5 * theta)*sin(0.5 * theta);
        wpi = sin(theta);
        wr = 1.0;
        wi = 0.0;
        for( m = 1; m<=mmax; m=m+2)
		{
            for (i = m; i<=n; i=i+istep)
			{
                j = i + mmax;
                tempr=double(wr)*data[j]-double(wi)*data[j+1];
                tempi=double(wr)*data[j+1]+double(wi)*data[j];
                data[j] = data[i] - tempr;
                data[j + 1] = data[i + 1] - tempi;
                data[i] = data[i] + tempr;
                data[i + 1] = data[i + 1] + tempi;
            }
            wtemp = wr;
            wr = wr * wpr - wi * wpi + wr;
            wi = wi * wpr + wtemp * wpi + wi;
        }
        mmax = istep;
    }
}

void realft(double data[], int &n, int &isign)
{
	int n2p3,i,i1,i2,i3,i4;
	double theta,c1,c2,wpr,wpi,wr,wi,wrs,wis,h1r,h1i,h2r;
	double h2i,wtemp,wri;
	wri=0.0;
    theta = 6.28318530717959 / 2.0 / n;
    c1 = 0.5;
    if (isign == 1)
	{
        c2 = -0.5;
        four1(data, n, 1);
	}
    else
	{
        c2 = 0.5;
        theta = -theta;
	}
    wpr = -2.0 * sin(0.5 * theta) * sin(0.5 * theta);
    wpi = sin(theta);
    wr = 1.0 + wpr;
    wi = wpi;
    n2p3 = 2 * n + 3;
    for (i = 2; i<=n / 2 + 1; i++)
	{
        i1 = 2 * i - 1;
        i2 = i1 + 1;
        i3 = n2p3 - i2;
        i4 = i3 + 1;
        wrs = float(wr);
        wis = float(wi);
        h1r = c1 * (data[i1] + data[i3]);
        h1i = c1 * (data[i2] - data[i4]);
        h2r = -c2 * (data[i2] + data[i4]);
        h2i = c2 * (data[i1] - data[i3]);
        data[i1] = h1r + wrs * h2r - wis * h2i;
        data[i2] = h1i + wrs * h2i + wis * h2r;
        data[i3] = h1r - wrs * h2r + wis * h2i;
        data[i4] = -h1i + wrs * h2i + wis * h2r;
        wtemp = wr;
        wr = wr * wpr - wi * wri + wr;
        wi = wi * wpr + wtemp * wpi + wi;
    }
    if( isign == 1 )
	{
        h1r = data[1];
        data[1] = h1r + data[2];
        data[2] = h1r - data[2];
	}
    else
	{
        h1r = data[1];
        data[1] = c1 * (h1r + data[2]);
        data[2] = c1 * (h1r - data[2]);
        four1(data, n, -1);
    }
}

void twofft(double data1[], double data2[], double fft1[],
			double fft2[], int& n)
{
	int j,n2,j2;
	double c1r,c1i,c2r,c2i,conjr,conji,h1r,h1i,h2r,h2i;
    c1r = 0.5;
    c1i = 0.0;
    c2r = 0.0;
    c2i = -0.5;
    for (j = 1; j<=n; j++)
	{
        fft1[2 * j - 1] = data1[j];
        fft1[2 * j] = data2[j];
    }
    four1(fft1, n, 1);
    fft2[1] = fft1[2];
    fft2[2] = 0.0;
    fft1[2] = 0.0;
    n2 = 2 * (n + 2);
    for (j = 2; j<=n / 2 + 1; j++)
	{
        j2 = 2 * j;
        conjr = fft1[n2 - j2 - 1];
        conji = -fft1[n2 - j2];
        h1r=c1r*(fft1[j2-1]+conjr)-c1i*(fft1[j2]+conji);
        h1i=c1i*(fft1[j2-1]+conjr)+c1r*(fft1[j2]+conji);
        h2r=c2r*(fft1[j2-1]-conjr)-c2i*(fft1[j2]-conji);
        h2i=c2i*(fft1[j2-1]-conjr)+c2r*(fft1[j2]-conji);
        fft1[j2 - 1] = h1r;
        fft1[j2] = h1i;
        fft1[n2 - j2 - 1] = h1r;
        fft1[n2 - j2] = -h1i;
        fft2[j2 - 1] = h2r;
        fft2[j2] = h2i;
        fft2[n2 - j2 - 1] = h2r;
        fft2[n2 - j2] = -h2i;
    }
}

void correl(double data1[], double data2[], int &n,double ans[])
{
	int no2,i,temp;
    double fft[129],dum,dum1,dum2;
	for(i=1; i<=128; i++)
		fft[i]=0.0;
	temp=-1;
    twofft(data1, data2, fft, ans, n);
    no2 = n / 2;
    for (i = 1; i<=no2 + 1; i++)
	{
      dum = ans[2 * i - 1];
      dum1 = fft[2 * i - 1] * dum + fft[2 * i] * ans[2 * i];
      ans[2 * i - 1] = dum1 / float(no2);
      dum2 = fft[2 * i] * dum - fft[2 * i - 1] * ans[2 * i];
      ans[2 * i] = dum2 / float(no2);
    }
    ans[2] = ans[n + 1];
    realft(ans, no2,temp);
    for(i=1; i<=128; i++)
		fft[i]=0.0;
}

void main()
{
    //program d12r7
    //driver for routine correl
	int n,n2,i,j;
	double data1[65],data2[65],ans[129],cmp;
    n = 64;
    n2 = 128;
    const double pi = 3.1415926;  
	for(i=0; i<=128; i++)
	{
		ans[i]=0.0;
	}
    for (i = 1; i<=n; i++)
	{
        data1[i] = 0.0;
        if (i>(n / 2 - n / 8) && i <(n / 2 + n / 8))
		{
            data1[i] = 1.0;
        }
		data2[i]=data1[i];
    }
    correl(data1,data2,n,ans);
    cout<<endl;
    cout<<"   n         correl     direct calc"<<endl;
    for (i = 0; i<=16; i++)
	{
        cmp = 0.0;
        for( j = 1; j<=n; j++)
		{
            cmp = cmp + data1[((i + j - 1)%n) + 1] * data2[j];
        }
		cout<<setprecision(0)<<setw(4)<<i;
        cout<<setprecision(6)<<setw(16)<<ans[i + 1];
        cout<<setprecision(6)<<setw(10)<<cmp<<endl;
	}
}