Лабораторная №1

lab1.cpp

#include <cmath>
#include <cstdlib>
#include <iostream>

#ifndef RANGE
#define RANGE 10000
#endif

#ifndef CORRELATION_OFFSET
#define CORRELATION_OFFSET 10
#endif

#define MIN(x, y) (x < y ? x : y)
#define MAX(x, y) (x > y ? x : y)

typedef unsigned int uint;

class AbstractSequence {
public:
	uint startelement;
	uint range;
	virtual uint getNext(uint element) = 0;
};

class Sequence1: public AbstractSequence {
public:
	Sequence1() {
		startelement = 1;
		range = 16284;
	}
	
	virtual uint getNext(uint element) {
		return (12 * element + 1) % 16284;
	}
};

class Sequence2: public AbstractSequence {
public:
	Sequence2() {
		startelement = 65535;
		range = 65536;
	}
	
	virtual uint getNext(uint element) {
		return (25173 * element + 13949) & 65535;
	}
};

class Sequence3: public AbstractSequence {
private:
	uint n;
	double s2;

public:
	Sequence3() {
		n = 1;
		s2 = sqrt(2);
		startelement = (s2-1) * RANGE;
		range = RANGE;
	}
	
	virtual uint getNext(uint element) {
		++n;
		uint result = uint(n*s2*RANGE) % RANGE;
		return (result > 0) ? result : startelement;
	}
};

class Sequence4: public AbstractSequence {
public:
	Sequence4() {
		startelement = rand() % RANGE;
		range = RANGE;
	}
	
	virtual uint getNext(uint element) {
		return rand() % RANGE;
	}
};

uint getPeriod(AbstractSequence *seq) {
	uint element = seq->getNext(seq->startelement);
	uint c = 1;
	while (element != seq->startelement) {
		if (element == seq->getNext(element))
			//return 0;
			return c;
		element = seq->getNext(element);
		++c;
	}
	return c;
}

double getMeanValue(AbstractSequence *seq) {
	uint sum = 0, period = getPeriod(seq);
	uint element = seq->startelement;
	for (uint i = 0; i < period; ++i) {
		sum += element;
		element = seq->getNext(element);
	}
	return (double(sum) / period) / seq->range;
}

double getDispersion(AbstractSequence *seq) {
	uint sum = 0, period = getPeriod(seq);
	uint element = seq->startelement;
	double meanValue = getMeanValue(seq);
	for (uint i = 0; i < period; ++i) {
		sum += pow(element - meanValue, 2);
		element = seq->getNext(element);
	}
	return (double(sum) / period) / seq->range;
}

double getCorrelation(AbstractSequence *seq) {
	uint element1 = seq->startelement;
	uint element2 = element1;
	uint i;
	double sum = 0;
	for (i = 0; i < CORRELATION_OFFSET; ++i)
		element2 = seq->getNext(element2);
	uint period = getPeriod(seq);
	double mv = getMeanValue(seq);
	for (i = 0; i < period; ++i) {
		sum += ((double(element1)/seq->range)-mv)*((double(element2)/seq->range)-mv);
		element1 = seq->getNext(element1);
		element2 = seq->getNext(element2);
	}
	double cov = sum / period;
	return cov / getDispersion(seq);
}

double getPi(AbstractSequence *seq) {
	uint circ = 0, period = getPeriod(seq), i;
	uint element = seq->startelement, next;
	for (i = 0; i < period; ++i) {
		next = seq->getNext(element);
		if (sqrt(pow(double(element)/seq->range - .5, 2) + pow(double(next)/seq->range - .5, 2)) < .5)
			++circ;
		element = seq->getNext(element);
	}
	return 4 * double(circ) / period;
}

void printPeriod(uint number, uint period) {
	if (period)
		std::cout << "Period of sequence " << number << " is " << period;
	else
		std::cout << "Sequence " << number << " has a fixed point";
	std::cout << std::endl;
}

double getChi2(AbstractSequence *seq, uint n) {
	uint *counter = new uint[n];
	uint element = seq->getNext(seq->startelement);
	uint c = 1, interval;
	for (interval = 0; interval < n; ++interval)
		counter[interval] = 0;
	while (element != seq->startelement) {
		interval = 0;
		while (interval * seq->range > element * n
			|| element * n >= (interval+1) * seq->range)
			++interval;
		++counter[interval];
		if (element == seq->getNext(element))
			break;
		element = seq->getNext(element);
		++c;
	}
	double chi2 = 0;
	//std::cout << "counter is:";
	for (interval = 0; interval < n; ++interval) {
		//std::cout << " " << counter[interval];
		chi2 += pow(double(counter[interval]) / c - 1, 2);
	}
	//std::cout << std::endl;
	delete[] counter;
	return chi2 / n;
}

int main(void) {
	Sequence1 seq1;
	Sequence2 seq2;
	Sequence3 seq3;
	Sequence4 seq4;
	
	printPeriod(1, getPeriod(&seq1));
	printPeriod(2, getPeriod(&seq2));
	printPeriod(3, getPeriod(&seq3));
	printPeriod(4, getPeriod(&seq4));
	
	std::cout << "Mean value for sequence 1 is " << getMeanValue(&seq1) << std::endl;
	std::cout << "Mean value for sequence 2 is " << getMeanValue(&seq2) << std::endl;
	std::cout << "Mean value for sequence 3 is " << getMeanValue(&seq3) << std::endl;
	std::cout << "Mean value for sequence 4 is " << getMeanValue(&seq4) << std::endl;
	
	std::cout << "Pi for sequence 1 is " << getPi(&seq1) << std::endl;
	std::cout << "Pi for sequence 2 is " << getPi(&seq2) << std::endl;
	std::cout << "Pi for sequence 3 is " << getPi(&seq3) << std::endl;
	std::cout << "Pi for sequence 4 is " << getPi(&seq4) << std::endl;
	
	std::cout << "Correlation for sequence 1 is " << getCorrelation(&seq1) << std::endl;
	std::cout << "Correlation for sequence 2 is " << getCorrelation(&seq2) << std::endl;
	std::cout << "Correlation for sequence 3 is " << getCorrelation(&seq3) << std::endl;
	std::cout << "Correlation for sequence 4 is " << getCorrelation(&seq4) << std::endl;
	
	std::cout << "Chi^2 for sequence 1 is " << getChi2(&seq1, 10) << std::endl;
	std::cout << "Chi^2 for sequence 2 is " << getChi2(&seq2, 10) << std::endl;
	std::cout << "Chi^2 for sequence 3 is " << getChi2(&seq3, 10) << std::endl;
	std::cout << "Chi^2 for sequence 4 is " << getChi2(&seq4, 10) << std::endl;
}