task1

clc
a = -1.5; b = -0.5;
delta = 0.1;
Passive_Search(a, b, 10^-4)
Dichotomia(a, b, delta)
Gold_Section(a, b)
Fibonacci(a, b)
Newton(a, b)


function value = y(x)
global func_call
value = 26*x.^6 + 21*x.^5 + 18*x.^4 + 4*x.^3 + 10*x.^2 + 15*x.^1 + sin(13*x) + sin(6*x) + sin(3*x);
func_call = func_call + 1;
end

function value = dy(x)
global func_call
value = 156*x.^5 + 105*x.^4 + 72*x.^3 + 12*x.^2 + 20*x.^1 + 15 + 13*cos(13*x) + 6*cos(6*x) + 3*cos(3*x);
func_call = func_call + 1;
end

function value = ddy(x)
global func_call
value = 780*x.^4 + 420*x.^3 + 216*x.^2 + 24*x.^1 + 20 - 169*sin(13*x) - 36*sin(6*x) - 9*sin(3*x);
func_call = func_call + 1;
end

function value = r_d(number)
exponent = floor(log10(abs(number))); % порядок старшей цифры
amount = 4; % нужное количество верных цифр
value = 10^(exponent - amount + 1)/2;
end

function Passive_Search(a, b, epsilon)
introduction = sprintf('\t\t\t\t Метод пассивного поиска\n');
fprintf(introduction)
counter = 0;
min = y(a);
for i = a:epsilon:b
    if y(i)<min
        min = y(i);
        argument = i;
    end
    counter = counter + 1;
end
formatSpec = 'X is %.3f, Y is %.3f, Count is %.f \n';
fprintf(formatSpec, argument, min, counter-1)
end

function Dichotomia(a, b, delta)
introduction = sprintf('\t\t\t\t Метод дихотомии\n');
fprintf(introduction)
global func_call
counter = 0;
func_call = 0;
while b-a > 2*r_d((a+b/2))
    Delta_b = delta*(b-a);
    c = (a+b)/2 - Delta_b;
    d = (a+b)/2 + Delta_b;
    if y(c) <= y(d)
        counter = counter + 1;
        b = d;
        argument = c;
        min = y(c);
        formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
        fprintf(formatSpec, argument, min, counter, func_call, a, b)
    else
        counter = counter + 1;
        a = c;
        argument = d;
        min = y(d);
        formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
        fprintf(formatSpec, argument, min, counter, func_call, a, b)
    end
end

while b-a > 6*Delta_b
    Delta_b = delta*(b-a);
    c = (a+b)/2 - Delta_b;
    d = (a+b)/2 + Delta_b;
    if y(c) <= y(d)
        counter = counter + 1;
        b = d;
        argument = c;
        min = y(c);
        formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
        fprintf(formatSpec, argument, min, counter, func_call, a, b)
    else
        counter = counter + 1;
        a = c;
        argument = d;
        min = y(d);
        formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
        fprintf(formatSpec, argument, min, counter, func_call, a, b)
    end
end
end

function Gold_Section(a, b)
introduction = sprintf('\t\t\t\t Метод золотого сечения\n');
fprintf(introduction)
counter = 0;
global func_call
func_call = 0;
c = (3-sqrt(5))/2*(b-a) + a;
d = (sqrt(5)-1)/2*(b-a) + a;
y_c = y(c);
y_d = y(d);
while b-a > 2*r_d((a+b)/2)
    if y_c <= y_d
        b = d;
        d = c;
        y_d = y_c;
        c = (3-sqrt(5))/2*(b-a) + a;
        y_c = y(c);
        argument = (a+b)/2;
        min = y(argument);
        counter = counter + 1;
        formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
        fprintf(formatSpec, argument, min, counter, func_call, a, b)
    else
        a = c;
        c = d;
        y_c = y_d;
        d = (sqrt(5)-1)/2*(b-a) + a;
        y_d = y(d);
        argument = (a+b)/2;
        min = y(argument);
        counter = counter + 1;
        formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
        fprintf(formatSpec, argument, min, counter, func_call, a, b)
    end
end
if y(c) < min
    counter = counter + 1;
    argument = c;
    min = y(c);
    formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
    fprintf(formatSpec, argument, min, counter, func_call, a, b)
elseif y(d) < min
    counter = counter + 1;
    argument = d;
    min = y(d);
    formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
    fprintf(formatSpec, argument, min, counter, func_call, a, b)
end
end

function Fibonacci(a, b)
introduction = sprintf('\t\t\t\t Метод Фибоначчи\n');
fprintf(introduction)
global func_call
func_call = 0;
counter = 0;
fib_array = [1 1];
index = 2;
while (b-a)/r_d((a+b)/2) > fib_array(index)
    index = index + 1;
    fib_array(index) = fib_array(index-2) + fib_array(index-1);
end

i = index;
c = a + (b-a)*fib_array(i-2)/fib_array(i);
d = a + (b-a)*fib_array(i-1)/fib_array(i);
y_c = y(c);
y_d = y(d);
while b-a > 2*r_d((a+b/2))
    if y_c <= y_d
        b = d;
        d = c;
        y_d = y_c;
        c = a + (b-a)*fib_array(i-2)/fib_array(i);
        y_c = y(c);
        argument = (a+b)/2;
        min = y(argument);
        counter = counter + 1;
        i = i - 1;
        formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
        fprintf(formatSpec, argument, min, counter, func_call, a, b)
    else
        a = c;
        c = d;
        y_c = y_d;
        d = a + (b-a)*fib_array(i-1)/fib_array(i);
        y_d = y(d);
        argument = (a+b)/2;
        min = y(argument);
        counter = counter + 1;
        i = i - 1;
        formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
        fprintf(formatSpec, argument, min, counter, func_call, a, b)
    end
end
if y(c) < min
    counter = counter + 1;
    argument = c;
    min = y(c);
    formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
    fprintf(formatSpec, argument, min, counter, func_call, a, b)
elseif y(d) < min
    counter = counter + 1;
    argument = d;
    min = y(d);
    formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
    fprintf(formatSpec, argument, min, counter, func_call, a, b)
end
end

function Newton(a, b)
introduction = sprintf('\t\t\t\t Метод касательных(Ньютона)\n');
fprintf(introduction)
dddy = @(x) 2*(12+120*x+960*x.^3-1000*cos(10*x)-864*cos(12*x)-2197*cos(13*x)-2916*cos(18*x));
if dy(a)*dddy(a) > 0
    x0 = a;
    x1 = b;
else
    x0 = b;
    x1 = a;
end
global func_call
func_call = 2;
counter = 0;
current_epsilon = realmax;
while current_epsilon > r_d((a+b/2))
    counter = counter + 1;
    x1 = x0 - dy(x0)/ddy(x0);
    current_epsilon = abs(x1 - x0);
    minumum = y(x1);
    tmp = [x0, x1];
    formatSpec = 'X is %.4f, Y is %.3f, Count is %.f, Number of function calls %.f, Segment is [%.4f, %.4f] \n';
    fprintf(formatSpec, x1, minumum, counter, func_call, min(tmp), max(tmp))
    x0 = x1;
end
end