parse error at x0

Hello I'm new to matlab coding and here Im getting this parse error and I cannot figure it out. From this code I need to find the minimum of the function using steepest descent method. And I would like to know this code correct or not please.

this is my func : F (x,y) = 10x2−4xy+7y2−455x−y−16

and the starting point is : [ 0,10 ]

thanks for help!

%steepest descent method

function f = target_function(x, y)
    f = 10 * x.^2 - 4 * x .* y + 7 * y.^2 - 20 * sqrt(5) * x + 4 * sqrt(5) * y - 16;
end

%parameters
x0 = [0 10];
eps = 0.01;

%initialization
point_min = x0';
target_func_min = target_function(point_min(1), point_min(2));
w = antigradient(point_min);
nw = norm(w);
tau = (1 + sqrt(5)) / 2;

%statistics
points(:, 1) = point_min;
target_func_values(1) = target_func_min;
iter_count = 0;
target_func_calls_count = 0;

%One-Dimensional Minimization Using the Golden Section Method
while nw > eps
     iter_count = iter_count + 1;
     kp = 0;
     step = 0;
   while abs(kp - step) < eps
        a = step;
        b = a + 2;
        step = step + 2;
        kp1 = ((b * (tau - 1) + a) / tau);
        kp2 = ((a * (tau - 1) + b) / tau);
        X = point_min + kp1 * w;
        f_X1 = target_function(X(1), X(2));
        X = point_min + kp2 * w;
        f_X2 = target_function(X(1), X(2));

        target_func_calls_count = target_func_calls_count + 2;
    while norm(b - a) > eps
       if (f_X1 > f_X2)
        kp = kp2;
        a = kp1;
        kp1 = kp2;
        kp2 = ((a * (tau - 1) + b) / tau);

        f_X1 = f_X2;

        X = point_min + kp2 * w;
        f_X2 = target_function(X(1), X(2));
       else
         kp = kp1;
         b = kp2;
         kp2 = kp1;
         kp1 = ((b * (tau - 1) + a) / tau);

         f_X2 = f_X1;
    
         X = point_min + kp1 * w;
         f_X1 = target_function(X(1), X(2));
       end
         target_func_calls_count = target_func_calls_count + 1;
    end
   end
     point_min = point_min + kp * w;
     w = antigradient(point_min);
     target_func_min = target_function(point_min(1), point_min(2));
     nw = norm(w);
     points(:, iter_count + 1) = point_min;
     target_func_values(iter_count + 1) = target_func_min;
end

Min = min(min(points(1, :)), min(points(2, :)));
Max = max(max(points(1, :)), max(points(2, :)));
space = linspace(Min - 5, Max + 5, 500);
[gridX, gridY] = meshgrid(space, space);
gridJ = target_function(gridX, gridY);

figure;
contour(gridX, gridY, gridJ, target_func_values, 'black', 'ShowText', 'on');
hold on;
plot(points(1, :), points(2, :), 'r.-');

fprintf(func count: %.0f\n',target_func_calls_count);
fprintf(iter: %.0f\n\n', iter_count);
fprintf(min point: (%2.2f; %2.2f)\n', point_min);
fprintf(min value: %2.2f\', target_func_min);

Answer 1

[Voss]

Looks like you are missing a single-quote at the beginning of each of your fprintf calls (and an "n" is missing in the last one):

fprintf(func count: %.0f\n',target_func_calls_count);
fprintf(iter: %.0f\n\n', iter_count);
fprintf(min point: (%2.2f; %2.2f)\n', point_min);
fprintf(min value: %2.2f\', target_func_min);

Should be:

fprintf('func count: %.0f\n',target_func_calls_count);
fprintf('iter: %.0f\n\n', iter_count);
fprintf('min point: (%2.2f; %2.2f)\n', point_min);
fprintf('min value: %2.2f\n', target_func_min);

[Janidu]

oh yes thanks!! And what about the x0 parameter? why its getting error?

[Voss]

I wasn't able to reproduce that particular error, but I think it's because function definitions need to be at the end of scripts, so you need to move the target_function definition down to the end of the script.

Like this:

%steepest descent method

%parameters
x0 = [0 10];
eps = 0.01;

%initialization
point_min = x0';

% ...
% ...
% (the rest of your code)
% ...
% ...

fprintf('func count: %.0f\n',target_func_calls_count);
fprintf('iter: %.0f\n\n', iter_count);
fprintf('min point: (%2.2f; %2.2f)\n', point_min);
fprintf('min value: %2.2f\n', target_func_min);


function f = target_function(x, y)
    f = 10 * x.^2 - 4 * x .* y + 7 * y.^2 - 20 * sqrt(5) * x + 4 * sqrt(5) * y - 16;
end

[Janidu]

I did that. But there are still errors. (

%steepest descent method

%parameters
x0 = [0 10];
eps = 0.01;

%initialization
point_min = x0';
target_func_min = target_function(point_min(1), point_min(2));
w = antigradient(point_min);

Unrecognized function or variable 'antigradient'.

nw = norm(w);
tau = (1 + sqrt(5)) / 2;

%statistics
points(:, 1) = point_min;
target_func_values(1) = target_func_min;
iter_count = 0;
target_func_calls_count = 0;

%One-Dimensional Minimization Using the Golden Section Method
while nw > eps
     iter_count = iter_count + 1;
     kp = 0;
     step = 0;
   while abs(kp - step) < eps
        a = step;
        b = a + 2;
        step = step + 2;
        kp1 = ((b * (tau - 1) + a) / tau);
        kp2 = ((a * (tau - 1) + b) / tau);
        X = point_min + kp1 * w;
        f_X1 = target_function(X(1), X(2));
        X = point_min + kp2 * w;
        f_X2 = target_function(X(1), X(2));

        target_func_calls_count = target_func_calls_count + 2;
    while norm(b - a) > eps
       if (f_X1 > f_X2)
        kp = kp2;
        a = kp1;
        kp1 = kp2;
        kp2 = ((a * (tau - 1) + b) / tau);

        f_X1 = f_X2;

        X = point_min + kp2 * w;
        f_X2 = target_function(X(1), X(2));
       else
         kp = kp1;
         b = kp2;
         kp2 = kp1;
         kp1 = ((b * (tau - 1) + a) / tau);

         f_X2 = f_X1;
    
         X = point_min + kp1 * w;
         f_X1 = target_function(X(1), X(2));
       end
         target_func_calls_count = target_func_calls_count + 1;
    end
   end
     point_min = point_min + kp * w;
     w = antigradient(point_min);
     target_func_min = target_function(point_min(1), point_min(2));
     nw = norm(w);
     points(:, iter_count + 1) = point_min;
     target_func_values(iter_count + 1) = target_func_min;
end

Min = min(min(points(1, :)), min(points(2, :)));
Max = max(max(points(1, :)), max(points(2, :)));
space = linspace(Min - 5, Max + 5, 500);
[gridX, gridY] = meshgrid(space, space);
gridJ = target_function(gridX, gridY);

figure;
contour(gridX, gridY, gridJ, target_func_values, 'black', 'ShowText', 'on');
hold on;
plot(points(1, :), points(2, :), 'r.-');

fprintf('func count: %.0f\n',target_func_calls_count);
fprintf('iter: %.0f\n\n', iter_count);
fprintf('min point: (%2.2f; %2.2f)\n', point_min);
fprintf('min value: %2.2f\', target_func_min);

function f = target_function(x, y)
    f = 10 * x.^2 - 4 * x .* y + 7 * y.^2 - 20 * sqrt(5) * x + 4 * sqrt(5) * y - 16;
end

[Voss]

I also got the error about "antigradient" being unrecognized. What is it?