Plot 3d graph with equation and variables

I have a function

ypred = 0.3969 - 0.0531*x1 -0.1386*x2 +0.0803*x1.^2 -0.0301*x2.^2 -0.0808*(x1.*x2)

the x1 and x2 values are:

x1 = [0;1;0.5;-0.5;-1;-0.5;0.5]
x2 = [0;0;0.866;0.866;0;-0.866;-0.866]

I plotted the graph using the code attached. This code doesn't seem to work that well because I tried for the same code on a graph that was previously obtained using the equation

ypred = 265 - 167.6*x1 -35.8*x2 +102.9*x1.^2 +47.9*x2.^2 +25.9*(x1.*x2)

It has a minimum point at 0.7940,0.1621. This is not obtained using the code..And the graph doesn't seem right either..

Answer 1

[Star Strider]

The first equation has a minimum far from your x1 and x2 ranges:

ypred1 = @(x) 0.3969 - 0.0531*x(1) -0.1386*x(2) +0.0803*x(1).^2 -0.0301*x(2).^2 -0.0808*(x(1).*x(2));
min_1 = fminsearch(ypred1, [0; 0])

produces:

min_1 =

      95.2347e+039
     511.6276e+039

The second equation produces a minimum about where you expected it:

ypred2 = @(x) 265 - 167.6*x(1) -35.8*x(2) +102.9*x(1).^2 +47.9*x(2).^2 +25.9*(x(1).*x(2));
min_2 = fminsearch(ypred2, [0; 0])

produces:

min_2 =

     794.3380e-003
     158.9462e-003

Is this what you want?

ADDED: Using the values for min_2, this seems correct for your second equation (that I called ypred2):

ypred2z = @(x1,x2) 265 - 167.6*x1 -35.8*x2 +102.9*x1.^2 +47.9*x2.^2 +25.9*(x1.*x2);
xvct = -0.5:0.1:2;
[X Y] = meshgrid(xvct, xvct);
Z = ypred2z(X,Y);

figure(1)
meshc(X, Y, Z)
hold on
plot3(min_2(1),min_2(2),val2,'*r')
hold off
xlabel('X_1')
ylabel('X_2')
zlabel('Y_{PRED}')
grid on

[Dilini]

Hi thanks a lot :). Everything seems to work except for min_1 = fminsearch(ypred1, [0; 0]). It says error in fminsearch..

[Star Strider]

I didn’t plot ypred_1 but I doubt it would be of any benefit. The ‘error’ it gives me is that it exceeded the maximum number of function evaluations. This isn’t really an error. When I use optimset to increase the number of iterations and function evaluations to 100000:

ypred1 = @(x) 0.3969 - 0.0531*x(1) -0.1386*x(2) +0.0803*x(1).^2 -0.0301*x(2).^2 -0.0808*(x(1).*x(2));
opts_1 = optimset('MaxFunEvals',100000,  'MaxIter',100000);
[min_1,fv_1] = fminsearch(ypred1, [-1000; -1000], opts_1)

it notes:

Exiting: Maximum number of iterations has been exceeded
         - increase MaxIter option.
         Current function value: -Inf 

min_1 =

      -3.2792e+153
     -16.2997e+153

fv_1 =

              -Inf

It gives positive values for x(1) and x(2) for zero or positive starting points:

min_1 =

       3.2792e+153
      16.2997e+153

fv_1 =

              -Inf

Note that the function value ( fv_1 here ) is ‘-Inf’ in both situations. The problem is with the function. It’s falling off the edge of the world. It won’t get any more accurate with more function evaluations.

ADDED:

When I plotted ypred1 with this code, it revealed itself to be a saddle point centred at [0, 0]. It has neither a finite minimum or maximum.

ypred1z = @(x1,x2) 0.3969 - 0.0531*x1 -0.1386*x2 +0.0803*x1.^2 -0.0301*x2.^2 -0.0808*(x1.*x2);

xvct = -100:1:100;
[X Y] = meshgrid(xvct, xvct);
Z = ypred1z(X,Y);

figure(1)
meshc(X, Y, Z)
xlabel('X_1')
ylabel('X_2')
zlabel('Y_{PRED}')
grid on

[Dilini]

Thanks a lot! It makes a lot of sense now :) :)

[Star Strider]

My pleasure!