How can i get optimization or interpolation value for this 3-data?

x = [30 34 38 42 46 50 54 58 62 66 70 30 34 38 42 46 54 58 62 66 70];

y = [70 66 62 58 54 50 46 42 38 34 30 30 34 38 42 46 54 58 62 66 70];

z = [306.2802 305.4982 305.6566 305.3331 305.4320 305.2000 305.7223 305.4895 305.6325...

305.8428 305.7818 306.7651 307.3100 307.2416 307.0577 307.2612 305.5037 305.1273 304.9247 305.3628 305.6063]

i want to get minumum z value .. help me

Answer 1

[Star Strider]

I doubt that any interpolation is necessary.

Juyst find (and if desired, plot) the minimum and associated values —

x = [30 34 38 42 46 50 54 58 62 66 70 30 34 38 42 46 54 58 62 66 70];
y = [70 66 62 58 54 50 46 42 38 34 30 30 34 38 42 46 54 58 62 66 70];
z = [306.2802 305.4982 305.6566 305.3331 305.4320 305.2000 305.7223 305.4895 305.6325...
    305.8428 305.7818 306.7651 307.3100 307.2416 307.0577 307.2612 305.5037 305.1273 304.9247 305.3628 305.6063];

[zmin, idx] = min(z)

zmin = 304.9247

idx = 19

figure
stem3(x, y, z)
hold on
plot3(x, y, z)
scatter3(x(idx), y(idx), z(idx), 75, 'r', 'v', 'filled')
hold off
grid on
text(x(idx), y(idx), z(idx), sprintf('  \\leftarrow z_{min} = %.4f',z(idx)), 'Horiz','left', 'Vert','middle', 'Rotation',15)

.

[youn chan choi]

i am weak for english , im sorry

i mean that

x, y = variables

z = result

there are three vairables, so i wanna get some relationship about x,y,z.

so i need to interpolate or solve relation about those data to get min z.

[youn chan choi]

Those data derived from my expriement. So i need to get minimum value of z

help me..

thank you

[Star Strider]

My code plots the corresponding values of all three variables.

Note that ‘x’ and ‘y’ do not have unique values (‘x’ repeats and ‘y’is symmetric), so it is difficult to determine the relationshiup between the three variables. I doubt that it is possible to develop any sort of analytic relationship between them.

What experiment created the data? A nonlinear relationship modellling the process that created the data could be possible, however it would be necessary to have a mathematical expression of that process to model it and extimate parameters that could then be used to calculate whatever the ‘true’ minimum is.

.

Answer 2

[Matt J]

i want to get minumum z value

That would simply be

[zmin,loc]=min(z)

Did you mean you also want the corresponding values of x and y? If so,

xmin=x(loc);
ymin=y(loc);

[youn chan choi]

i am weak for english , im sorry

i mean that

x, y = variables

z = result

there are three vairables, so i wanna get some relationship about x,y,z.

so i need to interpolate or solve relation about those data to get min z.