Find the maximum value and its position of a 10x10x10 matrix which meets a set of parameters.

I have a 10x10x10 matrix, M, which I found by taking 3 1x10 matrices, a b and c, and turning them into a 10x10x10 matrix, A, and then multiplied A by an unknown constant. I need to find the maximum value of M and its position while it's corresponding values of a, b and c are smaller than a set of parameters.

[Jan]

How do you turn 3 vectors to a 3D array? This details might be useful for the solution. How can you multiply by an "unknown" constant? Is this a symbolic calculation? What are the "corresponding values a,b,c"? What is "a set of parameters"? Please post the relevant part of the code or an example to create a small set of input data.

[Jack Holland]

I'll post my code, I think a better way of describing the constant is arbitrary, as in it will change depending on the situation and at the current moment I am unsure as to what the value will be. So if the maximum value for M has the position (6,4,5) then the corresponding value of a would be found and position 6 and b at 4 etc. As for the parameters I need to make sure that the values of a b and c meet the following requirements, where Q, F, h, and y are constants: (Q > Fy/(1/12*(c*h^3 - 2*a*b^3))

 h = 70
c = linspace(30,60,10); 
b = linspace(1,h-2,10);
a = linspace(1,14,10); 
[A,B,C]=meshgrid(a,b,c); 
Area=C.*h-2*B.*A;
M = D*Area;

Matrix A from my above question is "Area" in the code.

[Guillaume]

So if the max is found at (6,4,5) but the corresponding a,b,c don't fit the requirement, then what?

[Jack Holland]

I'm trying to find the biggest possible value which meets the requirement, so if the max doesn't fit then find the second biggest and if that doesn't fit then the third etc

Answer 1

[Guillaume]

h = 70;
c = linspace(30,60,10); 
b = linspace(1,h-2,10);
a = linspace(1,14,10); 
[A, B, C]=meshgrid(a,b,c); 
M = D *(C.*h-2*B.*A);
%Q = ...
%Fy  = ...

isinrange= Q > Fy./(1/12*(C*h^3 - 2*A.B.^3));
[maxM, idx] = max(M(isinrange));
aAtMax = A(idx);
bAtMax = B(idx);
cAtMax = C(idx);

[Jack Holland]

The isinrage function gives the error: Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.

[Stephen23]

Guillaume defined the variable isinrange, whereas the error message shows that you apparently tried to use a non-existent name, isinrage (the mind boggles at what that variable would measure!)

[Guillaume]

Saying that, the expression was missing a closing bracket (as does the original expression given in the original question). Now fixed.

Answer 2

[Veera Kanmani]

 max_value_position=max(M);
max_value=M(max(M));

[Stephen23]

How does

max_value_position=max(M);

return the position of the maximum value?

[Veera Kanmani]

sorry try this

   max_value =max(M);
 max_value_position=find(max(M))

[Stephen23]

Given that M is a 10x10x10 array, max(M) will return a 1x10x10 array. Using that as the input to find will return as many indices as there are non-zero maximum values. If all of the values are non-zero then it will simply be a list of all linear indices of that 1x10x10 array. Lets try it with a smaller example:

>> M = rand(3,3,3);
>> find(max(M))
ans =
   1
   2
   3
   4
   5
   6
   7
   8
   9

How does this list of all indices of non-zero values in the output of max help to solve the problem? How are we supposed to use these indices to "Find the maximum value and its position...", as the original question requests?

[Jack Holland]

max_value_position just returns a 100x1 matrix with numbers ranging from 1-100