For Loops with Multiple Arrays

I'm not able to figure out how to create a for loop that has multiple arrays as inputs. The input data is:

m = [1:1:11]

r = [1:1:100]

z = [0:1:50]

H = 50

z1 = 10

The equation is:

p(r,z) = sin((m*pi*z)/H)*sin((m*pi*z1)/H)*(1/(sqrt(r )))

I do not know how to set it up to get values of p(r,z) summed over the range of m. I also don't know how to get the values out of the loop so they can be used in other equations and plots. I've scoured the Answers board but I have not been able to construct any meaningful script yet - any and all insight is appreciated!

[James Tursa]

You need to rethink this formula. Your starting r value is 0 and you are dividing by sqrt(r).

[Aryn Sanojca]

Right, great point. That's a conceptual oversight - the formula stands, but r = [1:1:50]. Thanks for pointing that out.

Answer 1

[KALYAN ACHARJYA]

r=1:1:100;
z=1:1:50;
H=50;
z1=10;
z=??  % Define z, I assumed it as a scalar (single value)
syms m
p=vpa(symsum(sin((m*pi*z)/H)*sin((m*pi*z1)/H)*(1./sqrt(r)),m,1,11))

[Aryn Sanojca]

Thanks Kalyan. I'm installing the symbolic math toolbox now to try this solution.

z is not a scalar, but rather defined as z = 1:1:50. Would this solution iterate through the calculation of p for all values of r at each value for z, and all values of z for each value for r? Or is a for loop required to do that?

Answer 2

[Steven Lord]

m = [1:1:11];
r = [1:1:100];
z = [0:1:50];
whos

  Name      Size             Bytes  Class     Attributes

  m         1x11                88  double              
  r         1x100              800  double              
  z         1x51               408  double              

The variable m is a 1-by-11 vector. The variable z is a 1-by-51 vector. What size would you expect sin(m*pi*z) to be?

1. 1-by-11? If so how do you create 11 elements using z to perform the element-wise multiplication?
2. 1-by-51? If so how do you create 51 elements using m to perform the element-wise multiplication?
3. 11-by-51 or 51-by-11? These are actually possible using implicit expansion.
4. Something else? If so what size and how would you create that using just m and z?

A11_51 = m.'.*z;
A51_11 = m.*z.';
whos A11_51 A51_11

  Name         Size            Bytes  Class     Attributes

  A11_51      11x51             4488  double              
  A51_11      51x11             4488  double              

FYI the sinpi function may be of use to you.