Jus a simple expression (easy question)

Hi guys, I am just having some iussues with this formula, could some one please help me?

n=5, r=5.

[Ameer Hamza]

What is M? How is defined? How is defined?

[Paul Rogers]

M doesn't matter, let's say aij is this matrix.

a =

    1.7151   -0.1511   -0.0371   -0.0457    0.0323
    0.5975   -0.0172   -0.0483   -0.0186    0.0064
    0.0948   -0.0027   -0.0076   -0.0029    0.0010
    0.0266    0.0003   -0.0032   -0.0009    0.0001
    0.0064    0.0003   -0.0009   -0.0002    0.0000

Ti= cos(icos^-1(i))
Tj= cos(icos^-1(j))
n=5
r=5

Answer 1

[Ameer Hamza]

Try this

a = [...
    1.7151   -0.1511   -0.0371   -0.0457    0.0323
    0.5975   -0.0172   -0.0483   -0.0186    0.0064
    0.0948   -0.0027   -0.0076   -0.0029    0.0010
    0.0266    0.0003   -0.0032   -0.0009    0.0001
    0.0064    0.0003   -0.0009   -0.0002    0.0000];

n=5;
r=5;

i = 0:r-1;
j = 0:n-11;
Ti= cos(i.*acos(i));
Tj= cos(i.*acos(i));

result = sum(a.*Ti.'.*Tj, 'all')

Result

result =
   54.6082

[Paul Rogers]

I came up with something like this, but it's not working:

for i=1:n
    for j=r
        result = sum(a(i,j).*cos(i.*cos(i)).*cos(j.*cos(j)), 'all');
    end
end

it says:

Error using sum
Trailing string input must be 'double', 'native', or 'default'.

Error in chebishev_poli (line 24)
        result = sum(a(i,j).*cos(i.*cos(i)).*cos(j.*cos(j)), 'all');
        
        

Here's the whole code:

        clear
clc
close all

a_trasp= [1.71513    0.59747    0.09479    0.02658    0.00638
         -0.15109   -0.01716   -0.00273    0.00027    0.00025
         -0.03707   -0.04825   -0.00764   -0.00317   -0.00095
         -0.04567   -0.01861   -0.00295   -0.00091   -0.00023
          0.0323     0.00643    0.00102    0.00015    0.00001
          ];
      
a = a_trasp';  

%i=5; %x_i mass flow
%j=5; %N_j or x_j rotational speed
n=5; %number of mesuraments for x
r=5; %number of mesuraments for y

FlowMeasurements = chebpts(5,[-0.2,0.8]); % decido quali punti della massa mi servono secondo Chebyshev
SpeedMeasurements = chebpts(5,[25000, 55000]);  %in questa variante decido quali sono le velocità richieste da Chebyshev

for i=1:n
    for j=r
        result = sum(a(i,j).*cos(i.*cos(i)).*cos(j.*cos(j)), 'all');
    end
end

[Ameer Hamza]

Ok. I noticed that you are using R2014b. It that release, code in my answer will not work. The following code will work for R2014b

clear
clc
close all
a_trasp= [1.71513    0.59747    0.09479    0.02658    0.00638
         -0.15109   -0.01716   -0.00273    0.00027    0.00025
         -0.03707   -0.04825   -0.00764   -0.00317   -0.00095
         -0.04567   -0.01861   -0.00295   -0.00091   -0.00023
          0.0323     0.00643    0.00102    0.00015    0.00001
          ];
      
a = a_trasp';  
%i=5; %x_i mass flow
%j=5; %N_j or x_j rotational speed
n=5; %number of mesuraments for x
r=5; %number of mesuraments for y
FlowMeasurements = chebpts(5,[-0.2,0.8]); % decido quali punti della massa mi servono secondo Chebyshev
SpeedMeasurements = chebpts(5,[25000, 55000]);  %in questa variante decido quali sono le velocità richieste da Chebyshev

result = 0;
for i=1:n
    for j=1:r
        result = result + a(i,j).*cos(i.*cos(i)).*cos(j.*cos(j));
    end
end

[Walter Roberson]

Is the for j=r correct? Should it be for j=1:r ?

[Ameer Hamza]

Thanks for correction. It should be 1:r