multiplication of matrix with long data

Hi,

I have a long data (200K+ samples) from which a location vector L (3x1) and a matrix T (euler matrix 3x3) is generated and multiplied l = TL.

On the results of l (3x1) there are operations of sin and atan (to get the required results).

So far, I'm doing a for loop, which is not a Matlab way.

I'd like to speedup the performance of the code.

How can I do it?

[Walter Roberson]

What are you looping? The only part that you describe that involves the large data is the creation of L and T, and you do not describe the math involved in that.

Are you looping taking a subset of the data, doing the calculations, moving on to the next subset of data?

Thank you for taking the time to fill in that you are using R14SP2, that will help us not waste time suggesting some of the functions added recently.

[michael]

The loop is on the matrix and vector generation. Each time, I'm taking only single sample of the data (i.e. x(i), y(i), z(i), phi(i),theta(i), psi(i))

PS, I'd be glad if you can also add some notes on the changes in latest releases.

[Bruno Luong]

"So far, I'm doing a for loop, which is not a Matlab way. "

Anything allowed by MATLAB IS MATLAB way.

[Steven Lord]

Is there a specific reason you're still using release R14SP2 which is pretty close to twenty years old at this point?

There have been a lot of improvements in MATLAB in the past twenty years, which likely would improve performance of your code.

Answer 1

[Bruno Luong]

% Test data
N = 4;
Phi     = 2*pi*rand(1,N);
Theta   = 2*pi*rand(1,N);
Psi     = 2*pi*rand(1,N);
X       = rand(1,N);
Y       = rand(1,N);
Z       = rand(1,N);

Phi     = reshape(Phi,      1, 1, []);
Theta   = reshape(Theta,    1, 1, []);
Psi     = reshape(Psi,      1, 1, []);
X       = reshape(X,        1, 1, []);
Y       = reshape(Y,        1, 1, []);
Z       = reshape(Z,        1, 1, []);
sB = sin(Phi);   cB = cos(Phi);
sD = sin(Theta); cD = cos(Theta);
sE = sin(Psi);   cE = cos(Psi);
T = [ cD.*cE, -cB.*sE+cE.*sB.*sD,  sB.*sE+cB.*sD.*cE;
      cD.*sE,  cB.*cE+sB.*sD.*sE, -cE.*sB+cB.*sD.*sE;
         -sD,             sB.*cD,             cB.*cD ];
XYZ = [X; Y; Z];
xyz = pagemtimes(T, XYZ)

xyz = 
xyz(:,:,1) =

    0.3128
    0.5127
   -0.3960


xyz(:,:,2) =

   -0.7072
   -0.7636
    0.1150


xyz(:,:,3) =

   -0.1876
    0.0750
    1.0194


xyz(:,:,4) =

    1.2058
   -0.6237
    0.2521

% For older MATLAB
%XYZ = [X, Y, Z];
%xyz = sum(T.*XYZ,2)

[michael]

Please note that I'm working with R14 while the pagemtimes is from R2020b

[Bruno Luong]

You'll mtimesx (and few others) from File Exchange that work similarly for older MATLAB versions.

[Bruno Luong]

Or you can do this:

XYZ = [X, Y, Z];
xyz = sum(T.*XYZ,2)

[michael]

@Bruno Luong, Additional Question - I neet to perform inverse of the T Matrix (the 3*3 part).

How this can be done?

[Bruno Luong]

For inverse of T instead of

xyz = pagemtimes(T, XYZ);

do this

xyz = pagemrdivide(T, XYZ);

[michael]

Please note that I'm using old version Matlab R14

[Bruno Luong]

The inverse of T is its transpose T.', you need to form the inverse, noted here by iT

iT = [ cD.*cE,             cD.*sE,            -sD;
      -cB.*sE+cE.*sB.*sD,  cB.*cE+sB.*sD.*sE, sB.*cD;
       sB.*sE+cB.*sD.*cE,  cE.*sB+cB.*sD.*sE, cB.*cD ];
% For older MATLAB
XYZ = [X, Y, Z];
xyz = sum(iT.*XYZ,2)