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I have written the following code to implement a PCA algorithm. It works on standalone basis, however when I put it into a function that is called the following output is returned pca_funct[{{2,3,4},{4,5,6}},2] as opposed to the result of function evaluation. Any suggestions ?

pca_funct[X_, k_] := 
     Module[{Dim, m, n, mn, ones, Cv, phi0, lambda, phi},
         Dim = Dimensions[X]; m = Dim[[1]]; 
         n = Dim[[2]]; (*Compute dimensions of input matrix X*)
         mn = List /@ Mean[X];(*Compute column mean matrix for X and convert it into matrix form*)
         ones = ConstantArray[1, {m, 1}];
         X = X - ones.Transpose[mn]; (*Center columns of X around their means to get new matrix 
                 where columns have mean zero*)
         Cv = Transpose[X].X/m;(*Step 1 in algorithm. Compute covariance matrix*)
         phi0 = Eigenvectors[Cv]; (*Step 2 in algorithm. Compute Eigensystem*)
         lambda = Eigenvalues[Cv];
         phi = phi0[1 ;; k, 1 ;; n];
         phi]


X = {{2, 3, 4}, {4, 5, 6}}; k = 2;
phi = pca_funct[X, k];
phi // MatrixForm
pca_funct[{{2,3,4},{4,5,6}},2]
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  • $\begingroup$ what happens when you remove the "_" from the function name? also, you can't assign to an input. You are trying to write to X inside the Module. But X is passed parameter. $\endgroup$ – Nasser Feb 3 '15 at 12:22
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    $\begingroup$ Further to Nasser's comment. The underscore is a special character in Mathematica, you cannot use it in names for functions etc. See 'Pattern'. $\endgroup$ – Ymareth Feb 3 '15 at 12:27
  • $\begingroup$ I did that thanks, now I have this message. "RecursionLimit::reclim: Recursion depth of 1024 exceeded" I am just starting to use Mathematica. $\endgroup$ – V_W Feb 3 '15 at 12:59
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You are getting a few things about Mathematica syntax wrong. First you want to not use the underscore in variable names. Also, you can't reassign X when X is your function variable. Finally you have to use [[]] to get the elements of a list.

pcafunct[X_, k_] := 
Module[{Dim, m, n, mn, ones, Cv, phi0, lambda, phi, X1}, 
  Dim = Dimensions[X]; m = Dim[[1]];
  n = Dim[[2]];(*Compute dimensions of input matrix X*)
  mn = List /@Mean[X];
  (*Compute column mean matrix for X and convert it into 
  matrix form*)ones = ConstantArray[1, {m, 1}];
  X1 = X - ones.Transpose[mn];
  (*Center columns of X around their means to get new matrix where 
    columns have mean zero*)
  Cv = Transpose[X1].X1/m;
  (*Step 1 in algorithm.Compute covariance matrix*)
  phi0 = Eigenvectors[Cv];
  (*Step 2 in algorithm.Compute Eigensystem*)
  lambda = Eigenvalues[Cv];
  phi = phi0[[1 ;; k, 1 ;; n]];
  phi]

X = {{2, 3, 4}, {4, 5, 6}}; k = 2;
phi = pcafunct[X, k]
phi // MatrixForm
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Remove["Global`*"]
pcafunct[X_, k_] := Module[{dim, m, n, mn, X1, cv, phi0, lambda, phi},
dim = Dimensions[X];
m = dim[[1]]; n = dim[[2]]; (*Compute dimensions of input matrix X*)
mn = List /@ Mean[X];
X1 = X -ConstantArray[1, {m, 1}].Transpose[mn];
cv = Transpose[X1].X1/m;
phi0 = Eigenvectors[cv]; 
lambda = Eigenvalues[cv];
phi = phi0[[1 ;; k, 1 ;; n]];
phi
]
X = {{2, 3, 4}, {4, 5, 6}}; k = 2;
phi = pcafunct[X, k];
phi
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