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crossV = function(Matrix[double] X, Matrix[double] y, double lamda, Integer k) return (Matrix[double] R)
{
  #create empty lists
  dataset_X = list(); #empty list
  dataset_y = list();
  fs = ceil(nrow(X)/k);
  off = fs - 1;
  #devide X, y into lists of k matrices
  for (i in seq(1, k)) {  
    dataset_X = append(dataset_X, X[i*fs-off : min(i*fs, nrow(X)),]);
    dataset_y = append(dataset_y, y[i*fs-off : min(i*fs, nrow(y)),]);
  }

  beta_list = list();
  #keep one fold for testing in each iteration
  for (i in seq(1, k)) {
    [tmpX, testX] = remove(dataset_X, i); 
    [tmpy, testy] = remove(dataset_y, i);
    trainX = rbind(tmpX);
    trainy = rbind(tmpy);
    beta = SimlinRegDS(trainX, trainy, lamda, ncol(X));
    beta_list = append(beta_list, beta);
  }

  R = cbind(beta_list);
}

SimlinRegDS = function(Matrix[Double] X, Matrix[Double] y, Double lamda, Integer N) return (Matrix[double] beta)
{
  A = (t(X) %*% X) + diag(matrix(lamda, rows=N, cols=1));
  b = t(X) %*% y;
  beta = solve(A, b);
}


X = rand(rows=$1, cols=$2);
y = X %*% rand(rows=$2, cols=1);

R = crossV(X, y, 0.001, 7);

r = as.matrix(sum(R!=0));
write(r, $3);
#expected: "Result: $2*7
