#-------------------------------------------------------------
#
# Licensed to the Apache Software Foundation (ASF) under one
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# distributed with this work for additional information
# regarding copyright ownership.  The ASF licenses this file
# to you under the Apache License, Version 2.0 (the
# "License"); you may not use this file except in compliance
# with the License.  You may obtain a copy of the License at
#
#   http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing,
# software distributed under the License is distributed on an
# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
# KIND, either express or implied.  See the License for the
# specific language governing permissions and limitations
# under the License.
#
#-------------------------------------------------------------
checkR2 = function(Matrix[double] X, Matrix[double] y, Matrix[double] y_p,
          Matrix[double] beta, Integer icpt) return (Double R2_ad)
{
  n = nrow(X);
  m = ncol(X);
  m_ext = m;
  if (icpt == 1|icpt == 2)
      m_ext = m+1; #due to extra column ones
  avg_tot = sum(y)/n;
  ss_tot = sum(y^2);
  ss_avg_tot = ss_tot - n*avg_tot^2;
  y_res = y - y_p;
  avg_res = sum(y - y_p)/n;
  ss_res = sum((y - y_p)^2);
  R2 = 1 - ss_res/ss_avg_tot;
  dispersion = ifelse(n>m_ext, ss_res/(n-m_ext), NaN);
  R2_ad = ifelse(n>m_ext, 1-dispersion/(ss_avg_tot/(n-1)), NaN);
}

# Get the dataset
M = 4000;
A = rand(rows=M, cols=500, seed=42);
y = rand(rows=M, cols=1, seed=43);
R = matrix(0, rows=1, cols=20);

K = floor(ncol(A) * 0.1);
nComb = 5; #10

for (i in 1:nComb) {
  [newA1, Mout] = pca(X=A, K=K+i);
  beta1 = lmDS(X=newA1, y=y, icpt=1, reg=0.0001, verbose=FALSE);
  y_predict1 = lmPredict(X=newA1, B=beta1, icpt=1);
  R2_ad1 = checkR2(newA1, y, y_predict1, beta1, 1);
  R[,i] = R2_ad1;
}

R = sum(R);
write(R, $1, format="text");