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Use all cv::Mat in std::vector and change their value efficiently

I have a vector of matrices with the same number of columns, i.e. std::vector<cv::Mat> v and I want to apply a cv::PCA (without dimensionality reduction) using all of them. Finally, I want that the result is applied to original matrices too.

Code speaking, this is the only solution that I came so far:

std::vector<cv::Mat> v;
//fill v
cv::Mat bigMat;
for(size_t i=0; i<v.size(); i++)
  bigMat.push_back(v[i]);
cv::PCA pca(bigMat, cv::Mat(), CV_PCA_DATA_AS_ROW);
for(size_t i=0; i<v.size(); i++)
  bigMat = pca.project(bigMat);

But this doesn't effect v[i]. How can I do this efficiently? Notice that I have to use the projected version of bigMat later. This is the only solution that came to my mind:

cv::PCA pca(bigMat, cv::Mat(), CV_PCA_DATA_AS_ROW);
bigMat.release();
for (size_t i=0; i<v.size(); i++){
  v[i] = pca.project(v[i]);
  bigMat.push_back(v[i]);
}

But this is kinda ugly and I don't know how efficient could be. Is there any better solution (where efficiency is the top priority)?

If you wander, v[i] is the set of descriptors of the i-th image. If you ask yourself why there is no dimensionality reduction in my PCA, give a look at this paper.