C++: Eigen conservativeResize too expensive?

问题

I have some Eigen Matrices whose dimensions I don't know in advance, I only have an upper bound. I have a loop in which I fill those matrices (I initialize them using the upper bound) column by column until a stopping criterion is fulfilled (let's say after j iterations).

My problem is now: After the loop, I need those matrices for matrix multiplications (obviously using only the first j columns). The straightforward solution would be to use Eigen's conservativeResize and go right ahead and perform the matrix multiplication. Since the matrices tend to be quite large (100000+ dimensions) and (as far as I can see, not sure though) Eigen's conservativeResize reallocates the memory for the resized matrices and performs one deep copy, this solution is quite expensive.

I was thinking about writing my own custom matrix multiplication function, which uses the old (big) matrices, taking arguments specifying the number of columns to use. I fear though that Eigen's matrix multiplications are so much more optimized that in the end this solution is slower than just using conservative resizing and standard Eigen multiplication...

Should I just bite the bullet and use conservativeResize or does anyone have a better idea? BTW: The matrices we're talking about are used in 3 multiplications and 1 transpose after the loop/resize

Thanks in advance!

Edit: this is the relevant part of the code (where X is a MatrixXd, y is a VectorXd and numComponents is the number of latent variables PLS1 is supposed to use). The thing is though: at the beginning, numComponents will always be the number of dimensions in X (X.cols()) but the stopping criterion is supposed to check the relative improvement on the explained variance in the output vector (that, I have not implemented yet). If the relative improvement is too small, the algorithm is supposed to stop (since we are happy with the first j components) and then compute the regression coefficients. For that, I need the conservativeResize:

using namespace Eigen;
MatrixXd W,P,T,B;
VectorXd c,xMean;
double xMean;

W.resize(X.cols(),numComponents);
P.resize(X.cols(),numComponents);
T.resize(X.rows(),numComponents);
c.resize(numComponents);
xMean.resize(X.cols());
xMean.setZero();
yMean=0;
VectorXd yCopy=y;
//perform PLS1
for(size_t j=0; j< numComponents; ++j){
    VectorXd tmp=X.transpose()*y;
    W.col(j)=(tmp)/tmp.norm();
    T.col(j)=X*W.col(j);
    double divisorTmp=T.col(j).transpose()*T.col(j);
    c(j)=(T.col(j).transpose()*y);
    c(j)/=divisorTmp;
    P.col(j)=X.transpose()*T.col(j)/divisorTmp;
    X=X-T.col(j)*P.col(j).transpose();
    y=y-T.col(j)*c(j);
    if(/*STOPPINGCRITERION(TODO)*/ && j<numComponents-1){
        numComponents=j+1;
        W.conservativeResize(X.cols(),numComponents);
        P.conservativeResize(X.cols(),numComponents);
        T.conservativeResize(X.rows(),numComponents);
        c.conservativeResize(numComponents);
    }
}
//store regression matrix
MatrixXd tmp=P.transpose()*W;
B=W*tmp.inverse()*c;
yCopy=yCopy-T*c;
mse=(yCopy.transpose()*yCopy);
mse/=y.size();//Mean Square Error

回答1:

I think you could allocate large matrix once, then for multiplication use block create a view of its part which would contain meaningful data. You can reuse a big matrix then. This will spare you reallocations.

Following example fully demonstrates it.

./eigen_block_multiply.cpp:

#include <Eigen/Dense>
#include <iostream>
using namespace std;
using namespace Eigen;
int main()
{
  Matrix<float, 2, 3> small;
  small << 1,2,3,
           4,5,6;

  Matrix<float, 4, 4> big = Matrix<float, 4, 4>::Constant(0.6);
  cout << "Big matrix:\n";
  cout << big << endl;
  cout << "Block of big matrix:\n";
  cout << big.block(0,0,3,2) << endl;
  cout << "Small matrix:\n";
  cout << small << endl;
  cout << "Product:\n";
  cout << small * big.block(0,0,3,2) << endl;

  Matrix<float, 3, 3> small2;
  small2 << 1,2,3,
            4,5,6,
            7,8,9;
  big = Matrix<float, 4, 4>::Constant(6.66);
  cout << "Product2:\n";
  cout << small * big.block(0,0,3,3) << endl;
}

Output:

Big matrix:
0.6 0.6 0.6 0.6
0.6 0.6 0.6 0.6
0.6 0.6 0.6 0.6
0.6 0.6 0.6 0.6
Block of big matrix:
0.6 0.6
0.6 0.6
0.6 0.6
Small matrix:
1 2 3
4 5 6
Product:
3.6 3.6
  9   9
Product2:
39.96 39.96 39.96
 99.9  99.9  99.9

来源：https://stackoverflow.com/questions/24186398/c-eigen-conservativeresize-too-expensive

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