We got a lot of complaints from our users about the relative difficulty in installing it++, as well for its limited GPL license. We have decided to try and swith to Eigen linear library instead. Eigen has no installation since the code is composed of header files. It is licensed under LGPL3+ license.
Today I have created a pluggable interface that allows swapping it++ and Eigen underneath our GraphLab code. I have run some tests to verify speed and accuracy of Eigen vs. it++.
And here are the results:
| Framework and Algorithm | Running time (sec) | Training RMSE | Validation RMSE |
|---|---|---|---|
| it++ ls_solve_chol | 16.8 | 0.7000 | 0.9704 |
| it++ ls_solve | 17.8 | 0.7000 | 0.9704 |
| Eigen ldlt | 18.3 | 0.6745 | 0.9495 |
| Eigen llt | 18.7 | 0.6745 | 0.9495 |
| Eigen JacobiSVD | 63.0 | 0.6745 | 0.9495 |
Experiment details: I have used GraphLab's alternating least squares, with a subset of Netlix data. Dataset is described here. I let the algorithm run for 10 iterations, in release mode, on our AMD Opteron 8 core machine.
Experiment conclusions: It seems that Eigen is more accurate than it++. It slightly runs slower than it++ but accuracy of both training and validation RMSE is better.
Tho those of you who are familiar with it++ and would like to try out Eigen I made some short
list of compatible function calls of both systems.
| it++ | Eigen | |
|---|---|---|
| double matrix | mat | MatrixXd |
| double vector | vec | VectorXd |
| Value assignment | a.set(i,j,val) | a(i,j)=val |
| Get row | a.get_row(i) | a.row(i) |
| Identity matrix | eye(size) | Indentity(size) |
| Matrix/vecotr of ones | ones(size) | Ones(size) |
| Matrix/vecotr of zeros | zeros(size) | Zero(size) |
| Least squares solution | x=ls_solve(A,b) | x=A.ldlt().solve(b) |
| transpose | transpose(a) or a.transpose() | a.transpose() |
| set diagonal | a=diag(v) | a.diagonal()=v |
| sum values | a.sumsum() | a.sum |
| L2 norm | a.norm(2) | a.squaredNorm() |
| inverse | inv(a) | a.inverse() |
| outer product | outer_product(a,b) | a*b.transpose() |
| Eigenvalue of symmetric mat | eig_sym | VectorXcd eigs = T.eigenvalues() |
| Subvector | v.mid(1,n) | a.head(1,n) |
| Sum squares | sum_sqr(v) | v.array().pow(2).sum() |
| trace | trace(a) | a.trace() |
| min value | min(a) | a.minCoeff() |
| max value | max(a) | a.maxCoeff() |
| Random uniform | randu(size) | VectorXi::Random(size) |
| Concat vectors | concat(a,b) | VectorXi ret(a.size()+b.size()); ret << a,b; |
| Sort vector | Sort sorter.sort(0, a.size()-1, a) | std::sort(a.data(), a.data()+a.size()); |
| Sort index | Sort sorter.sort_index(0, a.size()-1, a) | N/A |
| Get columns | a.get_cols(cols_vec) | N/A |
| Random normal | randn(size) | N/A |
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