I want to solve an eigenvalue problem using TensorFlow. In particular, I have
e, v = tf.self_adjoint_eig(laplacian, name="eigendata")
eigenmap = v[:,1:4]
so I don't want to compute all eigenvectors.
In Matlab, I would use eigs(laplacian,4,'sm')
Looking at https://github.com/tensorflow/tensorflow/blob/master/tensorflow/python/ops/linalg_ops.py,
I see that tf.self_adjoint_eig calls gen_linalg_ops._self_adjoint_eig_v2.
However, I can't find gen_linalg_ops on Github or elsewhere.
Any advice on doing such linear algebra in TensorFlow, or is it best to go with other libraries in Python?
MATLAB function EIG calculates all the eigenvectors. MATLAB function EIGS only calculates a selected number of the eigenvectors using precompiled https://en.wikipedia.org/wiki/ARPACK which implements https://en.wikipedia.org/wiki/Lanczos_algorithm There is no native MATLAB Lanczos code in MATLAB, most likely because the Lanczos algorithm is unavoidably unstable with respect to round-off errors, especially in single precision, making more stable implementations tricky and/or expensive.
An alternative to EIGS function is https://www.mathworks.com/matlabcentral/fileexchange/48-lobpcg-m that implements https://en.wikipedia.org/wiki/LOBPCG natively in MATLAB.
SciPy has an interface to ARPACK as well as the Python native implementation https://docs.scipy.org/doc/scipy-1.1.0/reference/generated/scipy.sparse.linalg.lobpcg.html
Scikit uses ARPACK or LOBPCG for manifold spectral embedding http://scikit-learn.org/stable/modules/generated/sklearn.manifold.spectral_embedding.html and for spectral clustering http://scikit-learn.org/stable/modules/generated/sklearn.cluster.SpectralClustering.html
TensorFlow now has a native implementation of Lanczos https://github.com/tensorflow/tensorflow/blob/master/tensorflow/contrib/solvers/python/ops/lanczos.py