Diffusion Maps

This python script uses several libraries to perform dimensionality reduction using diffusion maps. I then generate some random data via jump trajectories and follow the instructions for diffusion maps as described by the paper "Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck Operators" found on: http://www.wisdom.weizmann.ac.il/~nadler/Publications/dm_nips05.pdf

Note:

In the future the installation requirements will be grouped inside of a Docker or Singularity file. We detail the installation instructions below.

Installing Anaconda

I might make changes in the repos to make it easier to install and manage. In the meantime, here is how I install my packages.

After anaconda installation, we did the following:

Creating a new Python environment: conda create -n yourenvname python=x.x anaconda

yourenvname is the name of the environment x.x is the version (we made two of those, 3.5 and 2.7)

Go into environment (in terminal): source activate yourenvname Exiting an environment: source deactivate

When you are inside an environment, running Python or installing packages works with that particular version of Python.

Installing packages

To run jupyter notebook, go to the right directory (after activating the right environment) and type: jupyter notebook (or use the anaconda launch tool).

install packages using conda: conda install package1 package2 package3 Install packages using pip: pip install package4 package5

package1 package2 package3 package4 package5 are packages to be installed

Packages we installed from conda: numpy matplotlib sympy scipy Packages we installed from pip: qutip QNET hmmlean

Create python 3.5 (with numpy matplotlib sympy scipy qutip QNET) Create python 2.7 (with numpy matplotlib sympy scipy)

Installing Boost

For the python 2, I also installed Boost to use the C++ library.

For Mac, use: brew install boost-python (see also http://www.pyimagesearch.com/2015/04/27/installing-boost-and-boost-python-on-osx-with-homebrew/ )

Also available to download directly on:

https://sourceforge.net/projects/boost/files/boost/1.62.0/

Installation: Source activate into desired environment. Open folder:

./bootstrap.sh ./b2 ./b2 install

Modified Qutip:

For some parts (specifically, running a “hybrid” simulation involving a c-number time series generated by an HMM fed into an open quantum system, as used in Cascading_kerr_cavities.ipynb), the qutip package had to be modified. Specifically, I used the “multiprocess” library instead of “multiprocessing” in parallel.py. Multiprocess can be installed using: pip install multiprocess. The reason this is necessary is that time dependent time series must be programmatically generated, and multiprocessing uses “pickle.py” to store functions. This library does not support function closures, making programmatic generation of time-dependent functions difficult.

Current repos:

Diffusion_maps:

Unless otherwise noted, run using Python 2.7.

First, generate trajectories. See make_quantum_jump_trajectories below.

To run the most recent analysis, use the notebooks:

Build_markov_kerr.ipynb
Build_markov_kerr_qubit.ipynb
Build_markov_absorptive.ipynb
Cascading_kerr_cavities.ipynb

make_quantum_jump_trajectories (folder):

The Ipython notebooks here generate quantum jump trajectories. These are saved into a subfolder called “trajectories” Run notebooks with Python 3.5. Quantum_state_diffusion (folder) Generates quantum state diffusion trajectories. Currently not used for other things, so skip if not necessary. To install, sdeint. Again, this can be installed using python setup.py install. Install in Python 3.5 To do a local installation, activate the right environment, clone a repo, cd into it, and use: python setup.py install Vp_trees_cpp (folder) Implementation in C++ for vantage point trees. Used by diffusion maps

Other repos (not currently using):

Vp_trees_cpp:

Runs with Python 2.7. A package with C++ bindings using boost, used by diffusion maps (below). Quantum_state_diffusion: There are several options for running this script, including Docker, Singularity (container services), as well as local installation. The README is comprehensive. Runs in Python 3.5

To do a local installation, activate the right environment, clone a repo, cd into it, and use: python setup.py install

Name		Name	Last commit message	Last commit date
Latest commit History 98 Commits
make_quantum_jump_trajectories		make_quantum_jump_trajectories
quantum_state_diffusion		quantum_state_diffusion
vp_trees_cpp		vp_trees_cpp
An_idea_to_improve_local_dimensionality_determination_with_MDS.ipynb		An_idea_to_improve_local_dimensionality_determination_with_MDS.ipynb
Diffusion_maps_absorptive_bistability-QSD.ipynb		Diffusion_maps_absorptive_bistability-QSD.ipynb
Diffusion_maps_absorptive_bistability.ipynb		Diffusion_maps_absorptive_bistability.ipynb
Diffusion_maps_kerr_bistable-QSD.ipynb		Diffusion_maps_kerr_bistable-QSD.ipynb
Diffusion_maps_kerr_bistable.ipynb		Diffusion_maps_kerr_bistable.ipynb
Diffusion_maps_kerr_qubit-QSD.ipynb		Diffusion_maps_kerr_qubit-QSD.ipynb
Diffusion_maps_kerr_qubit.ipynb		Diffusion_maps_kerr_qubit.ipynb
ISOMAP_kerr_bistable.ipynb		ISOMAP_kerr_bistable.ipynb
ISOMAP_kerr_qubit.ipynb		ISOMAP_kerr_qubit.ipynb
LTSA_kerr_bistable.ipynb		LTSA_kerr_bistable.ipynb
LTSA_kerr_qubit.ipynb		LTSA_kerr_qubit.ipynb
MLDS_MarchenkoPastur_and_dimension_MLE.ipynb		MLDS_MarchenkoPastur_and_dimension_MLE.ipynb
MLE_dimensionality_and_scale.ipynb		MLE_dimensionality_and_scale.ipynb
README.md		README.md
Separating_connected_components.ipynb		Separating_connected_components.ipynb
benchmark_diffusion_map.ipynb		benchmark_diffusion_map.ipynb
build_markov.py		build_markov.py
build_markov_absorptive-2.ipynb		build_markov_absorptive-2.ipynb
build_markov_absorptive.ipynb		build_markov_absorptive.ipynb
build_markov_kerr_cascade.ipynb		build_markov_kerr_cascade.ipynb
build_markov_kerr_qubit.ipynb		build_markov_kerr_qubit.ipynb
building_markov_model.ipynb		building_markov_model.ipynb
cascading_kerr_cavities.ipynb		cascading_kerr_cavities.ipynb
cascading_kerr_cavities_diffusion_coords.ipynb		cascading_kerr_cavities_diffusion_coords.ipynb
diffusion_maps.py		diffusion_maps.py
diffusion_maps_py3.py		diffusion_maps_py3.py
eigenvalues_versus_scale_(linear_and_kernelized).ipynb		eigenvalues_versus_scale_(linear_and_kernelized).ipynb
example_diffusion_maps_with_ICA_experiment.ipynb		example_diffusion_maps_with_ICA_experiment.ipynb
fubini_study.py		fubini_study.py
hmm_on_kerrs.ipynb		hmm_on_kerrs.ipynb
load_trajectory.py		load_trajectory.py
make_2D_test_distribution.ipynb		make_2D_test_distribution.ipynb
sample_diffusion_maps.htm		sample_diffusion_maps.htm
sample_systems.py		sample_systems.py
testing out if a particular function is a metric.ipynb		testing out if a particular function is a metric.ipynb
transition_rate_methods.py		transition_rate_methods.py

tabakg/diffusion_maps

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Diffusion Maps

Note:

Installing Anaconda

Installing packages

Installing Boost

Modified Qutip:

Current repos:

Diffusion_maps:

make_quantum_jump_trajectories (folder):

Other repos (not currently using):

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