{
    "info": {
        "author": "Bruno Messias; Thomas K Peron",
        "author_email": "messias.physics@gmail.com",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 4 - Beta",
            "Intended Audience :: Science/Research",
            "License :: OSI Approved :: MIT License",
            "Programming Language :: Python :: 3",
            "Topic :: Scientific/Engineering :: Information Analysis",
            "Topic :: Scientific/Engineering :: Mathematics",
            "Topic :: Scientific/Engineering :: Physics"
        ],
        "description": "# ![eMaTe](emate.png)\n\neMaTe is a python package implemented in tensorflow which the main goal is provide useful methods capable of estimate spectral densities and trace functions of large sparse matrices. \n\n## Install                                                                                                              \n```\npip install emate\n```\n\n## Kernel Polynomial Method (KPM)\n\nThe Kernel Polynomial Method can\u00a0estimate the spectral density of large sparse Hermitan matrices with a computational cost almost linear. This method combines three key ingredients: the Chebyshev expansion + the stochastic trace estimator + kernel smoothing.\n\n\n### Example\n\n```python\nimport igraph as ig\nimport numpy as np\n\nN = 3000\nG = ig.Graph.Erdos_Renyi(N, 3/N)\n\nW = np.array(G.get_adjacency().data, dtype=np.float64)\nvals = np.linalg.eigvalsh(W).real\n```\n\n```python\nfrom emate.hermitian import pykpm\nfrom stdog.utils.misc import ig2sparse \n\nW = ig2sparse(G)\n\nnum_moments = 300\nnum_vecs = 200\nextra_points = 10\nek, rho = pykpm(W, num_moments, num_vecs, extra_points)\n```\n\n```python\nimport matplotlib.pyplot as plt\nplt.hist(vals, density=True, bins=100, alpha=.9, color=\"steelblue\")\nplt.scatter(ek, rho, c=\"tomato\", zorder=999, alpha=0.9, marker=\"d\")\n\n```\n\n![](docs/source/imgs/kpm.png)\n\n## Stochastic Lanczos Quadrature (SLQ)\n\n\n>The problem of estimating the trace of matrix functions appears in applications ranging from machine learning and scientific computing, to computational biology.[2] \n\n### Example\n\n#### Computing the Estrada index\n\n```python\nfrom emate.symmetric.slq import pyslq\nimport tensorflow as tf\n\ndef trace_function(eig_vals):\n    return tf.exp(eig_vals)\n\nnum_vecs = 100\nnum_steps = 50\napproximated_estrada_index, _ = pyslq(L_sparse, num_vecs, num_steps,  trace_function)\nexact_estrada_index =  np.sum(np.exp(vals_laplacian))\napproximated_estrada_index, exact_estrada_index\n```\nThe above code returns\n\n```\n(3058.012, 3063.16457163222)\n```\n#### Entropy\n```python\nimport scipy\nimport scipy.sparse\n\ndef entropy(eig_vals):\n  s = 0.\n  for val in eig_vals:\n    if val > 0:\n      s += -val*np.log(val)\n  return s\n\nL = np.array(G.laplacian(normalized=True), dtype=np.float64)\nvals_laplacian = np.linalg.eigvalsh(L).real\n\nexact_entropy =  entropy(vals_laplacian)\n\n\ndef trace_function(eig_vals):\n  def entropy(val):\n    return tf.cond(val>0, lambda:-val*tf.log(val), lambda: 0.)\n  \n  return tf.map_fn(entropy, eig_vals)\n \nL_sparse = scipy.sparse.coo_matrix(L)\n    \nnum_vecs = 100\nnum_steps = 50\napproximated_entropy, _ = pyslq(L_sparse, num_vecs, num_steps,  trace_function)\n\napproximated_entropy, exact_entropy\n```\n```\n(-509.46283, -512.5283224633046)\n```\n[[1] Hutchinson, M. F. (1990). A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines. Communications in Statistics-Simulation and Computation, 19(2), 433-450.](https://www.tandfonline.com/doi/abs/10.1080/03610919008812866)\n\n[[2] Ubaru, S., Chen, J., & Saad, Y. (2017). Fast Estimation of tr(f(A)) via Stochastic Lanczos Quadrature. SIAM Journal on Matrix Analysis and Applications, 38(4), 1075-1099.](https://epubs.siam.org/doi/abs/10.1137/16M1104974)\n\n\n## Acknowledgements\n\nThis work has been supported also by FAPESP grants  11/50761-2  and  2015/22308-2.   Research  carriedout using the computational resources of the Center forMathematical  Sciences  Applied  to  Industry  (CeMEAI)funded by FAPESP (grant 2013/07375-0).",
        "description_content_type": "text/markdown",
        "docs_url": null,
        "download_url": "https://github.com/stdogpkg/emate/archive/v1.0.3.tar.gz",
        "downloads": {
            "last_day": -1,
            "last_month": -1,
            "last_week": -1
        },
        "home_page": "https://github.com/stdogpkg/emate",
        "keywords": "gpu,science,complex-networks,graphs,matrices,kpm,tensorflow,chebyshev,spectral,eigenvalues",
        "license": "MIT",
        "maintainer": "",
        "maintainer_email": "",
        "name": "emate",
        "package_url": "https://pypi.org/project/emate/",
        "platform": "",
        "project_url": "https://pypi.org/project/emate/",
        "project_urls": {
            "Download": "https://github.com/stdogpkg/emate/archive/v1.0.3.tar.gz",
            "Homepage": "https://github.com/stdogpkg/emate"
        },
        "release_url": "https://pypi.org/project/emate/1.0.3/",
        "requires_dist": null,
        "requires_python": "",
        "summary": "",
        "version": "1.0.3"
    },
    "last_serial": 5842241,
    "releases": {
        "1.0.2": [
            {
                "comment_text": "",
                "digests": {
                    "md5": "b1a36c7fd0d8a8bdfc4c657c98bb0860",
                    "sha256": "c0d48f318b11f6e18309eb2c3e9ac8dbc9c7aeba408b888e234f17b14f274527"
                },
                "downloads": -1,
                "filename": "emate-1.0.2.tar.gz",
                "has_sig": false,
                "md5_digest": "b1a36c7fd0d8a8bdfc4c657c98bb0860",
                "packagetype": "sdist",
                "python_version": "source",
                "requires_python": null,
                "size": 11857,
                "upload_time": "2019-09-04T15:44:18",
                "url": "https://files.pythonhosted.org/packages/a5/ac/043928319b0641082bb97d865a123d2ae6cd784fac8e1b126e34fa8a5aa4/emate-1.0.2.tar.gz"
            }
        ],
        "1.0.3": [
            {
                "comment_text": "",
                "digests": {
                    "md5": "291db3bd9678e56e92846aea3a094551",
                    "sha256": "67920f89ebec9bae6ff20671bf8bda5218bcdaf9742635f2ff5c367a1b60c382"
                },
                "downloads": -1,
                "filename": "emate-1.0.3.tar.gz",
                "has_sig": false,
                "md5_digest": "291db3bd9678e56e92846aea3a094551",
                "packagetype": "sdist",
                "python_version": "source",
                "requires_python": null,
                "size": 13543,
                "upload_time": "2019-09-17T15:19:14",
                "url": "https://files.pythonhosted.org/packages/a3/35/fa3d5b516d47303d85759efb3bbdc1e6c6a0b9c47f8f7f909348379540ab/emate-1.0.3.tar.gz"
            }
        ]
    },
    "urls": [
        {
            "comment_text": "",
            "digests": {
                "md5": "291db3bd9678e56e92846aea3a094551",
                "sha256": "67920f89ebec9bae6ff20671bf8bda5218bcdaf9742635f2ff5c367a1b60c382"
            },
            "downloads": -1,
            "filename": "emate-1.0.3.tar.gz",
            "has_sig": false,
            "md5_digest": "291db3bd9678e56e92846aea3a094551",
            "packagetype": "sdist",
            "python_version": "source",
            "requires_python": null,
            "size": 13543,
            "upload_time": "2019-09-17T15:19:14",
            "url": "https://files.pythonhosted.org/packages/a3/35/fa3d5b516d47303d85759efb3bbdc1e6c6a0b9c47f8f7f909348379540ab/emate-1.0.3.tar.gz"
        }
    ]
}