.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/dimension_reduction/diffusion_maps/grassmann_dmaps.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_dimension_reduction_diffusion_maps_grassmann_dmaps.py>`
        to download the full example code or to run this example in your browser via Binder

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_dimension_reduction_diffusion_maps_grassmann_dmaps.py:


Grassmannian Diffusion Maps
===========================

.. GENERATED FROM PYTHON SOURCE LINES 7-15

.. code-block:: default

    import numpy as np
    from UQpy.dimension_reduction.grassmann_manifold.projections.SVDProjection import SVDProjection
    from UQpy.dimension_reduction.grassmann_manifold import GrassmannOperations
    from UQpy.utilities.kernels import ProjectionKernel
    from UQpy.dimension_reduction.diffusion_maps.DiffusionMaps import DiffusionMaps
    import sys
    import matplotlib.pyplot as plt


.. GENERATED FROM PYTHON SOURCE LINES 16-17

Create the data

.. GENERATED FROM PYTHON SOURCE LINES 18-45

.. code-block:: default

    N = 3000
    r = 2 * np.random.rand(N)
    x = np.zeros((N, 3))
    c = np.zeros(N)

    phi = np.linspace(0, 2*np.pi, N)
    theta = np.arcsin(np.cos(phi)**2)

    X = r * np.cos(phi) * np.sin(theta)
    Y = r * np.sin(phi) * np.sin(theta)
    Z = r * np.cos(theta)

    c =X**2 + Y**2 + Z**2

    fig = plt.figure()
    plt.rcParams["figure.figsize"] = (5, 5)
    plt.rcParams.update({'font.size': 18})
    ax = fig.add_subplot(111, projection="3d")
    ax.scatter(X, Y, Z, c=c, cmap=plt.cm.Spectral,
    )
    ax.set_xlabel("x")
    ax.set_ylabel("y")
    ax.set_zlabel("z")
    ax.set_title("data")

    plt.show()


.. GENERATED FROM PYTHON SOURCE LINES 46-53

.. code-block:: default


    # Recast the data into a matrix
    data_matrix = np.concatenate([X.reshape(-1, 1), Y.reshape(-1, 1), Z.reshape(-1, 1)], axis=1)

    # Convert each data point into a 2d array with shape (1, 3)
    data = [data2dArray.reshape(1, -1).T for data2dArray in data_matrix]


.. GENERATED FROM PYTHON SOURCE LINES 54-57

Project each data point onto the Grassmann manifold using SVD. Use only 300 points from the origonal data.
Select the work with maximum rank (number of planes) from each data point (p=sys.maxsize).
Use the matrix of left eigenvectors to calculate the kernel (KernelComposition.LEFT).

.. GENERATED FROM PYTHON SOURCE LINES 58-62

.. code-block:: default


    Grassmann_projection = SVDProjection(data=data[::10], p="max")
    psi = Grassmann_projection.u


.. GENERATED FROM PYTHON SOURCE LINES 63-64

Plot the projected data on the Grassmann (3, 1) which is a unit sphere.

.. GENERATED FROM PYTHON SOURCE LINES 65-88

.. code-block:: default


    Grassmann_data = np.zeros((len(psi), 3))
    for i in range(len(psi)):
        Grassmann_data[i, :] = psi[i].data.reshape(1, -1)

    fig = plt.figure()
    plt.rcParams["figure.figsize"] = (8, 8)
    plt.rcParams.update({'font.size': 18})
    ax = fig.add_subplot(111, projection="3d")

    u, v = np.mgrid[0:2*np.pi:60j, 0:np.pi:60j]
    x = np.cos(u)*np.sin(v)
    y = np.sin(u)*np.sin(v)
    z = np.cos(v)
    ax.plot_surface(
        x, y, z,  rstride=1, cstride=1, color='c', alpha=0.2, linewidth=0)
    ax.scatter(Grassmann_data[:, 0], Grassmann_data[:, 1], Grassmann_data[:, 2], c=c[:len(psi)], s=3, cmap=plt.cm.Spectral,
    )
    ax.set_title("Grassmann (3, 1)")


    plt.show()


.. GENERATED FROM PYTHON SOURCE LINES 89-90

Diffusion maps with Grassmann kernel

.. GENERATED FROM PYTHON SOURCE LINES 91-98

.. code-block:: default

    kernel = ProjectionKernel()
    kernel.calculate_kernel_matrix(psi)


    Gdmaps_UQpy = DiffusionMaps(alpha=1.0, n_eigenvectors=5, is_sparse=True, n_neighbors=250,
                                kernel_matrix=kernel.kernel_matrix)


.. GENERATED FROM PYTHON SOURCE LINES 99-100

Plot the first and second eigenvectors

.. GENERATED FROM PYTHON SOURCE LINES 101-106

.. code-block:: default

    DiffusionMaps._plot_eigen_pairs(Gdmaps_UQpy.eigenvectors, pair_indices=[1, 2], color=Gdmaps_UQpy.eigenvectors[:, 1],
                                    figure_size=[5, 5], font_size=18)
    DiffusionMaps._plot_eigen_pairs(Gdmaps_UQpy.eigenvectors, pair_indices=[1, 2], color=Gdmaps_UQpy.eigenvectors[:, 2],
                                    figure_size=[5, 5], font_size=18)



.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_dimension_reduction_diffusion_maps_grassmann_dmaps.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/SURGroup/UQpy/master?urlpath=lab/tree/notebooks/auto_examples/dimension_reduction/diffusion_maps/grassmann_dmaps.ipynb
        :alt: Launch binder
        :width: 150 px



    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: grassmann_dmaps.py <grassmann_dmaps.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: grassmann_dmaps.ipynb <grassmann_dmaps.ipynb>`


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 .. rst-class:: sphx-glr-signature

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