==========
Quickstart
==========

Usage
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You can use XSpline as a univariate function or use it to get design matrix.

.. code-block:: python
    
    import numpy as np
    import matplotlib.pyplot as plt
    from xspline import XSpline

    spline = XSpline(knots=[0, 0.25, 0.5, 0.75, 1], degree=3)
    x = np.arange(0, 1.01, 0.01)


One is to use XSpline as a univariate function. In this case, user must provide
coefficients for the spline bases.

.. code-block:: python

    np.random.seed(123)
    spline.coef = np.random.randn(len(spline))
    y, design_mat = spline(x), spline.get_design_mat(x)

    fig, ax = plt.subplots(1, 2, figsize=(10, 3))
    ax[0].plot(x, y)
    ax[1].plot(x, design_mat)

.. image:: images/readme_usage_0.png

XSpline can be used to obtain derivatives.

.. code-block:: python

    dy, ddesign_mat = spline(x, order=1), spline.get_design_mat(x, order=1)

    fig, ax = plt.subplots(1, 2, figsize=(10, 3))
    ax[0].plot(x, dy)
    ax[1].plot(x, ddesign_mat)

.. image:: images/readme_usage_1.png

XSpline can be used to obtain definite integrals.

.. code-block:: python

    iy, idesign_mat = spline(x, order=-1), spline.get_design_mat(x, order=-1)

    fig, ax = plt.subplots(1, 2, figsize=(10, 3))
    ax[0].plot(x, iy)
    ax[1].plot(x, idesign_mat)

.. image:: images/readme_usage_2.png

XSpline can extrapolate with different polynomial options

.. code-block:: python

    np.random.seed(123)
    # constant extrapolation one the left and linear extrapolation on the right
    spline = XSpline(
        knots=[0, 0.25, 0.5, 0.75, 1],
        degree=3,
        ldegree=0,
        rdegree=1,
        coef=np.random.randn(len(spline)),
    )
    x = np.arange(-0.5, 1.51, 0.01)
    y, design_mat = spline(x), spline.get_design_mat(x)

    fig, ax = plt.subplots(1, 2, figsize=(10, 3))
    ax[0].plot(x, y)
    ax[1].plot(x, design_mat)
    for i in range(len(ax)):
        ax[i].vlines(
            [0, 1],
            ymin=0,
            ymax=1,
            transform=ax[i].get_xaxis_transform(),
            linestyle="--",
            linewidth=1,
            color="grey",
        )

.. image:: images/readme_usage_3.png