.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_FOR_README.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_examples_FOR_README.py:


=========================================
Tutorial for basic usage 
=========================================



.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /auto_examples/images/sphx_glr_FOR_README_001.png
          :alt: FOR README
          :class: sphx-glr-multi-img

    *

      .. image:: /auto_examples/images/sphx_glr_FOR_README_002.png
          :alt: FOR README
          :class: sphx-glr-multi-img

    *

      .. image:: /auto_examples/images/sphx_glr_FOR_README_003.png
          :alt: FOR README
          :class: sphx-glr-multi-img

    *

      .. image:: /auto_examples/images/sphx_glr_FOR_README_004.png
          :alt: FOR README
          :class: sphx-glr-multi-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [[-3.14159265 -1.          2.        ]
     [-3.14159265 -0.5         2.        ]
     [-3.14159265  0.          2.        ]
     [-3.14159265  0.5         2.        ]
     [-3.14159265  1.          2.        ]
     [-2.74889357 -1.          1.27648914]
     [-2.74889357 -0.5         1.707008  ]
     [-2.74889357  0.          1.94618514]
     [-2.74889357  0.5         1.99402057]
     [-2.74889357  1.          1.85051428]
     [-2.35619449 -1.          0.66312624]
     [-2.35619449 -0.5         1.45862137]
     [-2.35619449  0.          1.90056311]
     [-2.35619449  0.5         1.98895146]
     [-2.35619449  1.          1.72378641]
     [-1.57079633 -1.          0.109375  ]
     [-1.57079633 -0.5         1.234375  ]
     [-1.57079633  0.          1.859375  ]
     [-1.57079633  0.5         1.984375  ]
     [-1.57079633  1.          1.609375  ]
     [-0.78539816 -1.          0.66312624]
     [-0.78539816 -0.5         1.45862137]
     [-0.78539816  0.          1.90056311]
     [-0.78539816  0.5         1.98895146]
     [-0.78539816  1.          1.72378641]
     [-0.39269908 -1.          1.27648914]
     [-0.39269908 -0.5         1.707008  ]
     [-0.39269908  0.          1.94618514]
     [-0.39269908  0.5         1.99402057]
     [-0.39269908  1.          1.85051428]
     [ 0.         -1.          2.        ]
     [ 0.         -0.5         2.        ]
     [ 0.          0.          2.        ]
     [ 0.          0.5         2.        ]
     [ 0.          1.          2.        ]
     [ 0.39269908 -1.          2.72351086]
     [ 0.39269908 -0.5         2.292992  ]
     [ 0.39269908  0.          2.05381486]
     [ 0.39269908  0.5         2.00597943]
     [ 0.39269908  1.          2.14948572]
     [ 0.78539816 -1.          3.33687376]
     [ 0.78539816 -0.5         2.54137863]
     [ 0.78539816  0.          2.09943689]
     [ 0.78539816  0.5         2.01104854]
     [ 0.78539816  1.          2.27621359]
     [ 1.57079633 -1.          3.890625  ]
     [ 1.57079633 -0.5         2.765625  ]
     [ 1.57079633  0.          2.140625  ]
     [ 1.57079633  0.5         2.015625  ]
     [ 1.57079633  1.          2.390625  ]
     [ 2.35619449 -1.          3.33687376]
     [ 2.35619449 -0.5         2.54137863]
     [ 2.35619449  0.          2.09943689]
     [ 2.35619449  0.5         2.01104854]
     [ 2.35619449  1.          2.27621359]
     [ 2.74889357 -1.          2.72351086]
     [ 2.74889357 -0.5         2.292992  ]
     [ 2.74889357  0.          2.05381486]
     [ 2.74889357  0.5         2.00597943]
     [ 2.74889357  1.          2.14948572]
     [ 3.14159265 -1.          2.        ]
     [ 3.14159265 -0.5         2.        ]
     [ 3.14159265  0.          2.        ]
     [ 3.14159265  0.5         2.        ]
     [ 3.14159265  1.          2.        ]]

    Coefficients all same? True
    Knots all same? True

    Antiderivative of derivative:
     Coefficients differ by constant? True
    Knots all same? True

    Derivative of antiderivative:
     Coefficients the same? True
    Knots all same? True






|


.. code-block:: default
   :lineno-start: 8



    import ndsplines
    import numpy as np
    import matplotlib.pyplot as plt

    # generate grid of independent variables
    x = np.array([-1, -7/8, -3/4, -1/2, -1/4, -1/8, 0, 1/8, 1/4, 1/2, 3/4, 7/8, 1])*np.pi
    y = np.array([-1, -1/2, 0, 1/2, 1])
    meshx, meshy = np.meshgrid(x, y, indexing='ij')
    gridxy = np.stack((meshx, meshy), axis=-1)


    # generate denser grid of independent variables to interpolate
    sparse_dense = 2**7
    xx = np.concatenate([np.linspace(x[i], x[i+1], sparse_dense) for i in range(x.size-1)]) # np.linspace(x[0], x[-1], x.size*sparse_dense)
    yy = np.concatenate([np.linspace(y[i], y[i+1], sparse_dense) for i in range(y.size-1)]) # np.linspace(y[0], y[-1], y.size*sparse_dense)
    gridxxyy = np.stack(np.meshgrid(xx, yy, indexing='ij'), axis=-1)

    def plots(sparse_data, dense_data, ylabel='f(x,y)'):
        fig, axes = plt.subplots(1, 2, constrained_layout=True)
        for yidx in range(sparse_data.shape[1]):
            axes[0].plot(x, sparse_data[:, yidx], 'o', color='C%d'%yidx, label='y=%.2f'%y[yidx])
            axes[0].plot(xx, dense_data[:, np.clip(yidx*sparse_dense, 0, yy.size-1)], color='C%d'%yidx)# label='y=%.1f'%y[yidx])
        
        axes[0].legend()
        axes[0].set_xlabel('x')
        axes[0].set_ylabel(ylabel)
        for xidx in range(sparse_data.shape[0]//2):
            axes[1].plot(yy, dense_data[(xidx+3)*sparse_dense, :], '--', color='C%d'%xidx,)# label='x=%.1f'%x[xidx+3])
            axes[1].plot(y, sparse_data[xidx+3, :], 'o', color='C%d'%xidx, label='x=%.1f'%x[xidx+3],)
        
        axes[1].legend()
        axes[1].set_xlabel('y')
        plt.show()

    # evaluate a function to interpolate over input grid
    meshf = np.sin(meshx) * (meshy-3/8)**2 + 2

    # create the interpolating splane
    interp = ndsplines.make_interp_spline(gridxy, meshf)

    # evaluate spline over denser grid
    meshff = interp(gridxxyy)


    plots(meshf, meshff)


    ##

    # as subplots
    fig, axes = plt.subplots(1,2, constrained_layout=True)

    gridxxy = np.stack(np.meshgrid(xx, y, indexing='ij'), axis=-1)
    meshff = interp(gridxxy)

    for yidx in range(meshf.shape[1]):
        axes[0].plot(x, meshf[:, yidx], 'o', color='C%d'%yidx, label='y=%.1f'%y[yidx])
        axes[0].plot(xx, meshff[:, yidx], color='C%d'%yidx)
    axes[0].legend()
    axes[0].set_xlabel('$x$')
    axes[0].set_ylabel('$f(x,y)$')

    # y-dir plot
    gridxyy = np.stack(np.meshgrid(x, yy, indexing='ij'), axis=-1)

    meshff = interp(gridxyy)
    for xidx in range(meshf.shape[0]//2):
        axes[1].plot(yy, meshff[xidx*1+3, :], '--', color='C%d'%xidx, label='x=%.1f'%x[xidx*1+3])
        axes[1].plot(y, meshf[xidx*1+3, :], 'o', color='C%d'%xidx)
    
    axes[1].legend()
    axes[1].set_xlabel('$y$')
    # plt.ylabel(r'$\frac{\partial f(x,y)}{\partial y}$')
    plt.show()

    ##

    # we could also use tidy data format to make the grid

    tidy_data = np.dstack((gridxy, meshf)).reshape((-1,3))
    print(tidy_data)

    tidy_interp = ndsplines.make_interp_spline_from_tidy(tidy_data, [0,1], [2])

    print("\nCoefficients all same?", np.all(tidy_interp.coefficients == interp.coefficients))
    print("Knots all same?", np.all([np.all(knot0 == knot1) for knot0, knot1 in zip(tidy_interp.knots, interp.knots)]))

    # send to example of least squares
    ##
    # two ways to evaluate derivative - y direction

    deriv_interp = interp.derivative(1)
    deriv1 = deriv_interp(gridxy)
    deriv2 = interp(gridxxyy, nus=np.array([0,1]))

    plots(deriv1, deriv2, r'$\frac{\partial f(x,y)}{\partial y}$')

    ##
    # two ways to evaluate derivatives x-direction: create a derivative spline or call with nus:
    deriv_interp = interp.derivative(0)
    deriv1 = deriv_interp(gridxy)
    deriv2 = interp(gridxxyy, nus=np.array([1,0]))

    plots(deriv1, deriv2, r'$\frac{\partial f(x,y)}{\partial x}$')
    ##

    # Calculus demonstration
    interp1 = deriv_interp.antiderivative(0)
    coeff_diff = interp1.coefficients - interp.coefficients
    print("\nAntiderivative of derivative:\n","Coefficients differ by constant?", np.allclose(interp1.coefficients+2.0, interp.coefficients))
    print("Knots all same?", np.all([np.all(knot0 == knot1) for knot0, knot1 in zip(interp1.knots, interp.knots)]))

    antideriv_interp = interp.antiderivative(0)

    interp2 = antideriv_interp.derivative(0)
    print("\nDerivative of antiderivative:\n","Coefficients the same?", np.allclose(interp2.coefficients, interp.coefficients))
    print("Knots all same?", np.all([np.all(knot0 == knot1) for knot0, knot1 in zip(interp2.knots, interp.knots)]))


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

   **Total running time of the script:** ( 0 minutes  3.049 seconds)


.. _sphx_glr_download_auto_examples_FOR_README.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_