bilby.core.utils.calculus.BoundedRectBivariateSpline

class bilby.core.utils.calculus.BoundedRectBivariateSpline(x, y, z, bbox=[None, None, None, None], kx=3, ky=3, s=0, fill_value=None)

Bases: RectBivariateSpline

__init__(x, y, z, bbox=[None, None, None, None], kx=3, ky=3, s=0, fill_value=None)

__call__(x, y, dx=0, dy=0, grid=False)

Evaluate the spline or its derivatives at given positions.

Parameters:

x, yarray_like

Input coordinates.

If grid is False, evaluate the spline at points (x[i], y[i]), i=0, ..., len(x)-1. Standard Numpy broadcasting is obeyed.

If grid is True: evaluate spline at the grid points defined by the coordinate arrays x, y. The arrays must be sorted to increasing order.

The ordering of axes is consistent with np.meshgrid(..., indexing="ij") and inconsistent with the default ordering np.meshgrid(..., indexing="xy").

dxint

Order of x-derivative

Added in version 0.14.0.

dyint

Order of y-derivative

Added in version 0.14.0.

gridbool

Whether to evaluate the results on a grid spanned by the input arrays, or at points specified by the input arrays.

Added in version 0.14.0.

Examples

Suppose that we want to bilinearly interpolate an exponentially decaying function in 2 dimensions.

>>> import numpy as np
>>> from scipy.interpolate import RectBivariateSpline

We sample the function on a coarse grid. Note that the default indexing=”xy” of meshgrid would result in an unexpected (transposed) result after interpolation.

>>> xarr = np.linspace(-3, 3, 100)
>>> yarr = np.linspace(-3, 3, 100)
>>> xgrid, ygrid = np.meshgrid(xarr, yarr, indexing="ij")

The function to interpolate decays faster along one axis than the other.

>>> zdata = np.exp(-np.sqrt((xgrid / 2) ** 2 + ygrid**2))

Next we sample on a finer grid using interpolation (kx=ky=1 for bilinear).

>>> rbs = RectBivariateSpline(xarr, yarr, zdata, kx=1, ky=1)
>>> xarr_fine = np.linspace(-3, 3, 200)
>>> yarr_fine = np.linspace(-3, 3, 200)
>>> xgrid_fine, ygrid_fine = np.meshgrid(xarr_fine, yarr_fine, indexing="ij")
>>> zdata_interp = rbs(xgrid_fine, ygrid_fine, grid=False)

And check that the result agrees with the input by plotting both.

>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> ax1 = fig.add_subplot(1, 2, 1, aspect="equal")
>>> ax2 = fig.add_subplot(1, 2, 2, aspect="equal")
>>> ax1.imshow(zdata)
>>> ax2.imshow(zdata_interp)
>>> plt.show()

Methods

__init__(x, y, z[, bbox, kx, ky, s, fill_value])
ev(xi, yi[, dx, dy])	Evaluate the spline at points
get_coeffs()	Return spline coefficients.
get_knots()	Return a tuple (tx,ty) where tx,ty contain knots positions of the spline with respect to x-, y-variable, respectively.
get_residual()	Return weighted sum of squared residuals of the spline approximation: sum ((w[i]*(z[i]-s(x[i],y[i])))**2,axis=0)
integral(xa, xb, ya, yb)	Evaluate the integral of the spline over area [xa,xb] x [ya,yb].
partial_derivative(dx, dy)	Construct a new spline representing a partial derivative of this spline.

ev(xi, yi, dx=0, dy=0)

Evaluate the spline at points

Returns the interpolated value at (xi[i], yi[i]), i=0,...,len(xi)-1.

Parameters:

xi, yiarray_like

Input coordinates. Standard Numpy broadcasting is obeyed. The ordering of axes is consistent with np.meshgrid(..., indexing="ij") and inconsistent with the default ordering np.meshgrid(..., indexing="xy").

dxint, optional

Order of x-derivative

Added in version 0.14.0.

dyint, optional

Order of y-derivative

Added in version 0.14.0.

Examples

Suppose that we want to bilinearly interpolate an exponentially decaying function in 2 dimensions.

>>> import numpy as np
>>> from scipy.interpolate import RectBivariateSpline
>>> def f(x, y):
...     return np.exp(-np.sqrt((x / 2) ** 2 + y**2))

We sample the function on a coarse grid and set up the interpolator. Note that the default indexing="xy" of meshgrid would result in an unexpected (transposed) result after interpolation.

>>> xarr = np.linspace(-3, 3, 21)
>>> yarr = np.linspace(-3, 3, 21)
>>> xgrid, ygrid = np.meshgrid(xarr, yarr, indexing="ij")
>>> zdata = f(xgrid, ygrid)
>>> rbs = RectBivariateSpline(xarr, yarr, zdata, kx=1, ky=1)

Next we sample the function along a diagonal slice through the coordinate space on a finer grid using interpolation.

>>> xinterp = np.linspace(-3, 3, 201)
>>> yinterp = np.linspace(3, -3, 201)
>>> zinterp = rbs.ev(xinterp, yinterp)

And check that the interpolation passes through the function evaluations as a function of the distance from the origin along the slice.

>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> ax1 = fig.add_subplot(1, 1, 1)
>>> ax1.plot(np.sqrt(xarr**2 + yarr**2), np.diag(zdata), "or")
>>> ax1.plot(np.sqrt(xinterp**2 + yinterp**2), zinterp, "-b")
>>> plt.show()

get_coeffs()

Return spline coefficients.

get_knots()

Return a tuple (tx,ty) where tx,ty contain knots positions of the spline with respect to x-, y-variable, respectively. The position of interior and additional knots are given as t[k+1:-k-1] and t[:k+1]=b, t[-k-1:]=e, respectively.

get_residual()

Return weighted sum of squared residuals of the spline approximation: sum ((w[i]*(z[i]-s(x[i],y[i])))**2,axis=0)

integral(xa, xb, ya, yb)

Evaluate the integral of the spline over area [xa,xb] x [ya,yb].

Parameters:

xa, xbfloat

The end-points of the x integration interval.

ya, ybfloat

The end-points of the y integration interval.

Returns:

integfloat

The value of the resulting integral.

partial_derivative(dx, dy)

Construct a new spline representing a partial derivative of this spline.

Parameters:

dx, dyint

Orders of the derivative in x and y respectively. They must be non-negative integers and less than the respective degree of the original spline (self) in that direction (kx, ky).

Returns:

spline

A new spline of degrees (kx - dx, ky - dy) representing the derivative of this spline.

Notes

Added in version 1.9.0.