verde.datasets.CheckerBoard

class verde.datasets.CheckerBoard(amplitude=1000, region=(0, 5000, -5000, 0), w_east=None, w_north=None)[source]

Generate synthetic data in a checkerboard pattern.

The mathematical model is:

\[f(e, n) = a \sin\left(\frac{2\pi}{w_e} e\right) \cos\left(\frac{2\pi}{w_n} n\right)\]

in which \(e\) is the easting coordinate, \(n\) is the northing coordinate, \(a\) is the amplitude, and \(w_e\) and \(w_n\) are the wavelengths in the east and north directions, respectively.

Parameters:
amplitude : float

The amplitude of the checkerboard undulations.

region : tuple

The boundaries ([W, E, S, N]) of the region used to generate the synthetic data.

w_east : float

The wavelength in the east direction. Defaults to half of the West-East size of the evaluating region.

w_north : float

The wavelength in the north direction. Defaults to half of the South-North size of the evaluating region.

Examples

>>> synth = CheckerBoard()
>>> # Default values for the wavelengths are selected automatically
>>> print(synth.w_east_, synth.w_north_)
2500.0 2500.0
>>> # Checkerboard.grid produces an xarray.Dataset with data on a regular grid
>>> grid = synth.grid(shape=(11, 6))
>>> type(grid)
<class 'xarray.core.dataset.Dataset'>
>>> # scatter and profile generate pandas.DataFrame objects
>>> table = synth.scatter()
>>> print(sorted(table.columns))
['easting', 'northing', 'scalars']
>>> profile = synth.profile(point1=(0, 0), point2=(2500, -2500), size=100)
>>> print(sorted(profile.columns))
['distance', 'easting', 'northing', 'scalars']
Attributes:
region_

Used to fool the BaseGridder methods

w_east_

Use half of the E-W extent

w_north_

Use half of the N-S extent

Methods

filter(coordinates, data[, weights]) Filter the data through the gridder and produce residuals.
fit(coordinates, data[, weights]) Fit the gridder to observed data.
get_params([deep]) Get parameters for this estimator.
grid([region, shape, spacing, adjust, dims, …]) Interpolate the data onto a regular grid.
predict(coordinates) Evaluate the checkerboard function on a given set of points.
profile(point1, point2, size[, dims, …]) Interpolate data along a profile between two points.
scatter([region, size, random_state, dims, …]) Interpolate values onto a random scatter of points.
score(coordinates, data[, weights]) Score the gridder predictions against the given data.
set_params(**params) Set the parameters of this estimator.

Examples using verde.datasets.CheckerBoard

CheckerBoard.filter(coordinates, data, weights=None)

Filter the data through the gridder and produce residuals.

Calls fit on the data, evaluates the residuals (data - predicted data), and returns the coordinates, residuals, and weights.

No very useful by itself but this interface makes gridders compatible with other processing operations and is used by verde.Chain to join them together (for example, so you can fit a spline on the residuals of a trend).

Parameters:
coordinates : tuple of arrays

Arrays with the coordinates of each data point. Should be in the following order: (easting, northing, vertical, …).

data : array or tuple of arrays

The data values of each data point. If the data has more than one component, data must be a tuple of arrays (one for each component).

weights : None or array or tuple of arrays

If not None, then the weights assigned to each data point. If more than one data component is provided, you must provide a weights array for each data component (if not None).
Returns:
coordinates, residuals, weights

The coordinates and weights are same as the input. Residuals are the input data minus the predicted data.
CheckerBoard.fit(coordinates, data, weights=None)

Fit the gridder to observed data. NOT IMPLEMENTED.

This is a dummy placeholder for an actual method.

Parameters:
coordinates : tuple of arrays

Arrays with the coordinates of each data point. Should be in the following order: (easting, northing, vertical, …).

data : array or tuple of arrays

The data values of each data point. If the data has more than one component, data must be a tuple of arrays (one for each component).

weights : None or array or tuple of arrays

If not None, then the weights assigned to each data point. If more than one data component is provided, you must provide a weights array for each data component (if not None).
Returns:
self

This instance of the gridder. Useful to chain operations.
CheckerBoard.get_params(deep=True)

Get parameters for this estimator.

Parameters:
deep : boolean, optional

If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:
params : mapping of string to any

Parameter names mapped to their values.
CheckerBoard.grid(region=None, shape=None, spacing=None, adjust='spacing', dims=None, data_names=None, projection=None)

Interpolate the data onto a regular grid.

The grid can be specified by either the number of points in each dimension (the shape) or by the grid node spacing.

If the given region is not divisible by the desired spacing, either the region or the spacing will have to be adjusted. By default, the spacing will be rounded to the nearest multiple. Optionally, the East and North boundaries of the region can be adjusted to fit the exact spacing given. See verde.grid_coordinates for more details.

If the interpolator collected the input data region, then it will be used if region=None. Otherwise, you must specify the grid region.

Use the dims and data_names arguments to set custom names for the dimensions and the data field(s) in the output xarray.Dataset. Default names are provided.

Parameters:
region : list = [W, E, S, N]

The boundaries of a given region in Cartesian or geographic coordinates.

shape : tuple = (n_north, n_east) or None

The number of points in the South-North and West-East directions, respectively. If None and spacing is not given, defaults to (101, 101).

spacing : tuple = (s_north, s_east) or None

The grid spacing in the South-North and West-East directions, respectively.

adjust : {‘spacing’, ‘region’}

Whether to adjust the spacing or the region if required. Ignored if shape is given instead of spacing. Defaults to adjusting the spacing.

dims : list or None

The names of the northing and easting data dimensions, respectively, in the output grid. Defaults to ['northing', 'easting'] for Cartesian grids and ['latitude', 'longitude'] for geographic grids. NOTE: This is an exception to the “easting” then “northing” pattern but is required for compatibility with xarray.

data_names : list of None

The name(s) of the data variables in the output grid. Defaults to ['scalars'] for scalar data, ['east_component', 'north_component'] for 2D vector data, and ['east_component', 'north_component', 'vertical_component'] for 3D vector data.

projection : callable or None

If not None, then should be a callable object projection(easting, northing) -> (proj_easting, proj_northing) that takes in easting and northing coordinate arrays and returns projected northing and easting coordinate arrays. This function will be used to project the generated grid coordinates before passing them into predict. For example, you can use this to generate a geographic grid from a Cartesian gridder.
Returns:
grid : xarray.Dataset

The interpolated grid. Metadata about the interpolator is written to the attrs attribute.

See also

verde.grid_coordinates
Generate the coordinate values for the grid.
CheckerBoard.predict(coordinates)[source]

Evaluate the checkerboard function on a given set of points.

Parameters:
coordinates : tuple of arrays

Arrays with the coordinates of each data point. Should be in the following order: (easting, northing, vertical, …). Only easting and northing will be used, all subsequent coordinates will be ignored.
Returns:
data : array

The evaluated checkerboard function.
CheckerBoard.profile(point1, point2, size, dims=None, data_names=None, projection=None)

Interpolate data along a profile between two points.

Generates the profile using a straight line if the interpolator assumes Cartesian data or a great circle if geographic data.

Use the dims and data_names arguments to set custom names for the dimensions and the data field(s) in the output pandas.DataFrame. Default names are provided.

Includes the calculated distance to point1 for each data point in the profile.

Parameters:
point1 : tuple

The easting and northing coordinates, respectively, of the first point.

point2 : tuple

The easting and northing coordinates, respectively, of the second point.

size : int

The number of points to generate.

dims : list or None

The names of the northing and easting data dimensions, respectively, in the output dataframe. Defaults to ['northing', 'easting'] for Cartesian grids and ['latitude', 'longitude'] for geographic grids. NOTE: This is an exception to the “easting” then “northing” pattern but is required for compatibility with xarray.

data_names : list of None

The name(s) of the data variables in the output dataframe. Defaults to ['scalars'] for scalar data, ['east_component', 'north_component'] for 2D vector data, and ['east_component', 'north_component', 'vertical_component'] for 3D vector data.

projection : callable or None

If not None, then should be a callable object projection(easting, northing) -> (proj_easting, proj_northing) that takes in easting and northing coordinate arrays and returns projected northing and easting coordinate arrays. This function will be used to project the generated profile coordinates before passing them into predict. For example, you can use this to generate a geographic profile from a Cartesian gridder.
Returns:
table : pandas.DataFrame

The interpolated values along the profile.
CheckerBoard.scatter(region=None, size=300, random_state=0, dims=None, data_names=None, projection=None)

Interpolate values onto a random scatter of points.

If the interpolator collected the input data region, then it will be used if region=None. Otherwise, you must specify the grid region.

Use the dims and data_names arguments to set custom names for the dimensions and the data field(s) in the output pandas.DataFrame. Default names are provided.

Parameters:
region : list = [W, E, S, N]

The boundaries of a given region in Cartesian or geographic coordinates.

size : int

The number of points to generate.

random_state : numpy.random.RandomState or an int seed

A random number generator used to define the state of the random permutations. Use a fixed seed to make sure computations are reproducible. Use None to choose a seed automatically (resulting in different numbers with each run).

dims : list or None

The names of the northing and easting data dimensions, respectively, in the output dataframe. Defaults to ['northing', 'easting'] for Cartesian grids and ['latitude', 'longitude'] for geographic grids. NOTE: This is an exception to the “easting” then “northing” pattern but is required for compatibility with xarray.

data_names : list of None

The name(s) of the data variables in the output dataframe. Defaults to ['scalars'] for scalar data, ['east_component', 'north_component'] for 2D vector data, and ['east_component', 'north_component', 'vertical_component'] for 3D vector data.

projection : callable or None

If not None, then should be a callable object projection(easting, northing) -> (proj_easting, proj_northing) that takes in easting and northing coordinate arrays and returns projected northing and easting coordinate arrays. This function will be used to project the generated scatter coordinates before passing them into predict. For example, you can use this to generate a geographic scatter from a Cartesian gridder.
Returns:
table : pandas.DataFrame

The interpolated values on a random set of points.
CheckerBoard.score(coordinates, data, weights=None)

Score the gridder predictions against the given data.

Calculates the R^2 coefficient of determination of between the predicted values and the given data values. A maximum score of 1 means a perfect fit. The score can be negative.

If the data has more than 1 component, the scores of each component will be averaged.

Parameters:
coordinates : tuple of arrays

Arrays with the coordinates of each data point. Should be in the following order: (easting, northing, vertical, …).

data : array or tuple of arrays

The data values of each data point. If the data has more than one component, data must be a tuple of arrays (one for each component).

weights : None or array or tuple of arrays

If not None, then the weights assigned to each data point. If more than one data component is provided, you must provide a weights array for each data component (if not None).
Returns:
score : float

The R^2 score
CheckerBoard.set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns:
self