verde.VectorSpline2D

class verde.VectorSpline2D(poisson=0.5, mindist=10000.0, damping=None, force_coords=None, engine='auto')

Elastically coupled interpolation of 2-component vector data.

This gridder assumes Cartesian coordinates.

Uses the Green’s functions based on elastic deformation from [SandwellWessel2016]. The interpolation is done by estimating point forces that generate an elastic deformation that fits the observed vector data. The deformation equations are based on a 2D elastic sheet with a constant Poisson’s ratio. The data can then be predicted at any desired location.

The east and north data components are coupled through the elastic deformation equations. This coupling is controlled by the Poisson’s ratio, which is usually between -1 and 1. The special case of Poisson’s ratio -1 leads to an uncoupled interpolation, meaning that the east and north components don’t interfere with each other.

The point forces are traditionally placed under each data point. The force locations are set the first time fit is called. Subsequent calls will fit using the same force locations as the first call. This configuration results in an exact prediction at the data points but can be unstable.

[SandwellWessel2016] stabilize the solution using Singular Value Decomposition but we use ridge regression instead. The regularization can be controlled using the damping argument. Alternatively, you can specify the position of the forces manually using the force_coords argument. Regularization or forces not coinciding with data points will result in a least-squares estimate, not an exact solution. Note that the least-squares solution is required for data weights to have any effect.

Before fitting, the Jacobian (design, sensitivity, feature, etc) matrix for the spline is normalized using sklearn.preprocessing.StandardScaler without centering the mean so that the transformation can be undone in the estimated forces.

Parameters:

poissonfloat

The Poisson’s ratio for the elastic deformation Green’s functions. Default is 0.5. A value of -1 will lead to uncoupled interpolation of the east and north data components.

mindistfloat

A minimum distance between the point forces and data points. Needed because the Green’s functions are singular when forces and data points coincide. Acts as a fudge factor. A good rule of thumb is to use the average spacing between data points.

dampingNone or float

The positive damping regularization parameter. Controls how much smoothness is imposed on the estimated forces. If None, no regularization is used.

force_coordsNone or tuple of arrays

The easting and northing coordinates of the point forces. If None (default), then will be set to the data coordinates the first time fit is called.

enginestr

DEPRECATED: This option is deprecated and will be removed in Verde v2.0.0. The numba engine will be the only option. Computation engine for the Jacobian matrix and prediction. Can be 'auto', 'numba', or 'numpy'. If 'auto', will use numba if it is installed or numpy otherwise. The numba version is multi-threaded and usually faster, which makes fitting and predicting faster.

Attributes:

force_array

The estimated forces that fit the observed data.

region_tuple

The boundaries ([W, E, S, N]) of the data used to fit the interpolator. Used as the default region for the grid and scatter methods.

Methods

filter(coordinates, data[, weights])	Filter the data through the gridder and produce residuals.
fit(coordinates, data[, weights])	Fit the gridder to the given 2-component vector data.
get_metadata_routing()	Get metadata routing of this object.
get_params([deep])	Get parameters for this estimator.
grid([region, shape, spacing, dims, ...])	Interpolate the data onto a regular grid.
jacobian(coordinates, force_coords[, dtype])	Make the Jacobian matrix for the 2D coupled elastic deformation.
predict(coordinates)	Evaluate the fitted gridder on the 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_fit_request(*[, coordinates, data, weights])	Request metadata passed to the fit method.
set_params(**params)	Set the parameters of this estimator.
set_predict_request(*[, coordinates])	Request metadata passed to the predict method.
set_score_request(*[, coordinates, data, ...])	Request metadata passed to the score method.

Attributes

VectorSpline2D.data_names_defaults = [('scalars',), ('east_component', 'north_component'), ('east_component', 'north_component', 'vertical_component')]

VectorSpline2D.dims = ('northing', 'easting')

VectorSpline2D.extra_coords_name = 'extra_coord'

Methods

VectorSpline2D.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.

Not 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:

coordinatestuple of arrays

Arrays with the coordinates of each data point. Should be in the following order: (easting, northing, vertical, …). For the specific definition of coordinate systems and what these names mean, see the class docstring.

dataarray 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).

weightsNone 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.

VectorSpline2D.fit(coordinates, data, weights=None)

Fit the gridder to the given 2-component vector data.

The data region is captured and used as default for the grid and scatter methods.

All input arrays must have the same shape.

Parameters:

coordinatestuple 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.

datatuple of array

A tuple (east_component, north_component) of arrays with the vector data values at each point.

weightsNone or tuple array

If not None, then the weights assigned to each data point. Must be one array per data component. Typically, this should be 1 over the data uncertainty squared.

Returns:

self

Returns this estimator instance for chaining operations.

VectorSpline2D.get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest

A MetadataRequest encapsulating routing information.

VectorSpline2D.get_params(deep=True)

Get parameters for this estimator.

Parameters:

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict

Parameter names mapped to their values.

VectorSpline2D.grid(region=None, shape=None, spacing=None, dims=None, data_names=None, projection=None, coordinates=None, **kwargs)

Interpolate the data onto a regular grid.

The grid can be specified by two methods:

• Pass the actual coordinates of the grid points, as generated by verde.grid_coordinates or from an existing xarray.Dataset grid.

• Let the method define a new grid by either passing the number of points in each dimension (the shape) or by the grid node spacing. If the interpolator collected the input data region, then it will be used if region=None. Otherwise, you must specify the grid region. See verde.grid_coordinates for details. Other arguments for verde.grid_coordinates can be passed as extra keyword arguments (kwargs) to this method.

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 will be provided if none are given.

Parameters:

regionlist = [W, E, S, N]

The west, east, south, and north boundaries of a given region. Use only if coordinates is None.

shapetuple = (n_north, n_east) or None

The number of points in the South-North and West-East directions, respectively. Use only if coordinates is None.

spacingtuple = (s_north, s_east) or None

The grid spacing in the South-North and West-East directions, respectively. Use only if coordinates is None.

dimslist or None

The names of the northing and easting data dimensions, respectively, in the output grid. Default is determined from the dims attribute of the class. Must be defined in the following order: northing dimension, easting dimension. NOTE: This is an exception to the “easting” then “northing” pattern but is required for compatibility with xarray.

data_namesstr, list or 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.

projectioncallable 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.

coordinatestuple of arrays

Tuple of arrays containing the coordinates of the grid in the following order: (easting, northing, vertical, …). The easting and northing arrays could be 1d or 2d arrays, if they are 2d they must be part of a meshgrid. If coordinates are passed, region, shape, and spacing are ignored.

Returns:

gridxarray.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.

VectorSpline2D.jacobian(coordinates, force_coords, dtype='float64')

Make the Jacobian matrix for the 2D coupled elastic deformation.

The Jacobian is segmented into 4 parts, each relating a force component to a data component [SandwellWessel2016]:

| J_ee  J_ne |*|f_e| = |d_e|
| J_ne  J_nn | |f_n|   |d_n|

The forces and data are assumed to be stacked into 1D arrays with the east component on top of the north component.

Parameters:

coordinatestuple 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.

force_coordstuple of arrays

Arrays with the coordinates for the forces. Should be in the same order as the coordinate arrays.

dtypestr or numpy dtype

The type of the Jacobian array.

Returns:

jacobian2D array

The (n_data*2, n_forces*2) Jacobian matrix.

VectorSpline2D.predict(coordinates)

Evaluate the fitted gridder on the given set of points.

Requires a fitted estimator (see fit).

Parameters:

coordinatestuple 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:

datatuple of arrays

A tuple (east_component, north_component) of arrays with the predicted vector data values at each point.

VectorSpline2D.profile(point1, point2, size, dims=None, data_names=None, projection=None, **kwargs)

Interpolate data along a profile between two points.

Generates the profile along a straight line assuming Cartesian distances. Point coordinates are generated by verde.profile_coordinates. Other arguments for this function can be passed as extra keyword arguments (kwargs) to this method.

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 Cartesian distance from point1 for each data point in the profile.

To specify point1 and point2 in a coordinate system that would require projection to Cartesian (geographic longitude and latitude, for example), use the projection argument. With this option, the input points will be projected using the given projection function prior to computations. The generated Cartesian profile coordinates will be projected back to the original coordinate system. Note that the profile points are evenly spaced in projected coordinates, not the original system (e.g., geographic).

Warning

The profile calculation method with a projection has changed in Verde 1.4.0. Previous versions generated coordinates (assuming they were Cartesian) and projected them afterwards. This led to “distances” being incorrectly handled and returned in unprojected coordinates. For example, if projection is from geographic to Mercator, the distances would be “angles” (incorrectly calculated as if they were Cartesian). After 1.4.0, point1 and point2 are projected prior to generating coordinates for the profile, guaranteeing that distances are properly handled in a Cartesian system. With this change, the profile points are now evenly spaced in projected coordinates and the distances are returned in projected coordinates as well.

Parameters:

point1tuple

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

point2tuple

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

sizeint

The number of points to generate.

dimslist or None

The names of the northing and easting data dimensions, respectively, in the output dataframe. Default is determined from the dims attribute of the class. Must be defined in the following order: northing dimension, easting dimension. NOTE: This is an exception to the “easting” then “northing” pattern but is required for compatibility with xarray.

data_namesstr, list or 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.

projectioncallable or None

If not None, then should be a callable object projection(easting, northing, inverse=False) -> (proj_easting, proj_northing) that takes in easting and northing coordinate arrays and returns projected northing and easting coordinate arrays. Should also take an optional keyword argument inverse (default to False) that if True will calculate the inverse transform instead. This function will be used to project the profile end points before generating coordinates and passing them into predict. It will also be used to undo the projection of the coordinates before returning the results.

Returns:

tablepandas.DataFrame

The interpolated values along the profile.

VectorSpline2D.scatter(region=None, size=300, random_state=0, dims=None, data_names=None, projection=None, **kwargs)

Interpolate values onto a random scatter of points.

Point coordinates are generated by verde.scatter_points. Other arguments for this function can be passed as extra keyword arguments (kwargs) to this method.

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.

Warning

The scatter method is deprecated and will be removed in Verde 2.0.0. Use verde.scatter_points and the predict method instead.

Parameters:

regionlist = [W, E, S, N]

The west, east, south, and north boundaries of a given region.

sizeint

The number of points to generate.

random_statenumpy.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).

dimslist or None

The names of the northing and easting data dimensions, respectively, in the output dataframe. Default is determined from the dims attribute of the class. Must be defined in the following order: northing dimension, easting dimension. NOTE: This is an exception to the “easting” then “northing” pattern but is required for compatibility with xarray.

data_namesstr, list or 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.

projectioncallable 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:

tablepandas.DataFrame

The interpolated values on a random set of points.

VectorSpline2D.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.

Warning

The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly. The negative version will be used to maintain the behaviour of larger scores being better, which is more compatible with current model selection code.

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

Parameters:

coordinatestuple of arrays

Arrays with the coordinates of each data point. Should be in the following order: (easting, northing, vertical, …). For the specific definition of coordinate systems and what these names mean, see the class docstring.

dataarray 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).

weightsNone 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:

scorefloat

The R^2 score

VectorSpline2D.set_fit_request(*, coordinates: bool | None | str = '$UNCHANGED$', data: bool | None | str = '$UNCHANGED$', weights: bool | None | str = '$UNCHANGED$') → VectorSpline2D

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it to fit.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

coordinatesstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for coordinates parameter in fit.

datastr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for data parameter in fit.

weightsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for weights parameter in fit.

Returns:

selfobject

The updated object.

VectorSpline2D.set_params(**params)

Set the parameters of this estimator.

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

Parameters:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.

VectorSpline2D.set_predict_request(*, coordinates: bool | None | str = '$UNCHANGED$') → VectorSpline2D

Request metadata passed to the predict method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to predict if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it to predict.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

coordinatesstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for coordinates parameter in predict.

Returns:

selfobject

The updated object.

VectorSpline2D.set_score_request(*, coordinates: bool | None | str = '$UNCHANGED$', data: bool | None | str = '$UNCHANGED$', weights: bool | None | str = '$UNCHANGED$') → VectorSpline2D

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it to score.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

coordinatesstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for coordinates parameter in score.

datastr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for data parameter in score.

weightsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for weights parameter in score.

Returns:

selfobject

The updated object.

---

Examples using verde.VectorSpline2D

Vector Data

Vector Data