gstools.krige.Universal

class gstools.krige.Universal(model, cond_pos, cond_val, drift_functions, normalizer=None, trend=None, exact=False, cond_err='nugget', pseudo_inv=True, pseudo_inv_type='pinv', fit_normalizer=False, fit_variogram=False)[source]

Bases: Krige

Universal kriging.

Universal kriging is used to interpolate given data with a variable mean, that is determined by a functional drift.

This estimator is set to be unbiased by default. This means, that the weights in the kriging equation sum up to 1. Consequently no constant function needs to be given for a constant drift, since the unbiased condition is applied to all given drift functions.

Parameters:

model (CovModel) – Covariance Model used for kriging.
cond_pos (list) – tuple, containing the given condition positions (x, [y, z])
cond_val (numpy.ndarray) – the values of the conditions (nan values will be ignored)
drift_functions (list of callable, str or int) – Either a list of callable functions, an integer representing the polynomial order of the drift or one of the following strings:
- “linear” : regional linear drift (equals order=1)
- “quadratic” : regional quadratic drift (equals order=2)
normalizer (None or Normalizer, optional) – Normalizer to be applied to the input data to gain normality. The default is None.
trend (None or float or callable, optional) – A callable trend function. Should have the signature: f(x, [y, z, …]) This is used for detrended kriging, where the trended is subtracted from the conditions before kriging is applied. This can be used for regression kriging, where the trend function is determined by an external regression algorithm. If no normalizer is applied, this behaves equal to ‘mean’. The default is None.
exact (bool, optional) – Whether the interpolator should reproduce the exact input values. If False, cond_err is interpreted as measurement error at the conditioning points and the result will be more smooth. Default: False
cond_err (str, :class float or list, optional) – The measurement error at the conditioning points. Either “nugget” to apply the model-nugget, a single value applied to all points or an array with individual values for each point. The measurement error has to be <= nugget. The “exact=True” variant only works with “cond_err=’nugget’”. Default: “nugget”
pseudo_inv (bool, optional) – Whether the kriging system is solved with the pseudo inverted kriging matrix. If True, this leads to more numerical stability and redundant points are averaged. But it can take more time. Default: True
pseudo_inv_type (str or callable, optional) –

Here you can select the algorithm to compute the pseudo-inverse matrix:
- “pinv”: use pinv from scipy which uses SVD
- “pinvh”: use pinvh from scipy which uses eigen-values
If you want to use another routine to invert the kriging matrix, you can pass a callable which takes a matrix and returns the inverse. Default: “pinv”
fit_normalizer (bool, optional) – Whether to fit the data-normalizer to the given conditioning data. Default: False
fit_variogram (bool, optional) – Whether to fit the given variogram model to the data. Directional variogram fitting is triggered by setting any anisotropy factor of the model to anything unequal 1 but the main axes of correlation are taken from the model rotation angles. If the model is a spatio-temporal latlon model, this will raise an error. This assumes the sill to be the data variance and with standard bins provided by the standard_bins routine. Default: False

Attributes:

all_fields: list: All fields as stacked list.
cond_err: list: The measurement errors at the condition points.
cond_ext_drift: numpy.ndarray: The ext. drift at the conditions.
cond_mean: numpy.ndarray: Trend at the conditions.
cond_no: int: The number of the conditions.
cond_pos: list: The position tuple of the conditions.
cond_trend: numpy.ndarray: Trend at the conditions.
cond_val: list: The values of the conditions.
dim: int: Dimension of the field.
drift_functions: list of callable: The drift functions.
drift_no: int: Number of drift values per point.
exact: bool: Whether the interpolator is exact.
ext_drift_no: int: Number of external drift values per point.
field_names: list: Names of present fields.
field_shape: tuple: The shape of the field.
has_const_mean: bool: Whether the field has a constant mean or not.
int_drift_no: int: Number of internal drift values per point.
krige_size: int: Size of the kriging system.
latlon: bool: Whether the field depends on geographical coords.
mean: float or callable: The mean of the field.
mesh_type: str: The mesh type of the field.
model: CovModel: The covariance model of the field.
name: str: The name of the class.
normalizer: Normalizer: Normalizer of the field.
pos: tuple: The position tuple of the field.
pseudo_inv: bool: Whether pseudo inverse matrix is used.
pseudo_inv_type: str: Method selector for pseudo inverse calculation.
temporal: bool: Whether the field depends on time.
trend: float or callable: The trend of the field.
unbiased: bool: Whether the kriging is unbiased or not.
value_type: str: Type of the field values (scalar, vector).

Methods

`__call__`([pos, mesh_type, ext_drift, ...])	Generate the kriging field.
`delete_fields`([select])	Delete selected fields.
`get_mean`([post_process])	Calculate the estimated mean of the detrended field.
`get_store_config`(store[, default, fld_cnt])	Get storage configuration from given selection.
`mesh`(mesh[, points, direction, name])	Generate a field on a given meshio, ogs5py or PyVista mesh.
`plot`([field, fig, ax])	Plot the spatial random field.
`post_field`(field[, name, process, save])	Postprocessing field values.
`pre_pos`([pos, mesh_type, info])	Preprocessing positions and mesh_type.
`set_condition`([cond_pos, cond_val, ...])	Set the conditions for kriging.
`set_drift_functions`([drift_functions])	Set the drift functions for universal kriging.
`set_pos`(pos[, mesh_type, info])	Set positions and mesh_type.
`structured`(args, *kwargs)	Generate a field on a structured mesh.
`to_pyvista`([field_select, fieldname])	Create a VTK/PyVista grid of the stored field.
`transform`(method[, field, store, process])	Apply field transformation.
`unstructured`(args, *kwargs)	Generate a field on an unstructured mesh.
`vtk_export`(filename[, field_select, fieldname])	Export the stored field to vtk.

__call__(pos=None, mesh_type='unstructured', ext_drift=None, chunk_size=None, only_mean=False, return_var=True, post_process=True, store=True)

Generate the kriging field.

The field is saved as self.field and is also returned. The error variance is saved as self.krige_var and is also returned.

Parameters:

pos (list, optional) – the position tuple, containing main direction and transversal directions (x, [y, z])
mesh_type (str, optional) – ‘structured’ / ‘unstructured’
ext_drift (numpy.ndarray or None, optional) – the external drift values at the given positions (only for EDK)
chunk_size (int, optional) – Chunk size to cut down the size of the kriging system to prevent memory errors. Default: None
only_mean (bool, optional) – Whether to only calculate the mean of the kriging field. Default: False
return_var (bool, optional) – Whether to return the variance along with the field. Default: True
post_process (bool, optional) – Whether to apply mean, normalizer and trend to the field. Default: True
store (str or bool or list, optional) – Whether to store kriging fields (True/False) with default name or with specified names. The default is True for default names [“field”, “krige_var”] or “mean_field” if only_mean=True.

Returns:

field (numpy.ndarray) – the kriged field or mean_field
krige_var (numpy.ndarray, optional) – the kriging error variance (if return_var is True and only_mean is False)

delete_fields(select=None): Delete selected fields.

get_mean(post_process=True)

Calculate the estimated mean of the detrended field.

Parameters:: post_process (bool, optional) – Whether to apply field-mean and normalizer. Default: True
Returns:: mean – Mean of the Kriging System.
Return type:: float or None

Notes

Only not None if the Kriging System has a constant mean. This means, no drift is given and the given field-mean is constant. The result is neglecting a potential given trend.

get_store_config(store, default=None, fld_cnt=None)

Get storage configuration from given selection.

Parameters:

store (str or bool or list, optional) – Whether to store fields (True/False) with default names or with specified names. The default is True for default names.
default (str or list, optional) – Default field names. The default is “field”.
fld_cnt (None or int, optional) – Number of fields when using lists. The default is None.

Returns:

name (str or list) – Name(s) of field.
save (bool or list) – Whether to save field(s).

mesh(mesh, points='centroids', direction='all', name='field', **kwargs)

Generate a field on a given meshio, ogs5py or PyVista mesh.

Parameters:

mesh (meshio.Mesh or ogs5py.MSH or PyVista mesh) – The given mesh
points (str, optional) – The points to evaluate the field at. Either the “centroids” of the mesh cells (calculated as mean of the cell vertices) or the “points” of the given mesh. Default: “centroids”
direction (str or list, optional) – Here you can state which direction should be chosen for lower dimension. For example, if you got a 2D mesh in xz direction, you have to pass “xz”. By default, all directions are used. One can also pass a list of indices. Default: “all”
name (str or list of str, optional) – Name(s) to store the field(s) in the given mesh as point_data or cell_data. If to few names are given, digits will be appended. Default: “field”
**kwargs – Keyword arguments forwarded to __call__.

Notes

This will store the field in the given mesh under the given name, if a meshio or PyVista mesh was given.

See:

meshio: https://github.com/nschloe/meshio
ogs5py: https://github.com/GeoStat-Framework/ogs5py
PyVista: https://github.com/pyvista/pyvista

plot(field='field', fig=None, ax=None, **kwargs)

Plot the spatial random field.

Parameters:

field (str, optional) – Field that should be plotted. Default: “field”
fig (Figure or None) – Figure to plot the axes on. If None, a new one will be created. Default: None
ax (Axes or None) – Axes to plot on. If None, a new one will be added to the figure. Default: None
**kwargs – Forwarded to the plotting routine.

post_field(field, name='field', process=True, save=True)

Postprocessing field values.

Parameters:

field (numpy.ndarray) – Field values.
name (str, optional) – Name. to store the field. The default is “field”.
process (bool, optional) – Whether to process field to apply mean, normalizer and trend. The default is True.
save (bool, optional) – Whether to store the field under the given name. The default is True.

Returns:

field – Processed field values.

Return type:

numpy.ndarray

pre_pos(pos=None, mesh_type='unstructured', info=False)

Preprocessing positions and mesh_type.

Parameters:

pos (iterable) – the position tuple, containing main direction and transversal directions
mesh_type (str, optional) – ‘structured’ / ‘unstructured’ Default: “unstructured”
info (bool, optional) – Whether to return information

Returns:

iso_pos ((d, n), numpy.ndarray) – Isometrized position tuple.
shape (tuple) – Shape of the resulting field.
info (dict, optional) – Information about settings.

Warning

When setting a new position tuple that differs from the present one, all stored fields will be deleted.

set_condition(cond_pos=None, cond_val=None, ext_drift=None, cond_err=None, fit_normalizer=False, fit_variogram=False)

Set the conditions for kriging.

This method could also be used to update the kriging setup, when properties were changed. Then you can call it without arguments.

Parameters:

cond_pos (list, optional) – the position tuple of the conditions (x, [y, z]). Default: current.
cond_val (numpy.ndarray, optional) – the values of the conditions (nan values will be ignored). Default: current.
ext_drift (numpy.ndarray or None, optional) – the external drift values at the given conditions (only for EDK) For multiple external drifts, the first dimension should be the index of the drift term. When passing None, the extisting external drift will be used.
cond_err (str, :class float, list, optional) – The measurement error at the conditioning points. Either “nugget” to apply the model-nugget, a single value applied to all points or an array with individual values for each point. The measurement error has to be <= nugget. The “exact=True” variant only works with “cond_err=’nugget’”. Default: “nugget”
fit_normalizer (bool, optional) – Whether to fit the data-normalizer to the given conditioning data. Default: False
fit_variogram (bool, optional) – Whether to fit the given variogram model to the data. Directional variogram fitting is triggered by setting any anisotropy factor of the model to anything unequal 1 but the main axes of correlation are taken from the model rotation angles. If the model is a spatio-temporal latlon model, this will raise an error. This assumes the sill to be the data variance and with standard bins provided by the standard_bins routine. Default: False

set_drift_functions(drift_functions=None)

Set the drift functions for universal kriging.

Parameters:

drift_functions (list of callable, str or int) – Either a list of callable functions, an integer representing the polynomial order of the drift or one of the following strings:

“linear” : regional linear drift (equals order=1)

“quadratic” : regional quadratic drift (equals order=2)

Raises:

ValueError – If the given drift functions are not callable.

set_pos(pos, mesh_type='unstructured', info=False)

Set positions and mesh_type.

Parameters:

pos (iterable) – the position tuple, containing main direction and transversal directions
mesh_type (str, optional) – ‘structured’ / ‘unstructured’ Default: “unstructured”
info (bool, optional) – Whether to return information

Returns:

info – Information about settings.

Return type:

dict, optional

Warning

When setting a new position tuple that differs from the present one, all stored fields will be deleted.

structured(*args, **kwargs)

Generate a field on a structured mesh.

See __call__

to_pyvista(field_select='field', fieldname='field')

Create a VTK/PyVista grid of the stored field.

Parameters:

field_select (str, optional) – Field that should be stored. Can be: “field”, “raw_field”, “krige_field”, “err_field” or “krige_var”. Default: “field”
fieldname (str, optional) – Name of the field in the VTK file. Default: “field”

transform(method, field='field', store=True, process=False, **kwargs)

Apply field transformation.

Parameters:

method (str) – Method to use. See gstools.transform for available transformations.
field (str, optional) – Name of field to be transformed. The default is “field”.
store (str or bool, optional) – Whether to store field inplace (True/False) or under a given name. The default is True.
process (bool, optional) – Whether to process in/out fields with trend, normalizer and mean of given Field instance. The default is False.
**kwargs – Keyword arguments forwarded to selected method.

Raises:

ValueError – When method is unknown.

Returns:

Transformed field.

Return type:

numpy.ndarray

unstructured(*args, **kwargs)

Generate a field on an unstructured mesh.

See __call__

vtk_export(filename, field_select='field', fieldname='field')

Export the stored field to vtk.

Parameters:

filename (str) – Filename of the file to be saved, including the path. Note that an ending (.vtr or .vtu) will be added to the name.
field_select (str, optional) – Field that should be stored. Can be: “field”, “raw_field”, “krige_field”, “err_field” or “krige_var”. Default: “field”
fieldname (str, optional) – Name of the field in the VTK file. Default: “field”

property all_fields

All fields as stacked list.

Type:: list

property cond_err

The measurement errors at the condition points.

Type:: list

property cond_ext_drift

The ext. drift at the conditions.

Type:: numpy.ndarray

property cond_mean

Trend at the conditions.

Type:: numpy.ndarray

property cond_no

The number of the conditions.

Type:: int

property cond_pos

The position tuple of the conditions.

Type:: list

property cond_trend

Trend at the conditions.

Type:: numpy.ndarray

property cond_val

The values of the conditions.

Type:: list

default_field_names = ['field', 'krige_var', 'mean_field']

Default field names.

Type:: list

property dim

Dimension of the field.

Type:: int

property drift_functions

The drift functions.

Type:: list of callable

property drift_no

Number of drift values per point.

Type:: int

property exact

Whether the interpolator is exact.

Type:: bool

property ext_drift_no

Number of external drift values per point.

Type:: int

property field_names

Names of present fields.

Type:: list

property field_shape

The shape of the field.

Type:: tuple

property has_const_mean

Whether the field has a constant mean or not.

Type:: bool

property int_drift_no

Number of internal drift values per point.

Type:: int

property krige_size

Size of the kriging system.

Type:: int

property latlon

Whether the field depends on geographical coords.

Type:: bool

property mean

The mean of the field.

Type:: float or callable

property mesh_type

The mesh type of the field.

Type:: str

property model

The covariance model of the field.

Type:: CovModel

property name

The name of the class.

Type:: str

property normalizer

Normalizer of the field.

Type:: Normalizer

property pos

The position tuple of the field.

Type:: tuple

property pseudo_inv

Whether pseudo inverse matrix is used.

Type:: bool

property pseudo_inv_type

Method selector for pseudo inverse calculation.

Type:: str

property temporal

Whether the field depends on time.

Type:: bool

property trend

The trend of the field.

Type:: float or callable

property unbiased

Whether the kriging is unbiased or not.

Type:: bool

valid_value_types = ['scalar']

valid field value types.

Type:: list of str

property value_type

Type of the field values (scalar, vector).

Type:: str