API for landlab.grid.voronoi#

Python implementation of VoronoiDelaunayGrid, a class used to create and manage unstructured, irregular grids for 2D numerical models.

Do NOT add new documentation here. Grid documentation is now built in a semi- automated fashion. To modify the text seen on the web, edit the files docs/text_for_[gridfile].py.txt.

class VoronoiDelaunayGrid(x=None, y=None, reorient_links=True, xy_of_reference=(0.0, 0.0), xy_axis_name=('x', 'y'), xy_axis_units='-')[source]#

This inherited class implements an unstructured grid in which cells are Voronoi polygons and nodes are connected by a Delaunay triangulation. Uses scipy.spatial module to build the triangulation.

Create an unstructured grid from points whose coordinates are given by the arrays x, y.

Returns:

A newly-created grid.

Return type:

VoronoiDelaunayGrid

Examples

>>> from numpy.random import rand
>>> from landlab.grid import VoronoiDelaunayGrid
>>> x, y = rand(25), rand(25)
>>> vmg = VoronoiDelaunayGrid(x, y)  # node_x_coords, node_y_coords
>>> vmg.number_of_nodes
25

>>> import numpy as np
>>> x = [0, 0.1, 0.2, 0.3,
...      1, 1.1, 1.2, 1.3,
...      2, 2.1, 2.2, 2.3,]
>>> y = [0, 1, 2, 3,
...      0, 1, 2, 3,
...      0, 1, 2, 3]
>>> vmg = VoronoiDelaunayGrid(x, y)
>>> vmg.node_x
array([ 0. ,  1. ,  2. ,
0.1,  1.1,  2.1,
0.2,  1.2,  2.2,
0.3,  1.3,  2.3])
>>> vmg.node_y
array([ 0.,  0.,  0.,
1.,  1.,  1.,
2.,  2.,  2.,
3.,  3.,  3.])
array([[ 1,  3, -1, -1, -1, -1],
[ 2,  4,  3,  0, -1, -1],
[ 5,  4,  1, -1, -1, -1],
[ 4,  6,  0,  1, -1, -1],
[ 5,  7,  6,  3,  1,  2],
[ 8,  7,  4,  2, -1, -1],
[ 7,  9,  3,  4, -1, -1],
[ 8, 10,  9,  6,  4,  5],
[11, 10,  7,  5, -1, -1],
[10,  6,  7, -1, -1, -1],
[11,  9,  7,  8, -1, -1],
[10,  8, -1, -1, -1, -1]])


Create a Voronoi Delaunay grid from a set of points.

Create an unstructured grid from points whose coordinates are given by the arrays x, y.

Parameters:
• x (array_like) – x-coordinate of points

• y (array_like) – y-coordinate of points

• xy_of_reference (tuple, optional) – Coordinate value in projected space of (0., 0.) Default is (0., 0.)

Returns:

A newly-created grid.

Return type:

VoronoiDelaunayGrid

Examples

>>> from numpy.random import rand
>>> from landlab.grid import VoronoiDelaunayGrid
>>> x, y = rand(25), rand(25)
>>> vmg = VoronoiDelaunayGrid(x, y)  # node_x_coords, node_y_coords
>>> vmg.number_of_nodes
25


Indicates a node is bad index.

Indicates a link is active, and can carry flux

Indicates a link has a fixed gradient value, and behaves as a boundary

Indicates a link is inactive, and cannot carry flux

BC_NODE_IS_CLOSED = 4#

Indicates a boundary node is closed

BC_NODE_IS_CORE = 0#

Indicates a node is core.

Indicates a boundary node has a fixed gradient.

BC_NODE_IS_FIXED_VALUE = 1#

Indicates a boundary node has a fixed value.

BC_NODE_IS_LOOPED = 3#

Indicates a boundary node is wrap-around.

VALID_LOCATIONS = ('node', 'link', 'patch', 'corner', 'face', 'cell', 'grid')#

Grid elements on which fields can be placed.

__getitem__(name)#

Get the collection of fields from the named group.

__init__(x=None, y=None, reorient_links=True, xy_of_reference=(0.0, 0.0), xy_axis_name=('x', 'y'), xy_axis_units='-')[source]#

Create a Voronoi Delaunay grid from a set of points.

Create an unstructured grid from points whose coordinates are given by the arrays x, y.

Parameters:
• x (array_like) – x-coordinate of points

• y (array_like) – y-coordinate of points

• xy_of_reference (tuple, optional) – Coordinate value in projected space of (0., 0.) Default is (0., 0.)

Returns:

A newly-created grid.

Return type:

VoronoiDelaunayGrid

Examples

>>> from numpy.random import rand
>>> from landlab.grid import VoronoiDelaunayGrid
>>> x, y = rand(25), rand(25)
>>> vmg = VoronoiDelaunayGrid(x, y)  # node_x_coords, node_y_coords
>>> vmg.number_of_nodes
25


Adjacent corners for each grid corner.

Adjacent nodes for each grid node.

For each grid node, get the adjacent nodes ordered counterclockwise starting from the positive x axis.

Examples

>>> from landlab import RasterModelGrid, HexModelGrid
>>> grid = RasterModelGrid((4, 5))

>>> grid.active_adjacent_nodes_at_node[(-1, 6, 2), ]
array([[-1, -1, -1, -1],
[ 7, 11,  5,  1],
[-1,  7, -1, -1]])


Setting a node to closed causes all links touching it to be inactive.

>>> grid.status_at_node[6] = grid.BC_NODE_IS_CLOSED
array([[-1, -1, -1, -1],
[-1, -1, -1, -1],
[-1,  7, -1, -1]])

>>> grid.active_adjacent_nodes_at_node[7]
array([ 8, 12, -1,  2])
array([-1,  7, -1, -1])

>>> grid = HexModelGrid((3, 2))
>>> grid.status_at_node[0] = grid.BC_NODE_IS_CLOSED
array([[-1, -1, -1, -1, -1, -1],
[-1,  3, -1, -1, -1, -1],
[ 3, -1, -1, -1, -1, -1],
[ 4,  6,  5,  2, -1,  1],
[-1,  3, -1, -1, -1, -1],
[-1, -1,  3, -1, -1, -1],
[-1,  3, -1, -1, -1, -1]])

property active_face_dirs_at_corner#

Return face directions into each corner.

property active_faces#

Get array of active faces.

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> grid.active_faces
array([0, 1, 2, 3, 4, 5, 6])

>>> grid.status_at_node[6] = grid.BC_NODE_IS_CLOSED
>>> grid.active_faces
array([0, 2, 5])


Return link directions into each node.

A value of 1 indicates a link points toward a given node, while a value of -1 indicates a link points away from a node. Note that inactive links have a value of 0, but active and fixed links are both reported normally.

Returns:

Link directions relative to the nodes of a grid. The shape of the matrix will be number of nodes by the maximum number of links per node. A zero indicates no link at this position.

Return type:

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))

.--->.--->.--->.
^    ^    ^    ^
|    |    |    |
.--->5--->.--->.
^    ^    ^    ^
|    |    |    |
.--->.--->.--->.

>>> grid.active_link_dirs_at_node[5]
array([-1, -1,  1,  1], dtype=int8)


If we set the nodes along the left edge to be closed, the links attached to those nodes become inactive and so their directions are reported as 0.

>>> grid.status_at_node[grid.nodes_at_left_edge] = grid.BC_NODE_IS_CLOSED
array([[ 0,  0,  0,  0], [ 0, -1,  0,  0], [ 0, -1,  0,  0], [ 0,  0,  0,  0],
[ 0,  0,  0,  0], [-1, -1,  0,  1], [-1, -1,  1,  1], [ 0,  0,  1,  0],
[ 0,  0,  0,  0], [ 0,  0,  0,  1], [ 0,  0,  0,  1], [ 0,  0,  0,  0]],
dtype=int8)


Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
array([ 4,  5,  7,  8,  9, 11, 12])


Create and add an uninitialized array of values to the field.

Create a new array of the data field size, without initializing entries, and add it to the field as name. The units keyword gives the units of the new fields as a string. Remaining keyword arguments are the same as that for the equivalent numpy function.

This method is not valid for the group grid.

Parameters:
• name (str) – Name of the new field to add.

• at (str, optional) – Grid location to store values. If not given, values are assumed to be on node.

• units (str, optional) – Optionally specify the units of the field.

• clobber (bool, optional) – Raise an exception if adding to an already existing field.

Returns:

A reference to the newly-created array.

Return type:

numpy.ndarray

numpy.empty

See for a description of optional keywords.

empty

Equivalent method that does not initialize the new array.

zeros

Equivalent method that initializes the data to 0.

add_field(name, value_array, at='node', units='-', copy=False, clobber=False)#

Add an array of values to the field.

Add an array of data values to a collection of fields and associate it with the key, name. Use the copy keyword to, optionally, add a copy of the provided array.

In the case of adding to the collection grid, the added field is a numpy scalar rather than a numpy array.

Parameters:
• name (str) – Name of the new field to add.

• value_array (numpy.array) – Array of values to add to the field.

• at (str, optional) – Grid location to store values. If not given, values are assumed to be on node.

• units (str, optional) – Optionally specify the units of the field.

• copy (bool, optional) – If True, add a copy of the array to the field. Otherwise save add a reference to the array.

• clobber (bool, optional) – Raise an exception if adding to an already existing field.

Returns:

The data array added to the field. Depending on the copy keyword, this could be a copy of value_array or value_array itself.

Return type:

numpy.ndarray

Raises:

ValueError – If value_array has a size different from the field.

Examples

>>> import numpy as np
>>> from landlab.field import GraphFields
>>> field = GraphFields()
>>> field.new_field_location("node", 4)
>>> values = np.ones(4, dtype=int)
array([1, 1, 1, 1])


A new field is added to the collection of fields. The saved value array is the same as the one initially created.

>>> field.at_node["topographic__elevation"] is values
True


If you want to save a copy of the array, use the copy keyword. In addition, adding values to an existing field will remove the reference to the previously saved array. The clobber=False keyword changes this behavior to raise an exception in such a case.

>>> field.add_field(
...     "topographic__elevation", values, at="node", copy=True, clobber=True
... )
array([1, 1, 1, 1])
>>> field.at_node["topographic__elevation"] is values
False
...     "topographic__elevation", values, at="node", clobber=False
... )
Traceback (most recent call last):
FieldError: topographic__elevation


Create and add an array of values, fill with fill_value.

Parameters:
• name (str) – Name of the new field to add.

• fill_value (scalar) – Fill value.

• at (str, optional) – Grid location to store values. If not given, values are assumed to be on node.

• units (str, optional) – Optionally specify the units of the field.

• copy (bool, optional) – If True, add a copy of the array to the field. Otherwise save add a reference to the array.

• clobber (bool, optional) – Raise an exception if adding to an already existing field.

Returns:

A reference to the newly-created array.

Return type:

numpy.ndarray

Create and add an array of values, initialized to 1, to the field.

Create a new array of the data field size, filled with ones, and add it to the field as name. The units keyword gives the units of the new fields as a string. Remaining keyword arguments are the same as that for the equivalent numpy function.

This method is not valid for the group grid.

Parameters:
• name (str) – Name of the new field to add.

• at (str, optional) – Grid location to store values. If not given, values are assumed to be on node.

• units (str, optional) – Optionally specify the units of the field.

• clobber (bool, optional) – Raise an exception if adding to an already existing field.

Returns:

A reference to the newly-created array.

Return type:

numpy.ndarray

numpy.ones

See for a description of optional keywords.

add_empty

Equivalent method that does not initialize the new array.

add_zeros

Equivalent method that initializes the data to 0.

Examples

Add a new, named field to a collection of fields.

>>> from landlab.field import GraphFields
>>> field = GraphFields()
>>> field.new_field_location('node', 4)
array([ 1.,  1.,  1.,  1.])
>>> list(field.keys('node'))
['topographic__elevation']
>>> field['node']['topographic__elevation']
array([ 1.,  1.,  1.,  1.])
>>> field.at_node['topographic__elevation']
array([ 1.,  1.,  1.,  1.])


Create and add an array of values, initialized to 0, to the field.

Create a new array of the data field size, filled with zeros, and add it to the field as name. The units keyword gives the units of the new fields as a string. Remaining keyword arguments are the same as that for the equivalent numpy function.

Parameters:
• name (str) – Name of the new field to add.

• at (str, optional) – Grid location to store values. If not given, values are assumed to be on node.

• units (str, optional) – Optionally specify the units of the field.

• clobber (bool, optional) – Raise an exception if adding to an already existing field.

Returns:

A reference to the newly-created array.

Return type:

array

numpy.zeros

See for a description of optional keywords.

add_empty

Equivalent method that does not initialize the new array.

add_ones

Equivalent method that initializes the data to 1.

Examples

>>> from landlab.graph import Graph


First, a simple example with no diagonals.

>>> node_x, node_y = [0, 0, 0, 1, 1, 1, 2, 2, 2], [0, 1, 2, 0, 1, 2, 0, 1, 2]
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8))
array([[ 1,  3, -1, -1],
[ 2,  4,  0, -1],
[ 5,  1, -1, -1],
[ 4,  6,  0, -1],
[ 5,  7,  3,  1],
[ 8,  4,  2, -1],
[ 7,  3, -1, -1],
[ 8,  6,  4, -1],
[ 7,  5, -1, -1]])


Next, we add the diagonal from node 0 to node 4.

>>> node_x, node_y = [0, 0, 0, 1, 1, 1, 2, 2, 2], [0, 1, 2, 0, 1, 2, 0, 1, 2]
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8),
...          (0, 4))
array([[ 1,  4,  3, -1, -1],
[ 2,  4,  0, -1, -1],
[ 5,  1, -1, -1, -1],
[ 4,  6,  0, -1, -1],
[ 5,  7,  3,  0,  1],
[ 8,  4,  2, -1, -1],
[ 7,  3, -1, -1, -1],
[ 8,  6,  4, -1, -1],
[ 7,  5, -1, -1, -1]])

property all_corner_azimuths_map#

Get azimuths from every corner to every other corner.

property all_corner_distances_map#

Get distances from every corner to every other corner.

property all_node_azimuths_map#

Get azimuths from every node to every other node.

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> angles = grid.all_node_azimuths_map


The shape of the array is number_of_nodes by number_of_nodes and azimuth from a node to itself is zero.

>>> angles.shape == (grid.number_of_nodes, grid.number_of_nodes)
True
>>> angles.diagonal()
array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])


Angles are measured in radians and increase clockwise starting at north.

>>> angles *= 180. / np.pi
>>> angles[0, :4]
array([  0.,  90.,  90.,  90.])
>>> angles[0, ::4]
array([ 0.,  0.,  0.])
>>> angles[0, ::5]
array([  0.,  45.,  45.])

property all_node_distances_map#

Get distances from every node to every other node.

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> distances = grid.all_node_distances_map


The shape of the array is number_of_nodes by number_of_nodes and distance from a node to itself is zero.

>>> distances.shape == (grid.number_of_nodes, grid.number_of_nodes)
True
>>> distances.diagonal()
array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])


The distances from the first node to all nodes in its row and all the nodes in its column.

>>> distances[0, :4]
array([ 0.,  1.,  2.,  3.])
>>> distances[0, ::4]
array([ 0.,  1.,  2.])

property angle_of_face#

Get the angle of each face.

Find and return the angle of a face about the corner at the face head.

Get the angle of each link.

Examples

>>> import numpy as np
>>> from landlab.graph import Graph

>>> node_x, node_y = ([0, 1, 2, 0, 1, 2],
...                   [0, 0, 0, 1, 1, 1])
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5))
>>> graph.angle_of_link * 180. / np.pi
array([  0.,   0.,  90.,  90.,  90.,   0.,   0.])


Examples

>>> from landlab import HexModelGrid
>>> import numpy as np

>>> grid = HexModelGrid((3, 2), node_layout="hex")
>>> np.round(grid.angle_of_link[:3] / np.pi * 3.0)
array([ 0., 2.,  1.])
array([ 3.,  5.,  4.])

property area_of_cell#

Get the area of each cell.

property area_of_patch#

Get the area of each patch.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1, 2, 2, 2]
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8))
>>> patches = ((0, 3, 5, 2), (1, 4, 6, 3))
>>> graph.area_of_patch
array([ 1.,  1.])

as_dataarray(name, at=None, time=None)#

Create an xarray DataArray representation of a grid field.

Parameters:
• name (str) – Name of a field. This can either be a canonical field name (of the form “at_<element>:<field_name>”, or just the field name. In the latter case, use the at keyword to specify where the field is defined.

• at (str, optional) – The grid elements on which the field is defined. Use this only if name is not a canonical field name that already contains the grid element.

Returns:

The field represented as a newly-created xarray DataArray.

Return type:

DataArray

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> _ = grid.add_full("elevation", 3.0, at="node")

>>> grid.as_dataarray("at_node:elevation")
<xarray.DataArray 'at_node:elevation' (node: 12)>
array([ 3.,  3.,  3.,  3.,  3.,  3.,  3.,  3.,  3.,  3.,  3.,  3.])
Dimensions without coordinates: node

>>> all(
...     grid.as_dataarray("at_node:elevation")
...     == grid.as_dataarray("elevation", at="node")
... )
True

as_dataset(include='*', exclude=None, time=None)#

Create an xarray Dataset representation of a grid.

This method creates a new xarray Dataset object that contains the grid’s data fields. A particular grid type (e.g. a RasterModelGrid) should define its own as_dataset method to represent that particular grid type as a Dataset and then call this method to add the data fields.

Parameters:
• include (str or iterable or str) – Glob-style patterns of fields to include in the dataset.

• exclude (str or iterable or str) – Glob-style patterns of fields to exclude from the dataset.

Returns:

An xarray Dataset representation of a ModelGrid.

Return type:

Dataset

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))


Add some fields to the grid. Notice that we have defined a field named “elevation” at both nodes and links.

>>> _ = grid.add_full("elevation", 3.0, at="node")
>>> _ = grid.add_full("temperature", 5.0, at="node")

>>> ds = grid.as_dataset()
>>> sorted(ds.dims.items())
[('dim', 2), ('link', 17), ('node', 12)]
>>> sorted([var for var in ds.data_vars if var.startswith("at_")])

>>> grid.event_layers.add(1.0, rho=0.5)

>>> ds = grid.as_dataset()
>>> sorted(ds.dims.items())
[('cell', 2), ('dim', 2), ('layer', 1), ('link', 17), ('node', 12)]
>>> sorted([var for var in ds.data_vars if var.startswith("at_")])
'at_node:elevation', 'at_node:temperature']

at_cell = {}#
at_corner = {}#
at_face = {}#
at_grid = {}#
property at_layer#

EventLayers for each cell.

at_node = {}#
at_patch = {}#
property axis_name#

Get the name of each coordinate axis.

Returns:

The names of each axis.

Return type:

tuple of str

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((4, 5))
>>> grid.axis_name
('x', 'y')
>>> grid.axis_name = ('lon', 'lat')
>>> grid.axis_name
('lon', 'lat')

property axis_units#

Get units for each axis.

Returns:

The units (as a string) for each of a grid’s coordinates.

Return type:

tuple of str

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5), xy_spacing=(3., 2.))
>>> mg.axis_units
('-', '-')
>>> mg.axis_units = ("degrees_north", "degrees_east")
>>> mg.axis_units
('degrees_north', 'degrees_east')
>>> mg.axis_units = "m"
>>> mg.axis_units
('m', 'm')

property boundary_corners#

Get array of boundary corners.

property boundary_nodes#

Get array of boundary nodes.

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> mg.boundary_nodes
array([ 0,  1,  2,  3,  4,  5,  9, 10, 14, 15, 16, 17, 18, 19])

calc_aspect_at_node(slope_component_tuple=None, elevs='topographic__elevation', unit='degrees', ignore_closed_nodes=True)#

Get array of aspect of a surface.

Calculates at returns the aspect of a surface. Aspect is returned as radians clockwise of north, unless input parameter units is set to ‘degrees’.

If slope_component_tuple is provided, i.e., (slope_x, slope_y), the aspect will be calculated from these data.

If it is not, it will be derived from elevation data at the nodes, which can either be a string referring to a grid field (default: ‘topographic__elevation’), or an nnodes-long numpy array of the values themselves.

If ignore_closed_nodes is False, all proximal elevation values will be used in the calculation. If True, only unclosed nodes are used.

Parameters:
• slope_component_tuple ((slope_x_array, slope_y_array) (optional)) – Tuple of components of slope in the x and y directions, defined on nodes, if already known. If not, provide elevs.

• elevs (str or array (optional)) – Node field name or node array of elevations. If slope_component_tuple is not provided, must be set, but unused otherwise.

• unit ({'degrees', 'radians'}) – Controls the unit that the aspect is returned as.

• ignore_closed_nodes (bool) – If True, do not incorporate values at closed nodes into the calc.

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 4))
>>> z = mg.node_x ** 2 + mg.node_y ** 2
>>> mg.calc_aspect_at_node(elevs=z)
array([ 225.        ,  240.16585039,  255.2796318 ,  258.69006753,
209.83414961,  225.        ,  243.54632481,  248.77808974,
194.7203682 ,  206.45367519,  225.        ,  231.94498651,
191.30993247,  201.22191026,  218.05501349,  225.        ])
>>> z = z.max() - z
>>> mg.calc_aspect_at_node(elevs=z)
array([ 45.        ,  60.16585039,  75.2796318 ,  78.69006753,
29.83414961,  45.        ,  63.54632481,  68.77808974,
14.7203682 ,  26.45367519,  45.        ,  51.94498651,
11.30993247,  21.22191026,  38.05501349,  45.        ])

>>> mg = RasterModelGrid((4, 4), xy_spacing=(3., 2.))
>>> z = mg.node_x ** 2 + mg.node_y ** 2
>>> mg.calc_aspect_at_node(elevs=z)
array([ 236.30993247,  247.52001262,  259.97326008,  262.40535663,
220.75264634,  234.41577266,  251.13402374,  255.29210302,
201.54258265,  215.47930877,  235.73541937,  242.24162456,
196.69924423,  209.43534223,  229.19345757,  236.30993247])


Note that a small amount of asymmetry arises at the grid edges due to the “missing” nodes beyond the edge of the grid.

Calculate differences of node values over links.

Calculates the difference in quantity node_values at each link in the grid.

Parameters:
• node_values (ndarray or field name) – Values at grid nodes.

• out (ndarray, optional) – Buffer to hold the result.

Returns:

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> rmg = RasterModelGrid((3, 3))
>>> z = np.zeros(9)
>>> z[4] = 1.
array([ 0.,  0.,  0.,  1.,  0.,  1., -1.,  0., -1.,  0.,  0.,  0.])

calc_distances_of_nodes_to_point(coord, get_az=None, node_subset=None, out_distance=None, out_azimuth=None)#

Get distances for nodes to a given point.

Returns an array of distances for each node to a provided point. If “get_az” is set to ‘angles’, returns both the distance array and an array of azimuths from up/north. If it is set to ‘displacements’, it returns the azimuths as a 2xnnodes array of x and y displacements. If it is not set, returns just the distance array.

If “node_subset” is set as an ID, or list/array/etc of IDs method returns just the distance (and optionally azimuth) for that node. Point is provided as a tuple (x,y).

If out_distance (& out_azimuth) are provided, these arrays are used to store the outputs. This is recommended for memory management reasons if you are working with node subsets.

Note

Angles are returned in radians but measured clockwise from north.

Parameters:
• coord (tuple of float) – Coodinates of point as (x, y).

• get_az ({None, 'angles', 'displacements'}, optional) – Optionally calculate azimuths as either angles or displacements. The calculated values will be returned along with the distances as the second item of a tuple.

• node_subset (array_like, optional) – Calculate distances on a subset of grid nodes. The default is to calculate distances from the provided points to all nodes.

• out_distance (array_like, optional) – If provided, put the calculated distances here. Otherwise, create a new array.

• out_azimuth (array_like, optional) – If provided, put the calculated distances here. Otherwise, create a new array.

Returns:

If get_az is None return the array of distances. Otherwise, return a tuple of distances and azimuths.

Return type:

ndarray or tuple of ndarray

Notes

Once you start working with node subsets in Landlab, which can change size between loops, it’s quite possible for Python’s internal memory management to crap out after large numbers of loops (~>10k). This is to do with the way it block allocates memory for arrays of differing lengths, then cannot free this memory effectively. The solution - as implemented here - is to pre-allocate all arrays as nnodes long, then only work with the first [len_subset] entries by slicing (in a pseudo-C-style). Care has to be taken not to “accidentally” allow Python to allocate a new array you don’t have control over. Then, to maintain efficient memory allocation, we create some “dummy” nnode-long arrays to store intermediate parts of the solution in.

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((4, 5))


Calculate distances from point at (2., 1.) to a subset of nodes on the grid.

>>> grid.calc_distances_of_nodes_to_point((2, 1),
...     node_subset=(2, 6, 7, 8, 12))
array([ 1.,  1.,  0.,  1.,  1.])


Calculate distances from a point to all nodes on the grid.

>>> dist = grid.calc_distances_of_nodes_to_point((2, 1))
>>> dist.shape == (grid.number_of_nodes, )
True
>>> dist.take((2, 6, 7, 8, 12))
array([ 1.,  1.,  0.,  1.,  1.])


Put the distances into a buffer.

>>> out = np.empty(grid.number_of_nodes, dtype=float)
>>> dist = grid.calc_distances_of_nodes_to_point((2, 1),
...     out_distance=out)
>>> out is dist
True
>>> out.take((2, 6, 7, 8, 12))
array([ 1.,  1.,  0.,  1.,  1.])


Calculate azimuths along with distances. The azimuths are calculated in radians but measured clockwise from north.

>>> (_, azim) = grid.calc_distances_of_nodes_to_point((2, 1),
...     get_az='angles')
>>> azim.take((2, 6, 7, 8, 12)) * 180. / np.pi
array([ 180.,  270.,    0.,   90.,    0.])
>>> (_, azim) = grid.calc_distances_of_nodes_to_point((2, 1),
...     get_az='angles', node_subset=(1, 3, 11, 13))
>>> azim * 180. / np.pi
array([ 225.,  135.,  315.,   45.])


When calculating displacements, the first row contains displacements in x and the second displacements in y.

>>> (_, azim) = grid.calc_distances_of_nodes_to_point((2, 1),
...     get_az='displacements', node_subset=(2, 6, 7, 8, 12))
>>> azim
array([[ 0., -1.,  0.,  1.,  0.],
[-1.,  0.,  0.,  0.,  1.]])

calc_flux_div_at_cell(unit_flux, out=None)#

Calculate divergence of link-based fluxes at cells.

This function is very similar to the function calc_flux_div_at_node.

Given a flux per unit width across each cell face in the grid, calculate the net outflux (or influx, if negative) divided by cell area, at each cell.

Parameters:

unit_flux_at_links_across_faces (ndarray or field name) – Flux per unit width along links at faces (x number of faces) or link field.

Returns:

Flux divergence at cells.

Return type:

ndarray (x number of cells)

Examples

>>> from landlab import RasterModelGrid
>>> from landlab.grid.divergence import calc_flux_div_at_cell
>>> rg = RasterModelGrid((3, 4), xy_spacing=10.0)
>>> import numpy as np
>>> z[5] = 50.0
>>> z[6] = 36.0
>>> lg
array([ 0. ,  0. ,  0. ,  0. ,  5. ,  3.6,  0. ,  5. , -1.4, -3.6,  0. ,
-5. , -3.6,  0. ,  0. ,  0. ,  0. ])
>>> fg = lg[rg.link_at_face]  # there are 7 faces
>>> fg
array([ 5. ,  3.6,  5. , -1.4, -3.6, -5. , -3.6])
>>> calc_flux_div_at_cell(rg, -fg)
array([ 1.64,  0.94])
>>> rg.set_status_at_node_on_edges(right=rg.BC_NODE_IS_CLOSED)
>>> rg.set_status_at_node_on_edges(top=rg.BC_NODE_IS_CLOSED)
>>> unit_flux_at_faces = np.zeros(rg.number_of_faces)
>>> unit_flux_at_faces[rg.active_faces] = -fg[rg.active_faces]
>>> calc_flux_div_at_cell(rg, unit_flux_at_faces)
array([ 1.14,  0.22])
array([ 1.64,  0.94])


Notes

Performs a numerical flux divergence operation at cells.

calc_flux_div_at_node(unit_flux, out=None)#

Calculate divergence of link-based fluxes at nodes.

Given a flux per unit width across each face in the grid, calculate the net outflux (or influx, if negative) divided by cell area, at each node (zero or “out” value for nodes without cells).

Parameters:

unit_flux (ndarray or field name) – Flux per unit width along links (x number of links).

Returns:

Flux divergence at nodes.

Return type:

ndarray (x number of nodes)

Examples

>>> from landlab import RasterModelGrid
>>> from landlab.grid.divergence import calc_flux_div_at_node
>>> rg = RasterModelGrid((3, 4), xy_spacing=10.0)
>>> z[5] = 50.0
>>> z[6] = 36.0
>>> lg
array([ 0. ,  0. ,  0. ,  0. ,  5. ,  3.6,  0. ,  5. , -1.4, -3.6,  0. ,
-5. , -3.6,  0. ,  0. ,  0. ,  0. ])
>>> calc_flux_div_at_node(rg, -lg)
array([ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  1.64,  0.94,  0.  ,  0.  ,
0.  ,  0.  ,  0.  ])
>>> rg.set_status_at_node_on_edges(right=rg.BC_NODE_IS_CLOSED)
>>> rg.set_status_at_node_on_edges(top=rg.BC_NODE_IS_CLOSED)
array([ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  1.14,  0.22,  0.  ,  0.  ,
0.  ,  0.  ,  0.  ])
array([ 0.  ,  0.  ,  0.  ,  0.  ,  0.  ,  1.64,  0.94,  0.  ,  0.  ,
0.  ,  0.  ,  0.  ])


Notes

Performs a numerical flux divergence operation on nodes.

Calculates the gradient in node_values at each link in the grid, returning an array of length number_of_links.

Parameters:
• node_values (ndarray or field name (x number of nodes)) – Values at grid nodes.

• out (ndarray, optional (x number of links)) – Buffer to hold the result.

Returns:

Return type:

ndarray

Examples

>>> from landlab import RasterModelGrid
>>> rg = RasterModelGrid((3, 4), xy_spacing=10.0)
>>> z[5] = 50.0
>>> z[6] = 36.0
array([ 0. ,  0. ,  0. ,  0. ,  5. ,  3.6,  0. ,  5. , -1.4, -3.6,  0. ,
-5. , -3.6,  0. ,  0. ,  0. ,  0. ])

>>> from landlab import HexModelGrid
>>> hg = HexModelGrid((3, 3), spacing=10.0)
>>> z = hg.add_zeros("topographic__elevation", at="node", clobber=True)
>>> z[4] = 50.0
>>> z[5] = 36.0
array([ 0. ,  0. ,  0. ,  5. ,  5. ,  3.6,  3.6,  0. ,  5. , -1.4, -3.6,
0. , -5. , -5. , -3.6, -3.6,  0. ,  0. ,  0. ])


Calculate the components of the gradient at each patch.

If ignore_closed_nodes is True, closed nodes do not affect gradient calculations. If a closed node is present in a patch, the patch gradient is set to zero in both x and y directions.

Parameters:
• elevs (str or ndarray, optional) – Field name or array of node values.

• ignore_closed_nodes (bool) – If True, do not incorporate values at closed nodes into the calc.

• unit_normal (array with shape (num_patches, 3) (optional)) – The unit normal vector to each patch, if already known.

• slope_magnitude (array with size num_patches (optional)) – The slope of each patch, if already known.

Returns:

gradient_tuple – Len-2 tuple of arrays giving components of gradient in the x and y directions, in the units of units.

Return type:

(x_component_at_patch, y_component_at_patch)

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> z = mg.node_y
True
True

calc_hillshade_at_node(alt=45.0, az=315.0, slp=None, asp=None, unit='degrees', elevs='topographic__elevation')#

Parameters:
• alt (float) – Sun altitude (from horizon) - defaults to 45 degrees

• az (float) – Sun azimuth (CW from north) - defaults to 315 degrees

• slp (float) – slope of cells at surface - optional

• asp (float) – aspect of cells at surface (from north) - optional (with slp)

• unit (string) –

‘degrees’ (default) or ‘radians’ - only needed if slp and asp

are not provided

• specified (If slp and asp are both not) –

• as ('elevs' must be provided) –

• an (a grid field name (defaults to 'topographic__elevation') or) –

• case (nnodes-long array of elevation values. In this) –

• will (the method) –

• hillshade (calculate local slopes and aspects internally as part of the) –

• production.

Returns:

Return type:

ndarray of float

Notes

code taken from GeospatialPython.com example from December 14th, 2014 DEJH found what looked like minor sign problems, and adjusted to follow the ArcGIS algorithm <http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#/How_Hillshade_works/009z000000z2000000/>.

Remember when plotting that bright areas have high values. cmap=’Greys’ will give an apparently inverted color scheme. cmap=’gray’ has white associated with the high values, so is recommended for plotting.

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> mg = RasterModelGrid((5, 5), xy_spacing=1.)
>>> z = mg.x_of_node * np.tan(60. * np.pi / 180.)
array([ 0.625,  0.625,  0.625,  0.625,  0.625,  0.625,  0.625,  0.625,
0.625,  0.625,  0.625,  0.625,  0.625,  0.625,  0.625,  0.625,
0.625,  0.625,  0.625,  0.625,  0.625,  0.625,  0.625,  0.625,
0.625])


Calculate net link fluxes at nodes.

Given a flux per unit width along each link in the grid, calculate the net outflux (or influx, if negative) at each node. Fluxes are treated as zero for links that have no faces, and net fluxes are treated as zero for nodes that have no cell.

Parameters:
• unit_flux_at_links (ndarray or field name) – Flux per unit width associated with links.

• out (ndarray, optional) – Buffer to hold the result.

Returns:

Net flux at nodes.

Return type:

ndarray (x number of cells)

Examples

>>> from landlab import RasterModelGrid
>>> rg = RasterModelGrid((3, 4), xy_spacing=10.0)
>>> z[5] = 50.0
>>> z[6] = 36.0
>>> lg
array([ 0. ,  0. ,  0. ,  0. ,  5. ,  3.6,  0. ,  5. , -1.4, -3.6,  0. ,
-5. , -3.6,  0. ,  0. ,  0. ,  0. ])
>>> calc_net_flux_at_node(rg, -lg)
array([   0.,    0.,    0.,    0.,    0.,  164.,   94.,    0.,    0.,
0.,    0.,    0.])
>>> rg.set_status_at_node_on_edges(right=rg.BC_NODE_IS_CLOSED)
>>> rg.set_status_at_node_on_edges(top=rg.BC_NODE_IS_CLOSED)
>>> np.round(nlfn)
array([   0.,    0.,    0.,    0.,    0.,  114.,   22.,    0.,    0.,
0.,    0.,    0.])

>>> from landlab import HexModelGrid
>>> hg = HexModelGrid((3, 3), spacing=10.0)
>>> z = hg.add_zeros("topographic__elevation", at="node", clobber=True)
>>> z[4] = 50.0
>>> z[5] = 36.0
>>> lg
array([ 0. ,  0. ,  0. ,  5. ,  5. ,  3.6,  3.6,  0. ,  5. , -1.4, -3.6,
0. , -5. , -5. , -3.6, -3.6,  0. ,  0. ,  0. ])
>>> nlfn = calc_net_flux_at_node(hg, -lg)
>>> np.round(nlfn)
array([   0.,    0.,    0.,    0.,  152.,   96.,    0.,    0.,    0.,    0.])


Notes

This is essentially a line integral for the fluxes along the boundaries of each cell. Hence, the resulting output has dimensions of total flux (so, if the unit flux happens to be mass per time per face width, the output will be in mass per unit time). Because a line integral is undefined where there are no cells (i.e., perimeter nodes), the result is given as zeros for these nodes. The current algorithm uses fancy indexing (calling _calc_net_face_flux_at_cells) and could probably be made faster.

calc_slope_at_node(elevs='topographic__elevation', method='patch_mean', ignore_closed_nodes=True, return_components=False, **kwds)#

Array of slopes at nodes, averaged over neighboring patches.

Produces a value for node slope (i.e., mean gradient magnitude) at each node in a manner analogous to a GIS-style slope map. It averages the gradient on each of the patches surrounding the node, creating a value for node slope that better incorporates nonlocal elevation information. Directional information can still be returned through use of the return_components keyword.

Note that under these definitions, it is not always true that:

mag, cmp = mg.calc_slope_at_node(z)
mag ** 2 == cmp[0] ** 2 + cmp[1] ** 2  # not always true


If ignore_closed_nodes is False, all proximal elevation values will be used in the calculation. If True, only unclosed nodes are used.

Parameters:
• elevs (str or ndarray, optional) – Field name or array of node values.

• method ({'patch_mean', 'Horn'}) – By equivalence to the raster version, ‘patch_mean’ returns a scalar mean on the patches; ‘Horn’ returns a vector mean on the patches.

• ignore_closed_nodes (bool) – If True, do not incorporate values at closed nodes into the calc.

• return_components (bool) – If True, return a tuple, (array_of_magnitude, (array_of_slope_x_radians, array_of_slope_y_radians)). If false, return an array of floats of the slope magnitude.

Returns:

If return_components, returns (array_of_magnitude, (array_of_slope_x_radians, array_of_slope_y_radians)). If not return_components, returns an array of slope magnitudes.

Return type:

float array or length-2 tuple of float arrays

Examples

>>> import numpy as np
>>> from landlab import RadialModelGrid, RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> z = mg.node_x
>>> slopes = mg.calc_slope_at_node(elevs=z)
>>> np.allclose(slopes, 45. / 180. * np.pi)
True

>>> mg = RasterModelGrid((4, 5))
>>> z = - mg.node_y
>>> slope_mag, cmp = mg.calc_slope_at_node(elevs=z,
...                                        return_components=True)
>>> np.allclose(slope_mag, np.pi / 4.)
True
>>> np.allclose(cmp[0], 0.)
True
>>> np.allclose(cmp[1], - np.pi / 4.)
True

>>> mg = RadialModelGrid(n_rings=3)
>>> slope_at_node = np.round(mg.calc_slope_at_node(elevs=z), decimals=5)

>>> nodes_at_ring = [
... ]
>>> slope_at_node[nodes_at_ring[0]]
array([ 0.85707])
>>> slope_at_node[nodes_at_ring[1]]
array([ 0.79417,  0.79417,  0.79417,  0.79417,  0.79417,  0.79417])
>>> slope_at_node[nodes_at_ring[2]]
array([ 0.77542,  0.78453,  0.78453,  0.77542,  0.77542,  0.78453,
0.78453,  0.77542,  0.77542,  0.78453,  0.78453,  0.77542])

calc_slope_at_patch(elevs='topographic__elevation', ignore_closed_nodes=True, unit_normal=None)#

Calculate the slope (positive magnitude of gradient) at patches.

If ignore_closed_nodes is True, closed nodes do not affect slope calculations. If a closed node is present in a patch, the patch slope is set to zero.

Parameters:
• elevs (str or ndarray, optional) – Field name or array of node values.

• ignore_closed_nodes (bool) – If True, do not incorporate values at closed nodes into the calc.

• unit_normal (array with shape (num_patches, 3) (optional)) – The unit normal vector to each patch, if already known.

Returns:

slopes_at_patch – The slope (positive gradient magnitude) of each patch.

Return type:

n_patches-long array

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> z = mg.node_x
>>> S = mg.calc_slope_at_patch(elevs=z)
>>> S.size == mg.number_of_patches
True
>>> np.allclose(S, np.pi / 4.)
True

calc_unit_normal_at_patch(elevs='topographic__elevation')#

Calculate and return the unit normal vector <a, b, c> to a patch.

Parameters:

elevs (str or ndarray, optional) – Field name or array of node values.

Returns:

nhat – The unit normal vector <a, b, c> to each patch.

Return type:

num-patches x length-3 array

Examples

>>> from landlab import HexModelGrid
>>> mg = HexModelGrid((3, 3))
>>> z = mg.node_x * 3. / 4.
>>> mg.calc_unit_normal_at_patch(z)
array([[-0.6,  0. ,  0.8],
[-0.6,  0. ,  0.8],
[-0.6,  0. ,  0.8],
[-0.6,  0. ,  0.8],
[-0.6,  0. ,  0.8],
[-0.6,  0. ,  0.8],
[-0.6,  0. ,  0.8],
[-0.6,  0. ,  0.8],
[-0.6,  0. ,  0.8],
[-0.6,  0. ,  0.8]])

property cell_area_at_node#

Cell areas in a nnodes-long array.

Zeros are entered at all perimeter nodes, which lack cells.

Returns:

Cell areas as an n_nodes-long array.

Return type:

ndarray

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((4, 5), xy_spacing=(3, 4))
>>> grid.status_at_node[7] = grid.BC_NODE_IS_CLOSED
>>> grid.cell_area_at_node
array([  0.,   0.,   0.,   0.,   0.,
0.,  12.,  12.,  12.,   0.,
0.,  12.,  12.,  12.,   0.,
0.,   0.,   0.,   0.,   0.])

property cell_at_node#
property cells_at_corner#

Get the cells that touch each corner.

property cells_at_face#

Get the cells on either side of each face.

property cells_present_at_corner#

A boolean array, False where a cell has a closed corner or is

property cells_present_at_face#

A boolean array, False where a cell has a closed corner or is

property closed_boundary_corners#

Get array of closed boundary corners.

property closed_boundary_nodes#

Get array of closed boundary nodes.

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> mg.status_at_node[mg.nodes_at_top_edge] = mg.BC_NODE_IS_CLOSED
>>> mg.closed_boundary_nodes
array([15, 16, 17, 18, 19])

property core_cells#

Get array of core cells.

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((4, 5))


Initially all of the cells are “core”.

>>> grid.core_cells
array([0, 1, 2,
3, 4, 5])


Setting a node to closed causes its cell to no longer be core.

>>> grid.status_at_node[8] = grid.BC_NODE_IS_CLOSED
>>> grid.core_cells
array([0, 1, 3, 4, 5])

property core_corners#

Get array of core corners.

property core_nodes#

Get array of core nodes.

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> mg.core_nodes
array([ 6,  7,  8, 11, 12, 13])

property core_patches#

Get array of core patches.

property corner_at_core_patch#

Get array of corners associated with core patches.

property corner_at_face_tail#

Get corners at face tail.

property corner_at_patch#
property corner_x#
property corner_y#
property corners#

Get identifier for each corner.

property corners_at_cell#

Get the corners that define a cell.

property corners_at_face#

Get corners at either end of faces.

property default_group#

Return the name of the group into which fields are put by default.

delete_field(loc, name)#

Erases an existing field.

Parameters:
• loc (str) – Name of the group.

• name (str) – Name of the field.

Raises:

KeyError – If the named field does not exist.

Return an (nnodes, X) shape array of link IDs of which links are downwind of each node, according to values (array or field).

X is the maximum downwind links at any node. Nodes with fewer downwind links than this have additional slots filled with bad_index. Links are ordered anticlockwise from east.

Parameters:
• values (str or array) – Name of variable field defined at links, or array of values at links.

• bad_index (int) – Index to place in array indicating no link.

Returns:

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...                                 -2., -3., -4., -5.,
...                                 -1., -2., -1.,
...                                 -1., -2., -3., -4.,
...                                 -1., -2., -1.])
array([[ 0,  3],
[ 1,  4],
[ 2,  5],
[ 6, -1],
[ 7, 10],
[ 8, 11],
[ 9, 12],
[13, -1],
[14, -1],
[15, -1],
[16, -1],
[-1, -1]])

property ds#
property dual#
empty(*args, **kwds)#

Uninitialized array whose size is that of the field.

Return a new array of the data field size, without initializing entries. Keyword arguments are the same as that for the equivalent numpy function.

Parameters:

group (str) – Name of the group.

numpy.empty

See for a description of optional keywords.

ones

Equivalent method that initializes the data to 1.

zeros

Equivalent method that initializes the data to 0.

Examples

>>> from landlab.field import GraphFields
>>> field = GraphFields()
>>> field.new_field_location("node", 4)
>>> field.empty("node")
array([  2.31584178e+077,  -2.68156175e+154,   9.88131292e-324,
... 2.78134232e-309]) # Uninitialized memory


Note that a new field is not added to the collection of fields.

>>> list(field.keys("node"))
[]

property event_layers#

EventLayers for each cell.

property face_dirs_at_corner#

Return face directions into each corner.

property face_status_at_corner#
property faces_at_cell#

Get the faces that define a cell.

property faces_at_corner#

Get faces touching a corner.

field_units(field, at=None)#

Get units for a field.

Returns the unit string associated with the data array in group and field.

Parameters:
• field (str) – Name of the field withing group.

• at (str, optional) – Name of the group.

Returns:

The units of the field.

Return type:

str

Raises:

KeyError – If either field or group does not exist.

field_values(field, at=None)#

Return the values of a field.

Given a group and a field, return a reference to the associated data array.

Parameters:
• field (str) – Name of the field within group.

• at (str, optional) – Name of the group.

Returns:

The values of the field.

Return type:

array

Raises:
• landlab.field.errors.GroupError – If group does not exist

• landlab.field.errors.FieldError – If field does not exist

Examples

Create a group of fields called node.

>>> from landlab.field import GraphFields
>>> fields = GraphFields()
>>> fields.new_field_location("node", 4)


Add a field, initialized to ones, called topographic__elevation to the node group. The field_values method returns a reference to the field’s data.

>>> _ = fields.add_ones("topographic__elevation", at="node")
>>> fields.field_values("topographic__elevation", at="node")
array([ 1.,  1.,  1.,  1.])


Raise FieldError if field does not exist in group.

>>> fields.field_values("planet_surface__temperature", at="node")
...
Traceback (most recent call last):
FieldError: planet_surface__temperature


If group does not exists, raise GroupError.

>>> fields.field_values("topographic__elevation", at="cell")
...
Traceback (most recent call last):
GroupError: cell

fields(include='*', exclude=None)#

List of fields held by the grid.

The returned field names are returned as their canonical names. This is, as a string of the for “at_<location>:<name>”. This allows for fields with the same name to be defined at different grid locations. You could have, for example, a variable “elevation” defined at both nodes and links.

Both the include and exclude patterns are glob-style expressions, not regular expressions. If either include or exclude are lists, then the patterns are matched using an “or”.

The include filters are applied before the exclude filters.

Parameters:
• include (str, or iterable of str, optional) – Glob-style pattern for field names to include.

• exclude (str, or iterable of str, optional) – Glob-style pattern for field names to exclude.

Returns:

Filtered set of canonical field names held by the grid

Return type:

set

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))


Add some fields to the grid. Notice that we have defined a field named “elevation” at both nodes and links.

>>> _ = grid.add_full("elevation", 3.0, at="node")
>>> _ = grid.add_full("temperature", 5.0, at="node")

>>> sorted(grid.fields())
>>> sorted(grid.fields(include="at_node*"))
['at_node:elevation', 'at_node:temperature']
>>> sorted(grid.fields(include="at_node*", exclude="*temp*"))
['at_node:elevation']


Fields can also be defined at layers. In the following example we’ve filtered the results to just return the layer fields.

>>> grid.event_layers.add(1.0, rho=0.5)
>>> sorted(grid.fields(include="at_layer*"))
['at_layer:rho']


If a list, the fields are matched with an “or”.

>>> sorted(grid.fields(include=["at_node*", "*elevation*"]))

property fixed_faces#

Get array of fixed faces.

Returns the corner at the other end of the fixed face for a fixed

An array of the fixed_faces connected to fixed gradient boundary

Get array of fixed gradient boundary corners.

Returns the node at the other end of the fixed link for a fixed gradient boundary node.

Degenerate NodeStatus.FIXED_GRADIENT nodes (e.g., corners) are handled as in fixed_gradient_boundary_node_fixed_link, by pointing to a neighboring NodeStatus.FIXED_GRADIENT node.

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> leftedge = grid.nodes_at_left_edge
array([0, 4, 8])
array([ 3,  7, 10])
array([4, 5, 4])


Note that on a raster, some nodes (notably the corners) can be NodeStatus.FIXED_GRADIENT, but not have a true LinkStatus.FIXED neighboring link. In such cases, the link returned will be a closed link joining the corner node to a neighboring NodeStatus.FIXED_GRADIENT node (see example).

An AssertionError will be raised if for some reason a NodeStatus.FIXED_GRADIENT node exists which has neither a NodeStatus.FIXED_GRADIENT neighbor, or a LinkStatus.FIXED.

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> leftedge = grid.nodes_at_left_edge
array([0, 4, 8])
array([ 3,  7, 10])


Get array of fixed gradient boundary nodes.

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
array([15, 16, 17, 18, 19])


Examples

>>> from landlab import NodeStatus, RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> grid.status_at_node
array([1, 1, 1, 1,
1, 0, 0, 1,
1, 1, 1, 1], dtype=uint8)
0

>>> grid.status_at_node[:4] = NodeStatus.FIXED_GRADIENT
>>> grid.status_at_node
array([2, 2, 2, 2,
1, 0, 0, 1,
1, 1, 1, 1], dtype=uint8)
array([4, 5])

property fixed_value_boundary_corners#

Get array of fixed value boundary corners.

property fixed_value_boundary_nodes#

Get array of fixed value boundary nodes.

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((4, 5))


Initially all the perimeter nodes are fixed value boundary.

>>> grid.fixed_value_boundary_nodes
array([ 0,  1,  2,  3,  4, 5,  9, 10, 14, 15, 16, 17, 18, 19])


Set left, right, and bottom edges to closed.

>>> for edge in (grid.nodes_at_left_edge, grid.nodes_at_right_edge,
...              grid.nodes_at_bottom_edge):
...     grid.status_at_node[edge] = grid.BC_NODE_IS_CLOSED


Now nodes on just the top edge are fixed.

>>> grid.fixed_value_boundary_nodes
array([16, 17, 18])

freeze()#

Freeze the graph by making arrays read-only.

classmethod from_dict(kwds)[source]#

Create grid from dictionary.

Parameters:

params (dictionary) – Dictionary of required parameters to create a model grid.

Examples

>>> from landlab import RasterModelGrid
>>> params = {"shape": (3,4), "xy_spacing": 2}
>>> grid = RasterModelGrid.from_dict(params)
>>> grid.x_of_node
array([ 0.,  2.,  4.,  6.,  0.,  2.,  4.,  6.,  0.,  2.,  4.,  6.])
>>> grid.y_of_node
array([ 0.,  0.,  0.,  0.,  2.,  2.,  2.,  2.,  4.,  4.,  4.,  4.])

classmethod from_file(file_like)#

Create grid from a file-like object.

File to load either as a file-like object, path to an existing file, or the contents of a file as a string.

Parameters:

file_like – File-like object, filepath, or string.

Examples

>>> from io import StringIO
>>> from landlab import RasterModelGrid
>>> filelike = StringIO('''
... shape:
...     - 3
...     - 4
... xy_spacing: 2
... ''')
>>> grid = RasterModelGrid.from_file(filelike)
>>> grid.x_of_node
array([ 0.,  2.,  4.,  6.,  0.,  2.,  4.,  6.,  0.,  2.,  4.,  6.])
>>> grid.y_of_node
array([ 0.,  0.,  0.,  0.,  2.,  2.,  2.,  2.,  4.,  4.,  4.,  4.])

classmethod from_netcdf(fname)#
property frozen#
property groups#

List of group names.

Returns:

Names of field groupings.

Return type:

set

has_field(field, at=None)#

Check if a field is in a group.

Parameters:
• field (str) – Name of the field.

• at (str, optional) – Name of the group.

Returns:

True if the group contains the field, otherwise False.

Return type:

bool

Examples

Check if the field named topographic__elevation is contained in a group.

>>> from landlab.field import GraphFields

>>> fields = GraphFields()
>>> fields.new_field_location("node", 12)
>>> fields.has_field("topographic__elevation", at="node")
True
>>> fields.has_field("topographic__elevation", at="cell")
False

>>> fields = GraphFields()
>>> fields.new_field_location("node", 12)
>>> fields.has_field("node", "topographic__elevation")
True
>>> fields.has_field("cell", "topographic__elevation")
False

has_group(name)#

Check if a group exists.

Parameters:

name (str) – Name of the group.

Returns:

True if the field contains group, otherwise False.

Return type:

bool

Examples

Check if the field has the groups named node or cell.

>>> from landlab.field import GraphFields
>>> fields = GraphFields()
>>> fields.new_field_location('node', 12)
>>> fields.has_group('node')
True
>>> fields.has_group('cell')
False

imshow(*args, **kwds)#

Plot a data field.

This is a wrapper for plot.imshow_grid, and can take the same keywords. See that function for full documentation.

Parameters:

values (str, or array-like) – Name of a field or an array of values to plot.

landlab.plot.imshow_grid

LLCATS

GINF

keys(group)#

Return the field names in a group.

Parameters:

group (str) – Group name.

Returns:

Names of fields held in the given group.

Return type:

list

Examples

>>> from landlab.field import GraphFields
>>> fields = GraphFields()
>>> fields.new_field_location("node", 4)
>>> list(fields.keys("node"))
[]
>>> list(fields.keys("node"))
['topographic__elevation']

property length_of_face#

Get the length of faces.

Examples

>>> import numpy as np
>>> from landlab.graph import UniformRectilinearGraph

>>> graph = UniformRectilinearGraph((2, 3), spacing=(1, 2))
array([ 2.,  2.,  1.,  1.,  1.,  2.,  2.])


Return a boolean the same shape as links_at_node which flags links which are downwind of the node as True.

link_at_node_is_downwind iterates across the grid and identifies the link values at each link connected to a node. It then uses the link_dirs_at_node data structure to identify links carrying flux out of the node. It then return a boolean array the same shape as links_at_node flagging these links. e.g., for a raster, the returned array will be shape (nnodes, 4).

Parameters:
• values (str or array) – Name of variable field defined at links, or array of values at links.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array. Must be correct shape and boolean dtype.

Returns:

Boolean of which links are downwind at nodes.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...                                 -2., -3., -4., -5.,
...                                 -1., -2., -1.,
...                                 -1., -2., -3., -4.,
...                                 -1., -2., -1.])
array([[ True,  True, False, False],
[ True,  True, False, False],
[ True,  True, False, False],
[False,  True, False, False],
[ True,  True, False, False],
[ True,  True, False, False],
[ True,  True, False, False],
[False,  True, False, False],
[ True, False, False, False],
[ True, False, False, False],
[ True, False, False, False],
[False, False, False, False]], dtype=bool)


Return a boolean the same shape as links_at_node which flags links which are upwind of the node as True.

link_at_node_is_upwind iterates across the grid and identifies the link values at each link connected to a node. It then uses the link_dirs_at_node data structure to identify links bringing flux into the node. It then return a boolean array the same shape as links_at_node flagging these links. e.g., for a raster, the returned array will be shape (nnodes, 4).

Parameters:
• values (str or array) – Name of variable field defined at links, or array of values at links.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array. Must be correct shape and boolean dtype.

Returns:

Boolean of which links are upwind at nodes.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...                                 -2., -3., -4., -5.,
...                                 -1., -2., -1.,
...                                 -1., -2., -3., -4.,
...                                 -1., -2., -1.])
array([[False, False, False, False],
[False, False,  True, False],
[False, False,  True, False],
[False, False,  True, False],
[False, False, False,  True],
[False, False,  True,  True],
[False, False,  True,  True],
[False, False,  True,  True],
[False, False, False,  True],
[False, False,  True,  True],
[False, False,  True,  True],
[False, False,  True,  True]], dtype=bool)


Return link directions into each node.

A value of 1 indicates a link points toward a given node, while a value of -1 indicates a link points away from a node.

Returns:

Link directions relative to the nodes of a grid. The shape of the matrix will be number of nodes by the maximum number of links per node. A zero indicates no link at this position.

Return type:

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1, 2, 2, 2]
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8))
array([[-1, -1,  0,  0], [-1, -1,  1,  0], [-1,  1,  0,  0],
[-1, -1,  1,  0], [-1, -1,  1,  1], [-1,  1,  1,  0],
[-1,  1,  0,  0], [-1,  1,  1,  0], [ 1,  1,  0,  0]],
dtype=int8)


Return array of IDs of links with given angle.

Examples

>>> from landlab import HexModelGrid
>>> grid = HexModelGrid((3, 3))
array([  0,  1,  8,  9, 10, 17, 18])
array([  3,  5,  7, 11, 13, 15])
array([  2,  4,  6, 12, 14, 16])
0
>>> grid = HexModelGrid((3, 3), orientation='vertical')
array([  1,  3,  8, 10, 15, 17])
array([ 2,  5,  6,  9, 12, 13, 16])
array([ 0,  4,  7, 11, 14, 18])
>>> len(grid.link_with_angle(60.0, in_degrees=True))  # none at 60 deg
0


Links with a given node status.

Parameters:
• status_at_tail (NodeStatus, optional) – Status of the link tail node.

Returns:

Return type:

array of int

Examples

>>> from landlab import RasterModelGrid, NodeStatus
>>> grid = RasterModelGrid((4, 5))

>>> grid.status_at_node[13] = NodeStatus.FIXED_VALUE
>>> grid.status_at_node[2] = NodeStatus.CLOSED
... )
array([10, 11, 14, 15, 19])
... )
array([12, 16, 20, 23, 24])
... )
array([ 5,  7,  9, 18])

>>> grid.link_with_node_status(status_at_head=NodeStatus.CORE)
array([ 5,  6,  7,  9, 10, 11, 14, 15, 18, 19])
array([10, 11, 12, 14, 15, 16, 19, 20, 23, 24])
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])


Examples

>>> from landlab.graph import Graph
>>> node_x = [0, 1, 2, 0, 1, 2, 0, 1, 2]
>>> node_y = [0, 0, 0, 1, 1, 1, 2, 2, 2]
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8))
array([[ 0,  2, -1, -1], [ 1,  3,  0, -1], [ 4,  1, -1, -1],
[ 5,  7,  2, -1], [ 6,  8,  5,  3], [ 9,  6,  4, -1],
[10,  7, -1, -1], [11, 10,  8, -1], [11,  9, -1, -1]])


Get the links that define a patch.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1, 2, 2, 2]
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8))
>>> patches = ((0, 3, 5, 2), (1, 4, 6, 3))
array([[3, 5, 2, 0],
[4, 6, 3, 1]])


Map the largest magnitude of the links carrying flux from the node to the node.

map_downwind_node_link_max_to_node iterates across the grid and identifies the link values at each link connected to a node. It then uses the link_dirs_at_node data structure to identify links carrying flux out of the node, then maps the maximum magnitude of ‘var_name’ found on these links onto the node. If no downwind link is found, the value will be recorded as zero.

Parameters:
• var_name (array or field name) – Values defined at links.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Mapped values at nodes.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...                                  0.,  0.,  0.,  0.,
...                                 -1., -2., -1.,
...                                  0.,  0.,  0.,  0.,
...                                 -1., -2., -1.])
array([ 1.,  2.,  1.,  0.,
1.,  2.,  1.,  0.,
1.,  2.,  1.,  0.])

>>> values_at_nodes = rmg.add_empty("z", at="node")
>>> values_at_nodes
array([ 1.,  2.,  1.,  0.,
1.,  2.,  1.,  0.,
1.,  2.,  1.,  0.])
>>> rtn is values_at_nodes
True


Map the mean magnitude of the links carrying flux out of the node to the node.

map_downwind_node_link_mean_to_node iterates across the grid and identifies the link values at each link connected to a node. It then uses the link_dirs_at_node data structure to identify links carrying flux out of the node, then maps the mean magnitude of ‘var_name’ found on these links onto the node. Links with zero values are not included in the means, and zeros are returned if no upwind links are found.

Parameters:
• var_name (array or field name) – Values defined at links.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Mapped values at nodes.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...                                 -2., -3., -4., -5.,
...                                 -1., -2., -1.,
...                                 -1., -2., -3., -4.,
...                                 -1., -2., -1.])
array([ 1.5,  2.5,  2.5,  5. ,
1. ,  2. ,  2. ,  4. ,
1. ,  2. ,  1. ,  0. ])

>>> values_at_nodes = rmg.add_empty("z", at="node")
>>> values_at_nodes
array([ 1.5,  2.5,  2.5,  5. ,
1. ,  2. ,  2. ,  4. ,
1. ,  2. ,  1. ,  0. ])
>>> rtn is values_at_nodes
True


Iterate over a grid and identify the node at the head. For each link, the value of var_name at the head node is mapped to the corresponding link.

Parameters:
• var_name (array or field name) – Values defined at nodes.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
>>> rmg.at_node['z'] = np.array([ 0,  1,  2,  3,
...                               4,  5,  6,  7,
...                               8,  9, 10, 11])
array([  1.,   2.,   3.,   4.,   5.,   6.,   7.,   5.,   6.,   7.,   8.,
9.,  10.,  11.,   9.,  10.,  11.])

>>> values_at_links = rmg.empty(at='link')
array([  1.,   2.,   3.,   4.,   5.,   6.,   7.,   5.,   6.,   7.,   8.,
9.,  10.,  11.,   9.,  10.,  11.])
True


map_link_tail_node_to_link iterates across the grid and identifies the node at the “tail”, or the “from” node for each link. For each link, the value of ‘var_name’ at the “from” node is mapped to the corresponding link.

In a RasterModelGrid, each one node has two adjacent “link tails”. This means each node value is mapped to two corresponding links.

Parameters:
• var_name (array or field name) – Values defined at nodes.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
>>> rmg.at_node['z'] = np.array([ 0,  1,  2,  3,
...                               4,  5,  6,  7,
...                               8,  9, 10, 11])
array([  0.,   1.,   2.,   0.,   1.,   2.,   3.,   4.,   5.,   6.,   4.,
5.,   6.,   7.,   8.,   9.,  10.])

>>> values_at_links = rmg.empty(at='link')
array([  0.,   1.,   2.,   0.,   1.,   2.,   3.,   4.,   5.,   6.,   4.,
5.,   6.,   7.,   8.,   9.,  10.])
True


Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid, HexModelGrid

>>> grid = RasterModelGrid((3, 4))

>>> vx, vy = grid.map_link_vector_components_to_node(link_data)
>>> vx[5:7]
array([ 7.5, 8.5])

>>> grid = HexModelGrid((3, 3))
>>> vy
array([ 0.,  0.,  0.,  0.,  1.,  1.,  0.,  0.,  0.,  0.])


Map the vector sum of links around a patch to the patch.

The resulting vector is returned as a length-2 list, with the two items being arrays of the x component and the y component of the resolved vectors at the patches, respectively.

Parameters:
• var_name (array or field name) – Values defined at links.

• ignore_inactive_links (bool) – If True, do not incorporate inactive links into calc. If all links are inactive at a patch, record zero if out is None or leave the existing value if out.

• out (len-2 list of npatches-long arrays, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Return type:

len-2 list of arrays

Examples

>>> import numpy as np
>>> from landlab import HexModelGrid

>>> mg = HexModelGrid((4, 3))
>>> interior_nodes = mg.status_at_node == mg.BC_NODE_IS_CORE
>>> exterior_nodes = mg.status_at_node != mg.BC_NODE_IS_CORE


Add a ring of closed nodes at the edge:

>>> mg.status_at_node[exterior_nodes] = mg.BC_NODE_IS_CLOSED


This gives us 5 core nodes, 7 active links, and 3 present patches

>>> (mg.number_of_core_nodes == 5 and mg.number_of_active_links == 7)
True
>>> A.fill(9.0)  # any old values on the inactive links
>>> A[mg.active_links] = np.array([ 1., -1.,  1., -1., -1., -1., -1.])


This setup should give present patch 0 pure east, patch 1 zero (vorticity), and patch 2 westwards and downwards components.

>>> xcomp, ycomp = map_link_vector_sum_to_patch(mg, "vals")
>>> xcomp, ycomp = np.round(xcomp, decimals=5), np.round(ycomp, decimals=5)
>>> np.allclose(xcomp[(6, 9, 10),], [2.0, 0.0, -1.0])
True
>>> np.allclose(ycomp[(6, 9, 10),] / np.sqrt(3.0), [0.0, 0.0, -1.0])
True


These are the patches with LinksStatus.INACTIVE on all three sides:

>>> absent_patches = np.array([0, 1, 2, 4, 8, 11, 12, 15, 16, 17, 18])
>>> np.allclose(xcomp[absent_patches], 0.0)
True
>>> np.allclose(ycomp[absent_patches], 0.0)
True


Now demonstrate the remaining functionality:

>>> A = mg.at_link['vals'].copy()
>>> A.fill(1.0)
...     mg, A, ignore_inactive_links=False, out=[xcomp, ycomp]
... )
>>> np.allclose(xcomp[absent_patches], 0.0)
False
>>> np.allclose(ycomp[absent_patches], 0.0)
False


Map data defined on links to nodes.

Given a variable defined on links, breaks it into x and y components and assigns values to nodes by averaging each node’s attached links.

Parameters:

q (ndarray of floats (1D, length = number of links in grid)) – Variable defined on links

Returns:

x and y components of variable mapped to nodes (1D, length = number of nodes)

Return type:

ndarray, ndarray

_create_link_unit_vectors

sets up unit vectors at links and unit-vector sums at nodes

Notes

THIS ALGORITHM IS NOT CORRECT AND NEEDS TO BE CHANGED!

The concept here is that q contains a vector variable that is defined at each link. The magnitude is given by the value of q, and the direction is given by the orientation of the link, as described by its unit vector.

To map the link-vector values to the nodes, we break the values into x- and y-components according to each link’s unit vector. The x-component of q at a node is a weighted sum of the x-components of the links that are attached to that node. A good way to appreciate this is by example. Consider a 3x4 raster grid:

8--14---9--15--10--16--11
|       |       |       |
4       5       6       7
|       |       |       |
4--11---5---12--6---13--7
|       |       |       |
0       1       2       3
|       |       |       |
0---8---1---9---2--10---3


Imagine that for each node, we were to add up the unit vector components for each connected link; in other words, add up all the x components of the unit vectors associated with each link, and add up all the y components. Here’s what that would look like for the above grid (“vsx” and “vsy” stand for “vector sum x” and “vector sum y”):

• Corner nodes (0, 3, 8, 11): vsx = 1, vsy = 1

• Bottom and top nodes (1-2, 9-10): vsx = 2, vsy = 1

• Left and right nodes (4, 7): vsx = 1, vsy = 2

• All others: vsx = 2, vsy = 2

The process of creating unit-vector sums at nodes is handled by ModelGrid._create_link_unit_vectors() (and, for raster grids, by the overriding method RasterModelGrid._create_link_unit_vectors()). The node unit-vector sums are then stored in self.node_unit_vector_sum_x and self.node_unit_vector_sum_y.

How would you use this? Suppose you have a vector variable q defined at links. What’s the average at the nodes? We’ll define the average as follows. The terminology here is: $$q = (u,v)$$ represents the vector quantity defined at links, $$Q = (U,V)$$ represents its definition at nodes, $$(m,n)$$ represents the unit vector components at a link, and $$(S_x,S_y)$$ represents the unit-vector sum at a given node.

$U_i = \sum_{j=1}^{L_i} q_j m_j / S_{xi} V_i = \sum_{j=1}^{L_i} q_j n_j / S_{yi}$

Suppose that the vector q is uniform and equal to one. Then, at node 0 in the above grid, this works out to:

U_0 = (q_0 m_0) / 1 + (q_8 m_8) / 1 = (1 0)/ 1 + (1 1)/1 = 1
V_0 = (q_0 n_0) / 1 + (q_8 n_8) / 1 = (1 1) / 1 + (1 0) / 1 = 1


At node 1, in the bottom row but not a corner, we add up the values of q associated with THREE links. The x-vector sum of these links is 2 because there are two horizontal links, each with an x- unit vector value of unity. The y-vector sum is 1 because only one of the three (link #1) has a non-zero y component (equal to one). Here is how the numbers work out:

U_1 = (q_1 m_1) / 2 + (q_8 m_8) / 2 + (q_9 m_9) / 2
= (1 0) / 2 + (1 1) / 2 + (1 1) / 2 = 1
V_1 = (q_1 n_1) / 1 + (q_8 n_8) / 1 + (q_9 n_9) / 1
= (1 1) / 1 + (1 0) / 1 + (1 0) / 1 = 1


At node 5, in the interior, there are four connected links (two in-links and two out-links; two horizontal and two vertical). So, we add up the q values associated with all four:

U_5 = (q_1 m_1) / 2 + (q_5 m_5) / 2 + (q_11 m_11) / 2 + (q_12 m_12) / 2
= (1 0) / 2 + (1 0) / 2 + (1 1) / 2 + (1 1) / 2 = 1

V_5 = (q_1 n_1) / 2 + (q_5 n_5) / 2 + (q_11 n_11) / 2 + (q_12 n_12) / 2
= (1 1) / 2 + (1 1) / 2 + (1 0) / 2 + (1 0) / 2 = 1


To do this calculation efficiently, we use the following algorithm:

FOR each row in _node_inlink_matrix (representing one inlink @ each
node)
Multiply the link's q value by its unit x component ...
... divide by node's unit vector sum in x ...
... and add it to the node's total q_x
Multiply the link's q value by its unit y component ...
... divide by node's unit vector sum in y ...
... and add it to the node's total q_y


Examples

Example 1

q[:] = 1. Vector magnitude is $$\sqrt{2}$$, direction is $$(1,1)$$.

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4), xy_spacing=(2., 2.))
>>> grid.unit_vector_at_node
array([[ 1.,  1.],
[ 2.,  1.],
[ 2.,  1.],
[ 1.,  1.],
[ 1.,  2.],
[ 2.,  2.],
[ 2.,  2.],
[ 1.,  2.],
[ 1.,  1.],
[ 2.,  1.],
[ 2.,  1.],
[ 1.,  1.]])
array([[ 1.,  1.],
[ 1.,  1.],
[ 1.,  1.],
[ 1.,  1.],
[ 1.,  1.],
[ 1.,  1.],
[ 1.,  1.],
[ 1.,  1.],
[ 1.,  1.],
[ 1.,  1.],
[ 1.,  1.],
[ 1.,  1.]])


Example 2

Vector magnitude is 5, angle is 30 degrees from horizontal, forming a 3-4-5 triangle.

>>> import numpy as np
>>> q = np.array([4., 4., 4., 3., 3., 3., 3.,
...               4., 4., 4., 3., 3., 3., 3.,
...               4., 4., 4])
array([[ 4.,  3.],
[ 4.,  3.],
[ 4.,  3.],
[ 4.,  3.],
[ 4.,  3.],
[ 4.,  3.],
[ 4.,  3.],
[ 4.,  3.],
[ 4.,  3.],
[ 4.,  3.],
[ 4.,  3.],
[ 4.,  3.]])


..todo:

Fix and finish example 3 below.


Example 3: Hexagonal grid with vector as above. Here, q is pre-calculated to have the right values to represent a uniform vector with magnitude 5 and orientation 30 degrees counter-clockwise from horizontal.

map_max_of_link_nodes_to_link iterates across the grid and identifies the node values at both the “head” and “tail” of a given link. This function evaluates the value of ‘var_name’ at both the “to” and “from” node. The maximum value of the two node values is then mapped to the link.

Parameters:
• var_name (array or field name) – Values defined at nodes.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...     "z",
...     [
...         [0, 1, 2, 3],
...         [7, 6, 5, 4],
...         [8, 9, 10, 11],
...     ],
...     at="node",
... )
array([  1.,   2.,   3.,   7.,   6.,   5.,   4.,   7.,   6.,   5.,   8.,
9.,  10.,  11.,   9.,  10.,  11.])

>>> values_at_links = rmg.empty(at='link')
array([  1.,   2.,   3.,   7.,   6.,   5.,   4.,   7.,   6.,   5.,   8.,
9.,  10.,  11.,   9.,  10.,  11.])
True


Map the maximum value of a nodes’ links to the node.

map_max_of_node_links_to_node iterates across the grid and identifies the link values at each link connected to a node. This function finds the maximum value of ‘var_name’ of each set of links, and then maps this value to the node. Note no attempt is made to honor the directionality of the links.

Parameters:
• var_name (array or field name) – Values defined at links.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Mapped values at nodes.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
array([  3.,   4.,   5.,   6.,
10.,  11.,  12.,  13.,
14.,  15.,  16.,  16.])

>>> values_at_nodes = rmg.add_empty("z", at="node")
>>> values_at_nodes
array([  3.,   4.,   5.,   6.,
10.,  11.,  12.,  13.,
14.,  15.,  16.,  16.])
>>> rtn is values_at_nodes
True

map_max_of_patch_nodes_to_patch(var_name, ignore_closed_nodes=True, out=None)#

Map the maximum value of nodes around a patch to the patch.

Parameters:
• var_name (array or field name) – Values defined at nodes.

• ignore_closed_nodes (bool) – If True, do not incorporate closed nodes into calc. If all nodes are masked at a patch, record zero if out is None or leave the existing value if out.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Mapped values at patches.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab.grid.mappers import map_max_of_patch_nodes_to_patch
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
>>> rmg.at_node['vals'] = np.array([5., 4., 3., 2.,
...                                 3., 4., 3., 2.,
...                                 3., 2., 1., 0.])
>>> map_max_of_patch_nodes_to_patch(rmg, 'vals')
array([ 5., 4., 3.,
4., 4., 3.])

>>> rmg.at_node['vals'] = np.array([5., 4., 3., 2.,
...                                 3., 4., 3., 2.,
...                                 3., 2., 1., 0.])
>>> rmg.status_at_node[rmg.node_x > 1.5] = rmg.BC_NODE_IS_CLOSED
>>> ans = np.zeros(6, dtype=float)
>>> _ = map_max_of_patch_nodes_to_patch(rmg, 'vals', out=ans)
>>> ans
array([ 5., 4., 0.,
4., 4., 0.])


map_mean_of_link_nodes_to_link iterates across the grid and identifies the node values at both the “head” and “tail” of a given link. This function takes the sum of the two values of ‘var_name’ at both the “to” and “from” node. The average value of the two node values of ‘var_name’ is then mapped to the link.

Parameters:
• var_name (array or field name) – Values defined at nodes.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
>>> rmg.at_node['z'] = np.array([ 0,  1,  2,  3,
...                               4,  5,  6,  7,
...                               8,  9, 10, 11])
array([  0.5,   1.5,   2.5,   2. ,   3. ,   4. ,   5. ,   4.5,   5.5,
6.5,   6. ,   7. ,   8. ,   9. ,   8.5,   9.5,  10.5])

>>> values_at_links = rmg.empty(at='link')
array([  0.5,   1.5,   2.5,   2. ,   3. ,   4. ,   5. ,   4.5,   5.5,
6.5,   6. ,   7. ,   8. ,   9. ,   8.5,   9.5,  10.5])
True

map_mean_of_patch_nodes_to_patch(var_name, ignore_closed_nodes=True, out=None)#

Map the mean value of nodes around a patch to the patch.

Parameters:
• var_name (array or field name) – Values defined at nodes.

• ignore_closed_nodes (bool) – If True, do not incorporate closed nodes into calc. If all nodes are masked at a patch, record zero if out is None or leave the existing value if out.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Mapped values at patches.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab.grid.mappers import map_mean_of_patch_nodes_to_patch
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
>>> rmg.at_node['vals'] = np.array([5., 4., 3., 2.,
...                                 5., 4., 3., 2.,
...                                 3., 2., 1., 0.])
>>> map_mean_of_patch_nodes_to_patch(rmg, 'vals')
array([ 4.5, 3.5, 2.5,
3.5, 2.5, 1.5])

>>> rmg.at_node['vals'] = np.array([5., 4., 3., 2.,
...                                 5., 4., 3., 2.,
...                                 3., 2., 1., 0.])
>>> rmg.status_at_node[rmg.node_x > 1.5] = rmg.BC_NODE_IS_CLOSED
>>> ans = np.zeros(6, dtype=float)
>>> _ = map_mean_of_patch_nodes_to_patch(rmg, 'vals', out=ans)
>>> ans
array([ 4.5, 4. , 0. ,
3.5, 3. , 0. ])


map_min_of_link_nodes_to_link iterates across the grid and identifies the node values at both the “head” and “tail” of a given link. This function evaluates the value of ‘var_name’ at both the “to” and “from” node. The minimum value of the two node values is then mapped to the link.

Parameters:
• var_name (array or field name) – Values defined at nodes.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...     "z",
...     [
...         [ 0,  1,  2,  3],
...         [ 7,  6,  5,  4],
...         [ 8,  9, 10, 11],
...     ],
...     at="node",
... )
array([  0.,   1.,   2.,   0.,   1.,   2.,   3.,   6.,   5.,   4.,   7.,
6.,   5.,   4.,   8.,   9.,  10.])

>>> values_at_links = rmg.empty(at='link')
array([  0.,   1.,   2.,   0.,   1.,   2.,   3.,   6.,   5.,   4.,   7.,
6.,   5.,   4.,   8.,   9.,  10.])
True


Map the minimum value of a nodes’ links to the node.

map_min_of_node_links_to_node iterates across the grid and identifies the link values at each link connected to a node. This function finds the minimum value of ‘var_name’ of each set of links, and then maps this value to the node. Note no attempt is made to honor the directionality of the links.

Parameters:
• var_name (array or field name) – Values defined at links.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Mapped values at nodes.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
array([  0.,   0.,   1.,   2.,
3.,   4.,   5.,   6.,
10.,  11.,  12.,  13.])

>>> values_at_nodes = rmg.add_empty("z", at="node")
>>> values_at_nodes
array([  0.,   0.,   1.,   2.,
3.,   4.,   5.,   6.,
10.,  11.,  12.,  13.])
>>> rtn is values_at_nodes
True

map_min_of_patch_nodes_to_patch(var_name, ignore_closed_nodes=True, out=None)#

Map the minimum value of nodes around a patch to the patch.

Parameters:
• var_name (array or field name) – Values defined at nodes.

• ignore_closed_nodes (bool) – If True, do not incorporate closed nodes into calc. If all nodes are masked at a patch, record zero if out is None or leave the existing value if out.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Mapped values at patches.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab.grid.mappers import map_min_of_patch_nodes_to_patch
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
>>> rmg.at_node['vals'] = np.array([5., 4., 3., 2.,
...                                 5., 4., 3., 2.,
...                                 3., 2., 1., 0.])
>>> map_min_of_patch_nodes_to_patch(rmg, 'vals')
array([ 4., 3., 2.,
2., 1., 0.])

>>> rmg.at_node['vals'] = np.array([5., 4., 3., 2.,
...                                 5., 4., 3., 2.,
...                                 3., 2., 1., 0.])
>>> rmg.status_at_node[rmg.node_x > 1.5] = rmg.BC_NODE_IS_CLOSED
>>> ans = np.zeros(6, dtype=float)
>>> _ = map_min_of_patch_nodes_to_patch(rmg, 'vals', out=ans)
>>> ans
array([ 4., 4., 0.,
2., 2., 0.])

map_node_to_cell(var_name, out=None)#

Map values for nodes to cells.

map_node_to_cell iterates across the grid and identifies the all node values of ‘var_name’.

This function takes node values of ‘var_name’ and mapes that value to the corresponding cell area for each node.

Parameters:
• var_name (array or field name) – Values defined at nodes.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Mapped values at cells.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab.grid.mappers import map_node_to_cell
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
>>> _ = rmg.add_field("z", np.arange(12.), at="node")
>>> map_node_to_cell(rmg, 'z')
array([ 5.,  6.])

>>> values_at_cells = rmg.empty(at='cell')
>>> rtn = map_node_to_cell(rmg, 'z', out=values_at_cells)
>>> values_at_cells
array([ 5.,  6.])
>>> rtn is values_at_cells
True


Assign values to links using a weighted combination of node values.

Assign to each link a weighted combination of values v at nodes using the Lax-Wendroff method for upwind weighting.

c is a scalar or link vector that gives the link-parallel signed Courant number. Where c is positive, velocity is in the direction of the link; where negative, velocity is in the opposite direction.

As an example, consider 3x5 raster grid with the following values at the nodes in the central row:

0---1---2---3---4


Consider a uniform Courant value c = +0.2 at the horizontal links. The mapped link values should be:

.-0.4-.-1.4-.-2.4-.-3.4-.


Values at links when c = -0.2:

.-0.6-.-1.6-.-2.6-.-3.6-.

Parameters:
• v ((n_nodes,) ndarray) – Values at grid nodes.

• c (float or (n_links,) ndarray) – Courant number to use at links.

• out ((n_links,) ndarray, optional) – If provided, place calculated values in this array. Otherwise, create a new array.

Examples

>>> from landlab import RasterModelGrid
>>> import numpy as np
>>> grid = RasterModelGrid((3, 5))
>>> v[5:10] = np.arange(5)
array([ 0.4,  1.4,  2.4,  3.4])
array([ 0.6,  1.6,  2.6,  3.6])


Assign values to links from upstream nodes.

Assign to each link the value v associated with whichever of its two nodes lies upstream, according to link value u.

Consider a link k with tail node t(k) and head node t(h). Nodes have value v(n). We want to assign a value to links, v’(k). The assignment is:

v'(k) = v(t(k)) where u(k) > 0,
v'(k) = v(h(k)) where u(k) <= 0


As an example, consider 3x5 raster grid with the following values at the nodes in the central row:

0---1---2---3---4


Consider a uniform velocity value u = 1 at the horizontal links. The mapped link values should be:

.-0-.-1-.-2-.-3-.


If u < 0, the link values should be:

.-1-.-2-.-3-.-4-.

Parameters:
• v ((n_nodes,), ndarray) – Values at grid nodes.

• out ((n_links,) ndarray, optional) – If provided, place calculated values in this array. Otherwise, create a new array.

Examples

>>> from landlab import RasterModelGrid
>>> import numpy as np
>>> grid = RasterModelGrid((3, 5))
>>> v[5:10] = np.arange(5)
array([ 0.,  1.,  2.,  3.])
array([ 1.,  2.,  3.,  4.])


Map the largest magnitude of the links bringing flux into the node to the node.

map_upwind_node_link_max_to_node iterates across the grid and identifies the link values at each link connected to a node. It then uses the link_dirs_at_node data structure to identify links bringing flux into the node, then maps the maximum magnitude of ‘var_name’ found on these links onto the node. If no upwind link is found, the value will be recorded as zero.

Parameters:
• var_name (array or field name) – Values defined at links.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Mapped values at nodes.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...                                  1.4,  1.5,  1.6, -1.7,
...                                 -1.8, -1.9,  2.0,
...                                  2.1,  2.2, -2.3,  2.4,
...                                  2.5,  2.6, -2.7])
array([[ 1.4,  1.5,  1.6,  1.3],
[ 2.1,  2.2,  2. ,  2.4],
[ 2.5,  2.6,  2.3,  2.7]])

>>> values_at_nodes = rmg.add_empty("z", at="node")
>>> values_at_nodes.reshape((3, 4))
array([[ 1.4,  1.5,  1.6,  1.3],
[ 2.1,  2.2,  2. ,  2.4],
[ 2.5,  2.6,  2.3,  2.7]])
>>> rtn is values_at_nodes
True


Map the mean magnitude of the links bringing flux into the node to the node.

map_upwind_node_link_mean_to_node iterates across the grid and identifies the link values at each link connected to a node. It then uses the link_dirs_at_node data structure to identify links bringing flux into the node, then maps the mean magnitude of ‘var_name’ found on these links onto the node. Links with zero values are not included in the means, and zeros are returned if no upwind links are found.

Parameters:
• var_name (array or field name) – Values defined at links.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Mapped values at nodes.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...                                 -2., -3., -4., -5.,
...                                 -1., -2., -1.,
...                                 -1., -2., -3., -4.,
...                                 -1., -2., -1.])
array([ 0. ,  1. ,  2. ,  1. ,
2. ,  2. ,  3. ,  3. ,
1. ,  1.5,  2.5,  2.5])

>>> values_at_nodes = rmg.add_empty("z", at="node")
>>> values_at_nodes
array([ 0. ,  1. ,  2. ,  1. ,
2. ,  2. ,  3. ,  3. ,
1. ,  1.5,  2.5,  2.5])
>>> rtn is values_at_nodes
True


Map the the value found in one link array to a node, based on the largest magnitude value of links carrying fluxes out of the node, found in a second node array or field.

map_downwind_node_link_max_to_node iterates across the grid and identifies the link control_values at each link connected to a node. It then uses the link_dirs_at_node data structure to identify links carrying flux out of the node, then identifies the link with the maximum magnitude. The value of the second field ‘value_name’ at these links is then mapped onto the node. If no downwind link is found, the value will be recorded as zero.

Parameters:
• control_name (array or field name) – Values defined at nodes that dictate which end of the link to draw values from.

• value_name (array or field name) – Values defined at nodes from which values are drawn, based on control_name.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Mapped values at nodes.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...                                  0.,  0.,  0.,  0.,
...                                 -1., -2., -1.,
...                                  0.,  0.,  0.,  0.,
...                                 -1., -2., -1.])
array([  0.,   1.,   2.,   0.,
7.,   8.,   9.,   0.,
14.,  15.,  16.,   0.])

>>> values_at_nodes = rmg.add_empty("z", at="node")
...                                                   out=values_at_nodes)
>>> values_at_nodes
array([  0.,   1.,   2.,   0.,
7.,   8.,   9.,   0.,
14.,  15.,  16.,   0.])
>>> rtn is values_at_nodes
True


Map the the value found in one node array to a link, based on the maximum value found in a second node field or array.

map_value_at_max_node_to_link iterates across the grid and identifies the node values at both the “head” and “tail” of a given link. This function evaluates the value of ‘control_name’ at both the “to” and “from” node. The value of ‘value_name’ at the node with the maximum value of the two values of ‘control_name’ is then mapped to the link.

Parameters:
• control_name (array or field name) – Name of field defined at nodes or a node array that dictates which end of the link to draw values from.

• value_name (array or field name) – Name of field defined at nodes or node array from which values are drawn, based on control_name.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...     "z",
...     [
...         [0, 1, 2, 3],
...         [7, 6, 5, 4],
...         [8, 9, 10, 11],
...     ],
...     at="node",
... )
...     "vals_to_map",
...     [
...         [0, 10, 20, 30],
...         [70, 60, 50, 40],
...         [80, 90, 100, 110],
...     ],
...     at="node",
... )
array([  10.,   20.,   30.,   70.,   60.,   50.,   40.,   70.,   60.,
50.,   80.,   90.,  100.,  110.,   90.,  100.,  110.])


Map the the value found in one node array to a link, based on the minimum value found in a second node field or array.

map_value_at_min_node_to_link iterates across the grid and identifies the node values at both the “head” and “tail” of a given link. This function evaluates the value of ‘control_name’ at both the “to” and “from” node. The value of ‘value_name’ at the node with the minimum value of the two values of ‘control_name’ is then mapped to the link.

Parameters:
• control_name (array or field name) – Name of field defined at nodes or a node array that dictates which end of the link to draw values from.

• value_name (array or field name) – Name of field defined at nodes or node array from which values are drawn, based on control_name.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...     "z",
...     [
...         [0, 1, 2, 3],
...         [7, 6, 5, 4],
...         [8, 9, 10, 11],
...     ],
...     at="node",
... )
...     "vals_to_map",
...     [
...         [0, 10, 20, 30],
...         [70, 60, 50, 40],
...         [80, 90, 100, 110],
...     ],
...     at="node",
... )
array([   0.,   10.,   20.,    0.,   10.,   20.,   30.,   60.,   50.,
40.,   70.,   60.,   50.,   40.,   80.,   90.,  100.])


Map the the value found in one link array to a node, based on the largest magnitude value of links bringing fluxes into the node, found in a second node array or field.

map_upwind_node_link_max_to_node iterates across the grid and identifies the link control_values at each link connected to a node. It then uses the link_dirs_at_node data structure to identify links bringing flux into the node, then identifies the link with the maximum magnitude. The value of the second field ‘value_name’ at these links is then mapped onto the node. If no upwind link is found, the value will be recorded as zero.

Parameters:
• control_name (array or field name) – Values defined at nodes that dictate which end of the link to draw values from.

• value_name (array or field name) – Values defined at nodes from which values are drawn, based on control_name.

• out (ndarray, optional) – Buffer to place mapped values into or None to create a new array.

Returns:

Mapped values at nodes.

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...                                  0.,  0.,  0.,  0.,
...                                 -1., -2., -1.,
...                                  0.,  0.,  0.,  0.,
...                                 -1., -2., -1.])
array([  0.,   0.,   1.,   2.,
0.,   7.,   8.,   9.,
0.,  14.,  15.,  16.])

>>> values_at_nodes = rmg.add_empty("z", at="node")
... )
>>> values_at_nodes
array([  0.,   0.,   1.,   2.,
0.,   7.,   8.,   9.,
0.,  14.,  15.,  16.])
>>> rtn is values_at_nodes
True


Map magnitude and sign of vectors with components (ux, uy) onto grid links.

Examples

>>> from landlab import HexModelGrid
>>> import numpy
>>> hmg = HexModelGrid((3, 2))
>>> (numpy.round(10 * map_vectors_to_links(hmg, 1.0, 0.0))).astype(int)
array([10, -5,  5, -5,  5, 10, 10,  5, -5,  5, -5, 10])

property material_layers#

MaterialLayers for each cell.

merge(dual, node_at_cell=None, nodes_at_face=None)#
property midpoint_of_face#

Get the middle of faces.

Examples

>>> import numpy as np
>>> from landlab.graph import UniformRectilinearGraph

>>> graph = UniformRectilinearGraph((2, 3), spacing=(1, 2))
array([[ 1. ,  0. ], [ 3. ,  0. ],
[ 0. ,  0.5], [ 2. ,  0.5], [ 4. ,  0.5],
[ 1. ,  1. ], [ 3. ,  1. ]])

property ndim#

Number of spatial dimensions of the grid.

new_field_location(loc, size=None)#

Add a new quantity to a field.

Create an empty group into which new fields can be added. The new group is created but no memory allocated yet. The dictionary of the new group can be through a new at_ attribute of the class instance.

Parameters:
• loc (str) – Name of the new group to add to the field.

• size (int, optional) – Number of elements in the new quantity. If not provided, the size is set to be the size of the first field added to the group.

Raises:

ValueError – If the field already contains the group.

Examples

Create a collection of fields and add two groups, node and cell, to it.

>>> from landlab.field import GraphFields
>>> fields = GraphFields()
>>> fields.new_field_location("node", 12)
>>> fields.new_field_location("cell", 2)


The group names in the collection are retrieved with the groups attribute as a set.

>>> names = list(fields.groups)
>>> names.sort()
>>> names
['cell', 'node']


Access the new (empty) groups with the at_ attributes.

>>> fields.at_cell
FieldDataset('cell', size=2, fixed_size=True)
>>> fields.at_node
FieldDataset('node', size=12, fixed_size=True)

>>> fields.new_field_location("core_node")
>>> fields.at_core_node.size is None
True
>>> fields.at_core_node["air__temperature"] = [0, 1]
>>> fields.at_core_node.size
2

property node_at_cell#
property node_at_core_cell#

Get array of nodes associated with core cells.

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((4, 5))


Initially each cell’s node is core.

>>> grid.node_at_core_cell
array([ 6,  7,  8,
11, 12, 13])


Setting a node to closed causes means its cell is also “closed”.

>>> grid.status_at_node[8] = grid.BC_NODE_IS_CLOSED
>>> grid.node_at_core_cell
array([ 6,  7, 11, 12, 13])


Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1, 2, 2, 2]
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8))
array([1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 7, 8])


Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1, 2, 2, 2]
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8))
array([0, 1, 0, 1, 2, 3, 4, 3, 4, 5, 6, 7])

node_axis_coordinates(axis=0)#

Get the coordinates of nodes along a particular axis.

Return node coordinates from a given axis (defaulting to 0). Axis numbering is the same as that for numpy arrays. That is, the zeroth axis is along the rows, and the first along the columns.

Parameters:

axis (int, optional) – Coordinate axis.

Returns:

Coordinates of nodes for a given axis.

Return type:

ndarray

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((4, 5))
>>> grid.node_axis_coordinates(0)
array([ 0., 0., 0., 0., 0.,
1., 1., 1., 1., 1.,
2., 2., 2., 2., 2.,
3., 3., 3., 3., 3.])
>>> grid.node_axis_coordinates(1)
array([ 0., 1., 2., 3., 4.,
0., 1., 2., 3., 4.,
0., 1., 2., 3., 4.,
0., 1., 2., 3., 4.])

node_has_boundary_neighbor()#

Check if ModelGrid nodes have neighbors that are boundary nodes.

Checks to see if one of the eight neighbor nodes of node(s) with id has a boundary node. Returns True if a node has a boundary node, False if all neighbors are interior.

Parameters:

ids (int, or iterable of int) – ID of node to test.

Returns:

True if node has a neighbor with a boundary ID, False otherwise.

Return type:

boolean

Examples

    0,  1,  2,  3,
4,  5,  6,  7,  8,
9, 10,  11, 12, 13, 14,
15, 16, 17, 18, 19,
20, 21, 22, 23

>>> from landlab import HexModelGrid
>>> grid = HexModelGrid((5, 4))
>>> grid.node_has_boundary_neighbor()
array([ True,  True,  True,  True,  True,  True,  True,  True,  True,
True,  True, False, False,  True,  True,  True,  True,  True,
True,  True,  True,  True,  True,  True], dtype=bool)

>>> grid.node_has_boundary_neighbor()[6]
True
>>> grid.node_has_boundary_neighbor()[12]
False
>>> grid.node_has_boundary_neighbor()[((12, 0),)]
array([False,  True], dtype=bool)

node_is_boundary(ids, boundary_flag=None)#

Check if nodes are boundary nodes.

Check if nodes at given ids are boundary nodes. Use the boundary_flag to specify a particular boundary type status flag.

Parameters:
• ids (ndarray) – Node IDs to check.

• boundary_flag (int, optional) – A boundary type to check for.

Returns:

Array of booleans indicating if nodes are boundary nodes.

Return type:

ndarray

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> mg.node_is_boundary([0, 6])
array([ True, False], dtype=bool)
>>> mg.node_is_boundary([0, 6], boundary_flag=mg.BC_NODE_IS_CLOSED)
array([False, False], dtype=bool)

property node_x#
property node_y#
property nodes#

Get identifier for each node.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1]
>>> graph = Graph((node_y, node_x))
>>> graph.nodes
array([0, 1, 2, 3, 4, 5])

property nodes_at_face#

Get nodes at either end of links.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1, 2, 2, 2]
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8))
array([[0, 1], [1, 2],
[0, 3], [1, 4], [2, 5],
[3, 4], [4, 5],
[3, 6], [4, 7], [5, 8],
[6, 7], [7, 8]])

property nodes_at_patch#

Get the nodes that define a patch.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = ([0, 1, 2, 0, 1, 2, 0, 1, 2],
...                   [0, 0, 0, 1, 1, 1, 2, 2, 2])
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8))
>>> patches = ((0, 3, 5, 2), (1, 4, 6, 3))
>>> graph.nodes_at_patch
array([[4, 3, 0, 1],
[5, 4, 1, 2]])

property number_of_active_faces#

Total number of active faces.

Returns:

Total number of active faces in the grid.

Return type:

int

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> grid.number_of_active_faces
7


The number of active faces is updated when a node status changes.

>>> grid.status_at_node[6] = grid.BC_NODE_IS_CLOSED
>>> grid.number_of_active_faces
3


Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
17
>>> for edge in (mg.nodes_at_left_edge, mg.nodes_at_right_edge,
...              mg.nodes_at_bottom_edge):
...     mg.status_at_node[edge] = mg.BC_NODE_IS_CLOSED
10

property number_of_cells#

Get the number of cells.

property number_of_cells_present_at_corner#

Return the number of cells at a corner without a closed corner.

property number_of_cells_present_at_face#

Return the number of cells at a face without a closed corner.

property number_of_core_cells#

Number of core cells.

A core cell excludes all boundary cells.

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((4, 5))
>>> grid.number_of_core_cells
6

>>> grid.status_at_node[7] = grid.BC_NODE_IS_CLOSED
>>> grid.number_of_core_cells
5

property number_of_core_corners#

Number of core corners.

property number_of_core_nodes#

Number of core nodes.

The number of core nodes on the grid (i.e., excluding all boundary nodes).

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((4, 5))
>>> grid.number_of_core_nodes
6

>>> grid.status_at_node[7] = grid.BC_NODE_IS_CLOSED
>>> grid.number_of_core_nodes
5

property number_of_core_patches#

Number of core patches.

property number_of_corners#

Get total number of corners.

number_of_elements(name)#

Number of instances of an element.

Get the number of instances of a grid element in a grid.

Parameters:

name ({'node', 'cell', 'link', 'face', 'core_node', 'core_cell',) – ‘active_link’, ‘active_face’} Name of the grid element.

Returns:

Number of elements in the grid.

Return type:

int

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> mg.number_of_elements('node')
20
>>> mg.number_of_elements('core_cell')
6
31
17
>>> mg.status_at_node[8] = mg.BC_NODE_IS_CLOSED
31
13

property number_of_faces#

property number_of_fixed_faces#

Number of fixed faces.

Examples

>>> from landlab import NodeStatus, RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
0
3


Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1, 2, 2, 2]
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8))
True

property number_of_nodes#

Get total number of nodes.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1]
>>> graph = Graph((node_y, node_x))
>>> graph.number_of_nodes == 6
True

property number_of_patches#

Get the number of patches.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1, 2, 2, 2]
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8))
>>> patches = ((0, 3, 5, 2), (1, 4, 6, 3))
>>> graph.number_of_patches == 2
True


Return the number of patches at a link without a closed node.

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((3, 3))
>>> mg.status_at_node[mg.nodes_at_top_edge] = mg.BC_NODE_IS_CLOSED
array([[False,  True],
[False,  True],
[ True, False],
[ True,  True],
[False,  True],
[ True, False],
[ True, False],
[False, False],
[False, False],
[False, False],
[False, False],
[False, False]], dtype=bool)
array([1, 1, 1, 2, 1, 1, 1, 0, 0, 0, 0, 0])

property number_of_patches_present_at_node#

Return the number of patches at a node without a closed node.

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((3, 3))
>>> mg.status_at_node[mg.nodes_at_top_edge] = mg.BC_NODE_IS_CLOSED
>>> mg.patches_present_at_node
array([[ True, False, False, False],
[ True,  True, False, False],
[False,  True, False, False],
[False, False, False,  True],
[False, False,  True,  True],
[False, False,  True, False],
[False, False, False, False],
[False, False, False, False],
[False, False, False, False]], dtype=bool)
>>> mg.number_of_patches_present_at_node
array([1, 2, 1, 1, 2, 1, 0, 0, 0])

ones(*args, **kwds)#

Array, initialized to 1, whose size is that of the field.

Return a new array of the data field size, filled with ones. Keyword arguments are the same as that for the equivalent numpy function.

Parameters:

group (str) – Name of the group.

numpy.ones

See for a description of optional keywords.

empty

Equivalent method that does not initialize the new array.

zeros

Equivalent method that initializes the data to 0.

Examples

>>> from landlab.field import GraphFields
>>> field = GraphFields()
>>> field.new_field_location("node", 4)
>>> field.ones("node")
array([ 1.,  1.,  1.,  1.])
>>> field.ones("node", dtype=int)
array([1, 1, 1, 1])


Note that a new field is not added to the collection of fields.

>>> list(field.keys("node"))
[]

property open_boundary_corners#

Get array of open boundary corners.

property open_boundary_nodes#

Get array of open boundary nodes.

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> for edge in (mg.nodes_at_left_edge, mg.nodes_at_right_edge,
...              mg.nodes_at_bottom_edge):
...     mg.status_at_node[edge] = mg.BC_NODE_IS_CLOSED
>>> mg.open_boundary_nodes
array([16, 17, 18])

property patch_area_at_corner#

Cell areas in a ncorners-long array.

property patch_at_corner#

Get the patches on either side of each link.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = ([0, 1, 2, 0, 1, 2],
...                   [0, 0, 0, 1, 1, 1])
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5))
>>> patches = ((0, 3, 5, 2), (1, 4, 6, 3))
array([[ 0, -1], [ 1, -1],
[ 0, -1], [ 0,  1], [ 1, -1],
[ 0, -1], [ 1, -1]])

property patches_at_node#

Get the patches that touch each node.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = ([0, 1, 2, 0, 1, 2],
...                   [0, 0, 0, 1, 1, 1])
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5))
>>> patches = ((0, 3, 5, 2), (1, 4, 6, 3))
>>> graph.patches_at_node
array([[ 0, -1], [ 1,  0], [ 1, -1],
[ 0, -1], [ 0,  1], [ 1, -1]])


A boolean array, False where a patch has a closed node or is missing.

The array is the same shape as patches_at_link, and is designed to mask it.

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((3, 3))
>>> mg.status_at_node[mg.nodes_at_top_edge] = mg.BC_NODE_IS_CLOSED
array([[-1,  0],
[-1,  1],
[ 0, -1],
[ 1,  0],
[-1,  1],
[ 0,  2],
[ 1,  3],
[ 2, -1],
[ 3,  2],
[-1,  3],
[ 2, -1],
[ 3, -1]])
array([[False,  True],
[False,  True],
[ True, False],
[ True,  True],
[False,  True],
[ True, False],
[ True, False],
[False, False],
[False, False],
[False, False],
[False, False],
[False, False]], dtype=bool)
True
False

property patches_present_at_node#

A boolean array, False where a patch has a closed node or is missing.

The array is the same shape as patches_at_node, and is designed to mask it.

Note that in cases where patches may have more than 3 nodes (e.g., rasters), a patch is considered still present as long as at least 3 open nodes are present.

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((3, 3))
>>> mg.status_at_node[mg.nodes_at_top_edge] = mg.BC_NODE_IS_CLOSED
>>> mg.patches_at_node
array([[ 0, -1, -1, -1],
[ 1,  0, -1, -1],
[-1,  1, -1, -1],
[ 2, -1, -1,  0],
[ 3,  2,  0,  1],
[-1,  3,  1, -1],
[-1, -1, -1,  2],
[-1, -1,  2,  3],
[-1, -1,  3, -1]])
>>> mg.patches_present_at_node
array([[ True, False, False, False],
[ True,  True, False, False],
[False,  True, False, False],
[False, False, False,  True],
[False, False,  True,  True],
[False, False,  True, False],
[False, False, False, False],
[False, False, False, False],
[False, False, False, False]], dtype=bool)
>>> 1 in mg.patches_at_node * mg.patches_present_at_node
True
>>> 2 in mg.patches_at_node * mg.patches_present_at_node
False

property perimeter_corners#

Get corners on the convex hull of a Graph.

property perimeter_nodes#

Get nodes on the convex hull of a Graph.

Examples

>>> import numpy as np
>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1]
>>> graph = Graph((node_y, node_x))
>>> np.sort(graph.perimeter_nodes)
array([0, 2, 3, 5])

reset_status_at_node()#

Resolves values provided defined on links into the x and y directions. Returns values_along_x, values_along_y

return_array_or_field_values(field, at=None)#

Return field given a field name, or array of with the correct shape.

Given a group and a field, return a reference to the associated data array. field is either a string that is a field in the group or an array of the correct size.

This function is meant to serve like the use_field_name_or_array decorator for bound functions.

Parameters:
• field (str or array) – Name of the field withing group.

• at (str, optional) – Name of the group.

Returns:

The values of the field.

Return type:

numpy.ndarray

Raises:
• landlab.field.errors.GroupError – If group does not exist

• landlab.field.errors.FieldError – If field does not exist

Examples

Create a group of fields called node.

>>> import numpy as np
>>> from landlab.field import GraphFields
>>> fields = GraphFields()
>>> fields.new_field_location('node', 4)


Add a field, initialized to ones, called topographic__elevation to the node group. The field_values method returns a reference to the field’s data.

>>> _ = fields.add_ones("topographic__elevation", at="node")
>>> fields.field_values("topographic__elevation", at="node")
array([ 1.,  1.,  1.,  1.])


Alternatively, if the second argument is an array, its size is checked and returned if correct.

>>> vals = np.array([4., 5., 7., 3.])
>>> fields.return_array_or_field_values(vals, at="node")
array([ 4.,  5.,  7.,  3.])


Raise FieldError if field does not exist in group.

>>> fields.return_array_or_field_values("surface__temperature", at="node")
...
Traceback (most recent call last):
FieldError: surface__temperature


If group does not exists, Raise GroupError.

>>> fields.return_array_or_field_values("topographic__elevation", at="cell")
...
Traceback (most recent call last):
GroupError: cell


And if the array of values provided is incorrect, raise a ValueError.

>>> vals = np.array([3., 2., 1.])
>>> fields.return_array_or_field_values(vals, at="node")
...
Traceback (most recent call last):
ValueError: Array has incorrect size.

save(path, clobber=False)[source]#

Save a grid and fields.

This method uses pickle to save a Voronoi grid as a pickle file. At the time of coding, this is the only convenient output format for Voronoi grids, but support for netCDF is likely coming.

All fields will be saved, along with the grid.

The recommended suffix for the save file is ‘.grid’. This will be added to your save if you don’t include it.

This method is equivalent to save_grid, and load_grid can be used to load these files.

Caution: Pickling can be slow, and can produce very large files. Caution 2: Future updates to Landlab could potentially render old saves unloadable.

Parameters:
• path (str) – Path to output file.

• clobber (bool (defaults to false)) – Set to true to allow overwriting

Returns:

The name of the saved file (with the “.grid” extension).

Return type:

str

Examples

>>> from landlab import VoronoiDelaunayGrid
>>> import numpy as np

>>> grid = VoronoiDelaunayGrid(np.random.rand(20), np.random.rand(20))
>>> grid.save("mytestsave.grid")
'mytestsave.grid'

set_nodata_nodes_to_closed(node_data, nodata_value)#

Make no-data nodes closed boundaries.

Sets node status to BC_NODE_IS_CLOSED for all nodes whose value of node_data is equal to the nodata_value.

Any links connected to BC_NODE_IS_CLOSED nodes are automatically set to LinkStatus.INACTIVE boundary.

Parameters:
• node_data (ndarray) – Data values.

• nodata_value (float) – Value that indicates an invalid value.

Examples

The following example uses the following grid:

*--I--->o------>o------>o
^       ^       ^       ^
I       I       |       |
|       |       |       |
*--I--->*--I--->o------>o
^       ^       ^       ^
I       I       I       I
|       |       |       |
*--I--->*--I--->*--I--->*


Note

* indicates the nodes that are set to NodeStatus.CLOSED

o indicates the nodes that are set to NodeStatus.CORE

I indicates the links that are set to LinkStatus.INACTIVE

>>> import numpy as np
>>> import landlab as ll
>>> mg = ll.RasterModelGrid((3, 4))
>>> mg.status_at_node
array([1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1], dtype=uint8)
>>> h = np.array([-9999, -9999, -9999, -9999, -9999, -9999, 12345.,
...     0., -9999, 0., 0., 0.])
>>> mg.set_nodata_nodes_to_closed(h, -9999)
>>> mg.status_at_node
array([4, 4, 4, 4, 4, 4, 0, 1, 4, 1, 1, 1], dtype=uint8)


Make no-data nodes fixed gradient boundaries.

Set node status to BC_NODE_IS_FIXED_VALUE for all nodes whose value of node_data is equal to nodata_value.

Parameters:
• node_data (ndarray) – Data values.

• nodata_value (float) – Value that indicates an invalid value.

Examples

The following examples use this grid:

*--I--->*--I--->*--I--->*--I--->*--I--->*--I--->*--I--->*--I--->*
^       ^       ^       ^       ^       ^       ^       ^       ^
I       I       I       X       X       X       X       X       I
|       |       |       |       |       |       |       |       |
*--I--->*--I--->*--X--->o       o       o       o       o--X--->*
^       ^       ^       ^       ^       ^       ^       ^       ^
I       I       I       |       |       |       |       |       I
|       |       |       |       |       |       |       |       |
*--I--->*--I--->*--X--->o       o       o       o       o--X--->*
^       ^       ^       ^       ^       ^       ^       ^       ^
I       I       I       X       X       X       X       X       I
|       |       |       |       |       |       |       |       |
*--I--->*--I--->*--I--->*--I--->*--I--->*--I--->*--I--->*--I--->*


Note

X indicates the links that are set to LinkStatus.FIXED

I indicates the links that are set to LinkStatus.INACTIVE

o indicates the nodes that are set to NodeStatus.CORE

* indicates the nodes that are set to

>>> import numpy as np
>>> from landlab import RasterModelGrid
>>> rmg = RasterModelGrid((4, 9))
>>> rmg.status_at_node
array([1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 0, 0, 0, 0, 0, 0, 0, 1,
1, 0, 0, 0, 0, 0, 0, 0, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=uint8)

>>> z = rmg.zeros(at='node')
>>> z = np.array([
...     -99., -99., -99., -99., -99., -99., -99., -99., -99.,
...     -99., -99., -99.,   0.,   0.,   0.,   0.,   0., -99.,
...     -99., -99., -99.,   0.,   0.,   0.,   0.,   0., -99.,
...     -99., -99., -99., -99., -99., -99., -99., -99., -99.])

>>> rmg.set_nodata_nodes_to_fixed_gradient(z, -99)
>>> rmg.status_at_node
array([2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 0, 0, 0, 0, 0, 2,
2, 2, 2, 0, 0, 0, 0, 0, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2], dtype=uint8)

>>> rmg.status_at_link
array([4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 4,
4, 4, 2, 0, 0, 0, 0, 2, 4, 4, 4, 0, 0, 0, 0, 0, 4,
4, 4, 2, 0, 0, 0, 0, 2, 4, 4, 4, 2, 2, 2, 2, 2, 4,
4, 4, 4, 4, 4, 4, 4, 4], dtype=uint8)

size(group)#

Return the size of the arrays stored in a group.

Parameters:

group (str) – Group name.

Returns:

Array size.

Return type:

int

Examples

>>> from landlab.field import GraphFields
>>> fields = GraphFields()
>>> fields.new_field_location("node", 4)
>>> fields.size("node")
4

sort()#

Sort graph elements.

property status_at_corner#

Get array of the boundary status for each corner.

property status_at_face#

Get array of the status of all faces.

Get array of the status of all links.

Examples

>>> from landlab import RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> mg.status_at_node[mg.nodes_at_left_edge] = mg.BC_NODE_IS_CLOSED
array([4, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, 0, 2, 4, 0, 0, 0, 4, 4, 0, 0,
2, 4, 0, 0, 0, 4, 4, 4, 4, 4], dtype=uint8)

property status_at_node#

Get array of the boundary status for each node.

Examples

>>> import numpy as np
>>> from landlab import LinkStatus, NodeStatus, RasterModelGrid
>>> mg = RasterModelGrid((4, 5))
>>> mg.status_at_node.reshape((4, 5))
array([[1, 1, 1, 1, 1],
[1, 0, 0, 0, 1],
[1, 0, 0, 0, 1],
[1, 1, 1, 1, 1]], dtype=uint8)
False

>>> mg.status_at_node[mg.nodes_at_left_edge] = NodeStatus.FIXED_GRADIENT
>>> mg.status_at_node.reshape((4, 5))
array([[2, 1, 1, 1, 1],
[2, 0, 0, 0, 1],
[2, 0, 0, 0, 1],
[2, 1, 1, 1, 1]], dtype=uint8)
True

thaw()#

Thaw the graph by making arrays writable.

thawed()#
to_dict()#
to_json()#
to_netcdf(*args, **kwds)#

Write graph contents to a netCDF file.

See xarray.Dataset.to_netcdf for a complete list of parameters. Below are only the most common.

Parameters:
• path (str, optional) – Path to which to save this graph.

• mode ({'w', 'a'}, optional) – Write (‘w’) or append (‘a’) mode. If mode=’w’, any existing file at this location will be overwritten.

• format ({'NETCDF4', 'NETCDF4_CLASSIC', 'NETCDF3_64BIT', 'NETCDF3_CLASSIC'}, optional) –

File format for the resulting netCDF file:

• NETCDF4: Data is stored in an HDF5 file, using netCDF4 API features.

• NETCDF4_CLASSIC: Data is stored in an HDF5 file, using only netCDF 3 compatible API features.

• NETCDF3_64BIT: 64-bit offset version of the netCDF 3 file format, which fully supports 2+ GB files, but is only compatible with clients linked against netCDF version 3.6.0 or later.

• NETCDF3_CLASSIC: The classic netCDF 3 file format. It does not handle 2+ GB files very well.

All formats are supported by the netCDF4-python library. scipy.io.netcdf only supports the last two formats.

The default format is NETCDF4 if you are saving a file to disk and have the netCDF4-python library available. Otherwise, xarray falls back to using scipy to write netCDF files and defaults to the NETCDF3_64BIT format (scipy does not support netCDF4).

property unit_vector_at_corner#

Get a unit vector for each corner.

property unit_vector_at_face#

Make arrays to store the unit vectors associated with each face.

Make arrays to store the unit vectors associated with each link.

For each link, the x and y components of the link’s unit vector (that is, the link’s x and y dimensions if it were shrunk to unit length but retained its orientation).

Examples

The example below is a seven-node hexagonal grid, with six nodes around the perimeter and one node (#3) in the interior. There are four horizontal links with unit vector (1,0), and 8 diagonal links with unit vector (+/-0.5, +/-sqrt(3)/2) (note: sqrt(3)/2 ~ 0.866).

>>> from landlab.graph import TriGraph
>>> graph = TriGraph((3, 2), spacing=2.0, node_layout="hex", sort=True)

>>> np.round(graph.unit_vector_at_link[:, 0], decimals=5)
array([ 1. , -0.5,  0.5, -0.5,  0.5,  1. ,  1. ,  0.5, -0.5,  0.5, -0.5,
1. ])
array([ 0.     ,  0.86603,  0.86603,  0.86603,  0.86603,  0.     ,
0.     ,  0.86603,  0.86603,  0.86603,  0.86603,  0.     ])

property unit_vector_at_node#

Get a unit vector for each node.

Examples

>>> from landlab.graph import UniformRectilinearGraph
>>> graph = UniformRectilinearGraph((3, 3))
>>> graph.unit_vector_at_node
array([[ 1.,  1.],
[ 2.,  1.],
[ 1.,  1.],
[ 1.,  2.],
[ 2.,  2.],
[ 1.,  2.],
[ 1.,  1.],
[ 2.,  1.],
[ 1.,  1.]])

>>> from landlab.graph import TriGraph
>>> graph = TriGraph((3, 2), spacing=2.0, node_layout="hex", sort=True)

>>> unit_vector_at_node = np.round(graph.unit_vector_at_node, decimals=5)
>>> unit_vector_at_node[:, 0]
array([ 2.,  2.,  2.,  4.,  2.,  2.,  2.])
>>> unit_vector_at_node[:, 1]
array([ 1.73205,  1.73205,  1.73205,  3.4641 ,  1.73205,  1.73205,  1.73205])

property unit_vector_sum_xcomponent_at_corner#

Get array of x-component of unit vector sums at each corner.

property unit_vector_sum_xcomponent_at_node#

Get array of x-component of unit vector sums at each node.

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 3))
>>> len(grid.unit_vector_sum_xcomponent_at_node) == grid.number_of_nodes
True
>>> grid.unit_vector_sum_xcomponent_at_node
array([ 1.,  2.,  1.,  1.,  2.,  1.,  1.,  2.,  1.])

property unit_vector_sum_ycomponent_at_corner#

Get array of y-component of unit vector sums at each corner.

property unit_vector_sum_ycomponent_at_node#

Get array of y-component of unit vector sums at each node.

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 3))
>>> len(grid.unit_vector_sum_ycomponent_at_node) == grid.number_of_nodes
True
>>> grid.unit_vector_sum_ycomponent_at_node
array([ 1.,  1.,  1.,  2.,  2.,  2.,  1.,  1.,  1.])


Return an (nnodes, X) shape array of link IDs of which links are upwind of each node, according to values (field or array).

X is the maximum upwind links at any node. Nodes with fewer upwind links than this have additional slots filled with bad_index. Links are ordered anticlockwise from east.

Parameters:
• values (str or array) – Name of variable field defined at links, or array of values at links.

• bad_index (int) – Index to place in array indicating no link.

Returns:

Return type:

ndarray

Examples

>>> import numpy as np
>>> from landlab import RasterModelGrid

>>> rmg = RasterModelGrid((3, 4))
...                                 -2., -3., -4., -5.,
...                                 -1., -2., -1.,
...                                 -1., -2., -3., -4.,
...                                 -1., -2., -1.])
array([[-1, -1],
[ 0, -1],
[ 1, -1],
[ 2, -1],
[ 3, -1],
[ 7,  4],
[ 8,  5],
[ 9,  6],
[10, -1],
[14, 11],
[15, 12],
[16, 13]])

property x_of_corner#

Get x-coordinate of corner.

property x_of_node#

Get x-coordinate of node.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1]
>>> graph = Graph((node_y, node_x))
>>> graph.x_of_node
array([ 0.,  1.,  2.,  0.,  1.,  2.])

property xy_of_cell#

Get the centroid of each cell.

property xy_of_corner#

Get x and y-coordinates of corner.

property xy_of_face#
property xy_of_node#

Get x and y-coordinates of node.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1]
>>> graph = Graph((node_y, node_x))
>>> graph.xy_of_node[:, 0]
array([ 0.,  1.,  2.,  0.,  1.,  2.])
>>> graph.xy_of_node[:, 1]
array([ 0.,  0.,  0.,  1.,  1.,  1.])

property xy_of_patch#

Get the centroid of each patch.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1, 2, 2, 2]
>>> links = ((0, 1), (1, 2),
...          (0, 3), (1, 4), (2, 5),
...          (3, 4), (4, 5),
...          (3, 6), (4, 7), (5, 8),
...          (6, 7), (7, 8))
>>> patches = ((0, 3, 5, 2), (1, 4, 6, 3))
>>> graph.xy_of_patch
array([[ 0.5,  0.5],
[ 1.5,  0.5]])

property xy_of_reference#

Return the coordinates (x, y) of the reference point.

For RasterModelGrid and HexModelGrid the reference point is the minimum of x_of_node and of y_of_node. By default it is (0, 0). For VoronoiDelaunayGrid the reference point is (0, 0). For RadialModelGrid it is the (x, y) of the center point.

The intention of these coordinates is to provide a method to store the large float values of projected coordinates.

Example

>>> from landlab import RasterModelGrid
>>> rmg = RasterModelGrid((4, 5),
...       xy_of_reference = (12345, 678910))
>>> rmg.xy_of_reference
(12345, 678910)
>>> rmg.xy_of_reference = (98765, 43210)
>>> rmg.xy_of_reference
(98765, 43210)

property y_of_corner#

Get y-coordinate of corner.

property y_of_node#

Get y-coordinate of node.

Examples

>>> from landlab.graph import Graph
>>> node_x, node_y = [0, 1, 2, 0, 1, 2], [0, 0, 0, 1, 1, 1]
>>> graph = Graph((node_y, node_x))
>>> graph.y_of_node
array([ 0.,  0.,  0.,  1.,  1.,  1.])

zeros(*args, **kwds)#

Array, initialized to 0, whose size is that of the field.

Parameters:
• group (str) – Name of the group.

• size (Return a new array of the data field) –

• Keyword (filled with zeros.) –

• function. (arguments are the same as that for the equivalent numpy) –

• grid. (This method is not valid for the group) –

numpy.zeros

See for a description of optional keywords.

empty

Equivalent method that does not initialize the new array.

ones

Equivalent method that initializes the data to 1.

Examples

>>> from landlab.field import GraphFields
>>> field = GraphFields()
>>> field.new_field_location("node", 4)
>>> field.zeros("node")
array([ 0.,  0.,  0.,  0.])


Note that a new field is not added to the collection of fields.

>>> list(field.keys("node"))
[]

simple_poly_area(x, y)[source]#

Calculates and returns the area of a 2-D simple polygon.

Input vertices must be in sequence (clockwise or counterclockwise). x and y are arrays that give the x- and y-axis coordinates of the polygon’s vertices.

Parameters:
• x (ndarray) – x-coordinates of of polygon vertices.

• y (ndarray) – y-coordinates of of polygon vertices.

Returns:

out – Area of the polygon

Return type:

float

Examples

>>> import numpy as np
>>> from landlab.grid.voronoi import simple_poly_area
>>> x = np.array([3., 1., 1., 3.])
>>> y = np.array([1.5, 1.5, 0.5, 0.5])
>>> simple_poly_area(x, y)
2.0


If the input coordinate arrays are 2D, calculate the area of each polygon. Note that when used in this mode, all polygons must have the same number of vertices, and polygon vertices are listed column-by-column.

>>> x = np.array([[ 3.,  1.,  1.,  3.],
...               [-2., -2., -1., -1.]]).T
>>> y = np.array([[1.5, 1.5, 0.5, 0.5],
...               [ 0.,  1.,  2.,  0.]]).T
>>> simple_poly_area(x, y)
array([ 2. ,  1.5])