landlab.graph.structured_quad.structured_quad

class RectilinearGraph

Bases: StructuredQuadGraphExtras

Graph of a rectlinear grid of nodes.

Examples

>>> from landlab.graph import RectilinearGraph
>>> graph = RectilinearGraph(([0, 1, 2, 3], [1, 4, 8]))
>>> graph.number_of_nodes
12
>>> graph.y_of_node.reshape(graph.shape)
array([[0., 0., 0.],
       [1., 1., 1.],
       [2., 2., 2.],
       [3., 3., 3.]])
>>> graph.x_of_node.reshape(graph.shape)
array([[1., 4., 8.],
       [1., 4., 8.],
       [1., 4., 8.],
       [1., 4., 8.]])

Define a graph of connected nodes.

Parameters:

mesh (Dataset) – xarray Dataset that defines the topology in ugrid format.

__init__(nodes, sort=False)

Define a graph of connected nodes.

Parameters:

mesh (Dataset) – xarray Dataset that defines the topology in ugrid format.

__new__(**kwargs)

property adjacent_links_at_link

property adjacent_nodes_at_node

Get adjacent nodes.

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),
... )
>>> graph = Graph((node_y, node_x), links=links, sort=True)
>>> graph.adjacent_nodes_at_node
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),
... )
>>> graph = Graph((node_y, node_x), links=links, sort=True)
>>> graph.adjacent_nodes_at_node
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 angle_of_link

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 = Graph((node_y, node_x), links=links)
>>> graph.angle_of_link * 180.0 / np.pi
array([ 0.,  0., 90., 90., 90.,  0.,  0.])

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 = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.area_of_patch
array([1.,  1.])

property corner_nodes

property ds

freeze()

Freeze the graph by making arrays read-only.

classmethod from_dict(meta)

classmethod from_netcdf(fname)

property frozen

property horizontal_links

property length_of_link

Get the length of links.

Examples

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

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

property link_dirs_at_node

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:

(n_nodes, max_links_per_node) ndarray of int

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.link_dirs_at_node
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)

property links_at_node

Get links touching a node.

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.links_at_node
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]])

property links_at_patch

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))
>>> graph = Graph((node_y, node_x), links=links, patches=patches, sort=True)
>>> graph.links_at_patch
array([[3, 5, 2, 0],
       [4, 6, 3, 1]])

classmethod load(source)

merge(dual, node_at_cell=None, nodes_at_face=None)

property midpoint_of_link

Get the middle of links.

Examples

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

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

property ndim

property node_at_link_head

Get nodes at link head.

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

property node_at_link_tail

Get nodes at link tail.

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

property node_x

property node_y

property nodes

A shaped array of node ids.

Returns:

Node IDs in an array shaped as number_of_node_rows by number_of_node_columns.

Return type:

ndarray

property nodes_at_bottom_edge

property nodes_at_corners_of_grid

Nodes at corners of grid.

The nodes at at the corners of the grid. The nodes are returned counterclockwise starting with the upper-right.

Returns:

Nodes at the four corners.

Return type:

tuple of int

Examples

>>> from landlab.graph import UniformRectilinearGraph
>>> graph = UniformRectilinearGraph((4, 5))
>>> graph.nodes_at_corners_of_grid
(19, 15, 0, 4)

nodes_at_edge(edge)

property nodes_at_left_edge

property nodes_at_link

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.nodes_at_link
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 = Graph((node_y, node_x), links=links, patches=patches, sort=True)
>>> graph.nodes_at_patch
array([[4, 3, 0, 1],
       [5, 4, 1, 2]])

property nodes_at_right_edge

property nodes_at_top_edge

property number_of_links

Get nodes at link head.

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.number_of_links == 12
True

property number_of_node_columns

property number_of_node_rows

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 = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.number_of_patches == 2
True

property orientation_of_link

Return array of link orientation codes (one value per link).

Orientation codes are defined by LinkOrientation; 1 = E, 2 = ENE, 4 = NNE, 8 = N, 16 = NNW, 32 = ESE (using powers of 2 allows for future applications that might want additive combinations).

property parallel_links_at_link

Return similarly oriented links connected to each link.

Return IDs of links of the same orientation that are connected to each given link’s tail or head node.

The data structure is a numpy array of shape (n_links, 2) containing the IDs of the “tail-wise” (connected to tail node) and “head-wise” (connected to head node) links, or -1 if the link is inactive (e.g., on the perimeter) or it has no attached parallel neighbor in the given direction.

For instance, consider a 3x4 raster, in which link IDs are as shown:

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

Here’s a mapping of the tail-wise (shown at left or bottom of links) and head-wise (shown at right or top of links) links:

.----.----.----.
|    |    |    |
|    |    |    |
|    4    5    |
.---8.7--9.8---.
|   11   12    |
|    |    |    |
|    |    |    |
.----.----.----.

So the corresponding data structure would be mostly filled with -1, but for the 7 active links, it would look like:

4: [[-1, 11],
5:  [-1, 12],
7:  [-1,  8],
8:  [ 7,  9],
9:  [ 8, -1],
11: [ 4, -1],
12: [ 5, -1]]

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> pll = grid.parallel_links_at_link
>>> pll[4:13, :]
array([[-1, 11],
       [-1, 12],
       [-1, 13],
       [-1,  8],
       [ 7,  9],
       [ 8, -1],
       [ 3, -1],
       [ 4, -1],
       [ 5, -1]])

property patches_at_link

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))
>>> graph = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.patches_at_link
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 = Graph((node_y, node_x), links=links, patches=patches, sort=True)
>>> graph.patches_at_node
array([[ 0, -1], [ 1,  0], [ 1, -1],
       [ 0, -1], [ 0,  1], [ 1, -1]])

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])

static setup_node_y_and_x(coords)

property shape

sort()

Sort graph elements.

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_link

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. ])
>>> np.round(graph.unit_vector_at_link[:, 1], decimals=5)
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 vertical_links

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_link

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 = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.xy_of_patch
array([[0.5, 0.5],
       [1.5, 0.5]])

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.])

class StructuredQuadGraph

Bases: StructuredQuadGraphExtras

Define a graph of connected nodes.

Parameters:

mesh (Dataset) – xarray Dataset that defines the topology in ugrid format.

__init__(coords, shape=None, sort=False)

Define a graph of connected nodes.

Parameters:

mesh (Dataset) – xarray Dataset that defines the topology in ugrid format.

__new__(**kwargs)

property adjacent_links_at_link

property adjacent_nodes_at_node

Get adjacent nodes.

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),
... )
>>> graph = Graph((node_y, node_x), links=links, sort=True)
>>> graph.adjacent_nodes_at_node
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),
... )
>>> graph = Graph((node_y, node_x), links=links, sort=True)
>>> graph.adjacent_nodes_at_node
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 angle_of_link

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 = Graph((node_y, node_x), links=links)
>>> graph.angle_of_link * 180.0 / np.pi
array([ 0.,  0., 90., 90., 90.,  0.,  0.])

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 = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.area_of_patch
array([1.,  1.])

property corner_nodes

property ds

freeze()

Freeze the graph by making arrays read-only.

classmethod from_dict(meta)

classmethod from_netcdf(fname)

property frozen

property horizontal_links

property length_of_link

Get the length of links.

Examples

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

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

property link_dirs_at_node

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:

(n_nodes, max_links_per_node) ndarray of int

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.link_dirs_at_node
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)

property links_at_node

Get links touching a node.

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.links_at_node
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]])

property links_at_patch

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))
>>> graph = Graph((node_y, node_x), links=links, patches=patches, sort=True)
>>> graph.links_at_patch
array([[3, 5, 2, 0],
       [4, 6, 3, 1]])

classmethod load(source)

merge(dual, node_at_cell=None, nodes_at_face=None)

property midpoint_of_link

Get the middle of links.

Examples

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

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

property ndim

property node_at_link_head

Get nodes at link head.

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

property node_at_link_tail

Get nodes at link tail.

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

property node_x

property node_y

property nodes

A shaped array of node ids.

Returns:

Node IDs in an array shaped as number_of_node_rows by number_of_node_columns.

Return type:

ndarray

property nodes_at_bottom_edge

property nodes_at_corners_of_grid

Nodes at corners of grid.

The nodes at at the corners of the grid. The nodes are returned counterclockwise starting with the upper-right.

Returns:

Nodes at the four corners.

Return type:

tuple of int

Examples

>>> from landlab.graph import UniformRectilinearGraph
>>> graph = UniformRectilinearGraph((4, 5))
>>> graph.nodes_at_corners_of_grid
(19, 15, 0, 4)

nodes_at_edge(edge)

property nodes_at_left_edge

property nodes_at_link

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.nodes_at_link
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 = Graph((node_y, node_x), links=links, patches=patches, sort=True)
>>> graph.nodes_at_patch
array([[4, 3, 0, 1],
       [5, 4, 1, 2]])

property nodes_at_right_edge

property nodes_at_top_edge

property number_of_links

Get nodes at link head.

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.number_of_links == 12
True

property number_of_node_columns

property number_of_node_rows

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 = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.number_of_patches == 2
True

property orientation_of_link

Return array of link orientation codes (one value per link).

Orientation codes are defined by LinkOrientation; 1 = E, 2 = ENE, 4 = NNE, 8 = N, 16 = NNW, 32 = ESE (using powers of 2 allows for future applications that might want additive combinations).

property parallel_links_at_link

Return similarly oriented links connected to each link.

Return IDs of links of the same orientation that are connected to each given link’s tail or head node.

The data structure is a numpy array of shape (n_links, 2) containing the IDs of the “tail-wise” (connected to tail node) and “head-wise” (connected to head node) links, or -1 if the link is inactive (e.g., on the perimeter) or it has no attached parallel neighbor in the given direction.

For instance, consider a 3x4 raster, in which link IDs are as shown:

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

Here’s a mapping of the tail-wise (shown at left or bottom of links) and head-wise (shown at right or top of links) links:

.----.----.----.
|    |    |    |
|    |    |    |
|    4    5    |
.---8.7--9.8---.
|   11   12    |
|    |    |    |
|    |    |    |
.----.----.----.

So the corresponding data structure would be mostly filled with -1, but for the 7 active links, it would look like:

4: [[-1, 11],
5:  [-1, 12],
7:  [-1,  8],
8:  [ 7,  9],
9:  [ 8, -1],
11: [ 4, -1],
12: [ 5, -1]]

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> pll = grid.parallel_links_at_link
>>> pll[4:13, :]
array([[-1, 11],
       [-1, 12],
       [-1, 13],
       [-1,  8],
       [ 7,  9],
       [ 8, -1],
       [ 3, -1],
       [ 4, -1],
       [ 5, -1]])

property patches_at_link

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))
>>> graph = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.patches_at_link
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 = Graph((node_y, node_x), links=links, patches=patches, sort=True)
>>> graph.patches_at_node
array([[ 0, -1], [ 1,  0], [ 1, -1],
       [ 0, -1], [ 0,  1], [ 1, -1]])

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])

static setup_node_y_and_x(yx_at_node, shape=None)

property shape

sort()

Sort graph elements.

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_link

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. ])
>>> np.round(graph.unit_vector_at_link[:, 1], decimals=5)
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 vertical_links

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_link

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 = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.xy_of_patch
array([[0.5, 0.5],
       [1.5, 0.5]])

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.])

class StructuredQuadGraphExtras

Bases: StructuredQuadGraphTopology, Graph

Define a graph of connected nodes.

Parameters:

mesh (Dataset) – xarray Dataset that defines the topology in ugrid format.

__init__(node_y_and_x, sort=False)

Define a graph of connected nodes.

Parameters:

mesh (Dataset) – xarray Dataset that defines the topology in ugrid format.

__new__(**kwargs)

property adjacent_links_at_link

property adjacent_nodes_at_node

Get adjacent nodes.

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),
... )
>>> graph = Graph((node_y, node_x), links=links, sort=True)
>>> graph.adjacent_nodes_at_node
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),
... )
>>> graph = Graph((node_y, node_x), links=links, sort=True)
>>> graph.adjacent_nodes_at_node
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 angle_of_link

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 = Graph((node_y, node_x), links=links)
>>> graph.angle_of_link * 180.0 / np.pi
array([ 0.,  0., 90., 90., 90.,  0.,  0.])

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 = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.area_of_patch
array([1.,  1.])

property corner_nodes

property ds

freeze()

Freeze the graph by making arrays read-only.

classmethod from_dict(meta)

classmethod from_netcdf(fname)

property frozen

property horizontal_links

property length_of_link

Get the length of links.

Examples

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

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

property link_dirs_at_node

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:

(n_nodes, max_links_per_node) ndarray of int

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.link_dirs_at_node
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)

property links_at_node

Get links touching a node.

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.links_at_node
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]])

property links_at_patch

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))
>>> graph = Graph((node_y, node_x), links=links, patches=patches, sort=True)
>>> graph.links_at_patch
array([[3, 5, 2, 0],
       [4, 6, 3, 1]])

classmethod load(source)

merge(dual, node_at_cell=None, nodes_at_face=None)

property midpoint_of_link

Get the middle of links.

Examples

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

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

property ndim

property node_at_link_head

Get nodes at link head.

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

property node_at_link_tail

Get nodes at link tail.

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

property node_x

property node_y

property nodes

A shaped array of node ids.

Returns:

Node IDs in an array shaped as number_of_node_rows by number_of_node_columns.

Return type:

ndarray

property nodes_at_bottom_edge

property nodes_at_corners_of_grid

Nodes at corners of grid.

The nodes at at the corners of the grid. The nodes are returned counterclockwise starting with the upper-right.

Returns:

Nodes at the four corners.

Return type:

tuple of int

Examples

>>> from landlab.graph import UniformRectilinearGraph
>>> graph = UniformRectilinearGraph((4, 5))
>>> graph.nodes_at_corners_of_grid
(19, 15, 0, 4)

nodes_at_edge(edge)

property nodes_at_left_edge

property nodes_at_link

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.nodes_at_link
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 = Graph((node_y, node_x), links=links, patches=patches, sort=True)
>>> graph.nodes_at_patch
array([[4, 3, 0, 1],
       [5, 4, 1, 2]])

property nodes_at_right_edge

property nodes_at_top_edge

property number_of_links

Get nodes at link head.

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.number_of_links == 12
True

property number_of_node_columns

property number_of_node_rows

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 = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.number_of_patches == 2
True

property orientation_of_link

Return array of link orientation codes (one value per link).

Orientation codes are defined by LinkOrientation; 1 = E, 2 = ENE, 4 = NNE, 8 = N, 16 = NNW, 32 = ESE (using powers of 2 allows for future applications that might want additive combinations).

property parallel_links_at_link

Return similarly oriented links connected to each link.

Return IDs of links of the same orientation that are connected to each given link’s tail or head node.

The data structure is a numpy array of shape (n_links, 2) containing the IDs of the “tail-wise” (connected to tail node) and “head-wise” (connected to head node) links, or -1 if the link is inactive (e.g., on the perimeter) or it has no attached parallel neighbor in the given direction.

For instance, consider a 3x4 raster, in which link IDs are as shown:

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

Here’s a mapping of the tail-wise (shown at left or bottom of links) and head-wise (shown at right or top of links) links:

.----.----.----.
|    |    |    |
|    |    |    |
|    4    5    |
.---8.7--9.8---.
|   11   12    |
|    |    |    |
|    |    |    |
.----.----.----.

So the corresponding data structure would be mostly filled with -1, but for the 7 active links, it would look like:

4: [[-1, 11],
5:  [-1, 12],
7:  [-1,  8],
8:  [ 7,  9],
9:  [ 8, -1],
11: [ 4, -1],
12: [ 5, -1]]

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> pll = grid.parallel_links_at_link
>>> pll[4:13, :]
array([[-1, 11],
       [-1, 12],
       [-1, 13],
       [-1,  8],
       [ 7,  9],
       [ 8, -1],
       [ 3, -1],
       [ 4, -1],
       [ 5, -1]])

property patches_at_link

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))
>>> graph = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.patches_at_link
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 = Graph((node_y, node_x), links=links, patches=patches, sort=True)
>>> graph.patches_at_node
array([[ 0, -1], [ 1,  0], [ 1, -1],
       [ 0, -1], [ 0,  1], [ 1, -1]])

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])

property shape

sort()

Sort graph elements.

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_link

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. ])
>>> np.round(graph.unit_vector_at_link[:, 1], decimals=5)
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 vertical_links

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_link

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 = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.xy_of_patch
array([[0.5, 0.5],
       [1.5, 0.5]])

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.])

class StructuredQuadGraphTopology

Bases: object

__init__(shape)

__new__(**kwargs)

property corner_nodes

property horizontal_links

property link_dirs_at_node

property links_at_node

property nodes

A shaped array of node ids.

Returns:

Node IDs in an array shaped as number_of_node_rows by number_of_node_columns.

Return type:

ndarray

property nodes_at_bottom_edge

property nodes_at_corners_of_grid

Nodes at corners of grid.

The nodes at at the corners of the grid. The nodes are returned counterclockwise starting with the upper-right.

Returns:

Nodes at the four corners.

Return type:

tuple of int

Examples

>>> from landlab.graph import UniformRectilinearGraph
>>> graph = UniformRectilinearGraph((4, 5))
>>> graph.nodes_at_corners_of_grid
(19, 15, 0, 4)

nodes_at_edge(edge)

property nodes_at_left_edge

property nodes_at_link

property nodes_at_right_edge

property nodes_at_top_edge

property number_of_node_columns

property number_of_node_rows

property patches_at_link

property patches_at_node

property perimeter_nodes

property shape

property vertical_links

class StructuredQuadLayout

Bases: ABC

__init__()

__new__(**kwargs)

static corner_nodes(shape)

abstract static horizontal_links(shape)

abstract static link_dirs_at_node(shape)

abstract static links_at_node(shape)

abstract static links_at_patch(shape)

abstract static nodes_at_link(shape)

abstract static patches_at_link(shape)

abstract static patches_at_node(shape)

abstract static perimeter_nodes(shape)

abstract static vertical_links(shape)

class StructuredQuadLayoutCython

Bases: StructuredQuadLayout

__init__()

__new__(**kwargs)

static corner_nodes(shape)

static horizontal_links(shape)

static link_dirs_at_node(shape)

static links_at_node(shape)

static links_at_patch(shape)

Get links that define patches for a raster grid.

Examples

>>> from landlab.graph.structured_quad.structured_quad import (
...     StructuredQuadLayoutCython,
... )
>>> StructuredQuadLayoutCython.links_at_patch((3, 4))
array([[ 4,  7,  3,  0], [ 5,  8,  4,  1], [ 6,  9,  5,  2],
       [11, 14, 10,  7], [12, 15, 11,  8], [13, 16, 12,  9]])

static nodes_at_link(shape)

Examples

>>> from landlab.graph.structured_quad.structured_quad import (
...     StructuredQuadLayoutCython,
... )
>>> StructuredQuadLayoutCython.nodes_at_link((3, 4))
array([[ 0,  1], [ 1,  2], [ 2,  3],
       [ 0,  4], [ 1,  5], [ 2,  6], [ 3,  7],
       [ 4,  5], [ 5,  6], [ 6,  7],
       [ 4,  8], [ 5,  9], [ 6, 10], [ 7, 11],
       [ 8,  9], [ 9, 10], [10, 11]])

static patches_at_link(shape)

static patches_at_node(shape)

static perimeter_nodes(shape)

static vertical_links(shape)

class StructuredQuadLayoutPython

Bases: StructuredQuadLayout

__init__()

__new__(**kwargs)

static corner_nodes(shape)

static horizontal_links(shape)

static link_dirs_at_node(shape)

static links_at_node(shape)

static links_at_patch(shape)

static nodes_at_link(shape)

static patches_at_link(shape)

static patches_at_node(shape)

static perimeter_nodes(shape)

static vertical_links(shape)

class UniformRectilinearGraph

Bases: StructuredQuadGraphExtras

Graph of a structured grid of quadrilaterals.

Examples

>>> from landlab.graph import UniformRectilinearGraph
>>> graph = UniformRectilinearGraph((4, 3), spacing=(1, 2), origin=(-1, 0))
>>> graph.number_of_nodes
12
>>> graph.y_of_node.reshape(graph.shape)
array([[-1., -1., -1.],
       [ 0.,  0.,  0.],
       [ 1.,  1.,  1.],
       [ 2.,  2.,  2.]])
>>> graph.x_of_node.reshape(graph.shape)
array([[0.,  2.,  4.],
       [0.,  2.,  4.],
       [0.,  2.,  4.],
       [0.,  2.,  4.]])
>>> graph.links_at_node
array([[ 0,  2, -1, -1], [ 1,  3,  0, -1], [-1,  4,  1, -1],
       [ 5,  7, -1,  2], [ 6,  8,  5,  3], [-1,  9,  6,  4],
       [10, 12, -1,  7], [11, 13, 10,  8], [-1, 14, 11,  9],
       [15, -1, -1, 12], [16, -1, 15, 13], [-1, -1, 16, 14]])
>>> graph.link_dirs_at_node
array([[-1, -1,  0,  0], [-1, -1,  1,  0], [ 0, -1,  1,  0],
       [-1, -1,  0,  1], [-1, -1,  1,  1], [ 0, -1,  1,  1],
       [-1, -1,  0,  1], [-1, -1,  1,  1], [ 0, -1,  1,  1],
       [-1,  0,  0,  1], [-1,  0,  1,  1], [ 0,  0,  1,  1]], dtype=int8)
>>> graph.nodes_at_link
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], [ 6,  9], [ 7, 10], [ 8, 11],
       [ 9, 10], [10, 11]])
>>> graph.links_at_patch
array([[ 3,  5,  2,  0], [ 4,  6,  3,  1],
       [ 8, 10,  7,  5], [ 9, 11,  8,  6],
       [13, 15, 12, 10], [14, 16, 13, 11]])
>>> graph.nodes_at_patch
array([[ 4,  3,  0,  1], [ 5,  4,  1,  2],
       [ 7,  6,  3,  4], [ 8,  7,  4,  5],
       [10,  9,  6,  7], [11, 10,  7,  8]])

Define a graph of connected nodes.

Parameters:

mesh (Dataset) – xarray Dataset that defines the topology in ugrid format.

__init__(shape, spacing=1.0, origin=0.0, sort=False)

Define a graph of connected nodes.

Parameters:

mesh (Dataset) – xarray Dataset that defines the topology in ugrid format.

__new__(**kwargs)

property adjacent_links_at_link

property adjacent_nodes_at_node

Get adjacent nodes.

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),
... )
>>> graph = Graph((node_y, node_x), links=links, sort=True)
>>> graph.adjacent_nodes_at_node
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),
... )
>>> graph = Graph((node_y, node_x), links=links, sort=True)
>>> graph.adjacent_nodes_at_node
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 angle_of_link

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 = Graph((node_y, node_x), links=links)
>>> graph.angle_of_link * 180.0 / np.pi
array([ 0.,  0., 90., 90., 90.,  0.,  0.])

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 = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.area_of_patch
array([1.,  1.])

property corner_nodes

property ds

property dx

property dy

freeze()

Freeze the graph by making arrays read-only.

classmethod from_dict(meta)

classmethod from_netcdf(fname)

property frozen

property horizontal_links

property length_of_link

Get the length of links.

Examples

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

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

property link_dirs_at_node

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:

(n_nodes, max_links_per_node) ndarray of int

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.link_dirs_at_node
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)

property links_at_node

Get links touching a node.

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.links_at_node
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]])

property links_at_patch

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))
>>> graph = Graph((node_y, node_x), links=links, patches=patches, sort=True)
>>> graph.links_at_patch
array([[3, 5, 2, 0],
       [4, 6, 3, 1]])

classmethod load(source)

merge(dual, node_at_cell=None, nodes_at_face=None)

property midpoint_of_link

Get the middle of links.

Examples

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

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

property ndim

property node_at_link_head

Get nodes at link head.

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

property node_at_link_tail

Get nodes at link tail.

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

property node_x

property node_y

property nodes

A shaped array of node ids.

Returns:

Node IDs in an array shaped as number_of_node_rows by number_of_node_columns.

Return type:

ndarray

property nodes_at_bottom_edge

property nodes_at_corners_of_grid

Nodes at corners of grid.

The nodes at at the corners of the grid. The nodes are returned counterclockwise starting with the upper-right.

Returns:

Nodes at the four corners.

Return type:

tuple of int

Examples

>>> from landlab.graph import UniformRectilinearGraph
>>> graph = UniformRectilinearGraph((4, 5))
>>> graph.nodes_at_corners_of_grid
(19, 15, 0, 4)

nodes_at_edge(edge)

property nodes_at_left_edge

property nodes_at_link

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.nodes_at_link
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 = Graph((node_y, node_x), links=links, patches=patches, sort=True)
>>> graph.nodes_at_patch
array([[4, 3, 0, 1],
       [5, 4, 1, 2]])

property nodes_at_right_edge

property nodes_at_top_edge

property number_of_links

Get nodes at link head.

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),
... )
>>> graph = Graph((node_y, node_x), links=links)
>>> graph.number_of_links == 12
True

property number_of_node_columns

property number_of_node_rows

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 = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.number_of_patches == 2
True

property orientation_of_link

Return array of link orientation codes (one value per link).

Orientation codes are defined by LinkOrientation; 1 = E, 2 = ENE, 4 = NNE, 8 = N, 16 = NNW, 32 = ESE (using powers of 2 allows for future applications that might want additive combinations).

property origin

property parallel_links_at_link

Return similarly oriented links connected to each link.

Return IDs of links of the same orientation that are connected to each given link’s tail or head node.

The data structure is a numpy array of shape (n_links, 2) containing the IDs of the “tail-wise” (connected to tail node) and “head-wise” (connected to head node) links, or -1 if the link is inactive (e.g., on the perimeter) or it has no attached parallel neighbor in the given direction.

For instance, consider a 3x4 raster, in which link IDs are as shown:

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

Here’s a mapping of the tail-wise (shown at left or bottom of links) and head-wise (shown at right or top of links) links:

.----.----.----.
|    |    |    |
|    |    |    |
|    4    5    |
.---8.7--9.8---.
|   11   12    |
|    |    |    |
|    |    |    |
.----.----.----.

So the corresponding data structure would be mostly filled with -1, but for the 7 active links, it would look like:

4: [[-1, 11],
5:  [-1, 12],
7:  [-1,  8],
8:  [ 7,  9],
9:  [ 8, -1],
11: [ 4, -1],
12: [ 5, -1]]

Examples

>>> from landlab import RasterModelGrid
>>> grid = RasterModelGrid((3, 4))
>>> pll = grid.parallel_links_at_link
>>> pll[4:13, :]
array([[-1, 11],
       [-1, 12],
       [-1, 13],
       [-1,  8],
       [ 7,  9],
       [ 8, -1],
       [ 3, -1],
       [ 4, -1],
       [ 5, -1]])

property patches_at_link

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))
>>> graph = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.patches_at_link
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 = Graph((node_y, node_x), links=links, patches=patches, sort=True)
>>> graph.patches_at_node
array([[ 0, -1], [ 1,  0], [ 1, -1],
       [ 0, -1], [ 0,  1], [ 1, -1]])

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])

property shape

sort()

Sort graph elements.

property spacing

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_link

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. ])
>>> np.round(graph.unit_vector_at_link[:, 1], decimals=5)
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 vertical_links

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_link

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 = Graph((node_y, node_x), links=links, patches=patches)
>>> graph.xy_of_patch
array([[0.5, 0.5],
       [1.5, 0.5]])

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.])