""" Implementation of the FramedVoronoiGraph and its static layout:
HorizontalRectVoronoiGraph. This pattern is inspired from the developments of the HexModelGrid
.. codeauthor:: sebastien lenard
"""
from functools import cached_property
import numpy as np
from ...utils.decorators import make_return_array_immutable
from ..graph import Graph
from ..voronoi.voronoi import DelaunayGraph
[docs]
class HorizontalRectVoronoiGraph:
"""The horizontal rectangular frame for the FramedVoronoiGraph."""
[docs]
@staticmethod
def number_of_nodes(shape):
"""
Parameters
----------
shape: tuple of int
Number of rows and number of columns
Returns
-------
int
Number of nodes
Examples
--------
>>> from landlab.graph.framed_voronoi.framed_voronoi import (
... HorizontalRectVoronoiGraph,
... )
>>> HorizontalRectVoronoiGraph.number_of_nodes((3, 2))
6
"""
n_rows, n_cols = shape
return n_rows * n_cols
[docs]
@staticmethod
def xy_of_node(
shape,
xy_spacing=(1.0, 1.0),
xy_of_lower_left=(0.0, 0.0),
xy_min_spacing=(0.5, 0.5),
seed=200,
):
"""The x and y coordinates of the graph's nodes.
Calculation of the x-y coordinates is done following these steps:
1. Generate a rectangular, regular meshgrid.
2. Move the coordinates of the core nodes over a random distance around their
initial position, within a threshold calculated from *xy_spacing* and
*xy_min_spacing*.
3. Rectify the y-coordinates of the nodes of the left and right to ensure
that the leftmost node of a row has a lower y than the rightmost node.
This ensures that the ids of these nodes are not modified by subsequent
sorting operations on the graph and make it possible to get the
perimeter nodes in simple way.
Parameters
----------
shape : tuple of int
Number of rows and columns of nodes.
xy_spacing : float or tuple of float, optional
Node spacing along x and y coordinates. If ``float``, same spacing at *x* and *y*.
xy_of_lower_left : tuple, optional
Minimum *x*-of-node and *y*-of-node values. Depending on the grid,
a node may not be present at this location.
xy_min_spacing: float or tuple of float, optional
Final minimal spacing between nodes. Random moves of the core nodes
around their initial positions cannot be above this threshold:
``(xy_spacing - xy_min_spacing) / 2``. If ``float``, same minimal
spacing for *x* and *y*.
seed: int, optional
Seed used to generate the random *x* and *y* moves. When set, controls a
pseudo-randomness of moves to ensure reproducibility.
When ``None``, seed is random and the moves of coordinates are
completely random.
Returns
-------
x_of_node, y_of_node : ndarray of float
The arrays of *x* and *y* coordinates.
Examples
--------
>>> from landlab.graph.framed_voronoi.framed_voronoi import (
... HorizontalRectVoronoiGraph,
... )
>>> x_of_node, y_of_node = HorizontalRectVoronoiGraph.xy_of_node(
... (3, 3), seed=200
... )
Coordinates of the lower left node,
>>> x_of_node[0], y_of_node[0]
(0.0, 0.0)
*x* coordinates of the left and right edges,
>>> x_of_node[3], x_of_node[5]
(0.0, 2.0)
*y* coordinate of the middle row of the left edge,
>>> y_of_node[3]
0.749
"""
n_rows, n_cols = shape
max_move = (
(xy_spacing[0] - xy_min_spacing[0]) / 2,
(xy_spacing[1] - xy_min_spacing[1]) / 2,
)
if max_move[0] < 0.0 or max_move[1] < 0.0:
raise ValueError("minimum spacing must be greater than node spacing")
if np.allclose(max_move, 0.0):
raise ValueError("at least one of x and y moves must be greater than zero")
# Generation of a rectangular grid, coordinates must be float
x_of_node, y_of_node = np.meshgrid(
np.arange(n_cols, dtype=float) * xy_spacing[0] + xy_of_lower_left[0],
np.arange(n_rows, dtype=float) * xy_spacing[1] + xy_of_lower_left[1],
)
# Randomly move the coordinates of the core nodes of the grid. Move
# below +/- (spacing - min_spacing) / 2
xy_random_generator = np.random.default_rng(seed=seed)
x_moves = xy_random_generator.uniform(-max_move[0], max_move[0], shape)
y_moves = xy_random_generator.uniform(-max_move[1], max_move[1], shape)
x_of_node[1:-1, 1:-1] += x_moves[1:-1, 1:-1]
y_of_node[1:-1, 1:-1] += y_moves[1:-1, 1:-1]
# Control the node id attribution for left and right edge. For instance, for a 3x3 grid,
# make sure that node 3 is at the left of the 2nd row and node 5 at the right.
# For this, for each core row, set y of the leftmost node as the minimal y of the row
# and set y of the rightmost node as the maximal y of the row
for i in range(1, n_rows - 1):
y_of_node[i, 0] -= max_move[1] + 1.0e-3
y_of_node[i, n_cols - 1] += max_move[1] + 1.0e-3
return x_of_node.reshape(-1), y_of_node.reshape(-1)
[docs]
@staticmethod
def corner_nodes(shape):
"""
Parameters
----------
shape: tuple of int
Number of rows and number of columns
Returns
-------
ndarray of int
Ids of the corner nodes
Examples
--------
>>> from landlab.graph.framed_voronoi.framed_voronoi import (
... HorizontalRectVoronoiGraph,
... )
>>> HorizontalRectVoronoiGraph.corner_nodes((3, 4))
(11, 8, 0, 3)
"""
n_rows, n_cols = shape
return (n_rows * n_cols - 1, n_cols * (n_rows - 1), 0, n_cols - 1)
[docs]
@staticmethod
def number_of_perimeter_nodes(shape):
"""
Parameters
----------
shape: tuple of int
Number of rows and number of columns
Returns
-------
int
Number of perimeter nodes
Examples
--------
>>> from landlab.graph.framed_voronoi.framed_voronoi import (
... HorizontalRectVoronoiGraph,
... )
>>> HorizontalRectVoronoiGraph.number_of_perimeter_nodes((3, 4))
10
"""
if 1 in shape:
return np.prod(shape)
return 2 * shape[0] + 2 * (shape[1] - 2)
[docs]
@staticmethod
def perimeter_nodes(shape):
"""
Parameters
----------
shape: tuple of int
Number of rows and number of columns
Returns
-------
ndarray of int
Ids of the perimeter nodes
Examples
--------
>>> from landlab.graph.framed_voronoi.framed_voronoi import (
... HorizontalRectVoronoiGraph,
... )
>>> HorizontalRectVoronoiGraph.perimeter_nodes((3, 3))
array([2, 5, 8, 7, 6, 3, 0, 1])
"""
return np.concatenate(HorizontalRectVoronoiGraph.nodes_at_edge(shape))
[docs]
@staticmethod
def nodes_at_edge(shape):
"""
Parameters
----------
shape: tuple of int
Number of rows and number of columns
Returns
-------
right, top, left, bottom : ndarray of int
For each edge give the ids of the nodes present at the edge
Examples
--------
>>> from landlab.graph.framed_voronoi.framed_voronoi import (
... HorizontalRectVoronoiGraph,
... )
>>> HorizontalRectVoronoiGraph.nodes_at_edge((3, 3))
(array([2, 5]), array([8, 7]), array([6, 3]), array([0, 1]))
"""
n_rows, n_cols = shape
if n_rows == n_cols == 1:
return (np.array([0]),) + (np.array([], dtype=int),) * 3
(
northeast,
northwest,
southwest,
southeast,
) = HorizontalRectVoronoiGraph.corner_nodes(shape)
if n_rows > 1:
south = np.arange(southwest, southeast)
else:
south = np.array([southwest], dtype=int)
if n_cols > 1:
west = np.arange(northwest, southwest, -n_cols)
else:
west = np.array([northwest], dtype=int)
return (
np.arange(southeast, northeast, n_cols),
np.arange(northeast, northwest, -1),
west,
south,
)
[docs]
class FramedVoronoiGraph(DelaunayGraph):
"""VoronoiDelaunay graph based on a fixed lattice.
Graph of an unstructured grid of Voronoi Delaunay cells and
irregular patches. It is a special type of :class`~.VoronoiDelaunayGraph` in which
the initial set of points is arranged in a fixed lattice (e.g. like a
:class:`~.RasterModelGrid`) named here "layout" and the core points are
then moved from their initial position by a random distance, lower than a
certain threshold.
Examples
--------
>>> from landlab.graph import FramedVoronoiGraph
>>> graph = FramedVoronoiGraph((3, 3), seed=200)
>>> graph.number_of_nodes
9
>>> graph.x_of_node[2:4]
array([ 2., 0.])
>>> graph.y_of_node[2:4]
array([ 0. , 0.749])
>>> graph.y_of_node[5]
1.2509999999999999
>>> graph.number_of_links
16
>>> graph.number_of_patches
8
"""
[docs]
def __init__(
self,
shape,
xy_spacing=(1.0, 1.0),
xy_of_lower_left=(0.0, 0.0),
sort=False,
xy_min_spacing=(0.5, 0.5),
seed=200,
):
"""Create the graph.
Parameters
----------
shape : tuple of int
Number of rows and columns of nodes.
xy_spacing : float or tuple of float, optional
Node spacing along *x* and *y* coordinates. If ``float``, same spacing *x* and *y*
spacing.
xy_of_lower_left : tuple, optional
Minimum *x*-of-node and *y*-of-node values. Depending on the grid,
a node may not be present at this location.
sort: bool
If ``True``, nodes, links and patches are re-numbered according
certain their positions. Currently not used.
xy_min_spacing: float or tuple of float, optional
Final minimal spacing between nodes. Random moves of the core nodes
around their position cannot be above this threshold:
``(xy_spacing - xy_min_spacing) / 2``
If ``float``, same minimal spacing for *x* and *y*.
seed: int, optional
Seed used to generate the random *x* and *y* moves.
When set, controls a pseudo-randomness of moves to ensure
reproducibility. When ``None``, seed is random and the moves of coordinates are
completely random.
Returns
-------
FramedVoronoiGraph
A newly-created graph.
Examples
--------
Create a grid with 3 rows and 2 columns of nodes.
>>> from landlab.graph import FramedVoronoiGraph
>>> graph = FramedVoronoiGraph((3, 2))
>>> graph.number_of_nodes
6
"""
# 1. Check and format input arguments
#####################################
self._shape = shape
self._seed = seed
try:
xy_spacing = np.asfarray(np.broadcast_to(xy_spacing, 2))
except TypeError as exc:
raise TypeError("spacing must be a float or a tuple of floats") from exc
else:
self._xy_spacing = xy_spacing[0], xy_spacing[1]
try:
xy_of_lower_left = np.asfarray(np.broadcast_to(xy_of_lower_left, 2))
except TypeError as exc:
raise TypeError(
"xy of lower left must be a float or a tuple of floats"
) from exc
else:
self._xy_of_lower_left = xy_of_lower_left[0], xy_of_lower_left[1]
node_layout = self._node_layout = "rect"
orientation = self._orientation = "horizontal"
layouts = {
"horizontal_rect": HorizontalRectVoronoiGraph,
}
layout = layouts["_".join([orientation, node_layout])]
try:
xy_min_spacing = np.asfarray(np.broadcast_to(xy_min_spacing, 2))
except TypeError as exc:
raise TypeError(
"minimal spacing must be a float or a tuple of floats"
) from exc
else:
self._xy_min_spacing = xy_min_spacing[0], xy_min_spacing[1]
# 2. Construction of the layout and the x-y coordinates of nodes
################################################################
x_of_node, y_of_node = layout.xy_of_node(
self._shape,
xy_spacing=self._xy_spacing,
xy_of_lower_left=self._xy_of_lower_left,
xy_min_spacing=self._xy_min_spacing,
seed=self._seed,
)
# 3. Determination of the perimeter and edge nodes
#########################################
self._perimeter_nodes = layout.perimeter_nodes(self._shape)
(right, top, left, bottom) = layout.nodes_at_edge(self._shape)
self._nodes_at_right_edge = np.sort(np.append(right, top[0]))
self._nodes_at_top_edge = np.sort(np.append(top, left[0]))
self._nodes_at_left_edge = np.sort(np.append(left, bottom[0]))
self._nodes_at_bottom_edge = np.sort(np.append(bottom, right[0]))
perimeter_links = np.empty((len(self._perimeter_nodes), 2), dtype=int)
perimeter_links[:, 0] = self._perimeter_nodes
perimeter_links[:-1, 1] = self._perimeter_nodes[1:]
perimeter_links[-1, 1] = self._perimeter_nodes[0]
self._x_of_node = x_of_node
self._y_of_node = y_of_node
self._perimeter_links = perimeter_links
# 3. Instantiation of the parent class
######################################
if 1 in shape:
Graph.__init__(
self,
(y_of_node, x_of_node),
links=list(
zip(np.arange(len(y_of_node) - 1), np.arange(1, len(y_of_node)))
),
sort=False,
)
else:
DelaunayGraph.__init__(
self,
(y_of_node, x_of_node),
perimeter_links=perimeter_links,
sort=False,
)
@property
def shape(self):
return self._shape
@property
def xy_spacing(self):
return self._xy_spacing
@property
def orientation(self):
return self._orientation
@property
def node_layout(self):
return self._node_layout
@cached_property
@make_return_array_immutable
def perimeter_nodes(self):
return self._perimeter_nodes
@property
@make_return_array_immutable
def nodes_at_right_edge(self):
return self._nodes_at_right_edge
@property
@make_return_array_immutable
def nodes_at_top_edge(self):
return self._nodes_at_top_edge
@property
@make_return_array_immutable
def nodes_at_left_edge(self):
return self._nodes_at_left_edge
@property
@make_return_array_immutable
def nodes_at_bottom_edge(self):
return self._nodes_at_bottom_edge