import numpy as np
import matplotlib.pyplot as plt
from scipy.spatial.distance import cdist
from iwopy import Problem
import foxes.constants as FC
[docs]
class GeomRegGrids(Problem):
"""
A regular grid within a boundary geometry.
This optimization problem does not involve
wind farms.
Attributes
----------
boundary: foxes.utils.geom2d.AreaGeometry
The boundary geometry
min_dist: float
The minimal distance between points
n_grids: int
The number of grids
n_max: int
The maximal number of points
n_row_max: int
The maximal number of points in a row
max_dist: float
The maximal distance between points
D: float
The diameter of circle fully within boundary
:group: opt.problems.layout.geom_layouts
"""
[docs]
def __init__(
self,
boundary,
min_dist,
n_grids,
n_max=None,
n_row_max=None,
max_dist=None,
D=None,
):
"""
Constructor.
Parameters
----------
boundary: foxes.utils.geom2d.AreaGeometry
The boundary geometry
min_dist: float
The minimal distance between points
n_grids: int
The number of grids
n_max: int, optional
The maximal number of points
n_row_max: int, optional
The maximal number of points in a row
max_dist: float, optional
The maximal distance between points
D: float, optional
The diameter of circle fully within boundary
"""
super().__init__(name="geom_reg_grids")
self.boundary = boundary
self.n_grids = n_grids
self.n_max = n_max
self.n_row_max = n_row_max
self.min_dist = float(min_dist)
self.max_dist = float(max_dist) if max_dist is not None else max_dist
self.D = D
self._NX = [f"nx{i}" for i in range(self.n_grids)]
self._NY = [f"ny{i}" for i in range(self.n_grids)]
self._OX = [f"ox{i}" for i in range(self.n_grids)]
self._OY = [f"oy{i}" for i in range(self.n_grids)]
self._DX = [f"dx{i}" for i in range(self.n_grids)]
self._DY = [f"dy{i}" for i in range(self.n_grids)]
self._ALPHA = [f"alpha{i}" for i in range(self.n_grids)]
[docs]
def initialize(self, verbosity=1):
"""
Initialize the object.
Parameters
----------
verbosity: int
The verbosity level, 0 = silent
"""
super().initialize(verbosity)
pmin = self.boundary.p_min()
pmax = self.boundary.p_max()
self._span = pmax - pmin
self._diag = np.linalg.norm(self._span)
self.max_dist = self._diag if self.max_dist is None else self.max_dist
self._nrow = self.n_row_max
if self.n_row_max is None:
if self.n_max is None:
self._nrow = int(self._diag / self.min_dist)
if self._nrow * self.min_dist < self._diag:
self._nrow += 1
self._nrow += 1
else:
self._nrow = self.n_max
if self.n_max is None:
self.n_max = self.n_grids * self._nrow**2
elif self.n_max <= self._nrow:
self._nrow = self.n_max
self._pmin = pmin - self._diag - self.min_dist
self._pmax = pmax + self.min_dist
if verbosity > 0:
print(f"Grid data:")
print(f" pmin = {self._pmin}")
print(f" pmax = {self._pmax}")
print(f" min dist = {self.min_dist}")
print(f" max dist = {self.max_dist}")
print(f" n row max = {self._nrow}")
print(f" n max = {self.n_max}")
print(f" n grids = {self.n_grids}")
self.apply_individual(self.initial_values_int(), self.initial_values_float())
[docs]
def var_names_int(self):
"""
The names of int variables.
Returns
-------
names: list of str
The names of the int variables
"""
return list(np.array([self._NX, self._NY]).T.flat)
[docs]
def initial_values_int(self):
"""
The initial values of the int variables.
Returns
-------
values: numpy.ndarray
Initial int values, shape: (n_vars_int,)
"""
return np.full(self.n_grids * 2, 2, dtype=FC.ITYPE)
[docs]
def min_values_int(self):
"""
The minimal values of the integer variables.
Use -self.INT_INF for unbounded.
Returns
-------
values: numpy.ndarray
Minimal int values, shape: (n_vars_int,)
"""
return np.ones(self.n_grids * 2, dtype=FC.ITYPE)
[docs]
def max_values_int(self):
"""
The maximal values of the integer variables.
Use self.INT_INF for unbounded.
Returns
-------
values: numpy.ndarray
Maximal int values, shape: (n_vars_int,)
"""
return np.full(self.n_grids * 2, self._nrow, dtype=FC.ITYPE)
[docs]
def var_names_float(self):
"""
The names of float variables.
Returns
-------
names: list of str
The names of the float variables
"""
return list(
np.array([self._OX, self._OY, self._DX, self._DY, self._ALPHA]).T.flat
)
[docs]
def initial_values_float(self):
"""
The initial values of the float variables.
Returns
-------
values: numpy.ndarray
Initial float values, shape: (n_vars_float,)
"""
n = 5
vals = np.zeros((self.n_grids, n), dtype=FC.DTYPE)
vals[:, :2] = self._pmin + self._diag + self.min_dist + self._span / 2
vals[:, 2:4] = 2 * self.min_dist
vals[:, 5:] = 0
return vals.reshape(self.n_grids * n)
[docs]
def min_values_float(self):
"""
The minimal values of the float variables.
Use -numpy.inf for unbounded.
Returns
-------
values: numpy.ndarray
Minimal float values, shape: (n_vars_float,)
"""
n = 5
vals = np.zeros((self.n_grids, n), dtype=FC.DTYPE)
vals[:, :2] = self._pmin
vals[:, 2:4] = self.min_dist
vals[:, 5:] = -self._diag / 3
return vals.reshape(self.n_grids * n)
[docs]
def max_values_float(self):
"""
The maximal values of the float variables.
Use numpy.inf for unbounded.
Returns
-------
values: numpy.ndarray
Maximal float values, shape: (n_vars_float,)
"""
n = 5
vals = np.zeros((self.n_grids, n), dtype=FC.DTYPE)
vals[:, :2] = self._pmax
vals[:, 2:4] = self.max_dist
vals[:, 4] = 90.0
vals[:, 5:] = self._diag / 3
return vals.reshape(self.n_grids * n)
[docs]
def apply_individual(self, vars_int, vars_float):
"""
Apply new variables to the problem.
Parameters
----------
vars_int: np.array
The integer variable values, shape: (n_vars_int,)
vars_float: np.array
The float variable values, shape: (n_vars_float,)
Returns
-------
problem_results: Any
The results of the variable application
to the problem
"""
vint = vars_int.reshape(self.n_grids, 2)
vflt = vars_float.reshape(self.n_grids, 5)
nx = vint[:, 0]
ny = vint[:, 1]
ox = vflt[:, 0]
oy = vflt[:, 1]
dx = vflt[:, 2]
dy = vflt[:, 3]
a = np.deg2rad(vflt[:, 4])
s = vflt[:, 5:]
n_points = self.n_max
nax = np.stack([np.cos(a), np.sin(a), np.zeros_like(a)], axis=-1)
naz = np.zeros_like(nax)
naz[:, 2] = 1
nay = np.cross(naz, nax)
valid = np.zeros(n_points, dtype=bool)
pts = np.full((n_points, 2), np.nan, dtype=FC.DTYPE)
n0 = 0
for gi in range(self.n_grids):
n = nx[gi] * ny[gi]
n1 = n0 + n
if n1 <= n_points:
qts = pts[n0:n1].reshape(nx[gi], ny[gi], 2)
else:
qts = np.zeros((nx[gi], ny[gi], 2), dtype=FC.DTYPE)
qts[:, :, 0] = ox[gi]
qts[:, :, 1] = oy[gi]
qts[:] += (
np.arange(nx[gi])[:, None, None] * dx[gi] * nax[gi, None, None, :2]
)
qts[:] += (
np.arange(ny[gi])[None, :, None] * dy[gi] * nay[gi, None, None, :2]
)
qts = qts.reshape(n, 2)
if n1 > n_points:
n1 = n_points
qts = qts[: (n1 - n0)]
pts[n0:] = qts
# set out of boundary points invalid:
if self.D is None:
valid[n0:n1] = self.boundary.points_inside(qts)
else:
valid[n0:n1] = self.boundary.points_inside(qts) & (
self.boundary.points_distance(qts) >= self.D / 2
)
# set points invalid which are too close to other grids:
if n0 > 0:
dists = cdist(qts, pts[:n0])
valid[n0:n1][np.any(dists < self.min_dist, axis=1)] = False
n0 = n1
if n0 >= n_points:
break
return pts, valid
[docs]
def apply_population(self, vars_int, vars_float):
"""
Apply new variables to the problem,
for a whole population.
Parameters
----------
vars_int: np.array
The integer variable values, shape: (n_pop, n_vars_int)
vars_float: np.array
The float variable values, shape: (n_pop, n_vars_float)
Returns
-------
problem_results: Any
The results of the variable application
to the problem
"""
n_pop = vars_int.shape[0]
vint = vars_int.reshape(n_pop, self.n_grids, 2)
vflt = vars_float.reshape(n_pop, self.n_grids, 5)
nx = vint[:, :, 0]
ny = vint[:, :, 1]
ox = vflt[:, :, 0]
oy = vflt[:, :, 1]
dx = vflt[:, :, 2]
dy = vflt[:, :, 3]
a = np.deg2rad(vflt[:, :, 4])
s = vflt[:, :, 5:]
n_points = self.n_max
nax = np.stack([np.cos(a), np.sin(a), np.zeros_like(a)], axis=-1)
naz = np.zeros_like(nax)
naz[:, :, 2] = 1
nay = np.cross(naz, nax)
valid = np.zeros((n_pop, n_points), dtype=bool)
pts = np.full((n_pop, n_points, 2), np.nan, dtype=FC.DTYPE)
for pi in range(n_pop):
n0 = 0
for gi in range(self.n_grids):
n = nx[pi, gi] * ny[pi, gi]
n1 = n0 + n
if n1 <= n_points:
qts = pts[pi, n0:n1].reshape(nx[pi, gi], ny[pi, gi], 2)
else:
qts = np.zeros((nx[pi, gi], ny[pi, gi], 2), dtype=FC.DTYPE)
qts[:, :, 0] = ox[pi, gi]
qts[:, :, 1] = oy[pi, gi]
qts[:] += (
np.arange(nx[pi, gi])[:, None, None]
* dx[pi, gi]
* nax[pi, gi, None, None, :2]
)
qts[:] += (
np.arange(ny[pi, gi])[None, :, None]
* dy[pi, gi]
* nay[pi, gi, None, None, :2]
)
qts = qts.reshape(n, 2)
if n1 > n_points:
n1 = n_points
qts = qts[: (n1 - n0)]
pts[pi, n0:] = qts
# set out of boundary points invalid:
if self.D is None:
valid[pi, n0:n1] = self.boundary.points_inside(qts)
else:
valid[pi, n0:n1] = self.boundary.points_inside(qts) & (
self.boundary.points_distance(qts) >= self.D / 2
)
# set points invalid which are too close to other grids:
if n0 > 0:
dists = cdist(qts, pts[pi, :n0])
valid[pi, n0:n1][np.any(dists < self.min_dist, axis=1)] = False
n0 = n1
if n0 >= n_points:
break
return pts, valid
[docs]
def get_fig(
self, xy=None, valid=None, ax=None, title=None, true_circle=True, **bargs
):
"""
Return plotly figure axis.
Parameters
----------
xy: numpy.ndarary, optional
The xy coordinate array, shape: (n_points, 2)
valid: numpy.ndarray, optional
Boolean array of validity, shape: (n_points,)
ax: pyplot.Axis, optional
The figure axis
title: str, optional
The figure title
true_circle: bool
Draw points as circles with diameter self.D
bars: dict, optional
The boundary plot arguments
Returns
-------
ax: pyplot.Axis
The figure axis
"""
if ax is None:
__, ax = plt.subplots()
hbargs = {"fill_mode": "inside_lightgray"}
hbargs.update(bargs)
self.boundary.add_to_figure(ax, **hbargs)
if xy is not None:
if valid is not None:
xy = xy[valid]
if not true_circle or self.D is None:
ax.scatter(xy[:, 0], xy[:, 1], color="orange")
else:
for x, y in xy:
ax.add_patch(
plt.Circle((x, y), self.D / 2, color="blue", fill=True)
)
ax.set_aspect("equal", adjustable="box")
ax.set_xlabel("x [m]")
ax.set_ylabel("y [m]")
if title is None:
if xy is None:
title = f"Optimization area"
else:
l = len(xy) if xy is not None else 0
dists = cdist(xy, xy)
np.fill_diagonal(dists, 1e20)
title = f"N = {l}, min_dist = {np.min(dists):.1f} m"
ax.set_title(title)
return ax