mirror of
https://github.com/apachecn/ailearning.git
synced 2026-02-11 14:26:04 +08:00
236 lines
43 KiB
Markdown
236 lines
43 KiB
Markdown
# 森林火灾模拟
|
||
|
||
之前我们已经构建好了一些基础，但是还没有开始对火灾进行模拟。
|
||
|
||
## 随机生长
|
||
|
||
* 在原来的基础上,我们要先让树生长，即定义 `grow_trees()` 方法
|
||
* 定义方法之前，我们要先指定两个属性：
|
||
* 每个位置随机生长出树木的概率
|
||
* 每个位置随机被闪电击中的概率
|
||
* 为了方便，我们定义一个辅助函数来生成随机 `bool` 矩阵，大小与森林大小一致
|
||
* 按照给定的生长概率生成生长的位置，将 `trees` 中相应位置设为 `True`
|
||
|
||
In [1]:
|
||
|
||
```py
|
||
import numpy as np
|
||
|
||
class Forest(object):
|
||
""" Forest can grow trees which eventually die."""
|
||
def __init__(self, size=(150,150), p_sapling=0.0025, p_lightning=5.0e-6):
|
||
self.size = size
|
||
self.trees = np.zeros(self.size, dtype=bool)
|
||
self.fires = np.zeros((self.size), dtype=bool)
|
||
self.p_sapling = p_sapling
|
||
self.p_lightning = p_lightning
|
||
|
||
def __repr__(self):
|
||
my_repr = "{}(size={})".format(self.__class__.__name__, self.size)
|
||
return my_repr
|
||
|
||
def __str__(self):
|
||
return self.__class__.__name__
|
||
|
||
@property
|
||
def num_cells(self):
|
||
"""Number of cells available for growing trees"""
|
||
return np.prod(self.size)
|
||
|
||
@property
|
||
def tree_fraction(self):
|
||
"""
|
||
Fraction of trees
|
||
"""
|
||
num_trees = self.trees.sum()
|
||
return float(num_trees) / self.num_cells
|
||
|
||
@property
|
||
def fire_fraction(self):
|
||
"""
|
||
Fraction of fires
|
||
"""
|
||
num_fires = self.fires.sum()
|
||
return float(num_fires) / self.num_cells
|
||
|
||
def _rand_bool(self, p):
|
||
"""
|
||
Random boolean distributed according to p, less than p will be True
|
||
"""
|
||
return np.random.uniform(size=self.trees.shape) < p
|
||
|
||
def grow_trees(self):
|
||
"""
|
||
Growing trees.
|
||
"""
|
||
growth_sites = self._rand_bool(self.p_sapling)
|
||
self.trees[growth_sites] = True
|
||
|
||
```
|
||
|
||
测试：
|
||
|
||
In [2]:
|
||
|
||
```py
|
||
forest = Forest()
|
||
print forest.tree_fraction
|
||
|
||
forest.grow_trees()
|
||
print forest.tree_fraction
|
||
|
||
```
|
||
|
||
```py
|
||
0.0
|
||
0.00293333333333
|
||
|
||
```
|
||
|
||
## 火灾模拟
|
||
|
||
* 定义 `start_fires()`：
|
||
* 按照给定的概率生成被闪电击中的位置
|
||
* 如果闪电击中的位置有树，那么将其设为着火点
|
||
* 定义 `burn_trees()`：
|
||
* 如果一棵树的上下左右有火，那么这棵树也会着火
|
||
* 定义 `advance_one_step()`：
|
||
* 进行一次生长，起火，燃烧
|
||
|
||
In [3]:
|
||
|
||
```py
|
||
import numpy as np
|
||
|
||
class Forest(object):
|
||
""" Forest can grow trees which eventually die."""
|
||
def __init__(self, size=(150,150), p_sapling=0.0025, p_lightning=5.0e-6):
|
||
self.size = size
|
||
self.trees = np.zeros(self.size, dtype=bool)
|
||
self.fires = np.zeros((self.size), dtype=bool)
|
||
self.p_sapling = p_sapling
|
||
self.p_lightning = p_lightning
|
||
|
||
def __repr__(self):
|
||
my_repr = "{}(size={})".format(self.__class__.__name__, self.size)
|
||
return my_repr
|
||
|
||
def __str__(self):
|
||
return self.__class__.__name__
|
||
|
||
@property
|
||
def num_cells(self):
|
||
"""Number of cells available for growing trees"""
|
||
return np.prod(self.size)
|
||
|
||
@property
|
||
def tree_fraction(self):
|
||
"""
|
||
Fraction of trees
|
||
"""
|
||
num_trees = self.trees.sum()
|
||
return float(num_trees) / self.num_cells
|
||
|
||
@property
|
||
def fire_fraction(self):
|
||
"""
|
||
Fraction of fires
|
||
"""
|
||
num_fires = self.fires.sum()
|
||
return float(num_fires) / self.num_cells
|
||
|
||
def _rand_bool(self, p):
|
||
"""
|
||
Random boolean distributed according to p, less than p will be True
|
||
"""
|
||
return np.random.uniform(size=self.trees.shape) < p
|
||
|
||
def grow_trees(self):
|
||
"""
|
||
Growing trees.
|
||
"""
|
||
growth_sites = self._rand_bool(self.p_sapling)
|
||
self.trees[growth_sites] = True
|
||
|
||
def start_fires(self):
|
||
"""
|
||
Start of fire.
|
||
"""
|
||
lightning_strikes = (self._rand_bool(self.p_lightning) &
|
||
self.trees)
|
||
self.fires[lightning_strikes] = True
|
||
|
||
def burn_trees(self):
|
||
"""
|
||
Burn trees.
|
||
"""
|
||
fires = np.zeros((self.size[0] + 2, self.size[1] + 2), dtype=bool)
|
||
fires[1:-1, 1:-1] = self.fires
|
||
north = fires[:-2, 1:-1]
|
||
south = fires[2:, 1:-1]
|
||
east = fires[1:-1, :-2]
|
||
west = fires[1:-1, 2:]
|
||
new_fires = (north | south | east | west) & self.trees
|
||
self.trees[self.fires] = False
|
||
self.fires = new_fires
|
||
|
||
def advance_one_step(self):
|
||
"""
|
||
Advance one step
|
||
"""
|
||
self.grow_trees()
|
||
self.start_fires()
|
||
self.burn_trees()
|
||
|
||
```
|
||
|
||
In [4]:
|
||
|
||
```py
|
||
forest = Forest()
|
||
|
||
for i in range(100):
|
||
forest.advance_one_step()
|
||
|
||
```
|
||
|
||
使用 `matshow()` 显示树木图像：
|
||
|
||
In [5]:
|
||
|
||
```py
|
||
import matplotlib.pyplot as plt
|
||
from matplotlib import cm
|
||
|
||
%matplotlib inline
|
||
|
||
plt.matshow(forest.trees, cmap=cm.Greens)
|
||
|
||
plt.show()
|
||
|
||
```
|
||
|
||
|
||
|
||
查看不同着火概率下的森林覆盖率趋势变化：
|
||
|
||
In [6]:
|
||
|
||
```py
|
||
forest = Forest()
|
||
forest2 = Forest(p_lightning=5e-4)
|
||
|
||
tree_fractions = []
|
||
|
||
for i in range(2500):
|
||
forest.advance_one_step()
|
||
forest2.advance_one_step()
|
||
tree_fractions.append((forest.tree_fraction, forest2.tree_fraction))
|
||
|
||
plt.plot(tree_fractions)
|
||
|
||
plt.show()
|
||
|
||
```
|
||
|
||
 |