我有几个点和一条曲线,被描述为两个列表,包括位置。我尝试获取点和曲线之间的差异列表。我试图遵循这个web,但我不明白这个command:
X = fmin_cobyla(objective, x0=[0.5,0.5], cons=[c1])
请问在我的案例中正确的论点是什么?
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import fmin_cobyla
data = np.loadtxt('O_Cout.dat', unpack=True, usecols=[0, 2])
z_1v1 = np.polyfit(data[0], data[1], 2)
f_1v1 = np.poly1d(z_1v1)
# Creating more points on the streamline - defining new time with more steps
x_new = list(np.arange(0,100000,1))
y_new = f_1v1(x_new)
# Plot figure with size
fig, ax = plt.subplots()
ax.scatter(data[0], data[1])
ax.plot(x_new, y_new)
def objective(X):
x,y = X
return np.sqrt((x - P[0])**2 + (y - P[1])**2)
def c1(X):
x,y = X
return f(x) - y
for i in range(len(data[1])-1):
P = (data[0][i], data[1][i])
print(P)
X = fmin_cobyla(objective, x0=[0.5,0.5], cons=[c1])
print ('The minimum distance is', objective(X))
# Save the figure
plt.tight_layout()
plt.savefig('OC_parabola.png')
答案 0 :(得分:2)
您找到的脚本适用于已知函数 f(x) 但 IIUC 您不知道 f(x):您的曲线仅由坐标 (x,y) 定义,而您不知道 f( x) 使得 y=f(x)。
在这种情况下,您可以使用相同的基础知识。
给定一个点 P
和由坐标(x,y)定义的曲线,点P到曲线上一点的距离可以简单地定义为
我们希望最小化,即在定义的域中找到最小值/a。
例如
import numpy as np
import matplotlib.pyplot as plt
# Here I define a function f(x) to
# generate y coordinates, but let us
# suppose we don't know it and that
# we got only x and y
def f(x):
return np.cbrt( np.exp(2*x) -1 )
# This is what we really got
x = np.linspace(-2, 2, 1000)
y = f(x)
# The point P
P = (.5, .5)
fig, ax = plt.subplots(figsize=(7, 7))
ax.plot(x, y, lw=4)
ax.plot(*P, 'or')
ax.text(
P[0], P[1],
f" P ({P[0]}, {P[1]})",
ha='left', va='center',
fontsize=15
)
ax.set(
xlim=(-2, 2),
ylim=(-2, 2),
)
plt.show()
让我们定义函数 d,即点 P 与曲线之间的距离
def distance(x, y, x0, y0):
d_x = x - x0
d_y = y - y0
dis = np.sqrt( d_x**2 + d_y**2 )
return dis
现在计算给定 P 和 (x,y) 之间的 d 并找到最小值
from scipy.signal import argrelmin
# compute distance
dis = distance(x, y, P[0], P[1])
# find the minima
min_idxs = argrelmin(dis)[0]
# take the minimum
glob_min_idx = min_idxs[np.argmin(dis[min_idxs])]
# coordinates and distance
min_x = x[glob_min_idx]
min_y = y[glob_min_idx]
min_d = dis[glob_min_idx]
和绘图结果
fig, ax = plt.subplots(figsize=(7, 7))
ax.plot(x, y, lw=4)
ax.plot(
[P[0], min_x],
[P[1], min_y],
'k--', lw=1,
label=f'distance {min_d:.2f}'
)
ax.plot(*P, 'or')
ax.text(
P[0], P[1],
f" P ({P[0]}, {P[1]})",
ha='left', va='center',
fontsize=15
)
ax.set(
xlim=(-2, 2),
ylim=(-2, 2),
)
ax.legend()
plt.show()
改进,可以定义一个简单的函数来返回所有的最小距离,例如
import numpy as np
import matplotlib.pyplot as plt
def distance(x, y, x0, y0):
"""
Return distance between point
P[x0,y0] and a curve (x,y)
"""
d_x = x - x0
d_y = y - y0
dis = np.sqrt( d_x**2 + d_y**2 )
return dis
def min_distance(x, y, P, precision=5):
"""
Compute minimum/a distance/s between
a point P[x0,y0] and a curve (x,y)
rounded at `precision`.
ARGS:
x, y (array)
P (tuple)
precision (int)
Returns min indexes and distances array.
"""
# compute distance
d = distance(x, y, P[0], P[1])
d = np.round(d, precision)
# find the minima
glob_min_idxs = np.argwhere(d==np.min(d)).ravel()
return glob_min_idxs, d
即使有多个最小值也能工作
def f(x):
return x**2
x = np.linspace(-2, 2, 1000)
y = f(x)
P = (0, 1)
min_idxs, dis = min_distance(x, y, P)
fig, ax = plt.subplots(figsize=(7, 7))
ax.plot(x, y, lw=4)
for idx in min_idxs:
ax.plot(
[P[0], x[idx]],
[P[1], y[idx]],
'--', lw=1,
label=f'distance {dis[idx]:.2f}'
)
ax.plot(*P, 'or')
ax.text(
P[0], P[1],
f" P ({P[0]}, {P[1]})",
ha='left', va='center',
fontsize=15
)
ax.set(
xlim=(-2, 2),
ylim=(-1, 3),
)
ax.legend()
plt.show()
def f(x):
return np.sqrt(4 - x**2)
x = np.linspace(-2, 2, 21)
y = f(x)
P = (0, 0)
min_idxs, dis = min_distance(x, y, P)
fig, ax = plt.subplots(figsize=(7, 7))
ax.plot(x, y, lw=4)
for idx in min_idxs:
ax.plot(
[P[0], x[idx]],
[P[1], y[idx]],
'--', lw=1,
label=f'distance {dis[idx]:.2f}'
)
ax.plot(*P, 'or')
ax.text(
P[0], P[1],
f" P ({P[0]}, {P[1]})",
ha='left', va='center',
fontsize=15
)
ax.set(
xlim=(-2, 2),
ylim=(-1, 3),
)
ax.legend(loc='upper left', bbox_to_anchor=(1,1))
plt.show()