菜鸟教程(scipy):
https://www.runoob.com/scipy/scipy-module.html
scipy.interpolate:
https://docs.scipy.org/doc/scipy/tutorial/interpolate.html
## Scipy(02):scipy.interpolate 插值子模块 ### 1 一维插值 #### 1.1 interp1d() # 1.线性插值 # 2.临近点插值 # 3.前点插值 # 4.后点插值 # 5.零阶样条插值 # 6.一阶样条插值 # 7.三阶样条插值 # 8.五阶样条插值 ### 2 二维插值 #### 2.1 interp2d() # 1.线性插值 # 2.三阶样条插值 # 3.五阶样条插值 ### 3 离散数据插值到网格 #### 3.1 griddata() # 1.nearest 临近点插值 # 2.linear 线性插值 # 3.cubic 三阶样条插值 |
### 1 一维插值 已知离散点数据集,构造一个解析函数,使得函数曲线经过这些点,并能够求出曲线上其他点的值,这一过程称为一维插值。 |
#### 1.1 interp1d() scipy.interpolate.interp1d(x,y,kind) 参数x和参数y表示离散点的x坐标和y坐标,参数kind用于指定插值方法。 kind:插值方法: 1.线性插值 2.临近点插值 3.前点插值 4.后点插值 5.零阶样条插值 6.一阶样条插值 7.三阶样条插值 8.五阶样条插值 |
import numpy as np
from scipy import interpolate
import matplotlib.pyplot as plt
# 原始样本点
x = np.linspace(0,10,11)
y = np.exp(-np.sin(x)/3.0)
fig = plt.figure(figsize=(6,4), dpi=100, facecolor='#eaeaea' )
plt.rcdefaults()
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
ax = fig.add_subplot()
ax1.plot(x,y,'o',label='原始数据')
ax1.legend()
# 插值获取更多的点,注意因为是插值,所以x的范围不能超过原来的x范围
x_new = np.linspace(0,10,100)
# 根据原始样本点,按照不同插值方法,获取函数,计算插值后的数值
fig = plt.figure( figsize=(12,10), dpi=100, facecolor="#eaeaea")
# 1.线性插值
f_linear = interpolate.interp1d(x,y,kind='linear')
y_new = f_linear(x_new)
ax1 = fig.add_subplot(4,2,1)
ax1.plot(x_new,f_linear(x_new),'.',label='线性插值')
ax1.plot(x,y,'.',c='r',label='原始数')
ax1.legend()
# 2.临近点插值
f_nearest = interpolate.interp1d(x,y,kind='nearest')
ax2 = fig.add_subplot(4,2,2)
ax2.plot(x_new,f_nearest(x_new),'.',label='临近点插值')
ax2.plot(x,y,'.',c='r',label='原始数据')
ax2.legend()
# 3.前点插值
f_previous = interpolate.interp1d(x,y,kind='previous')
ax3 = fig.add_subplot(4,2,3)
ax3.plot(x_new,f_previous(x_new),'.',label='前点插值')
ax3.plot(x,y,'.',c='r',label='原始数据')
ax3.legend()
# 4.后点插值
f_next = interpolate.interp1d(x,y,kind='next')
ax4 = fig.add_subplot(4,2,4)
ax4.plot(x_new,f_next(x_new),'.',label='后点插值')
ax4.plot(x,y,'.',c='r',label='原始数据')
ax4.legend()
# 5.零阶样条插值
f_zero = interpolate.interp1d(x,y,kind='zero')
ax5 = fig.add_subplot(4,2,5)
ax5.plot(x_new,f_zero(x_new),'.',label='零阶样条插值')
ax5.plot(x,y,'.',c='r',label='原始数据')
ax5.legend()
# 6.一阶样条插值
f_slinear = interpolate.interp1d(x,y,kind='slinear')
ax6 = fig.add_subplot(4,2,6)
ax6.plot(x_new,f_slinear(x_new),'.',label='一阶样条插值')
ax6.plot(x,y,'.',c='r',label='原始数据')
ax6.legend()
# 7.三阶样条插值
f_cubic = interpolate.interp1d(x,y,kind='cubic')
ax7 = fig.add_subplot(4,2,7)
ax7.plot(x_new,f_cubic(x_new),'.',label='三阶样条插值')
ax7.plot(x,y,'.',c='r',label='原始数据')
ax7.legend()
# 8.五阶样条插值
f_quadratic = interpolate.interp1d(x,y,kind='quadratic')
ax8 = fig.add_subplot(4,2,8)
ax8.plot(x_new,f_quadratic(x_new),'.',label='五阶样条插值')
ax8.plot(x,y,'.',c='r',label='原始数据')
ax8.legend()
#wspace 子图横向间距, hspace 代表子图间的纵向距离,left 代表位于图像不同位置
plt.subplots_adjust(left=None, bottom=0.15, right=None, top=None, wspace=0.2, hspace=0.6)
### 2 二维插值 |
#### 2.1 interp2d() scipy.interpolate.interp2d(x,y,z,kind) 参数x,y,z是用来逼近函数z=f(x,y)的数组,x和y是一维数组,z是二维数组,kind用于指定插值方法 kind插值方法: 1.线性插值 linear 2.三阶样条插值 cubic 3.五阶样条插值 quadratic |
为了测量一个长6m,宽4m的房间的地暖温度,再房间地面上均匀设置了20行30列的温度传感器矩阵,输出一个20行30列的二维数组,数组的每一个元素对应一个传感器的实测温度 |
import numpy as np
import matplotlib.pyplot as plt
# 生成20行,30列矩阵
y,x = np.mgrid[-2:2:20j,-3:3:30j]
# 模拟温度数据
z = x*np.exp( -x**2-y**2)*10 + 20
plt.pcolor(x,y,z, cmap=plt.cm.hsv)
plt.colorbar()
plt.axis('equal')
plt.show()
# 插值目标,80行120列
y_new,x_new = np.mgrid[-2:2:80j,-3:3:120j]
# 插值时要求输入的是一维,所以使用的时候,其实很方便
print(x[0,:],'\n',y[:,0])
[-3. -2.79310345 -2.5862069 -2.37931034 -2.17241379 -1.96551724
-1.75862069 -1.55172414 -1.34482759 -1.13793103 -0.93103448 -0.72413793
-0.51724138 -0.31034483 -0.10344828 0.10344828 0.31034483 0.51724138
0.72413793 0.93103448 1.13793103 1.34482759 1.55172414 1.75862069
1.96551724 2.17241379 2.37931034 2.5862069 2.79310345 3. ]
[-2. -1.78947368 -1.57894737 -1.36842105 -1.15789474 -0.94736842
-0.73684211 -0.52631579 -0.31578947 -0.10526316 0.10526316 0.31578947
0.52631579 0.73684211 0.94736842 1.15789474 1.36842105 1.57894737
1.78947368 2. ]
from scipy import interpolate
# 绘图设置
fig = plt.figure( figsize=(12,10),dpi=100)
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
# 原始数据
ax1 = fig.add_subplot(2,2,1)
ax1.set_title("原始数据")
mappable = ax1.pcolormesh( x,y,z, cmap=plt.cm.jet )
plt.colorbar(mappable,ax=ax1)
# 线性插值
f1 = interpolate.interp2d( x[0,:], y[:,0], z, kind='linear')
# 生成插值数据
z1 = f1(x_new[0,:], y_new[:,0])
# 绘图
ax2 = fig.add_subplot(2,2,2)
ax2.set_title('线性插值')
mappable = ax2.pcolor(x_new,y_new,z1, cmap=plt.cm.jet)
fig.colorbar(mappable,ax=ax2)
# 三阶样条插值
f2 = interpolate.interp2d( x[0,:], y[:,0], z, kind='cubic')
z2 = f2(x_new[0,:], y_new[:,0])
ax3 = fig.add_subplot(2,2,3)
ax3.set_title("三阶样条插值")
mappable = ax3.pcolor( x_new,y_new,z2, cmap=plt.cm.jet )
plt.colorbar(mappable,ax=ax3)
# 五阶样条插值
f3 = interpolate.interp2d( x[0,:], y[:,0], z, kind='quintic')
z3 = f3(x_new[0,:], y_new[:,0])
ax4 = fig.add_subplot(2,2,4)
ax4.set_title('五阶样条插值')
mappable = ax4.pcolor(x_new,y_new,z3, cmap=plt.cm.jet)
fig.colorbar(mappable,ax=ax4)
#wspace 子图横向间距, hspace 代表子图间的纵向距离,left 代表位于图像不同位置
plt.subplots_adjust(left=None, bottom=0.15, right=None, top=None, wspace=0.2, hspace=0.4)
### 3 离散数据插值到网格 |
#### 3.1 griddata griddata(points,values,xi,method =‘linear’,fill_value = nan,rescale = False ) 参数:points:离散数据点的位置信息元素 values:离散数据点的值 xi:网格数据 method:nearest 临近点插值 :linear 线性插值 :cubic 三阶样条插值 |
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import griddata
lons = np.random.random(300)*180 # 经度从0-180°,随机生成300个点
lats = np.random.random(300)*90 # 纬度从0-90°,随机生成300个点
# 生成300个温度点
temperature = ((lons-90)/45)*np.exp(-((lons-90)/45)**2-((lats-45)/45)**2)
# 将矩形区域裁剪成三角形区域,网格数据变成了离散数据
triangle = np.where( ( (lons<90)&(lats<lons) )|((lons>=90)&(lats<180-lons)) )
lons = lons[triangle]
lats = lats[triangle]
temperature = temperature[triangle]
# 绘图
fig = plt.figure( figsize=(8,6),dpi=120 )
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
plt.title('原始数据')
plt.scatter( lons, lats, s=3, c=temperature, cmap=plt.cm.hsv )
plt.colorbar()
plt.axis('equal')
plt.xlabel('lons')
plt.ylabel('lats')
# 生成目标网格
lat_grid,lon_grid = np.mgrid[0:90:91j,0:180:181j]
lon_grid
array([[ 0., 1., 2., ..., 178., 179., 180.],
[ 0., 1., 2., ..., 178., 179., 180.],
[ 0., 1., 2., ..., 178., 179., 180.],
...,
[ 0., 1., 2., ..., 178., 179., 180.],
[ 0., 1., 2., ..., 178., 179., 180.],
[ 0., 1., 2., ..., 178., 179., 180.]])
# 先画一下原始图片
fig = plt.figure( figsize=(10,8),dpi=100)
ax1 = fig.add_subplot(2,2,1)
mappable = ax1.scatter( lons, lats, s=3, c=temperature, cmap=plt.cm.hsv )
ax1.set_title('原始数据')
ax1.set_xlabel('lons')
ax1.set_ylabel('lats')
ax1.axis('equal')
plt.colorbar(mappable, ax=ax1)
# 临近点插值
temp_nearest = griddata((lons,lats), temperature, (lon_grid,lat_grid), method='nearest')
ax2 = fig.add_subplot(2,2,2)
mappable = ax2.scatter( lon_grid, lat_grid, s=3, c=temp_nearest, cmap=plt.cm.hsv )
ax2.set_title('临近点插值')
ax2.set_xlabel('lons')
ax2.set_ylabel('lats')
ax2.axis('equal')
plt.colorbar(mappable, ax=ax2)
# 线性插值
temp_linear = griddata((lons,lats), temperature, (lon_grid,lat_grid), method='linear')
plt.subplot(2,2,3)
plt.scatter( lon_grid, lat_grid, s=3, c=temp_linear, cmap=plt.cm.hsv )
plt.title('线性插值')
plt.colorbar()
plt.axis('equal')
# 三阶样条插值
temp_cubic = griddata((lons,lats), temperature, (lon_grid,lat_grid), method='cubic',fill_value=0)
plt.subplot(2,2,4)
plt.scatter( lon_grid, lat_grid, s=3, c=temp_cubic, cmap=plt.cm.hsv )
plt.title('三阶样条插值')
plt.colorbar()
plt.axis('equal')
plt.subplots_adjust(left=None, bottom=0.15, right=None, top=None, wspace=0.2, hspace=0.4)
plt.show()