Matlab、Python、R语言和MeteoInfoLab计算相关系数

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1 Matlab计算相关系数

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clc;clear;close all
data=xlsread('testdata.xlsx');
X=data(:,1);
Y=data(:,2);
Z=data(:,3);
%corr默认情况下计算的是Pearson相关系数
%Pearson相关系数：
[r,p]=corr(X,Y,'type','Pearson');
%Spearman相关系数：
[r1,p1]=corr(X,Y,'type','Spearman');
%Kendall相关系数：
[r2,p2]=corr(X,Y,'type','kendall');
%偏相关分析.在控制变量C影响的条件下，计算得到A、B之间的相关系数
[R,P] = partialcorr(X,Y,Z);
% 对于相关系数的大小所表示的意义目前在统计学界尚不一致，但通常按下是这样认为的：
% 相关系数      相关程度
% 0.00-±0.30    微相关
% ±0.30-±0.50  实相关
% ±0.50-±0.80  显著相关
% ±0.80-±1.00  高度相关

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2 Python计算相关系数

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#导入依赖库
import numpy as np
import pandas as pd
data = pd.DataFrame({'A':np.random.randint(1, 100, 10), 
'B':np.random.randint(1, 100, 10),
'C':np.random.randint(1, 100, 10)})
data.corr()   # 计算pearson相关系数
data.corr('kendall')      # Kendall Tau相关系数
data.corr('spearman')     # spearman秩相关
#计算多个列表的相关系数矩阵
import pandas as pd
import numpy as np
if __name__ == '__main__':
unstrtf_lst = [[2.136, 1.778, 1.746, 2.565, 1.873, 2.413, 1.813, 1.72, 1.932, 1.987, 2.035, 2.178, 2.05, 2.016, 1.645, 1.756, 1.886, 2.106, 2.138, 1.914, 1.984, 1.906, 1.871, 1.939, 1.81, 1.93, 1.898, 1.802, 2.008, 1.724, 1.823, 1.636, 1.774, 2.055, 1.934, 1.629, 2.519, 2.093, 2.004, 1.793, 1.564, 1.962, 2.176, 1.846, 1.816, 2.018, 1.708, 2.465, 1.899, 1.523, 1.41, 2.102, 2.065, 2.402, 2.091, 1.867, 1.77, 1.466, 2.029, 1.659, 1.626, 1.977, 1.837, 2.13, 2.241, 2.184, 2.345, 1.833, 2.113, 1.764, 1.859, 1.868, 1.835, 1.906, 2.237, 1.846, 1.871, 1.769, 1.928, 1.831, 1.875, 2.039, 2.24, 1.835, 1.851]
, [2.171, 1.831, 1.714, 2.507, 1.793, 2.526, 1.829, 1.705, 1.954, 2.017, 2.022, 2.16, 2.059, 1.966, 1.661, 1.752, 1.884, 2.203, 2.182, 1.97, 2.003, 1.875, 1.852, 1.884, 1.774, 1.916, 1.936, 1.809, 1.926, 1.717, 1.841, 1.59, 1.781, 2.016, 1.898, 1.657, 2.458, 2.134, 2.032, 1.785, 1.575, 1.959, 2.11, 1.854, 1.826, 1.992, 1.706, 2.419, 1.854, 1.514, 1.37, 2.084, 2.024, 2.398, 1.955, 1.859, 1.759, 1.441, 2.059, 1.653, 1.583, 1.987, 1.84, 2.106, 2.262, 2.13, 2.371, 1.776, 2.117, 1.733, 1.814, 1.839, 1.822, 1.883, 2.23, 1.803, 1.894, 1.783, 1.911, 1.813, 1.85, 2.004, 2.191, 1.823, 1.809]
, [2.157, 1.873, 1.802, 2.761, 1.733, 2.506, 1.842, 1.765, 1.938, 2.058, 1.932, 2.196, 2.004, 2.126, 1.664, 1.698, 1.899, 2.073, 2.117, 2.083, 1.972, 1.969, 1.865, 1.937, 1.752, 1.939, 1.927, 1.804, 2.07, 1.725, 1.846, 1.5, 1.804, 2.1, 1.932, 1.773, 2.431, 2.088, 2.08, 1.812, 1.592, 1.953, 2.044, 2.019, 1.846, 2.061, 1.771, 2.254, 1.891, 1.536, 1.356, 1.952, 2.222, 2.427, 2.015, 1.873, 1.79, 1.384, 1.981, 1.665, 1.815, 2.006, 1.869, 2.102, 2.249, 2.27, 2.296, 1.814, 2.099, 1.702, 1.688, 1.89, 1.82, 1.927, 2.162, 1.825, 1.998, 1.811, 2.0, 1.842, 1.793, 2.115, 2.301, 1.789, 1.826]
, [2.127, 1.744, 1.747, 2.548, 1.939, 2.296, 1.808, 1.71, 1.901, 1.906, 2.074, 2.167, 2.113, 2.044, 1.632, 1.821, 1.94, 2.076, 2.114, 1.837, 1.978, 1.904, 1.872, 1.98, 1.886, 1.923, 1.875, 1.799, 1.992, 1.704, 1.812, 1.715, 1.756, 2.061, 1.94, 1.554, 2.592, 2.065, 1.983, 1.802, 1.57, 1.955, 2.215, 1.765, 1.796, 2.006, 1.662, 2.573, 1.915, 1.543, 1.439, 2.16, 2.012, 2.42, 2.268, 1.886, 1.767, 1.527, 2.073, 1.65, 1.567, 2.016, 1.819, 2.153, 2.225, 2.237, 2.327, 1.877, 2.115, 1.804, 1.939, 1.867, 1.84, 1.905, 2.302, 1.883, 1.798, 1.725, 1.893, 1.846, 1.916, 2.025, 2.268, 1.867, 1.877]
, [2.089, 1.664, 1.72, 2.441, 2.031, 2.321, 1.773, 1.702, 1.935, 1.968, 2.119, 2.191, 2.023, 1.925, 1.621, 1.75, 1.822, 2.074, 2.139, 1.764, 1.982, 1.873, 1.895, 1.955, 1.829, 1.945, 1.853, 1.794, 2.046, 1.75, 1.793, 1.741, 1.752, 2.042, 1.965, 1.532, 2.598, 2.086, 1.923, 1.771, 1.517, 1.98, 2.338, 1.743, 1.794, 2.014, 1.693, 2.618, 1.938, 1.5, 1.476, 2.216, 2.003, 2.361, 2.13, 1.85, 1.764, 1.513, 2.001, 1.669, 1.538, 1.897, 1.819, 2.163, 2.226, 2.099, 2.386, 1.865, 2.121, 1.818, 2.0, 1.876, 1.858, 1.908, 2.254, 1.874, 1.791, 1.759, 1.908, 1.822, 1.944, 2.012, 2.201, 1.863, 1.892]
]
column_lst = ['whole_year', 'spring', 'summer', 'autumn', 'winter']
# 计算列表两两间的相关系数
data_dict = {} # 创建数据字典，为生成Dataframe做准备
for col, gf_lst in zip(column_lst, unstrtf_lst):
data_dict[col] = gf_lst
unstrtf_df = pd.DataFrame(data_dict)
cor1 = unstrtf_df.corr() # 计算相关系数，得到一个矩阵
print(cor1)
print(unstrtf_df.columns.tolist())

3 R语言计算相关系数

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setwd("F:/Rpeng/14")
data <- read.csv('testdata.csv',header = TRUE)
a=data$R
b=data$P
rt1<-cor.test (a,b,method = 'pearson')
rt2<-cor.test (a,b,method = 'kendall')
rt3<-cor.test (a,b,method = 'spearman')

4 MeteoinfoLab计算相关系数

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#1 spearman
from mipylib.numeric import stats
y = [1,2,3,4,5]
x = [5,6,7,8,7]
r = stats.spearmanr(x, y)
print r
#2 pearson
from mipylib.numeric import stats
y = [29.81,30.04,41.7,43.71,28.75,37.73,52.25,32.41,25.67,28.17,25.71,36.05,37.62,34.28,38.82,40.15,35.69,28.36,39.56,52.56,54.14,50.76,39.35,43.16]
x = [51.6,46,64.3,83.4,65.9,49.5,88.6,101.4,55.9,41.8,33.4,57.3,66.5,40.5,72.3,70,83.3,65.8,63.1,83.4,102,94,77,77]
r, p = stats.pearsonr(x, y)
print r, p
#3 Kendall’s tau
from mipylib.numeric import stats
x1 = [12, 2, 1, 12, 2]
x2 = [1, 4, 7, 1, 0]
tau = stats.kendalltau(x1, x2)
print tau
#4 corrcoef
y = [29.81,30.04,41.7,43.71,28.75,37.73,52.25,32.41,25.67,28.17,25.71,36.05,37.62,34.28,38.82,40.15,35.69,28.36,39.56,52.56,54.14,50.76,39.35,43.16]
x = [51.6,46,64.3,83.4,65.9,49.5,88.6,101.4,55.9,41.8,33.4,57.3,66.5,40.5,72.3,70,83.3,65.8,63.1,83.4,102,94,77,77]
r = corrcoef(x, y)
print r
y1 = array(x) * 2
r1 = corrcoef(x, y1)
print r1
#5 Ridge Regression
from miml import datasets
from miml.regression import RidgeRegression
x = array([[234.289,      235.6,        159.0,    107.608, 1947,   60.323],
[259.426,      232.5,        145.6,    108.632, 1948,   61.122],
[258.054,      368.2,        161.6,    109.773, 1949,   60.171],
[284.599,      335.1,        165.0,    110.929, 1950,   61.187],
[328.975,      209.9,        309.9,    112.075, 1951,   63.221],
[346.999,      193.2,        359.4,    113.270, 1952,   63.639],
[365.385,      187.0,        354.7,    115.094, 1953,   64.989],
[363.112,      357.8,        335.0,    116.219, 1954,   63.761],
[397.469,      290.4,        304.8,    117.388, 1955,   66.019],
[419.180,      282.2,        285.7,    118.734, 1956,   67.857],
[442.769,      293.6,        279.8,    120.445, 1957,   68.169],
[444.546,      468.1,        263.7,    121.950, 1958,   66.513],
[482.704,      381.3,        255.2,    123.366, 1959,   68.655],
[502.601,      393.1,        251.4,    125.368, 1960,   69.564],
[518.173,      480.6,        257.2,    127.852, 1961,   69.331],
[554.894,      400.7,        282.7,    130.081, 1962,   70.551]])
y = array([83.0,  88.5,  88.2,  89.5,  96.2,  98.1,  99.0, 100.0, 101.2,
104.6, 108.4, 110.8, 112.6, 114.2, 115.7, 116.9])
model = RidgeRegression(0.0057)
model.fit(x, y)
print(model.predict(x[:10,:]))

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