numpy 相關統計
阿新 • • 發佈：2020-11-28
1.numpy.amin() 計算最小值
numpy.amin(a[, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue, where=np._NoValue])
例子如下：
import numpy as np x = np.array([[11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30], [31, 32, 33, 34, 35]]) #最小值 y = np.amin(x)#11 #每列最小值 y = np.amin(x, axis=0) print(y) # [11 12 13 14 15] #每行最小值 y = np.amin(x, axis=1) print(y) # [11 16 21 26 31]
其實直接使用x.min()也是同樣的效果
print(x.min()) #11 print(x.min(axis=0)) #[11 12 13 14 15] print(x.min(axis=1)) #[11 16 21 26 31]
最大值也是同樣的用法，就不贅述了
2.計算極差（也就是最大值和最小值的差）
numpy.ptp(a, axis=None, out=None, keepdims=np._NoValue)
例子如下：
import numpy as np np.random.seed(20200623) x = np.random.randint(0, 20, size=[4, 5]) print(x) # [[10 2 1 1 16] # [18 11 10 14 10] # [11 1 9 18 8] # [16 2 0 15 16]] #極差 print(np.ptp(x)) # 18 #計算每列極差 print(np.ptp(x, axis=0)) #[ 8 10 10 17 8] #計算每行極差 print(np.ptp(x, axis=1)) # [15 8 17 16]
同理，使用x.ptp()也是OK的
3.計算分位數
numpy.percentile(a, q, axis=None, out=None, overwrite_input=False, interpolation='linear', keepdims=False)
- a：array，用來算分位數的物件，可以是多維的陣列。
- q：介於0-100的float，用來計算是幾分位的引數，如四分之一位就是25，如要算兩個位置的數就[25,75]。
- axis：座標軸的方向，一維的就不用考慮了，多維的就用這個調整計算的維度方向，取值範圍0/1
np.random.seed(20200623) x = np.random.randint(0, 20, size=[4, 5]) print(x) # [[10 2 1 1 16] # [18 11 10 14 10] # [11 1 9 18 8] # [16 2 0 15 16]] #如果只求某個分位數，直接使用int，如果是多個，則使用list print(np.percentile(x, 25)) #2.0 print(np.percentile(x, [25, 50])) # [ 2. 10.] print(np.percentile(x, [25, 50], axis=0)) # [[10.75 1.75 0.75 10.75 9.5 ] # [13.5 2. 5. 14.5 13. ]] print(np.percentile(x, [25, 50], axis=1)) # [[ 1. 10. 8. 2.] # [ 2. 11. 9. 15.]]
4.計算中位數
numpy.median(a, axis=None, out=None, overwrite_input=False, keepdims=False)
例子
import numpy as np np.random.seed(20200623) x = np.random.randint(0, 20, size=[4, 5]) print(x) # [[10 2 1 1 16] # [18 11 10 14 10] # [11 1 9 18 8] # [16 2 0 15 16]] print(np.percentile(x, 50)) print(np.median(x)) # 10.0 print(np.percentile(x, 50, axis=0)) print(np.median(x, axis=0)) # [13.5 2. 5. 14.5 13. ] print(np.percentile(x, 50, axis=1)) print(np.median(x, axis=1)) # [ 2. 11. 9. 15.]
注意：中位數和分位數都不可以使用x.median() 或者是x.percentile()
5.計算均值,沿軸的元素的總和除以元素的數量
numpy.mean(a[, axis=None, dtype=None, out=None, keepdims=np._NoValue)])
例子
import numpy as np x = np.array([[11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30], [31, 32, 33, 34, 35]]) y = np.mean(x) print(y) # 23.0 y = np.mean(x, axis=0) print(y) # [21. 22. 23. 24. 25.] y = np.mean(x, axis=1) print(y) # [13. 18. 23. 28. 33.] #是否可以使用x.mean() print(x.mean()) #23.0
我們驗證一下分母是否會考慮空值
a=np.array([1,2,3,4,5,np.nan]) print(a) #[ 1. 2. 3. 4. 5. nan] print(a.mean()) #nan print(np.mean(a)) #nan print(a[:-1].mean()) #3.0
6.計算加權平均值
numpy.average(a[, axis=None, weights=None, returned=False])
mean和average都是計算均值的函式，在不指定權重的時候average和mean是一樣的。指定權重後，average可以計算加權平均值。
計算加權平均值（將各數值乘以相應的權數，然後加總求和得到總體值，再除以總的單位數。）
import numpy as np x = np.array([[11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30], [31, 32, 33, 34, 35]]) y = np.average(x) print(y) # 23.0 y = np.average(x, axis=0) print(y) # [21. 22. 23. 24. 25.] y = np.average(x, axis=1) print(y) # [13. 18. 23. 28. 33.] y = np.arange(1, 26).reshape([5, 5]) print(y) # [[ 1 2 3 4 5] # [ 6 7 8 9 10] # [11 12 13 14 15] # [16 17 18 19 20] # [21 22 23 24 25]] z = np.average(x, weights=y) print(z) # 27.0 z = np.average(x, axis=0, weights=y) print(z) # [25.54545455 26.16666667 26.84615385 27.57142857 28.33333333] z = np.average(x, axis=1, weights=y) print(z) # [13.66666667 18.25 23.15384615 28.11111111 33.08695652]
第一行的均值怎麼的來的：
sum(x[0]*y[0]/y[0].sum()) #13.666666666666668
也就是說分母其實就是y的求和，而mean的分母是個數
7.計算方差
numpy.var(a[, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue])
ddof=0：是“Delta Degrees of Freedom”，表示自由度的個數
要注意方差和樣本方差的無偏估計，方差公式中分母上是n；樣本方差無偏估計公式中分母上是n-1（n為樣本個數），證明的連結
import numpy as np x = np.array([[11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30], [31, 32, 33, 34, 35]]) y = np.var(x) print(y) # 52.0 y = np.mean((x - np.mean(x)) ** 2) print(y) # 52.0 y = np.var(x, ddof=1) print(y) # 54.166666666666664 y = np.sum((x - np.mean(x)) ** 2) / (x.size - 1) print(y) # 54.166666666666664 y = np.var(x, axis=0) print(y) # [50. 50. 50. 50. 50.] y = np.var(x, axis=1) print(y) # [2. 2. 2. 2. 2.] print(x.var())
8.計算標準差
numpy.std(a[, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue])
標準差是一組資料平均值分散程度的一種度量，是方差的算術平方根
import numpy as np x = np.array([[11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30], [31, 32, 33, 34, 35]]) y = np.std(x) print(y) # 7.211102550927978 y = np.sqrt(np.var(x)) print(y) # 7.211102550927978 y = np.std(x, axis=0) print(y) # [7.07106781 7.07106781 7.07106781 7.07106781 7.07106781] y = np.std(x, axis=1) print(y) # [1.41421356 1.41421356 1.41421356 1.41421356 1.41421356]
9.計算協方差矩陣
numpy.cov(m, y=None, rowvar=True, bias=False, ddof=None, fweights=None,aweights=None)
例子
import numpy as np x = [1, 2, 3, 4, 6] y = [0, 2, 5, 6, 7] print(np.cov(x)) # 3.7 #樣本方差 print(np.cov(y)) # 8.5 #樣本方差 print(np.cov(x, y)) # [[3.7 5.25] # [5.25 8.5 ]] print(np.var(x)) # 2.96 #方差 print(np.var(x, ddof=1)) # 3.7 #樣本方差 print(np.var(y)) # 6.8 #方差 print(np.var(y, ddof=1)) # 8.5 #樣本方差 z = np.mean((x - np.mean(x)) * (y - np.mean(y))) #協方差 print(z) # 4.2 z = np.sum((x - np.mean(x)) * (y - np.mean(y))) / (len(x) - 1) #樣本協方差 print(z) # 5.25 z = np.dot(x - np.mean(x), y - np.mean(y)) / (len(x) - 1) #樣本協方差 print(z) # 5.25
10.計算相關係數
numpy.corrcoef(x, y=None, rowvar=True, bias=np._NoValue, ddof=np._NoValue)
理解了np.cov()函式之後，很容易理解np.correlate()，二者引數幾乎一模一樣。
np.cov()描述的是兩個向量協同變化的程度，它的取值可能非常大，也可能非常小，這就導致沒法直觀地衡量二者協同變化的程度。相關係數實際上是正則化的協方差，n個變數的相關係數形成一個n維方陣
import numpy as np np.random.seed(20200623) x, y = np.random.randint(0, 20, size=(2, 4)) print(x) # [10 2 1 1] print(y) # [16 18 11 10] z = np.corrcoef(x, y) print(z) # [[1. 0.48510096] # [0.48510096 1. ]] a = np.dot(x - np.mean(x), y - np.mean(y)) b = np.sqrt(np.dot(x - np.mean(x), x - np.mean(x))) c = np.sqrt(np.dot(y - np.mean(y), y - np.mean(y))) print(a / (b * c)) # 0.4851009629263671
11.直方圖
numpy.digitize(x, bins, right=False)
- x：numpy陣列
- bins：一維單調陣列，必須是升序或者降序
- right：間隔是否包含最右
- 返回值：x在bins中的位置
import numpy as np x = np.array([0.2, 6.4, 3.0, 1.6]) bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0]) inds = np.digitize(x, bins) print(inds) # [1 4 3 2] for n in range(x.size): print(bins[inds[n] - 1], "<=", x[n], "<", bins[inds[n]]) # 0.0 <= 0.2 < 1.0 # 4.0 <= 6.4 < 10.0 # 2.5 <= 3.0 < 4.0 # 1.0 <= 1.6 < 2.5 import numpy as np x = np.array([1.2, 10.0, 12.4, 15.5, 20.]) bins = np.array([0, 5, 10, 15, 20]) inds = np.digitize(x, bins, right=True) print(inds) # [1 2 3 4 4] inds = np.digitize(x, bins, right=False) print(inds) # [1 3 3 4 5]