numpy.trace是求shape的對角線上的元素的和,具體看 https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.trace.html
或者搜尋 numpy.trace, 二維的比較好理解,對於三維以上的對角線(三維的對角線不止2條,該選哪兩條呢)就不好理解了,以下是本人的理解
# 3-D array 的trace演算法 import numpy as np a = np.arange(8).reshape((2,2,2)) print 'a =',a print np.trace(a) x0 = a[0,0,0] + a[1,1,0]#即 0 + 6 print 'a[1,1,0] =', a[1,1,0],';','x0 =',x0 x1 = a[0,0,1] + a[1,1,1]#即 1 + 7 print 'a[1,1,1] =', a[1,1,1],';','x1 =',x1 #當然你可能認為6 = 2 + 4;或者 8 = 5 + 3,確實一個立方體應該是4條對角線,但是是不是都可以呢 #請看下面的3-D b = np.array([ [ [100, 198], [2, 3]], [ [4, 5], [6,7]]]) print 'b =',b print np.trace(b) y0 = b[0,0,0] + b[1,1,0]#即 0 + 6 print 'y0 = b[0,0,0] + b[1,1,0] = %d + %d = %d' % (b[0,0,0], b[1,1,0], y0) y1 = b[0,0,1] + b[1,1,1]#即 1 + 7 print 'y1 = b[0,0,1] + b[1,1,1] = %d + %d = %d' % (b[0,0,1], b[1,1,1], y1) #事實證明只能是其中的固定方向的 #之所以能以此種方式思考是因為2-D的直觀 c = np.array([[2, 8], [4,5]]) print 'c =', c print 'trace =', np.trace(c) trace_c = c[0,0] + c[1,1] print 'c[0,0] + c[1,1] = %d + %d = %d' % (c[0,0], c[1,1], trace_c) #來看看4-D的 d = np.arange(32).reshape((2,2,2,4)) print 'd =', d #猜猜看這個trace結果是什麼shape, #(2, 4),只要去掉前面 2個維度即可 print 'np.trace(d).shape =', np.trace(d).shape print 'np.trace(d) =', np.trace(d) td00 = d[0,0,0,0] + d[1,1,0,0] print 'td00 = ' + 'd[0,0,0,0] + d[1,1,0,0] = %d + %d = %d' % (d[0,0,0,0], d[1,1,0,0], td00) td01 = d[0,0,0,1] + d[1,1,0,1] print 'td01 = ' + 'd[0,0,0,1] + d[1,1,0,1] = %d + %d = %d' % (d[0,0,0,1], d[1,1,0,1], td01) td02 = d[0,0,0,2] + d[1,1,0,2] print 'td02 = ' + 'd[0,0,0,2] + d[1,1,0,2] = %d + %d = %d' % (d[0,0,0,2], d[1,1,0,2], td02) td03 = d[0,0,0,3] + d[1,1,0,3] print 'td03 = ' + 'd[0,0,0,3] + d[1,1,0,3] = %d + %d = %d' % (d[0,0,0,3], d[1,1,0,3], td03) print td10 = d[0,0,1,0] + d[1,1,1,0] print 'td10 = ' + 'd[0,0,1,0] + d[1,1,1,0] = %d + %d = %d' % (d[0,0,1,0], d[1,1,1,0], td10) td11 = d[0,0,1,1] + d[1,1,1,1] print 'td11 = ' + 'd[0,0,1,1] + d[1,1,1,1] = %d + %d = %d' % (d[0,0,1,1], d[1,1,1,1], td11) td12 = d[0,0,1,2] + d[1,1,1,2] print 'td12 = ' + 'd[0,0,1,2] + d[1,1,1,2] = %d + %d = %d' % (d[0,0,1,2], d[1,1,1,2], td12) td13 = d[0,0,1,3] + d[1,1,1,3] print 'td13 = ' + 'd[0,0,1,3] + d[1,1,1,3] = %d + %d = %d' % (d[0,0,1,3], d[1,1,1,3], td13)
以下是執行結果:(python 2.7, numpy:1.14.2:
a = [[[0 1] [2 3]] [[4 5] [6 7]]] [6 8] a[1,1,0] = 6 ; x0 = 6 a[1,1,1] = 7 ; x1 = 8 b = [[[100 198] [ 2 3]] [[ 4 5] [ 6 7]]] [106 205] y0 = b[0,0,0] + b[1,1,0] = 100 + 6 = 106 y1 = b[0,0,1] + b[1,1,1] = 198 + 7 = 205 c = [[2 8] [4 5]] trace = 7 c[0,0] + c[1,1] = 2 + 5 = 7 d = [[[[ 0 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 26 27] [28 29 30 31]]]] np.trace(d).shape = (2, 4) np.trace(d) = [[24 26 28 30] [32 34 36 38]] td00 = d[0,0,0,0] + d[1,1,0,0] = 0 + 24 = 24 td01 = d[0,0,0,1] + d[1,1,0,1] = 1 + 25 = 26 td02 = d[0,0,0,2] + d[1,1,0,2] = 2 + 26 = 28 td03 = d[0,0,0,3] + d[1,1,0,3] = 3 + 27 = 30 td10 = d[0,0,1,0] + d[1,1,1,0] = 4 + 28 = 32 td11 = d[0,0,1,1] + d[1,1,1,1] = 5 + 29 = 34 td12 = d[0,0,1,2] + d[1,1,1,2] = 6 + 30 = 36 td13 = d[0,0,1,3] + d[1,1,1,3] = 7 + 31 = 38