我正在尝试编写一个将 2d-ndarray 映射到 2d-ndarray 的函数。输入数组的行可以独立处理,输入的行和输出的行之间应该是一一对应的。对于输入的每一行,应计算该行的给定顺序的多项式展开(参见文档字符串的示例)。当前的实施有效;但是,它需要对“powerMatrix”中的行和行的重复进行显式循环)。一次调用 numpy.power 是否可以获得相同的结果?顺便说一句:结果行中条目的顺序对我来说并不重要。
import numpy
def polynomialFeatures(x, order):
""" Generate polynomial features of given order for data x.
For each row of ndarray x, the polynomial expansions are computed, i.e
for row [x1, x2] and order 2, the following row of the result matrix is
computed: [1, x1, x1**2, x2, x1*x2, x1**2*x2, x2**2, x1*x2**2, x1**2*x2**2]
Parameters
----------
x : array-like
2-D array; for each of its rows, the polynomial features are created
order : int
The order of the polynomial features
Returns
-------
out : ndarray
2-D array of shape (x.shape[0], (order+1)**x.shape[1]) containing the
polynomial features computed for the rows of the array x
Examples
--------
>>> polynomialFeatures([[1, 2, 3], [-1, -2, -3]], 2)
array([[ 1 3 9 2 6 18 4 12 36 1 3 9 2 6 18 4 12
36 1 3 9 2 6 18 4 12 36]
[ 1 -3 9 -2 6 -18 4 -12 36 -1 3 -9 2 -6 18 -4 12
-36 1 -3 9 -2 6 -18 4 -12 36]])
"""
x = numpy.asarray(x)
# TODO: Avoid duplication of rows
powerMatrix = numpy.array([range(order+1)] * x.shape[1]).T
# TODO: Avoid explicit loop, and use numpy's broadcasting
F = []
for i in range(x.shape[0]):
X = numpy.power(x[i], powerMatrix).T
F.append(numpy.multiply.reduce(cartesian(X), axis=1))
return numpy.array(F)
print numpy.all(polynomialFeatures([[1, 2, 3], [-1, -2, -3]], 2) ==
numpy.array([[1, 3, 9, 2, 6, 18, 4, 12, 36, 1,
3, 9, 2, 6, 18, 4, 12, 36, 1, 3,
9, 2, 6, 18, 4, 12, 36],
[1, -3, 9, -2, 6, -18, 4, -12, 36, -1,
3, -9, 2, -6, 18, -4, 12, -36, 1, -3,
9, -2, 6, -18, 4, -12, 36]]))
谢谢,扬
编辑:这里定义了缺少的函数笛卡尔:Using numpy to build an array of all combination of two arrays