含义

A universal function (or ufunc for short) is a function that operates on ndarrays in an element-by-element fashion, supporting array broadcasting, type casting and several other standard features.

Broadcast

broadcast规则：

  1. The arrays all have exactly the same shape.
  2. The arrays all have the same number of dimensions and the length of each dimensions is either a common length or 1.
  3. The arrays that have too few dimensions can have their shapes prepended with a dimension of length 1 to satisfy property 2.

Example

If a.shape is (5,1), b.shape is (1,6), c.shape is (6,) and d.shape is () so that d is a scalar, then a, b, c, and d are all broadcastable to dimension (5,6); and

  • a acts like a (5,6) array where a[:,0] is broadcast to the other columns,
  • b acts like a (5,6) array where b[0,:] is broadcast to the other rows,
  • c acts like a (1,6) array and therefore like a (5,6) array where c[:] is broadcast to every row, and finally,
  • d acts like a (5,6) array where the single value is repeated.

常见的ufunc

  • 数学操作：add、substract、multiply、divide、absolute、exp、log、log10、sqrt、square
  • 三角函数：sin、cos、tan、arcsin、arccos、arctan、sinh、cosh、tanh、arctanh、deg2rad、rad2deg
  • 比较函数：greater、less_equal、not_equal、equal、maximum、minimum
  • 浮点函数：isinf、isnan、floor、`ceil