类似 accumarray 的函数¶
| 日期 | 2010-03-31 (最后修改), 2010-03-31 (创建) |
|---|
accum，类似 MATLAB 的 accumarray 的函数¶
NumPy 不包含等效于 MATLAB 的 accumarray 函数的函数。以下函数 accum 非常接近。
请注意，accum 可以处理 n 维数组，并允许指定结果的数据类型。
在 [1]
from itertools import product
import numpy as np
def accum(accmap, a, func=None, size=None, fill_value=0, dtype=None):
"""
An accumulation function similar to Matlab's `accumarray` function.
Parameters
----------
accmap : ndarray
This is the "accumulation map". It maps input (i.e. indices into
`a`) to their destination in the output array. The first `a.ndim`
dimensions of `accmap` must be the same as `a.shape`. That is,
`accmap.shape[:a.ndim]` must equal `a.shape`. For example, if `a`
has shape (15,4), then `accmap.shape[:2]` must equal (15,4). In this
case `accmap[i,j]` gives the index into the output array where
element (i,j) of `a` is to be accumulated. If the output is, say,
a 2D, then `accmap` must have shape (15,4,2). The value in the
last dimension give indices into the output array. If the output is
1D, then the shape of `accmap` can be either (15,4) or (15,4,1)
a : ndarray
The input data to be accumulated.
func : callable or None
The accumulation function. The function will be passed a list
of values from `a` to be accumulated.
If None, numpy.sum is assumed.
size : ndarray or None
The size of the output array. If None, the size will be determined
from `accmap`.
fill_value : scalar
The default value for elements of the output array.
dtype : numpy data type, or None
The data type of the output array. If None, the data type of
`a` is used.
Returns
-------
out : ndarray
The accumulated results.
The shape of `out` is `size` if `size` is given. Otherwise the
shape is determined by the (lexicographically) largest indices of
the output found in `accmap`.
Examples
--------
>>> from numpy import array, prod
>>> a = array([[1,2,3],[4,-1,6],[-1,8,9]])
>>> a
array([[ 1, 2, 3],
[ 4, -1, 6],
[-1, 8, 9]])
>>> # Sum the diagonals.
>>> accmap = array([[0,1,2],[2,0,1],[1,2,0]])
>>> s = accum(accmap, a)
array([9, 7, 15])
>>> # A 2D output, from sub-arrays with shapes and positions like this:
>>> # [ (2,2) (2,1)]
>>> # [ (1,2) (1,1)]
>>> accmap = array([
[[0,0],[0,0],[0,1]],
[[0,0],[0,0],[0,1]],
[[1,0],[1,0],[1,1]],
])
>>> # Accumulate using a product.
>>> accum(accmap, a, func=prod, dtype=float)
array([[ -8., 18.],
[ -8., 9.]])
>>> # Same accmap, but create an array of lists of values.
>>> accum(accmap, a, func=lambda x: x, dtype='O')
array([[[1, 2, 4, -1], [3, 6]],
[[-1, 8], [9]]], dtype=object)
"""
# Check for bad arguments and handle the defaults.
if accmap.shape[:a.ndim] != a.shape:
raise ValueError("The initial dimensions of accmap must be the same as a.shape")
if func is None:
func = np.sum
if dtype is None:
dtype = a.dtype
if accmap.shape == a.shape:
accmap = np.expand_dims(accmap, -1)
adims = tuple(range(a.ndim))
if size is None:
size = 1 + np.squeeze(np.apply_over_axes(np.max, accmap, axes=adims))
size = np.atleast_1d(size)
# Create an array of python lists of values.
vals = np.empty(size, dtype='O')
for s in product(*[range(k) for k in size]):
vals[s] = []
for s in product(*[range(k) for k in a.shape]):
indx = tuple(accmap[s])
val = a[s]
vals[indx].append(val)
# Create the output array.
out = np.empty(size, dtype=dtype)
for s in product(*[range(k) for k in size]):
if vals[s] == []:
out[s] = fill_value
else:
out[s] = func(vals[s])
return out
示例¶
一个基本示例 - 对 3x3 数组的对角线（带环绕）求和
在 [2]
from numpy import array, prod
a = array([[1,2,3],[4,-1,6],[-1,8,9]])
accmap = array([[0,1,2],[2,0,1],[1,2,0]])
在 [3]
s = accum(accmap, a)
s
Out[3]
使用乘法累积，从 3x3 数组到 2x2 数组
在 [4]
accmap = array([
[[0,0],[0,0],[0,1]],
[[0,0],[0,0],[0,1]],
[[1,0],[1,0],[1,1]],
])
accum(accmap, a, func=prod, dtype=float)
Out[4]
创建一个包含要累积到输出数组中每个位置的值的列表的数组
在 [5]
accum(accmap, a, func=lambda x: x, dtype='O')
Out[5]
使用 accum 将 1D 数组中的某些值排列到 2D 数组中（请注意，为此使用 accum 过于复杂；花式索引就足够了）
在 [6]
subs = np.array([[k,5-k] for k in range(6)])
subs
Out[6]
在 [7]
vals = array(range(10,16))
accum(subs, vals)
Out[7]
章节作者：WarrenWeckesser