accumarray like functionΒΆ

accum, a function like MATLAB's accumarray¶

NumPy doesn't include a function that is equivalent to MATLAB's accumarray function. The following function, accum, is close.

Note that accum can handle n-dimensional arrays, and allows the data type of the result to be specified.

In [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

Examples¶

A basic example--sum the diagonals (with wrapping) of a 3 by 3 array:

In [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]])
In [3]:
s = accum(accmap, a)
s
Out[3]:
array([ 9,  7, 15])

Accumulate using multiplication, going from a 3 by 3 array to 2 by 2 array:

In [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]:
array([[ -8.,  18.],
       [ -8.,   9.]])

Create an array of lists containing the values to be accumulated in each position in the output array:

In [5]:
accum(accmap, a, func=lambda x: x, dtype='O')
Out[5]:
array([[[1, 2, 4, -1], [3, 6]],
       [[-1, 8], [9]]], dtype=object)

Use `accum` to arrange some values from a 1D array in a 2D array (note that using `accum` for this is overkill; fancy indexing would suffice):

In [6]:
subs = np.array([[k,5-k] for k in range(6)])
subs
Out[6]:
array([[0, 5],
       [1, 4],
       [2, 3],
       [3, 2],
       [4, 1],
       [5, 0]])
In [7]:
vals = array(range(10,16))
accum(subs, vals)
Out[7]:
array([[ 0,  0,  0,  0,  0, 10],
       [ 0,  0,  0,  0, 11,  0],
       [ 0,  0,  0, 12,  0,  0],
       [ 0,  0, 13,  0,  0,  0],
       [ 0, 14,  0,  0,  0,  0],
       [15,  0,  0,  0,  0,  0]])

Section author: WarrenWeckesser