numpy 独立滚动矩阵的行

new9mtju  于 2023-10-19  发布在  其他
关注(0)|答案(6)|浏览(122)

我有一个矩阵(2d numpy ndarray,准确地说):

A = np.array([[4, 0, 0],
              [1, 2, 3],
              [0, 0, 5]])

我想根据另一个数组中的滚动值独立地滚动A的每一行:

r = np.array([2, 0, -1])

也就是说,我想这样做:

print np.array([np.roll(row, x) for row,x in zip(A, r)])

[[0 0 4]
 [1 2 3]
 [0 5 0]]

有没有一种方法可以有效地做到这一点?也许使用花哨的索引技巧?

dojqjjoe

dojqjjoe1#

你可以使用高级索引。它是否是最快的方法可能取决于数组的大小。例如,对于大行,这可能比其他方法慢。

rows, column_indices = np.ogrid[:A.shape[0], :A.shape[1]]

# Always use a negative shift, so that column_indices are valid.
# Alternative: r %= A.shape[1]
r[r < 0] += A.shape[1]
column_indices = column_indices - r[:, np.newaxis]

result = A[rows, column_indices]
kxxlusnw

kxxlusnw2#

numpy.lib.stride_tricks.as_strided stricks(焦v双关语)再次!

说到 * 花哨的索引技巧 *,有 * 臭名昭著 * -np.lib.stride_tricks.as_strided。这个想法/技巧是从第一列开始得到一个切片部分,直到倒数第二列,并在最后连接。这确保了我们可以根据需要向前迈进,以利用np.lib.stride_tricks.as_strided,从而避免实际回滚的需要。这就是整个想法!
现在,在实际实现方面,我们将使用scikit-image's view_as_windows来优雅地使用np.lib.stride_tricks.as_strided。因此,最终的实现将是-

from skimage.util.shape import view_as_windows as viewW

def strided_indexing_roll(a, r):
    # Concatenate with sliced to cover all rolls
    a_ext = np.concatenate((a,a[:,:-1]),axis=1)

    # Get sliding windows; use advanced-indexing to select appropriate ones
    n = a.shape[1]
    return viewW(a_ext,(1,n))[np.arange(len(r)), (n-r)%n,0]

这里有一个样本运行-

In [327]: A = np.array([[4, 0, 0],
     ...:               [1, 2, 3],
     ...:               [0, 0, 5]])

In [328]: r = np.array([2, 0, -1])

In [329]: strided_indexing_roll(A, r)
Out[329]: 
array([[0, 0, 4],
       [1, 2, 3],
       [0, 5, 0]])

对标

# @seberg's solution
def advindexing_roll(A, r):
    rows, column_indices = np.ogrid[:A.shape[0], :A.shape[1]]    
    r[r < 0] += A.shape[1]
    column_indices = column_indices - r[:,np.newaxis]
    return A[rows, column_indices]

让我们对具有大量行和列的阵列进行一些基准测试-

In [324]: np.random.seed(0)
     ...: a = np.random.rand(10000,1000)
     ...: r = np.random.randint(-1000,1000,(10000))

# @seberg's solution
In [325]: %timeit advindexing_roll(a, r)
10 loops, best of 3: 71.3 ms per loop

#  Solution from this post
In [326]: %timeit strided_indexing_roll(a, r)
10 loops, best of 3: 44 ms per loop
hzbexzde

hzbexzde3#

如果你想要更一般的解决方案(处理任何形状和任何轴),我修改了@seberg的解决方案:

def indep_roll(arr, shifts, axis=1):
    """Apply an independent roll for each dimensions of a single axis.

    Parameters
    ----------
    arr : np.ndarray
        Array of any shape.

    shifts : np.ndarray
        How many shifting to use for each dimension. Shape: `(arr.shape[axis],)`.

    axis : int
        Axis along which elements are shifted. 
    """
    arr = np.swapaxes(arr,axis,-1)
    all_idcs = np.ogrid[[slice(0,n) for n in arr.shape]]

    # Convert to a positive shift
    shifts[shifts < 0] += arr.shape[-1] 
    all_idcs[-1] = all_idcs[-1] - shifts[:, np.newaxis]

    result = arr[tuple(all_idcs)]
    arr = np.swapaxes(result,-1,axis)
    return arr
taor4pac

taor4pac4#

通过使用快速傅里叶变换,我们可以在频域中应用变换,然后使用逆快速傅里叶变换来获得行移位。
所以这是一个纯numpy的解决方案,只需要一行:

import numpy as np
from numpy.fft import fft, ifft

# The row shift function using the fast fourrier transform
#   rshift(A,r) where A is a 2D array, r the row shift vector
def rshift(A,r):
     return np.real(ifft(fft(A,axis=1)*np.exp(2*1j*np.pi/A.shape[1]*r[:,None]*np.r_[0:A.shape[1]][None,:]),axis=1).round())

这将应用左移,但我们可以简单地否定指数指数将函数转换为右移函数:

ifft(fft(...)*np.exp(-2*1j...)

它可以这样使用:

# Example:

A = np.array([[1,2,3,4],
              [1,2,3,4],
              [1,2,3,4]])

r = np.array([1,-1,3])

print(rshift(A,r))
2nc8po8w

2nc8po8w5#

我实现了一个纯numpy.lib.stride_tricks.as_strided解决方案,如下所示

from numpy.lib.stride_tricks import as_strided

def custom_roll(arr, r_tup):
    m = np.asarray(r_tup)
    arr_roll = arr[:, [*range(arr.shape[1]),*range(arr.shape[1]-1)]].copy() #need `copy`
    strd_0, strd_1 = arr_roll.strides
    n = arr.shape[1]
    result = as_strided(arr_roll, (*arr.shape, n), (strd_0 ,strd_1, strd_1))

    return result[np.arange(arr.shape[0]), (n-m)%n]

A = np.array([[4, 0, 0],
              [1, 2, 3],
              [0, 0, 5]])

r = np.array([2, 0, -1])

out = custom_roll(A, r)

Out[789]:
array([[0, 0, 4],
       [1, 2, 3],
       [0, 5, 0]])
sf6xfgos

sf6xfgos6#

基于divakar的优秀答案,您可以轻松地将此逻辑应用于3D数组(这是我首先来到这里的问题)。这里有一个例子-基本上是扁平化您的数据,滚动它并在以下情况下重塑它:

def applyroll_30(cube, threshold=25, offset=500):
    flattened_cube = cube.copy().reshape(cube.shape[0]*cube.shape[1], cube.shape[2])

    roll_matrix = calc_roll_matrix_flattened(flattened_cube, threshold, offset)

    rolled_cube = strided_indexing_roll(flattened_cube, roll_matrix, cube_shape=cube.shape)

    rolled_cube = triggered_cube.reshape(cube.shape[0], cube.shape[1], cube.shape[2])
    return rolled_cube

def calc_roll_matrix_flattened(cube_flattened, threshold, offset):
    """ Calculates the number of position along time axis we need to shift
        elements in order to trig the data.
        We return a 1D numpy array of shape (X*Y, time) elements
    """

    # armax(...) finds the position in the cube (3d) where we are above threshold
    roll_matrix = np.argmax(cube_flattened > threshold, axis=1) + offset
    # ensure we don't have index out of bound
    roll_matrix[roll_matrix>cube_flattened.shape[1]] = cube_flattened.shape[1]          
    return roll_matrix


def strided_indexing_roll(cube_flattened, roll_matrix_flattened, cube_shape):
    # Concatenate with sliced to cover all rolls
    # otherwise we shift in the wrong direction for my application
    roll_matrix_flattened = -1 * roll_matrix_flattened

    a_ext = np.concatenate((cube_flattened, cube_flattened[:, :-1]), axis=1)

    # Get sliding windows; use advanced-indexing to select appropriate ones
    n = cube_flattened.shape[1]
    result = viewW(a_ext,(1,n))[np.arange(len(roll_matrix_flattened)), (n - roll_matrix_flattened) % n, 0]
    result = result.reshape(cube_shape)
    return result

Divakar的回答并没有公正地说明这在大型数据立方体上的效率有多高。我已经在一个400 x400 x2000的数据格式为int 8的时间。一个等价的for循环大约需要5.5秒,Seberg的答案大约需要3.0秒,而strided_indexing.~ 0.5秒。

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