Lets say I have a Python Numpy array a.
a = numpy.array([1,2,3,4,5,6,7,8,9,10,11])
I want to create a matrix of sub sequences from this array of length 5 with stride 3. The results matrix hence will look as follows:
numpy.array([[1,2,3,4,5],[4,5,6,7,8],[7,8,9,10,11]])
One possible way of implementing this would be using a for-loop.
result_matrix = np.zeros((3, 5)) for i in range(0, len(a), 3): result_matrix[i] = a[i:i+5]
Is there a cleaner way to implement this in Numpy?
Answers:
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Method 1
Approach #1 : Using broadcasting –
def broadcasting_app(a, L, S ): # Window len = L, Stride len/stepsize = S
nrows = ((a.size-L)//S)+1
return a[S*np.arange(nrows)[:,None] + np.arange(L)]Approach #2 : Using more efficient NumPy strides –
def strided_app(a, L, S ): # Window len = L, Stride len/stepsize = S
nrows = ((a.size-L)//S)+1
n = a.strides[0]
return np.lib.stride_tricks.as_strided(a, shape=(nrows,L), strides=(S*n,n))Sample run –
In [143]: a
Out[143]: array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
In [144]: broadcasting_app(a, L = 5, S = 3)
Out[144]:
array([[ 1, 2, 3, 4, 5],
[ 4, 5, 6, 7, 8],
[ 7, 8, 9, 10, 11]])
In [145]: strided_app(a, L = 5, S = 3)
Out[145]:
array([[ 1, 2, 3, 4, 5],
[ 4, 5, 6, 7, 8],
[ 7, 8, 9, 10, 11]])Method 2
Starting in Numpy 1.20, we can make use of the new sliding_window_view to slide/roll over windows of elements.
And coupled with a stepping [::3], it simply becomes:
from numpy.lib.stride_tricks import sliding_window_view # values = np.array([1,2,3,4,5,6,7,8,9,10,11]) sliding_window_view(values, window_shape = 5)[::3] # array([[ 1, 2, 3, 4, 5], # [ 4, 5, 6, 7, 8], # [ 7, 8, 9, 10, 11]])
where the intermediate result of the sliding is:
sliding_window_view(values, window_shape = 5) # array([[ 1, 2, 3, 4, 5], # [ 2, 3, 4, 5, 6], # [ 3, 4, 5, 6, 7], # [ 4, 5, 6, 7, 8], # [ 5, 6, 7, 8, 9], # [ 6, 7, 8, 9, 10], # [ 7, 8, 9, 10, 11]])
Method 3
Modified version of @Divakar’s code with checking to ensure that memory is contiguous and that the returned array cannot be modified. (Variable names changed for my DSP application).
def frame(a, framelen, frameadv):
"""frame - Frame a 1D array
a - 1D array
framelen - Samples per frame
frameadv - Samples between starts of consecutive frames
Set to framelen for non-overlaping consecutive frames
Modified from Divakar's 10/17/16 11:20 solution:
https://stackoverflow.com/questions/40084931/taking-subarrays-from-numpy-array-with-given-stride-stepsize
CAVEATS:
Assumes array is contiguous
Output is not writable as there are multiple views on the same memory
"""
if not isinstance(a, np.ndarray) or
not (a.flags['C_CONTIGUOUS'] or a.flags['F_CONTIGUOUS']):
raise ValueError("Input array a must be a contiguous numpy array")
# Output
nrows = ((a.size-framelen)//frameadv)+1
oshape = (nrows, framelen)
# Size of each element in a
n = a.strides[0]
# Indexing in the new object will advance by frameadv * element size
ostrides = (frameadv*n, n)
return np.lib.stride_tricks.as_strided(a, shape=oshape,
strides=ostrides, writeable=False)All methods was sourced from stackoverflow.com or stackexchange.com, is licensed under cc by-sa 2.5, cc by-sa 3.0 and cc by-sa 4.0