I am working with audio in TensorFlow, and would like to obtain a series of sequences which could be obtained from sliding a window over my data, so to speak. Examples to illustrate my situation:
Current Data Format:
Shape = [batch_size, num_features]
example = [
[1, 2, 3],
[4, 5, 6],
[7, 8, 9],
[10, 11, 12],
[13, 14, 15]
]
What I want:
Shape = [batch_size - window_length + 1, window_length, num_features]
example = [
[
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
],
[
[4, 5, 6],
[7, 8, 9],
[10, 11, 12]
],
[
[7, 8, 9],
[10, 11, 12],
[13, 14, 15]
],
]
My current solution is to do something like this:
list_of_windows_of_data = []
for x in range(batch_size - window_length + 1):
list_of_windows_of_data.append(tf.slice(data, [x, 0], [window_length,
num_features]))
windowed_data = tf.squeeze(tf.stack(list_of_windows_of_data, axis=0))
And this does the transform. However, it also creates 20,000 operations which slows TensorFlow down a lot when creating a graph. If anyone else has a fun and more efficient way to do this, please do share.
You can do that using tf.map_fn as follows:
example = tf.constant([
[1, 2, 3],
[4, 5, 6],
[7, 8, 9],
[10, 11, 12],
[13, 14, 15]
]
)
res = tf.map_fn(lambda i: example[i:i+3], tf.range(example.shape[0]-2), dtype=tf.int32)
sess=tf.InteractiveSession()
res.eval()
This prints
array([[[ 1, 2, 3],
[ 4, 5, 6],
[ 7, 8, 9]],
[[ 4, 5, 6],
[ 7, 8, 9],
[10, 11, 12]],
[[ 7, 8, 9],
[10, 11, 12],
[13, 14, 15]]])
You could use the built-in tf.extract_image_patches:
example = tf.constant([
[1, 2, 3],
[4, 5, 6],
[7, 8, 9],
[10, 11, 12],
[13, 14, 15]
]
)
res = tf.reshape(tf.extract_image_patches(example[None,...,None],
[1,3,3,1], [1,1,1,1], [1,1,1,1], 'VALID'), [-1,3,3])
Related
I'd like to write a numpy function that takes an MxN array A, a window length L, and an MxP array idxs of starting indices into the M rows of A that selects P arbitrary slices of length L from each of the M rows of A. Except, I would love for this to work on the last dimension of A, and not necessarily care how many dimensions A has, so all dims of A and idxs match except the last one. Examples:
If A is just 1D:
A = np.array([1, 2, 3, 4, 5, 6])
window_len = 3
idxs = np.array([1, 3])
result = magical_routine(A, idxs, window_len)
Where result is a 2x3 array since I selected 2 slices of len 3:
np.array([[ 2, 3, 4],
[ 4, 5, 6]])
If A is 2D:
A = np.array([[ 1, 2, 3, 4, 5, 6],
[ 7, 8, 9,10,11,12],
[13,14,15,16,17,18]])
window_len = 3
idxs = np.array([[1, 3],
[0, 1],
[2, 2]])
result = magical_routine(A, idxs, window_len)
Where result is a 3x2x3 array since there are 3 rows of A, and I selected 2 slices of len 3 from each row:
np.array([[[ 2, 3, 4], [ 4, 5, 6]],
[[ 7, 8, 9], [ 8, 9,10]],
[[15,16,17], [15,16,17]]])
And so on.
I have discovered an number of inefficient ways to do this, along with ways that work for a specific number of dimensions of A. For 2D, the following is pretty tidy:
col_idxs = np.add.outer(idxs, np.arange(window_len))
np.take_along_axis(A[:, np.newaxis], col_idxs, axis=-1)
I can't see a nice way to generalize this for 1D and other D's though...
Is anyone aware of an efficient way that generalizes to any number of dims?
For your 1d case
In [271]: A=np.arange(1,7)
In [272]: idxs = np.array([1,3])
Using the kind of iteration that this questions usually gets:
In [273]: np.vstack([A[i:i+3] for i in idxs])
Out[273]:
array([[2, 3, 4],
[4, 5, 6]])
Alternatively generate all indices, and one indexing. linspace is handy for this (though it's not the only option):
In [278]: j = np.linspace(idxs,idxs+3,3,endpoint=False)
In [279]: j
Out[279]:
array([[1., 3.],
[2., 4.],
[3., 5.]])
In [282]: A[j.T.astype(int)]
Out[282]:
array([[2, 3, 4],
[4, 5, 6]])
for the 2d
In [284]: B
Out[284]:
array([[ 1, 2, 3, 4, 5, 6],
[ 7, 8, 9, 10, 11, 12],
[13, 14, 15, 16, 17, 18]])
In [285]: idxs = np.array([[1, 3],
...: [0, 1],
...: [2, 2]])
In [286]: j = np.linspace(idxs,idxs+3,3,endpoint=False)
In [287]: j
Out[287]:
array([[[1., 3.],
[0., 1.],
[2., 2.]],
[[2., 4.],
[1., 2.],
[3., 3.]],
[[3., 5.],
[2., 3.],
[4., 4.]]])
With a bit of trial and error, pair up the indices to get:
In [292]: B[np.arange(3)[:,None,None],j.astype(int).transpose(1,2,0)]
Out[292]:
array([[[ 2, 3, 4],
[ 4, 5, 6]],
[[ 7, 8, 9],
[ 8, 9, 10]],
[[15, 16, 17],
[15, 16, 17]]])
Or iterate as in the first case, but with an extra layer:
In [294]: np.array([[B[j,i:i+3] for i in idxs[j]] for j in range(3)])
Out[294]:
array([[[ 2, 3, 4],
[ 4, 5, 6]],
[[ 7, 8, 9],
[ 8, 9, 10]],
[[15, 16, 17],
[15, 16, 17]]])
With sliding windows:
In [295]: aa = np.lib.stride_tricks.sliding_window_view(A,3)
In [296]: aa.shape
Out[296]: (4, 3)
In [297]: aa
Out[297]:
array([[1, 2, 3],
[2, 3, 4],
[3, 4, 5],
[4, 5, 6]])
In [298]: aa[[1,3]]
Out[298]:
array([[2, 3, 4],
[4, 5, 6]])
and
In [300]: bb = np.lib.stride_tricks.sliding_window_view(B,(1,3))
In [301]: bb.shape
Out[301]: (3, 4, 1, 3)
In [302]: bb[np.arange(3)[:,None],idxs,0,:]
Out[302]:
array([[[ 2, 3, 4],
[ 4, 5, 6]],
[[ 7, 8, 9],
[ 8, 9, 10]],
[[15, 16, 17],
[15, 16, 17]]])
I got it! I was almost there:
def magical_routine(A, idxs, window_len=2000):
col_idxs = np.add.outer(idxs, np.arange(window_len))
return np.take_along_axis(A[..., np.newaxis, :], col_idxs, axis=-1)
I just needed to always add the new axis to A's second to last dim, and then leave remaining axes alone.
I have a numpy array of 2D shape
a=np.array([[1,2,3,4,5,6],
[7,8,9,10,11,12],
[13,14,15,16,17,18]])
and trying to convert into 3D shape of dimension (3,3,2) i.e,
np.array([[ 1,2,3],
[7,8,9],
[13,14,15]])
in 3rd dimension with index 1 and
np.array([[4,5,6],
[10,11,12],
[16,17,18]])
in 3rd dimension with index 2.
I tried to reshape as a.reshape(3,3,2) and getting this
array([[[ 1, 2, 3],
[ 4, 5, 6]],
[[ 7, 8, 9],
[10, 11, 12]],
[[13, 14, 15],
[16, 17, 18]]])
Any suggestions to convert this?
Use swapaxes:
a.reshape(3,2,3).swapaxes(0,1)
output:
array([[[ 1, 2, 3],
[ 7, 8, 9],
[13, 14, 15]],
[[ 4, 5, 6],
[10, 11, 12],
[16, 17, 18]]])
I have numpy.ndarray like this:
array([[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12],
[ 2, 6, 8, 8, 12, 15, 20, 12, 7, 7, 3]], dtype=int64)
I want to switch axes so it looks like this:
[[2, 2],
[3, 6],
[4, 8],
....
....
[11, 7],
[12, 3]]
How can I do it?
You can transpose the array with array.T. See the documentation for np.ndarray.T.
>>> x = np.array([[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12],
... [ 2, 6, 8, 8, 12, 15, 20, 12, 7, 7, 3]])
>>> x
array([[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12],
[ 2, 6, 8, 8, 12, 15, 20, 12, 7, 7, 3]])
>>> x.T
array([[ 2, 2],
[ 3, 6],
[ 4, 8],
[ 5, 8],
[ 6, 12],
[ 7, 15],
[ 8, 20],
[ 9, 12],
[10, 7],
[11, 7],
[12, 3]])
>>>
Consider the follow ndarray lm -
In [135]: lm
Out[135]:
array([[[15, 7],
[ 2, 3],
[ 0, 4]],
[[ 8, 12],
[ 6, 5],
[17, 10]],
[[16, 13],
[30, 1],
[14, 9]]])
In [136]: lm.shape
Out[136]: (3, 3, 2)
I want to filter out members of the first axes (lm[0], lm[1], ...) where at least one of the elements is greater than 20. Since lm[2, 1, 0] is the only element fulfills this condition, I would expect the following result -
array([[[15, 7],
[ 2, 3],
[ 0, 4]],
[[ 8, 12],
[ 6, 5],
[17, 10]]]
i.e lm[2] has at least one element > 20, so it is filtered out of the result set. How can I achieve this?
Two ways to do so with np.all and np.any with axis arg -
In [14]: lm[(lm<=20).all(axis=(1,2))]
Out[14]:
array([[[15, 7],
[ 2, 3],
[ 0, 4]],
[[ 8, 12],
[ 6, 5],
[17, 10]]])
In [15]: lm[~(lm>20).any(axis=(1,2))]
Out[15]:
array([[[15, 7],
[ 2, 3],
[ 0, 4]],
[[ 8, 12],
[ 6, 5],
[17, 10]]])
To make it generic for ndarrays to work along the last two axes, use axis=(-2,-1) instead.
I have a square matrix and like to break it into some smaller matrices. For example, assume we have a matrix with the shape of [4,4] and would like to convert it into 4 smaller matrices with size [2,2].
input:
[9, 9, 9, 9,
8, 8, 8, 8,
7, 7, 7, 7,
6, 6, 6, 6]
output:
[[9, 9 | [9, 9,
8, 8] | 8, 8],
---------------
[7, 7 | [7, 7,
6, 6] | 6, 6]]
You can use repeated calls to torch.split for this.
>>> x
tensor([[ 1, 2, 3, 4],
[ 5, 6, 7, 8],
[ 9, 10, 11, 12],
[13, 14, 15, 16]])
>>> [z for y in x.split(2) for z in y.split(2, dim=1)]
[tensor([[1, 2],
[5, 6]]), tensor([[3, 4],
[7, 8]]), tensor([[ 9, 10],
[13, 14]]), tensor([[11, 12],
[15, 16]])]
Given a tensor with the shape of 4*4 or 1*16 the easiest way to do this is by view function or reshape:
a = torch.tensor([9, 9, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 6, 6, 6, 6])
# a = a.view(4,4)
a = a.view(2, 2, 2, 2)
# output:
tensor([[[[9, 9],
[9, 9]],
[[8, 8],
[8, 8]]],
[[[7, 7],
[7, 7]],
[[6, 6],
[6, 6]]]])