I am trying to create a custom layer that is similar to Max Pooling or the first step of a separable convolution.
For example with a 2-Tensor in which I want to extract the non-overlapping 2x2 patches:
if I have the [4,4] tensor
[[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9,10,11],
[12,13,14,15]]
I want to end up with the following [2,2,4] Tensor
[[[ 0, 1, 4, 5],[ 2, 3, 6, 7]],
[[ 8, 9,12,13],[10,11,14,15]]]
For a 3-Tensor, I want something similar but to also separate out the 3rd dimension. tf.extract_image_patches almost does what I want, but it folds the "depth" dimension into each patch.
Ideally if I had a tensor of shape [32,64,7] and wanted to extract all the [2,2] patches out of it: I would end up with a shape of [16,32,7,4]
To be clear, I just want to extract the patches, not to actually do max pooling nor separable convolution.
Since I am not actually augmenting the data, I suspect that you can do it with some tf.reshape trickery... Is there any nice way to achieve this in tensorflow without resorting to slicing+stitching/for loops?
Also, what is the correct terminology for this operation? Windowing? Tiling?
Turns out this is really easy to do with tf.transpose. The solution that ended up working for me is:
#Assume x is in BHWC form
def pool(x,size=2):
channels = x.get_shape()[-1]
x = tf.extract_image_patches(
x,
ksizes=[1,size,size,1],
strides=[1,size,size,1],
rates=[1,1,1,1],
padding="SAME"
)
x = tf.reshape(x,[-1],x.get_shape()[1:3]+[size**2,channels])
x = tf.transpose(x,[0,1,2,4,3])
return x
Related
I am processing symmetric second order tensors (of stress) using numpy. In order to transform the tensors I have to generate a fully populated tensor, do the transformation and then recover the symmetric tensor in the rotated frame.
My input is a 2D numpy array of symmetric tensors (nx6). The code below works, but I'm pretty sure there must be a more efficient and/or elegant way to manipulate the arrays but I can't seem to figure it out.
I anyone can anyone suggest an improvement I'd be very grateful? The sample input is just 2 symmetric tensors but in use this could be millions of tensors, hence the concernr with efficiency
Thanks,
Doug
# Sample symmetric input (S11, S22, S33, S12, S23, S13)
sym_tens_in=np.array([[0,9], [1,10], [2,11], [3,12], [4,13], [5,14]])
# Expand to full tensor
tens_full=np.array([[sym_tens_in[0], sym_tens_in[3], sym_tens_in[4]],
[sym_tens_in[3], sym_tens_in[1], sym_tens_in[5]],
[sym_tens_in[4], sym_tens_in[5], sym_tens_in[2]]])
# Transpose and reshape to n x 3 x 3
tens_full=np.transpose(tens_full, axes=(2, 0, 1))
# This where the work on the full tensor will go....
# Reshape for extraction of the symmetric tensor
tens_full=np.reshape(tens_full, (2,9))
# Create an array for the test ouput symmetric tensor
sym_tens_out=np.empty((2,6), dtype=np.int32)
# Extract the symmetric components
sym_tens_out[:,0]=tens_full[:,0]
sym_tens_out[:,1]=tens_full[:,4]
sym_tens_out[:,2]=tens_full[:,8]
sym_tens_out[:,3]=tens_full[:,2]
sym_tens_out[:,4]=tens_full[:,3]
sym_tens_out[:,5]=tens_full[:,5]
# Transpose....
sym_tens_out=np.transpose(sym_tens_out)
This won't be any faster, but it's more compact:
In [166]: idx=np.array([0,3,4,3,1,5,4,5,2]).reshape(3,3)
In [167]: sym_tens_in[idx].transpose(2,0,1)
Out[167]:
array([[[ 0, 3, 4],
[ 3, 1, 5],
[ 4, 5, 2]],
[[ 9, 12, 13],
[12, 10, 14],
[13, 14, 11]]])
The transpose could be done first:
sym_tens_in.T[:,idx]
Similarly the reverse mapping can be done with:
In [168]: idx1 = [0,4,8,1,2,5]
In [171]: tens_full.reshape(2,-1)[:,idx1]
Out[171]:
array([[ 0, 1, 2, 3, 4, 5],
[ 9, 10, 11, 12, 13, 14]])
with the optional transpose.
OK - Based on the answers provided here I found a really cool solution. Now, I have to say that in my original question I omitted the actual reason that I was trying to get the full tensor into nx3x3 form. Basically, I'm implementing a function to rotate 2nd order stress tensors which requires solution of σ′=R⋅σ⋅RT.
I was planning to use numpy.matmul for the matrix multiplication but to transform multiple stress tensors, matmul requires the 3x3 tensors to be in the last two indices of the nx3x3 matrix - hence the effort to get the data into nx3x3 from from the original 3x3xn form....
However, after I let go of numpy.matmul as my target solution and embraced numpy.einsum instead....... everything became much easier....
# Sample symmetric input (S11, S22, S33, S12, S23, S13)
sym_tens_in=np.array([[0,9], [1,10], [2,11], [3,12], [4,13], [5,14]])
idx=np.array([0,3,5,3,1,4,5,4,2]).reshape(3,3)
full=sym_tens_in[idx]
full_transformed=np.einsum('ij, jkn, lk->nil', rot_mat, full, rot_mat)
Thanks for the inspiration!!!!
I have a tf.Tensor of, for example, shape (31, 6, 6, 3).
I want to perform tf.signal.fft2d on the shapes 6, 6 so, in other words, in the middle. However, the description says:
Computes the 2-dimensional discrete Fourier transform over the inner-most 2 dimensions of input
I could do it with a for loop but I fear it might be very ineffective. Is there a fastest way?
The result must have the same output shape of course.
Thanks to this I implemented this solution using tf.transpose:
in_pad = tf.transpose(in_pad, perm=[0, 3, 1, 2])
out = tf.signal.fft2d(tf.cast(in_pad, tf.complex64))
out = tf.transpose(out, perm=[0, 2, 3, 1])
I use tensorflow in python easily for math ops such as reduce_sum or reduce_mean like this
array = np.ndarray(shape=(2, 2, 3), buffer=np.array([[[1, 2, 3], [4, 5, 6]],
[[7, 8, 9], [10, 11, 12]]]),
dtype=int)
mean = tf.reduce_mean(array)
sum = tf.reduce_sum(array)
with tf.Session() as sess:
print(sess.run(mean))
print(sess.run(sum))
from this, I can get the mean and sum of a tensor into one value, howerver, when I do these ops in C++, I get some problem, like this
Sum(root.WithOpName("sum"), tensor_input, 1)
In this example, the second param tensor_input is a tensor of shape [1, 160, 160, 3].
Differently,I have to set the third param to a number in range of (-rank, rank), but this can not get my wanted result for suming all values in the tensor such as in python, rather than, it Computes the sum of elements across dimensions of a tensor. so how can I get the same result such as in python for suming all values into one value.
It would be helpful if anyone can help me
I have solved it, when you want to reduce your sum or mean result, if you do this on a tensor in shapr [1, 160, 160, 3], you can use like this
Sum(root.WithOpName("sum"), tensor_input, {0, 1, 2, 3})
The last prama is range of (0, rank(tensor_input))
I'm trying to efficiently replicate numpy's ndarray.choose() method.
Here's a numpy example of what I'm looking for:
b = np.arange(15).reshape(3, 5)
c = np.array([1,0,4])
c.choose(b.T) # trying to replicate in tensorflow
-> array([ 1, 5, 14])
The best I've been able to do with this is generate a batch_size square matrix (which is huge if batch size is huge) and take the diagonal of it:
tf_b = tf.constant(b)
tf_c = tf.constant(c)
sess.run(tf.diag_part(tf.gather(tf.transpose(tf_b), tf_c)))
-> array([ 1, 5, 14])
Is there a way to do this that is just linear in the first dimension (instead of squared)?
Yeah, there's an easier way to do this. Flatten your b array to 1-d, so it's [0, 1, 2, ..., 13, 14]. Take an array of indices that are in the range of the number of 'choices' you are taking (3 in your case). That will be [0, 1, 2]. Multiply this range by the second dimension of your original shape, which is the number of options for each choice (5 in your case). That gives you [0, 5, 10]. Then add your indices to this to obtain [1, 5, 14]. Now you're good to call tf.gather().
Here is some code that I've taken from here that does a similar thing for RNN outputs. Yours will be slightly different, but the idea is the same.
index = tf.range(0, batch_size) * max_length + (length - 1)
flat = tf.reshape(output, [-1, out_size])
relevant = tf.gather(flat, index)
return relevant
In a big picture, the operation is pretty straightforward. You use the range operation to get the index of the beginning of each row, then add the index of where you are in each row. I think doing it in 1D is easiest, so that's why we flatten it.
In all of the examples it seems that addSample(input, target) is used with 1 dimensional arrays, such as:
INPUT = 5
OUTPUT = 1
input = [5, 5, 5, 5, 5]
target = [1]
ds = SequentialDataSet(5, 1)
#add data using addSample
How does one do this when the input is multi-dimensional in this way:
input = [[5, 5, 5, 5, 5], [5, 5, 5, 5, 5]]
target = [1]
How does one use addSample with such structures? I tried this:
ds = SequentialDataSet(2, 1)
ds.addSample(input, target)
and get the error message:
Could not broadcast input array from shape (2, 5) into shape 2.
Meaning the SequentialDataSet(2, 1) does not work for this structure, but SequentialDataSet((2, 5), 1) also errors. This should be easy but I cannot find the answer.
It looks like you're trying to train some sort of Feed Forward network, perhaps a multi-layer perceptron? 5 layers in, one or more hidden layers, and a single output layer but it's not clear so this is a leap on my end.
Either way your input layer should be a single array. If you have a structure, or multi-dimensional array you'll need to collapse it and feed it in as a single set of data. So for your 5x2 suggestion you'd simply have 10 elements on the input, and you would be responsible for "parsing" your input structures consistently as they're fed into the network. For a 5x5 structure you'd have 25 inputs etc.
In my experience a big part of the success/challenge with ANNs is structuring the data in so that the input form is normalized and represented in a way that the network can mathematically find a pattern with.
According to the post linked beneath you should just input one array:
Pybrain multi dimensional data input
For SequentialDataSet I used this example:
data = [(1,2), (1,3), (10,2), (2,0), (2,9), (4,3), (1,2), (10,5)]
ds = SequentialDataSet(2,2)
for sample, next_sample in zip(data, cycle(test_data[1:])):
ds.addSample(sample, next_sample)