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# tf.contrib.periodic_resample.periodic_resample

Periodically resample elements of a tensor to conform to shape.

This function implements a slightly more generic version of the subpixel convolutions found in this paper.

The formula for computing the elements in the output tensor is as follows:

T = values tensor of rank R

S = desired shape of output tensor (vector of length R)

P = output tensor of rank R

$$(T_1,\\ldots,T_R)$$ = shape(T)

$$[S_1,\\ldots,S_q,\\ldots,S_R]$$ = elements of vector S

A single element in S is left unspecified (denoted $$S_q=-1$$).

Let $$f_i$$ denote the (possibly non-integer) factor that relates the original dimension to the desired dimensions, $$S_i=f_i T_i$$, for $$i\\neq q$$ where $$f_i>0$$.

Define the following:

$$g_i=\\lceil f_i\\rceil$$

$$t=\\prod_i T_i$$

$$s=\\prod_{i\\neq q} S_i$$

$$S_q$$ can then be defined by $$S_q=\\lfloor t/s\\rfloor$$. The elements of the resulting tensor are defined as

$$P_{s_1,\\ldots,s_R}=T_{h_1,\\ldots,h_q,\\ldots,h_R}$$.

The $$h_i$$ ($$i\\neq q$$) are defined by $$h_i=\\lfloor s_i/g_i\\rfloor$$.

$$h_q=S_q\\sum_{j\\neq q}^{q-1}G_j \\mathrm{mod}(s_j,g_j) + s_q$$, where $$G_j=\\prod_{i}^{j-1}g_i$$ ($$G_0=1$$).

One drawback of this method is that whenever the output dimensions are slightly less than integer multiples of the input dimensions, many of the tensor elements are repeated in an inefficient way. This is resolved by specifying that all desired dimensions are integer multiples of the input tensor.

#### For example:

input is [[ 0  1  2  3]
[ 4  5  6  7]
[ 8  9 10 11]]

tf.periodic_resample(input, [6, None]) ==> [[ 0  1]
[ 2  3]
[ 4  5]
[ 6  7]
[ 8  9]
[10 11]]


values A Tensor. Must be one of the following types: float32, float64, int32, uint8, int16, int8, complex64, int64, qint8, quint8, qint32, bfloat16, uint16, complex128, half, uint32, uint64. The tensor of rank R to periodic_resample
shape A tf.TensorShape or list of ints. A 1-D tensor representing the desired shape of the output tensor. Exactly one element of this tensor must have the value None which represents that this dimension of values can be adjusted downward in order to accommodate increases in other dimensions. The specified sizes of the non-adjustable dimensions must by at least as large as in the values tensor.
name A name for the operation (optional).

A Tensor. Has the same type as values. Periodically resampled tensor that has dimensions specified as in shape except that the dimension specified as None will be minimally decreased as necessary.

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