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jhr |
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# Data Layout in Diderot
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This note describes the data layout conventions used in the Diderot
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implementation for images and tensors.
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## Tensors
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The axes of tensors and tensor fields are listed from slowest to fastest (which is the opposite of nrrd files).
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### Tensor construction
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The CFG IR expression
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```
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T = CONS[T_1, ..., T_d]
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```
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will construct a tensor with type `tensor[d_1,...,d_n,d]`, where the `T_i`
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tensors have the type `tensor[d_1,...,d_n]`. Thus the dimensions of a tensor
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are listed from slowest to fastest (the opposite of Nrrd file headers).
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### Tensor indexing
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If we have
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````diderot
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tensor[d_1,...,d_n] T;
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````
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then the expression
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````diderot
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T[i_1,...,i_n]
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````
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is translated to the following address arithmetic:
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````
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T + i_n + d_n * (i_{n-1} + d_{n-1} * ( ... d_2 * i_1) ... )
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````
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## Differentiation
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The gradiant operator returns a field of higher order than its argument.
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For example
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````diderot
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field#2(3)[2] F;
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field#1(3)[2,3] G = ∇ F;
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tensor[2,3] T = G(x);
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````
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Again, the dimensions are slowest to fastest, so T can be thought of
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as a two-element array of three-vectors.
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## Images and Nrrd Files
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Image values are represented using the [Nrrd file format](http://teem.sourceforge.net/nrrd/format.html)
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from teem.
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### `LoadVoxels`
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The nrrd convention is to list indices from fastest to slowest (opposite
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the C convention). If we are sampling a `4x4` grid of voxels from an image
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with type `image(2)[2])`, then the data will have the following layout in the nrrd file:
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````
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... x00 y00 x10 y10 x20 y20 x30 y30 ...
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... x01 y01 x11 y11 x21 y21 x31 y31 ...
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... x02 y02 x12 y12 x22 y22 x32 y32 ...
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... x03 y03 x13 y13 x23 y23 x33 y33 ...
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````
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When we load these voxels into memory, however, we swizzle them to fit the type `tensor[2,4,4]`.
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The following IR expression shows how the voxel tensor would be constructed:
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```
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CONS[
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CONS[
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CONS[x00, x10, x20, x30],
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CONS[x01, x11, x21, x31],
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CONS[x02, x12, x22, x32],
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CONS[x03, x13, x23, x33]],
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CONS[
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CONS[y00, y10, y20, y30],
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CONS[y01, y11, y21, y31],
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CONS[y02, y12, y22, y32],
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CONS[y03, y13, y23, y33]]
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]
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```
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