Shape and axes

Each tensor has a shape, the number of elements in each axis, of the type Tensor_Shape; an indefinite array of natural numbers. For example, the shape of a 2 × 3 matrix is (2, 3) and the shape of a vector of 100 elements is (1 => 100).

The shape of a tensor can be retrieved using the function Shape and the axes with the function Axes. The total number of elements in the tensor is queried with the function Elements.

The functions Rows returns the number of elements for a 1-D tensor (vector) or rows of a 2-D tensor (matrix). Columns requires a tensor with at least two axes and returns the number of columns.

Summary

It is true that T.Shape'Length = T.Axes and Elements (T.Shape) = T.Elements for a tensor T.

Image

The image of a tensor can be obtained with the function Image:

Orka.OS.Put_Line (Tensor.Image);

Changing the shape

Sometimes the shape of a tensor needs to be changed. For example, Tensor (Tensor mod 2.0 = 0.0) returns a 1-D tensor. The function Reshape can be used to create a new tensor that has the given shape and the elements of the original tensor. The function can be given either a shape or the number of elements:

Tensor_1 : constant CPU_Tensor := To_Tensor ([1.0, 2.0, 3.0, 4.0, 5.0, 6.0]);
Tensor_2 : constant CPU_Tensor := Tensor_1.Reshape ([2, 3]);

The given shape or size must match the number of elements of the tensor. Elements cannot be removed or added by providing a shape or size that is smaller or larger than the current size of the tensor.

Calling Reshape with the current number of elements as the first parameter will just flatten the tensor to a 1-D tensor. This is a common operation, and you can call the function Flatten instead if you want, which will do the same thing.

Concatenating

Concatenating tensors is possible with the operator &. This will concatenate two tensors in the first axis, increasing the number of rows to the sum of the rows of the two tensors. For multidimensional tensors, the size of the first axis (the number of rows) can be different, but the size of the other axes must be equal.

The result of concatenating two vectors with the & operator is another vector:

Tensor_1 : constant CPU_Tensor := To_Tensor ([1.0, 2.0]);
Tensor_2 : constant CPU_Tensor := To_Tensor ([3.0, 4.0, 5.0]);

Tensor_3 : constant CPU_Tensor := Tensor_1 & Tensor_2;

The image of Tensor_3 will be:

tensor([ 1.0, 2.0, 3.0, 4.0, 5.0])

The function Concatenate can be used to concatenate tensors in axes other than the first axis by specifying the parameter Dimension. For example, given the following two tensors:

Tensor_1 : constant CPU_Tensor := Diagonal ([1.0, 2.0, 3.0]);
Tensor_2 : constant CPU_Tensor := To_Tensor ([4.0, 5.0, 6.0, 7.0, 8.0, 9.0], [3, 2]);

The tensors can be concatenated horizontally with:

Tensor_3 : constant CPU_Tensor := Tensor_1.Concatenate (Tensor_2, Dimension => 2);

The image of Tensor_3 will be:

tensor([[ 1.0, 0.0, 0.0, 4.0, 5.0],
        [ 0.0, 2.0, 0.0, 6.0, 7.0],
        [ 0.0, 0.0, 3.0, 8.0, 9.0]])

The & operator would have concatenated the tensors vertically, as if Concatenate was called with Dimension set to 1:

Tensor_4 : constant CPU_Tensor := Tensor_2.Reshape ((2, 3));
Tensor_5 : constant CPU_Tensor := Tensor_1 & Tensor_4;

The image of Tensor_3 will be:

tensor([[ 1.0, 0.0, 0.0],
        [ 0.0, 2.0, 0.0],
        [ 0.0, 0.0, 3.0],
        [ 4.0, 5.0, 6.0],
        [ 7.0, 8.0, 9.0]])