Function einsum

Tensor contraction over specified indices and outer product.

einsum allows defining Tensors by defining their element-wise computation. This computation is based on Einstein summation.

Some special cases include:

Matrix multiplication:

const x = tf.tensor2d([[1, 2, 3], [4, 5, 6]]);
const y = tf.tensor2d([[0, 1], [2, 3], [4, 5]]);
x.print();
y.print();
tf.einsum('ij,jk->ik', x, y).print();
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Dot product:

const x = tf.tensor1d([1, 2, 3]);
const y = tf.tensor1d([0, 1, 2]);
x.print();
y.print();
tf.einsum('i,i->', x, y).print();
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Batch dot product:

const x = tf.tensor2d([[1, 2, 3], [4, 5, 6]]);
const y = tf.tensor2d([[0, 1, 2], [3, 4, 5]]);
x.print();
y.print();
tf.einsum('bi,bi->b', x, y).print();
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Outer prouduct:

const x = tf.tensor1d([1, 3, 5]);
const y = tf.tensor1d([2, 4, 6]);
x.print();
y.print();
tf.einsum('i,j->ij', x, y).print();
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Matrix transpose:

const x = tf.tensor2d([[1, 2], [3, 4]]);
x.print();
tf.einsum('ij->ji', x).print();
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Batch matrix transpose:

const x = tf.tensor3d([[[1, 2], [3, 4]], [[-1, -2], [-3, -4]]]);
x.print();
tf.einsum('bij->bji', x).print();
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Limitations:

This implementation of einsum has the following limitations:

• Does not support >2 input tensors.
• Does not support duplicate axes for any given input tensor. E.g., equation 'ii->' is not supported.
• The ... notation is not supported.

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