Basic operations

Introduzione a TensorFlow in Python

Isaiah Hull

Visiting Associate Professor of Finance, BI Norwegian Business School

What is a TensorFlow operation?

The image shows operations and tensors in a TensorFlow graph, as drawn by TensorBoard. Two pairs of matrices are combined using the add operation. The resulting sums are then multiplied.

What is a TensorFlow operation?

The image shows operations and tensors in a TensorFlow graph, as drawn by TensorBoard. One add operation is shown.

What is a TensorFlow operation?

The image shows operations and tensors in a TensorFlow graph, as drawn by TensorBoard. Two add operations are shown.

What is a TensorFlow operation?

The image shows operations and tensors in a TensorFlow graph, as drawn by TensorBoard. Two pairs of matrices are combined using the add operation. The resulting sums are then multiplied.

Applying the addition operator

#Import constant and add from tensorflow
from tensorflow import constant, add

# Define 0-dimensional tensors
A0 = constant([1])
B0 = constant([2])

# Define 1-dimensional tensors
A1 = constant([1, 2])
B1 = constant([3, 4])

# Define 2-dimensional tensors
A2 = constant([[1, 2], [3, 4]])
B2 = constant([[5, 6], [7, 8]])

Applying the addition operator

# Perform tensor addition with add()
C0 = add(A0, B0)
C1 = add(A1, B1)
C2 = add(A2, B2)

Performing tensor addition

The add() operation performs element-wise addition with two tensors
Element-wise addition requires both tensors to have the same shape:
- Scalar addition: $1+2=3$
- Vector addition: $[1,2]+[3,4]=[4,6]$
- Matrix addition: $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} + \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} = \begin{bmatrix} 6 & 8 \\ 10 & 12 \end{bmatrix}$
The add() operator is overloaded

How to perform multiplication in TensorFlow

Element-wise multiplication performed using multiply() operation
- The tensors multiplied must have the same shape
- E.g. [1,2,3] and [3,4,5] or [1,2] and [3,4]
Matrix multiplication performed with matmul() operator
- The matmul(A,B) operation multiplies A by B
- Number of columns of A must equal the number of rows of B

Applying the multiplication operators

# Import operators from tensorflow
from tensorflow import ones, matmul, multiply

# Define tensors
A0 = ones(1)
A31 = ones([3, 1])
A34 = ones([3, 4])
A43 = ones([4, 3])

What types of operations are valid?
- multiply(A0, A0), multiply(A31, A31), and multiply(A34, A34)
- matmul(A43, A34), but not matmul(A43, A43)

Summing over tensor dimensions

The reduce_sum() operator sums over the dimensions of a tensor
- reduce_sum(A) sums over all dimensions of A
- reduce_sum(A, i) sums over dimension i

# Import operations from tensorflow
from tensorflow import ones, reduce_sum

# Define a 2x3x4 tensor of ones
A = ones([2, 3, 4])

Summing over tensor dimensions

# Sum over all dimensions
B = reduce_sum(A)

# Sum over dimensions 0, 1, and 2
B0 = reduce_sum(A, 0)
B1 = reduce_sum(A, 1)
B2 = reduce_sum(A, 2)

Let's practice!

Introduzione a TensorFlow in Python