import tensorflow as tf

Creating a tensor

You should always assign the dtype when creating a tensor.

x = tf.range(start=12, dtype=tf.float32)

Tensor Attributes

Tensor Shape

x.shape

TensorShape([12])

tf.size(x)

<tf.Tensor: shape=(), dtype=int32, numpy=12>

Tensor Data Type

x.dtype

tf.float32

Changing a Tensor

Use tf.reshape

Will accept the tensor, and the shape, with the shape in the form of: (# of rows, # of columns)
If you know all but one of the dimensions, you can leave the unknown dimension as -1: (# of rows, -1)

print(x)

tf.Tensor([ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11.], shape=(12,), dtype=float32)

Here I’m explcitly defining the reshaping as (3,4)

print(tf.reshape(x, shape=(3, 4)))

tf.Tensor(
[[ 0.  1.  2.  3.]
 [ 4.  5.  6.  7.]
 [ 8.  9. 10. 11.]], shape=(3, 4), dtype=float32)

Here I left the column number blank, and it filled in automatically:

print(tf.reshape(x, shape=(3, -1)))

tf.Tensor(
[[ 0.  1.  2.  3.]
 [ 4.  5.  6.  7.]
 [ 8.  9. 10. 11.]], shape=(3, 4), dtype=float32)

Ones, Random, Constant Tensor

print(tf.ones(shape=(3, 4)))

tf.Tensor(
[[1. 1. 1. 1.]
 [1. 1. 1. 1.]
 [1. 1. 1. 1.]], shape=(3, 4), dtype=float32)

Keep in mind you can change a lot of parameters w.r.t. $, , $ etc. since this is a random normal distribution. There are more distributions as well if need be.

print(tf.random.normal(shape=(3, 4)))

tf.Tensor(
[[ 2.202327   -0.26792583 -0.74406874 -0.6372847 ]
 [ 0.46985132 -0.3888988   0.47005928  0.08380948]
 [-0.6244405   0.47245353 -1.8344202  -1.2178894 ]], shape=(3, 4), dtype=float32)

print(tf.constant([[1, 2, 3], [4, 5, 6]]))

tf.Tensor(
[[1 2 3]
 [4 5 6]], shape=(2, 3), dtype=int32)

Tensor Operations

These operations are performed elementwise: - Addition - Subtraction - Multiplication - Division - Exponentiation

Definition of elementwise in this context:

Given vectors $x$ and $y$, an elementwise operation (for example addition) will be performed between each corresponding element in the given vectors:

If:

$\bar{x} := [x_1, \dots , x_n]$
$\bar{y} := [y_1, \dots, y_n]$

then:

\[ \begin{aligned} \bar{x} + \bar{y} &= \begin{bmatrix} x_1 + y_1 \\ x_2 + y_2 \\ \vdots \\ x_n + y_n \end{bmatrix} \end{aligned} \]

Example:

x = tf.constant([1, 2, 4, 8])
y = tf.constant([2, 2, 2, 2])

Addition:

print(x + y)

tf.Tensor([ 3  4  6 10], shape=(4,), dtype=int32)

Subtraction

print(x - y)

tf.Tensor([-1  0  2  6], shape=(4,), dtype=int32)

Multiplication

print(x * y)

tf.Tensor([ 2  4  8 16], shape=(4,), dtype=int32)

Division

print(x / y)

tf.Tensor([0.5 1.  2.  4. ], shape=(4,), dtype=float64)

Exponentiation

print(x ** y)

tf.Tensor([ 1  4 16 64], shape=(4,), dtype=int32)

Dot Product

If:

$\bar{x} := [x_1, \dots , x_n]$
$\bar{y} := [y_1, \dots, y_n]$

Then the dot product ($\bullet$) is defined:

\[ \bar{x} \bullet \bar{y} = \sum_{i=1}^{n} x_i \cdot y_i \]

tf.tensordot(tf.constant([1, 2, 3]), tf.constant([8, 8, 8]), axes=1)

<tf.Tensor: shape=(), dtype=int32, numpy=48>

Broadcasting

Look at the explanation NumPy provides

x = tf.reshape(tf.range(start=12), shape=(3, 4))
y = tf.range(start=4)

print("================= Matrix of shape 3x4 =================")
print(x.numpy(), "\n")
print("================= Vector of shape 1x3 =================")
print(y.numpy())

print("================== Sum of shape 3x4 ===================")
print(tf.math.add(x, y).numpy())

================= Matrix of shape 3x4 =================
[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]] 

================= Vector of shape 1x3 =================
[0 1 2 3]
================== Sum of shape 3x4 ===================
[[ 0  2  4  6]
 [ 4  6  8 10]
 [ 8 10 12 14]]