I have prepared a Google Colab for the syntax of some more basic Tensor functions and operations. Also do check out the official documentation of TensorFlow for more information and knowledge.

**tf.constant**

The `tf.constant`

function in TensorFlow is used to create a constant tensor with a specified value. The basic syntax for creating a constant tensor is:

`import tensorflow as tf # Creating a constant tensor `

my_tensor = tf.constant(value, dtype=tf.float32)

2D tensors and 3D tensors using tf.constant

`import tensorflow as tf `# Creating a 2D tensor (matrix)

matrix_2d = tf.constant([[1, 2, 3],

[4, 5, 6],

[7, 8, 9]], dtype=tf.float32)

# Creating a 3D tensor

tensor_3d = tf.constant([[[1, 2, 3],

[4, 5, 6]],

[[7, 8, 9],

[10, 11, 12]]], dtype=tf.float32)

2D and 3D tensors are commonly used in various machine learning and deep learning applications, especially when working with data like images, time series, or spatial data, which require multi-dimensional representations.

**Note:** Mixed type of tensors can’t be formed using tf.constant. For Example:

`import tensorflow as tf`

tensor_1 = tf.constant([1,2,3,4,’i’])

**2. Identity (Eye) Tensor:**

The `tf.eye`

function is used to create an identity (or eye) tensor. An identity tensor is a square matrix where all elements in the main diagonal are set to 1, and all other elements are 0.

Here’s an example of creating a 3×3 identity tensor using TensorFlow:

`import tensorflow as tf`

# Creating a 3x3 identity tensor

identity_tensor = tf.eye(3, dtype=tf.float32)

**3. Zero Tensor:**

The `tf.zeros`

function is used to create a tensor filled with zeros. You can specify the shape and data type of the tensor.

Here’s an example of creating a 2×4 zero tensor with TensorFlow:

`import tensorflow as tf`

# Creating a 2x4 zero tensor

zero_tensor = tf.zeros([2, 4], dtype=tf.float32)

**4. Rank, Shape and Size**

`import tensorflow as tf`

# Create a tensor

tensor = tf.constant([[1, 2], [3, 4]])

# Get the rank of the tensor

rank = tf.rank(tensor)

print(“Rank of the tensor:”, rank.numpy()) # Output: 2

# Get the shape of the tensor

shape = tf.shape(tensor)

print("Shape of the tensor:", shape.numpy()) # Output: [2 2]

# Get the size of the tensor

size = tf.size(tensor)

print("Size of the tensor:", size.numpy()) # Output: 4

Understanding the rank, shape, and size of tensors is fundamental when working with TensorFlow, as it allows you to manipulate and reshape tensors effectively in various machine learning tasks.

**5. Indexing and Slicing**

In TensorFlow, you can perform indexing and slicing operations on tensors similarly to how you would in Python. You can access specific elements or sub-tensors within a tensor using indices. Here’s an overview of indexing in TensorFlow:

- Indexing a 1D Tensor (Vector):

You can access elements of a 1D tensor (vector) using square brackets and integer indices.

vector = tf.constant([1, 2, 3, 4, 5])

element = vector[2] # Accessing the third element (index 2)

print(element.numpy()) # Outputs: 3

sub_tensor = vector[1:4] # Access elements from index 1 to 3 (excludes 4)

print(sub_tensor.numpy()) # Outputs: [2 3 4]

- Indexing a 2D Tensor (Matrix):

` matrix = tf.constant([[1, 2, 3],`

[4, 5, 6],

[7, 8, 9]])

element = matrix[1, 2] # Accessing the element at row 1, column 2

print(element.numpy()) # Outputs: 6

sub_matrix = matrix[1:3, 0:2] # Accessing a sub-matrix

print(sub_matrix.numpy())

# Outputs:

# [[4 5]

# [7 8]]

These are the fundamental ways to perform indexing and slicing in TensorFlow. You can apply similar principles for higher-dimensional tensors. Indexing is particularly useful for extracting specific data points or sub-tensors when working with complex machine learning models.

**6. tf.math**

In TensorFlow, you can work with complex numbers and perform various operations on them using the `tf.complex` function, as well as `tf.sqrt`, `tf.abs`, and the basic arithmetic operations (`+`, `-`, `*`, and `/`). Here’s how to use these operations with complex numbers:

`import tensorflow as tf`# Creating complex numbers

z1 = tf.complex(3.0, 4.0) # 3 + 4i

z2 = tf.complex(1.0, 2.0) # 1 + 2i

# Square root

sqrt_z1 = tf.sqrt(z1)

# Absolute value

abs_z1 = tf.abs(z1)

# Addition

sum_z = z1 + z2

# Subtraction

diff_z = z1 - z2

# Multiplication

product_z = z1 * z2

# Division

quotient_z = z1 / z2

These operations allow you to work with complex numbers in TensorFlow, making it suitable for various applications, including signal processing and quantum computing simulations.

**7. tf.math (Continued)**

`import tensorflow as tf`# Creating a sample tensor

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

# Reduce Sum

sum_all = tf.reduce_sum(tensor) # Output: 21

# Reduce Max

max_value = tf.reduce_max(tensor) # Output: 6

# Argmax

max_index = tf.argmax(tensor) # Output: 5 (index of the maximum value)

# Power

squared = tf.pow(tensor, 2) # Output: [[ 1 4 9]

# [16 25 36]]

# Top_k

top_values, top_indices = tf.math.top_k(tensor, k=2)

# Output (Top 2 Values): [3 6]

# Output (Top 2 Indices): [2 2]

- tf.reduce_sum(tensor) — Reduce Sum:

The ‘tf.reduce_sum’ function is used to compute the sum of all elements in the ‘tensor’. - tf.reduce_max(tensor) — Reduce Max:

The ‘tf.reduce_max’ function calculates the maximum value in the ‘tensor’. - tf.argmax(tensor) — Argmax:

The ‘tf.argmax’ function returns the indices of the maximum values in the ‘tensor’. - tf.pow(tensor, 2)` — Power (Squared):

The ‘tf.pow’ function is used to calculate the element-wise power of the `tensor`. - tf.math.top_k(tensor, k=2) — Top_k:

The ‘tf.math.top_k’ function returns the top k values and their indices in the ‘tensor’.

These operations showcase common operations in TensorFlow for reducing, extracting information, and performing element-wise computations on tensors. They are frequently used in various machine learning and numerical applications.

**8. tf.einsum (V.imp and powerful)**

Suppose you have two tensors, `A`

and `B`

, and you want to compute their matrix multiplication (dot product). You can achieve this using `tf.einsum`

as follows:

`import tensorflow as tf`

# Define two input tensors

A = tf.constant([[1, 2],

[3, 4]])

B = tf.constant([[5, 6],

[7, 8]])

# Use tf.einsum to perform matrix multiplication

result = tf.einsum('ij,jk->ik', A, B)

# Output[[19 22]

[43 50]]

In this example, `'ij,jk->ik'`

is the Einstein summation notation that defines the operation. It specifies that you want to compute the dot product of `A`

and `B`

. The result is stored in the `result`

tensor.

You can use `tf.einsum`

for a wide range of operations, such as element-wise multiplication, summation, contraction, and more. The notation is powerful and flexible, allowing you to express complex operations concisely. You’ll need to understand the Einstein summation notation to use `tf.einsum`

effectively, and the TensorFlow documentation provides detailed examples and explanations to help you get started with it.

**9. tf.linalg**

The ‘tf.linalg’ module in TensorFlow provides a wide range of methods for linear algebra operations, making it an important tool for tasks such as solving systems of linear equations, performing matrix factorizations, computing eigenvalues and eigenvectors, and more. Here are some important methods and functions available in ‘tf.linalg’:

`import tensorflow as tf`# Create sample matrices

A = tf.constant([[1.0, 2.0], [3.0, 4.0]], dtype=tf.float32)

B = tf.constant([[5.0, 6.0], [7.0, 8.0]], dtype=tf.float32)

# Matrix Transposition

transposed_A = tf.linalg.matrix_transpose(A)

# Matrix Multiplication

matmul_result = tf.linalg.matmul(A, B)

# Matrix Inversion

A_inverse = tf.linalg.inv(A)

# Solve Linear System

linear_system_solution = tf.linalg.solve(A, B)

# QR Decomposition

q, r = tf.linalg.qr(A)

# SVD (Singular Value Decomposition)

s, u, v = tf.linalg.svd(A)

# Cholesky Decomposition

cholesky_L = tf.linalg.cholesky(A)

# Eigenvalue and Eigenvector Computations

eigenvalues, eigenvectors = tf.linalg.eigh(A)

# Matrix Norm

matrix_norm = tf.linalg.norm(A)

**10. Other important functions**

Try running and checking the outputs of some of the following more important functions.

`import tensorflow as tf`# Reshaping (tf.reshape)

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

reshaped_tensor = tf.reshape(original_tensor, (2, 3))

# Concatenating (tf.concat)

tensor1 = tf.constant([1, 2])

tensor2 = tf.constant([3, 4])

concatenated_tensor = tf.concat([tensor1, tensor2], axis=0)

# Adding Dimensions (tf.expand_dims)

original_tensor = tf.constant([1, 2, 3])

expanded_tensor = tf.expand_dims(original_tensor, axis=1)

# Padding (tf.pad)

t3 = tf.constant([[1, 2], [3, 4]])

paddings = tf.constant([[1,2],

[3,4]])

print(tf.pad(t3,paddings,'CONSTANT', constant_values = 0)) #zero is default value for constant padding

paddings = tf.constant([[2, 2,], [2, 2]])

print(tf.pad(t3,paddings,'REFLECT'))

print(tf.pad(t3,paddings,'SYMMETRIC'))

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