Course Content

Introduction to TensorFlow

1. Tensors

Welcome to TensorFlow Introduction to Tensors Tensor Properties Applications of Tensors Batches Creating Tensors Data Types Basic Operations: Arithmetic Basic Operations: Linear Algebra Challenge: Creating a Neural Network Layer Transformations Reduction Operations Quiz: TensorFlow Basics

2. Basics of TensorFlow

Gradient Tape Graph Execution Neural Network Implementation Quiz: Conclusion Summary

Reduction Operations

In the world of tensor operations, there are numerous tasks where we need to reduce the dimensions of our data, either by summarizing it across one axis or more. For instance, if we have a 2D tensor (a matrix), a reduction operation might compute a value for each row or each column, resulting in a 1D tensor (a vector). TensorFlow offers a set of operations to accomplish this, and in this chapter, we'll explore the most commonly used reduction operations.

Sum, Mean, Maximum, and Minimum

TensorFlow offers the following methods for these calculations:

tf.reduce_sum(): Computes the sum of all elements in the tensor or along a specific axis;
tf.reduce_mean(): Calculates the mean of the tensor elements;
tf.reduce_max(): Determines the maximum value in the tensor;
tf.reduce_min(): Finds the minimum value in the tensor.


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import tensorflow as tf

tensor = tf.constant([[1., 2., 3.], [4., 5., 6.], [7., 8., 9.]])

# Calculate sum of all elements
total_sum = tf.reduce_sum(tensor)
print("Total Sum:", total_sum.numpy())

# Calculate mean of all elements
mean_val = tf.reduce_mean(tensor)
print("Mean Value:", mean_val.numpy())

# Determine the maximum value
max_val = tf.reduce_max(tensor)
print("Maximum Value:", max_val.numpy())

# Find the minimum value
min_val = tf.reduce_min(tensor)
print("Minimum Value:", min_val.numpy())

Note

The .numpy() method was used to convert the tensors into NumPy arrays, offering a clearer visual presentation of the numbers when displayed.

Operations along specific axes

Tensors can have multiple dimensions, and sometimes we want to perform reductions along a specific axis. The axis parameter allows us to specify which axis or axes we want to reduce.

axis=0: Perform the operation along the rows (resulting in a column vector);
axis=1: Perform the operation along the columns (resulting in a row vector);
It's possible to reduce along multiple axes simultaneously by providing a list to the axis parameter;
When the tensor's rank is reduced, you can use keepdims=True to retain the reduced dimension as 1.

For a 2D tensor (matrix):


              1234567891011121314151617181920
            
import tensorflow as tf

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

# Calculate the sum of each column 
col_sum = tf.reduce_sum(tensor, axis=0)
print("Column-wise Sum:", col_sum.numpy())

# Calculate the maximum of each row 
col_max = tf.reduce_max(tensor, axis=1)
print("Row-wise Max:", col_max.numpy())

# Calculate the mean of the whole tensor (reduce along both directions)
# Equivalent to not specifying the axis at all
total_mean = tf.reduce_mean(tensor, axis=(0, 1))
print("Total Mean:", total_mean.numpy())

# Calculate the mean of the whole tensor (keeping reduced dimensions)
total_mean_dim = tf.reduce_mean(tensor, axis=(0, 1), keepdims=True)
print("Total Mean (saving dimensions):", total_mean_dim.numpy())

Note

When you execute a reduction operation along a specific axis, you essentially eliminate that axis from the tensor, aggregating all the tensors within that axis element-wise. The same effect will remain for any number of dimensions.

Here's how it looks for a 3D tensor:


              12345678910111213141516171819
            
import tensorflow as tf

tensor = tf.constant([
    [[1, 2], [3, 4]], 
    [[5, 6], [7, 8]], 
    [[9, 10], [11, 12]]
])

# Calculate the sum along axis 0
sum_0 = tf.reduce_sum(tensor, axis=0)
print("Sum axis 0:\n", sum_0.numpy())

# Calculate the sum along axis 1
sum_1 = tf.reduce_sum(tensor, axis=1)
print("Sum axis 1:\n", sum_1.numpy())

# Calculate the sum along axes 0 and 1
sum_0_1 = tf.reduce_sum(tensor, axis=(0, 1))
print("Sum axes 0 and 1:\n", sum_0_1.numpy())

Note

Many other reduction operations exist in TensorFlow, but they operate on the same principles.

Task

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Background

You are a data scientist at a weather research agency. You've been given a tensor containing weather readings from various cities over several days. The tensor has the following structure:

Dimension 1: Represents different cities.
Dimension 2: Represents different days.
Each entry in the tensor is a tuple of (temperature, humidity).

Objective

Calculate the average temperature for each city over all the days.
Calculate the maximum humidity reading across all cities for each day.

Note

In this tensor, the first number in each tuple represents the temperature (in Celsius) and the second number represents the humidity (in percentage) for that day and city.

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Section 1. Chapter 12

Reduction Operations

Sum, Mean, Maximum, and Minimum

TensorFlow offers the following methods for these calculations:

tf.reduce_sum(): Computes the sum of all elements in the tensor or along a specific axis;
tf.reduce_mean(): Calculates the mean of the tensor elements;
tf.reduce_max(): Determines the maximum value in the tensor;
tf.reduce_min(): Finds the minimum value in the tensor.


              12345678910111213141516171819
            
import tensorflow as tf

tensor = tf.constant([[1., 2., 3.], [4., 5., 6.], [7., 8., 9.]])

# Calculate sum of all elements
total_sum = tf.reduce_sum(tensor)
print("Total Sum:", total_sum.numpy())

# Calculate mean of all elements
mean_val = tf.reduce_mean(tensor)
print("Mean Value:", mean_val.numpy())

# Determine the maximum value
max_val = tf.reduce_max(tensor)
print("Maximum Value:", max_val.numpy())

# Find the minimum value
min_val = tf.reduce_min(tensor)
print("Minimum Value:", min_val.numpy())

Note

The .numpy() method was used to convert the tensors into NumPy arrays, offering a clearer visual presentation of the numbers when displayed.

Operations along specific axes

Tensors can have multiple dimensions, and sometimes we want to perform reductions along a specific axis. The axis parameter allows us to specify which axis or axes we want to reduce.

axis=0: Perform the operation along the rows (resulting in a column vector);
axis=1: Perform the operation along the columns (resulting in a row vector);
It's possible to reduce along multiple axes simultaneously by providing a list to the axis parameter;
When the tensor's rank is reduced, you can use keepdims=True to retain the reduced dimension as 1.

For a 2D tensor (matrix):


              1234567891011121314151617181920
            
import tensorflow as tf

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

# Calculate the sum of each column 
col_sum = tf.reduce_sum(tensor, axis=0)
print("Column-wise Sum:", col_sum.numpy())

# Calculate the maximum of each row 
col_max = tf.reduce_max(tensor, axis=1)
print("Row-wise Max:", col_max.numpy())

# Calculate the mean of the whole tensor (reduce along both directions)
# Equivalent to not specifying the axis at all
total_mean = tf.reduce_mean(tensor, axis=(0, 1))
print("Total Mean:", total_mean.numpy())

# Calculate the mean of the whole tensor (keeping reduced dimensions)
total_mean_dim = tf.reduce_mean(tensor, axis=(0, 1), keepdims=True)
print("Total Mean (saving dimensions):", total_mean_dim.numpy())

Note

When you execute a reduction operation along a specific axis, you essentially eliminate that axis from the tensor, aggregating all the tensors within that axis element-wise. The same effect will remain for any number of dimensions.

Here's how it looks for a 3D tensor:


              12345678910111213141516171819
            
import tensorflow as tf

tensor = tf.constant([
    [[1, 2], [3, 4]], 
    [[5, 6], [7, 8]], 
    [[9, 10], [11, 12]]
])

# Calculate the sum along axis 0
sum_0 = tf.reduce_sum(tensor, axis=0)
print("Sum axis 0:\n", sum_0.numpy())

# Calculate the sum along axis 1
sum_1 = tf.reduce_sum(tensor, axis=1)
print("Sum axis 1:\n", sum_1.numpy())

# Calculate the sum along axes 0 and 1
sum_0_1 = tf.reduce_sum(tensor, axis=(0, 1))
print("Sum axes 0 and 1:\n", sum_0_1.numpy())

Note

Many other reduction operations exist in TensorFlow, but they operate on the same principles.

Task

Swipe to show code editor

Background

You are a data scientist at a weather research agency. You've been given a tensor containing weather readings from various cities over several days. The tensor has the following structure:

Dimension 1: Represents different cities.
Dimension 2: Represents different days.
Each entry in the tensor is a tuple of (temperature, humidity).

Objective

Calculate the average temperature for each city over all the days.
Calculate the maximum humidity reading across all cities for each day.

Note

In this tensor, the first number in each tuple represents the temperature (in Celsius) and the second number represents the humidity (in percentage) for that day and city.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Thanks for your feedback!

Section 1. Chapter 12

Switch to desktop for real-world practiceContinue from where you are using one of the options below