Course Content
Introduction to TensorFlow
Introduction to TensorFlow
Reduction Operations
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.
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):
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:
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
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.
Thanks for your feedback!
Reduction Operations
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.
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):
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:
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
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.
Thanks for your feedback!
Reduction Operations
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.
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):
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:
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
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.
Thanks for your feedback!
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.
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):
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:
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
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.