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TensorFlow-Einrichtung

Installation

pip install tensorflow

Import

# Import the TensorFlow library with the alias tf
import tensorflow as tf

Tensor-Typen

Einfache Tensor-Erstellung

# Create a 1D tensor
tensor_1D = tf.constant([1, 2, 3])

# Create a 2D tensor
tensor_2D = tf.constant([[1, 2, 3], [4, 5, 6]])

# Create a 3D tensor
tensor_3D = tf.constant([[[1, 2], [3, 4]], [[5, 6],[7, 8]]])

Tensor-Eigenschaften

• Rang: Gibt die Anzahl der Dimensionen eines Tensors an. Beispielsweise besitzt eine Matrix einen Rang von 2. Der Rang eines Tensors kann mit dem Attribut .ndim abgerufen werden:

print(f'Rank of a tensor: {tensor.ndim}')

• Shape: Beschreibt, wie viele Werte in jeder Dimension vorhanden sind. Eine 2x3-Matrix hat die Form (2, 3). Die Länge des Shape-Parameters entspricht dem Rang des Tensors (seiner Anzahl an Dimensionen). Die Form eines Tensors kann mit dem Attribut .shape abgerufen werden:

print(f'Shape of a tensor: {tensor.shape}')

• Typen: Tensors existieren in verschiedenen Datentypen. Zu den gängigen Typen zählen float32, int32 und string. Der Datentyp eines Tensors kann mit dem Attribut .dtype abgerufen werden:

print(f'Data type of a tensor: {tensor.dtype}')

Tensorachsen

Anwendungen von Tensoren

• Table Data

• Textsequenzen

• Numerische Sequenzen

• Bildverarbeitung

• Videobearbeitung

Batches

Methoden zur Tensor-Erstellung

# Create a 2x2 constant tensor
tensor_const = tf.constant([[1, 2], [3, 4]])

# Create a variable tensor
tensor_var = tf.Variable([[1, 2], [3, 4]])

# Zero tensor of shape (3, 3)
tensor_zeros = tf.zeros((3, 3))

# Ones tensor of shape (2, 2)
tensor_ones = tf.ones((2, 2))

# Tensor of shape (2, 2) filled with 6
tensor_fill = tf.fill((2, 2), 6)

# Generate a sequence of numbers starting from 0, ending at 9
tensor_range = tf.range(10)

# Create 5 equally spaced values between 0 and 10
tensor_linspace = tf.linspace(0, 10, 5)

# Tensor of shape (2, 2) with random values normally distributed 
tensor_random = tf.random.normal((2, 2), mean=4, stddev=0.5)

# Tensor of shape (2, 2) with random values uniformly distributed 
tensor_random = tf.random.uniform((2, 2), minval=-2, maxval=2)

Konvertierungen

• NumPy zu Tensor

# Create a NumPy array based on a Python list
numpy_array = np.array([[1, 2], [3, 4]])

# Convert a NumPy array to a tensor
tensor_from_np = tf.convert_to_tensor(numpy_array)

• Pandas zu Tensor

# Create a DataFrame based on dictionary
df = pd.DataFrame({'A': [1, 2], 'B': [3, 4]})

# Convert a DataFrame to a tensor
tensor_from_df = tf.convert_to_tensor(df.values)

• Konstanter Tensor zu variablem Tensor

# Create a variable from a tensor
tensor = tf.random.normal((2, 3))
variable_1 = tf.Variable(tensor)

# Create a variable based on other generator
variable_2 = tf.Variable(tf.zeros((2, 2)))

Datentypen

# Creating a tensor of type float16
tensor_float = tf.constant([1.2, 2.3, 3.4], dtype=tf.float16)

# Convert tensor_float from float32 to int32
tensor_int = tf.cast(tensor_float, dtype=tf.int32)

Arithmetik

• Addition

c1 = tf.add(a, b)  
c2 = a + b

# Changes the object inplace without creating a new one
a.assign_add(b)

• Subtraktion

c1 = tf.subtract(a, b)  
c2 = a - b 

# Inplace substraction
a.assign_sub(b)

• Elementweise Multiplikation

c1 = tf.multiply(a, b)  
c2 = a * b

• Division

c1 = tf.divide(a, b)  
c2 = a / b 

Broadcasting

Lineare Algebra

• Matrixmultiplikation

product1 = tf.matmul(matrix1, matrix2)
product2 = matrix1 @ matrix2

• Matrixinversion

inverse_mat = tf.linalg.inv(matrix)

• Transponieren

transposed = tf.transpose(matrix)

• Skalarprodukt

# Dot product along axes
dot_product_axes1 = tf.tensordot(matrix1, matrix2, axes=1)
dot_product_axes0 = tf.tensordot(matrix1, matrix2, axes=0)

Umformen

# Create a tensor with shape (3, 2)
tensor = tf.constant([[1, 2], [3, 4], [5, 6]])

# Reshape the tensor to shape (2, 3)
reshaped_tensor = tf.reshape(tensor, (2, 3))

Slicing

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

# Slice tensor to extract sub-tensor from index (0, 1) of size (1, 2)
sliced_tensor = tf.slice(tensor, begin=(0, 1), size=(1, 2))

# Slice tensor to extract sub-tensor from index (1, 0) of size (2, 2)
sliced_tensor = tf.slice(tensor, (1, 0), (2, 2))

Modifizieren mit Slicing

# Create a tensor
tensor = tf.Variable([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

# Change the entire first row 
tensor[0, :].assign([0, 0, 0])

# Modify the second and the third columns 
tensor[:, 1:3].assign(tf.fill((3,2), 1))

Konkatenation

# Create two tensors
tensor1 = tf.constant([[1, 2, 3], [4, 5, 6]])
tensor2 = tf.constant([[7, 8, 9]])

# Concatenate tensors vertically (along rows)
concatenated_tensor = tf.concat([tensor1, tensor2], axis=0)

# Concatenate tensors horizontally (along columns)
concatenated_tensor = tf.concat([tensor3, tensor4], axis=1)

Reduktionsoperationen

# Calculate sum of all elements
total_sum = tf.reduce_sum(tensor)

# Calculate mean of all elements
mean_val = tf.reduce_mean(tensor)

# Determine the maximum value
max_val = tf.reduce_max(tensor)

# Find the minimum value
min_val = tf.reduce_min(tensor)

Gradient Tape

# Define input variables
x = tf.Variable(tf.fill((2, 3), 3.0))
z = tf.Variable(5.0)

# Start recording the operations
with tf.GradientTape() as tape:
    # Define the calculations
    y = tf.reduce_sum(x * x + 2 * z)
    
# Extract the gradient for the specific inputs (x and z)
grad = tape.gradient(y, [x, z])

print(f"The gradient of y with respect to x is:\n{grad[0].numpy()}")
print(f"The gradient of y with respect to z is: {grad[1].numpy()}")

@tf.function

@tf.function
def compute_gradient_conditional(x):
    with tf.GradientTape() as tape:
        if tf.reduce_sum(x) > 0:
            y = x * x
        else:
            y = x * x * x
    return tape.gradient(y, x)

x = tf.constant([-2.0, 2.0])
grad = compute_gradient_conditional(x)
print(f"The gradient at x = {x.numpy()} is {grad.numpy()}")