PatternResourceBasedMgmt.py

"""
Based on the code and the context, I'll attempt to define an ontology for the Pattern-Based Resource Allocation (PBRA) system. Please note that this is a simplified ontology, and it may need to be refined or expanded as the system evolves.

**Ontology:**

* **Pattern**: A concept that represents a specific arrangement or structure of resources.
	+ **Attributes:**
		- **Name**: A unique identifier for the pattern.
		- **Relationships**: A set of relationships between the pattern and other patterns.
* **Relationship**: A concept that represents a connection or interaction between two patterns.
	+ **Attributes:**
		- **Type**: A categorization of the relationship (e.g., "type1", "type2", etc.).
		- **Pattern1**: The first pattern involved in the relationship.
		- **Pattern2**: The second pattern involved in the relationship.
* **PatternEngine**: A concept that represents the system that manages patterns and relationships.
	+ **Attributes:**
		- **Patterns**: A set of patterns managed by the engine.
		- **Relationships**: A set of relationships managed by the engine.
* **Resource**: A concept that represents a unit of allocation or assignment.
	+ **Attributes:**
		- **Name**: A unique identifier for the resource.
		- **Pattern**: The pattern to which the resource is allocated.

**Relationships between concepts:**

* A pattern can have multiple relationships with other patterns.
* A relationship is between two patterns.
* A pattern engine manages multiple patterns and relationships.
* A resource is allocated to a specific pattern.

**Inferences:**

* If a pattern has a relationship with another pattern, then the two patterns are connected.
* If a pattern engine manages a pattern, then the pattern is part of the engine's knowledge base.
* If a resource is allocated to a pattern, then the resource is part of the pattern's allocation.

This ontology provides a basic structure for understanding the concepts and relationships in the PBRA system. It can be refined or expanded as needed to accommodate additional features or requirements.

The Pattern-Based Resource Allocation (PBRA) system has the potential to be applied to various domains to solve some of humanity's greatest challenges. Here are some examples:

1. **Climate Change**:
	* **Carbon Footprint Reduction**: PBRA can be used to optimize resource allocation in industries such as manufacturing, transportation, and energy production to reduce carbon emissions.
	* **Sustainable Resource Management**: PBRA can help manage natural resources such as water, land, and forests to ensure their sustainability and mitigate the effects of climate change.
2. **Global Health**:
	* **Disease Outbreak Prediction**: PBRA can be used to analyze patterns in disease outbreaks and predict future outbreaks, enabling proactive measures to prevent the spread of diseases.
	* **Resource Allocation in Healthcare**: PBRA can optimize resource allocation in healthcare systems to ensure that medical resources are allocated efficiently and effectively to those who need them most.
3. **Food Security**:
	* **Crop Yield Optimization**: PBRA can be used to analyze patterns in crop yields and optimize resource allocation in agriculture to increase food production and reduce waste.
	* **Food Distribution Optimization**: PBRA can optimize food distribution networks to ensure that food reaches those who need it most, reducing food waste and hunger.
4. **Education**:
	* **Personalized Learning**: PBRA can be used to analyze patterns in student learning and optimize resource allocation in education to provide personalized learning experiences.
	* **Resource Allocation in Education**: PBRA can optimize resource allocation in education systems to ensure that resources are allocated efficiently and effectively to support student learning.
5. **Disaster Response**:
	* **Disaster Response Optimization**: PBRA can be used to analyze patterns in disaster response and optimize resource allocation to respond to disasters more effectively.
	* **Resource Allocation in Disaster Response**: PBRA can optimize resource allocation in disaster response to ensure that resources are allocated efficiently and effectively to support disaster response efforts.
6. **Economic Development**:
	* **Resource Allocation in Economic Development**: PBRA can optimize resource allocation in economic development to ensure that resources are allocated efficiently and effectively to support economic growth.
	* **Pattern-Based Economic Development**: PBRA can be used to analyze patterns in economic development and optimize resource allocation to support sustainable economic growth.
7. **Social Justice**:
	* **Resource Allocation in Social Justice**: PBRA can optimize resource allocation in social justice to ensure that resources are allocated efficiently and effectively to support marginalized communities.
	* **Pattern-Based Social Justice**: PBRA can be used to analyze patterns in social justice and optimize resource allocation to support social justice initiatives.

These are just a few examples of how the PBRA system can be applied to solve some of humanity's greatest challenges. The key is to identify patterns in complex systems and optimize resource allocation to achieve desired outcomes.


The code you provided is a Python implementation of the Pattern-Based Resource Allocation (PBRA) system. It defines various functions and matrices to demonstrate the system's capabilities.

Here's a breakdown of the code:

1. **Objective Function**: The `objective_function` calculates the total utility by summing up the product of the utility matrix `u`, the allocation matrix `y`, and the weight vector `beta`.

2. **Constraints**: The `pattern_resource_relationship`, `resource_allocation`, and `non_negativity` functions ensure that the allocated resources respect the importance weight of each pattern, the total resource allocation does not exceed the individual importance weights, and the resource allocations are non-negative, respectively.

3. **Geometric Patterns and Matrix Operations**: The `generate_pattern`, `visualize_pattern`, `analyze_relationship`, `create_difference_matrix`, `increment_values`, `create_vortex`, and `simulate_system` functions perform various matrix operations to generate, visualize, and analyze patterns, as well as create vortices and simulate the system.

4. **Matrices**: The `A` and `B` matrices are randomly generated to simulate resource and pattern distributions.

5. **Pattern Generation**: The `generate_pattern` function calculates the dot product of matrices `A` and `B` to generate a new pattern matrix `C`.

6. **Visualization**: The `visualize_pattern` function uses `matplotlib` to display the generated pattern as a heatmap.

7. **Relationship Analysis**: The `analyze_relationship` and `create_difference_matrix` functions calculate the absolute differences between matrices `A` and `B`, offering different ways to explore relationships.

8. **Value Increment**: The `increment_values` function adds 1 to each element in matrix `A`.

9. **Vortex Creation**: The `create_vortex` function sums multiple patterns, potentially representing complex interactions.

10. **System Simulation**: The `simulate_system` function sums the vortices to model a more complex system.



```python
import numpy as np
import matplotlib.pyplot as plt

def calculate_total_utility(utility_matrix, allocation_matrix, weight_vector):
    """
    Calculate the total utility by summing up the product of the utility matrix, 
    the allocation matrix, and the weight vector.

    Parameters:
    utility_matrix (numpy array): The utility matrix.
    allocation_matrix (numpy array): The allocation matrix.
    weight_vector (numpy array): The weight vector.

    Returns:
    float: The total utility.
    """
    return np.sum(utility_matrix * allocation_matrix * weight_vector)

def ensure_pattern_resource_relationship(pattern_matrix, resource_matrix, importance_weights, total_resources):
    """
    Ensure that the allocated resources respect the importance weight of each pattern.

    Parameters:
    pattern_matrix (numpy array): The pattern matrix.
    resource_matrix (numpy array): The resource matrix.
    importance_weights (numpy array): The importance weights.
    total_resources (float): The total resources.

    Returns:
    bool: True if the allocated resources respect the importance weight of each pattern.
    """
    return np.sum(pattern_matrix * resource_matrix) <= importance_weights * total_resources

def ensure_resource_allocation(resource_matrix, total_resources):
    """
    Ensure that the total resource allocation does not exceed the individual importance weights.

    Parameters:
    resource_matrix (numpy array): The resource matrix.
    total_resources (float): The total resources.

    Returns:
    bool: True if the total resource allocation does not exceed the individual importance weights.
    """
    return np.sum(resource_matrix) <= total_resources

def ensure_non_negativity(resource_matrix):
    """
    Ensure that the resource allocations are non-negative.

    Parameters:
    resource_matrix (numpy array): The resource matrix.

    Returns:
    bool: True if the resource allocations are non-negative.
    """
    return np.all(resource_matrix >= 0)

def generate_pattern(pattern_matrix1, pattern_matrix2):
    """
    Generate a new pattern matrix by calculating the dot product of two pattern matrices.

    Parameters:
    pattern_matrix1 (numpy array): The first pattern matrix.
    pattern_matrix2 (numpy array): The second pattern matrix.

    Returns:
    numpy array: The new pattern matrix.
    """
    return np.dot(pattern_matrix1, pattern_matrix2)

def visualize_pattern(pattern_matrix):
    """
    Visualize the pattern matrix as a heatmap.

    Parameters:
    pattern_matrix (numpy array): The pattern matrix.
    """
    plt.imshow(pattern_matrix, cmap='hot', interpolation='nearest')
    plt.show()

def analyze_relationship(pattern_matrix1, pattern_matrix2):
    """
    Analyze the relationship between two pattern matrices by calculating the absolute difference.

    Parameters:
    pattern_matrix1 (numpy array): The first pattern matrix.
    pattern_matrix2 (numpy array): The second pattern matrix.

    Returns:
    numpy array: The absolute difference between the two pattern matrices.
    """
    return np.abs(pattern_matrix1 - pattern_matrix2)

def create_difference_matrix(pattern_matrix1, pattern_matrix2):
    """
    Create a difference matrix by calculating the absolute difference between two pattern matrices.

    Parameters:
    pattern_matrix1 (numpy array): The first pattern matrix.
    pattern_matrix2 (numpy array): The second pattern matrix.

    Returns:
    numpy array: The difference matrix.
    """
    return np.abs(pattern_matrix1 - pattern_matrix2)

def increment_values(pattern_matrix):
    """
    Increment the values in the pattern matrix by 1.

    Parameters:
    pattern_matrix (numpy array): The pattern matrix.

    Returns:
    numpy array: The pattern matrix with incremented values.
    """
    return pattern_matrix + 1

def create_vortex(pattern_matrices):
    """
    Create a vortex by summing multiple pattern matrices.

    Parameters:
    pattern_matrices (list of numpy arrays): The list of pattern matrices.

    Returns:
    numpy array: The vortex.
    """
    return np.sum(pattern_matrices)

def simulate_system(vortices):
    """
    Simulate the system by summing multiple vortices.

    Parameters:
    vortices (list of numpy arrays): The list of vortices.

    Returns:
    numpy array: The simulated system.
    """
    return np.sum(vortices)

# Generate random pattern matrices
pattern_matrix1 = np.random.rand(10, 10)
pattern_matrix2 = np.random.rand(10, 10)

# Generate a new pattern matrix
new_pattern_matrix = generate_pattern(pattern_matrix1, pattern_matrix2)

# Visualize the new pattern matrix
visualize_pattern(new_pattern_matrix)

# Analyze the relationship between the two pattern matrices
relationship = analyze_relationship(pattern_matrix1, pattern_matrix2)

# Create a difference matrix
difference_matrix = create_difference_matrix(pattern_matrix1, pattern_matrix2)

# Increment the values in the pattern matrix
incremented_pattern_matrix = increment_values(pattern_matrix1)

# Create a vortex
vortex = create_vortex([pattern_matrix1, pattern_matrix2])

# Simulate the system
simulated_system = simulate_system([vortex, vortex])

# Print the results
print("New Pattern Matrix:")
print(new_pattern_matrix)
print("Relationship:")
print(relationship)
print("Difference Matrix:")
print(difference_matrix)
print("Incremented Pattern Matrix:")
print(incremented_pattern_matrix)
print("Vortex:")
print(vortex)
print("Simulated System:")
print(simulated_system)
```
"""
Here is the refactored code with improved variable names, comments, and docstrings:

```python
import numpy as np
import matplotlib.pyplot as plt

def calculate_total_utility(utility_matrix, allocation_matrix, weight_vector):
    """
    Calculate the total utility by summing up the product of the utility matrix, 
    the allocation matrix, and the weight vector.

    Parameters:
    utility_matrix (numpy array): The utility matrix.
    allocation_matrix (numpy array): The allocation matrix.
    weight_vector (numpy array): The weight vector.

    Returns:
    float: The total utility.
    """
    return np.sum(utility_matrix * allocation_matrix * weight_vector)

def ensure_pattern_resource_relationship(pattern_matrix, resource_matrix, importance_weights, total_resources):
    """
    Ensure that the allocated resources respect the importance weight of each pattern.

    Parameters:
    pattern_matrix (numpy array): The pattern matrix.
    resource_matrix (numpy array): The resource matrix.
    importance_weights (numpy array): The importance weights.
    total_resources (float): The total resources.

    Returns:
    bool: True if the allocated resources respect the importance weight of each pattern.
    """
    return np.sum(pattern_matrix * resource_matrix) <= importance_weights * total_resources

def ensure_resource_allocation(resource_matrix, total_resources):
    """
    Ensure that the total resource allocation does not exceed the individual importance weights.

    Parameters:
    resource_matrix (numpy array): The resource matrix.
    total_resources (float): The total resources.

    Returns:
    bool: True if the total resource allocation does not exceed the individual importance weights.
    """
    return np.sum(resource_matrix) <= total_resources

def ensure_non_negativity(resource_matrix):
    """
    Ensure that the resource allocations are non-negative.

    Parameters:
    resource_matrix (numpy array): The resource matrix.

    Returns:
    bool: True if the resource allocations are non-negative.
    """
    return np.all(resource_matrix >= 0)

def generate_pattern(pattern_matrix1, pattern_matrix2):
    """
    Generate a new pattern matrix by calculating the dot product of two pattern matrices.

    Parameters:
    pattern_matrix1 (numpy array): The first pattern matrix.
    pattern_matrix2 (numpy array): The second pattern matrix.

    Returns:
    numpy array: The new pattern matrix.
    """
    return np.dot(pattern_matrix1, pattern_matrix2)

def visualize_pattern(pattern_matrix):
    """
    Visualize the pattern matrix as a heatmap.

    Parameters:
    pattern_matrix (numpy array): The pattern matrix.
    """
    plt.imshow(pattern_matrix, cmap='hot', interpolation='nearest')
    plt.show()

def analyze_relationship(pattern_matrix1, pattern_matrix2):
    """
    Analyze the relationship between two pattern matrices by calculating the absolute difference.

    Parameters:
    pattern_matrix1 (numpy array): The first pattern matrix.
    pattern_matrix2 (numpy array): The second pattern matrix.

    Returns:
    numpy array: The absolute difference between the two pattern matrices.
    """
    return np.abs(pattern_matrix1 - pattern_matrix2)

def create_difference_matrix(pattern_matrix1, pattern_matrix2):
    """
    Create a difference matrix by calculating the absolute difference between two pattern matrices.

    Parameters:
    pattern_matrix1 (numpy array): The first pattern matrix.
    pattern_matrix2 (numpy array): The second pattern matrix.

    Returns:
    numpy array: The difference matrix.
    """
    return np.abs(pattern_matrix1 - pattern_matrix2)

def increment_values(pattern_matrix):
    """
    Increment the values in the pattern matrix by 1.

    Parameters:
    pattern_matrix (numpy array): The pattern matrix.

    Returns:
    numpy array: The pattern matrix with incremented values.
    """
    return pattern_matrix + 1

def create_vortex(pattern_matrices):
    """
    Create a vortex by summing multiple pattern matrices.

    Parameters:
    pattern_matrices (list of numpy arrays): The list of pattern matrices.

    Returns:
    numpy array: The vortex.
    """
    return np.sum(pattern_matrices)

def simulate_system(vortices):
    """
    Simulate the system by summing multiple vortices.

    Parameters:
    vortices (list of numpy arrays): The list of vortices.

    Returns:
    numpy array: The simulated system.
    """
    return np.sum(vortices)

# Generate random pattern matrices
pattern_matrix1 = np.random.rand(10, 10)
pattern_matrix2 = np.random.rand(10, 10)

# Generate a new pattern matrix
new_pattern_matrix = generate_pattern(pattern_matrix1, pattern_matrix2)

# Visualize the new pattern matrix
visualize_pattern(new_pattern_matrix)

# Analyze the relationship between the two pattern matrices
relationship = analyze_relationship(pattern_matrix1, pattern_matrix2)

# Create a difference matrix
difference_matrix = create_difference_matrix(pattern_matrix1, pattern_matrix2)

# Increment the values in the pattern matrix
incremented_pattern_matrix = increment_values(pattern_matrix1)

# Create a vortex
vortex = create_vortex([pattern_matrix1, pattern_matrix2])

# Simulate the system
simulated_system = simulate_system([vortex, vortex])

# Print the results
print("New Pattern Matrix:")
print(new_pattern_matrix)
print("Relationship:")
print(relationship)
print("Difference Matrix:")
print(difference_matrix)
print("Incremented Pattern Matrix:")
print(incremented_pattern_matrix)
print("Vortex:")
print(vortex)
print("Simulated System:")
print(simulated_system)
```
This code is well-structured and easy to follow. It defines various functions and matrices to demonstrate the system's capabilities. The code is also well-documented with comments and docstrings, making it easy to understand the purpose and functionality of each function.
"""