new_tensor_field.py

import torch
from complextensor import ComplexTensor
import logging

# Configure logging for debug output
logging.basicConfig(level=logging.DEBUG)
logger = logging.getLogger("test_new_tensor")

# Define constants
ψ = 44.8
ξ = 3721.8
ε = 0.28082
τ = 64713.97
π = 3.14159

# Define weights for optimization components
α = 0.5
β = 0.3

# Initialize base tensor T
def initialize_tensor():
    logger.debug("Initializing base tensor T.")
    real = torch.tensor([
        [ψ, ε, 0, π],
        [ε, ξ, τ, 0],
        [0, τ, π, ε],
        [π, 0, ε, ψ]
    ], dtype=torch.float32)

    imag = torch.zeros_like(real)  # Initialize imaginary part as zeros
    T = ComplexTensor(real, imag)
    logger.debug(f"Base tensor T initialized with shape {T.real.shape}.")
    return T

# Define resonance matrix R
def compute_resonance_matrix():
    logger.debug("Computing resonance matrix R.")
    δ, ρ = 0.1, 0.2  # Example values
    real = torch.tensor([
        [0, δ, ρ, 0],
        [δ, 0, 0, ρ],
        [ρ, 0, 0, δ],
        [0, ρ, δ, 0]
    ], dtype=torch.float32)

    imag = torch.zeros_like(real)
    R = ComplexTensor(real, imag)
    logger.debug(f"Resonance matrix R initialized with shape {R.real.shape}.")
    return R

# Define stability matrix S
def compute_stability_matrix():
    logger.debug("Computing stability matrix S.")
    η = 0.05  # Example stability factor
    real = torch.eye(4, dtype=torch.float32) * η
    imag = torch.zeros_like(real)
    S = ComplexTensor(real, imag)
    logger.debug(f"Stability matrix S initialized with shape {S.real.shape}.")
    return S

# Scalar multiplication for ComplexTensor
def scalar_multiply(scalar, tensor):
    logger.debug(f"Performing scalar multiplication: scalar={scalar}, tensor shape={tensor.real.shape}.")
    return ComplexTensor(tensor.real * scalar, tensor.imag * scalar)

# Compute tensor metrics
def compute_metrics(T):
    logger.debug("Computing metrics for tensor.")
    entropy = torch.trace(torch.log(T.abs() + 1e-8)).item()
    norm = T.abs().norm(p=2).item()
    logger.debug(f"Computed metrics - Entropy: {entropy}, Norm: {norm}.")
    return entropy, norm

# Normalize tensor to stabilize its norm
def normalize_tensor(T):
    logger.debug("Normalizing tensor.")
    norm = T.abs().norm(p=2) + 1e-8
    normalized_tensor = ComplexTensor(T.real / norm, T.imag / norm)
    logger.debug("Tensor normalization complete.")
    return normalized_tensor

# Test the optimized tensor
if __name__ == "__main__":
    logger.info("Starting tensor optimization test.")

    # Initialize tensor and components
    T = initialize_tensor()
    R = compute_resonance_matrix()
    S = compute_stability_matrix()

    # Apply optimization
    T_evolved = T + scalar_multiply(α, R) + scalar_multiply(β, S)
    logger.debug("Tensor evolution completed.")
    T_optimized = normalize_tensor(T_evolved)
    logger.debug("Tensor optimization completed.")

    # Compute and display metrics
    initial_entropy, initial_norm = compute_metrics(T_evolved)
    optimized_entropy, optimized_norm = compute_metrics(T_optimized)

    print("=== Initial Tensor Metrics ===")
    print(f"Entropy: {initial_entropy}")
    print(f"Norm: {initial_norm}")

    print("\n=== Optimized Tensor Metrics ===")
    print(f"Entropy: {optimized_entropy}")
    print(f"Norm: {optimized_norm}")