Module libquantum.entropy

This module contains functions related to entropy Please refer to Garces, 2020

"""
This module contains functions related to entropy
Please refer to Garces, 2020
"""

import numpy as np
from libquantum import utils
from libquantum.scales import EPSILON
from typing import Tuple

"""
Entropy
"""


# FOR TONES
def snr_mean_max(tfr_coeff_complex: np.ndarray) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Computes the snr lin energy, snr in bits, and snr entropy defined in Garces (2020)

    :param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real.
    :return: three np.ndarrays with snr lin energy, snr in bits, and snr entropy respectively
    """
    # Evaluate Log energy entropy (LEE) = log(p) and Shannon Entropy (SE) = -p*log(p)
    # Assumes linear spectral coefficien ts (not power), takes the square
    energy = np.abs(tfr_coeff_complex)**2
    energy_mean = np.mean(energy)
    snr_lin = energy/energy_mean
    # Surprisal = log(p)
    snr_bits = 0.5*utils.log2epsilon(snr_lin + EPSILON)

    # SNR entropy per pixel
    snr_entropy = snr_lin*snr_bits
    # Scale by max
    snr_entropy /= np.max(snr_lin)

    return snr_lin, snr_bits, snr_entropy


def snr_mean_max_baseline(tfr_coeff_complex: np.ndarray) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Computes the baseline mean energy and the snr max for a template signal

    :param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real.
    :return: three np.ndarrays with energy max, mean energy and snr max respectively
    """
    # Evaluate Log energy entropy (LEE) = log(p) and Shannon Entropy (SE) = -p*log(p)
    # Assumes linear spectral coefficien ts (not power), takes the square
    energy = np.abs(tfr_coeff_complex)**2
    energy_lin_mean = np.mean(energy)
    energy_lin_max = np.max(energy)
    snr_lin = energy/energy_lin_mean
    snr_lin_max = np.max(snr_lin)

    return energy_lin_max, energy_lin_mean, snr_lin_max


def snr_ref_max(tfr_coeff_complex: np.ndarray,
                energy_mean: float,
                snr_max: float) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Computes the snr energy, snr bits and snr entropy from baseline mean energy and max snr

    :param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real.
    :param energy_mean: baseline mean energy.
    :param snr_max: baseline max linear snr
    :return: three np.ndarrays with snr energy, snr bits and snr entropy respectively
    """
    # Evaluate Log energy entropy (LEE) = log(p) and Shannon Entropy (SE) = -p*log(p)
    # Assumes linear spectral coefficien ts (not power), takes the square
    energy = np.abs(tfr_coeff_complex)**2
    snr_lin = energy/energy_mean
    # Surprisal = log(p)
    snr_bits = 0.5*utils.log2epsilon(snr_lin)

    # SNR entropy per pixel
    snr_entropy = snr_lin*snr_bits
    # Scale by max
    snr_entropy /= snr_max

    return snr_lin, snr_bits, snr_entropy


# FOR TRANSIENTS
def snr_mean_max_profile(tfr_coeff_complex: np.ndarray) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Computes the snr lin energy, snr in bits, and snr entropy defined in Garces (2020)

    :param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real.
    :return: three np.ndarrays with snr energy, snr bits and snr entropy respectively
    """
    # Evaluate Log energy entropy (LEE) = log(p) and Shannon Entropy (SE) = -p*log(p)
    # Assumes linear spectral coefficien ts (not power), takes the square
    energy = np.abs(tfr_coeff_complex)**2
    energy_mean = np.mean(energy)
    print('Energy_mean = ', energy_mean)
    snr_lin = energy/energy_mean
    # Surprisal = log(p)
    snr_bits = 0.5*utils.log2epsilon(snr_lin)

    # SNR entropy per pixel
    snr_entropy = snr_lin*snr_bits
    # Scale by max
    snr_entropy /= np.max(snr_lin)

    return snr_lin, snr_bits, snr_entropy


def snr_ref_max_profile(tfr_coeff_complex: np.ndarray,
                        energy_mean: float,
                        snr_max: float) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Computes the snr energy, snr bits and snr entropy from
    frequency-dependent noise model/profile mean energy and max snr per band

    :param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real.
    :param energy_mean: baseline frequency-dependent mean energy.
    :param snr_max: baseline max frequency-dependent linear snr
    :return: three np.ndarrays with snr energy, snr bits and snr entropy respectively
    """
    # Evaluate Log energy entropy (LEE) = log(p) and Shannon Entropy (SE) = -p*log(p)
    # Assumes linear spectral coefficien ts (not power), takes the square
    energy = np.abs(tfr_coeff_complex)**2
    snr_lin = energy/energy_mean
    # Surprisal = log(p)
    snr_bits = 0.5*utils.log2epsilon(snr_lin + EPSILON)

    # SNR entropy per pixel
    snr_entropy = snr_lin*snr_bits
    # Scale by max
    snr_entropy /= snr_max

    return snr_lin, snr_bits, snr_entropy

Functions

def snr_mean_max(tfr_coeff_complex: numpy.ndarray) ‑> Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Computes the snr lin energy, snr in bits, and snr entropy defined in Garces (2020)

:param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real. :return: three np.ndarrays with snr lin energy, snr in bits, and snr entropy respectively

Expand source code

def snr_mean_max(tfr_coeff_complex: np.ndarray) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Computes the snr lin energy, snr in bits, and snr entropy defined in Garces (2020)

    :param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real.
    :return: three np.ndarrays with snr lin energy, snr in bits, and snr entropy respectively
    """
    # Evaluate Log energy entropy (LEE) = log(p) and Shannon Entropy (SE) = -p*log(p)
    # Assumes linear spectral coefficien ts (not power), takes the square
    energy = np.abs(tfr_coeff_complex)**2
    energy_mean = np.mean(energy)
    snr_lin = energy/energy_mean
    # Surprisal = log(p)
    snr_bits = 0.5*utils.log2epsilon(snr_lin + EPSILON)

    # SNR entropy per pixel
    snr_entropy = snr_lin*snr_bits
    # Scale by max
    snr_entropy /= np.max(snr_lin)

    return snr_lin, snr_bits, snr_entropy

def snr_mean_max_baseline(tfr_coeff_complex: numpy.ndarray) ‑> Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Computes the baseline mean energy and the snr max for a template signal

:param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real. :return: three np.ndarrays with energy max, mean energy and snr max respectively

Expand source code

def snr_mean_max_baseline(tfr_coeff_complex: np.ndarray) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Computes the baseline mean energy and the snr max for a template signal

    :param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real.
    :return: three np.ndarrays with energy max, mean energy and snr max respectively
    """
    # Evaluate Log energy entropy (LEE) = log(p) and Shannon Entropy (SE) = -p*log(p)
    # Assumes linear spectral coefficien ts (not power), takes the square
    energy = np.abs(tfr_coeff_complex)**2
    energy_lin_mean = np.mean(energy)
    energy_lin_max = np.max(energy)
    snr_lin = energy/energy_lin_mean
    snr_lin_max = np.max(snr_lin)

    return energy_lin_max, energy_lin_mean, snr_lin_max

def snr_mean_max_profile(tfr_coeff_complex: numpy.ndarray) ‑> Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Computes the snr lin energy, snr in bits, and snr entropy defined in Garces (2020)

:param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real. :return: three np.ndarrays with snr energy, snr bits and snr entropy respectively

Expand source code

def snr_mean_max_profile(tfr_coeff_complex: np.ndarray) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Computes the snr lin energy, snr in bits, and snr entropy defined in Garces (2020)

    :param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real.
    :return: three np.ndarrays with snr energy, snr bits and snr entropy respectively
    """
    # Evaluate Log energy entropy (LEE) = log(p) and Shannon Entropy (SE) = -p*log(p)
    # Assumes linear spectral coefficien ts (not power), takes the square
    energy = np.abs(tfr_coeff_complex)**2
    energy_mean = np.mean(energy)
    print('Energy_mean = ', energy_mean)
    snr_lin = energy/energy_mean
    # Surprisal = log(p)
    snr_bits = 0.5*utils.log2epsilon(snr_lin)

    # SNR entropy per pixel
    snr_entropy = snr_lin*snr_bits
    # Scale by max
    snr_entropy /= np.max(snr_lin)

    return snr_lin, snr_bits, snr_entropy

def snr_ref_max(tfr_coeff_complex: numpy.ndarray, energy_mean: float, snr_max: float) ‑> Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Computes the snr energy, snr bits and snr entropy from baseline mean energy and max snr

:param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real. :param energy_mean: baseline mean energy. :param snr_max: baseline max linear snr :return: three np.ndarrays with snr energy, snr bits and snr entropy respectively

Expand source code

def snr_ref_max(tfr_coeff_complex: np.ndarray,
                energy_mean: float,
                snr_max: float) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Computes the snr energy, snr bits and snr entropy from baseline mean energy and max snr

    :param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real.
    :param energy_mean: baseline mean energy.
    :param snr_max: baseline max linear snr
    :return: three np.ndarrays with snr energy, snr bits and snr entropy respectively
    """
    # Evaluate Log energy entropy (LEE) = log(p) and Shannon Entropy (SE) = -p*log(p)
    # Assumes linear spectral coefficien ts (not power), takes the square
    energy = np.abs(tfr_coeff_complex)**2
    snr_lin = energy/energy_mean
    # Surprisal = log(p)
    snr_bits = 0.5*utils.log2epsilon(snr_lin)

    # SNR entropy per pixel
    snr_entropy = snr_lin*snr_bits
    # Scale by max
    snr_entropy /= snr_max

    return snr_lin, snr_bits, snr_entropy

def snr_ref_max_profile(tfr_coeff_complex: numpy.ndarray, energy_mean: float, snr_max: float) ‑> Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

Computes the snr energy, snr bits and snr entropy from frequency-dependent noise model/profile mean energy and max snr per band

:param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real. :param energy_mean: baseline frequency-dependent mean energy. :param snr_max: baseline max frequency-dependent linear snr :return: three np.ndarrays with snr energy, snr bits and snr entropy respectively

Expand source code

def snr_ref_max_profile(tfr_coeff_complex: np.ndarray,
                        energy_mean: float,
                        snr_max: float) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Computes the snr energy, snr bits and snr entropy from
    frequency-dependent noise model/profile mean energy and max snr per band

    :param tfr_coeff_complex: Complex coefficients for time-frequency representation. Can be real.
    :param energy_mean: baseline frequency-dependent mean energy.
    :param snr_max: baseline max frequency-dependent linear snr
    :return: three np.ndarrays with snr energy, snr bits and snr entropy respectively
    """
    # Evaluate Log energy entropy (LEE) = log(p) and Shannon Entropy (SE) = -p*log(p)
    # Assumes linear spectral coefficien ts (not power), takes the square
    energy = np.abs(tfr_coeff_complex)**2
    snr_lin = energy/energy_mean
    # Surprisal = log(p)
    snr_bits = 0.5*utils.log2epsilon(snr_lin + EPSILON)

    # SNR entropy per pixel
    snr_entropy = snr_lin*snr_bits
    # Scale by max
    snr_entropy /= snr_max

    return snr_lin, snr_bits, snr_entropy