add reversed LPPL model

[GXY2017]

The normal LPPL model fits and predicts future market trends by capturing the cyclicity and acceleration in price trends.
A reversed LPPL model may be also useful in describing the cyclicity and deceleration in price trends.
it could be achieved by changing m to -m and allowing a negative value of -m， and change (tc-t) to (t - tc).

y_2 = a + np.power(t - tc, -m) * (b + ((c1 * np.cos(w * np.log(t - tc))) + (c2 * np.sin(w * np.log(t - tc)))))

[ano]

import numpy as np

def reversed_lppl(t, tc, m, a, b, c1, c2, w):
    """
    Reversed Log-Periodic Power Law (LPPL) model.

    Parameters:
    t (float or np.ndarray): Time or array of time values.
    tc (float): Critical time at which the market trend changes.
    m (float): Negative exponent to describe the deceleration in price trends.
    a (float): Constant term.
    b (float): Coefficient for the power law term.
    c1 (float): Coefficient for the cosine term.
    c2 (float): Coefficient for the sine term.
    w (float): Frequency of oscillations.

    Returns:
    float or np.ndarray: The reversed LPPL value(s) at time t.
    """
    term1 = np.power(t - tc, -m)
    term2 = b + ((c1 * np.cos(w * np.log(t - tc))) + (c2 * np.sin(w * np.log(t - tc))))
    y_2 = a + term1 * term2
    return y_2

# Example usage:
t = np.linspace(1, 10, 100)  # array of time values from 1 to 10
tc = 5  # assumed critical time
m = 0.5  # assumed negative exponent value
a = 1  # assumed constant term value
b = 2  # assumed power law coefficient value
c1 = 1  # assumed cosine term coefficient value
c2 = 1  # assumed sine term coefficient value
w = 6  # assumed frequency of oscillations value

# Get the reversed LPPL values
y_2_values = reversed_lppl(t, tc, m, a, b, c1, c2, w)

In the reversed_lppl function, the parameters t, tc, m, a, b, c1, c2, and w correspond to the variables in your equation. The t parameter can be a single float value or a NumPy array of float values, which allows you to evaluate the reversed LPPL model at multiple time points simultaneously. The function returns the evaluated y_2 value(s) as per the provided equation.