import math
import numpy as np
import matplotlib.pyplot as plt
import sounddevice as sd

sample_rate = 44100
seconds = 5

N = 100 # number of string segments
I = int(sample_rate * seconds) # number of samples to simulate

# string parameters
rho = 8000 # density, steel, kg/m^3
radius = 0.001 # meters
S = math.pi*radius**2 # string cross sectional area, assuming circular
mu = S*rho # linear mass density
T = 1200 # string tension, N
c = math.sqrt(T/mu) # transverse wave velocity
kappa = 0.001 # stiffness coefficient
sigma = 0.5 # damping coefficient
L = 0.5 # length of string
strike_position = 0.2 # x of impulse location
impulse_width = 0.02 # x of impulse width
impulse_velocity = 1000.0 # x/t of impulse magnitude
sample_position = 0.1 # percentage along L of sampling for audio

dx = L / N # delta x
dt = 1/sample_rate
#dt = 0.2 * dx / c
if(dx**2 < (c*dt)**2 + 4*(kappa*dt/(dx**2))**2):
    print("warning: possibly unstable due to not enough segments, increase N")

# derived constants
r1 = c * dt/dx 
r2 = (c * dt/dx) ** 2
s1 = kappa * dt/dx**2
s2 = (kappa * dt/dx**2) ** 2

# string grid
x = np.linspace(0, L, N + 1) # linspace my beloved

# state vectors
y_last = np.zeros(N + 1)
y_current = np.zeros(N + 1)
y_next = np.zeros(N + 1)
# output
y_sample = np.zeros(I)

# vector of initial velocity across the string as a result of the impulse
v0 = impulse_velocity * np.exp(-((x - strike_position) ** 2)/(2 * impulse_width ** 2))

# initial conditions:
# y(x, 0) = 0 and dy/dt(x, 0) = v0(x)
# boundary conditions: y(0, t) = y(L, t) = 0 as well as all dy/dts thereafter

def show_plot():
    plt.plot(np.arange(0, N+1, 1), y_current)
    plt.grid()
    plt.show()

# first iteration
for n in range(2, N-2):
    y_current[n] = dt * v0[n] + 0.5 * r1**2 * (y_last[n-1] - 2*y_last[n] + y_last[n+1])
    # y_xx = y_last[n+1] - 2*y_last[n] + y_last[n-1]
    # y_xxxx = y_last[n-2] - 4*y_last[n-1] + 6*y_last[n] - 4*y_last[n+1] + y_last[n+2]

    # term1 = (2 - 2*sigma*dt) * y_current[n]
    # term2 = (2*sigma*dt - 1) * y_last[n]
    # term3 = r2 * y_xx - s2 * y_xxxx
    # y_current[n] = dt * v0[n] + 0.5 * r1**2 *(term1 + term2 + term3)

n_sample = int(sample_position * L * N)
y_sample[0] = y_last[n_sample]
y_sample[1] = y_current[n_sample]

# rest of the iterations
for i in range(2, I):

    for n in range(2, N-2):
        # simple wave equation
        # y_next[n] = 2*y_current[n] - y_last[n] + r**2 * (y_current[n-1] - 2*y_current[n] + y_current[n+1])
        
        # stiff wave equation
        y_xx = y_current[n+1] - 2*y_current[n] + y_current[n-1]
        y_xxxx = y_current[n-2] - 4*y_current[n-1] + 6*y_current[n] - 4*y_current[n+1] + y_current[n+2]

        term1 = (2 - 2*sigma*dt) * y_current[n]
        term2 = (2*sigma*dt - 1) * y_last[n]
        term3 = r2 * y_xx - s2 * y_xxxx
        y_next[n] = term1 + term2 + term3

    y_next[0] = 0
    y_next[1] = 0
    y_next[N-1] = 0
    y_next[N-2] = 0

    # y_sample[i] = math.tanh(y_next[n_sample])
    y_sample[i] = y_next[n_sample]

    y_last = y_current.copy()
    y_current = y_next.copy()

    if(i % 1000 == 0):
        print(i/I * 100, "% complete")

plt.plot(np.arange(0, I, 1), y_sample)
plt.grid()
plt.show()

sd.play(y_sample, sample_rate)
sd.wait()