# coding: utf-8
from __future__ import division, unicode_literals
from lab import *

import numpy as np
import matplotlib.pyplot as plt
import uncertainties.umath as u

mass   = lambda x: ufloat(x, 0.01)*0.001
length = lambda x: ufloat(x, 0.5)*0.01

##
## Costants
##

mL = [ (16.47, 251.0) # violet
     , (5.49,  252.7) # black
     , (6.16,  287.7) # green
     , (1.48,  188.8) # white
     ]

mu = [mass(m)/length(l) for m,l in mL] # linear density (kg/m)
pp = mass(50.03)                       # tare mass (kg)
g  = 9.80665                           # acceleration due to gravity (m/s^2)

sigma   = 0.8   # frequency uncertainty

## green string 
## T,L,μ constant, plot ν(n)

m  = mass(400.21) + pp
L  = length(98.5)
T  = m*g

n  = np.arange(1,8)
nu = np.array([23.97, 48.20, 72.54, 96.97, 122.20, 147.10, 171.30])

# linear regression y=kx where
# y=ν, x=n, k=1/(2L)√(T/μ)
x = np.linspace(0,8,100)
k = simple_linear(n, nu, sigma)
f = lambda x: k.n*x

plt.figure(1)
plt.xlim(0,8)
plt.ylim(0,200)
plt.xlabel('n armonica')
plt.ylabel('frequenza di risonanza (Hz)')
plt.scatter(n, nu, color='#468174')
plt.plot(x, f(x), '#5ca897')
plt.show()

# χ² test
alpha = chi_squared_fit(n, nu, f, sigma, s=1)

v0 = 2*L*k           # actual propagation velocity
v  = u.sqrt(T/mu[2]) # theoretical propagation velocity

print '''
χ²: α={:.3f}, α>ε: {}
k:  ({})1/s
v°: ({})m/s
v:  ({})m/s
'''.format(alpha, alpha>epsilon, k, v0, v)


##
## green string
## T,μ,n constant, plot ν(T), n=2

M  = [mass(i)+pp for i in [700.45, 499.95, 450.16, 400.19, 200.16, 140.92]]
T  = np.array([g*i.n for i in M])
nu = np.array([60.26, 52.20, 49.70, 47.06, 34.96, 31.22])

# linear regression y=kx where
# y=ν, x=√T, k=1/(L√μ)
x = np.linspace(1, 8, 100)
k = simple_linear(np.sqrt(T), nu, sigma)
f = lambda x: k.n*np.sqrt(x)

plt.figure(2)
plt.xlabel('Tensione (N)')
plt.ylabel('Frequenza 2ª armonica (Hz)')
plt.scatter(T, nu, color='#673f73')
plt.plot(x, f(x), '#975ca8')
plt.show()

# χ² test
alpha = chi_squared_fit(T, nu, f, sigma, s=1)
print "χ²: α={}, α>ε: {}".format(alpha, alpha>epsilon)

##
## green string
## T,μ,n constant, plot ν(L), n=2

m = mass(400.21) + pp
T = m*g

L  = np.array([116.5, 104.5, 95.4, 82.2, 75.0, 64.5, 54.7])*0.01
nu = np.array([44.58, 49.43, 54.60, 63.58, 69.34, 80.75, 96.40])

# linear regression y=kx where
# y=ν, x=1/L, k=n/2 √(T/μ)
x = np.linspace(0.5, 1.25, 100)
k = simple_linear(1/L, nu, sigma)
f = lambda x: k.n/x

plt.figure(3)
plt.xlabel('Lunghezza corda (m)')
plt.ylabel('Frequenza 2ª armonica (Hz)')
plt.scatter(L, nu, color='#844855')
plt.plot(x, f(x), '#a85c6c')
plt.show()

# χ² test
alpha = chi_squared_fit(L, nu, f, sigma, s=1)
print "χ^2: α={}, α>ε: {}".format(alpha, alpha>epsilon)

##
## every string
## T,n,L constant, plot ν(μ), n=2

m = mass(400.21) + pp
L = length(98.5)
n = 2

mu = np.array([i.n for i in mu])
nu = np.array([26.90, 47.23, 47.60, 78.20])

# linear regression y=kx where
# y=ν, x=1/√μ, k=√T/L
x = np.linspace(0.0005,0.007,100)
k = simple_linear(1/np.sqrt(mu), nu, sigma)
f = lambda x: k.n/np.sqrt(x)

plt.figure(4)
plt.xlabel('Densità lineare (kg/m)')
plt.ylabel('Frequenza 2ª armonica')
plt.scatter(mu, nu, color='#44507c')
plt.plot(x, f(x), '#5c6ca8')
plt.show()

# χ² test
alpha = chi_squared_fit(mu, nu, f, sigma, s=1)
print "χ²: α={}, α>ε: {}".format(alpha, alpha>epsilon)