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

import numpy               as np
import uncertainties.umath as um
import matplotlib.pyplot   as plt
from lab import *

## Impedence of an inductor (I)
## (all SI units)

R = ufloat(996, 4) # resistor
L = ufloat(0.014561, 0.000009)
C = ufloat(10e-12, 1e-12)

# frequency
nu = array(  2e3,  10e3,  25e3,  50e3,  75e3, 100e3, 125e3, 150e3, 175e3, 200e3,
           225e3, 250e3, 260e3, 270e3, 275e3, 285e3, 300e3, 350e3, 375e3)

# V input
Va = array(10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0,
           10.0, 10.0,  8.2, 10.0, 10.0, 8.20, 10.0, 10.0, 10.0)/2

# V output
Vb = array( 10.0,    9.4,   7.8,   5.0,    3.28,  2.20,  1.44,  0.96, 0.56, 0.32, 0.144,
           0.085, 0.0396, 0.069, 75.4e-3, 0.144, 0.194, 0.320, 0.360)/2

# time offset Va - Vb
Oab = array(  12e-6,  6.0e-6,  5.2e-6, 4.2e-6, 3.5e-6, 3.08e-6, 2.64e-6, 2.36e-6,
            2.08e-6, 1.88e-6, 1.71e-6, 260e-9, 260e-9,  280e-9,  280e-9,  300e-9,
             250e-9,  220e-9,  180e-9)

# time offset I - V
Oiv = array( 110e-6, 26.0e-6, 11.2e-6, 5.9e-6, 4.2e-6, 3.36e-6, 2.80e-6, 2.40e-6,
            2.12e-6, 1.90e-6, 1.74e-6, 280e-9, 260e-9,  270e-9,  280e-9,  280e-9,
             260e-9,  220e-9,  184e-9)


om  = 2*np.pi*nu # angular frequency
I   = Vb/R.n     # output current 
Vab = Va - Vb    # tension drop
Fab = om * Oab   # phase difference Vᵢ - Vₒ
Fiv = om * Oiv   # phase difference I - Vₒ

Z  = Vab/I  * np.exp(1j*Fiv) # impedance
H1 = Vab/Vb * np.exp(1j*Fab) # transfer function ΔV→Vb
H2 = Vb/Va  * np.exp(1j*Fab) # transfer function Va→Vb


# estimate uncertainties
Evb, Eva = ufloat(Vb[0], 1e-3), ufloat(Va[0], 0.1)
sigmaF   = (om[0]*ufloat(Oiv[0], 3e-5)).s
sigmaZ   = (R*(Eva - Evb)/Evb).s
sigmaH1  = ((Eva - Evb)/Evb).s
sigmaH2  = ((Evb - Eva)/Evb).s


# plot and fit Z(ν)
plt.figure(4)
plt.clf()

# magnitude
plt.subplot(2, 1, 1)
plt.title('impedance (RL circuit)')
plt.ylabel('magnitude (kΩ)')
plt.semilogx(nu, abs(Z)/1e3, 'o', color="#36913d", markersize=4.5)

# fit Y=kX where Y=|Z|, X=ν, k=2πL
k = simple_linear(nu, abs(Z), sigmaZ)
L = k/(2*np.pi)
f = lambda x: k.n*x

x = np.arange(nu.min()-10, nu.max(), 10)
plt.semilogx(x, f(x)/1e3, color='#589f22')

# phase
plt.subplot(2, 1, 2)
plt.xlabel('frequency (Hz)')
plt.ylabel('phase (rad)')
plt.semilogx(nu, Fiv, 'o', color="#36913d", markersize=4.5)
plt.show()


alpha = chi_squared_fit(nu, abs(Z), f, sigmaZ)

print(mformat('''
k: {}
L: {} H

χ² test:
  α={:.2f}, α>ε: {}
''', k, L,
     alpha, alpha>epsilon))



# plot, fit H₁(ν)
plt.figure(5)
plt.clf()

# magnitude
plt.subplot(2,1,1)
plt.title('transfer function 1')
plt.ylabel('magnitude (Vout-Vin / Vout)')
plt.semilogx(nu, abs(H1), 'o', color="#9b2e83", markersize=4.5)

# fit Y=kX where Y=|H1|, X=ν, k=2πL/R
k = simple_linear(nu, abs(H1), sigmaH1)
L = k*R/(2*np.pi)
f = lambda x: k.n/x

x = np.arange(nu.min()-10, nu.max(), 10)
plt.semilogx(x, f(x), color='#9b2e83')

# phase
plt.subplot(2,1,2)
plt.xlabel('frequency (Hz)')
plt.ylabel('phase (rad)')
plt.semilogx(nu, Fab, 'o', color="#3a44ad", markersize=4.5)
plt.show()

alpha = check_measures(R*C, RCo)
beta  = chi_squared_fit(nu, abs(H1), f, sigmaH1)

print(mformat('''
k:   {} Hz
RC:  {} s
RCₒ: {} s

compatibility test:
  α={:.2f}, α>ε: {}

χ² test:
  β={:.2f}, β>ε: {}
''', k, R*C, RCo,
     alpha, alpha>epsilon,
     beta, beta>epsilon))


# plot, fit H₂(ν)
plt.figure(6)
plt.clf()

# magnitude
plt.subplot(2,1,1)
plt.title('transfer function 2')
plt.ylabel('magnitude (Vout / Vin)')
plt.semilogx(nu, abs(H2), 'o', color="#9b2e83", markersize=4.5)

# fit Y=a+bX where Y=1/|H₂|², X=1/ν², a=1, b=1/(2πRC)²
a,b = linear(1/nu**2, 1/abs(H2)**2, 0.01)
RCo = 1/(2*np.pi*um.sqrt(b))
f   = lambda x: 1/np.sqrt(1 + b.n/x**2)                 # magnitude
g   = lambda x: -np.pi/2 + np.arctan(2*np.pi*x*R.n*C.n) # phase

x = np.arange(nu.min()-10, nu.max(), 10)
plt.semilogx(x, f(x), color='#9b2e83')

# phase
plt.subplot(2,1,2)
plt.xlabel('frequency (Hz)')
plt.ylabel('phase (rad)')
plt.semilogx(nu, Fab, 'o', color="#3a44ad", markersize=4.5)
plt.semilogx(x, g(x))
plt.show()

alpha = check_measures(R*C, RCo)
beta  = chi_squared_fit(nu, abs(H2), f, sigmaH2)
gamma = chi_squared_fit(nu, Fab, g, sigmaF)

print(mformat('''
b:   {}
RC:  {} s
RCₒ: {} s

compatibility test:
  α={:.2f}, α>ε: {}

χ² test (magnitude):
  β={:.2f}, β>ε: {}

χ² test (phase):
γ={:.2f}, γ>ε: {}
''', b, R*C, RCo,
     alpha, alpha>epsilon,
     beta, beta>epsilon,
     gamma, gamma>epsilon))