# 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)


## measured quantities
R  = ufloat(996, 4)    # resistor
Rl = ufloat(19.9, 0.1) # internal resistance (inductor)

# frequency
nu = array(60, 100, 200, 500, 800, 1.2e3, 1.6e3, 2e3, 3e3, 5e3,
           10e3, 15e3, 20e3, 30e3, 40e3, 50e3, 80e3, 100e3, 200e3, 300e3)

# V input
Va = array(9.60, 9.60, 9.60, 9.60, 9.60, 9.60, 9.60, 9.80, 9.80, 9.80,
           9.80, 9.60, 9.60, 9.80, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0)/2

# V output
Vb = array(9.40, 9.40, 9.20, 9.20, 9.20, 9.20, 9.20, 9.40, 9.20, 9.20,
           8.30, 7.45, 6.81, 5.77, 5.20, 4.63, 3.45, 2.96, 1.73, 1.21)/2

# time offset Va - Vb
Oab = -array(100e-6, 80e-6, 20e-6,   20e-6,  12e-6,   8e-6,   8e-6,   8e-6, 6e-6, 3e-6,
            4.5e-6, 4.1e-6, 3.9e-6, 3.5e-6, 3.1e-6, 2.8e-6, 2.1e-6, 1.8e-6, 1.1e-6, 780e-9)

# time offset I - V
Oiv = array( 3e-4,  2.1e-4, 1e-4,  65e-6,  88e-6, 80e-6,  78e-6,  72e-6,   56e-6,  40e-6,
            22e-6, 16.1e-6, 12.2e-6, 8.2e-6, 6.1e-6, 4.9e-6, 3.1e-6, 2.5e-6, 1.26e-6, 840e-9)


## derived quantities
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], 0.15), ufloat(Va[0], 0.15)

# uncertainties Oiv
sigmaOiv = array(5e-4,  5e-4,  5e-4,  1e-06, 1e-06, 1e-06, 1e-06, 1e-06, 1e-06, 1e-06,
                 1e-06, 1e-07, 1e-07, 1e-07, 1e-07, 1e-07, 1e-07, 1e-07, 5e-08, 5e-08)

# uncertainties Oab
sigmaOab = array(5e-06, 5e-06, 5e-06, 5e-06, 2e-06, 2e-06, 2e-06, 2e-06, 2e-06, 2e-06,
                 2e-07, 2e-07, 2e-07, 2e-07, 2e-07, 2e-07, 2e-07, 2e-07, 2e-07, 2e-08)

# phase uncertainties
sigmaFiv = sigmaOiv * 2*np.pi*nu
sigmaFab = sigmaOab * 2*np.pi*nu

# magnitude ucnertainties
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.xscale('log')
plt.ylabel('magnitude (kΩ)')
plt.scatter(nu, abs(Z)/1e3, color="#36913d")

x = np.arange(nu.min()-10, nu.max()+2e3, 10)

# fit |Z|(ω) = √(Rl² + (iωL)²)
f = lambda x, Rl, L: np.sqrt(Rl**2 + (2*np.pi*L * x)**2)
f, (Rlo, L1) = curve(nu, abs(Z), f, sigmaZ, guess=[Rl.n, 0.04], method='trf')
plt.plot(x, f(x)/1e3, color="#36913d")

alpha = check_measures(Rl, Rlo)
beta  = chi_squared_fit(nu, abs(Z), f, sigmaZ)

print(mformat('''
# fit magnitude Z
L₁:  {} H
Rlₒ₁: {} Ω

compatibility test Rl/Rlₒ₁:
  α={:.2f}, α>ε: {}

χ² test:
  β={:.2f}, β>ε: {}
''', L1, Rlo,
     alpha, alpha>epsilon,
     beta, beta>epsilon))

# phase
plt.subplot(2, 1, 2)
plt.xscale('log')
plt.xlabel('frequency (Hz)')
plt.ylabel('phase (rad)')
plt.scatter(nu, Fiv, color="#33859d")

# fit ∠Z(ω) = arctan(ωL/Rl)
f = lambda x, Rl, L: np.arctan(2*np.pi*x*L/Rl)
f, (Rlo2, L2) = curve(nu, Fiv, f, sigmaFiv, guess=[Rl.n, L1.n])
plt.plot(x, f(x), color="#245361")
plt.show()

alpha = check_measures(Rl, Rlo2)
beta  = chi_squared_fit(nu, Fiv, f, sigmaFiv)

print(mformat('''
# fit phase Z 
L₂:  {} H
Rlₒ₂: {} Ω

compatibility test Rl/Rlₒ₂:
  α={:.2f}, α>ε: {}

χ² test:
  β={:.2f}, β>ε: {}
''', L2, Rlo2,
     alpha, alpha>epsilon,
     beta, beta>epsilon))


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

# magnitude
plt.subplot(2,1,1)
plt.title('transmission function 1')
plt.xscale('log')
plt.ylabel('amplitude (Vout-Vin / Vout)')
plt.scatter(nu, abs(H1), color="#2e3340")

# fit |H₁|(ω) = √(Rl² + (iωL)²)/R
f = lambda x, R, L: np.sqrt(Rl.n**2 + (2*np.pi*L*x)**2)/R
f, (Ro1, L1) = curve(nu, abs(H1), f, sigmaH1, guess=[R.n, L1.n]) # NB. does not converge adding Rl
plt.plot(x, f(x), color="#61778d")

alpha = check_measures(R, Ro1)
beta  = chi_squared_fit(nu, abs(H1), f, sigmaH1)

print(mformat('''
# fit magnitude H₁
L₁:   {} H
Rₒ₁:  {} Ω

compatibility test R/Rₒ₁:
  α={:.2f}, α>ε: {}

χ² test:
  γ={:.2f}, γ>ε: {}
''', L1, Ro1,
     alpha, alpha>epsilon,
     beta,  beta>epsilon))

# phase
plt.subplot(2,1,2)
plt.xscale('log')
plt.xlabel('frequency (Hz)')
plt.ylabel('phase (rad)')
plt.scatter(nu, Fab, color="#a54242")

# fit ∠H₁(ω) = arctan(-ωL/(R+Rl))
f = lambda x, Re, L: np.arctan(-2*np.pi*L/Re * x)
f, (Re, L2) = curve(nu, Fab, f, sigmaFab, guess=[Rl.n+R.n, L1.n])
plt.plot(x, f(x), color='#cc6666')
plt.show()

alpha = check_measures(Rl+R, Re)
beta  = chi_squared_fit(nu, Fab, f, 2*sigmaFab)

print(mformat('''
# fit phase H₁
L₂: {} H
Re: {} Ω

compatibility test (Rl+R)/Re:
  α={:.2f}, α>ε: {}

χ² test:
  β={:.2f}, γ>ε: {}
''', L2, Re,
     alpha, alpha>epsilon,
     beta,  beta>epsilon))


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

# magnitude
plt.subplot(2,1,1)
plt.title('transmission function 2')
plt.xscale('log')
plt.ylabel('amplitude (Vout / Vin)')
plt.scatter(nu, abs(H2), color='#845336')

# fit |H₂|(ω) = R/√((Rl+R)² + (ωL)²) ≈ 1/√(1 + (iωL)²)
f = lambda x, R, L: 1/np.sqrt(1 + (2*np.pi*L*x/R)**2)
f, (Ro1, L1) = curve(nu, abs(H2), f, sigmaH2, guess=[R.n, L1.n])
plt.plot(x, f(x), color="#8c4f4a")

alpha = check_measures(R, Ro1)
beta  = chi_squared_fit(nu, abs(H2), f, sigmaH2)

print(mformat('''
# fit magnitude H₂
L₁:   {} H
Rₒ₁:  {} Ω

compatibility test R/Rₒ₁:
  α={:.2f}, α>ε: {}

χ² test:
  γ={:.2f}, γ>ε: {}
''', L1, Ro1,
     alpha, alpha>epsilon,
     beta,  beta>epsilon))

# phase
plt.subplot(2,1,2)
plt.xscale('log')
plt.xlabel('frequency (Hz)')
plt.ylabel('phase (rad)')
plt.scatter(nu, Fab, color='#5c6652')

# fit ∠H₁(ω) = arctan(-ωL/(R+Rl))
f = lambda x, Re, L: np.arctan(-2*np.pi*L/Re * x)
f, (Re, L2) = curve(nu, Fab, f, sigmaFab, guess=[Rl.n+R.n, L1.n])
plt.plot(x, f(x), color='#718062')
plt.show()

alpha = check_measures(Rl+R, Re)
beta  = chi_squared_fit(nu, Fab, f, 2*sigmaFab)

print(mformat('''
# fit phase H₂
L₂: {} H
Re: {} Ω

compatibility test (Rl+R)/Re:
  α={:.2f}, α>ε: {}

χ² test:
  β={:.2f}, γ>ε: {}
''', L2, Re,
     alpha, alpha>epsilon,
     beta,  beta>epsilon))
plt.show()