#!/usr/bin/env python
# *-----------------------------------------------------------------------*
# |                                                                       |
# |  Copyright (c) 2019 by Paul Scherrer Institute (http://www.psi.ch)    |
# |                                                                       |
# |              Author Thierry Zamofing (thierry.zamofing@psi.ch)        |
# *-----------------------------------------------------------------------*
'''
Trajectory comparison:
pvt: position velocity time
p0t: position velocity=0 time
ift: inverse fourier transformation

-> look at trajectory and frequency components
'''
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt

def gen_pvt(p,v,t,ts):
  '''generates a pvt motion
     p: position array
     v: velocity array
     t: time array
     ts: servo cycle time
     !!! it is assumed, that the time intervals are constant !!!
     '''
  return
  pvt=np.ndarray(len(tt))*0
  t[-1]/ts

  tt1=np.arange(0,t[1]-t[0],ts)
  for i in range(len(t)-1):
    d=p[i]
    c=v[i]
    a=(-2*(p[i+1]-p[i]-v[i]*w)+w*(v[i+1]-v[i]))/w**3
    b=(3*w*(p[i+1]-p[i]-v[i]*w)-w**2*(v[i+1]-v[i]))/w**3
    pvt[i*n:(i+1)*n]=a*tt1**3+b*tt1**2+c*tt1+d

  return pvt

w=40.  # ms step between samples
ts=.2 # sampling time
n=int(w/ts)# servo cycle between samples
k=8  #number of unique samples

t = np.arange(0, w*(k+1), w)  #time array of trajectory

#p=3.*np.cos(t)+4.             #position array of trajectory
np.random.seed(10)
p=np.random.random(k+1)*4.  #position array of trajectory
#p=3.*np.sin(1.3+2.*t/(w*k)*2.*np.pi)+10.         #position array of trajectory
#p+=np.cos(1.5*t/(w*k)*2.*np.pi)         #position array of trajectory


p[-1]=p[0]                # put the first position at the end

tt = np.arange(t[0],t[-1], ts) #time array of servo cycles
ax=plt.gca()
ax.xaxis.set_ticks(t)
markerline, stemlines, baseline = ax.stem(t, p, '-')


#best trajectory with lowest frequency
p_iftf=np.fft.fft(p[:-1])
ft=np.hstack((p_iftf[:k/2],np.zeros((n-1)*k),p_iftf[k/2:]))
pp_ift=np.fft.ifft(ft)*n

ax.plot(tt,pp_ift,'-b',label='ift')

#plt.figure()
#ax=plt.gca()
#ax.xaxis.set_ticks(x)
#markerline, stemlines, baseline = ax.stem(x, y, '-')

#PVT move
p2=np.hstack((p[-2],p,p[1]))

v=(p2[2:]-p2[:-2])/(w*2)

gen_pvt(p,v,t,ts)


pp_pvt=np.ndarray(len(tt))*0
tt1=tt[:n]
for i in range(len(t)-1):
  d=p[i]
  c=v[i]
  a=( -2*(p[i+1]-p[i]-v[i]*w)+   w*(v[i+1]-v[i]))/w**3
  b=(3*w*(p[i+1]-p[i]-v[i]*w)-w**2*(v[i+1]-v[i]))/w**3
  pp_pvt[i*n:(i+1)*n]=a*tt1**3+b*tt1**2+c*tt1+d

ax.plot(tt,pp_pvt,'-g',label='pvt')

#PVT move with stop 
v*=0
pp_p0t=np.ndarray(len(tt))*0
for i in range(len(t)-1):
  d=p[i]
  c=v[i]
  a=( -2*(p[i+1]-p[i]-v[i]*w)+   w*(v[i+1]-v[i]))/w**3
  b=(3*w*(p[i+1]-p[i]-v[i]*w)-w**2*(v[i+1]-v[i]))/w**3
  pp_p0t[i*n:(i+1)*n]=a*tt1**3+b*tt1**2+c*tt1+d

ax.plot(tt,pp_p0t,'-r',label='p0t')

ax.legend(loc='best')
plt.show(block=False)


fig=plt.figure()
ax=fig.add_subplot(1,1,1)#ax=plt.gca()

#normalize with l -> value of k means amplitude of k at a given frequency
pp_iftf=np.fft.rfft(pp_ift)/(2*n)
pp_pvtf=np.fft.rfft(pp_pvt)/(2*n)
pp_p0tf=np.fft.rfft(pp_p0t)/(2*n)

f=np.fft.rfftfreq(pp_ift.shape[0], d=ts*1E-3)
f=f[1:] #remove dc value frequency

mag=abs(pp_iftf[1:])#; mag=20*np.log10(abs(mag))
ax.semilogx(f,mag,'-b',label='ift')  # Bode magnitude plot
mag=abs(pp_pvtf[1:])#; mag=20*np.log10(abs(mag))
ax.semilogx(f,mag,'-g',label='pvt')  # Bode magnitude plot
mag=abs(pp_p0tf[1:])#; mag=20*np.log10(abs(mag))
ax.semilogx(f,mag,'-r',label='p0t')  # Bode magnitude plot
#ax.yaxis.set_label_text('dB ampl')
ax.yaxis.set_label_text('ampl')
ax.xaxis.set_label_text('frequency [Hz]')
plt.grid(True)

ax.legend(loc='best')
plt.show(block=False)
plt.show()