new figures: paper
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37
kalman/graphics/figure_func.py
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kalman/graphics/figure_func.py
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import matplotlib.pyplot as plt
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import numpy as np
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from itertools import cycle
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import argparse
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import pickle
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import yaml
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from matplotlib import rc
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rc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})
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rc('text', usetex=True)
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u = np.linspace(-2,2,100)
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utrue = 1
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venc1 = 0.9*utrue
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venc2 = 0.6*utrue
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fig1, ax1 = plt.subplots(1,1,figsize=(8, 5))
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J1 = 1 - np.cos((utrue-u)/venc1*np.pi)
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J2 = 1 - np.cos((utrue-u)/venc2*np.pi)
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lwidth = 2
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font_size = 28
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ax1.plot(u, J1, color = 'orangered', label = '$venc = 0.9 u_{true}$', linestyle='-',linewidth=lwidth)
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ax1.plot(u, J2, color = 'dodgerblue', label = '$venc = 0.6 u_{true}$', linestyle='-',linewidth=lwidth)
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ax1.axvline(x=1,color = 'black',linewidth = lwidth , label = '$u_{true}$')
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ax1.legend(fontsize=20, loc= 'upper right')
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ax1.tick_params(axis='both', which='major', labelsize=22)
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ax1.set_yticks([])
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ax1.set_xlabel('$u$',fontsize=font_size)
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plt.show()
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fig1.savefig('functionals.png', dpi=500, bbox_inches='tight')
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170
kalman/graphics/figure_func2.py
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kalman/graphics/figure_func2.py
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import matplotlib.pyplot as plt
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import numpy as np
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from itertools import cycle
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import argparse
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import pickle
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import yaml
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from matplotlib import rc
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rc('font',**{'family':'sans-serif','sans-serif':['Helvetica']})
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rc('text', usetex=True)
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fig1, ax1 = plt.subplots(1,1,figsize=(8, 5))
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lwidth = 2
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font_size = 28
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################ Flow Parameters
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Rd = 2.5
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Rt = 0.5
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GradP = 4
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mu = 0.5
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fac = 1
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nr = 50
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VENC = 0.6
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gamma = 267.513e6 # rad/Tesla/sec Gyromagnetic ratio for H nuclei
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Bo = 1.5 # Tesla Magnetic Field Strenght
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TE = 5e-3 # Echo-time
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M = np.ones(nr) # Magnetization
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phi0 = gamma*Bo*TE # Reference phase
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phi02 = phi0%3.14
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M1 = np.pi/(gamma*VENC)
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ff = np.pi/(1000*gamma*M1)
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uv = np.arange(-4*VENC,4*VENC,ff)
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r = np.linspace(-Rd, Rd, nr)
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dr = r[2]-r[1]
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vmax = 1
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v = vmax/Rt**2*( Rt**2 - r**2 )*(np.abs(r)<Rt); # Poiseuille Formula
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ai = v/vmax
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theta = np.linspace(-4,5,2000)
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vtest = np.linspace(-5,5,2000)
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JF = 0*theta
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jv = 0*theta
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JV = 0*theta
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Mjv = np.zeros([len(theta),len(ai)])
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jv0 = 0*theta
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JV0 = 0*theta
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Mjv0 = np.zeros([len(theta),len(ai)])
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#################################### MAGNETIZACION FROM V
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phiv = phi02 + v*np.pi/VENC
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modv = np.ones(phiv.shape)
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M1 = modv*np.cos(phi02) + 1j*modv*np.sin(phi02)
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M2 = modv*np.cos(phiv) + 1j*modv*np.sin(phiv)
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################################### FFT to COMPLEX M
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S1 = np.fft.fft(M1)
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S2 = np.fft.fft(M2)
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################################### SubSampling
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a1 = 0
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a2 = 1
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##### FILLED WITH ZEROS
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US1 = S1
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US2 = 0*S2
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US2[a1::a2] = S2[a1::a2]
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MR1 = np.fft.ifft(US1)
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MR2 = np.fft.ifft(US2)
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vrec1 = (np.angle(MR2)-phi02)*VENC/(np.pi)
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for k in range(len(ai)):
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jv0 = 1-np.cos(np.pi*(vrec1[k]-vtest)/VENC)
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Mjv0[:,k] = jv0[:]
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JV0 = JV0 + jv0
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for k in range(len(ai)):
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jv = 1-np.cos(np.pi*(vrec1[k]-theta*ai[k])/VENC)
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Mjv[:,k] = jv[:]
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JV = JV + jv
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NJV1 = JV*100/np.max(JV)
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MV = Mjv0
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V =NJV1
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left, bottom, width, height = [0.2, 0.2, 0.1, 0.1]
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fig = plt.figure(figsize=(12, 6), dpi=100)
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ax1 = plt.subplot(1,2,1)
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ch1 = 20
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ch2 = 23
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ax0 = fig.add_axes([left, bottom, width, height])
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ax0.plot(r,v,'b-')
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ax0.plot([r[ch1]],[v[ch1]],color='xkcd:coral',marker='o')
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ax0.plot([r[ch2]],[v[ch2]],color='xkcd:azure',marker='o')
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ax0.set_xlim((-1.5,1.5))
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#for k in range(22,39):
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# if k!=ch1 and k!=ch2 and np.sum(MV[:,k])!=0:
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# ax1.plot(vtest, MV[:,k],color='xkcd:beige',alpha=0.8)
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ax1.plot(vtest, MV[:,ch1],color='xkcd:coral',label='$v_1$')
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ax1.plot(vtest, MV[:,ch2],color='xkcd:azure',label='$v_2$')
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m1x = vtest[np.where( np.abs(MV[:,ch1] - np.min(MV[:,ch1]))<0.001 )]
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m1y = np.min(MV[:,ch1])
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m2x = vtest[np.where( np.abs(MV[:,ch2] - np.min(MV[:,ch2]))<0.001 )]
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#m2x = vtest[np.where(MV[:,ch2]==np.min(MV[:,ch2]))]
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m2y = np.min(MV[:,ch2])
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ax1.plot([m1x],[m1y],color='xkcd:coral',marker='o')
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ax1.plot([m2x],[m2y],color='xkcd:azure',marker='o')
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ax1.axvline(x=v[ch1], color='xkcd:coral', linestyle='--',label='$v_{1,true}$')
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ax1.axvline(x=v[ch2], color='xkcd:azure', linestyle='--',label='$v_{2,true}$')
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ax1.set_xlabel(r'$u$',fontsize=20)
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ax1.set_ylabel(r'$J_i(u)$',fontsize=20)
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#ax1.legend(loc='upper right', bbox_to_anchor=(0.5, 1.05),ncol=2, fancybox=True, shadow=True,fontsize=15)
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ax1.set_yticks([])
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ax1.set_xticks([])
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ax1.set_xlim((-3.5,3.5))
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ax1.set_ylim((-1.0,2.4))
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ax2 = plt.subplot(1,2,2)
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ax2.plot(theta,V,'b-')
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ax2.axvline(x=1, color='k', linestyle='--')
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ax2.set_xlabel(r'$\theta$',fontsize=20)
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ax2.set_ylabel(r'$J_T(\theta)$',fontsize=20)
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plt.yticks([])
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ax2.set_xticks([])
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plt.title(r'$\theta_{true}=1$' + '\n' +'$venc < v_{max}$',fontsize=15)
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plt.xlim((-2,3))
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plt.show()
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#ax1.plot(u, J1, color = 'orangered', label = '$venc = 0.9 u_{true}$', linestyle='-',linewidth=lwidth)
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#ax1.plot(u, J2, color = 'dodgerblue', label = '$venc = 0.6 u_{true}$', linestyle='-',linewidth=lwidth)
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#ax1.axvline(x=1,color = 'black',linewidth = lwidth , label = '$u_{true}$')
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ax1.legend(fontsize=20, loc= 'upper right')
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ax1.tick_params(axis='both', which='major', labelsize=22)
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ax1.set_yticks([])
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ax1.set_xlabel('$u$',fontsize=font_size)
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plt.show()
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#fig1.savefig('functionals.png', dpi=500, bbox_inches='tight')
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