In [ ]:
import prettyplotlib as ppl
# prettyplotlib imports
import matplotlib.pyplot as plt
from prettyplotlib import brewer2mpl
In [55]:
from collections import OrderedDict
try:
from operators import *
except ImportError:
import sys
sys.path.append ( "../eoldas_ng/")
from operators import *
state_config = OrderedDict ()
state_config['n'] = FIXED
state_config['cab'] = VARIABLE
state_config['car'] = FIXED
state_config['cbrown'] = FIXED
state_config['cw'] = FIXED
state_config['cm'] = FIXED
state_config['lai'] = VARIABLE
state_config['ala'] = FIXED
state_config['bsoil'] = FIXED
state_config['psoil'] = FIXED
# Now define the default values
default_par = OrderedDict ()
default_par['n'] = 1.5
default_par['cab'] = 40.
default_par['car'] = 10.
default_par['cbrown'] = 0.01
default_par['cw'] = 0.018 # Say?
default_par['cm'] = 0.0065 # Say?
default_par['lai'] = 2
default_par['ala'] = 45.
default_par['bsoil'] = 1.
default_par['psoil'] = 0.1
parameter_min = OrderedDict()
parameter_max = OrderedDict()
min_vals = [ 0.8, 0.2, 0.0, 0.0, 0.0043, 0.0017,0.01, 40, 0., 0., 0.]
max_vals = [2.5, 77., 5., 1., 0.0713, 0.0331, 8., 50., 2., 1.]
for i, param in enumerate ( state_config.keys() ):
parameter_min[param] = min_vals[i]
parameter_max[param] = max_vals[i]
# Define parameter transformations
transformations = {
'lai': lambda x: np.exp ( -x/2. ), \
'cab': lambda x: np.exp ( -x/100. ), \
'car': lambda x: np.exp ( -x/100. ), \
'cw': lambda x: np.exp ( -50.*x ), \
'cm': lambda x: np.exp ( -100.*x ), \
'ala': lambda x: x/90. }
inv_transformations = {
'lai': lambda x: -2*np.log ( x ), \
'cab': lambda x: -100*np.log ( x ), \
'car': lambda x: -100*np.log( x ), \
'cw': lambda x: (-1/50.)*np.log ( x ), \
'cm': lambda x: (-1/100.)*np.log ( x ), \
'ala': lambda x: 90.*x }
# Define the state grid. In time in this case
state_grid = np.arange ( 1, 366 )
# Define the state
# L'etat, c'est moi
state = State ( state_config, state_grid, default_par, \
parameter_min, parameter_max )
# Set the transformations
state.set_transformations ( transformations, inv_transformations )
In [56]:
from gp_emulator import MultivariateEmulator
angles = [ [15, 15, 0] ]
#emulator, samples, validate = create_emulators ( state, [""], angles=angles )
#for i,(s,v,r) in enumerate(angles):
# fname = "%02d_sza_%02d_vza_000_raa" % (s,v)
# emulator[i].dump_emulator(fname)
#emulators = {}
#emulators[(s,v)] = emulator[0]
emulators = {}
for i,(s,v,r) in enumerate(angles):
fname = "%02d_sza_%02d_vza_000_raa.npz" % (s,v)
emulators[(v,s)]= MultivariateEmulator ( dump=fname )
Decomposing the input dataset into basis functions... Done!
====> Using 8 basis functions
In [57]:
b_min = np.array([433.0, 457.5, 542.5, 650.0, 697.5, 732.5, 773.0, 784.5, 855.0, 935.0, 1565.0, 2100.0])
b_max = np.array([453.0, 522.5, 577.5, 680.0, 712.5, 747.5, 793.0, 899.5, 875.0, 955.0, 1655.0, 2280.0])
from create_emulators import *
def cab_traj ( t ):
out = t*0.
w = np.where( t <= 0.5 )[0]
out[w] = 10.5 + 70*t[w]
w = np.where(t > 0.5)[0]
out[w] = 80.5 - 70.*t[w]
return out
trajectories = {
'lai': lambda t: (0.21 + 3.51 * (np.sin(np.pi*t)**5)),
'cab': cab_traj}
# 'cw': lambda t: (0.068/5 + 0.01*np.sin(np.pi * t+0.1) * \
# np.sin(6*np.pi*t + 0.1) ),
# 'bsoil': lambda t: (2.5*(0.2 + 0.18*np.sin(np.pi*t) * \
# np.sin(6*np.pi*t)) )
#}
# Now, create some simulated data...
parameter_grid = create_parameter_trajectories ( state, trajectories )
plt.plot ( np.arange(1, 366), parameter_grid[6, :], label="LAI" )
plt.xlabel( "DoY" )
plt.ylabel ("LAI [$m^{2}m^{-2}$]")
# Now forward model the observations...
doys, vza, sza, raa, rho = create_observations ( state, parameter_grid, \
42, -8., b_min=b_min, b_max=b_max)
In [58]:
[plt.plot ( doys, rho[i,:]) for i in xrange(12)]
Out[58]:
[[<matplotlib.lines.Line2D at 0x2b1e60c046d0>],
[<matplotlib.lines.Line2D at 0x2b1e60c04950>],
[<matplotlib.lines.Line2D at 0x2b1e60c0b050>],
[<matplotlib.lines.Line2D at 0x2b1e60c0b690>],
[<matplotlib.lines.Line2D at 0x2b1e60c0bcd0>],
[<matplotlib.lines.Line2D at 0x2b1e60c24790>],
[<matplotlib.lines.Line2D at 0x2b1e60c24c10>],
[<matplotlib.lines.Line2D at 0x2b1e60c24590>],
[<matplotlib.lines.Line2D at 0x2b1e60c2b650>],
[<matplotlib.lines.Line2D at 0x2b1e60c2bc90>],
[<matplotlib.lines.Line2D at 0x2b1e60c2e310>],
[<matplotlib.lines.Line2D at 0x2b1e60c2e950>]]
In [59]:
mu_prior = OrderedDict ()
prior_inv_cov = OrderedDict ()
for param in state.parameter_min.iterkeys():
mu_prior[param] = np.array([default_par[param]])
prior_inv_cov['n'] = 0.5
prior_inv_cov['cab'] = 60.
prior_inv_cov['car'] = 20.
prior_inv_cov['cbrown'] = 1.
prior_inv_cov['cw'] = 0.1
prior_inv_cov['dm'] = 0.1
prior_inv_cov['lai'] = 5.
prior_inv_cov['ala'] = 90.
prior_inv_cov['bsoil'] = 3
prior_inv_cov['bsoil'] = 2.
for k in prior_inv_cov.iterkeys():
prior_inv_cov[k] = np.array([1./( prior_inv_cov[k]**2 )])
prior = Prior ( mu_prior, prior_inv_cov )
In [60]:
temporal = TemporalSmoother ( state_grid, 5500, required_params=["cab"] )
In [61]:
rho_big = np.zeros(( 12,365))
mask = np.zeros(( 365, 4))
band_pass = np.zeros((12,2101), dtype=np.bool)
n_bands = b_min.shape[0]
bw = np.zeros( n_bands )
bh = np.zeros( n_bands )
wv = np.arange ( 400, 2501 )
for i in xrange( n_bands ):
band_pass[i,:] = np.logical_and ( wv >= b_min[i], \
wv <= b_max[i] )
bw[i] = b_max[i] - b_min[i]
bh[i] = ( b_max[i] + b_min[i] )/2.
for i in state_grid:
if i in doys:
rho_big[:, i] = rho[:, doys==i].squeeze()
mask[ i, :] = [ 1, vza[doys==i], sza[doys==i], raa[doys==i] ]
bu = np.array( [0.004, 0.00416142, 0.00440183, 0.00476245, 0.00489983, 0.00502003, 0.00516772, 0.00537035, \
0.00544934, 0.0057241, 0.00800801, 0.01] )
obs = ObservationOperatorTimeSeriesGP( state_grid, state, rho_big, mask, emulators, bu, band_pass, bw )
In [62]:
x_dict = {}
for i,k in enumerate(state.parameter_max.keys()):
if state.state_config[k] == VARIABLE:
x_dict[k] = ( parameter_grid[i, :] )*0 + np.random.rand(365)*mu_prior[k]
else:
x_dict[k] = parameter_grid[i, 0]
In [63]:
state.add_operator ( "Prior", prior )
state.add_operator ( "Model", temporal )
state.add_operator ( "Obs", obs )
In [64]:
retval = state.optimize ( x_dict )
Prior 34.388291
Model 253953790.135043
Obs 151018.880161
Prior 98.440074
Model 4306701988.632087
Obs 283520.610381
Prior 34.313814
Model 251210064.657731
Obs 150329.148138
Prior 27.716354
Model 542402053.070929
Obs 49369.855305
Prior 34.063198
Model 242039518.007158
Obs 148011.019357
Prior 34.062468
Model 242012953.446160
Obs 148004.274535
Prior 25.641685
Model 67123854.101267
Obs 65708.562152
Prior 24.346738
Model 16396811.353727
Obs 2365.883318
Prior 24.318678
Model 9584941.755332
Obs 1193.492620
Prior 23.965484
Model 6834313.108830
Obs 1141.998172
Prior 23.403001
Model 5389150.810424
Obs 951.241437
Prior 22.814278
Model 4878414.636236
Obs 863.691079
Prior 22.436716
Model 4518867.028823
Obs 777.896820
Prior 22.015272
Model 4238629.088858
Obs 716.853037
Prior 21.388278
Model 3958598.851796
Obs 655.527832
Prior 20.581198
Model 4075275.502109
Obs 561.562138
Prior 21.375675
Model 3953012.369933
Obs 653.408569
Prior 21.375631
Model 3952993.077837
Obs 653.401177
Prior 20.933823
Model 3875231.990581
Obs 590.408801
Prior 20.477374
Model 3717400.908197
Obs 547.761128
Prior 20.078893
Model 3653242.105959
Obs 521.425882
Prior 19.871682
Model 3547468.502300
Obs 515.432234
Prior 19.835581
Model 3456407.204033
Obs 515.242346
Prior 19.748019
Model 3355763.303753
Obs 515.742748
Prior 19.647366
Model 3287339.598323
Obs 521.340586
Prior 19.570894
Model 3209689.710215
Obs 526.525324
Prior 19.552688
Model 3153756.321974
Obs 527.501634
Prior 19.548551
Model 3108302.519369
Obs 528.588526
Prior 19.566622
Model 3075494.662234
Obs 527.004016
Prior 19.602937
Model 3058228.188128
Obs 527.159792
Prior 19.622994
Model 3036346.180748
Obs 528.609773
Prior 19.650278
Model 3021213.869491
Obs 527.669951
Prior 19.700302
Model 3009817.520463
Obs 526.765928
Prior 19.778643
Model 3001868.713711
Obs 522.989051
Prior 19.800045
Model 2993156.871528
Obs 522.731571
Prior 19.839704
Model 2986167.994181
Obs 522.499726
Prior 19.900622
Model 2982068.805796
Obs 521.209655
Prior 20.030140
Model 2983031.983360
Obs 522.240969
Prior 19.903676
Model 2981744.032173
Obs 521.222599
Prior 19.903682
Model 2981743.458148
Obs 521.222623
Prior 19.965687
Model 2978922.396102
Obs 521.608996
Prior 20.032521
Model 2976631.460448
Obs 520.346127
Prior 20.096541
Model 2974566.064961
Obs 520.142418
Prior 20.201609
Model 2972102.653695
Obs 518.558242
Prior 20.270727
Model 2969826.034588
Obs 517.753245
Prior 20.358387
Model 2967891.207870
Obs 517.480146
Prior 20.457041
Model 2967067.709157
Obs 516.320862
Prior 20.608786
Model 2966659.876957
Obs 515.244996
Prior 20.759657
Model 2966056.156105
Obs 514.916767
Prior 20.841424
Model 2964914.249978
Obs 514.175081
Prior 20.972898
Model 2963676.243198
Obs 512.801716
Prior 21.172752
Model 2963453.476666
Obs 511.281883
Prior 21.349479
Model 2962909.927865
Obs 509.141937
Prior 21.478560
Model 2962258.778576
Obs 507.703803
Prior 21.583386
Model 2962147.237019
Obs 506.830370
Prior 21.751338
Model 2962436.943191
Obs 505.502782
Prior 21.587033
Model 2962105.711996
Obs 506.799212
Prior 21.587046
Model 2962105.568117
Obs 506.799101
Prior 21.668908
Model 2961736.405310
Obs 506.126942
Prior 21.896860
Model 2962324.049658
Obs 504.726856
Prior 21.671776
Model 2961718.290792
Obs 506.107599
Prior 21.671792
Model 2961718.192229
Obs 506.107492
Prior 21.783856
Model 2961524.303205
Obs 505.385856
Prior 22.098184
Model 2963807.678592
Obs 504.227176
Prior 21.785256
Model 2961515.723509
Obs 505.379414
Prior 21.785264
Model 2961515.676027
Obs 505.379378
Prior 21.940813
Model 2961621.154741
Obs 504.734612
Prior 21.791673
Model 2961478.618914
Obs 505.350048
Prior 21.791710
Model 2961478.415234
Obs 505.349880
Prior 21.866052
Model 2961310.471365
Obs 505.026973
Prior 22.214019
Model 2963065.888730
Obs 502.839459
Prior 21.868225
Model 2961299.025030
Obs 505.011211
Prior 21.868239
Model 2961298.952640
Obs 505.011110
Prior 22.039995
Model 2961299.075445
Obs 503.847986
Prior 22.322294
Model 2964755.392917
Obs 501.912628
Prior 22.040655
Model 2961297.790631
Obs 503.842781
Prior 22.040666
Model 2961297.770136
Obs 503.842697
Prior 22.180712
Model 2962030.114130
Obs 502.810403
Prior 22.041428
Model 2961296.344316
Obs 503.836694
Prior 22.041441
Model 2961296.320786
Obs 503.836593
Prior 22.110886
Model 2961416.523331
Obs 503.307328
Prior 22.042532
Model 2961294.386257
Obs 503.828011
Prior 22.042551
Model 2961294.353028
Obs 503.827859
Prior 22.076672
Model 2961295.684729
Obs 503.563732
Prior 22.359948
Model 2962673.305637
Obs 501.761010
Prior 22.078313
Model 2961291.157997
Obs 503.552023
Prior 22.078331
Model 2961291.108430
Obs 503.551893
Prior 22.218353
Model 2961448.836481
Obs 502.606416
Prior 22.081589
Model 2961282.563617
Obs 503.528679
Prior 22.081627
Model 2961282.467792
Obs 503.528410
Prior 22.149802
Model 2961238.185591
Obs 503.055909
Prior 22.536133
Model 2967507.469675
Obs 500.026084
Prior 22.150471
Model 2961237.362886
Obs 503.049841
Prior 22.150488
Model 2961237.341742
Obs 503.049681
Prior 22.341905
Model 2962693.956472
Obs 501.428425
Prior 22.151196
Model 2961236.517185
Obs 503.043257
Prior 22.151216
Model 2961236.494795
Obs 503.043078
Prior 22.246210
Model 2961547.744245
Obs 502.209689
Prior 22.152017
Model 2961235.619472
Obs 503.035811
Prior 22.152041
Model 2961235.594181
Obs 503.035593
Prior 22.199039
Model 2961288.978305
Obs 502.616364
Prior 22.153108
Model 2961234.524075
Obs 503.025922
Prior 22.153143
Model 2961234.490733
Obs 503.025604
Prior 22.176070
Model 2961237.238115
Obs 502.819502
Prior 22.555972
Model 2963568.565014
Obs 499.881910
Prior 22.177835
Model 2961233.144237
Obs 502.804073
Prior 22.177859
Model 2961233.089626
Obs 502.803864
Prior 22.365540
Model 2961606.774963
Obs 501.256476
Prior 22.180464
Model 2961227.312033
Obs 502.781117
Prior 22.180501
Model 2961227.232583
Obs 502.780795
Prior 22.272685
Model 2961223.362284
Obs 501.998722
Prior 22.644878
Model 2969741.574346
Obs 500.980315
Prior 22.273163
Model 2961222.491538
Obs 501.996770
Prior 22.273172
Model 2961222.476048
Obs 501.996734
Prior 22.457539
Model 2963192.742304
Obs 501.366568
Prior 22.273682
Model 2961221.582176
Obs 501.994652
Prior 22.273692
Model 2961221.565684
Obs 501.994613
Prior 22.365245
Model 2961636.669392
Obs 501.651383
Prior 22.274282
Model 2961220.578037
Obs 501.992208
Prior 22.274294
Model 2961220.559061
Obs 501.992161
Prior 22.319677
Model 2961287.694019
Obs 501.814693
Prior 22.275139
Model 2961219.229404
Obs 501.988722
Prior 22.275156
Model 2961219.202590
Obs 501.988650
Prior 22.297395
Model 2961219.526830
Obs 501.899983
Prior 22.629764
Model 2963718.811120
Obs 499.495518
Prior 22.298626
Model 2961218.712558
Obs 501.889943
Prior 22.298694
Model 2961218.669830
Obs 501.889389
Prior 22.463071
Model 2961794.073036
Obs 500.623889
Prior 22.299990
Model 2961217.901225
Obs 501.878836
Prior 22.300072
Model 2961217.855536
Obs 501.878170
Prior 22.381286
Model 2961339.593901
Obs 501.234947
Prior 22.301501
Model 2961217.112941
Obs 501.866539
Prior 22.301608
Model 2961217.061458
Obs 501.865667
Prior 22.341378
Model 2961238.235181
Obs 501.546523
Prior 22.303325
Model 2961216.316681
Obs 501.851714
Prior 22.303490
Model 2961216.253035
Obs 501.850375
Prior 22.322419
Model 2961218.141501
Obs 501.697600
Prior 22.305850
Model 2961215.494134
Obs 501.831220
Prior 22.306213
Model 2961215.402574
Obs 501.828276
Prior 22.314313
Model 2961215.103905
Obs 501.762783
Prior 22.319662
Model 2961216.734457
Obs 501.719727
Prior 22.314653
Model 2961215.164234
Obs 501.760045
Prior 22.314313
Model 2961215.103905
Obs 501.762783
Prior 22.790910
Model 2968499.632860
Obs 497.553174
Prior 22.315181
Model 2961213.418969
Obs 501.753682
Prior 22.315195
Model 2961213.392496
Obs 501.753536
Prior 22.550814
Model 2962817.365435
Obs 499.475126
Prior 22.316164
Model 2961211.580757
Obs 501.743387
Prior 22.316180
Model 2961211.551353
Obs 501.743219
Prior 22.432939
Model 2961507.156854
Obs 500.567089
Prior 22.317440
Model 2961209.302526
Obs 501.730029
Prior 22.317462
Model 2961209.264649
Obs 501.729801
Prior 22.375063
Model 2961233.946581
Obs 501.138391
Prior 22.320459
Model 2961204.401366
Obs 501.698463
Prior 22.320516
Model 2961204.315835
Obs 501.697870
Prior 22.347759
Model 2961191.255950
Obs 501.415901
Prior 22.815168
Model 2964763.338512
Obs 498.185126
Prior 22.349494
Model 2961189.258655
Obs 501.401717
Prior 22.349545
Model 2961189.201731
Obs 501.401300
Prior 22.580101
Model 2961958.644912
Obs 499.659146
Prior 22.351491
Model 2961187.106600
Obs 501.385407
Prior 22.351553
Model 2961187.042879
Obs 501.384905
Prior 22.465270
Model 2961321.738753
Obs 500.491121
Prior 22.354094
Model 2961184.538696
Obs 501.364185
Prior 22.354182
Model 2961184.456314
Obs 501.363466
Prior 22.409593
Model 2961193.068208
Obs 500.920141
Prior 22.359878
Model 2961179.788232
Obs 501.317144
Prior 22.360120
Model 2961179.618113
Obs 501.315179
Prior 22.384830
Model 2961174.374184
Obs 501.116254
Prior 22.394089
Model 2961178.567379
Obs 501.042544
Prior 22.894315
Model 2969332.809262
Obs 497.632449
Prior 22.394926
Model 2961177.271952
Obs 501.035315
Prior 22.394942
Model 2961177.246502
Obs 501.035170
Prior 22.642014
Model 2963036.842196
Obs 499.122000
Prior 22.395845
Model 2961175.908969
Obs 501.027376
Prior 22.395864
Model 2961175.881593
Obs 501.027213
Prior 22.518286
Model 2961553.774725
Obs 500.024531
Prior 22.396936
Model 2961174.373065
Obs 501.017959
Prior 22.396960
Model 2961174.340729
Obs 501.017755
Prior 22.457462
Model 2961228.113695
Obs 500.509128
Prior 22.398641
Model 2961172.151995
Obs 501.003263
Prior 22.398681
Model 2961172.102353
Obs 501.002918
Prior 22.428034
Model 2961168.001842
Obs 500.753219
Prior 22.913361
Model 2965210.125658
Obs 497.231029
Prior 22.429598
Model 2961167.731436
Obs 500.739758
Prior 22.431386
Model 2961167.532986
Obs 500.724392
Prior 22.669892
Model 2962172.379134
Obs 498.831443
Prior 22.432902
Model 2961167.457061
Obs 500.711377
Prior 22.588763
Model 2961604.535081
Obs 499.440021
Prior 22.434372
Model 2961167.464333
Obs 500.698762
Prior 22.536033
Model 2961359.094965
Obs 499.855215
Prior 22.435770
Model 2961167.545114
Obs 500.686781
Prior 22.434583
Model 2961167.471915
Obs 500.696953
Prior 22.434372
Model 2961167.464333
Obs 500.698762
Prior 23.005192
Model 2971540.866720
Obs 497.803108
Prior 22.435210
Model 2961166.812613
Obs 500.693094
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Model 2961166.785389
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Model 2963664.440728
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Model 2961166.171426
Obs 500.687049
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Model 2961166.143292
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Model 2961744.393247
Obs 499.801200
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Model 2961165.555894
Obs 500.680677
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Model 2961165.525968
Obs 500.680350
Prior 22.506151
Model 2961289.168939
Obs 500.228118
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Model 2961164.946768
Obs 500.673621
Prior 22.438156
Model 2961164.913254
Obs 500.673205
Prior 22.472102
Model 2961186.815529
Obs 500.447638
Prior 22.439371
Model 2961164.307270
Obs 500.665018
Prior 22.439462
Model 2961164.265866
Obs 500.664402
Prior 22.455770
Model 2961166.239583
Obs 500.555326
Prior 22.441282
Model 2961163.563342
Obs 500.652154
Prior 22.441479
Model 2961163.501390
Obs 500.650833
Prior 22.448622
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In [68]:
plt.plot(retval['lai'])
Out[68]:
[<matplotlib.lines.Line2D at 0x1357ec10>]
In [65]:
Content source: jgomezdans/eoldas_ng_notebooks
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