Interactive gaussian anamorphosis modeling with hermite polynomials

In [1]:

    

#general imports
import pygslib    
import pandas as pd
import matplotlib.pyplot as plt
from scipy.stats import norm
import numpy as np

#make the plots inline
%matplotlib inline
#%matplotlib notebook


    

In [2]:

    

#get the data in gslib format into a pandas Dataframe
data= pd.DataFrame({'Z':[2.582,3.087,3.377,3.974,4.321,5.398,8.791,12.037,12.586,16.626]})
data['Declustering Weight'] = 1.0
data


    

    
Out[2]:







  

    

      

      
Z
      
Declustering Weight
    
  
  

    

      
0
      
2.582
      
1.0
    
    

      
1
      
3.087
      
1.0
    
    

      
2
      
3.377
      
1.0
    
    

      
3
      
3.974
      
1.0
    
    

      
4
      
4.321
      
1.0
    
    

      
5
      
5.398
      
1.0
    
    

      
6
      
8.791
      
1.0
    
    

      
7
      
12.037
      
1.0
    
    

      
8
      
12.586
      
1.0
    
    

      
9
      
16.626
      
1.0
    
  

In [3]:

    

# Fit anamorphosis by changing, zmax, zmin, and extrapolation function
PCI, H, raw, zana, gauss, z, P, raw_var, PCI_var, fig1 = pygslib.nonlinear.anamor(
                 z = data['Z'], 
                 w = data['Declustering Weight'], 
                 zmin = data['Z'].min()-0.1, 
                 zmax = data['Z'].max()+1,
                 zpmin = None,
                 zpmax = data['Z'].max()+1.5,
                 ymin=-2.9, ymax=2.9,
                 ndisc = 5000,
                 ltail=1, utail=4, ltpar=1, utpar=1.8, K=30)


    

    




Raw Variance 21.852658090000006
Variance from PCI 21.555664573944906
zamin 3.5831255436568172
zamax 17.62284064974921
yamin -0.5284856971394278
yamax 1.8407081416283257
zpmin 2.582186575932491
zpmax 17.626
ypmin -1.644628925785157
ypmax 2.9






    

In [4]:

    

PCI


    

    
Out[4]:





array([ 7.27790000e+00, -4.28017669e+00,  1.23871656e+00,  8.36635528e-01,
       -6.68299991e-01, -2.67099171e-01,  3.81680849e-01,  1.21473386e-01,
       -2.34521491e-01, -9.19686922e-02,  1.63655484e-01,  9.40550953e-02,
       -1.34835534e-01, -9.94912223e-02,  1.27990204e-01,  9.92405431e-02,
       -1.31132432e-01, -9.16450599e-02,  1.37233489e-01,  7.78705229e-02,
       -1.42399754e-01, -5.99727890e-02,  1.44727712e-01,  4.00525389e-02,
       -1.43555404e-01, -1.99037236e-02,  1.38964127e-01,  8.96923975e-04,
       -1.31445919e-01,  1.60246501e-02,  1.21684077e-01])

In [5]:

    

ZV, PV, fig2 = pygslib.nonlinear.anamor_blk( PCI, H, r = 0.6, gauss = gauss, Z = z,
                  ltail=1, utail=1, ltpar=1, utpar=1,
                  raw=raw, zana=zana)


    

In [6]:

    

# the pair ZV, PV define the CDF in block support
# let's plot the CDFs
plt.plot (raw,P, '--k', label = 'exp point' ) 
plt.plot (z,P, '-g', label = 'ana point(fixed)' )  #point support (from gaussian anamorphosis)
plt.plot (ZV, PV, '-m',  label = 'ana block(fixed)')  #block support 
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)


    

    
Out[6]:





<matplotlib.legend.Legend at 0x18eee3fe5f8>






    

In [7]:

    

cutoff = np.arange(0,10, 0.1)
tt = []
gg = []
label = []

# calculate GTC from gaussian in block support 
t,ga,gb = pygslib.nonlinear.gtcurve (cutoff = cutoff, z=ZV, p=PV, varred = 1, ivtyp = 0, zmin = 0, zmax = None,
             ltail = 1, ltpar = 1, middle = 1, mpar = 1, utail = 1, utpar = 1,maxdis = 1000)
tt.append(t)
gg.append(ga)
label.append('DGM with block support')

# calculate GTC using undirect lognormal 
t,ga,gb = pygslib.nonlinear.gtcurve (cutoff = cutoff, z=z, p=P, varred = 0.4, ivtyp = 2, zmin = 0, zmax = None,
             ltail = 1, ltpar = 1, middle = 1, mpar = 1, utail = 1, utpar = 1,maxdis = 1000)
tt.append(t)
gg.append(ga)
label.append('Indirect Lognormal Correction')

# calculate GTC using affine 
t,ga,gb = pygslib.nonlinear.gtcurve (cutoff = cutoff, z=z, p=P, varred = 0.4, ivtyp = 1, zmin = 0, zmax = None,
             ltail = 1, ltpar = 1, middle = 1, mpar = 1, utail = 1, utpar = 1,maxdis = 1000)
tt.append(t)
gg.append(ga)
label.append('Affine Correction')

# calculate GTC in point support  
t,ga,gb = pygslib.nonlinear.gtcurve (cutoff = cutoff, z=z, p=P, varred = 1, ivtyp = 2, zmin = 0, zmax = None,
             ltail = 1, ltpar = 1, middle = 1, mpar = 1, utail = 1, utpar = 1,maxdis = 1000)
tt.append(t)
gg.append(ga)
label.append('Point (anamorphosis without support effect)')


    

In [8]:

    

fig = pygslib.nonlinear.plotgt(cutoff = cutoff, t = tt, g = gg, label = label)


    

In [9]:

    

PCI, H, raw, zana, gauss, raw_var, PCI_var, ax2 = pygslib.nonlinear.anamor_raw(
                         z = data['Z'], 
                         w = data['Declustering Weight'], 
                         K=30)


    

    




Raw Variance 21.852658090000006
Variance from PCI 17.711466254644904






    

In [10]:

    

PCI


    

    
Out[10]:





array([ 7.27790000e+00, -3.82759336e+00,  1.24799451e+00,  6.92707152e-01,
       -6.28915708e-01, -2.09662489e-01,  3.54248744e-01,  9.63864927e-02,
       -2.37930194e-01, -7.09406273e-02,  1.98369413e-01,  6.10707998e-02,
       -1.93103671e-01, -4.65978068e-02,  1.99154287e-01,  2.41314403e-02,
       -2.04493057e-01,  4.12778575e-03,  2.03539527e-01, -3.45670477e-02,
       -1.94519949e-01,  6.37931546e-02,  1.77830408e-01, -8.92156210e-02,
       -1.54998367e-01,  1.09170439e-01,  1.28023728e-01, -1.22843431e-01,
       -9.89695792e-02,  1.30114975e-01,  6.97202334e-02])

In [12]:

    

print (zana)


    

    




[ 2.582       3.42678628  4.18832472  4.31839029  4.499497    5.60005213
  7.95648663 10.99765187 13.13519958 16.626     ]

In [ ]: