%%javascript
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from IPython import display

Imports ..

import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d import axes3d
import pandas as pd

from rotate import rotanimate
import matplotlib.animation as animation
import subprocess
from IPython.display import Image

from matplotlib import cm
from IPython.display import Video
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import scale
plt.style.use('seaborn-whitegrid')

plt.rcParams["figure.figsize"] = [10,6]

#import numpy as np
#import matplotlib.pyplot as plt
#from mpl_toolkits.mplot3d import Axes3D
from sklearn import decomposition
from sklearn import datasets
from sklearn.preprocessing import StandardScaler

from itertools import chain
import math

import seaborn as sns; sns.set() # styling

from functools import reduce
import functools
import operator

from numpy.polynomial import polynomial as P

from scipy.interpolate import CubicSpline


#### Defaults
sns.set_style("darkgrid", {"axes.facecolor": ".9"})
plt.rcParams.update({'font.size': 12})
import seaborn as sns; sns.set() # styling

Functions

def foldl(func, acc, xs):
  return functools.reduce(func, xs, acc)

# tests
#print(foldl(operator.sub, 0, [1,2,3])) # -6
#print(foldl(operator.add, 'L', ['1','2','3'])) # 'L123'

def scanl_plus(data):
    '''
    returns list of successive reduced values from the list (see haskell foldl)
    '''
    return [0] + [sum(data[:(k+1)]) for (k,v) in enumerate(data)]

def make1D (data):
      return np.array(list(map (lambda x : [x],data)))

def celsius_to_fahr(temp):
    return 9/5 * temp + 32

def gen_answers_from_alphas(inputs, new_alphas):
  return (np.matmul(inputs,new_alphas))


def polyfitx(x, y, degree):
    results = {}

    coeffs = np.polyfit(x, y, degree)

     # Polynomial Coefficients
    results['polynomial'] = coeffs.tolist()

    # r-squared
    p = np.poly1d(coeffs)
    # fit values, and mean
    yhat = p(x)                         # or [p(z) for z in x]
    ybar = np.sum(y)/len(y)          # or sum(y)/len(y)
    ssreg = np.sum((yhat-ybar)**2)   # or sum([ (yihat - ybar)**2 for yihat in yhat])
    sstot = np.sum((y - ybar)**2)    # or sum([ (yi - ybar)**2 for yi in y])
    results['determination'] = ssreg / sstot

    return results

def showECResults (title,ec_alphas, actual_alphas, principle_vals,ans, ans_scaler):
    AxH2 = principle_vals.dot (ec_alphas)
    new_nnAnsH2 = ans_scaler.inverse_transform (AxH2)
    rH2 = np.corrcoef(ans,(new_nnAnsH2.reshape(-1,)))
    rSq = (rH2[1,0])**2
    print(rSq)
    fig, ax = plt.subplots(1,2)
    ax[0].plot(ans,new_nnAnsH,'o', color='green',marker=".", markersize=1);
    ax[1].plot(ec_alphas, color='green',marker=".", markersize=10);
    ax[1].plot(actual_alphas, ':o', color='orange',marker=".", markersize=12);
    fig.suptitle(title)
    plt.show()

def left_inverse (m ):
    return (np.linalg.solve (m.T.dot(m), m.T))

# Two ways to compute this ..
# rsq = 1 - residual / sum((y - y.mean())**2) 
#or
# rsq = 1 - residual / (n * y.var())
# https://stackoverflow.com/questions/3054191/converting-numpy-lstsq-residual-value-to-r2
def lstsq_rsq (output_from_lstsq, inputs, answers):
    rsq_ = 1 - output_from_lstsq[1] / sum ((answers - answers.mean())**2)
    return (rsq_[0])

def drawVector (origins,vectors):
    vectors_np = np.array(vectors)
    #origins = ([[0,0],[0,0]])
    V = vectors_np
    origins_t = zip(*origins) 

    fig, ax = plt.subplots()
    fig.set_size_inches(8,8)
    origins_l = np.array(list(map(lambda t: list(t),origins_t)))

    q = ax.quiver(*origins_l, (list(V[:,0])), (list(V[:,1])), color=['r','b','g','r'], scale=1,units='xy')
    ax.set_aspect('equal')
    lim = 7
    plt.xlim(-lim,lim)
    plt.ylim(-lim,lim)

    plt.title('Vector Tutorial',fontsize=10)

    #plt.savefig('savedFig.png', bbox_inches='tight')
    #print (type(q))

    plt.show()

    
    
# Reduce Example
#reduce(lambda a,b: a+b, [1,2,3,4,5], 0)b

Notes

New Fitness Scaling Method
Selection Methods
Is Crossover Necessary?

• Refactor ... FEM .. i.e. Fitness, Engine, and Metrics modules
• Learn Chart or some graphing in Haskell
• Use Cubic Splines as representation ..
• Try gross evolution then hand the population to new run with tiny deltas ..

Software versions ..

• v04d_hack_301_pareto_splines - Spawned from v04d_hack_301_pareto. Adding cubic splines.
• v04d_hack_301_pareto_newIC - Tried initializing population with single gaussian and then using pareto to add some inflections. Added too many!

• v04d_hack_301_pareto - Up to date graphing functions. Simple pareto with two weights, smoothness and fit. No fitness scaling. No PSO. Reduces 301 cols to 50 by skipping uniformly. Fitness E. 10 steps per sec. Threading forkOS.

• v04d_hack_301 - Old graphing functions. Full 301 fitness. No fitness scaling. No PSO. Fitness D. 1 step per sec. Threading forkOS.

• v04d_hack - Old graphing functions. Fitness C. PSO polyVals. 30 steps per second (problematic?). Threading forkOS.

• v04f_rank_poly - Old graphing fuctions. Fitness Scaling. PolyVals.

Probs / To Do

• Add noise to fitness?
• Look at result of alphas and find one that has the correct amount of smoothness. Don't just rely on the generation method. This way we could go back to the straight 301 with no PSO!
• Go back to MSE and compare
• Do R G B in sections?
• Limit the size of transitions not just the number of transitions.
• Initialize with gaussian (tried it .. added deep transitions)
• Add crossover
• Read selection paper .. search for more?
• Select 10 points and use cubic spline fit.
• Make 'c' changes logarithmic ..?
• What about assembling piecewise lines end to end .. Seems easy to evolve.
• Make the curve fit of columnar results the fitness ..
• Remove last point which goes way high ..?
• Find memory leak ..
  • Make 'random' datatype outside of World which must be strict and go to MVar.Strict
  • Or go back to really old version and find original memory leak .. Two problems?
• What is the Linear Algebra solution to the PCA space?
• List all the problems
  • Graphing large vectors
  • Why were pca_alphas 21! (not 20)
  • Skipping generation
  • Delay in 'bDead'
  • Occasional crazy scatterplot
  • Adding printout solves generation skip?
  • Adding printout solves memory leak
• Incredible Pareto Video and Part II and Part III and Base and his university site and his website with source code.

x = [1,2,3,4,5,6,7,8]
np.array_split(x,2)

[array([1, 2, 3, 4]), array([5, 6, 7, 8])]

Read In the Raw Data

Read No Noise Full File PSD Data

df=pd.read_csv('nonoise.txt', sep=' ',header=None, index_col=False)
noNoise = df.values
nnInputs = noNoise[:,0:301] # Do not include index 301 (from zero)
nnAnswers = noNoise[:,301]

And noisy data .. (Jay says it's 'Green' channel)

df=pd.read_csv('withnoise.txt', sep=' ',header=None, index_col=False)
withNoise = df.values
wnInputs = withNoise[:,0:301] # Do not include index 301 (from zero)
wnAnswers = withNoise[:,301]

Read the Solution (Alphas)

df=pd.read_csv('solution.txt', sep=' ',header=None, index_col=False)
solution_alphas = df.values
#alphasT = np.transpose(alphas)

For fun let's look at the alphas (The 'Solution')**

### Data Prep ..

PCA Intro and Reversal

Make fitness cases by stitching together ins and out

ans1D =  make1D (nnAnswers) # Why did I have to do this?
fCases = np.append (nnInputs,ans1D,axis=1)
ansN1D =  make1D (wnAnswers) # Why did I have to do this?
fCasesN = np.append (wnInputs,ansN1D,axis=1)

Scale everything

# Separate the Scaler since we have to unscale later
nnAnswers_scaler = StandardScaler()
nnAnswers_scaled = nnAnswers_scaler.fit_transform(make1D(nnAnswers)) # Returns scaled data

wnAnswers_scaler = StandardScaler()
wnAnswers_scaled = wnAnswers_scaler.fit_transform(make1D(wnAnswers)) # Returns scaled data

# Here we don't need to unscale later
nnInputs_scaler = StandardScaler()
nnInput_scaled  = nnInputs_scaler.fit_transform(nnInputs) # Returns scaled data
wnInputs_scaler = StandardScaler()
wnInputs_scaled = wnInputs_scaler.fit_transform(wnInputs) # Returns scaled data
fcases_scaler   = StandardScaler()
fcases_scaled   = fcases_scaler.fit_transform(fCases)      # Returns scaled data
fcasesN_scaler  = StandardScaler()
fcasesN_scaled  = fcasesN_scaler.fit_transform(fCasesN)     # Returns scaled data

Do the PCAs on both nonoise and noisy data

# # Restrict to 20 Cols of PCA to match Haskell

# pca = decomposition.PCA(n_components=20)          # Creates PCA object
# #pca = decomposition.PCA()                        # Creates PCA object
# principle_vals = pca.fit_transform(ins_scaled)    # Returns values in PCA space
# vr = scanl_plus ( pca.explained_variance_ratio_ ) # make it cumulative (TPP)
# nnPCAs = pca.components_
# #print("Variance Ratios =>\n", vr,"\n")
# principle_vals.shape
# nnPCAs.shape

# pcaN = decomposition.PCA(n_components=20)          # Creates PCA object
# principle_valsN = pcaN.fit_transform(insN_scaled)  # Return values in PCA space
# vrN = scanl_plus ( pcaN.explained_variance_ratio_ ) # make it cumulative (TPP)
# wnPCAs = pcaN.components_
# print("Variance Ratios =>\n", vr,"\n")

PCA's from SolveIt

Testing

toy_ins = np.array([[1, 4, 3],
          [4, 6, 2],
          [3, 5, 4],
          [2, 2, 1],
          [6, 6, 1]])

good_ans = np.array([18, 22, 25,  9, 21])

Set up the variables

#theInputs = toy_ins
#theAnswers = good_ans
theInputs = nnInput_scaled
theAnswers = nnAnswers_scaled
print(type(theInputs))
print(type(theAnswers))

<class 'numpy.ndarray'>
<class 'numpy.ndarray'>

toy_pca = decomposition.PCA(n_components=20)          # Creates PCA object
toy_princ_vals = toy_pca.fit_transform(theInputs)          # Returns values in PCA space
toy_vr = scanl_plus ( toy_pca.explained_variance_ratio_ ) # make it cumulative (TPP)
toy_pcas = toy_pca.components_

print(toy_princ_vals.shape)
print(toy_pcas.shape)
print(toy_vr)
print ("PCA Comoponents -> ", toy_pcas)
fileLoc = "/home/poliquin/projects/haskell/spectral_gloss/v04f_rank_poly/princ_vals.txt"
np.savetxt(fileLoc, toy_pcas, delimiter=" ")
#toy_princ_vals

(2696, 20)
(20, 301)
[0, 0.6451305526885969, 0.8787441855101644, 0.969589930346075, 0.9819021285116154, 0.9900781178484294, 0.9944059631086525, 0.9970722530205748, 0.9981092875973703, 0.9988144335897361, 0.9992615141113722, 0.9995618209466858, 0.9997226786785737, 0.9998232231028523, 0.9998876794241796, 0.9999267586743797, 0.9999483384695654, 0.9999609739943436, 0.9999691794925978, 0.9999752360910276, 0.9999798750098277]
PCA Comoponents ->  [[ 0.05417707  0.05426636  0.05436478 ...  0.05305204  0.05293906
   0.05285003]
 [-0.04666828 -0.04730076 -0.04797522 ...  0.06354007  0.06343562
   0.06331325]
 [-0.07145471 -0.07178997 -0.07210116 ... -0.05442511 -0.05428631
  -0.05416527]
 ...
 [ 0.13707347  0.09589262  0.05664363 ... -0.01824525 -0.00740694
  -0.01540639]
 [-0.02340342 -0.02643498 -0.02058622 ...  0.14581786  0.23709236
   0.25801936]
 [ 0.12231762  0.07705105  0.03527201 ...  0.11695219  0.13035027
   0.14630297]]

Scale the outs

good_ans_scaler = StandardScaler()
#good_ans_scaled   = good_ans_scaler.fit_transform(make1D(theAnswers)) # Returns scaled data
good_ans_scaled   = good_ans_scaler.fit_transform(theAnswers) # Returns scaled data
good_ans_scaled

array([[-0.09891512],
       [-0.992661  ],
       [ 0.22974179],
       ...,
       [ 1.12491251],
       [ 0.74211336],
       [ 0.45913732]])

Compute the input column means

These are required to get the alphas back into real space

col_means = np.array(list(map (lambda i: np.mean (theInputs[:,i]), range(0,len(theInputs[0]),1))))
print("Column means -> ", col_means)

Column means ->  [ 9.85034672e-17 -1.31447771e-16 -1.72957593e-16 -4.57925817e-17
 -1.12010632e-17  4.48042526e-17  1.25188353e-17  1.64721517e-16
  1.02127341e-16 -1.80534783e-16 -1.18928935e-16  1.66368732e-16
  6.78652650e-17 -4.94164551e-17 -1.05421771e-17 -1.65380403e-16
 -1.75263694e-16  1.77240352e-16  9.22440495e-17  3.01110933e-16
  6.25941765e-17 -6.58886068e-17 -4.80986830e-17 -3.03087591e-17
 -2.22703491e-16 -9.02673913e-17  9.22440495e-18 -1.00809568e-16
  7.05008093e-17  2.44776174e-16  1.01139011e-16  2.26986250e-16
  1.01468454e-16 -3.13959211e-16  1.02786227e-16  1.14316733e-16
 -2.24021263e-17  7.24774675e-17 -7.51130118e-17  9.05968344e-17
  1.80534783e-16  1.05421771e-17  9.86681887e-17 -9.88329102e-19
 -5.66642019e-17 -1.48249365e-17 -1.41660505e-16  2.09196327e-16
 -1.55167669e-16 -2.05901896e-17 -1.42319391e-16  4.20039868e-17
  7.67602269e-17  1.23376416e-16 -1.41660505e-16  2.94851515e-17
 -6.62180498e-17  1.58132656e-16  3.42620755e-17  5.83114170e-17
 -1.83664491e-16 -3.68976198e-17 -1.78887567e-16  1.73287036e-16
  2.15455744e-16  2.67178301e-16 -9.29029356e-17  1.12010632e-16
  3.95331641e-17  2.04254681e-17  1.27165011e-16  0.00000000e+00
  8.10429864e-17  3.95331641e-18  2.04254681e-17 -2.52353364e-16
 -3.03087591e-17 -1.97665820e-17 -1.35730530e-16  2.76732149e-17
 -1.19917264e-16  5.33697715e-17  9.22440495e-18 -1.62085973e-16
  1.18599492e-16  8.76318470e-17 -2.96498731e-17 -8.89496192e-17
  7.84074421e-17 -1.42978277e-16 -2.04254681e-17 -1.37048302e-16
 -1.50226024e-16  1.25847239e-16  2.96498731e-17  7.64307839e-17
  9.88329102e-17  2.37198984e-17 -2.63554427e-17  9.61973659e-17
  1.90418074e-16  1.64721517e-16  4.28275944e-17 -7.77485560e-17
 -1.44296049e-16  8.03841003e-17  1.31777214e-18  1.62744859e-16
  1.04762885e-16 -1.29141669e-16  4.87575690e-17 -3.42620755e-17
 -1.16622834e-16 -2.50376706e-17  3.95331641e-18 -1.87782529e-16
 -3.18900857e-16  8.82907331e-17  1.41660505e-16  3.49209616e-17
  4.87575690e-17 -1.58791542e-16 -3.29443034e-18 -2.33245668e-16
  3.95331641e-17 -5.86408601e-17 -8.56551888e-18 -2.17432402e-17
 -6.78652650e-17  1.80534783e-16 -1.12010632e-16  4.87575690e-17
 -3.88742780e-17  7.64307839e-17 -6.58886068e-18 -5.66642019e-17
  1.93053618e-16 -2.10843542e-17 -1.18599492e-16  1.60109315e-16
 -9.88329102e-17  6.39119486e-17 -3.42620755e-17  1.12669518e-16
  8.82907331e-17  1.83170327e-16 -1.20576150e-16  2.56306680e-16
 -1.38366074e-17  2.50376706e-17 -1.61427087e-16 -6.52297207e-17
 -4.21687084e-17 -9.42207077e-17 -5.40286576e-17  3.22854173e-17
 -1.64721517e-17  6.58886068e-19 -6.85241511e-17  9.22440495e-17
  7.70896700e-17 -9.22440495e-17  6.98419232e-17 -1.59450428e-16
 -6.98419232e-17 -2.24021263e-17 -2.37198984e-17 -1.71310378e-17
  6.58886068e-18  8.63140749e-17 -1.72628150e-16 -3.62387337e-17
 -1.46931593e-16  1.27165011e-16 -2.24021263e-17 -3.22854173e-17
 -2.28633466e-16  1.84488099e-17 -7.11596953e-17 -8.10429864e-17
 -6.85241511e-17 -2.08866884e-16 -6.45708347e-17 -4.74397969e-17
 -1.05751214e-16 -2.06231339e-16  2.37198984e-17 -1.40013289e-16
  1.50226024e-16 -1.00150682e-16 -1.94371390e-17  7.34657966e-17
 -4.80986830e-17  7.57718978e-17 -2.15455744e-16  1.71310378e-17
  1.23870581e-16  1.26506125e-16  6.58886068e-17 -3.95331641e-18
 -1.71310378e-17  5.86408601e-17 -1.68015947e-16  2.10843542e-17
  2.20726833e-16  1.14646176e-16  4.41453666e-17 -1.35071644e-16
 -1.70651492e-16 -1.58132656e-17  9.48795938e-17  1.36389416e-16
  1.54838226e-16 -6.12764043e-17 -1.44954935e-17  1.62744859e-16
  7.24774675e-18 -1.06739543e-16  1.77899238e-17 -5.66642019e-17
  1.52861568e-16 -6.72063789e-17  1.58132656e-17 -1.71310378e-17
 -5.66642019e-17 -5.07342272e-17 -6.72063789e-17  8.03841003e-17
 -3.09676452e-17  7.24774675e-17 -2.63554427e-16  8.56551888e-17
  2.37198984e-17 -8.30196446e-17  1.08057315e-16  0.00000000e+00
 -1.44954935e-16  9.22440495e-17  3.68976198e-17 -6.58886068e-18
  1.44954935e-17  1.05421771e-16 -6.06175183e-17  3.55798477e-17
 -6.72063789e-17  9.61973659e-17 -6.58886068e-17  1.44954935e-16
 -5.53464297e-17 -2.63554427e-18 -1.06739543e-16 -1.84488099e-16
  5.13931133e-17  3.68976198e-17 -7.90663282e-18 -9.48795938e-17
  8.30196446e-17  3.95331641e-18 -7.64307839e-17 -2.41152301e-16
  8.56551888e-17  8.82907331e-17 -1.06739543e-16 -3.68976198e-17
  1.46272707e-16  2.37198984e-16  1.29141669e-16  1.97665820e-17
 -1.58132656e-16 -2.24021263e-16  0.00000000e+00  2.50376706e-17
 -1.13328404e-16  2.95180958e-16  5.27108854e-18  1.31777214e-17
  2.37198984e-17  5.66642019e-17 -2.10843542e-17  2.37198984e-17
  2.63554427e-17 -1.31777214e-18 -1.51543796e-16  2.37198984e-17
 -4.25640400e-16 -1.52861568e-16  1.10692859e-16 -7.90663282e-18
 -1.18599492e-17  2.26656807e-16 -4.08509362e-17  9.75151381e-17
 -3.68976198e-17  1.33094986e-16 -5.27108854e-18 -1.97665820e-17
  1.69992606e-16  3.68976198e-17  1.02786227e-16 -2.31927896e-16
 -5.53464297e-17]

Solve for Alphas

#print (toy_princ_vals.shape)
#print (good_ans_scaled.shape)
pca_l_sq_scaled = np.linalg.lstsq(toy_princ_vals,good_ans_scaled,rcond=None)
print ("PCA Alphas (outs scaled) = ",pca_l_sq_scaled[0],"\n") 
pca_l_sq_scaled

PCA Alphas (outs scaled) =  [[ 6.78170269e-02]
 [-1.01594231e-02]
 [ 6.03470821e-02]
 [-8.73015346e-04]
 [-4.44310097e-03]
 [ 2.06643293e-03]
 [-1.92712148e-03]
 [ 5.46940716e-03]
 [-5.55982885e-03]
 [ 1.45246442e-03]
 [-1.60921457e-03]
 [-3.31126529e-03]
 [ 2.09471966e-03]
 [-9.25254756e-05]
 [-1.00536558e-03]
 [-8.66158366e-04]
 [ 9.82543760e-04]
 [ 1.18738206e-03]
 [-4.63167325e-05]
 [ 1.03544498e-03]] 

(array([[ 6.78170269e-02],
        [-1.01594231e-02],
        [ 6.03470821e-02],
        [-8.73015346e-04],
        [-4.44310097e-03],
        [ 2.06643293e-03],
        [-1.92712148e-03],
        [ 5.46940716e-03],
        [-5.55982885e-03],
        [ 1.45246442e-03],
        [-1.60921457e-03],
        [-3.31126529e-03],
        [ 2.09471966e-03],
        [-9.25254756e-05],
        [-1.00536558e-03],
        [-8.66158366e-04],
        [ 9.82543760e-04],
        [ 1.18738206e-03],
        [-4.63167325e-05],
        [ 1.03544498e-03]]),
 array([3.63361183e-06]),
 20,
 array([723.54741585, 435.40386836, 271.51603737,  99.95648835,
         81.45417511,  59.26237522,  46.51541248,  29.00947106,
         23.92118626,  19.04741597,  15.61082303,  11.42520923,
          9.0327957 ,   7.23229196,   5.63139905,   4.1847243 ,
          3.20213645,   2.58045132,   2.21695859,   1.94022268]))

Make sure $R^2$ is good ..

lstsq_rsq (pca_l_sq_scaled,toy_princ_vals,good_ans_scaled )

0.9999999986522211

Get the Alphas into Real Space

print(good_ans_scaler.scale_)
print(good_ans_scaler.mean_)
print(good_ans_scaler.var_)
good_ans_scaler_scale = good_ans_scaler.scale_

[1.]
[-2.74096604e-16]
[1.]

# Flatten the PCA space Alphas (lstsq puts them in arrays)
print(pca_l_sq_scaled[0])
theAlphas = list(chain(*pca_l_sq_scaled[0]))
print(theAlphas)
real_alphas = toy_pca.inverse_transform(theAlphas)
# unscale ..
unscaled_real_alphas = (real_alphas - col_means) * good_ans_scaler_scale

[[ 6.78170269e-02]
 [-1.01594231e-02]
 [ 6.03470821e-02]
 [-8.73015346e-04]
 [-4.44310097e-03]
 [ 2.06643293e-03]
 [-1.92712148e-03]
 [ 5.46940716e-03]
 [-5.55982885e-03]
 [ 1.45246442e-03]
 [-1.60921457e-03]
 [-3.31126529e-03]
 [ 2.09471966e-03]
 [-9.25254756e-05]
 [-1.00536558e-03]
 [-8.66158366e-04]
 [ 9.82543760e-04]
 [ 1.18738206e-03]
 [-4.63167325e-05]
 [ 1.03544498e-03]]
[0.06781702690833816, -0.010159423113796674, 0.06034708208694862, -0.000873015345645118, -0.004443100966043903, 0.002066432930260635, -0.001927121479514913, 0.005469407164784872, -0.005559828848051578, 0.0014524644155808476, -0.0016092145653626572, -0.003311265290781823, 0.002094719662176753, -9.252547564826967e-05, -0.0010053655812420112, -0.000866158365849512, 0.0009825437596887017, 0.0011873820581651767, -4.6316732485720504e-05, 0.0010354449829850713]

plt.plot(unscaled_real_alphas*1e2, ':o', color='orange',marker=".", markersize=5)
plt.plot(solution_alphas, ':o', color='green',marker=".", markersize=5)

[<matplotlib.lines.Line2D at 0x7f06e34aa880>]

Didn't work with reduced columns ... even though $R^2$ was excellent on the fitted alphas and the cumulative variance was excellent for two columns with the PCA.

ec_poly_rank01 = [0.8449558038279152,0.3132323191294367,-3.170415724563437,1.196680832431206,-3.4090217730428867,1.2159916999473972,2.449045012147218,-1.3410438248372558,2.0011437805053585,1.6435425161047663,1.079507139889698,-0.9662912417532618,-0.681489063622115,2.0348960776593583,1.3357098116970163,2.8531162916810406,1.74191157403334,0.9367496821294496,2.86493257456703,1.2199986399684761]

Now with EC Generated PCA Alphas

Set up the variables

ec_poly_rank01 = [0.8449558038279152,0.3132323191294367,-3.170415724563437,1.196680832431206,-3.4090217730428867,1.2159916999473972,2.449045012147218,-1.3410438248372558,2.0011437805053585,1.6435425161047663,1.079507139889698,-0.9662912417532618,-0.681489063622115,2.0348960776593583,1.3357098116970163,2.8531162916810406,1.74191157403334,0.9367496821294496,2.86493257456703,1.2199986399684761]
ec_poly_rank02 = [-2.2903971252789237,-0.8490632737961835,2.262458982671257,-0.8069591047539595,0.6894203536153004,-0.6171083535123605,-0.9023723456124368,0.3406312610317968,0.8556792419677984,-2.5549244352205362,-3.1233535688870315,-1.6796339414159907,-1.4048001853600092,-1.1537072537286406,0.30381222797926943,0.6489631524030987,1.8269325952337965,0.7779829786153122,2.3360175243516745,-1.2792054280372775]
ec_poly_rank03 = [-3.000580693731758,-1.616919310739846,-3.1196855808825683,-2.4178548774090958,2.4910666989554096,-0.9295743298745123,-0.24251282962350726,-0.49168554087123306,0.5982905385341685,-1.8290045970351996,2.027666805794077,-0.7321177791364367,-1.960655832837145,-0.8355711436154789,-2.5553485363600683,2.316377283440344,-3.0630638230793665,-1.1361804486825684,3.2294903418242438,-1.7716819050231118]
ec_poly_rank04 = [-2.118979075660875,-0.8181113501129376,0.45554965516158097,1.6939636406876686,1.722423753355394,-1.4146365525151103,2.937505194384543,-1.344293717862398,-2.7868557404477223,-1.6777532735072358]
ec_poly_rank05 = [-2.118970836618096,-0.8071114992800736,0.45555406358168316,1.6940247484427933,1.7224635030504603,-1.4146349077108737,2.9374563509262654,-1.344293717862398,-2.786849022383858,-1.6777535541722342]
ec_poly_rank06 = [ 1901.9694717555956, 976.084773231719, 420.7889559374729, 120.18740602516412, -16.228005496389024, -56.51649761011385, -49.225954138942264, -26.330498594068036, -6.168069023205003, 3.622007141155014, 3.1614382334843607, -2.604606493038448, -6.845071714786641, -3.780590885943122, 8.378938913241605, 24.496782128191462, 29.571789881746923, -4.199174874092952, -120.35881220642845, -381.1269600497172,  ]
ec_poly_rank07 = [ -620.8833339342359, 10.4010617478322, -107.07872071111768, -90.68448506686305, 3.7908545251129118, 45.252630810276045, 20.299450645279368, -17.744346973419646, -28.23960558298023, -13.394604806299975, 0.13714013833633024, -4.7604732757323625, -18.684882496390642, -18.58720285529115, 2.3322805952293457, 18.797086430940848, 0.252798675740205, -27.857788774341877, 19.258801459742337, -6.389566345166293, -1530.2382315795187,  ]
ec_poly_rank08 = [ -68581.93942645036, -83.33060277040215, -8673.470932210192, -10644.228362761613, -3037.4960218097713, 3657.9151125096682, 5128.1875202519595, 3165.520461454146, 945.5274638742906, -7.87150587146006, -22.621350734913406, 58.01819207977177, -1.547882143783182, 116.92989414102252, 363.45627007839596, -160.0191808346556, -1948.7541295149047, -2626.121590030612, 1897.4501064666247, 169.8595487890511, -92283.92921908444,  ]
ec_poly_rank09 = [ 752.7761822760516, -22.64864066062456, 140.18817813964256, 113.23278825031595, -8.929920108105227, -54.183344855346824, -15.220848737049742, 30.315215656663877, 30.204841568974313, -4.382350313775963, -29.199124859047387, -17.732877110509786, 13.884218536725637, 26.215537618886362, 2.081875416413935, -26.030947170669506, -9.057127017093961, 31.508579317993128, -17.280549765868603, 3.1524291704794325, 1886.4815636058465,  ]
ec_poly_rank10 = [ 71623.98561467548, 52.63942587598647, 8808.475445559092, 12233.275892326066, 6247.8835843556135, 402.3421380698238, -1416.7796839894752, -738.0150882757755, -21.269295480669268, -99.39144110500537, -375.5157698265052, -240.71858267581496, 75.68362407336534, -3.9001922388836874e-2, -194.77893687520483, 867.9266889439069, 3660.651305178472, 4594.320808335531, -1744.8056190104821, 854.133089124423, 124668.86619416502,  ]
ec_poly_rank11 = [ -261049.19034145496, -53105.039911091655, -276.7216730821912, 5825.047798711957, 3003.7359899862004, 859.27536101944, 131.8902316227554, 5.935989043226144, 1.0798802819318018e-2, -0.41668433218953316, -3.9076141688590346e-2, 1.0006650241320992e-2, 4.088012359922541e-2, -9.906451598767335, -53.08542726847258, -31.39168137336123, 544.6858784051209, 2365.430285334152, 3797.555464552106, -8027.533070493025,  ]
ec_poly_rank12 = [ 3318.471243624394, 1441.5320171988342, 408.43826544916004, -63.70992292184629, -194.46682579704895, -147.2210532469899, -36.3755131319243, 65.4726232961448, 120.35195579143185, 117.73688951233387, 67.3676694193956, -7.929585326725207, -79.42284696729236, -119.65414474752623, -109.61953051863848, -45.949044339866845, 51.913319919490334, 134.52964897803892, 115.28814454025452, -136.77684230555204,  ]
ec_poly_rank13 = [ -4366.2672718183585, -1913.4244599412034, -573.4471857655572, 30.866268576884448, 191.4812535542364, 124.85075259468873, -18.360617553223975, -143.55260646035686, -202.46532965668632, -183.45526827104328, -101.77126867084536, 10.16945789817042, 112.50533567221477, 167.65442472971398, 150.03842135157691, 55.80665838146285, -87.4398944139516, -210.92462998470498, -194.97130363728277, 140.71996732564847,  ]
ec_poly_rank14 = [ 1902.1276822865698, -50.67484169868943, 363.05702674733243, 283.3612082637628, -34.5140160851205, -148.74429859711879, -44.89591150081032, 74.12133196436521, 73.47899861050064, -16.37587501936798, -79.26185658662877, -45.79449493631218, 41.29866479861926, 77.02826881574802, 13.197693378614925, -67.79271773707704, -34.85651860350963, 67.22933179051317, -46.126783764135254, 4.400121411972903,  ]







#theInputs = toy_ins
#theAnswers = good_ans
theInputs = nnInput_scaled
theAnswers = nnAnswers_scaled
ecAlphas = np.array(ec_poly_rank14)
#print(type(theInputs))
#print(type(theAnswers))
ecAlphas.shape

(20,)

Convert the ECPolys to ECAlphas

Note: Here is how to do an (inverse_transform)[https://stackoverflow.com/questions/32750915/pca-inverse-transform-manually)

• The correct way to transform is
  data_reduced = np.dot(data - pca.mean_, pca.components_.T)
• The inverse_transform is just the inverse process of transform
  data_original = np.dot(data_reduced, pca.components_) + pca.mean_

Compute the polynomial

Note that the length of the fitness case inputs is 20, and the range of x's is
$\ \ \ \ \ 0.0 < x < 3.0$

# def calcValue (ind, anX):
#  return ( foldl (lambda power_value, b,:
#         (power_value[0]+1,(power_value[1]+b*anX**power_value[0])),
#                 (0.0,0.0), ind) )[1]

# def polyVals (ecVals,theLen):
# #  return list( map (\x -> calcValue ecVals x) [0.0,maxXValue/(fromIntegral len)..maxXValue])
#          return list(map (lambda x : calcValue (ecVals,x),np.arange(0,3, 3/theLen)))

# def dot (theAs, theBs):
#    return ( sum (list (map (lambda a,b : a*b, theAs, theBs))))

# ecAlphas = polyVals(ecPolys,10)

toy_pca = decomposition.PCA(n_components=20)          # Creates PCA object
toy_princ_vals = toy_pca.fit_transform(theInputs)          # Returns values in PCA space
toy_vr = scanl_plus ( toy_pca.explained_variance_ratio_ ) # make it cumulative (TPP)
toy_pcas = toy_pca.components_

# print ("PCA Comoponents -> ", toy_pcas)
# fileLoc = "/home/poliquin/projects/haskell/spectral_gloss/v04f_rank_poly/princ_vals.txt"
# np.savetxt(fileLoc, toy_pcas, delimiter=" ")

print(toy_princ_vals.shape)
print(toy_pcas.shape)
print(toy_vr)
toy_princ_vals

(2696, 20)
(20, 301)
[0, 0.6451305526885978, 0.8787441855101644, 0.9695899303460751, 0.9819021285116155, 0.9900781178484295, 0.9944059631086526, 0.9970722530205749, 0.9981092875973704, 0.9988144335897362, 0.9992615141113723, 0.9995618209466859, 0.9997226786785738, 0.9998232231028524, 0.9998876794241797, 0.9999267586743799, 0.9999483384695655, 0.9999609739943437, 0.9999691794925979, 0.9999752360910277, 0.9999798750098278]

array([[-3.23476764e+00, -5.12165867e+00,  1.25500298e+00, ...,
         7.51627005e-02, -3.32100741e-02, -1.08073340e-02],
       [-8.68377900e+00,  1.04906671e+01, -5.06496140e+00, ...,
        -2.72652174e-01,  7.27964704e-02,  3.49044013e-01],
       [ 3.23035325e+00, -7.81672539e-01,  1.16987125e-01, ...,
        -1.66845463e-01, -1.32087549e-02, -1.55179524e-02],
       ...,
       [ 1.56874553e+01, -1.48383271e+01, -1.46261156e+00, ...,
        -6.12433881e-02, -5.73434678e-03,  1.77302931e-02],
       [ 3.52793088e+00,  5.19658359e+00,  9.11698704e+00, ...,
        -3.74485037e-02, -2.68046055e-02,  3.56070551e-02],
       [ 6.37373617e+00, -1.89114411e+01, -2.58412094e+00, ...,
         1.44590025e-02, -4.18638496e-02,  9.33403665e-04]])

Scale the outs

good_ans_scaler = StandardScaler()
#good_ans_scaled   = good_ans_scaler.fit_transform(make1D(theAnswers)) # Returns scaled data
good_ans_scaled   = good_ans_scaler.fit_transform(theAnswers) # Returns scaled data
good_ans_scaled

array([[-0.09891512],
       [-0.992661  ],
       [ 0.22974179],
       ...,
       [ 1.12491251],
       [ 0.74211336],
       [ 0.45913732]])

Compute the input column means

These are required to get the alphas back into real space

col_means = np.array(list(map (lambda i: np.mean (theInputs[:,i]), range(0,len(theInputs[0]),1))))
#print("Column means -> ", col_means)

Get the Alphas into Real Space

print(good_ans_scaler.scale_)
print(good_ans_scaler.mean_)
print(good_ans_scaler.var_)
good_ans_scaler_scale = good_ans_scaler.scale_

[1.]
[-2.74096604e-16]
[1.]

# Flatten the PCA space Alphas (lstsq puts them in arrays)
#print(pca_l_sq_scaled[0])
#theAlphas = list(chain(*pca_l_sq_scaled[0]))
#print(theAlphas)
real_alphas = toy_pca.inverse_transform(ecAlphas)
# unscale ..
unscaled_real_alphas = (real_alphas - col_means) * good_ans_scaler_scale

fig = plt.figure()
ax1 = fig.add_axes([0.1, 0.5, 0.8, 0.4])
ax2 = fig.add_axes([0.1, 0.1, 0.8, 0.4])

ax1.plot((unscaled_real_alphas*1)-1800, ':o', color='orange',marker=".", markersize=5)
ax2.plot(solution_alphas*5e3, ':o', color='green',marker=".", markersize=5)

[<matplotlib.lines.Line2D at 0x7f06e33c7e20>]

Save this plot style ..

# Flatten the PCA space Alphas (lstsq puts them in arrays)
#print(pca_l_sq_scaled[0])
#theAlphas = list(chain(*pca_l_sq_scaled[0]))
#print(theAlphas)
real_alphas = toy_pca.inverse_transform(ecAlphas)
# unscale ..
unscaled_real_alphas = (real_alphas - col_means) * good_ans_scaler_scale

ec_301_rank01 = [ -8055426.915451925, -7384411.293149285, -6758498.978475503, -6175151.495988338, -5631950.790746583, -5126594.454645077, -4656891.10759733, -4220755.9296018155, -3816206.3398034703, -3441357.81873616, -3094419.870005229, -2773692.117741973, -2477560.536233168, -2204493.8081995533, -1953039.8082668586, -1721822.208241797, -1509537.2008732758, -1314950.3388461345, -1136893.4858208369, -974261.8763977339, -826011.2819488553, -691155.279323697, -568762.6194980355, -457954.6932965249, -357903.09138076036, -267827.25575447513, -186992.22009671814, -114706.43629224815, -50319.68458584075, 6778.935156106478, 57162.93353739146, 101370.28548296468, 139905.21020050225, 173239.87955061434, 201816.0570711094, 226046.66984888833, 246317.3153819725, 262987.70552391704, 276393.04955336504, 286845.37836274534, 294634.81171218335, 300030.770447458, 303283.1355344045, 304623.3557164222, 304265.50555680116, 302407.29558332474, 299231.0362090957, 294904.55706074246, 289582.0833030956, 283405.0705080404, 276502.99957461, 268994.1331674074, 260986.2351011748, 252577.25406074806, 243855.97300772538, 234902.62558794452, 225789.4808173135, 216581.39728762387, 207336.34809874618, 198105.91768900506, 188935.77170159272, 179866.10099156687, 170932.04084530045, 162164.0664522129, 153588.36563717647, 145227.18983118454, 137099.18422766693, 129219.69804223925, 121601.07576467186, 114252.93026345775, 107182.39857553554, 100394.38118648028, 93891.76557980888, 87675.63480794488, 81745.46181185225, 76099.29019136426, 70733.90210380498, 65644.9739446145, 60827.220440342615, 56274.52776155986, 51980.07624095057, 47936.45326008427, 44135.756847111756, 40569.69050689134, 37229.64978481187, 34106.80104583887, 31192.15293106172, 28476.620935255472, 25951.085530689306, 23606.444244602157, 21433.658080426445, 19423.792655960497, 17568.054415267707, 15857.822255107678, 14284.67489117662, 12840.414274344235, 11517.085352417693, 10306.992458733033, 9202.712595064811, 8197.105862950562, 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-89286.37888441543, -101972.73598274002, -116245.82248254758, -132278.2544830766, -150258.73327466953, -170393.30361446447, -192906.69237088462, -218043.7315624526, -246070.869964752, -277277.77761123376, -311979.04766905244, -350516.000330263, -393258.5935215576, -440607.445402307, -492995.9737910436, -550892.657834729, -614803.4274132118, -685274.1859532628, -762893.4725125147, -848295.2691835457, -942161.960062343, -1045227.4482234033, -1158280.437345909, -1282167.8848417522, -1417798.6335467377, -1566147.2292510478, -1728257.931564187, -1905248.9258329924, -2098316.7440591375, -2308740.902994715, -2537888.767831222, -2787220.650138367, -3058295.148954928, -3352774.744184105, -3672431.6517008482, -4019153.949838153, -4394951.987183696, -4801965.081887289, -5242468.522953397, -5718880.884271856, -6233771.662423327, -6789869.249584744, -7390069.253153375, -8037443.17400667, -8735247.455618633, -9486932.91656212, -1.0296154579240153e7, -1.1166781908008516e7, -1.2102909470175808e7, -1.3108868033696886e7, -1.4189236115710046e7, -1.5348851996408815e7, -1.6592826213084254e7, -1.792655454952506e7, -1.935573153631868e7, -2.0886364477959096e7, -2.2524788023033995e7, -2.4277679294137247e7, -2.6152073594531454e7, -2.8155380708969574e7, -3.029540181647496e7, -3.2580347033274766e7, -3.501885360448373e7, -3.762000476354262e7, -4.0393349278829485e7, -4.334892170728063e7, -4.6497263375284456e7, -4.984944410754196e7, -5.341708472502578e7,  ]


ec_301 = ec_301_rank03

fig = plt.figure()
ax1 = fig.add_axes([0.1, 0.5, 0.8, 0.4])
ax2 = fig.add_axes([0.1, 0.1, 0.8, 0.4])

ax1.plot(ec_301, ':o', color='orange',marker=".", markersize=5)
ax2.plot(solution_alphas, ':o', color='green',marker=".", markersize=5)

[<matplotlib.lines.Line2D at 0x7f06e32beeb0>]

vals = [47,
31,
7,
17,
48,
48,
12,
12,
49,
49,
45,
45,
30,
30,
45,
45,
34,
34,
43,
43,
45,
49,
45,
30,
49,
32,
30,
35,
32,
48,
35,
49,
48,
37,
47,
49,
27,
37,
42,
47,
41,
27,
40,
42,
23,
41,
9,
21,
40,
23,
49,
9,
49,
21,
6,
48,
49,
46,
49,
38,
6,
32,
48,
34,
46,
38,
38,
44,
32,
24,
34,
37,
47,
38,
48,
44,
15,
43,
24,
40,
37,
48,
47,
44,
48,
11,
15,
46,
43,
41,
40,
48,
44,
11,
46,
41,
]
plt.hist (vals,10)

(array([ 5.,  4.,  3.,  4.,  4.,  5., 10., 12., 14., 35.]),
 array([ 6. , 10.3, 14.6, 18.9, 23.2, 27.5, 31.8, 36.1, 40.4, 44.7, 49. ]),
 <BarContainer object of 10 artists>)

vals2 = [46,
0,
11,
16,
49,
37,
47,
47,
8,
8,
36,
36,
42,
42,
25,
25,
49,
49,
22,
22,
37,
37,
44,
44,
24,
24,
37,
22,
37,
40,
22,
39,
40,
36,
39,
26,
36,
30,
26,
14,
28,
30,
22,
14,
10,
28,
21,
22,
29,
7,
10,
13,
8,
21,
45,
10,
29,
39,
7,
32,
13,
18,
8,
40,
45,
24,
10,
37,
49,
39,
18,
32,
37,
18,
37,
40,
2,
37,
24,
40,
37,
24,
49,
5,
18,
43,
37,
37,
2,
37,
40,
24,
5,
43,]
plt.hist(vals2,10)

(array([ 3.,  8.,  9.,  5., 14.,  8.,  4., 21., 12., 10.]),
 array([ 0. ,  4.9,  9.8, 14.7, 19.6, 24.5, 29.4, 34.3, 39.2, 44.1, 49. ]),
 <BarContainer object of 10 artists>)

a1 =  [3.691766719870376,-0.45324900807013624,-0.6328292749187538,-2.4535591603731506,-2.3727872551809885,-1.9460216714302947,4.5952277749396475e-3,0.8325415193018809,1.027536028016753,2.7377092570830164,1.5899359750092992,0.6684960875681845,-0.15622141479450996,-2.9682333783614756,-5.3155913592340385,1.8235720358087686,-0.7542570389962948,-1.3472992949259823,-2.22681085587215,-4.1508377463665305,-3.917334748357891,-1.7501534041098994,-1.23296127019783,0.15912149007148518,1.0304571857764917,-4.619730466267905,-4.305964363892311,-4.116905387153439,-3.225765438531903,-0.4046531430717525,1.2838787279733133,0.7028396876989982,3.183751092660421e-2,-0.2769715072483617,-2.5906480967923593,-2.8697339882728676,-3.38249581408716,-5.481526607314231,3.012566052899944,0.8495701568955267,-1.285452013627972,-3.1917379080585233,2.7863646310937042,2.063854665277214,1.6607207350368633,1.072015865250422,1.0015850769579413,0.3489883700457623,-0.5216945944609553,-0.5979082456440877,-2.7046078033658496]
a2 = [5.119576327976686,3.389858601260996,-0.29735043223280005,-24.358205173234346,-5.942067049088909,-13.525236952691815,-21.458897445056135,22.112901418860663,12.28542424688947,6.318260898503328,5.574494383956134,2.79530166904775,-6.162601017545893,-7.765652505387489,-2.0996858355638324,27.923971020576996,20.586288978416757,19.84180537891801,13.729877615353406,8.688029943624134,-9.792200960672211,1.2247827592050353,3.274861381248855,7.234205393497277,7.2936795793691225,12.263104538631577,12.974969284096245,13.557519374896238,15.10856753210703,15.323757991709195,-7.622829446309562,4.636864392584174,5.210385190177541,6.401898634471012,6.922911165467717,8.425519738599167,9.186516404116185,-18.24551641441196,-3.396039024387502,3.0668297715255974,5.9622422692115995,8.220889253340014,10.345407690569552,23.025790562010084,-19.397854938589422,-14.727857896643895,-13.406877717625878,-6.7194634567314235,4.304418937513685,6.756200871788217,7.957623152606171]
a3 = [-2.7104365773573202,-1.848637147901614,2.5403914824687694,3.771377769119905,-0.3613288936750335,-1.3592290693214542,-2.2652158972631256,2.43293455861744,1.4679925196784498,1.0236207551060987,-0.10816785361743136,-0.5087255061714702,-1.5544889076368846,-1.580788680335209,2.184179400024669,2.0633586726673396,-2.4814652311731233,2.6458840898618727,2.5083952723605254,2.0596313842356206,1.836976434977101,1.6318394735208575,3.8987219290173254,0.7874033177070401,-2.5828977027148436,2.9269420293210686,2.9176369343789137,-3.3726466974031677,1.0544140264251995,4.398701409031363,-1.4246131368343398,1.1187252096628515,1.5674103340159533,2.9071670053327985,3.1466688525465005,-2.461319582830882,-1.5247684263928345,1.0988918667494454,2.7219860360631833,-1.6143198808257877,-0.30481759117918106,0.3755997636249161,0.6070348240760972,-2.7102188216555296,-2.5615084965960317,1.823708397708172,-0.6849838518311357,-0.29694219865173,0.7438229221410806,2.031019119929322,2.237876562166073]
a4 = [-2.7104365773573202,-1.163285572719956,2.105543025556544,3.771377769119905,0.5714729259503932,-1.3592290693214542,-2.608584580901142,2.43293455861744,1.6172524158926722,1.0236207551060987,-0.10816785361743136,-0.7522161276766719,1.5674103340159533,-1.9546568601138397,2.184179400024669,2.0831030054108157,-1.5744936701454124,2.6458840898618727,2.5083952723605254,2.0596313842356206,1.6491118661941004,1.6318394735208575,3.8987219290173254,0.5099012906500029,-1.580788680335209,3.0784495998992667,2.9176369343789137,-3.3726466974031677,2.9071670053327985,5.370886827195094,-1.4516636543305195,-0.6313335478092625,-1.258054859831411,1.955609877932364,3.1466688525465005,-2.2652158972631256,0.6070348240760972,1.4689263112947626,2.767912407711239,-1.6143198808257877,-0.3585260114443922,0.3755997636249161,2.0633586726673396,-2.5828977027148436,-2.5615084965960317,-2.4814652311731233,-0.6849838518311357,-0.29694219865173,0.6937921349909545,1.681834817290608,3.049286229047923]
a5 = [-2.255460093442913,-1.4246131368343398,-0.30481759117918106,3.771377769119905,-0.3613288936750335,-1.3592290693214542,-2.2652158972631256,2.43293455861744,1.10231906111375,1.0236207551060987,-0.10816785361743136,-0.30214411551698905,-1.5544889076368846,-1.6978381132695326,2.184179400024669,2.0633586726673396,0.26648777900010145,2.6458840898618727,2.5083952723605254,2.125434019227187,1.836976434977101,2.9176369343789137,1.6318394735208575,-2.4814652311731233,-2.5828977027148436,2.9269420293210686,2.8623392908554384,-2.7927928045384727,1.955609877932364,4.398701409031363,0.6110152746561872,1.4746839470962154,1.5674103340159533,2.9071670053327985,3.1466688525465005,-2.461319582830882,-1.5247684263928345,-1.440943195346969,2.5465233107226304,-1.6143198808257877,2.5403914824687694,0.3755997636249161,1.823708397708172,-2.7102188216555296,-2.5615084965960317,0.6070348240760972,-0.6849838518311357,-0.5087255061714702,0.7438229221410806,2.031019119929322,2.237876562166073]
a6 = [-1.4323721185907048,-0.6543048015720982,-0.30481759117918106,2.881381407006314,-0.22441244101500502,1.955609877932364,-2.2652158972631256,2.43293455861744,2.9071670053327985,1.0236207551060987,-0.10816785361743136,-0.30214411551698905,-1.5544889076368846,-2.516261301796894,2.5403914824687694,2.0633586726673396,0.26648777900010145,2.1432931564255417,2.5083952723605254,-1.4896117955516452,1.5446394420862442,2.9176369343789137,1.6318394735208575,2.9269420293210686,-2.5828977027148436,-2.4814652311731233,2.574698339139731,-2.7927928045384727,1.10231906111375,3.0291126314217425,0.6110152746561872,1.4746839470962154,1.5674103340159533,0.31409007401198874,1.8887540209461617,-2.297633613929693,-1.5247684263928345,2.4631496843189087,2.5465233107226304,1.823708397708172,2.184179400024669,-1.3592290693214542,0.6070348240760972,-2.7102188216555296,-2.5615084965960317,-1.6143198808257877,-0.6849838518311357,-0.5087255061714702,1.004116292889437,2.031019119929322,2.237876562166073]
testD = [3.691766719870376,-0.45324900807013624,-0.6328292749187538,-2.4535591603731506,-2.3727872551809885,-1.9460216714302947,4.5952277749396475e-3,0.8325415193018809,1.027536028016753,2.7377092570830164,1.5899359750092992,0.6684960875681845,-0.15622141479450996,-2.9682333783614756,-5.3155913592340385,1.8235720358087686,-0.7542570389962948,-1.3472992949259823,-2.22681085587215,-4.1508377463665305,-3.917334748357891,-1.7501534041098994,-1.23296127019783,0.15912149007148518,1.0304571857764917,-4.619730466267905,-4.305964363892311,-4.116905387153439,-3.225765438531903,-0.4046531430717525,1.2838787279733133,0.7028396876989982,3.183751092660421e-2,-0.2769715072483617,-2.5906480967923593,-2.8697339882728676,-3.38249581408716,-5.481526607314231,3.012566052899944,0.8495701568955267,-1.285452013627972,-3.1917379080585233,2.7863646310937042,2.063854665277214,1.6607207350368633,1.072015865250422,1.0015850769579413,0.3489883700457623,-0.5216945944609553,-0.5979082456440877,-2.7046078033658496]

plt.plot(testD,':o', color='green',marker=".", markersize=5)

[<matplotlib.lines.Line2D at 0x7f06e31e5640>]

#import numpy as np
#import matplotlib.pyplot as plt

#plt.style.use('seaborn-poster')

x = [0, 1, 2]
y = [1, 3, 2]

# use bc_type = 'natural' adds the constraints as we described above
f = CubicSpline(x,y, bc_type='natural')
x_new = np.linspace(0, 2, 100)
y_new = f(x_new)

plt.figure(figsize = (10,8))
plt.plot(x_new, y_new, 'b')
plt.plot(x, y, 'ro')
plt.title('Cubic Spline Interpolation')
plt.xlabel('x')
plt.ylabel('y')
plt.show()

yIn = [3.691766719870376,-0.45324900807013624,-0.6328292749187538,-2.4535591603731506,-2.3727872551809885,-1.9460216714302947,4.5952277749396475e-3,0.8325415193018809,1.027536028016753,2.7377092570830164,1.5899359750092992,0.6684960875681845,-0.15622141479450996,-2.9682333783614756,-5.3155913592340385,1.8235720358087686,-0.7542570389962948,-1.3472992949259823,-2.22681085587215,-4.1508377463665305,-3.917334748357891,-1.7501534041098994,-1.23296127019783,0.15912149007148518,1.0304571857764917,-4.619730466267905,-4.305964363892311,-4.116905387153439,-3.225765438531903,-0.4046531430717525,1.2838787279733133,0.7028396876989982,3.183751092660421e-2,-0.2769715072483617,-2.5906480967923593,-2.8697339882728676,-3.38249581408716,-5.481526607314231,3.012566052899944,0.8495701568955267,-1.285452013627972,-3.1917379080585233,2.7863646310937042,2.063854665277214,1.6607207350368633,1.072015865250422,1.0015850769579413,0.3489883700457623,-0.5216945944609553,-0.5979082456440877,-2.7046078033658496]
y = yIn[::5]
x = np.linspace(-3,3,11)
print (len(x))
print (len(y))
# use bc_type = 'natural' adds the constraints as we described above
f = CubicSpline(x, y, bc_type='natural')
x_new = np.linspace(-3,3,100)
y_new = f(x_new)

plt.figure(figsize = (10,8))
plt.plot(x_new, y_new, 'b')
plt.plot(x, y, 'ro')
plt.plot (x, y, ':o',color='orange')
plt.title('Cubic Spline Interpolation')
plt.xlabel('x')
plt.ylabel('y')
plt.show()

11
11

x = [0, 1, 2]
y = [1, 3, 2]

# Generated by Haskell
coef =  [[1.0,2.5,-5.551e-16,-0.50],[-7.5495e-15,5.5,-3.0,0.500]]


xa = np.linspace (0,1,100)
xb = np.linspace (1,2,100)

f1d = list(map (lambda xp : 1 + 2.5*xp            - 0.5*xp**3,xa))
f2d = list(map (lambda xp : 0 + 5.5*xp -3.0*xp**2 + 0.5*xp**3,xb))

#f1e = list(map (lambda xp : -0.5 +   0*xp + 2.5*xp**2 + 1.0*xp**3,xa))
#f2e = list(map (lambda xp :  0.5 - 3.0*xp + 5.5*xp**2 + 0.0*xp**3,xb))

plt.plot (f1d+f2d)

[<matplotlib.lines.Line2D at 0x7f06e30de250>]

#  [(0,1),(1,3),(2,2),(3,3)]

# From Haskell
c =  [[1.0000000000000033,2.9333333333333282,4.440892098500626e-15,-0.9333333333333398],
      [-1.6000000000000087,10.733333333333388,-7.800000000000053,1.6666666666666796],
      [17.60000000000015,-18.06666666666686,6.600000000000078,-0.7333333333333434]]

xa = np.linspace (0,1,100)
xb = np.linspace (1,2,100)
xc = np.linspace (2,3,100)

f1d = list(map (lambda xp : c[0][0]   + c[0][1]*xp  + c[0][2]*xp**2  + c[0][3]*xp**3,xa))
f2d = list(map (lambda xp : c[1][0]   + c[1][1]*xp  + c[1][2]*xp**2  + c[1][3]*xp**3,xb))
f3d = list(map (lambda xp : c[2][0]   + c[2][1]*xp  + c[2][2]*xp**2  + c[2][3]*xp**3,xc))

# f1d = list(map (lambda xp : c[0][3]   + c[0][2]*xp  + c[0][1]*xp**2  + c[0][0]*xp**3,xa))
# f2d = list(map (lambda xp : c[1][3]   + c[1][2]*xp  + c[1][1]*xp**2  + c[1][0]*xp**3,xb))
# f3d = list(map (lambda xp : c[2][3]   + c[2][2]*xp  + c[2][1]*xp**2  + c[2][0]*xp**3,xc))

plt.plot (f1d+f2d+f3d)
#plt.plot ([0,100,200,300],[1,3,3,1],'ro')

[<matplotlib.lines.Line2D at 0x7f06e3033c40>]

From Web Spline Calculator

Web Calculator

display.Image("/home/poliquin/projects/haskell/jayai02/jup_plot/v03/cspline_web_calc01.png",width=600,height=300)

Matches Haskell

c = [[0.9999999999999994,2.750000000000003,2.220446049250313e-16,-0.7500000000000011],[-0.5000000000000115,7.250000000000012,-4.5000000000000036,0.7500000000000004]]

xa = np.linspace (0,1,100)
xb = np.linspace (1,2,100)


f1d = list(map (lambda xp : c[0][0]   + c[0][1]*xp  + c[0][2]*xp**2  + c[0][3]*xp**3,xa))
f2d = list(map (lambda xp : c[1][0]   + c[1][1]*xp  + c[1][2]*xp**2  + c[1][3]*xp**3,xb))

# f1d = list(map (lambda xp : c[0][3]   + c[0][2]*xp  + c[0][1]*xp**2  + c[0][0]*xp**3,xa))
# f2d = list(map (lambda xp : c[1][3]   + c[1][2]*xp  + c[1][1]*xp**2  + c[1][0]*xp**3,xb))
# f3d = list(map (lambda xp : c[2][3]   + c[2][2]*xp  + c[2][1]*xp**2  + c[2][0]*xp**3,xc))

plt.plot (f1d+f2d)
#plt.plot ([0,100,200,300],[1,3,3,1],'ro')

[<matplotlib.lines.Line2D at 0x7f06e3009b20>]

Looks Ok Too ..

c0 = [[5.000000000000245,-4.792863896083825,3.915756607852927e-13,-20.820030784273072],
         [1.6271550129487422,28.93558597443294,-112.42816623505523,104.10015392134437],
         [61.558194598593616,-270.7196119537839,386.99716364530633,-173.35836267885642],
         [-197.4440251571947,592.6211205655104,-572.2703169316873,181.92588938669655],
         [498.8324084349582,-1148.0699634148677,878.305586385296,-221.01186153468765],
         [-991.742878283198,1833.0806100214477,-1109.1281292389167,220.64007527069305],
         [913.1805401403936,-1341.791754017871,654.6898507829285,-105.99288399261171],
         [-236.4722160560117,300.5693262627075,-127.38685411258632,18.14627551461289],
         [64.55271920077064,-75.7118428082681,29.396966333652983,-3.629255102920226]]

c1 = [[0.6809008024547628,-5.352471023282419,3.7925218521195347e-13,24.32996800428968],[2.546619923378176,-24.009662232515016,62.190637364109165,-44.770740178053224],[-22.295600065556137,100.20143771215652,-144.8278625436774,70.23953754849492],[114.95984030053329,-357.3166968414753,363.52562029369045,-118.03953016904872],[-273.9029471653472,614.8402718232228,-446.6051869268906,106.99680517000165],[380.98111006026977,-694.9278426280114,426.5735560405987,-87.04291548944056],[-650.9115628718789,1024.8932789255696,-528.8826226002797,89.89341388850005],[759.7797862279035,-990.3800769312636,430.7713563791651,-62.432614520935715],[-700.3019831739266,834.7221348210246,-329.68789851762165,43.18672643695139],[589.8670408308051,-598.7990029620133,201.24585621683758,-22.36065069075972]]

c2 = [[0.3697510140897484,-2.382471912348456,2.988165270778609e-13,11.258057763153081],[1.1264349086274366,-9.949310857724797,25.222796484588237,-16.767271664166643],[-11.731723767831587,54.34148252457029,-81.92852581923725,42.76124072684749],[89.4360748596659,-282.8845129004218,292.7670246529756,-96.01488907767573],[-229.3913784313862,514.184120327206,-371.4568363700471,88.49173898427506],[296.79700892348274,-538.1926543825318,330.12768010311135,-67.4159313430936],[-482.91529037920066,761.3278444552734,-391.8281525845583,66.2795932286972],[465.53161249204646,-593.5963025036519,253.37382215778743,-36.133418635167246],[-396.9570201904919,484.514488349521,-195.839007364368,26.257252131798815],[488.2588258527212,-499.05867392071747,168.44734903201712,-18.716372114668562]]

c = [[0.3697510140897484,-2.382471912348456,2.988165270778609e-13,11.258057763153081],[1.1264349086274366,-9.949310857724797,25.222796484588237,-16.767271664166643],[-11.731723767831587,54.34148252457029,-81.92852581923725,42.76124072684749],[89.4360748596659,-282.8845129004218,292.7670246529756,-96.01488907767573],[-229.3913784313862,514.184120327206,-371.4568363700471,88.49173898427506],[296.79700892348274,-538.1926543825318,330.12768010311135,-67.4159313430936],[-482.91529037920066,761.3278444552734,-391.8281525845583,66.2795932286972],[465.53161249204646,-593.5963025036519,253.37382215778743,-36.133418635167246],[-396.9570201904919,484.514488349521,-195.839007364368,26.257252131798815],[488.2588258527212,-499.05867392071747,168.44734903201712,-18.716372114668562]]

print (len (c))
plen = 5
d = 0.3
xa = np.linspace (  0,  d,plen)
xb = np.linspace (  d,2*d,plen)
xc = np.linspace (2*d,3*d,plen)
xd = np.linspace (3*d,4*d,plen)
xe = np.linspace (4*d,5*d,plen)
xf = np.linspace (5*d,6*d,plen)
xg = np.linspace (6*d,7*d,plen)
xh = np.linspace (7*d,8*d,plen)
xi = np.linspace (8*d,9*d,plen)
#xj = np.linspace (9*d,2,100)

print(xa)
print(xb)

f1d = list(map (lambda xp : c[0][0]   + c[0][1]*xp  + c[0][2]*xp**2  + c[0][3]*xp**3,xa))
f2d = list(map (lambda xp : c[1][0]   + c[1][1]*xp  + c[1][2]*xp**2  + c[1][3]*xp**3,xb))
f3d = list(map (lambda xp : c[2][0]   + c[2][1]*xp  + c[2][2]*xp**2  + c[2][3]*xp**3,xc))
f4d = list(map (lambda xp : c[3][0]   + c[3][1]*xp  + c[3][2]*xp**2  + c[3][3]*xp**3,xd))
f5d = list(map (lambda xp : c[4][0]   + c[4][1]*xp  + c[4][2]*xp**2  + c[4][3]*xp**3,xe))
f6d = list(map (lambda xp : c[5][0]   + c[5][1]*xp  + c[5][2]*xp**2  + c[5][3]*xp**3,xf))
f7d = list(map (lambda xp : c[6][0]   + c[6][1]*xp  + c[6][2]*xp**2  + c[6][3]*xp**3,xg))
f8d = list(map (lambda xp : c[7][0]   + c[7][1]*xp  + c[7][2]*xp**2  + c[7][3]*xp**3,xh))
f9d = list(map (lambda xp : c[8][0]   + c[8][1]*xp  + c[8][2]*xp**2  + c[8][3]*xp**3,xi))
#f10d = list(map (lambda xp : c[9][0]   + c[9][1]*xp  + c[9][2]*xp**2  + c[9][3]*xp**3,xj))

# Haskell Computation ..
haskellSol0 = [5.000000000000245,4.707931039585815,4.388879319274968,4.0158620791712885,3.561896559378359,2.99999999999976,2.99999999999995,2.3301724010356857,1.6603448020713962,1.1254310025891439,0.8603448020709905,0.9999999999990088,1.0000000000005898,1.6193793562711605,2.553741472438176,3.578413910469891,4.468724232334324,4.9999999999999005,4.999999999999744,5.024310173880679,4.700689308176038,4.264913355530808,3.952758268590401,3.9999999999997726,4.000000000002785,4.555379948208554,5.41950129485997,6.305932667408456,6.928242693305947,7.000000000001933,7.0,6.330170033295872,5.1093055123935756,3.6233559748422977,2.1582709581939525,0.9999999999995453,1.000000000002501,0.36393991861154973,0.18327665557058026,0.3206434332247454,0.6386734739202211,1.0000000000015916,0.9999999999983231,1.2940702922659852,1.5175878653328425,1.6940702922657351,1.8470351461317023,1.9999999999976694,1.9999999999991758,2.1717789123186932,2.3623718830917326,2.5670753977049188,2.7811859415448765,2.999999999998195]
haskellSol1 = [5.000000000000245,4.707931039585815,4.388879319274968,4.0158620791712885,3.561896559378359,2.99999999999976,2.99999999999995,2.3301724010356857,1.6603448020713962,1.1254310025891439,0.8603448020709905,0.9999999999990088,1.0000000000005898,1.6193793562711605,2.553741472438176,3.578413910469891,4.468724232334324,4.9999999999999005,4.999999999999744,5.024310173880679,4.700689308176038,4.264913355530808,3.952758268590401,3.9999999999997726,4.000000000002785,4.555379948208554,5.41950129485997,6.305932667408456,6.928242693305947,7.000000000001933,7.0,6.330170033295872,5.1093055123935756,3.6233559748422977,2.1582709581939525,0.9999999999995453,1.000000000002501,0.36393991861154973,0.18327665557058026,0.3206434332247454,0.6386734739202211,1.0000000000015916,0.9999999999983231,1.2940702922659852,1.5175878653328425,1.6940702922657351,1.8470351461317023,1.9999999999976694,1.9999999999991758,2.1717789123186932,2.3623718830917326,2.5670753977049188,2.7811859415448765,2.999999999998195]
haskellSol = [5.000000000000245,4.631751757306844,4.210802811690759,3.6844524602292945,2.99999999999976,2.99999999999995,2.1574454310023485,1.3675915649273875,0.8939419163884725,0.9999999999990088,1.0000000000005898,1.8322165186832322,3.0688309285979614,4.271029874213795,4.999999999999872,4.999999999999744,4.966813494265466,4.482084720680746,4.006313586755368,3.9999999999998863,4.000000000002785,4.753654504257327,5.877830188681628,6.813090778766423,7.000000000001933,7.0,6.065443488715914,4.381594524601496,2.506948298186444,0.9999999999995453,1.000000000002501,0.2814465408828255,0.22079171291363764,0.5497410284892794,1.0000000000015916,0.9999999999983231,1.355645347759861,1.610238623749268,1.8097125878631743,1.9999999999975557,1.9999999999991758,2.2178470680715208,2.4632537920816304,2.7270336200503067,2.999999999998195]
print (len(haskellSol))
ans_xx = (f1d+f2d+f3d+f4d+f5d+f6d+f7d+f8d+f9d) #+f10)
plt.plot (f1d+f2d+f3d+f4d+f5d+f6d+f7d+f8d+f9d) #+f10)
plt.plot ([0,plen,2*plen,3*plen,4*plen,5*plen,6*plen,7*plen,8*plen], 
            [f1d[0],f2d[0],f3d[0],f4d[0],f5d[0],f6d[0],f7d[0],f8d[0],f9d[0]], ':o', color = "orange")
plt.plot (haskellSol, 'o', color = "green")

10
[0.    0.075 0.15  0.225 0.3  ]
[0.3   0.375 0.45  0.525 0.6  ]
45

[<matplotlib.lines.Line2D at 0x7f06e2ccbc70>]

allS = [5.000000000000245,4.707931039585815,4.388879319274968,4.0158620791712885,3.561896559378359,2.99999999999976,2.99999999999995,2.3301724010356857,1.6603448020713962,1.1254310025891439,0.8603448020709905,0.9999999999990088,1.0000000000005898,1.6193793562711605,2.553741472438176,3.578413910469891,4.468724232334324,4.9999999999999005,4.999999999999744,5.024310173880679,4.700689308176038,4.264913355530808,3.952758268590401,3.9999999999997726,4.000000000002785,4.555379948208554,5.41950129485997,6.305932667408456,6.928242693305947,7.000000000001933,7.0,6.330170033295872,5.1093055123935756,3.6233559748422977,2.1582709581939525,0.9999999999995453,1.000000000002501,0.36393991861154973,0.18327665557058026,0.3206434332247454,0.6386734739202211,1.0000000000015916,0.9999999999983231,1.2940702922659852,1.5175878653328425,1.6940702922657351,1.8470351461317023,1.9999999999976694,1.9999999999991758,2.1717789123186932,2.3623718830917326,2.5670753977049188,2.7811859415448765,2.999999999998195]

plt.plot (allS, ':o', color = "green")

[<matplotlib.lines.Line2D at 0x7f06e2cfe970>]

fig = plt.figure()
ax1 = fig.add_axes([0.1, 0.5, 0.8, 0.4])
ax2 = fig.add_axes([0.1, 0.1, 0.8, 0.4])

ax1.plot(ec_301, ':o', color='orange',marker=".", markersize=5)
ax2.plot(solution_alphas, ':o', color='green',marker=".", markersize=5)

[<matplotlib.lines.Line2D at 0x7f06e2bebd90>]

# populationSize = 50 :: Int
# individualLen = 51::Int --101 :: Int -- polynomial order plus one
# alterPopFraction = 0.3 :: Double
# alterEltFraction = 0.05 :: Double --0.03 :: Double
# maxXValue = 3.0 :: Double
# generationCount = 1000 --00
# randSeed = 12323::Int -- 1111::Int --4455::Int -- 34567::Int --23456::Int --12345::Int --4391 --3221 --1111 -- 3121 --12345 --21311 --123 -- 12345 -- 1234
# maxValue = 1000 :: Double
# noiseLevel = 0.0 --0.007 :: Double -- about 2 percent
# stepsPerSec = 10 :: Float

# smoothWeight   = 0.95
# accuracyWeight = 0.05

# maxInflections = (fromIntegral individualLen)/2.0::Double

# 10 coefs
# 9 xRanges

xr = [[0.0,   0.075,  0.15  ,0.225,  0.30],
      [0.3,   0.375,  0.45  ,0.525,  0.60],
      [0.6,   0.675,  0.75  ,0.825,  0.90],
      [0.90,  0.975,  1.05  ,1.125,  1.20],
      [1.20,  1.275,  1.35  ,1.425,  1.50],
      [1.50,  1.575,  1.65  ,1.725,  1.80],
      [1.80,  1.875,  1.95  ,2.025,  2.1],
      [2.1,   2.175,  2.25  ,2.325,  2.4],
      [2.40,  2.475,  2.55  ,2.625,  2.70]]

splineCoefs =\
[[0.6809008024547628,-5.352471023282419,3.7925218521195347e-13,24.32996800428968],[2.546619923378176,-24.009662232515016,62.190637364109165,-44.770740178053224],[-22.295600065556137,100.20143771215652,-144.8278625436774,70.23953754849492],[114.95984030053329,-357.3166968414753,363.52562029369045,-118.03953016904872],[-273.9029471653472,614.8402718232228,-446.6051869268906,106.99680517000165],[380.98111006026977,-694.9278426280114,426.5735560405987,-87.04291548944056],[-650.9115628718789,1024.8932789255696,-528.8826226002797,89.89341388850005],[759.7797862279035,-990.3800769312636,430.7713563791651,-62.432614520935715],[-700.3019831739266,834.7221348210246,-329.68789851762165,43.18672643695139],[589.8670408308051,-598.7990029620133,201.24585621683758,-22.36065069075972]]

#splinePairs =
#[SplinePair 0.0 0.6809008024544488,SplinePair 0.3 (-0.26793136841378823),SplinePair 0.6 0.8589721564887725,SplinePair 0.8999999999999999 1.7797480878585252,SplinePair 1.1999999999999997 5.684389181561089,SplinePair 1.4999999999999996 4.61000743273847,SplinePair 1.7999999999999994 4.5750317669719545,SplinePair 2.099999999999999 1.4948632259813541,SplinePair 2.399999999999999 1.042151199446214,SplinePair 2.699999999999999 6.733710789057884e-2,SplinePair 2.9999999999999987 0.9451692457892924]

#ecVals =

subsample_sol = np.array(solution_alphas[::6])
plt.plot(ans_xx,':o', color = "orange",markersize = 4)
plt.plot(subsample_sol*5.5, ':o',markersize = 4)
plt.plot ([0,plen,2*plen,3*plen,4*plen,5*plen,6*plen,7*plen,8*plen], 
            [f1d[0],f2d[0],f3d[0],f4d[0],f5d[0],f6d[0],f7d[0],f8d[0],f9d[0]], 'o', color = "red")

[<matplotlib.lines.Line2D at 0x7f06e2be47f0>]

subsample_sol = np.array(solution_alphas[::6])
fig9, ax9 = plt.subplots()
ax9.set_title ("EC vs Actual No Noise Response Curve")
ax9.plot(ans_xx,':o', color = "orange",markersize = 4,label="EC Sol")
ax9.plot(subsample_sol*5.5, ':o',markersize = 4, label = "Known Sol")
ax9.plot ([0,plen,2*plen,3*plen,4*plen,5*plen,6*plen,7*plen,8*plen], 
            [f1d[0],f2d[0],f3d[0],f4d[0],f5d[0],f6d[0],f7d[0],f8d[0],f9d[0]], 'o', color = "red", label = "EC Spline Pos")
ax9.legend()
#ax9.set_xlabel(r'$\Delta_i$', fontsize=15)
#ax9.set_ylabel(r'$\Delta_{i+1}$', fontsize=15)
#ax9.set_title('Volume and percent change')
ax9.set_xlabel( 'Pseudo Wavelength')

Text(0.5, 0, 'Pseudo Wavelength')

#Best guy -> 4.048659455579973e-6
bg = [0.2583382302328207,3.626041084001584e-2,0.5291385308389235,2.079623468591992,5.612860764140267,4.861354570987686,4.446104216252994,1.8184185557752086,0.7506778314830624,0.6619122409600563,4.782497499368079,-0.8572901144021609,2.4120847842264306,1.6007629547156865,-2.541755035400462,-0.3630980491894617,1.9885551235507388,2.008774557026396,-2.3135494581621487,0.43935452862606295,-0.3901394865074467,1.82177367643736,2.444557126525101,1.7617824456563094,-0.5433466523411205,2.375950982010881,5.5312969639141674e-2,-1.1734537460501537,-2.5906372946275584,2.2109796084366473,0.7908345512011739,0.6998828237977799,0.5504121114614919,3.1899329575202997,-0.25217225437093255,-0.7307755227414765,-0.8558348305189797,-1.877731697736756,-0.5991766044199482,-1.3977960126592597,-1.64219357729717,-1.3863214252990776,-0.15947863630994102,-0.17907537356308373,-1.1212682125929474,0.7818632983379034,-2.9955903395968813,-1.1368226344314984,1.4419737912305768,1.4381573104096055,-2.363030620619389]

# 5.5 hrs approx

plt.plot(solution_alphas, ':o', color='green',marker=".", markersize=5)

[<matplotlib.lines.Line2D at 0x7f06e2b13b20>]

Now let's start looking at the noisy data while I investigate edge cases in the spline algs ..

# Stitch together
m2x =  np.array(list(map (lambda x : [x],wnAnswers))) # Why did I have to do this?
print(m2x.shape)
raw301sN = np.append (wnInputs,m2x,axis=1)
print(fCases.shape)
print (wnInputs.shape)

(2696, 1)
(2696, 302)
(2696, 301)

# Scale
from sklearn import preprocessing

scaler301N = preprocessing.StandardScaler().fit(raw301sN)
scaled_301sN = scaler301N.transform(raw301sN)
scaled_301sN

array([[-0.16998473, -0.17147829, -0.17198631, ..., -0.42975773,
        -0.42743939, -0.09254587],
       [-0.85175612, -0.86374345, -0.87265059, ...,  1.20272339,
         1.19750062, -0.98752192],
       [ 0.56246442,  0.59140529,  0.61835959, ..., -0.30589648,
        -0.3115256 ,  0.24478691],
       ...,
       [ 1.732621  ,  1.73598262,  1.74201102, ..., -0.24932618,
        -0.25943941,  1.10721124],
       [-0.71342013, -0.71819731, -0.72305177, ..., -0.01202794,
        -0.01612902,  0.76201013],
       [ 0.93092287,  0.9681667 ,  1.00254087, ..., -0.96420591,
        -0.97060905,  0.45121197]])

# Write it out ..
np.savetxt("fcases_301sN.txt", scaled_301sN, delimiter=" ")

!pwd

/home/poliquin/projects/haskell/jayai02/jup_plot/v03

!cp /home/poliquin/projects/haskell/jayai02/jup_plot/v03/fcases_301sN.txt /home/poliquin/projects/haskell/spectral_gloss/v04d_hack_301_pareto_splines/v03

Jay suggested trying the linear algebra approach on subsampled inputs ..

# No Noise Linear Algebra Solution
m,c,d,e = np.linalg.lstsq(nnInputs,nnAnswers,rcond=None)
plt.plot(solution_alphas,'--' ,markersize=3,color="orange")
plt.plot(m,'o',markersize=0.5)

[<matplotlib.lines.Line2D at 0x7f06e08eaaf0>]

# With Noise, Subsampled Linear Algebra Solution

# Subsample
wn_sub_inputs = list(map (lambda x: x[::20],wnInputs)) # every 20th
sub_solution = solution_alphas[::20] # every 20th

mn,cn,dn,en = np.linalg.lstsq(wn_sub_inputs,wnAnswers,rcond=None)

plt.plot(sub_solution*20,'-0' ,markersize=4,color="orange",label="Subsampled Real Solution")
plt.plot(mn,'-o',markersize=3,label='Subsampled Linear Algebra Solution')
plt.title ("Subsampled (301 -> 15) with Noisy Data Solution Comparison ")
plt.xlabel("Pseudo Wavelength")
plt.legend()

<matplotlib.legend.Legend at 0x7f06da7b99a0>

# With Noise, Subsampled Linear Algebra Solution

# Subsample
wn_sub_inputs = list(map (lambda x: x[::6],wnInputs)) # every 6th
sub_solution = solution_alphas[::6] # every 6th

mn,cn,dn,en = np.linalg.lstsq(wn_sub_inputs,wnAnswers,rcond=None)

plt.plot(sub_solution*20,'-0' ,markersize=4,color="orange",label="Subsampled Real Solution")
plt.plot(mn,'-o',markersize=3,label='Subsampled Linear Algebra Solution')
plt.title ("Subsampled (301 -> 51) with Noisy Data Solution Comparison ")
plt.xlabel("Pseudo Wavelength")
plt.legend()

<matplotlib.legend.Legend at 0x7f06da65f190>

#fig, ax = plt.subplots(5, 2, sharex='col', sharey='row')
fig, ax = plt.subplots(7, 2, figsize = (12,40),constrained_layout=True,)
#plt.subplots_adjust(wspace = 0.1, hspace = 0.6)
# axes are in a two-dimensional array, indexed by [row, col]
for i in range(7):
    for j in range(2):
        skip = ((i+1) + j) * 6
        wn_sub_inputs = list(map (lambda x: x[::skip],wnInputs))
        sub_solution = solution_alphas[::skip]
        mn,cn,dn,en = np.linalg.lstsq(wn_sub_inputs,wnAnswers,rcond=None)  
        max_sol = max(sub_solution)
        max_inputs = max(mn)
        ax[i, j].plot(mn,'-o',markersize=3,label='Subsampled Linear Algebra Solution')
        ax[i, j].plot(sub_solution*(max_inputs/max_sol),'-0' ,markersize=4,color="orange",label="Subsampled Real Solution")

        ax[i, j].set_title("Approximate bSubsample Points -> " + 
                                             str(math.trunc(301/skip)))

        fig.suptitle ("Real Solution vs Linear Algebra Least Sq Using Subsamples")

#fig

# wn_sub_inputs = list(map (lambda x: x[::6],wnInputs)) # every 6th
# sub_solution = solution_alphas[::6] # every 6th

# mn,cn,dn,en = np.linalg.lstsq(wn_sub_inputs,wnAnswers,rcond=None)

# plt.plot(sub_solution*20,'-0' ,markersize=4,color="orange",label="Subsampled Real Solution")
# plt.plot(mn,'-o',markersize=3,label='Subsampled Linear Algebra Solution')
# plt.title ("Subsampled (301 -> 51) with Noisy Data Solution Comparison ")
# plt.xlabel("Pseudo Wavelength")
# plt.legend()

# ax9.set_title ("EC vs Actual No Noise Response Curve")
# ax9.plot(ans_xx,':o', color = "orange",markersize = 4,label="EC Sol")
# ax9.plot(subsample_sol*5.5, ':o',markersize = 4, label = "Known Sol")
# ax9.plot ([0,plen,2*plen,3*plen,4*plen,5*plen,6*plen,7*plen,8*plen], 
#             [f1d[0],f2d[0],f3d[0],f4d[0],f5d[0],f6d[0],f7d[0],f8d[0],f9d[0]], 'o', color = "red", label = "EC Spline Pos")
# ax9.legend()
# #ax9.set_xlabel(r'$\Delta_i$', fontsize=15)
# #ax9.set_ylabel(r'$\Delta_{i+1}$', fontsize=15)
# #ax9.set_title('Volume and percent change')
# ax9.set_xlabel( 'Pseudo Wavelength')