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simplisma.py
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simplisma.py
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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import random
import scipy.optimize as optimize
#generate some sample data array
#create random normalised gaussian functions
#Number of Spectral Components
nPure = 5
#Allowed Noise Percentage
noise = 5
x0 = np.zeros(nPure)
sigma = np.zeros(nPure)
for i in range(nPure):
x0[i] = random.uniform(-100, 100)
sigma[i] = random.uniform(3, 25)
x = np.linspace(start = -120, stop = 120, num = 2000)
gx = np.zeros((len(x),5))
plt.subplot(3, 1, 1)
plt.subplots_adjust(left=0.1, bottom=0.075, right=0.95, top=0.9, wspace=0.2, hspace=0.5)
for i in range(5):
gx[:,i] = np.exp(-(x-x0[i])**2/(2*sigma[i]**2))/np.sqrt(2*np.pi*sigma[i]**2)
plt.plot(gx[:,i])
plt.title('Real Components')
#create array with random normalised linear combination of gaussian functions
nspec = 200
array = np.zeros((len(x), nspec))
idx = list(range(nPure))
for i in range(nspec):
randj = np.zeros(nPure)
random.shuffle(idx)
for j in range(nPure):
randj[j] = random.uniform(0, 1-np.sum(randj))
array[:,i] = gx[:,idx[j]]*randj[j]
#Main Algorithm
def simplisma(d, nr, error):
def wmat(c,imp,irank,jvar):
dm=np.zeros((irank+1, irank+1))
dm[0,0]=c[jvar,jvar]
for k in range(irank):
kvar=np.int(imp[k])
dm[0,k+1]=c[jvar,kvar]
dm[k+1,0]=c[kvar,jvar]
for kk in range(irank):
kkvar=np.int(imp[kk])
dm[k+1,kk+1]=c[kvar,kkvar]
return dm
nrow,ncol=d.shape
dl = np.zeros((nrow, ncol))
imp = np.zeros(nr)
mp = np.zeros(nr)
w = np.zeros((nr, ncol))
p = np.zeros((nr, ncol))
s = np.zeros((nr, ncol))
error=error/100
mean=np.mean(d, axis=0)
error=np.max(mean)*error
s[0,:]=np.std(d, axis=0)
w[0,:]=(s[0,:]**2)+(mean**2)
p[0,:]=s[0,:]/(mean+error)
imp[0] = np.int(np.argmax(p[0,:]))
mp[0] = p[0,:][np.int(imp[0])]
l=np.sqrt((s[0,:]**2)+((mean+error)**2))
for j in range(ncol):
dl[:,j]=d[:,j]/l[j]
c=np.dot(dl.T,dl)/nrow
w[0,:]=w[0,:]/(l**2)
p[0,:]=w[0,:]*p[0,:]
s[0,:]=w[0,:]*s[0,:]
print('purest variable 1: ', np.int(imp[0]+1), mp[0])
for i in range(nr-1):
for j in range(ncol):
dm=wmat(c,imp,i+1,j)
w[i+1,j]=np.linalg.det(dm)
p[i+1,j]=w[i+1,j]*p[0,j]
s[i+1,j]=w[i+1,j]*s[0,j]
imp[i+1] = np.int(np.argmax(p[i+1,:]))
mp[i+1] = p[i+1,np.int(imp[i+1])]
print('purest variable '+str(i+2)+': ', np.int(imp[i+1]+1), mp[i+1])
sp=np.zeros((nrow, nr))
for i in range(nr):
sp[0:nrow,i]=d[0:nrow,np.int(imp[i])]
plt.subplot(3, 1, 2)
plt.plot(sp)
plt.title('Estimate Components')
concs = np.dot(np.linalg.pinv(sp), d)
plt.subplot(3, 1, 3)
for i in range(nr):
plt.plot(concs[i])
plt.title('Concentrations')
plt.show()
return sp, concs
#Run Simplisma
sp, concs = simplisma(array, nPure, noise)