MCRLLM 0.0.35

MCRLLM: Multivariate Curve Resolution by Log-Likelihood Maximization

MCRLLM: Multivariate Curve Resolution by Log-Likelihood Maximization.

X = CS
where
X(nxk): Spectroscopic data where n spectra acquired over k energy levels
C(nxa): Composition map based on a MCRLLM components
S(axk): Spectra of the a components as computed by MCRLLM

Method first presented in

Lavoie F.B., Braidy N. and Gosselin R. (2016) Including Noise Characteristics in MCR to improve Mapping and Component Extraction from Spectral Images, Chemometrics and Intelligent Laboratory Systems, 153, 40-50.

Input data

Algorithm is designed to treat 2D data X(nxk) matrices where n spectra acquired over k energy levels.
3D spectral image X(n1,n2,k) can be unfolded to 2D matrix X(n1xn2,k) prior to MCRLLM analysis. Composition maps can then be obtained by folding C(n1xn2,a) matrices into 2D chemical maps C(n1,n2,a).

Input and output arguments

MCRLLM requires 3 inputs : X dat, number of components to compute (nb) and use of phi exponent.
Refer to paper above for use of phi. To optimize phi: 'phi' or to set phi to 1: 'standard'
decomposition = mcr.mcrllm(X,nb,'phi')

Results

Show S and C for each iteration (all) or only for final results (final).
S_all = decomposition.allS
S_final = decomposition.S
C_all = decomposition.allC
C_final = decomposition.C

Example

Compute MCRLLM using 7 components and optimizing phi exponent.
import MCRLLM as mcr
decomposition = mcr.mcrllm(X,7,'phi')
#Iterate each component 20 times
decomposition.iterate(20)
S_final = decomposition.S
C_final = decomposition.C
plt.figure()
plt.plot(S_final.T)
plt.title('S',fontsize=16)
plt.figure()
plt.plot(C_final)
plt.title('C',fontsize=16)