spect_em_pvmm_lback {EMpeaksR}

Spectrum adapted ECM algorithm by PVMM with a linear background

Description

Perform a peak fitting based on the spectrum adapted ECM algorithm by pseudo-Voigt mixture model with a linear background.

Usage

spect_em_pvmm_lback(x, y, mu, sigma, eta, mix_ratio, x_lower, x_upper, conv.cri, maxit)

Arguments

x

measurement steps

y

intensity

mu

mean of the components

sigma

standard deviation of the components

eta

mixing ratio of Gauss and Lorentz distribution

mix_ratio

mixture ratio of the components

x_lower

lower limit of the measurement steps. Default is a minimum of x

x_upper

upper limit of the measurement steps. Default is a maximum of x

conv.cri

criterion of the convergence

maxit

maximum number of the iteration

Details

Peak fitting is conducted by spectrum adapted ECM algorithm.

Value

mu

estimated mean of the components

sigma

estimated standard deviation of the components

eta

estimated mixing ratio of Gauss and Lorentz distribution

mix_ratio

estimated mixture ratio of the components

it

number of the iteration to reach the convergence

LL

variation of the weighted log likelihood values

MU

variation of mu

SIGMA

variation of sigma

ETA

variation of beta

MIX_RATIO

variation of mix_ratio

W_K

decomposed component of the spectral data

convergence

message for the convergence in the calculation

cal_time

calculation time to complete the peak fitting. Unit is seconds

References

Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2019). Spectrum adapted expectation-maximization algorithm for high-throughput peak shift analysis. Science and technology of advanced materials, 20(1), 733-745.

Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2021). Spectrum adapted expectation-conditional maximization algorithm for extending high–throughput peak separation method in XPS analysis. Science and Technology of Advanced Materials: Methods, 1(1), 45-55.

Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2023). High-throughput XPS spectrum modeling with autonomous background subtraction for 3 d 5/2 peak mapping of SnS. Science and Technology of Advanced Materials: Methods, 3(1), 2159753.

Examples

#generating the synthetic spectral data based on three component Pseudo-Voigt mixture model.
x              <- seq(0, 100, by = 0.5)
K              <- 3
true_mu        <- c(35, 50, 65)
true_sigma     <- c(3, 3, 3)
true_mix_ratio <- c(0.5/3, 0.5/3, 0.5/3, 0.5)
true_eta       <- c(0.4, 0.6, 0.1)
degree         <- 4

#Normalized Pseudo-Voigt distribution
  truncated_pv <- function(x, mu, sigma, eta) {
    (eta*dcauchy(x, mu, sqrt(2*log(2))*sigma) + (1-eta)*dnorm(x, mu, sigma)) /
      sum(eta*dcauchy(x, mu, sqrt(2*log(2))*sigma) + (1-eta)*dnorm(x, mu, sigma))
  }

y <- c(true_mix_ratio[1]*truncated_pv(x = x,
                                      mu = true_mu[1],
                                      sigma = true_sigma[1],
                                      eta = true_eta[1])*10^degree +
       true_mix_ratio[2]*truncated_pv(x = x,
                                      mu = true_mu[2],
                                      sigma = true_sigma[2],
                                      eta = true_eta[2])*10^degree +
       true_mix_ratio[3]*truncated_pv(x = x,
                                      mu = true_mu[3],
                                      sigma = true_sigma[3],
                                      eta = true_eta[3])*10^degree +
       true_mix_ratio[4]*(c(500*x + 15000) / sum(500*x + 15000))*10^degree)

plot(y~x, main = "genrated synthetic spectral data")

#Peak fitting by EMpeaksR
#Initial values
mu_init        <- c(30, 40, 60)
sigma_init     <- c(4, 4, 4)
mix_ratio_init <- rep(1/(length(mu_init)+3), length(mu_init)+3)
eta_init       <- c(1, 1, 1)

#Coducting calculation
SP_ECM_PV_LBACK_res <- spect_em_pvmm_lback(x = x,
                                           y = y,
                                           mu = mu_init,
                                           sigma = sigma_init,
                                           eta = eta_init,
                                           mix_ratio = mix_ratio_init,
                                           x_lower = min(x),
                                           x_upper = max(x),
                                           conv.cri = 1e-2,
                                           maxit = 2000)

#Plot fitting curve and trace plot of parameters
show_pvmm_lback_curve(spect_em_pvmm_lback_res = SP_ECM_PV_LBACK_res,
                      x = x,
                      y = y,
                      mix_ratio_init = mix_ratio_init,
                      mu_init = mu_init,
                      sigma_init = sigma_init,
                      eta_init = eta_init,
                      x_lower = min(x),
                      x_upper = max(x))

#Showing the result of spect_em_pvmm_lback()
print(cbind(SP_ECM_PV_LBACK_res$mu, SP_ECM_PV_LBACK_res$sigma, SP_ECM_PV_LBACK_res$eta,
            SP_ECM_PV_LBACK_res$mix_ratio[1:K]))

print(cbind(true_mu, true_sigma, true_eta, true_mix_ratio[1:K]))