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Peak Fitting

Source: R/peak_fit.R
peak_fit.Rd

Fitting of a single spectral line by lineshape functions with variable parameters.

Usage

peak_fit(
  x,
  profile = "voigt",
  wL = NULL,
  wG = NULL,
  A = NULL,
  wlgth.min = NULL,
  wlgth.max = NULL,
  id = NULL,
  max.iter = 200
)

Arguments

x

A data frame or tibble of spectra, one spectrum per row. Column names are the wavelengths (e.g. "396.15"); an optional identifier column can be given with id.

profile

A character specifying the lineshape function to be used: "lorentzian", "gaussian", "voigt" (exact) or "pseudo_voigt".

wL

A numeric specifying the Lorentzian full width at half maximum (initial guess)

wG

A numeric specifying the Gaussian full width at half maximum (initial guess)

A

A numeric specifying the peak area (initial guess)

wlgth.min

A numeric specifying the lower bound of the wavelength subset

wlgth.max

A numeric specifying the upper bound of the wavelength subset

id

A character specifying the name of the column holding the spectra id (optional)

max.iter

A numeric specifying the maximum number of iteration (200 by default)

Value

A tibble with one row per spectrum and the columns:

  • id column (or spectrum, the row number, when id = NULL),

  • data: the fitted data (x, y),

  • fit: the nls model object,

  • tidied: the estimated parameters with their standard errors,

  • augmented: the data with fitted values (.fitted) and residuals (.resid).

Details

The function uses minpack.lm::nlsLM, which is based on the Levenberg-Marquardt algorithm for searching the minimum value of the square of the sum of the residuals. Each spectrum (row of x) is fitted separately with the model $$y = y_0 + A \cdot f(x; x_c, w)$$ where \(f\) is a unit-area Gaussian, Lorentzian, Voigt or pseudo-Voigt profile (see gaussian_profile(), lorentzian_profile(), voigt_profile() and pseudo_voigt_profile()). The fitted parameters are y0, xc, A and the width(s) wG and/or wL (full widths at half maximum). The Voigt profile is evaluated exactly in C++; the pseudo-Voigt (Thompson-Cox-Hastings) approximation is faster but accurate to about 1\

Initial values that are not supplied are estimated from the data: the peak center from the position of the maximum, the width from the full width at half maximum, and the area from the integrated intensity above the minimum. The center is constrained to the fitted wavelength range and the widths and area to positive values. If the fit of a spectrum fails, a warning is issued and the corresponding fit, tidied and augmented entries are NULL.

Author

Christian L. Goueguel

Examples

data(forageLIBS)
mean_spectrum <- colMeans(forageLIBS[-(1:14)])
wl <- as.numeric(names(mean_spectrum))
# the H-alpha line of the hydrogen of the samples, Stark-broadened
halpha <- tibble::as_tibble(as.list(mean_spectrum[wl > 653.5 & wl < 659.5]))
res <- peak_fit(halpha, profile = "lorentzian")
res$tidied[[1]]
#> # A tibble: 4 × 5
#>   term  estimate std.error statistic   p.value
#>   <chr>    <dbl>     <dbl>     <dbl>     <dbl>
#> 1 y0     2298.    96.1          23.9 1.54e- 34
#> 2 xc      656.     0.00935   70231.  2.78e-265
#> 3 wL        1.70   0.0459       37.1 2.27e- 46
#> 4 A     26000.   773.           33.6 1.12e- 43