Provide Manual Initial Guesses

When auto-detection fails or the fit converges to a wrong solution, supply your own initial guesses.

Problem

fit_peaks auto-detects peaks and generates initial parameters, but sometimes:

The auto-detected peaks are wrong (e.g., noise spike selected instead of real peak)
The fit converges to a local minimum instead of the physical solution
You know the approximate peak parameters from prior measurements

Solution

Set up example data to work with:

using OpticalSpectroscopy
using CurveFitModels

x = collect(range(1950, 2150, length=600))
y = lorentzian([0.3, 2040.0, 15.0, 0.0], x) .+
    lorentzian([0.5, 2060.0, 20.0, 0.0], x) .+
    0.01 .+ 0.004 .* randn(length(x))

Option 1: Provide Detected Peaks

Run find_peaks separately, filter or modify the results, and pass them to fit_peaks:

# Detect peaks
peaks = find_peaks(x, y, min_prominence=0.02)

# Keep only the peaks you want
selected = filter(p -> 2000 < p.position < 2100, peaks)

# Pass to fit_peaks
result = fit_peaks(x, y, (1950, 2150); peaks=selected)

Option 2: Provide the Full Parameter Vector

For complete control, pass p0 — the initial parameter vector. The layout depends on the model:

For Lorentzian or Gaussian (3 params per peak + baseline):

p0 = [A₁, x₁, Γ₁, ..., Aₙ, xₙ, Γₙ, c₀, c₁]

Aᵢ — amplitude of peak i
xᵢ — center position of peak i
Γᵢ — width of peak i (FWHM for Lorentzian, σ for Gaussian)
c₀, c₁ — baseline coefficients (constant, linear)

For Pseudo-Voigt (4 params per peak + baseline):

p0 = [A₁, x₁, σ₁, η₁, ..., c₀, c₁]

ηᵢ — mixing parameter (0 = Gaussian, 1 = Lorentzian)

Example — single Lorentzian with linear baseline:

p0 = [
    0.5,      # amplitude
    2060.0,   # center (cm⁻¹)
    20.0,     # FWHM (cm⁻¹)
    0.01,     # baseline constant
    0.0       # baseline slope
]

result = fit_peaks(x, y, (1950, 2150); p0=p0, n_peaks=1)

Example — two Lorentzians with constant baseline:

p0 = [
    0.3, 2040.0, 15.0,   # peak 1
    0.5, 2060.0, 20.0,   # peak 2
    0.01                  # baseline constant
]

result = fit_peaks(x, y, (1950, 2150); p0=p0, n_peaks=2, baseline_order=0)

Tips

The p0 vector length must equal n_peaks × params_per_peak + baseline_order + 1
If n_peaks is not specified with p0, it is inferred from the vector length
Good initial guesses don't need to be exact — within a factor of 2 is usually sufficient
If the fit still doesn't converge, try narrowing the fitting region