How to fix and freeze parameters

PeakSpec.fixed holds one or more parameters constant throughout the optimisation. This is useful when:

• A parameter is known from literature (e.g. \(E\) from thermally-stimulated conductivity measurements).
• The kinetic order \(b\) is to be held at the theoretical value.
• The retrapping ratio \(R\) has been determined from a separate experiment.

---

Syntax

There are two equivalent forms:

# Form 1: explicit value — parameter is fixed to this number
tl.PeakSpec(
    model="go_kg",
    init={"Tm": 490.0, "Im": 5000.0, "E": 1.5, "b": 1.8},
    fixed={"b": 1.8},          # b is held at 1.8
)

# Form 2: True — parameter is fixed to its value in `init`
tl.PeakSpec(
    model="go_kg",
    init={"Tm": 490.0, "Im": 5000.0, "E": 1.5, "b": 1.8},
    fixed={"b": True},         # b is held at init["b"] = 1.8
)

In both cases the parameter does not appear in the optimisation vector, so the Jacobian and covariance matrix are smaller.

---

Fix E to a literature value

import tldecpy as tl

T, I = tl.load_refglow("x001")

peak = tl.PeakSpec(
    name="P1",
    model="fo_rq",
    init={"Tm": 490.0, "Im": 1500.0, "E": 1.20},
    fixed={"E": 1.20},          # known from TSC measurement
)

result = tl.fit_multi(T, I, peaks=[peak], bg=None, beta=1.0)
fitted = result.peaks[0].params
print(f"Fitted Tm={fitted['Tm']:.2f} K  Im={fitted['Im']:.1f}")
print(f"Fixed  E ={fitted['E']:.4f} eV  (unchanged)")

---

Fix the kinetic order b in a GO model

peak_go_fo = tl.PeakSpec(
    name="P1",
    model="go_kg",
    init={"Tm": 490.0, "Im": 3000.0, "E": 1.4, "b": 1.0},
    fixed={"b": 1.0},           # force first-order behaviour
)

peak_go_so = tl.PeakSpec(
    name="P1",
    model="go_kg",
    init={"Tm": 490.0, "Im": 3000.0, "E": 1.4, "b": 2.0},
    fixed={"b": 2.0},           # force second-order behaviour
)

---

Fix R in the OTOR model

peak_otor = tl.PeakSpec(
    name="OTOR",
    model="otor_lw",
    init={"Tm": 470.0, "Im": 1400.0, "E": 1.35, "R": 0.20},
    fixed={"R": 0.20},          # R from independent experiment
)

---

Fix multiple parameters simultaneously

peak_all_fixed = tl.PeakSpec(
    name="P_ref",
    model="fo_rq",
    init={"Tm": 490.0, "Im": 1000.0, "E": 1.20},
    fixed={"Tm": 490.0, "E": 1.20},    # only Im is free
)

With only Im free, the fit reduces to a simple linear scaling and is guaranteed to converge.

---

Setting fixed=False explicitly

Passing fixed={"b": False} (boolean False) leaves b free for optimisation. This is the same as not including b in fixed at all.

---

Inspect which parameters were fixed

for pk in result.peaks:
    spec_fixed = pk  # PeakResult does not carry the original spec
    # compare pk.params to your original init to see what moved
    for name, val in result.peaks[0].params.items():
        print(f"  {name}: {val:.6g}")