"""
Collect numerical, masking, simulation, plotting, and export utilities shared by
analysis workflows.
This module belongs to :mod:`pyfli.analysis` and is part of PyFLI post-processing,
diagnostics, statistical comparison, and result-loading utilities for fitted FLI/FLIM
datasets. Public API includes functions :func:`circular_convolution_fft`,
:func:`single_ex_decay_summed_overtime`, :func:`gate_j`, :func:`Pj_continuous_mono`,
:func:`Pj_from_samples_mono`, :func:`multimodal_normal`, :func:`recovery_plot`,
:func:`threshold_masking`, :func:`data_masking`, and
:func:`save_3d_array_as_tiff_sequence`.
"""
import math
import os
from typing import Any
import matplotlib.pyplot as plt
import numpy as np
import tifffile
from scipy.integrate import quad
from scipy.stats import pearsonr
from pyfli import logging
from pyfli.plot_style import dark_palette, legend_outside
from ..data_vnp.color_processor import ColorProcessor
[docs]
def circular_convolution_fft(
x: np.ndarray, h: np.ndarray, broadcast_irf: bool = True
) -> np.ndarray:
"""
Run the circular convolution FFT routine.
Parameters
----------
x : np.ndarray
Input array, coordinate, or signal being transformed.
h : np.ndarray
IRF, image height, or temporal kernel used by the routine.
broadcast_irf : bool
Whether a shared IRF should be broadcast to every pixel.
Returns
-------
np.ndarray
Circular convolution result with the same length as the input decay.
"""
x = np.asarray(x)
h = np.asarray(h)
if x.ndim != 3 or h.ndim != 3:
raise ValueError(
f"x and h must be 3D arrays, got x.ndim={x.ndim}, h.ndim={h.ndim}"
)
if x.shape[-1] != h.shape[-1]:
raise ValueError(
f"Last dimension (convolution axis) must match: {x.shape[-1]} vs {h.shape[-1]}"
)
# Broadcast h to match x (for pixel-wise or shared IRFs)
if broadcast_irf:
if h.shape[0] != x.shape[0] or h.shape[1] != x.shape[1]:
h = np.broadcast_to(h, x.shape)
# h = np.broadcast_to(h, x.shape)
# Perform FFT along the last axis (axis=2)
X_fft = np.fft.fft(x, axis=2)
H_fft = np.fft.fft(h, axis=2)
# Frequency-domain multiplication
Y_fft = X_fft * H_fft
# Inverse FFT to get real-valued circular convolution result
y = np.real(np.fft.ifft(Y_fft, axis=2))
return y
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def single_ex_decay_summed_overtime(
tau: np.ndarray,
irf_data: np.ndarray,
alpha: float = 1.0,
err: float = 0.0,
laser_period: float = 12.5,
seed: int | None = None,
) -> tuple[Any, ...]:
"""
Run the single ex decay summed overtime routine.
Parameters
----------
tau : np.ndarray
Lifetime value or lifetime map in nanoseconds.
irf_data : np.ndarray
Instrument response data used to convolve or simulate decays.
alpha : float
Regularization strength, fraction value, or significance threshold used by the
routine.
err : float
Noise or perturbation level applied to simulated decays.
laser_period : float
Laser repetition period in nanoseconds.
seed : int | None
Random seed used for reproducible sampling.
Returns
-------
tuple[Any, ...]
Tuple containing the integrated single-exponential decay and time samples.
"""
if seed is not None:
np.random.seed(seed)
M, N, T = irf_data.shape
tau = np.asarray(tau, dtype=float)
# Ensure tau is broadcastable to (M, N, T)
tau = np.broadcast_to(tau[..., np.newaxis], (M, N, T))
# Time vector
t = np.linspace(0, laser_period, T)[np.newaxis, np.newaxis, :] # (1, 1, T)
# --- Avoid division by zero ---
zero_mask = (tau <= 0) | ~np.isfinite(tau)
safe_tau = np.where(
zero_mask, np.inf, tau
) # τ=0 → inf => exp(-t/inf)=1, then we zero it later
# --- Theoretical single exponential decay ---
f_t = (1.0 / safe_tau) * np.exp(-t / safe_tau)
# Zero out pixels where tau=0 or invalid
f_t[zero_mask] = 0.0
# --- Normalize IRF per pixel ---
I_sum = np.sum(irf_data, axis=2, keepdims=True)
if np.any(I_sum <= 0):
raise ValueError("One or more IRF pixels sum to zero; cannot normalize.")
I_t = irf_data / I_sum
# --- Circular convolution along time axis (axis=2) ---
s_ti = circular_convolution_fft(f_t, I_t)
# --- Add Gaussian noise ---
if np.isscalar(err):
noise = np.random.normal(0, err, size=s_ti.shape)
else:
noise = np.asarray(err, dtype=float)
if noise.shape != s_ti.shape:
raise ValueError("Shape mismatch: 'err' array must match signal shape")
# --- Final weighted signal ---
s_t = alpha * s_ti + (1.0 - alpha) * noise
s_t = np.clip(s_t, 0.0, None)
# Ensure f_t is zero wherever tau=0
s_t[zero_mask] = 0.0
return f_t, s_t, I_t, t
[docs]
def gate_j(m: int, T: float) -> np.ndarray:
"""
Run the gate j routine.
Parameters
----------
m : int
Gate, harmonic, or interval index.
T : float
Time axis or acquisition period used by the calculation.
Returns
-------
np.ndarray
Integrated gate image or trace for the requested gate index.
"""
buckets = []
for j in range(1, m + 1):
a = (j - 1) * T / m
b = j * T / m
buckets.append((a, b))
return buckets
[docs]
def Pj_continuous_mono(
f: np.ndarray, m: int, T: float, epsabs: float = 1e-8, epsrel: float = 1e-8
) -> Any:
"""
Run the pj continuous mono routine.
Parameters
----------
f : np.ndarray
Decay basis, distribution, or signal function used by the calculation.
m : int
Gate, harmonic, or interval index.
T : float
Time axis or acquisition period used by the calculation.
epsabs : float
Absolute integration tolerance.
epsrel : float
Relative integration tolerance.
Returns
-------
Any
Object produced by pj continuous mono.
"""
gates = np.array(gate_j(m, T)) # list-of-tuples → 2D array for slicing
a_vals, b_vals = gates[:, 0], gates[:, 1]
# Vectorized numerical integration using np.vectorize wrapper
def integrate_interval(a: np.ndarray, b: np.ndarray) -> np.ndarray:
"""
Run the integrate interval routine.
Parameters
----------
a : np.ndarray
Lower integration or interval bound.
b : np.ndarray
Upper integration or interval bound.
Returns
-------
np.ndarray
Integrated signal over the requested interval.
"""
val, _ = quad(f, a, b, epsabs=epsabs, epsrel=epsrel)
return val
integrate_vec = np.vectorize(integrate_interval)
Pj = integrate_vec(a_vals, b_vals)
return Pj
[docs]
def Pj_from_samples_mono(
t_samples: np.ndarray, y_samples: np.ndarray, m: int, T: float
) -> Any:
"""
Run the pj from samples mono routine.
Parameters
----------
t_samples : np.ndarray
Sample times used to integrate a mono-exponential decay.
y_samples : np.ndarray
Sampled mono-exponential values integrated over gates.
m : int
Gate, harmonic, or interval index.
T : float
Time axis or acquisition period used by the calculation.
Returns
-------
Any
Object produced by pj from samples mono.
"""
H, W, Tn = y_samples.shape
gates = gate_j(m, T)
# Ensure time axis and sample consistency
if t_samples.shape[0] != Tn:
raise ValueError("Length of t_samples must match y_samples.shape[-1].")
# Interpolate gate edges and ensure inclusion
Pj = np.zeros((H, W, m), dtype=float)
for j, (a, b) in enumerate(gates):
# Create boolean mask for time bins within gate
mask = (t_samples >= a) & (t_samples <= b)
# If gate falls outside sampled range, skip safely
if not np.any(mask):
continue
# Extract y and t segments for integration
t_sub = t_samples[mask]
y_sub = y_samples[..., mask]
# Include exact gate edges via vectorised linear interpolation (H,W pixels)
if t_sub[0] > a:
idx = int(np.clip(np.searchsorted(t_samples, a, side="right"), 1, Tn - 1))
w = (a - t_samples[idx - 1]) / (
t_samples[idx] - t_samples[idx - 1] + 1e-300
)
y_a = (
y_samples[..., idx - 1] * (1.0 - w) + y_samples[..., idx] * w
) # (H, W)
y_sub = np.concatenate((y_a[..., np.newaxis], y_sub), axis=-1)
t_sub = np.concatenate(([a], t_sub))
if t_sub[-1] < b:
idx = int(np.clip(np.searchsorted(t_samples, b, side="left"), 0, Tn - 2))
w = (b - t_samples[idx]) / (t_samples[idx + 1] - t_samples[idx] + 1e-300)
y_b = (
y_samples[..., idx] * (1.0 - w) + y_samples[..., idx + 1] * w
) # (H, W)
y_sub = np.concatenate((y_sub, y_b[..., np.newaxis]), axis=-1)
t_sub = np.concatenate((t_sub, [b]))
# Integrate over time using trapezoidal rule (vectorized along last axis)
Pj[..., j] = np.trapz(y_sub, x=t_sub, axis=-1)
# Normalize to obtain probability distribution per pixel
Pj_sum = np.sum(Pj, axis=-1, keepdims=True)
Pj /= np.maximum(Pj_sum, 1e-12)
return Pj
[docs]
def multimodal_normal(
n_samples: int = 10000,
mus: np.ndarray | None = None,
sigma: float | None = None,
weights: np.ndarray | None = None,
seed: int | None = None,
) -> tuple[Any, ...]:
"""
Run the multimodal normal routine.
Parameters
----------
n_samples : int
Number of samples, components, gates, or iterations used by the routine.
mus : np.ndarray | None
Gaussian component means used by the multimodal sampler.
sigma : float | None
Standard deviation used by a sampler or noise model.
weights : np.ndarray | None
Sampling or model weights used by the routine.
seed : int | None
Random seed used for reproducible sampling.
Returns
-------
tuple[Any, ...]
Tuple containing sampled values from the configured normal mixture.
"""
np.random.seed(seed)
if mus is None:
raise ValueError("You must provide a list of means (mus).")
mus = np.array(mus)
n_modes = len(mus)
# Ensure sigma matches mus
if sigma is None:
sigma = np.ones(n_modes) * 1.0 # default sigma = 1 for all modes
elif isinstance(sigma, (int, float)):
sigma = np.full(n_modes, sigma)
else:
sigma = np.array(sigma)
assert len(sigma) == n_modes, (
"sigma must be a single value or same length as mus"
)
# Equal weights if none provided
if weights is None:
weights = np.ones(n_modes) / n_modes
else:
weights = np.array(weights)
weights /= weights.sum() # normalize
# Number of samples per mode
samples_per_mode = np.random.multinomial(n_samples, weights)
# Generate samples for each mode
samples = []
samples_2d = np.zeros(
(n_modes, n_samples), dtype=float
) # n_samples cols = max possible
for i, (mu_val, s, n) in enumerate(zip(mus, sigma, samples_per_mode)):
samp = np.random.normal(loc=mu_val, scale=s, size=n)
samples.append(samp)
samples_2d[i, :n] = samp
samples = np.concatenate(samples)
# Ensure all values are positive (reflect negatives)
samples = np.abs(samples)
return samples, samples_2d
[docs]
def recovery_plot(
gt_dict: np.ndarray, est_dict: np.ndarray, keys_to_plot: np.ndarray | None = None
) -> np.ndarray:
"""
Plots Ground Truth vs Estimates for specific keys.
Handles data shapes: (N, X, Y) or (N, Batch, X, Y).
Args:
gt_dict: Dictionary of Ground Truth arrays.
est_dict: Dictionary of Estimated arrays.
keys_to_plot: List of strings (keys). If None, plots all keys in gt_dict.
"""
if keys_to_plot is None:
keys_to_plot = list(gt_dict.keys())
# 1. Automatic Grid Arrangement
num_plots = len(keys_to_plot)
if num_plots == 0:
return
cols = min(num_plots, 4)
rows = math.ceil(num_plots / cols)
fig, axes = plt.subplots(rows, cols, figsize=(5 * cols, 4.5 * rows), squeeze=False)
axes = axes.flatten()
for i, key in enumerate(keys_to_plot):
ax = axes[i]
# Ensure data is numpy array and flatten (X, Y) -> (X*Y,)
x = np.array(gt_dict[key]).flatten()
y = np.array(est_dict[key]).flatten()
# Calculate Pearson Correlation across all pixels
r_val, _ = pearsonr(x, y)
# 2. Scatter Plot
# Using the style from your reference image
ax.scatter(x, y, color="#1c3f73", alpha=0.5, s=15, edgecolors="none")
# 3. Identity Line (y = x) - UPDATED TO RED DASH
all_vals = np.concatenate([x, y])
# Calculate limits: start slightly below the absolute minimum
data_min = np.min(all_vals)
data_max = np.max(all_vals)
buffer = (data_max - data_min) * 0.05
plot_min = data_min - buffer
plot_max = data_max + buffer
ax.plot(
[plot_min, plot_max],
[plot_min, plot_max],
color="#8c2e24",
linestyle="--",
linewidth=1.5,
zorder=5,
)
# 4. Styling & Formatting
ax.set_title(key, fontsize=15)
ax.set_xlabel("Ground truth", fontsize=12)
# FORCE AXIS TO START FROM LESSER THAN MINIMUM
ax.set_xlim(plot_min, plot_max)
ax.set_ylim(plot_min, plot_max)
if i % cols == 0:
ax.set_ylabel("Estimate", fontsize=12)
# Display r-value
ax.text(
0.05,
0.92,
f"$r = {r_val:.3f}$",
transform=ax.transAxes,
fontsize=13,
fontweight="bold",
)
# Clean background and spines
ax.grid(True, linestyle="-", alpha=0.2)
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
# Hide unused axes
for j in range(i + 1, len(axes)):
axes[j].axis("off")
plt.tight_layout()
plt.show()
return fig
[docs]
def threshold_masking(
fli: np.ndarray, irf: np.ndarray, threshold: int = 100
) -> tuple[Any, ...]:
"""
Run the threshold masking routine.
Parameters
----------
fli : np.ndarray
FLI lifetime map or decay-derived image to threshold.
irf : np.ndarray
Instrument response function aligned with the decay signal.
threshold : int
Threshold used to mask, classify, or validate data.
Returns
-------
tuple[Any, ...]
Tuple containing thresholded mask arrays and metadata.
"""
if threshold is None:
raise ValueError("no thershold value provided")
else:
intensity = np.sum(fli, axis=-1)
mask = intensity > threshold
mask = mask.astype(bool)
if mask.ndim < fli.ndim:
mask_expanded = mask[..., np.newaxis]
masked_fli = fli * mask_expanded
masked_irf = irf * mask_expanded
else:
masked_fli = fli * mask
masked_irf = irf * mask
return masked_fli, masked_irf
[docs]
def data_masking(*arrays: Any, mask: np.ndarray, return_list: bool = False) -> Any:
"""
Run the data masking routine.
Parameters
----------
*arrays : Any
Additional positional values accepted by the routine.
mask : np.ndarray
Boolean or labeled mask selecting pixels for the operation.
return_list : bool
If ``True``, return a list of masks instead of a combined mask.
Returns
-------
Any
Object produced by data masking.
"""
mask = mask.astype(bool)
results = []
for arr in arrays:
if not isinstance(arr, np.ndarray):
raise TypeError("All inputs must be numpy arrays")
if mask.ndim < arr.ndim:
expand_dims = arr.ndim - mask.ndim
mask_expanded = mask[(...,) + (None,) * expand_dims]
else:
mask_expanded = mask
try:
masked = arr * mask_expanded
except ValueError:
raise ValueError("Mask is not broadcastable to array shape")
results.append(masked)
if len(results) == 1:
return results[0]
return results if return_list else tuple(results)
[docs]
def save_3d_array_as_tiff_sequence(
array_3d: np.ndarray, output_folder: str, prefix: str = "frame"
) -> None:
"""
Saves a 3D numpy array (H, W, T) as a series of 2D TIFF files.
Parameters:
- array_3d: The numpy array of shape (H, W, T)
- output_folder: Path to the folder where TIFs will be saved
- prefix: Filename prefix (e.g., 'frame_001.tif')
"""
# Create the directory if it doesn't exist
if not os.path.exists(output_folder):
os.makedirs(output_folder)
_, _, T = array_3d.shape
logging.info(f"Saving {T} frames to '{output_folder}'...")
for t in range(T):
# Extract the 2D slice (X, Y) at time t
# Note: tifffile expects (H, W), so we take [:, :, t]
frame = array_3d[:, :, t]
# Format filename with leading zeros for correct sorting (e.g., frame_005.tif)
file_name = f"{prefix}_{t:03d}.tif"
file_path = os.path.join(output_folder, file_name)
# Save the slice
tifffile.imwrite(file_path, frame.astype(np.float32))
logging.info("Saving complete.")
[docs]
def save_as_uint16_sequence(
data: np.ndarray, output_folder: str, prefix: str = "frame"
) -> None:
"""
Saves (H, W, T) array as 16-bit integer TIFFs.
"""
if not os.path.exists(output_folder):
os.makedirs(output_folder)
# 1. Handle Negative Values (Safety for uint16)
# Background subtraction in your class might leave tiny negatives
data = np.maximum(data, 0)
# 2. Optional: Auto-Scaling (Only use if data is 0.0 - 1.0 or very small)
# If your data is already raw photon counts, skip this step.
if data.max() <= 1.0 and data.max() > 0:
data = data * 65535
# 3. Cast to uint16
# This will truncate decimals (e.g., 1.9 becomes 1)
data_uint16 = data.astype(np.uint16)
_, _, T = data_uint16.shape
for t in range(T):
frame = data_uint16[:, :, t]
file_path = os.path.join(output_folder, f"{prefix}_{t:03d}.tif")
tifffile.imwrite(file_path, frame)
logging.info(f"Saved {T} files to {output_folder} in uint16 format.")
[docs]
def random_true_pixel(bool_array: np.ndarray) -> Any:
"""
Run the random true pixel routine.
Parameters
----------
bool_array : np.ndarray
Boolean array from which a true pixel is selected.
Returns
-------
Any
Object produced by random true pixel.
"""
true_indices = np.flatnonzero(bool_array)
if true_indices.size == 0:
return None
random_linear_idx = np.random.choice(true_indices)
pix_x, pix_y = np.unravel_index(random_linear_idx, bool_array.shape)
return int(pix_x), int(pix_y)
[docs]
def PhasorFreqComputaion(
laser_period: float = 12.5,
gate_delay: np.ndarray | None = None,
num_gates: int | None = None,
) -> np.ndarray: # all the units in ns
"""
Run the phasor freq computaion routine.
Parameters
----------
laser_period : float
Laser repetition period in nanoseconds.
gate_delay : np.ndarray | None
Delay of each gate relative to the excitation pulse.
num_gates : int | None
Number of acquisition gates used for frequency computation.
Returns
-------
np.ndarray
Phasor frequency-domain representation for the input decay.
"""
freq = 1000.0 / laser_period
if gate_delay is None or num_gates is None:
effective_freq = freq
else:
effective_freq = 1000.0 / (
num_gates * gate_delay
) # frequency is computed in the MHz if the gate delays are in ns
return effective_freq
[docs]
def save_plot(
save_dir: str,
name: str,
fig: Any | None = None,
dpi: int = 300,
close: bool = False,
) -> None:
# Saves a plot. Handles subplots (pass fig) or direct plots (uses current)
"""
Save plot.
Parameters
----------
save_dir : str
Directory where outputs are saved.
name : str
Dataset, experiment, figure, or output name.
fig : Any | None
Matplotlib figure object to update or save.
dpi : int
Resolution used when saving a figure.
close : bool
Whether to close the figure after saving.
Returns
-------
None
No object is returned; the function save plot.
"""
path = os.path.join(save_dir, f"{name}.png")
target = fig if fig is not None else plt
try:
target.savefig(path, bbox_inches="tight", dpi=dpi)
except Exception as e:
logging.error(f"ERROR saving {name}: {e!s}")
if close:
plt.close(fig) if fig else plt.close()
[docs]
def plot_pixel_diagnostic(
binned_decay: np.ndarray,
all_fitset: np.ndarray,
names: Any,
pixel: np.ndarray | None = None,
mask: np.ndarray | None = None,
t: np.ndarray | None = None,
yscale: str = "log",
model_type: str = "BI-EXPONENTIAL",
colors: Any | None = None,
figsize: tuple[int, ...] = (12, 6),
raw_style: str = "bar",
map_aspect: str = "equal",
show_colorbar: bool = True,
show: bool = True,
) -> np.ndarray:
"""
Plot pixel diagnostic.
Parameters
----------
binned_decay : np.ndarray
Binned decay cube used for fitting or diagnostics.
all_fitset : np.ndarray
Collection of fit-result dictionaries used for comparison or plotting.
names : Any
Dataset names used in summaries and plots.
pixel : np.ndarray | None
Selected pixel coordinate.
mask : np.ndarray | None
Boolean or labeled mask selecting pixels for the operation.
t : np.ndarray | None
Time axis or acquisition period used by the calculation.
yscale : str
Scale used for the y-axis.
model_type : str
FLI/FLIM model family, such as mono- or bi-exponential.
colors : Any | None
Color sequence used for plotted sources or groups.
figsize : tuple[int, ...]
Figure size passed to Matplotlib.
raw_style : str
Style used to draw raw pixel decay data.
map_aspect : str
Aspect ratio used when rendering lifetime maps.
show_colorbar : bool
Whether to draw a colorbar.
show : bool
Whether to display the generated plot.
Returns
-------
np.ndarray
Matplotlib figure or axes containing the pixel diagnostic plot.
"""
jet_m = ColorProcessor().lowest_zero("jet")
if pixel is None:
if mask is None:
raise ValueError("Provide either pixel=(row, col) or mask.")
x, y = random_true_pixel(mask)
else:
x, y = pixel
raw = np.asarray(binned_decay[x, y, :], dtype=float)
bins = raw.shape[-1]
if t is not None:
xs = np.asarray(t, dtype=float).ravel()
if len(xs) != bins:
raise ValueError(
f"t length ({len(xs)}) does not match decay bins ({bins}); "
"x-axis and data would be misaligned."
)
xlabel = "Time (ns)"
else:
xs = np.arange(bins)
xlabel = "Gate #"
if colors is None:
colors = dark_palette(len(all_fitset))
fig = plt.figure(figsize=figsize)
gs = fig.add_gridspec(2, 2, width_ratios=[1.1, 2], height_ratios=[3, 1])
ax_map = fig.add_subplot(gs[:, 0]) # full-height left panel
ax_top = fig.add_subplot(gs[0, 1])
ax_bot = fig.add_subplot(gs[1, 1], sharex=ax_top)
intensity = np.sum(binned_decay, axis=-1) # (H, W)
display_intensity = intensity if mask is None else intensity * mask
im = ax_map.imshow(display_intensity, cmap=jet_m, aspect=map_aspect)
# imshow's x-axis = columns, y-axis = rows -> mark pixel at (col, row)=(y, x)
ax_map.scatter(y, x, marker="x", c="red", s=80, linewidths=2)
ax_map.set_title("Intensity (Summed)")
# ax_map.set_xlabel("Column"); ax_map.set_ylabel("Row")
if show_colorbar:
fig.colorbar(im, ax=ax_map, fraction=0.046, pad=0.04)
if raw_style == "bar":
width = (xs[1] - xs[0]) if len(xs) > 1 else 1.0
ax_top.bar(
xs,
raw,
width=width,
color="0.8",
edgecolor="none",
zorder=1,
label="Raw Data",
)
elif raw_style == "step":
ax_top.plot(
xs,
raw,
color="0.7",
lw=0.9,
drawstyle="steps-mid",
zorder=1,
label="Raw Data",
)
else: # "line"
ax_top.plot(xs, raw, color="0.7", lw=0.9, zorder=1, label="Raw Data")
for i, fs in enumerate(all_fitset):
label = names[i] if i < len(names) else f"Fit {i + 1}"
fit = np.asarray(fs["fit_map"][x, y, :], dtype=float)
ax_top.plot(
xs, fit, color=colors[i], lw=1.3, zorder=2 + i, label=f"Fit: {label}"
)
ax_top.set_yscale(yscale) # log / linear switch
ax_top.set_ylabel("Photon Counts")
ax_top.set_title(f"Fit Diagnostics ({model_type}) [pixel {x}, {y}]")
legend_outside(ax_top, ncol=2, fontsize=8, framealpha=0.9)
if yscale == "log":
pos = raw[raw > 0]
if pos.size:
ax_top.set_ylim(bottom=max(pos.min() * 0.1, 1e-3))
ax_bot.axhline(0, color="black", lw=0.8, zorder=1)
for i, fs in enumerate(all_fitset):
label = names[i] if i < len(names) else f"Fit {i + 1}"
res = np.asarray(fs["residual_map"][x, y, :], dtype=float)
ax_bot.plot(xs, res, color=colors[i], lw=1.0, label=f"{label} residuals")
ax_bot.set_ylabel("Residuals")
ax_bot.set_xlabel(xlabel)
fig.tight_layout()
if show:
plt.show()
return fig
