06 — Power Spectra Comparison
Purpose: Compare the two-point statistics of Agora test maps, DDPM-generated samples, and Gaussian realisations.
This notebook computes and plots the angular auto- and cross-power spectra for the CIB and tSZ channels:
Auto-spectra — Cℓ^{CIB} and Cℓ^{tSZ} for all three sample types, binned over 300 < ℓ < 4000 in bins of Δℓ = 60.
Cross-spectrum — Cℓ^{CIB×tSZ} probing spatial correlation between dusty star-forming galaxies and hot gas traced by tSZ.
Residuals — (C_ℓ^{Agora} − C_ℓ^{DDPM}) / σ(C_ℓ^{Agora}) to quantify agreement within sample variance.
Multi-frequency correlations — cross-correlation coefficients between the 95, 150, and 857 GHz CIB channels (Appendix B).
Inputs:
Test maps and DDPM samples:
data/low_pass/2mJy/*.npyGaussian baseline:
data/low_pass/2mJy/gaussian_cib_tsz_2mJy_lp.npyILC noise power spectra:
data/ilc/ilc_weights_residuals_agora_fg_model.npy
Outputs: power spectrum comparison plots (Figure 4), multi-frequency correlation plots (Figure 9).
Key module functions:
foregrounds_diffusion.flatmaps.map2clforegrounds_diffusion.flatmaps.cl2mapforegrounds_diffusion.preprocessing.renormalize_dm_maps
Paper reference: §4.3 (Figure 4), Appendix B (Figure 9).
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Building wheels for collected packages: foregrounds_diffusion
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[notice] To update, run: pip install --upgrade pip
1 Configuration
Map geometry and ℓ-binning. The 6° × 6° patches at 1.41′/px give a minimum multipole of ℓ_min ≈ 1/6° ≈ 10 and a Nyquist multipole of ℓ_Nyq ≈ 6° × 256 / (6° × 1.41′ / 60°) ≈ 7700. We analyse 300 < ℓ < 4000 in bins of Δℓ = 60 to match the ℓ-range used in the paper’s power spectrum comparison.
[ ]:
import numpy as np
import matplotlib.pyplot as plt
from pathlib import Path
from foregrounds_diffusion.flatmaps import map2cl
from foregrounds_diffusion.preprocessing import renormalize_dm_maps, denormalize_dm_maps
from foregrounds_diffusion.moments import mean_cls, mean_cross_cls
PTSRC = 2
flatskymapparams = [256, 256, 1.40625, 1.40625] # [nx, ny, dx_arcmin, dy_arcmin]
LMIN, LMAX, LBIN = 300, 4000, 60
N_MAPS = 500 # maximum patches to analyse
PROJECT_ROOT = Path("/home/apb86/cmb_foregrounds_diffusion")
PATCHES_DIR = Path(f"data/low_pass/{PTSRC}mJy")
2 Load and denormalise maps
Load the normalised .npy arrays and the norm_params file written by 03_patch_extraction.ipynb. Denormalise each channel back to physical units (µK) using denormalize_dm_maps before computing power spectra, so that Cℓ values are in µK².
[ ]:
# Load normalised training patches (channels-last: shape (N, H, W, 1)) and
# the DDPM sample array (channels-first: shape (N, 2, H, W)).
# norm_params = [cib_mean, cib_std, tsz_mean, tsz_std] — saved by notebook 03
# (both channels z-scored; denormalise with denormalize_dm_maps).
cib_maps = np.load(PATCHES_DIR / f"CIB_map_150GHz_256_st6_minmax_{PTSRC}mJy_zero_lp.npy")
tsz_maps = np.load(PATCHES_DIR / f"tSZ3_map_150GHz_256_st6_minmax_{PTSRC}mJy_norm_lp.npy")
ddpm_raw = np.load(PROJECT_ROOT / "data" / "low_pass" / f"{PTSRC}mJy" / f"new_samples_cib_tsz_{PTSRC}mJy_zero_norm_6x6_w_au_lp.npy")
gauss_maps = np.load(PATCHES_DIR / f"gaussian_cib_tsz_{PTSRC}mJy_lp.npy")
train_maps = np.concatenate([cib_maps, tsz_maps], axis=-1) # (N, H, W, 2)
print(f"train_maps shape: {train_maps.shape}")
print(f"ddpm_raw shape: {ddpm_raw.shape}")
# Load saved normalisation parameters from patch extraction
norm_params = np.load(PATCHES_DIR / f"norm_params_{PTSRC}mJy.npy")
cib_mean, cib_std, tsz_mean, tsz_std = norm_params
print(f"CIB — mean: {cib_mean:.4f} std: {cib_std:.4f}")
print(f"tSZ — mean: {tsz_mean:.4f} std: {tsz_std:.4f}")
ddpm_renorm = denormalize_dm_maps(ddpm_raw, cib_mean, cib_std, tsz_mean, tsz_std)
print(f"Denormalised DDPM — CIB range: [{ddpm_renorm[:,0].min():.4f}, {ddpm_renorm[:,0].max():.4f}]")
print(f"Denormalised DDPM — tSZ range: [{ddpm_renorm[:,1].min():.4f}, {ddpm_renorm[:,1].max():.4f}]")
# DDPM samples are (N, 2, H, W) channels-first; Agora/Gaussian are (N, H, W, 1)
ddpm_cib = ddpm_renorm[:, 0] # (N, H, W)
ddpm_tsz = ddpm_renorm[:, 1]
agora_cib = cib_maps[:, :, :, 0]
agora_tsz = tsz_maps[:, :, :, 0]
# gauss_maps shape depends on generation; handle both (N, 2, H, W) and (N, H, W, 2)
if gauss_maps.ndim == 4 and gauss_maps.shape[1] == 2:
gauss_cib = gauss_maps[:, 0]
gauss_tsz = gauss_maps[:, 1]
else:
gauss_cib = gauss_maps[:, :, :, 0]
gauss_tsz = gauss_maps[:, :, :, 1]
n_maps = min(N_MAPS, len(agora_cib), len(ddpm_cib), len(gauss_cib))
print(f"Using {n_maps} maps from each source for power spectrum estimation")
3 Inspect sample maps
Quick sanity check: print pixel statistics and display a randomly selected Agora and DDPM patch side-by-side. Useful for catching normalisation errors or loading mistakes before the expensive power-spectrum computation.
[13]:
cib_ddpm_1 = ddpm_tsz[3]
print(np.min(cib_ddpm_1))
print(np.max(cib_ddpm_1))
print(np.mean(cib_ddpm_1))
print(np.std(cib_ddpm_1))
plt.imshow(cib_ddpm_1)
plt.colorbar()
-5.1153903
-1.3764648
-4.0962086
0.754244
[13]:
<matplotlib.colorbar.Colorbar at 0x7fafd83c5fd0>
[14]:
cib_agora_1 = agora_tsz[4,:,:]
print(np.min(cib_agora_1))
print(np.max(cib_agora_1))
print(np.mean(cib_agora_1))
print(np.std(cib_agora_1))
plt.imshow(cib_agora_1)
plt.colorbar()
-17.703312607014137
9.040638558318697
0.061315292845084246
2.2010691284847526
[14]:
<matplotlib.colorbar.Colorbar at 0x7fafd2dd3490>
[ ]:
# Compute binned power spectra over the test set.
# mean_cls returns (el, mean_cl, std_cl) — the standard deviation across N maps
# gives the sample variance, not the noise on the mean. Divide by sqrt(N) for
# the error on the mean if comparing to theory predictions.
el, cl_cib_agora, cl_cib_agora_err = mean_cls(agora_cib[:n_maps], flatskymapparams, LMIN, LMAX, LBIN)
_, cl_cib_ddpm, cl_cib_ddpm_err = mean_cls(ddpm_cib[:n_maps], flatskymapparams, LMIN, LMAX, LBIN)
_, cl_cib_gauss, cl_cib_gauss_err = mean_cls(gauss_cib[:n_maps], flatskymapparams, LMIN, LMAX, LBIN)
_, cl_tsz_agora, cl_tsz_agora_err = mean_cls(agora_tsz[:n_maps], flatskymapparams, LMIN, LMAX, LBIN)
_, cl_tsz_ddpm, cl_tsz_ddpm_err = mean_cls(ddpm_tsz[:n_maps], flatskymapparams, LMIN, LMAX, LBIN)
_, cl_tsz_gauss, cl_tsz_gauss_err = mean_cls(gauss_tsz[:n_maps], flatskymapparams, LMIN, LMAX, LBIN)
_, cl_cross_agora, _ = mean_cross_cls(agora_cib[:n_maps], agora_tsz[:n_maps], flatskymapparams, LMIN, LMAX, LBIN)
_, cl_cross_ddpm, _ = mean_cross_cls(ddpm_cib[:n_maps], ddpm_tsz[:n_maps], flatskymapparams, LMIN, LMAX, LBIN)
_, cl_cross_gauss, _ = mean_cross_cls(gauss_cib[:n_maps], gauss_tsz[:n_maps], flatskymapparams, LMIN, LMAX, LBIN)
4 Compute power spectra
mean_cls loops over N patches, calls map2cl for each, and returns the mean and standard deviation of the power spectrum across the sample. mean_cross_cls similarly computes the cross-spectrum between the CIB and tSZ channels. A positive cross-spectrum indicates that CIB-bright and tSZ-bright regions are spatially correlated — expected because both tracers peak in massive halos.
[16]:
fig, axes = plt.subplots(1, 3, figsize=(15, 5))
for ax, cl_a, err_a, cl_d, err_d, cl_g, title in zip(
axes,
[cl_cib_agora, cl_tsz_agora, cl_cross_agora],
[cl_cib_agora_err, cl_tsz_agora_err, np.zeros_like(cl_cross_agora)],
[cl_cib_ddpm, cl_tsz_ddpm, cl_cross_ddpm],
[cl_cib_ddpm_err, cl_tsz_ddpm_err, np.zeros_like(cl_cross_ddpm)],
[cl_cib_gauss, cl_tsz_gauss, cl_cross_gauss],
[r"$C_\ell^{\rm CIB}$", r"$C_\ell^{\rm tSZ}$", r"$C_\ell^{\rm CIB \times tSZ}$"],
):
ax.fill_between(el, cl_a - err_a, cl_a + err_a, alpha=0.3, color="C0")
ax.fill_between(el, cl_d - err_d, cl_d + err_d, alpha=0.3, color="C1")
ax.plot(el, cl_a, label="Agora", color="C0")
ax.plot(el, cl_d, label="DDPM", color="C1")
ax.plot(el, cl_g, label="Gaussian", color="C2", linestyle="--")
ax.set_xlabel(r"$\ell$"); ax.set_ylabel(title); ax.legend()
ax.set_yscale("log")
plt.tight_layout()
plt.show()
5 Results and residuals
Plot the mean power spectra with 1σ error bands (sample variance across N patches). The residual panel shows (Agora − DDPM) / σ_Agora in units of the Agora sample variance: values within ±2 indicate agreement within the Agora statistical scatter. Persistent bias at high ℓ would indicate the DDPM has not learnt the correct small-scale power.
[17]:
# Fractional residuals normalised by Agora sample variance
resid_cib = (cl_cib_agora - cl_cib_ddpm) / (cl_cib_agora_err + 1e-30)
resid_tsz = (cl_tsz_agora - cl_tsz_ddpm) / (cl_tsz_agora_err + 1e-30)
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))
ax1.axhline(0, color="k", lw=0.8, ls="--")
ax1.plot(el, resid_cib)
ax1.set_xlabel(r"$\ell$"); ax1.set_ylabel(r"$(C_\ell^{\rm Agora} - C_\ell^{\rm DDPM}) / \sigma$")
ax1.set_title("CIB residuals")
ax2.axhline(0, color="k", lw=0.8, ls="--")
ax2.plot(el, resid_tsz)
ax2.set_xlabel(r"$\ell$"); ax2.set_title("tSZ residuals")
plt.tight_layout(); plt.show()
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