""" 11 — Pearson correlation between POD coefficients and (raw inputs, derived inputs, output metrics). Fits PCA on the first TRAIN_SIZE samples, projects all 2000 onto the basis, computes Pearson R between each PC coefficient and a curated set of raw / derived / output quantities, then renders a single table- style heatmap. """ import numpy as np import matplotlib.pyplot as plt from matplotlib.gridspec import GridSpec from matplotlib.transforms import blended_transform_factory from sklearn.decomposition import PCA from scipy import stats from _utils import ( load_data, compute_rth, CHIP_AREA, PARAM_IDX, TRAIN_SIZE, N_MODES, PLOTS_DIR, ) FS = 20 LATEX = { # Raw "Q1": r"$Q_1$", "Q2": r"$Q_2$", "m1": r"$\dot{m}_1$", "m2": r"$\dot{m}_2$", "T_in1": r"$T_{\mathrm{in},1}$", "T_in2": r"$T_{\mathrm{in},2}$", # Derived "Q_total": r"$Q_1 + Q_2$", "m_total": r"$\dot{m}_1 + \dot{m}_2$", "T_in_avg": r"$\bar{T}_{\mathrm{in}}$", "Q1 - Q2": r"$Q_1 - Q_2$", "m1 - m2": r"$\dot{m}_1 - \dot{m}_2$", "T_in1 - T_in2": r"$T_{\mathrm{in},1} - T_{\mathrm{in},2}$", "Q1 / m1": r"$Q_1 / \dot{m}_1$", "Q2 / m2": r"$Q_2 / \dot{m}_2$", "Q1/m1 - Q2/m2": r"$Q_1/\dot{m}_1 - Q_2/\dot{m}_2$", # Outputs "Tmax_chip1": r"$T_{\max,\mathrm{chip1}}$", "Tmax_chip2": r"$T_{\max,\mathrm{chip2}}$", "Rth1": r"$R_{\mathrm{th},1}$", "Rth2": r"$R_{\mathrm{th},2}$", } DESC = { "Q1": "Chip 1 heat load", "Q2": "Chip 2 heat load", "m1": "Inlet 1 mass flow rate", "m2": "Inlet 2 mass flow rate", "T_in1": "Inlet 1 temperature", "T_in2": "Inlet 2 temperature", "Q_total": "Total heat load", "m_total": "Total mass flow rate", "T_in_avg": "Mean inlet temperature", "Q1 - Q2": "Heat load difference", "m1 - m2": "Flow rate difference", "T_in1 - T_in2": "Inlet temp. difference", "Q1 / m1": "Side 1 thermal load", "Q2 / m2": "Side 2 thermal load", "Q1/m1 - Q2/m2": "Thermal load difference", "Tmax_chip1": "Chip 1 peak temperature", "Tmax_chip2": "Chip 2 peak temperature", "Rth1": "Chip 1 thermal resistance", "Rth2": "Chip 2 thermal resistance", } def build_features(parameters, fields, coords): Q1 = parameters[:, PARAM_IDX["Q1"]] * CHIP_AREA Q2 = parameters[:, PARAM_IDX["Q2"]] * CHIP_AREA m1 = parameters[:, PARAM_IDX["m1"]] m2 = parameters[:, PARAM_IDX["m2"]] T1 = parameters[:, PARAM_IDX["T_in1"]] T2 = parameters[:, PARAM_IDX["T_in2"]] rth1, rth2, tmax1, tmax2 = compute_rth(fields, coords, parameters) return { # Raw "Q1": Q1, "Q2": Q2, "m1": m1, "m2": m2, "T_in1": T1, "T_in2": T2, # Derived "Q_total": Q1 + Q2, "m_total": m1 + m2, "T_in_avg": (T1 + T2) / 2, "Q1 - Q2": Q1 - Q2, "m1 - m2": m1 - m2, "T_in1 - T_in2": T1 - T2, "Q1 / m1": Q1 / m1, "Q2 / m2": Q2 / m2, "Q1/m1 - Q2/m2": Q1 / m1 - Q2 / m2, # Outputs "Tmax_chip1": tmax1, "Tmax_chip2": tmax2, "Rth1": rth1, "Rth2": rth2, } def main(): parameters, fields, coords, _ = load_data() pca = PCA(n_components=N_MODES).fit(fields[:TRAIN_SIZE]) coeffs = pca.transform(fields) var = pca.explained_variance_ratio_ feats = build_features(parameters, fields, coords) n_raw, n_derived, n_out = 6, 9, 4 names = list(feats.keys()) sep1, sep2 = n_raw - 0.5, n_raw + n_derived - 0.5 cat_labels = [ ("Raw Inputs", n_raw / 2 - 0.5), ("Derived Inputs", n_raw + n_derived / 2 - 0.5), ("Outputs", n_raw + n_derived + n_out / 2 - 0.5), ] n_p = len(names) R = np.zeros((n_p, N_MODES)) for j, n in enumerate(names): for i in range(N_MODES): R[j, i], _ = stats.pearsonr(feats[n], coeffs[:, i]) fig = plt.figure(figsize=(16, 14)) gs = GridSpec(1, 3, width_ratios=[5.0, 2.75, 0.15], wspace=0.0) ax_table = fig.add_subplot(gs[0, 0]) ax_heat = fig.add_subplot(gs[0, 1]) ax_cbar = fig.add_subplot(gs[0, 2]) im = ax_heat.imshow(R, cmap="RdBu_r", vmin=-1, vmax=1, aspect="auto") ax_heat.set_xticks(range(N_MODES)) ax_heat.set_xticklabels([f"PC{i+1}\n({var[i]*100:.1f}%)" for i in range(N_MODES)], fontsize=FS - 4) ax_heat.xaxis.set_ticks_position("top") ax_heat.xaxis.set_label_position("top") ax_heat.set_yticks([]) for j in range(n_p): for i in range(N_MODES): r = R[j, i] color = "white" if abs(r) > 0.55 else "black" ax_heat.text(i, j, f"{r:+.2f}", ha="center", va="center", fontsize=FS - 2, color=color) for s in [sep1, sep2]: ax_heat.axhline(y=s, color="black", linewidth=2.5) cbar = fig.colorbar(im, cax=ax_cbar) cbar.set_label("Pearson $R$", fontsize=FS - 2) cbar.ax.tick_params(labelsize=FS - 4) ax_table.set_xlim(0, 1) ax_table.set_ylim(n_p - 0.5, -0.5) ax_table.axis("off") trans_top = blended_transform_factory(ax_table.transData, ax_table.transAxes) for x, h in [(0.05, "Type"), (0.34, "Description"), (0.79, "Symbol")]: ax_table.text(x, 1.03, h, fontsize=FS - 2, ha="center", va="bottom", fontweight="bold", transform=trans_top) for s in [sep1, sep2]: ax_table.plot([0.0, 1.0], [s, s], color="black", linewidth=2.5, transform=ax_table.transData, clip_on=False) ax_table.plot([0.10, 0.10], [-0.5, n_p - 0.5], color="gray", linewidth=0.5, alpha=0.5) ax_table.plot([0.58, 0.58], [-0.5, n_p - 0.5], color="gray", linewidth=0.5, alpha=0.5) for label, y_pos in cat_labels: ax_table.text(0.05, y_pos, label, fontsize=FS - 2, ha="center", va="center", rotation=90, fontweight="bold") for j, n in enumerate(names): ax_table.text(0.12, j, DESC.get(n, n), fontsize=FS - 2, ha="left", va="center") ax_table.text(0.60, j, LATEX.get(n, n), fontsize=FS - 2, ha="left", va="center") PLOTS_DIR.mkdir(parents=True, exist_ok=True) out = PLOTS_DIR / "pearson_correlation.png" plt.savefig(out, dpi=300, bbox_inches="tight") print(f"Saved {out}") plt.close() if __name__ == "__main__": main()