| """Generate the exact parameter figures; matplotlib is optional for the codec.""" |
| from pathlib import Path |
| import numpy as np |
| import matplotlib |
| matplotlib.use("Agg") |
| import matplotlib.pyplot as plt |
| from matplotlib.colors import ListedColormap |
|
|
| ROOT=Path(__file__).resolve().parents[1] |
| OUT=ROOT/"figures" |
| OUT.mkdir(exist_ok=True) |
| plt.rcParams.update({"font.family":"DejaVu Sans","font.size":10, |
| "axes.spines.top":False,"axes.spines.right":False, |
| "axes.labelcolor":"#183242","text.color":"#183242", |
| "axes.edgecolor":"#83939a","savefig.bbox":"tight"}) |
| teal,blue,orange="#167f83","#233e70","#b95f25" |
|
|
| d=np.arange(2,33) |
| fig,ax=plt.subplots(figsize=(7.4,3.8)) |
| ax.step(d,np.ceil(d/2),where="mid",color=teal,lw=2.4,label="Exact optimum: convolution with a linear relabeling") |
| ax.plot(d,d+1,color=blue,lw=1.8,ls="--",label="Standard constant scalar rays") |
| ax.scatter([16],[8],color=orange,s=48,zorder=4) |
| ax.annotate("GF(256), 65,536 data sites\n24 updates per changed byte",(16,8),xytext=(18,3.0), |
| arrowprops={"arrowstyle":"->","color":orange},fontsize=9) |
| ax.set(xlabel="Dimension d of each data/parity layer",ylabel="Minimum bits per scalar symbol", |
| xlim=(1.5,32.5),ylim=(0,35)) |
| ax.set_xticks([2,4,8,12,16,20,24,28,32]) |
| ax.grid(axis="y",alpha=.2) |
| ax.legend(loc="upper left",frameon=False,fontsize=8.5) |
| fig.tight_layout() |
| for ext in ("pdf","png"):fig.savefig(OUT/f"alphabet_law.{ext}",dpi=170) |
| plt.close(fig) |
|
|
| fig,ax=plt.subplots(figsize=(7.4,3.6)) |
| ax.plot(d,d+1,color=blue,lw=2,label="Absolute support lower bound: d + 1") |
| ax.step(d,np.ceil(3*d/2),where="mid",color=teal,lw=2,label="Explicit construction at the optimal alphabet") |
| ax.scatter(np.arange(2,7),np.arange(2,7)+1,s=40,color=orange,zorder=4, |
| label="Exact examples attaining both bounds (d = 2 through 6)") |
| ax.set(xlabel="Dimension d of each layer",ylabel="Parity sites changed by one source update", |
| xlim=(1.5,32.5),ylim=(0,52)) |
| ax.grid(axis="y",alpha=.2) |
| ax.legend(frameon=False,loc="upper left",fontsize=8.3) |
| fig.tight_layout() |
| for ext in ("pdf","png"):fig.savefig(OUT/f"update_support.{ext}",dpi=170) |
| plt.close(fig) |
|
|
| fig,ax=plt.subplots(figsize=(7.4,2.4)) |
| sizes=np.arange(1,11) |
| general=np.array([int(x>=3) for x in sizes]) |
| commuting=np.array([int(x==3 or x>=5) for x in sizes]) |
| matrix=np.vstack([commuting,general]) |
| ax.imshow(matrix,cmap=ListedColormap(["#f0d9cc","#d5eeeb"]),vmin=0,vmax=1,aspect="auto") |
| for i in range(2): |
| for j in range(10):ax.text(j,i,"YES" if matrix[i,j] else "NO",ha="center",va="center",fontsize=9) |
| ax.set_xticks(range(10),sizes) |
| ax.set_yticks([0,1],["Normalized commuting maps","Arbitrary binary matrix maps"]) |
| ax.set_xlabel("Source and parity packet length, in bits") |
| ax.set_title("GF(4) geometry, three standard rays, equal packet widths",fontsize=11,pad=12) |
| for spine in ax.spines.values():spine.set_visible(False) |
| ax.set_xticks(np.arange(-.5,10,1),minor=True) |
| ax.set_yticks(np.arange(-.5,2,1),minor=True) |
| ax.grid(which="minor",color="white",lw=3) |
| ax.tick_params(which="minor",bottom=False,left=False) |
| fig.tight_layout() |
| for ext in ("pdf","png"):fig.savefig(OUT/f"noncommuting_gap.{ext}",dpi=170) |
| plt.close(fig) |
|
|
