{ "cells": [ { "cell_type": "markdown", "id": "ch20-cell00", "metadata": {}, "source": [ "# Numerical Methods: Approximation You Can Trust\n", "\n", "*Mathematical Rules of Thumb · Jason Karpeles · Chapter 20*\n", "\n", "Approximation You Can Trust\n", "\n", "Open [the interactive reader](reader.html) to explore the supported parameter choices without running code. Saved figures and calculations below can be read as they are. All example inputs are constructed.\n", "\n", "Optional reproduction requires Python, NumPy, Matplotlib and IPython. Code is marked collapsed, although viewer support varies. All mathematical functions and inputs are included here; no author-machine paths or other notebooks are required." ] }, { "cell_type": "code", "execution_count": 1, "id": "ch20-cell01", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:58:17.384938Z", "iopub.status.busy": "2026-10-03T00:58:17.384854Z", "iopub.status.idle": "2026-10-03T00:58:17.431124Z", "shell.execute_reply": "2026-10-03T00:58:17.431059Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustrated-setup" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Calculation definitions loaded; all inputs are constructed.\n" ] } ], "source": [ "import io\n", "import matplotlib\n", "matplotlib.use('Agg')\n", "from IPython.display import Image, Markdown, display\n", "from cycler import cycler\n", "\"\"\"Constructed teaching calculations shared by readers and portable notebooks.\n", "\n", "Requires NumPy and Matplotlib. No measurements, online data or trained models.\n", "All stochastic illustrations use stated, fixed seeds.\n", "\"\"\"\n", "import math\n", "import itertools\n", "from collections import deque\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "def canvas(xlabel, ylabel, title, two=False):\n", " fig, axes = plt.subplots(1, 2 if two else 1, figsize=(10, 4.4), layout='constrained')\n", " for ax in np.atleast_1d(axes):\n", " ax.grid(alpha=.18)\n", " ax.set(xlabel=xlabel, ylabel=ylabel)\n", " np.atleast_1d(axes)[0].set_title(title)\n", " return fig, axes\n", "\n", "\n", "def integer_ticks(ax, axis='x'):\n", " from matplotlib.ticker import MaxNLocator\n", " (ax.xaxis if axis=='x' else ax.yaxis).set_major_locator(MaxNLocator(integer=True))\n", "\n", "\n", "def bits(x):\n", " return f'{x:.6g} bit'+('' if x==1 else 's')\n", "\n", "\n", "def result(fig, ax, metrics, text):\n", " for a in np.atleast_1d(ax):\n", " if a.get_legend_handles_labels()[0]:\n", " old=a.get_legend()\n", " a.legend(fontsize=9,loc=old._loc if old is not None else 'best')\n", " return fig, metrics, text\n", "\n", "\n", "def illustrate(chapter, demo, p):\n", " \"\"\"Return an executed figure, metrics and interpretation for one example.\"\"\"\n", " fig,metrics,text=globals()[f'chapter_{chapter:02d}'](demo, p)\n", " # Mark a selected point on comparisons whose full curve stays fixed.\n", " if (chapter,demo) in {(9,1),(11,1),(11,3),(13,2),(15,1),(15,2),(15,3),\n", " (16,1),(17,2),(17,3),(18,3),(19,3),(20,3),(22,2),(23,3)}:\n", " ax=fig.axes[0];ax.axvline(p,color='#a26913',linestyle=':',label='Selected input')\n", " ax.legend(fontsize=9)\n", " return fig,metrics,text\n", "\n", "\n", "def chapter_01(d, p):\n", " if d == 1:\n", " x=np.linspace(0,.2,201); exact=(1+x)**5; linear=1+5*x\n", " fig,ax=canvas('Fractional input increase', 'Response multiplier', 'Where linearization bends')\n", " ax.plot(x,exact,label='Exact fifth power');ax.plot(x,linear,'--',label='Linear estimate');ax.axvline(p,color='#a26913',linestyle=':',label='Selected input')\n", " a=(1+p)**5;b=1+5*p;m={'Exact multiplier':a,'Linear estimate':b,'Absolute error':abs(a-b)}\n", " t=f'An input increase of {100*p:g}% gives {a:.6g}, versus {b:.6g} from linearization. Judge the {abs(a-b):.6g} error against your tolerance.'\n", " elif d == 2:\n", " k=np.arange(1,21);tails=p**k/(1-p)\n", " fig,ax=canvas('First omitted exponent k','Infinite tail','Tail = first omitted term × 1/(1−r)')\n", " ax.semilogy(k,tails,label='Exact tail');ax.semilogy(k,p**k,'--',label='First omitted term');ax.scatter([5],[p**5/(1-p)],color='#a26913',zorder=3,label='Tail after exponent 4 (k=5)');integer_ticks(ax)\n", " m={'Ratio r':p,'Tail from r^5 onward':p**5/(1-p),'Tail / first term':1/(1-p)}\n", " t=f'The tail starting at r^5 equals r^5/(1-r). At r={p:g}, its multiplier over the first omitted term is {1/(1-p):.6g}; a ratio near one makes the tail much larger.'\n", " elif d==3:\n", " x=np.linspace(-3,3,301);y=x*x+p*x+1\n", " fig,ax=canvas('x','x² + b x + 1','Roots change at the discriminant boundary')\n", " ax.plot(x,y,label=f'b={p:g}');ax.axhline(0,color='gray');disc=p*p-4\n", " m={'Discriminant':disc,'Real root count':2 if disc>0 else 1 if disc==0 else 0,'Vertex x':-p/2}\n", " t=f'The discriminant b²-4 is {disc:g}. This gives '+('two distinct real roots.' if disc>0 else 'one repeated real root.' if disc==0 else 'no real roots; the two roots are complex conjugates.')\n", " elif d==4:\n", " r=np.linspace(.005,.25,250);fig,ax=canvas('Growth rate per period (%)','Rule-of-70 error (% of exact time)','How far the rule of 70 drifts as the rate grows')\n", " ax.plot(100*r,100*(.7/r-np.log(2)/np.log1p(r))/(np.log(2)/np.log1p(r)),label='(70/rate% − exact) / exact');ax.axhline(0,color='gray');ax.axvline(100*p,color='#a26913',linestyle=':',label='Selected rate')\n", " ex=math.log(2)/math.log1p(p);est=70/(100*p);m={'Rate per period (%)':100*p,'Exact doubling time (periods)':ex,'Rule-of-70 estimate (periods)':est,'Estimate error (periods)':est-ex}\n", " t=f'At {100*p:g}% per period the exact doubling time is {ex:.4g} periods; the rule of 70 says {est:.4g}. '+('Good enough for mental arithmetic.' if abs(est-ex)/ex<.03 else f'The shortcut is {100*abs(est-ex)/ex:.2g}% too short at this high rate, because 70 matches continuous growth and ln(1+r) falls below r as r grows.')\n", " elif d==5:\n", " x=np.linspace(-4,8,1201);x=x[np.abs(x-3)>.05];y=(x+1)/(x-3)\n", " fig,ax=canvas('x','(x+1)/(x-3)','Multiplying by x−3 flips the inequality when x<3')\n", " ax.plot(x[x<3],y[x<3],color='#136f75',label='(x+1)/(x-3)');ax.plot(x[x>3],y[x>3],color='#136f75');ax.axhline(0,color='gray');ax.axvline(3,color='gray',linestyle='dashed',label='Excluded x=3')\n", " ax.axvspan(-1,3,color='#136f75',alpha=.12,label='True solution [-1, 3)');ax.plot([-4,-1],[-9.5,-9.5],lw=5,color='#a26913',label='Naive answer x ≤ -1');ax.set(ylim=(-10,10))\n", " v=(p+1)/(p-3);true=v<=0;naive=p+1<=0;ax.scatter([p],[v],color='black',zorder=3,label=f'Test x={p:g}')\n", " m={'Test x':p,'(x+1)/(x-3)':v,'Truly satisfies':'yes' if true else 'no','Naive x ≤ -1 says':'yes' if naive else 'no'}\n", " t=f'At x={p:g} the fraction equals {v:.4g}, so the inequality is '+('true' if true else 'false')+'. Cross-multiplying without a sign check gives x+1 ≤ 0, which says '+('true' if naive else 'false')+'. '+('The two agree here only because x>3 keeps the denominator positive.' if true==naive else 'They disagree because x<3 makes the denominator negative, which reverses the inequality.')\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_02(d,p):\n", " if d==1:\n", " x=np.linspace(.5,3,151);fig,ax=canvas('Linear scale factor','Relative size','Similar shapes scale by different powers')\n", " ax.plot(x,x**2,label='Area');ax.plot(x,x**3,label='Volume');ax.axvline(p,color='#a26913',linestyle=':',label='Selected input')\n", " m={'Area factor':p*p,'Volume factor':p**3,'Boundary / area factor':1/p};t=f'A similar shape scaled by {p:g} has area multiplied by {p*p:g}, volume by {p**3:g}, and boundary-to-area ratio by {1/p:.6g}. These multipliers hold only when every length scales by the same factor.'\n", " elif d==2:\n", " radius=10.;x=np.linspace(0,12,151);exact=radius-np.sqrt(radius**2-(x/2)**2);estimate=x*x/(8*radius)\n", " fig,ax=canvas('Chord length','Sagitta (same length units)','Shallow arcs and their approximation');ax.plot(x,exact,label='Exact');ax.plot(x,estimate,'--',label='c²/(8R)');ax.axvline(p,color='#a26913',linestyle=':',label='Selected input')\n", " a=radius-math.sqrt(radius**2-(p/2)**2);b=p*p/(8*radius);m={'Radius':radius,'Exact sagitta':a,'Approximate sagitta':b,'Relative error (vs exact sagitta)':abs(a-b)/a};t=f'With radius 10 and chord {p:g}, sagitta is {a:.6g}. The shallow-arc estimate is {b:.6g}; its relative error grows as the chord becomes less shallow.'\n", " elif d==3:\n", " n=np.arange(3,81);ratio=n*np.sin(2*np.pi/n)/(2*np.pi)\n", " fig,ax=canvas('Polygon side count','Fractional missing area','Inscribed polygons approach a circle');ax.loglog(n,1-ratio,label='Exact missing fraction');ax.loglog(n,2*np.pi**2/(3*n*n),'--',label='Leading n⁻² scale');ax.axvline(p,color='#a26913',linestyle=':',label='Selected input');ax.set_xticks([3,5,10,20,40,80]);ax.set_xticklabels(['3','5','10','20','40','80']);ax.minorticks_off()\n", " err=1-p*math.sin(2*math.pi/p)/(2*math.pi);m={'Sides':p,'Circle area fraction missing':err};t=f'The regular {p:g}-gon misses {100*err:.6g}% of its unit-circle area. The n⁻² curve is an asymptotic comparison, not an exact formula for small polygons.'\n", " elif d==4:\n", " a,b=3.,4.;fig,ax=canvas('x (length units)','y (length units)','Can sides 3, 4 and c close into a triangle?')\n", " lo,hi=b-a,a+b;ok=lo1e-9 else ''\n", " t=f'The vector and its opposite share the component ratio y/x. Here atan2 gives {correct:.6g}°.{wrap} '+('Plain atan also gives '+f'{wrong:.6g}°, because x>0 places this vector in the half-plane plain atan covers.' if same else f'Plain atan gives {wrong:.6g}°, which points along the opposite vector.')\n", " elif d==3:\n", " x=np.logspace(-12,-1,120);direct=1-np.cos(x);stable=2*np.sin(x/2)**2\n", " fig,ax=canvas('Angle (radians)','Relative difference from stable identity','Subtraction can erase a small quantity');ax.loglog(x,np.maximum(abs(direct-stable)/stable,1e-18),label='Direct subtraction error');ax.axvline(p,color='#a26913');a=1-math.cos(p);b=2*math.sin(p/2)**2\n", " rel=abs(a-b)/b;m={'Direct 1 − cos(x)':a,'Half-angle identity':b,'Relative difference':rel};t=f'At x={p:g}, direct subtraction gives {a:.10g}, while the equivalent half-angle expression gives {b:.10g}. '+('Binary64 rounding made cos(x) exactly 1, so the direct result was erased.' if a==0 else f'The direct result survives but has lost digits: its relative difference is {rel:.2g}.')\n", " elif d==4:\n", " A=math.radians(30);b=10.;h=b*math.sin(A);fig,ax=canvas('x (length units)','y (length units)','Side a swings from C; how many places meet the base?')\n", " C=(b*math.cos(A),h);ax.plot([0,22],[0,0],color='gray',label='Base line from A');ax.plot([0,C[0]],[0,C[1]],lw=3,label='Side b=10');th=np.linspace(0,2*np.pi,300);ax.plot(C[0]+p*np.cos(th),C[1]+p*np.sin(th),':',color='#a26913',label=f'Reach of side a={p:g}')\n", " xs=[] if p1e-9]\n", " for x in xs: ax.plot([C[0],x],[C[1],0],lw=2,color='#136f75')\n", " ax.scatter(xs,[0]*len(xs),color='#136f75',zorder=3,label='Valid vertex B' if xs else None);ax.set(xlim=(-3,22),ylim=(-8,14));ax.set_aspect('equal')\n", " m={'Height b·sin A':h,'Side a':p,'Number of triangles':len(xs)}\n", " t={0:f'a={p:g} is shorter than the height {h:g}, so side a cannot reach the base: no triangle. Arcsin would fail with sin B>1.',2:f'a={p:g} is between the height {h:g} and b=10, so it meets the base twice: two valid triangles. Arcsin returns only the acute B; the obtuse angle 180° minus B is also valid.',1:f'a={p:g} is at least b=10, so only one meeting point lies on the correct side of A: one triangle.'}[len(xs)]\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_04(d,p):\n", " if d==1:\n", " x=np.linspace(80,120,201);fig,ax=canvas('x','Square root','Tangent estimates need an error budget');ax.plot(x,np.sqrt(x),label='Exact');ax.plot(x,10+(x-100)/20,'--',label='Tangent at 100');ax.axvline(100+p,color='#a26913',linestyle=':',label='Selected input');a=math.sqrt(100+p);b=10+p/20;bound=p*p/(8*min(100,100+p)**1.5)\n", " m={'Exact':a,'Linear estimate':b,'Actual error':abs(a-b),'Remainder bound':bound};t=f'For x=100+{p:g}, the linear estimate differs by {abs(a-b):.6g}. Bounding the second derivative on the intervening interval certifies error at most {bound:.6g}.'\n", " elif d==2:\n", " step=(p+2/p)/2;x=np.linspace(.1,max(3,step+.5),301);fig,ax=canvas('x','x² − 2','Newton follows a tangent');ax.plot(x,x*x-2,label='Function');ax.plot(x,p*p-2+2*p*(x-p),'--',label='Tangent');ax.axhline(0,color='gray');ax.scatter([p,step],[p*p-2,0],color='#a26913',zorder=3,label='Start and next x')\n", " m={'Starting x':p,'Next x':step,'Next residual':step*step-2};t=f'The tangent from x={p:g} crosses zero at {step:.6g}. '+(f'The step overshot: the residual grew from {abs(p*p-2):.6g} to {abs(step*step-2):.6g}. Newton is reliable only near the root, so bracket first.' if abs(step*step-2)>abs(p*p-2) else f'The residual shrank from {abs(p*p-2):.6g} to {abs(step*step-2):.6g}, so this step helped.')\n", " elif d==3:\n", " x=np.arange(1,101);a=x.astype(float)**(-p);partial=np.cumsum(a);fig,ax=canvas('Terms retained','Partial sum','A p-series threshold is about the infinite tail');ax.plot(x,partial,label=f'p={p:g}');tail=100**(1-p)/(p-1) if p>1 else 'No finite tail bound'\n", " m={'Exponent p':p,'100-term sum':partial[-1],'Integral upper bound on tail':tail};t='Adding n⁻ᵖ forever gives a finite total only when p>1. '+(f'At p={p:g}, the tail after 100 is at most {tail:.6g}.' if p>1 else 'A finite partial sum does not establish convergence; this selected series diverges.')\n", " elif d==4:\n", " x=1.;k=np.arange(0,11);part=np.cumsum([x**j/math.factorial(j) for j in k]);err=abs(math.e-part);nxt=np.array([x**(j+1)/math.factorial(j+1) for j in k])\n", " fig,ax=canvas('Polynomial degree n','Error at x=1','Taylor error for eˣ tracks the first omitted term');ax.semilogy(k,err,'o-',label=r'Actual error $|e-T_n(1)|$');ax.semilogy(k,nxt,'s',linestyle='dashed',label='First omitted term 1/(n+1)!');ax.axvline(p,color='#a26913',linestyle=':',label='Selected degree');integer_ticks(ax)\n", " e=err[p];s=nxt[p];m={'Degree n':p,'Actual error':e,'First omitted term':s,'Actual / omitted':e/s}\n", " t=f'Stopping at degree {p} leaves error {e:.3g}. The first omitted term {s:.3g} predicts it within a factor {e/s:.3g}, so you can read the error budget before computing e. '+('At this low degree the later terms still add a noticeable share.' if e/s>1.2 else 'Higher degrees make the first omitted term almost the whole story.')\n", " elif d==5:\n", " x=np.linspace(-.5,.5,1001);x=x[np.abs(x)>.004];y=(np.sin(x)+p)/x\n", " fig,ax=canvas('x','(sin x + a) / x','L\\'Hôpital needs 0/0 first');ax.plot(x[x<0],y[x<0],color='#136f75',label=f'a={p:g}');ax.plot(x[x>0],y[x>0],color='#136f75');ax.axhline(1,color='#a26913',linestyle='dashed',label='Blind L\\'Hôpital: cos 0 / 1 = 1');ax.set(ylim=(-6,6))\n", " r=(math.sin(.01)+p)/.01;m={'Numerator at x=0':p,'Form at x=0':'0/0' if p==0 else 'nonzero/0','Ratio at x=0.01':r,'Blind L\\'Hôpital answer':1}\n", " t=(f'With a=0 the form is 0/0, so L\\'Hôpital applies and the limit really is 1; the ratio at x=0.01 is {r:.6g}.' if p==0 else f'With a={p:g} the numerator tends to {p:g} while the denominator tends to 0, so the ratio blows up (it is {r:.4g} at x=0.01) and has no finite limit. Differentiating anyway still returns 1, a wrong answer.')\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_05(d,p):\n", " if d==1:\n", " n=np.arange(max(21,math.ceil(math.log(.01)/math.log(p))+4));x=1-p**n;error=p**n;certificate=p**n/(1-p)*(1-p)\n", " fig,ax=canvas('Iteration','Absolute error','A contraction supplies a certificate');ax.semilogy(n,error,lw=4,alpha=.45,label='Exact error to fixed point 1');ax.semilogy(n,certificate,'--',label='Contraction bound (coincides here)');ax.axhline(.01,color='gray',linestyle=':',label='Target .01');ax.axvline(math.ceil(math.log(.01)/math.log(p)),color='#a26913',label='Steps needed');m={'Contraction q':p,'Error after 10 steps':p**10,'Steps for error ≤ .01':math.ceil(math.log(.01)/math.log(p))};t=f'T(x)=q x+(1-q), starting at zero, has error qⁿ. At q={p:g}, {m[\"Steps for error ≤ .01\"]} steps suffice for .01 error. In this affine example the bound equals the exact error, so the two curves coincide. q must be strictly below one.'\n", " elif d==2:\n", " x=np.linspace(0,1,501);fig,ax=canvas('x in [0,1]','xⁿ','Pointwise convergence is not uniform');ax.plot(x,x**p,label=f'n={p:g}');ax.scatter([1],[1],label='Endpoint remains 1');m={'Value at x=.9':.9**p,'Value at x=1':1,'Supremum error to pointwise limit':1};t=f'Increasing n suppresses xⁿ at every fixed x<1, but a boundary layer remains near one. The supremum difference from the discontinuous pointwise limit is 1 for every n; this is not uniform convergence.'\n", " elif d==3:\n", " n=np.arange(1,31);tail=p**(n+1)/(1-p);fig,ax=canvas('Last retained exponent n','Uniform remainder ceiling','A geometric majorant controls every x');ax.semilogy(n,tail,label='Geometric bound on the tail');ax.yaxis.set_major_formatter(__import__('matplotlib').ticker.LogFormatterSciNotation(labelOnlyBase=False));m={'Uniform |x| ceiling q':p,'Remainder after exponent 10':p**11/(1-p)};t=f'For |x|≤{p:g}<1, the series sum xⁿ is uniformly controlled by sum qⁿ. Its tail after exponent 10 is at most {m[\"Remainder after exponent 10\"]:.6g}; the bound deteriorates as q approaches one.'\n", " elif d==4:\n", " pos=iter(1/np.arange(1,10**6,2));neg=iter(-1/np.arange(2,10**6,2));s=0.;path=[]\n", " for _ in range(3000): s+=next(pos) if s<=p else next(neg);path.append(s)\n", " fig,ax=canvas('Terms used','Running sum','Same terms ±1/n, new order, new sum');ax.semilogx(range(1,3001),path,label='Rearranged sum');ax.axhline(math.log(2),color='gray',linestyle='dashed',label='Usual order: ln 2 ≈ 0.693');ax.axhline(p,color='#a26913',linestyle=':',label=f'Target {p:g}')\n", " m={'Target':p,'Sum after 3000 terms':path[-1],'Usual-order sum ln 2':math.log(2)}\n", " t=f'Adding positives while at or below {p:g} and negatives while above steers the running sum to {path[-1]:.4g}. '+'The terms are exactly those of the ln 2 series; only the order changed. Because the sum of |terms| diverges, order is part of the answer.'\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_06(d,p):\n", " if d==1:\n", " theta=np.linspace(0,2*np.pi,361);z=np.exp(1j*theta);fig,ax=canvas('Real part','Imaginary part','A power multiplies the argument');ax.plot(z.real,z.imag,'--',color='#9aa3a8',label='Unit circle');ang=np.linspace(0,np.radians(135*p),400);rad=.25+.12*ang/(2*np.pi);ax.plot(rad*np.cos(ang),rad*np.sin(ang),color='#a26913',label='Unwrapped angle path');point=np.exp(1j*np.radians(135));out=point**p;ax.quiver(0,0,point.real,point.imag,angles='xy',scale_units='xy',scale=1,color='#9aa3a8',label='Input z (135°)');ax.quiver(0,0,out.real,out.imag,angles='xy',scale_units='xy',scale=1,color='#136f75',label=f'Output z^{p:g}');ax.set(xlim=(-1.3,1.3),ylim=(-1.3,1.3));ax.set_aspect('equal');unwrapped=135*p;principal=math.degrees(np.angle(out));turns=round((unwrapped-principal)/360);m={'Input argument (degrees)':135,'Unwrapped output argument':unwrapped,'Principal output argument':principal,'Full turns lost by principal value':turns};t=f'Integer power {p:g} multiplies the argument: 135°×{p:g}={unwrapped:g}°. '+(f'The principal argument wraps this to {principal:.6g}°, dropping {turns} full turn{\"s\" if turns!=1 else \"\"}; only the unwrapped angle records them.' if turns else f'Here {unwrapped:g}° already lies in (−180°,180°], so no wrap occurs.')\n", " elif d==2:\n", " k=np.arange(0,7);fig,ax=canvas('Derivative order k','Cauchy upper bound','A larger analytic disk gives stronger bounds')\n", " for R in (1,2,4):\n", " b=np.array([math.factorial(int(n))*3/R**n for n in k]);ax.semilogy(k,b,'o-',lw=2.5 if R==p else 1,alpha=1 if R==p else .35,label=f'k! M / Rᵏ, R={R}'+(' (selected)' if R==p else ''))\n", " integer_ticks(ax);m={'Disk radius R':p,'Boundary bound M':3,'Second derivative ceiling':6/p**2};t=f'If the function is analytic on and inside this disk and its boundary modulus is at most 3, |f″(0)|≤6/R²={6/p**2:.6g}. Doubling the radius cuts this ceiling by four. A function that stays tame across a wide disk cannot bend sharply at its center.'\n", " elif d==3:\n", " theta=np.linspace(0,2*np.pi,501);z=np.exp(1j*theta);w=z**3+p;fig,ax=canvas('Real part','Imaginary part','Boundary image and roots of z³ + a');ax.plot(w.real,w.imag,label='Mapped unit-circle boundary');ax.scatter([0],[0],color='#a26913',label='Origin');roots=np.roots([1,0,0,p]);ax.plot(np.cos(theta),np.sin(theta),':',color='#9aa3a8',label='Unit circle |z|=1');ax.scatter(roots.real,roots.imag,marker='x',s=70,color='#aa4e37',zorder=3,label='Roots of z³+a');ax.set(xlim=(-1.4,2.4),ylim=(-1.3,2.3));ax.set_aspect('equal');count=int(np.sum(abs(roots)<1-1e-10));m={'Constant a':p,'Strict domination |a| < 1':p<1,'Zeros strictly inside disk':count};t=f'For a={p:g}, '+('Rouché compares z³ with a on |z|=1 and gives three interior zeros.' if p<1 else 'strict boundary domination fails. At a=1 the zeros lie on the boundary; above one they lie outside. The failed theorem test must not be treated as a zero-count proof.')\n", " elif d==4:\n", " theta=np.linspace(0,2*np.pi,4001)[:-1];poles=np.array([.5,1.5]);res=np.array([-1.,1.]);z=p*np.exp(1j*theta);I=np.sum(1/((z-.5)*(z-1.5))*1j*z)*(2*np.pi/len(theta));inside=abs(poles)1e-16 else 'Below 1e-16 (rounding level)','Steps to reach 10⁻⁶':hit if hit else 'More than 60'};t=f'Matrix diag(1,{p:g},0.3), start (1,1,1)/√3. Each step multiplies the error by about {p:g}. '+(f'The error passes 10⁻⁶ in {hit} steps.' if hit else f'After 60 steps the error is still {err[-1]:.3g}. A ratio this close to one needs about {math.ceil(math.log(1e-6)/math.log(p))} steps, so use a shift or a different method.')\n", " elif d==5:\n", " rng=np.random.default_rng(705);U,_=np.linalg.qr(rng.standard_normal((50,2)));V,_=np.linalg.qr(rng.standard_normal((2,2)));A=U@np.diag([1.,1/p])@V.T;xt=np.array([1.,1.]);b=A@xt;Q,R=np.linalg.qr(A);xq=np.linalg.solve(R,Q.T@b);xn=np.linalg.solve(A.T@A,A.T@b);eq=np.linalg.norm(xq-xt)/np.linalg.norm(xt);en=np.linalg.norm(xn-xt)/np.linalg.norm(xt)\n", " ks=np.logspace(0,8,60);fig,ax=canvas('Condition number κ of A','Relative error in the solution','Normal equations square the condition number');ax.loglog(ks,np.maximum(ks*2.2e-16,1e-17),color='#136f75',label='QR scale: κ × 2.2×10⁻¹⁶');ax.loglog(ks,np.minimum(ks**2*2.2e-16,10),ls='dashed',color='#a26913',label='Normal equations scale: κ² × 2.2×10⁻¹⁶');ax.scatter([p],[max(eq,1e-17)],s=90,color='#136f75',zorder=3,label='Actual QR error');ax.scatter([p],[max(en,1e-17)],s=90,marker='s',color='#aa4e37',zorder=3,label='Actual normal-equations error');ax.set_ylim(1e-17,20)\n", " m={'Condition number of A':float(p),'Condition number of AᵀA':float(p)**2,'QR relative error':eq,'Normal-equations relative error':en};t=f'A is a constructed 50×2 matrix with κ={p:g} and an exact fit, so the true answer is (1,1). QR works with A directly and loses about log10 κ={math.log10(p):.0f} digits; its error is {eq:.2g}. The normal equations solve with AᵀA, whose condition number is κ²={p**2:.3g}. '+('At this mild conditioning both errors are tiny, so the difference does not matter yet.' if p**2<1e8 else f'Their error is {en:.2g}, about {en/max(eq,1e-16):.2g} times worse. Squaring κ doubles the digits lost.' if p**2<1e15 else f'κ² is past 1/2.2×10⁻¹⁶, so AᵀA is singular to working precision and the normal-equations answer is wrong in the leading digits (error {en:.2g}), while QR still has about {-math.log10(max(eq,1e-16)):.0f} correct digits.')\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_08(d,p):\n", " if d==1:\n", " a,b=43,p;trace=[]\n", " while b:trace.append(b);a,b=b,a%b\n", " fig,ax=canvas('Euclidean step','Value','Remainders reveal the gcd');ax.plot(range(len(trace)),trace,'o-',label='Input a, then nonzero remainders');ax.set_xlim(-.5,max(len(trace),3)-.5);integer_ticks(ax);g=math.gcd(p,43);inv=pow(p,-1,43) if g==1 else 'Does not exist';m={'gcd(a,43)':g,'Inverse modulo 43':inv};t=f'For a={p:g}, gcd(a,43)={g}. '+(f'The inverse is {inv}, checked by a×inverse mod43=1.' if g==1 else '43 ≡ 0 mod 43, so a has no inverse and you cannot divide by it modulo 43.')\n", " elif d==2:\n", " n=np.arange(0,60);selected=[k for k in n if k%3==2 and k%5==p];fig,ax=canvas('Integer candidate','Remainder','Two congruences select one class modulo 15');ax.scatter(n,n%3,s=10,label='mod 3');ax.scatter(n,n%5,s=10,label='mod 5');ax.scatter(selected,[2]*len(selected),s=100,facecolors='none',edgecolors='#a26913',label='Both conditions');ax.set_ylim(-.5,7.5);r=next(k for k in range(15) if k%3==2 and k%5==p);m={'Remainder modulo 3':2,'Remainder modulo 5':p,'Solution modulo 15':r};t=f'The simultaneous conditions x≡2 mod3 and x≡{p:g} mod5 select x≡{r} mod15. Because 3 and 5 share no factor, exactly one remainder out of 15 works, so the circled points repeat every 15.'\n", " elif d==3:\n", " prime=np.ones(p+1,dtype=bool);prime[:2]=False\n", " for k in range(2,math.isqrt(p)+1):\n", " if prime[k]:prime[k*k::k]=False\n", " x=np.arange(2,p+1);counts=np.cumsum(prime)[2:];fig,ax=canvas('Upper limit n','Prime count','An asymptotic estimate is not an exact count');ax.plot(x,counts,label='Sieve count');ax.plot(x,x/np.log(x),'--',label='n/log n');m={'Exact prime count':int(prime.sum()),'n/log n estimate':p/math.log(p)};t=f'The sieve finds {int(prime.sum())} primes through {p:g}. n/log n gives {p/math.log(p):.6g}; the true count is {int(prime.sum())/(p/math.log(p)):.3f} times the estimate. The formula promises only that this ratio tends to 1 as n grows. It gets there very slowly and not steadily: from n=100 to n=2000 it wanders between about 1.14 and 1.26.'\n", " elif d==4:\n", " k=np.arange(1,26);vals=np.array([pow(p,int(e),11) for e in k]);order=next(e for e in range(1,11) if pow(p,e,11)==1);fig,ax=canvas('Exponent k','aᵏ mod 11','Powers repeat with a fixed period');ax.plot(k,vals,'o-',color='#136f75',label=f'{p}ᵏ mod 11');ax.scatter(k[vals==1],vals[vals==1],s=123,facecolors='none',edgecolors='#aa4e37',zorder=3,label='Value 1: cycle restarts');ax.axvline(23,color='#a26913',ls=':',label='k=23');ax.set_ylim(0,14.5);integer_ticks(ax);integer_ticks(ax,'y');m={'Base a':p,'Period (order of a mod 11)':order,'23 mod period':23%order,f'{p}²³ mod 11':pow(p,23,11)};t=f'The powers of {p} repeat every {order} steps, so only the exponent mod {order} matters. 23 mod {order} = {23%order}, so {p}²³ ≡ {pow(p,23%order,11)} mod 11 without computing a 23-fold product. '+('Fermat\\'s period 10 always works mod 11; here it is the true period.' if order==10 else f'Fermat\\'s exponent 10 also works, because {order} divides 10, but the true period is shorter.')\n", " elif d==5:\n", " divs=[k for k in range(1,p+1) if p%k==0];r=math.sqrt(p);small=[k for k in divs if k<=r];tests=math.isqrt(p)-1\n", " fig,ax=canvas('Divisor d','Partner n/d',f'Divisors of {p} pair up across √n');ax.plot([0,p+1],[0,p+1],ls='dotted',color='#9aa3a8',label='d = n/d line');ax.scatter(small,[p//k for k in small],s=70,color='#136f75',zorder=3,label='Small partner d ≤ √n');big=[k for k in divs if k>r];ax.scatter(big,[p//k for k in big],s=70,marker='s',color='#a26913',zorder=3,label='Large partner d > √n');ax.axvline(r,color='#aa4e37',ls='dashed',label=f'√{p} ≈ {r:.3g}');ax.set_xscale('log');ax.set_yscale('log');ax.set(xlim=(.8,p*1.3),ylim=(.8,p*1.3))\n", " m={'n':p,'√n':r,'Divisors found':len(divs),'Trial divisors needed (2 to ⌊√n⌋)':tests,'Prime':len(divs)==2}\n", " t=f'Every divisor d of {p} comes with a partner {p}/d, and one of the two is at most √{p}≈{r:.4g}. '+(f'So testing 2 through {math.isqrt(p)} ({tests} trials) is enough: none divides {p}, so {p} is prime. Testing past √n would only find partners of divisors already ruled out.' if len(divs)==2 else f'The small divisors {\", \".join(map(str,small))} already reveal all {len(divs)} divisors; the large ones are their partners. '+(f'Here √{p} is a whole number, so {math.isqrt(p)} is its own partner and sits on the diagonal.' if math.isqrt(p)**2==p else f'{p} looks prime at a glance, but the trial divisor {small[1]} finds {p}={small[1]}×{p//small[1]} well before √n.'))\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_09(d,p):\n", " if d==1:\n", " k=np.arange(0,9);choose=[math.comb(8,int(i)) for i in k];ordered=[math.perm(8,int(i)) for i in k];fig,ax=canvas('Selected people k','Outcome count','Distinct jobs multiply committee counts');integer_ticks(ax);ax.semilogy(k,choose,'o-',label='Unordered committee');ax.semilogy(k,ordered,'o-',label='Distinct ordered jobs');m={'Committee count':math.comb(8,p),'Job assignments':math.perm(8,p),'Multiplicity k!':math.factorial(p)};t=f'For {p:g} of eight people, {math.comb(8,p)} committees become {math.perm(8,p)} assignments to distinct jobs. Each committee has exactly {math.factorial(p)} orderings.'\n", " elif d==2:\n", " counts=np.bincount([sum(bits) for bits in itertools.product([0,1],repeat=p)],minlength=p+1);fig,ax=canvas('Number of ones','Binary strings','Counting a small exhaustive space');ax.bar(range(p+1),counts,label='Exact exhaustive count');integer_ticks(ax);integer_ticks(ax,'y');m={'Total strings':2**p,'At least one 1':2**p-1,'Balanced count':math.comb(p,p//2)};t=f'Enumerating all {2**p} binary strings confirms the binomial counts. Excluding only the all-zero string leaves {2**p-1}. The tallest bar is in the middle: {math.comb(p,p//2)} strings have exactly {p//2} ones.'\n", " elif d==3:\n", " strings=list(itertools.product([0,1],repeat=p));orbits={min(s[i:]+s[:i] for i in range(p)) for s in strings};sizes={s:sum(min(t[i:]+t[:i] for i in range(p))==s for t in strings) for s in orbits};fig,ax=canvas('Rotation orbit size','Number of orbits','Uniform division fails for necklaces');vals=sorted(set(sizes.values()));ax.bar(vals,[list(sizes.values()).count(k) for k in vals]);ax.set_xticks(vals);integer_ticks(ax,'y');m={'Binary necklaces':len(orbits),'Naive 2ⁿ/n':2**p/p,'Distinct orbit sizes':', '.join(map(str,vals))};t=f'Rotation orbits do not all have size {p:g}. Constant strings have orbit size one, so dividing {2**p} by {p:g} does not count the {len(orbits)} distinct necklaces.'\n", " elif d==4:\n", " n=np.arange(1,11);D=[1,0]\n", " for i in range(2,11):D.append((i-1)*(D[-1]+D[-2]))\n", " D=np.array(D[1:]);fig,ax=canvas('Number of people n','Probability nobody gets own hat','The no-match chance settles near 1/e fast');ax.plot(n,D/np.array([math.factorial(int(i)) for i in n]),'o-',color='#136f75',label='Exact D(n)/n!');ax.axhline(1/math.e,color='#a26913',ls='dashed',label='1/e ≈ 0.3679');ax.scatter([p],[D[p-1]/math.factorial(p)],s=140,facecolors='none',edgecolors='#aa4e37',zorder=3,label=f'Selected n={p}');integer_ticks(ax);ax.set_ylim(0,.55);m={'People n':p,'Derangements D(n)':int(D[p-1]),'Arrangements n!':math.factorial(p),'Exact probability':D[p-1]/math.factorial(p),'n!/e rounded':round(math.factorial(p)/math.e)};t=f'With {p} people there are {math.factorial(p)} ways to hand back hats and {D[p-1]} leave nobody with their own. '+(f'That is {D[p-1]/math.factorial(p):.4g}, already within {abs(D[p-1]/math.factorial(p)-1/math.e):.2g} of 1/e. Rounding n!/e gives the exact count, so the shortcut is safe.' if p>=4 else f'That is {D[p-1]/math.factorial(p):.4g}, still visibly off 1/e. Even so, rounding n!/e={math.factorial(p)/math.e:.4g} gives the exact count {D[p-1]}.')\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_10(d,p):\n", " edges={'path':[(0,1),(1,2),(2,3)],'triangle-isolate':[(0,1),(1,2),(2,0)],'cycle':[(0,1),(1,2),(2,3),(3,0)]}\n", " if d==1:\n", " es=edges[p];adj={i:[] for i in range(4)}\n", " for a,b in es:adj[a].append(b);adj[b].append(a)\n", " seen={0};queue=deque([0])\n", " while queue:\n", " for j in adj[queue.popleft()]:\n", " if j not in seen:seen.add(j);queue.append(j)\n", " fig,ax=canvas('x (layout only)','y (layout only)','Edge count needs a structural condition');xy=np.array([[0,0],[1,0],[1,1],[0,1]])\n", " for a,b in es:ax.plot(xy[[a,b],0],xy[[a,b],1],color='#136f75')\n", " ax.scatter(xy[:,0],xy[:,1],s=150);[ax.annotate(str(i),xy[i]+np.array([.05,-.09])) for i in range(4)];ax.set(xlim=(-.2,1.25),ylim=(-.2,1.2));ax.set_aspect('equal');tree=len(seen)==4 and len(es)==3;m={'Vertices':4,'Edges':len(es),'Reachable from vertex 0':len(seen),'Tree':tree};t=f'This graph has {len(es)} edges and {len(seen)} reachable vertices. It '+('is a tree: connected with n−1 edges.' if tree else ('is not a tree. It has n−1=3 edges but is disconnected, so the edge count alone cannot replace connectivity.' if len(seen)<4 else 'is not a tree. It is connected but has 4 edges, one more than n−1=3, so it contains a cycle.'))\n", " elif d==2:\n", " theta=2*np.pi*np.arange(p)/p;xy=np.column_stack([np.cos(theta),np.sin(theta)]);fig,ax=canvas('x (layout only)','y (layout only)','Odd cycles obstruct two-coloring' if p%2 else 'Even cycles two-color consistently');ax.plot(xy[:,0],xy[:,1],color='#136f75');ax.plot(xy[[-1,0],0],xy[[-1,0],1],color='#aa4e37' if p%2 else '#136f75',lw=3,label='Closing edge: same colors (conflict)' if p%2 else 'Closing edge: colors differ');ax.scatter(xy[:,0],xy[:,1],c=['#136f75' if i%2==0 else '#b77518' for i in range(p)],s=130);ax.set_aspect('equal');m={'Cycle length':p,'Bipartite':p%2==0};t=f'An alternating two-coloring '+('closes consistently on this even cycle.' if p%2==0 else 'conflicts at the closing edge on this odd cycle. One odd cycle rules out bipartiteness.')\n", " elif d==3:\n", " es=edges[p];degrees=[sum(i in e for e in es) for i in range(4)];odd=sum(v%2 for v in degrees);fig,ax=canvas('Vertex','Degree','Euler trails use every edge');ax.bar(range(4),degrees);integer_ticks(ax);integer_ticks(ax,'y');m={'Odd-degree vertices':odd,'Euler trail possible on edge component':odd in (0,2)};t=f'There are {odd} odd-degree vertices. '+('Zero odd vertices: you can walk every edge once and end where you started.' if odd==0 else 'Two odd vertices: you can walk every edge once, but you must start at one odd vertex and finish at the other.' if odd==2 else 'More than two odd vertices: no walk covers every edge exactly once.')+(' Vertex 3 has no edges and is ignored, since the walk only has to cover edges.' if 0 in degrees else '')\n", " elif d==4:\n", " import heapq;E={'S':[('A',2),('B',3)],'B':[('A',p)],'A':[('T',1)],'T':[]};V=['S','A','B','T'];dist={v:math.inf for v in V};dist['S']=0;done=set();h=[(0,'S')]\n", " while h:\n", " d0,u=heapq.heappop(h)\n", " if u in done:continue\n", " done.add(u)\n", " for v,w in E[u]:\n", " if v not in done and d0+w',shrinkA=11,shrinkB=11,lw=2.5 if (u,v)==('B','A') else 1.2,color='#aa4e37' if (u,v)==('B','A') and p<0 else '#136f75'));ax[0].annotate(f'{w:g}',((xy[u][0]+xy[v][0])/2+.04,(xy[u][1]+xy[v][1])/2+.04))\n", " ax[0].scatter(*zip(*xy.values()),s=300,color='#dbe7e8',zorder=3);[ax[0].annotate(v,xy[v],ha='center',va='center',zorder=4) for v in V];ax[0].set(xlim=(-.3,2.3),ylim=(-1,1),xticks=[],yticks=[]);i=np.arange(4);ax[1].bar(i-.2,[dist[v] for v in V],.4,label='Dijkstra answer');ax[1].bar(i+.2,[true[v] for v in V],.4,label='True shortest (Bellman-Ford)');ax[1].set(xticks=i,xticklabels=V,xlabel='Vertex',ylabel='Path length from S',title=f'Edge B to A weight {p:g}');integer_ticks(ax[1],'y');wrong=[v for v in V if dist[v]!=true[v]];m={'Weight on B→A':p,'Dijkstra distance to T':dist['T'],'True distance to T':true['T'],'Vertices Dijkstra gets wrong':', '.join(wrong) if wrong else 'None'};t=f'Dijkstra settles A at length 2 before it looks at B. '+('All weights are nonnegative, so no later path can undercut a settled vertex. Every answer is correct.' if p>=0 else (f'The detour S→B→A costs 3{p:+g}={3+p:g}, still longer than 2, so Dijkstra happens to be right. A negative edge removes the guarantee, not every correct answer.' if 3+p>=2 else f'The detour S→B→A costs 3{p:+g}={3+p:g}, shorter than 2. Dijkstra already locked A, so it reports {\", \".join(wrong)} too long. Use Bellman-Ford when any weight is negative.'))\n", " elif d==5:\n", " G={'K4':(4,6,False,True),'K5':(5,10,False,False),'K3,3':(6,9,True,False)};n,e,bip,planar=G[p];b=3*n-6\n", " fig,ax=canvas('Graph','Number of edges',f'{p}: the 3n−6 screen can only rule planarity out');names=list(G);x=np.arange(3)\n", " ax.bar(x-.2,[G[g][1] for g in names],.4,color=['#aa4e37' if g==p else '#9fc2c4' for g in names],label='Edges m');ax.bar(x+.2,[3*G[g][0]-6 for g in names],.4,color='#d8b47a',label='Planar ceiling 3n−6');ax.set(xticks=x,xticklabels=names);integer_ticks(ax,'y')\n", " m={'Vertices n':n,'Edges m':e,'Ceiling 3n−6':b,'Screen rejects planarity':e>b,'Actually planar':planar}\n", " t=f'{p} has n={n} and m={e}, against the ceiling 3n−6={b}. '+({'K4':'It passes the screen and is planar: draw one vertex inside the triangle of the other three.','K5':'Ten edges exceed nine, so the screen proves K5 is not planar without any drawing.','K3,3':'Nine edges are under twelve, so the screen passes, yet K3,3 is not planar. Passing proves nothing. For a graph with no triangles the sharper ceiling 2n−4=8 does catch it.'}[p])\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_11(d,p):\n", " if d==1:\n", " n=np.arange(1,51);exact=np.array([math.lgamma(int(k)+1) for k in n]);base=.5*np.log(2*np.pi*n)+n*np.log(n)-n;fig,ax=canvas('n','Relative factorial error','The first Stirling correction helps');ax.semilogy(n,abs(np.expm1(base-exact)),label='Leading formula');ax.semilogy(n,abs(np.expm1(base+1/(12*n)-exact)),label='Log correction');m={'n':p,'Leading relative error':abs(math.expm1(.5*math.log(2*math.pi*p)+p*math.log(p)-p-math.lgamma(p+1))),'Corrected relative error':abs(math.expm1(.5*math.log(2*math.pi*p)+p*math.log(p)-p+1/(12*p)-math.lgamma(p+1)))};t=f'At n={p}, the leading Stirling formula misses n! by {100*m[\"Leading relative error\"]:.3g}%. Adding 1/(12n) to the log cuts the miss to about 1 part in {1/m[\"Corrected relative error\"]:,.0f}. Working with log n! keeps huge factorials from overflowing. A few checked values do not prove the correction always works this well.'\n", " elif d==2:\n", " x=np.logspace(0,5,200);fig,ax=canvas('x','Term magnitude','Dominant balance locates a transition');ax.loglog(x,x,label='x');ax.loglog(x,p/x,label='a/x');ax.axvline(math.sqrt(p),color='#a26913',linestyle=':',label='Balance scale √a');m={'Parameter a':p,'Balance scale x':math.sqrt(p)};t=f'The competing terms x and a/x are equal at x=√a={math.sqrt(p):.6g}. For x below {math.sqrt(p):.6g}, a/x is the bigger term; above it, x is. Near the crossing neither term can be dropped.'\n", " elif d==3:\n", " x=np.logspace(0,7,100);exact=x/(np.sqrt(x*x+x)+x);leading=np.full_like(x,.5);fig,ax=canvas('x','Difference','Equivalent leading terms can cancel');ax.semilogx(x,exact,label='Rationalized exact difference');ax.semilogx(x,leading,'--',label='Limit 1/2');value=p/(math.sqrt(p*p+p)+p);m={'Exact difference':value,'Gap to limit 1/2':.5-value,'Naively subtract leading equivalents':0,'Correct limiting value':.5};t=f'√(x²+x)−x is {value:.10g} at x={p:,} and tends to 1/2. Replacing each large term by x and subtracting would incorrectly give zero.'\n", " elif d==4:\n", " n=np.arange(2,81);fig,ax=canvas('n','Value (log scale)','Exponential growth eventually beats any power');ax.semilogy(n,np.log(n),label='log n');ax.semilogy(n,n.astype(float)**p,label=f'n^{p}');ax.semilogy(n,2.0**n,label='2^n');ax.set_ylim(.5,1e24);cross=next(int(k) for k in range(2,1000) if 2.0**k>float(k)**p);ax.axvline(cross,color='#a26913',linestyle=':',label=f'2^n passes n^{p} at n={cross}');integer_ticks(ax);m={'Power k':p,'Last n where n^k ≥ 2^n':cross-1,'First n where 2^n > n^k':cross,'n^k at n=100':float(100**p),'2^n at n=100':2.0**100};t=f'With k={p}, the power n^{p} matches or beats 2^n up to n={cross-1}; from n={cross} on, 2^n wins and the gap grows without limit. '+('Even a small power leads for a few steps, so short tests can mislead.' if p==2 else ('A bigger power only delays the takeover; it never prevents it.' if p==5 else f'Even n^10 loses, but only after n={cross-1}. Below that, the exponential looks like the slower function.'))\n", " elif d==5:\n", " tq,wq=np.polynomial.laguerre.laggauss(150);exact=float(np.sum(wq/(1+p*tq)));K=np.arange(1,31);terms=np.array([(-1)**k*math.factorial(k)*p**k for k in range(30)]);err=np.abs(np.cumsum(terms)-exact);best=int(K[np.argmin(err)]);fig,ax=canvas('Terms kept K','Absolute error (log scale)','More terms help, then hurt');ax.semilogy(K,err,'o-',ms=4,label='|partial sum − exact|');ax.axvline(best,color='#a26913',linestyle=':',label=f'Smallest error at K={best}');integer_ticks(ax);m={'Small parameter x':p,'Exact integral':exact,'Best number of terms':best,'Smallest error':float(err.min()),'Error with 30 terms':float(err[-1])};t=f'The series 1 − 1!x + 2!x² − … for ∫e^(−t)/(1+xt)dt diverges for every x>0, yet at x={p:g} keeping {best} terms gives error {err.min():.2g}. Terms shrink until k is near 1/x={1/p:g}, then grow. '+(f'With 30 terms the error explodes to {err[-1]:.2g}: adding terms past the smallest one makes things worse.' if err[-1]>1 else f'Thirty terms already overshoot: the error is back up to {err[-1]:.2g}, worse than the best truncation.')+' Stop near the smallest term.'\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_12(d,p):\n", " if d==1:\n", " n=np.arange(1,1001);exact=-np.expm1(n*np.log1p(-p));approx=-np.expm1(-n*p);fig,ax=canvas('Independent opportunities n','At least one event probability','Rare events accumulate');ax.plot(n,exact,label='Exact independent model');ax.plot(n,approx,'--',label='Poisson approximation');ax.plot(n,np.minimum(1,n*p),':',label='Union bound');ax.axvline(100,color='#a26913',linestyle=':',label='n=100 (reported)');m={'Per-opportunity probability':p,'Exact risk at n=100':-math.expm1(100*math.log1p(-p)),'Union ceiling at n=100':min(1,100*p)};t=f'Over 100 opportunities at p={p:g}, the chance of at least one event is {-math.expm1(100*math.log1p(-p)):.4g} if they are independent. The union bound n·p={min(1,100*p):.4g} is a ceiling that holds even without independence. '+('Here it caps at 1, which tells you nothing; use the exact formula if independence is credible.' if 100*p>=1 else 'For rare events the two nearly agree, so n·p is a safe quick estimate.')+' A shared cause (one storm, one bad batch) breaks the independent formula.'\n", " elif d==2:\n", " prevalence=np.logspace(-4,-.3,200);sens=.95;fpr=.05;posterior=sens*prevalence/(sens*prevalence+fpr*(1-prevalence));fig,ax=canvas('Prior prevalence','Probability after a positive result','Base rates change positive-result meaning');ax.semilogx(prevalence,posterior);a=sens*p/(sens*p+fpr*(1-p));ax.scatter([p],[a]);m={'Sensitivity':sens,'False-positive rate':fpr,'Prior probability':p,'Posterior probability':a};t=f'Under the stipulated .95 sensitivity and .05 false-positive rate, prior probability {p:g} becomes {a:.6g} after a positive result. Picture 100,000 people: {95000*p:,.0f} true positives against {5000*(1-p):,.0f} false positives. '+('False alarms swamp the real cases, so a positive is still probably wrong.' if a<.5 else 'Cases are common enough that a positive is now probably right.')+' Inputs are made up for illustration.'\n", " elif d==3:\n", " n=np.logspace(2,6,100);se=np.sqrt(.3*.7/n);fig,ax=canvas('Independent simulations n','Monte Carlo standard error','More trials improve precision slowly');ax.loglog(n,se,label='√(.3×.7/n)');ax.scatter([p],[math.sqrt(.21/p)],label='Model SE at selected n');rng=np.random.default_rng(1203);estimate=float(np.mean(rng.random(p)<.3));ax.scatter([p],[max(abs(estimate-.3),1e-6)],marker='x',s=70,color='#aa4e37',label='This run: distance of estimate from .3');m={'Seed':1203,'Trials':p,'Simulated estimate':estimate,'Model standard error':math.sqrt(.21/p),'True constructed probability':.3};t=f'Seed 1203 gives estimate {estimate:.6g} from {p:g} independent Bernoulli trials, missing the true .3 by {abs(estimate-.3):.3g}, about {abs(estimate-.3)/math.sqrt(.21/p):.2g} model standard errors. Quadrupling the simulation budget halves the model standard error; it does not fix an incorrect probability model.'\n", " elif d==4:\n", " k=np.arange(1,int(4*math.sqrt(p))+2);prob=-np.expm1(np.cumsum(np.log1p(-(k-1)/p)));fig,ax=canvas('Number of items drawn k','Probability of at least one repeat','Collisions arrive near the square root');ax.plot(k,prob,label='Exact: 1 − ∏(1 − i/N)');ax.plot(k,-np.expm1(-k*(k-1)/(2*p)),linestyle='dashed',label='Approx: 1 − exp(−k(k−1)/(2N))');half=int(k[np.argmax(prob>=.5)]);ax.axvline(half,color='#a26913',linestyle=':',label=f'50% reached at k={half}');ax.axhline(.5,color='gray',linestyle=':');integer_ticks(ax);m={'Equally likely values N':p,'Items for 50% repeat chance':half,'1.1774·√N':1.1774*math.sqrt(p),'Items as share of N':half/p};t=f'With {p:,} equally likely values, a repeat becomes more likely than not after only {half} draws, about 1.18√N. That is {100*half/p:.3g}% of the possible values. '+('This is the classic birthday surprise: 23 people suffice.' if p==365 else ('Growing N by a factor of 100 grows the threshold only about tenfold (119 here, 1,178 at N=1,000,000).' if p<10**6 else 'Even a million IDs collide after about 1,178 draws, so random IDs need far more room than their count suggests.'))\n", " elif d==5:\n", " i=np.arange(1,p+1);wait=p/(p-i+1);cum=np.cumsum(wait);total=float(cum[-1]);fig,ax=canvas('New coupons collected','Expected draws so far','The last few coupons cost the most');ax.plot(i,cum,label='Expected total draws, N·Σ1/k');ax.plot(i,i,color='gray',linestyle='dashed',label='One draw per new coupon');half=int(i[np.argmax(cum>=total/2)]);ax.axvline(half,color='#a26913',linestyle=':',label=f'Half of all draws spent by coupon {half}');integer_ticks(ax);tail=int(math.ceil(.1*p));lastshare=float((cum[-1]-cum[-tail-1])/total);m={'Distinct coupons N':p,'Expected draws for all':total,'N ln N + 0.5772N':p*math.log(p)+.5772*p,'Draws per coupon':total/p,'Share spent on last 10%':lastshare};t=f'Collecting all {p} equally likely coupons takes {total:.4g} draws on average, about N ln N + 0.577N = {p*math.log(p)+.5772*p:.4g}, or {total/p:.3g} draws per coupon. Half of those draws are already spent by coupon {half} of {p}, and '+('the last coupon' if tail==1 else f'the last {tail} coupons')+f' alone take'+('s' if tail==1 else '')+f' {100*lastshare:.3g}% of the effort. '+('Even with only 10 types, the final one takes on average 10 draws by itself.' if p==10 else 'Finishing a set is dominated by hunting for the rare missing pieces, so budgets based on N draws fail badly.')\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def wilson(k,n,z=1.96):\n", " q=k/n;den=1+z*z/n;center=(q+z*z/(2*n))/den;half=z*math.sqrt(q*(1-q)/n+z*z/(4*n*n))/den\n", " return center-half,center+half\n", "\n", "\n", "def chapter_13(d,p):\n", " if d==1:\n", " n=np.arange(10,501);fig,ax=canvas('Total observations n','95% planning half-width','Precision depends on independent information');ax.plot(n,1.96*12/np.sqrt(n),label='Independent observations, σ=12');deff=1+4*p;ax.plot(n,1.96*12*np.sqrt(deff/n),'--',label=f'Clusters of 5, within-cluster correlation ρ={p:g}');ax.axhline(3,color='gray',linestyle=':',label='Target half-width 3');target=(1.96*12/3)**2;need=5*math.ceil(target*deff/5);ax.axvline(need,color='#a26913',linestyle=':',label=f'Needed: {need}');m={'Design effect':deff,'Independent target n (unrounded)':target,'Target × design effect':target*deff,'Clustered observations needed':need};t=f'With clusters of five and within-cluster correlation ρ={p:g}, the design effect (how much clustering inflates variance) is {deff:g}. The unrounded target {target:.6g} times {deff:g} is {target*deff:.6g}, rounded up to whole clusters of five: {need}. The displayed planning formula assumes equal clusters and a specified variance; repeated measurements do not automatically count as independent observations.'\n", " elif d==2:\n", " n=np.arange(10,1001);exact=-np.expm1(math.log(.05)/n);fig,ax=canvas('Independent zero-event trials n','One-sided 95% upper bound','No observed failures does not mean zero risk');ax.plot(n,exact,label='Exact binomial upper bound');ax.plot(n,3/n,'--',label='Rule of three');m={'Zero-event trials':p,'Exact upper bound':-math.expm1(math.log(.05)/p),'Rule-of-three bound':3/p};t=f'With zero events in {p:g} independent identical trials, the exact one-sided 95% upper bound is {m[\"Exact upper bound\"]:.6g}. Rule 3/n is a close approximation, not a probability of safety.'\n", " elif d==3:\n", " n=20;k=np.arange(n+1);intervals=np.array([wilson(int(a),n) for a in k]);wald=k/n+np.array([-1,1])[:,None]*1.96*np.sqrt((k/n)*(1-k/n)/n);fig,ax=canvas('Observed successes k (n=20)','Interval endpoint','Wilson remains informative at the extremes');ax.plot(k,intervals[:,0],label='Wilson lower');ax.plot(k,intervals[:,1],label='Wilson upper');ax.plot(k,wald[0],'--',label='Wald lower');ax.plot(k,wald[1],'--',label='Wald upper');ax.axvline(p,color='#a26913',linestyle=':',label='Selected k');integer_ticks(ax);lo,hi=wilson(p,n);lo=max(0.,lo) if abs(lo)<1e-12 else lo;hi=min(1.,hi) if abs(hi-1)<1e-12 else hi;m={'Successes':p,'Trials':n,'Wilson lower':lo,'Wilson upper':hi};t=f'For {p:g}/20 successes, Wilson gives [{lo:.6g},{hi:.6g}]. '+('Wald gives [0,0] here, claiming certainty from 20 trials. Wilson does not.' if p==0 else ('Wald gives [{:.3g},{:.3g}], with an impossible negative lower end.'.format(.1-1.96*math.sqrt(.09/20),.1+1.96*math.sqrt(.09/20)) if p==2 else 'Near the middle, Wald and Wilson nearly agree; the difference matters at the extremes.'))\n", " elif d==4:\n", " rng=np.random.default_rng(1333);sims,nmax=4000,1000;z=np.cumsum(rng.standard_normal((sims,nmax)),axis=1)/np.sqrt(np.arange(1,nmax+1));looks=np.linspace(nmax/p,nmax,p).astype(int)-1;hit=(np.abs(z[:,looks])>1.96).any(axis=1);fig,ax=canvas('Planned looks at the data','False-positive rate (no real effect)','Peeking and stopping on p<.05 inflates errors');allk=[1,2,5,10,20,50];rates=[float((np.abs(z[:,np.linspace(nmax/j,nmax,j).astype(int)-1])>1.96).any(axis=1).mean()) for j in allk];ax.plot(allk,rates,'o-',label='Simulated: stop at first p<.05');ax.axhline(.05,color='gray',linestyle='dashed',label='Promised 5%');ax.scatter([p],[hit.mean()],s=90,color='#a26913',zorder=3,label=f'Selected: {p} look'+('' if p==1 else 's'));ax.set_xscale('log');ax.set_xticks(allk,[str(j) for j in allk]);m={'Looks':p,'Simulated false-positive rate':float(hit.mean()),'Nominal rate':.05,'Simulated null experiments':sims,'Seed':1333};t=f'With no true effect and '+('a single look at the end,' if p==1 else f'{p} equally spaced looks,')+f' stopping at the first p<.05 declares a false discovery in {100*hit.mean():.3g}% of {sims} simulated experiments. '+('One planned look keeps the promised 5%, up to simulation noise.' if p==1 else f'That is about {hit.mean()/.05:.2g} times the promised 5%. Each extra look is another chance for noise to cross the line. Fix the look schedule in advance or use a sequential correction.')\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_14(d,p):\n", " if d==1:\n", " arrival=np.linspace(.1,9.9,201);fig,ax=canvas('Arrival rate λ (per hour)','Mean system time (hours)','Queues become fragile near capacity');ax.plot(arrival,1/(10-arrival),label='Stable M/M/1');ax.axvline(p,color='#a26913',label=f'Selected λ={p:g}');stable=p<10\n", " if not stable:ax.text(p-.15,ax.get_ylim()[1]*.6,'λ ≥ μ: unstable,\\nno stationary mean',ha='right',color='#aa4e37')\n", " m={'Utilization':p/10,'Mean system time':1/(10-p) if stable else 'No stationary mean','Mean customers in system':p/(10-p) if stable else 'Unstable'};t=f'At service rate 10/hour and arrivals {p:g}/hour, '+(f'mean system time is {1/(10-p):.6g} hours under the M/M/1 assumptions.' if stable else 'the stationary formula is inapplicable: demand meets or exceeds service capacity.')\n", " elif d==2:\n", " n=np.arange(51);fig,ax=canvas('Steps after shock','Remaining shock fraction','AR(1) dependence persists');hl=math.log(.5)/math.log(p);ax.plot(n,p**n,label='Remaining fraction φⁿ');ax.axhline(.5,color='gray',linestyle=':',label='Half remaining');ax.axvline(hl,color='#a26913',linestyle=':',label=f'Half-life {hl:.3g} steps');m={'AR coefficient':p,'Half-life in steps':math.log(.5)/math.log(p),'Long-run variance factor':(1+p)/(1-p)};t=f'A shock is multiplied by φ={p:g} each step (it keeps {100*p:g}% per step), with half-life {math.log(.5)/math.log(p):.3g} steps. A long average is {(1+p)/(1-p):.3g} times as noisy (in variance) as an average of the same number of independent readings. '+('Even this weak persistence costs some precision, though half of a shock is gone within one step.' if p<.5 else 'Lingering shocks make neighboring readings repeat each other, so persistence costs precision.')\n", " elif d==3:\n", " count=np.arange(0,31);pmf=np.array([math.exp(-p)*p**int(k)/math.factorial(int(k)) for k in count]);fig,ax=canvas('Arrival count in one hour','Probability','Rate times exposure determines the Poisson count');ax.bar(count,pmf);m={'Hourly arrival rate':p,'Mean count in one hour':p,'Probability of any arrival':-math.expm1(-p),'Mean wait (hours)':1/p};t=f'A constant Poisson rate {p:g}/hour gives mean count {p:g} in one hour and mean exponential wait {1/p:.6g} hour{\"\" if p==1 else \"s\"}. Changing or dependent arrival rates need a different model.'\n", " elif d==4:\n", " rng=np.random.default_rng(1421);steps=rng.choice([-1,1],size=(2000,p));walk=np.cumsum(steps,axis=1);n=np.arange(1,p+1);fig,ax=canvas('Steps taken n','Position (steps from start)','Random-walk spread grows like √n');[ax.plot(n,walk[i],lw=.7,alpha=.6,label='Five sample walks' if i==0 else None) for i in range(5)];ax.plot(n,np.sqrt(n),color='k',linestyle='dashed',label='±√n');ax.plot(n,-np.sqrt(n),color='k',linestyle='dashed');ax.plot(n,np.sqrt((walk**2).mean(axis=0)),color='#a26913',label='Simulated RMS distance (2000 walks)');integer_ticks(ax);rms=float(np.sqrt((walk[:,-1]**2).mean()));m={'Steps':p,'Theory √n':math.sqrt(p),'Simulated RMS distance':rms,'Typical distance / steps':rms/p,'Seed':1421};t=f'After {p:,} fair ±1 steps, the typical distance from start is about √{p:,}={math.sqrt(p):.4g} steps (simulation: {rms:.4g}). That is only {100*rms/p:.2g}% of the steps taken. '+('Ten times more steps would move the walker only about 3.16 times farther.' if p<10000 else 'A hundredfold increase in steps from 100 to 10,000 only multiplied the typical distance by ten.')\n", " elif d==5:\n", " t=np.linspace(0,30,301);mean=10;scale=mean/math.gamma(1.5);expo=np.exp(-t/mean);weib=np.exp(-((p+t)/scale)**2+(p/scale)**2);fig,ax=canvas('Extra minutes of waiting t','P(still waiting after t more)','Exponential waits do not age');ax.plot(t,expo,label='Exponential (memoryless), mean 10');ax.plot(t,weib,linestyle='dashed',label='Aging wait, mean 10, '+('no time waited yet' if p==0 else f'after {p:g} min already'));m={'Minutes already waited':p,'Exponential: expected extra wait':mean,'Aging model: expected extra wait':float(np.trapezoid(np.exp(-((p+np.linspace(0,200,200001))/scale)**2+(p/scale)**2),np.linspace(0,200,200001))),'Exponential: P(over 10 more)':math.exp(-1),'Aging model: P(over 10 more)':math.exp(-((p+10)/scale)**2+(p/scale)**2)};t=('Before any waiting, a memoryless (exponential) wait has mean' if p==0 else f'After {p:g} minutes already waited, a memoryless (exponential) wait still has mean')+f' {mean} more minutes and a {100*math.exp(-1):.3g}% chance of lasting 10 more'+('. ' if p==0 else ': the past wait is forgotten. ')+('At time zero the two models are just two different shapes with the same 10-minute mean.' if p==0 else f'An aging wait with the same 10-minute mean (Weibull shape 2) now expects only {m[\"Aging model: expected extra wait\"]:.3g} more minutes. ')+('' if p==0 else ('\"Overdue\" reasoning is valid only for aging processes, never for exponential ones.' if p>=15 else 'Whether waiting longer makes the end nearer depends on the model, not on intuition.'))\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def entropy(p):\n", " p=np.asarray(p);return float(-np.sum(p[p>0]*np.log2(p[p>0])))\n", "\n", "\n", "def chapter_15(d,p):\n", " if d==1:\n", " x=np.linspace(0,1,201);h=[entropy([a,1-a]) for a in x];fig,ax=canvas('Bernoulli probability p','Entropy (bits)','Uncertainty peaks at equal probabilities');ax.plot(x,h);m={'Entropy in bits':entropy([p,1-p]),'Effective alphabet size':2**entropy([p,1-p])};t=f'At p={p:g}, entropy is {bits(m[\"Entropy in bits\"])}. '+(f'The rare outcome carries {bits(-math.log2(p))} of surprisal when it happens. ' if p<.5 else '')+('A rare event has high surprisal when it occurs, but low average entropy because it is rare.' if p<.1 else ('Neither outcome is rare here; equal probabilities give the maximum 1 bit.' if p==.5 else 'As p moves away from .5 toward zero, entropy falls because outcomes become more predictable.'))\n", " elif d==2:\n", " truth=np.array([.8,.2]);x=np.linspace(.01,.99,201);cross=-.8*np.log2(x)-.2*np.log2(1-x);fig,ax=canvas('Model probability q for outcome 1','Bits per outcome','A mismatched model costs extra information');ax.plot(x,cross,label='Cross-entropy');ax.axhline(entropy(truth),color='gray',linestyle='dashed',label='True entropy');ce=-.8*math.log2(p)-.2*math.log2(1-p);m={'True entropy':entropy(truth),'Cross-entropy':ce,'Perplexity':2**ce,'KL divergence (bits)':ce-entropy(truth)};t=f'True probabilities are (.8,.2), while the model assigns ({p:g},{1-p:g}). Cross-entropy is {bits(ce)}, the average cost of coding real outcomes with the model. '+(f'The excess over the true entropy, {ce-entropy(truth):.4g} bits, is the price of the wrong model (KL divergence). ' if abs(p-.8)>1e-9 else 'Here the model matches the truth, so the excess (the KL divergence) is zero. ')+f'Perplexity {2**ce:.4g} means the model is as unsure as a fair pick among that many options.'\n", " elif d==3:\n", " x=np.linspace(0,.5,201);capacity=[1-entropy([a,1-a]) for a in x];fig,ax=canvas('Bit-flip probability ε','Capacity (bits per channel use)','Noise limits a binary symmetric channel');ax.plot(x,capacity);m={'Flip probability':p,'Channel capacity':1-entropy([p,1-p])};t=f'The ideal memoryless binary symmetric channel has capacity {bits(m[\"Channel capacity\"])} per use at flip probability {p:g}. '+('A perfect channel: every bit gets through.' if p==0 else ('Each sent bit is pure noise; no code can recover anything.' if p==.5 else f'So you need about {1/m[\"Channel capacity\"]:.3g} sent bits per data bit, even with ideal coding. Real codes need somewhat more.'))\n", " elif d==4:\n", " snr=np.logspace(-1,4,300);cap=.5*np.log2(1+snr);fig,ax=canvas('Signal-to-noise power ratio (log scale)','Capacity (bits per real sample)','Capacity grows with the log of signal power');ax.semilogx(snr,cap,label='C = ½ log₂(1 + SNR)');s=10**(p/10);c=.5*math.log2(1+s);c2=.5*math.log2(1+2*s);ax.scatter([s],[c],s=80,color='#a26913',zorder=3,label=f'Selected: {p} dB');ax.scatter([2*s],[c2],s=60,marker='x',color='#aa4e37',zorder=3,label='Same, with double the power');m={'SNR (dB)':p,'SNR as a power ratio':s,'Capacity (bits per real sample)':c,'Capacity with double power':c2,'Gain from doubling power (bits)':c2-c};t=f'At {p} dB (power ratio {s:g}), the ideal Gaussian channel carries {bits(round(c,4))} per real sample. Doubling signal power adds {c2-c:.3g} bits. '+('When signal equals noise, doubling power still buys a 58% capacity gain. At high SNR the same doubling adds only about half a bit on top of many.' if p==0 else 'At high SNR each doubling adds only about half a bit per real sample, so more bandwidth (more samples per second) usually beats more power.')\n", " elif d==5:\n", " k=np.arange(1,25);fpr=(1-np.exp(-k/p))**k;kopt=p*math.log(2);kb=int(k[np.argmin(fpr)]);fig,ax=canvas('Hash functions k','False-positive rate (log scale)','Too few or too many hashes both hurt');ax.semilogy(k,fpr,'o-',ms=4,label=f'(1 − e^(−k/{p:g}))^k, {p:g} bits per item');ax.axvline(kopt,color='#a26913',linestyle=':',label=f'Optimum (m/n)·ln 2 = {kopt:.3g}');integer_ticks(ax);m={'Bits per item m/n':p,'Ideal k = (m/n) ln 2':kopt,'Best whole k':kb,'False-positive rate at best k':float(fpr.min()),'False-positive rate at k=1':float(fpr[0]),'Rate at k=24':float(fpr[-1])};t=f'With {p:g} bits per stored item, the false-positive rate is smallest near k=(m/n)ln 2={kopt:.3g}; the best whole number is {kb}, giving {100*fpr.min():.3g}%. One hash gives {100*fpr[0]:.3g}%, and 24 hashes give {100*fpr[-1]:.3g}% because the bit array fills up. '+('With so little memory, even the best k leaves about 1 false alarm in 7 lookups of absent items.' if p==4 else ('Each doubling of memory squares the best rate, roughly.' if p==8 else 'At 16 bits per item the best rate falls below 0.1%, but only near the optimum k.'))\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_16(d,p):\n", " if d==1:\n", " corr=np.linspace(-1,1,201);var=.5+.5*corr;fig,ax=canvas('Correlation ρ','Area standard uncertainty (cm²)','Covariance can reinforce or cancel first-order error');ax.plot(corr,np.sqrt(np.maximum(var,0)));u=math.sqrt(max(.5+.5*p,0));m={'Nominal area (cm²)':50,'First-order standard uncertainty (cm²)':u,'Expanded uncertainty k=2 (cm²)':2*u};t=f'A=LW with L=10±.1 cm, W=5±.05 cm, and correlation {p:g} gives first-order u(A)={u:.6g} cm². '+('The linear terms cancel exactly here; this does not imply zero nonlinear uncertainty.' if p==-1 else ('With no correlation, the two contributions add in quadrature.' if p==0 else 'Positive correlation makes the contributions reinforce, giving the largest uncertainty.' if p>0 else 'Negative correlation partly cancels the contributions.'))\n", " elif d==2:\n", " n=np.arange(1,501);fig,ax=canvas('Repeated readings n','RMS error','A fixed bias survives averaging');ax.plot(n,np.sqrt(1/n+p*p),label='RMS total');ax.plot(n,1/np.sqrt(n),'--',label='Random component');ax.axhline(abs(p),linestyle=':',label='Bias floor');m={'Single-reading random SD':1,'Fixed bias':p,'RMS error after 100 readings':math.sqrt(.01+p*p)};t=f'With independent unit-SD noise and fixed bias {p:g}, MSE of the mean is 1/n+b². After 100 readings the RMS error is {math.sqrt(.01+p*p):.3g}. '+('With no bias, more readings keep helping.' if p==0 else f'Averaging cannot push the error below the bias {p:g}; only calibration removes it.')\n", " elif d==3:\n", " rng=np.random.default_rng(1603);z=rng.normal(2,p,100000);y=z*z;fig,ax=canvas('Transformed value x²','Probability density','A nonlinear transform shifts the center');ax.hist(y,bins=80,density=True,label='100,000 constructed samples');ax.axvline(4,color='#a26913',label='Square of input mean');m={'Seed':1603,'Monte Carlo mean of x²':float(y.mean()),'Exact mean of x²':4+p*p,'Monte Carlo standard deviation':float(y.std(ddof=1)),'Straight-line estimate of SD (4σ)':4*p};t=f'For Gaussian x with mean 2 and SD {p:g}, E[x²]=4+σ²={4+p*p:g}. The constructed Monte Carlo result differs from squaring the mean. '+f'Straight-line estimate 4σ={4*p:.3g} versus simulated SD {float(y.std(ddof=1)):.3g}: '+('close enough here.' if abs(y.std(ddof=1)-4*p)<.05*4*p else 'the gap grows with σ, so simulate instead.')+''\n", " elif d==4:\n", " u=np.array([4.,2.,1.]);v=u.copy();v[p-1]/=2;base=math.sqrt((u*u).sum());new=math.sqrt((v*v).sum());fig,ax=canvas('Contributor','Standard uncertainty (mm)','Halve the biggest term first');x=np.arange(1,4);ax.bar(x-.2,u,.4,label='Before');ax.bar(x+.2,v,.4,label=f'After halving contributor {p}');ax.axhline(base,color='gray',linestyle='dashed',label=f'Combined before {base:.3g} mm');ax.axhline(new,color='#a26913',linestyle=':',label=f'Combined after {new:.3g} mm');ax.set_xticks(x,['1 (4 mm)','2 (2 mm)','3 (1 mm)']);m={'Combined before (mm)':base,'Combined after (mm)':new,'Reduction (%)':100*(1-new/base)};t=f'Contributions 4, 2 and 1 mm combine as √(16+4+1)={base:.4g} mm. Halving contributor {p} gives {new:.4g} mm, a {100*(1-new/base):.3g}% cut. '+('Squaring makes the largest term dominate, so this is the effort that pays.' if p==1 else 'Squaring makes the 4 mm term dominate, so effort spent here barely moves the total.')\n", " elif d==5:\n", " from math import lgamma\n", " def tcdf(x,v):\n", " z=np.linspace(0,x,4001);pdf=np.exp(lgamma((v+1)/2)-lgamma(v/2)-.5*math.log(v*math.pi)-(v+1)/2*np.log1p(z*z/v));return .5+float(np.sum((pdf[1:]+pdf[:-1])/2*np.diff(z)))\n", " nus=np.array([2,3,4,5,6,8,10,15,20,30,50,100]);cov=[100*(2*tcdf(2,v)-1) for v in nus];fig,ax=canvas('Effective degrees of freedom ν','Coverage of ±2u (%)','k=2 means about 95% only with enough data');ax.semilogx(nus,cov,'o-',label='Student t coverage of ±2u');ax.axhline(95.45,color='gray',linestyle='dashed',label='Normal limit 95.45%');c=100*(2*tcdf(2,p)-1);ax.scatter([p],[c],s=80,color='#a26913',zorder=3,label=f'Selected ν={p}')\n", " kneed=2.;lo,hi=1.9,20.\n", " for _ in range(50):\n", " mid=(lo+hi)/2;lo,hi=(mid,hi) if 2*tcdf(mid,p)-1<.9545 else (lo,mid)\n", " kneed=(lo+hi)/2;m={'Degrees of freedom':p,'Coverage of ±2u (%)':c,'Factor needed for 95.45% coverage':kneed};t=f'With ν={p} effective degrees of freedom, the interval ±2u covers about {c:.3g}% of a Student t distribution. Reaching the normal 95.45% would need k≈{kneed:.3g}. '+('With only a few readings, k=2 badly overstates the confidence.' if p<5 else ('The shortfall is now small, but report ν so a reader can check it.' if p<30 else 'With this much data, k=2 is close to its nominal 95% meaning.'))\n", "\n", "#### chapter_17\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_17(d,p):\n", " if d==1:\n", " r=np.linspace(0,.2,201);npv=400/(1+r)+400/(1+r)**2+400/(1+r)**3-1000;fig,ax=canvas('Annual discount rate','NPV (hypothetical currency units)','The discount rate can reverse a decision');ax.plot(r,npv);ax.axhline(0,color='gray');a=sum(400/(1+p)**k for k in (1,2,3))-1000;ax.scatter([p],[a]);m={'Initial cost':1000,'Three year-end payments':400,'Assumed annual rate':p,'NPV':a};t=f'Three year-end payments of 400 against cost 1000 have NPV {a:.6g} at assumed rate {100*p:g}%, so the project '+('passes' if a>0 else 'fails')+' the positive-NPV screen (the break-even rate is about 9.7%). These hypothetical cash flows illustrate timing, not a current investment recommendation.'\n", " elif d==2:\n", " x=np.linspace(0,.8,201);fig,ax=canvas('Fractional loss','Required fractional recovery','Loss and recovery use different bases');ax.plot(x,x/(1-x));m={'Loss fraction':p,'Required gain fraction':p/(1-p)};t=f'A {100*p:g}% loss leaves {100*(1-p):g}% of the original value. Recovering requires {100*p/(1-p):.6g}% of the reduced base.'\n", " elif d==3:\n", " periods=np.arange(1,13);effective=(1+.12/periods)**periods-1;fig,ax=canvas('Compounding periods per year','Effective annual rate','Quoted annual rates need a convention');ax.plot(periods,effective,'o-');m={'Nominal annual rate':.12,'Periods per year':p,'Effective annual rate':(1+.12/p)**p-1};t=f'A nominal annual rate of 12% compounded '+('once' if p==1 else f'{p:g} times')+f' per year gives effective annual rate {100*((1+.12/p)**p-1):.6g}%. Compare rates only after matching the convention.'\n", " elif d==4:\n", " r=np.linspace(1,25,200);fig,ax=canvas('Annual return r (%)','Rule of 72 minus exact (years)','Where the rule of 72 is right');ax.plot(r,72/r-np.log(2)/np.log(1+r/100),label='72/r minus exact ln2/ln(1+r/100)');ax.axhline(0,color='gray',lw=.8);ex=math.log(2)/math.log(1+p/100);ax.scatter([p],[72/p-ex],color='#a26913',zorder=3);ax.axvline(p,color='#a26913',linestyle=':',label='Selected rate');m={'Annual return (%)':p,'Exact doubling time (years)':ex,'Rule of 72 (years)':72/p,'Rule error (years)':72/p-ex};t=f'At {p:g}% a year, money doubles in {ex:.3g} years; the rule says {72/p:.3g}. '+('The shortcut is within a few days here, good enough for mental math.' if abs(72/p-ex)<.1 else ('At low rates the rule runs about a year long; 70/r is closer.' if p<5 else 'At high rates the rule runs short; use the exact formula when the answer matters.'))\n", " elif d==5:\n", " g=np.linspace(0,.0475,300);fig,ax=canvas('Growth rate g (%)','Value of growing perpetuity','Value explodes as growth approaches the discount rate');ax.plot(100*g,100/(.05-g),label='V = 100/(r−g), r=5%');ax.axvline(5,color='gray',linestyle='dashed',label='g = r: formula breaks');v=100/(.05-p);v2=100/(.05-p-.0025);ax.scatter([100*p],[v],s=80,color='#a26913',zorder=3,label=f'Selected g={100*p:g}%');ax.set_xlim(0,5.2);m={'Discount rate r (%)':5,'Growth rate g (%)':100*p,'Value (next payment 100)':v,'Value if g is 0.25 point higher':v2,'Change from that 0.25 point (%)':100*(v2/v-1)};t=f'With next payment 100, r=5% and g={100*p:g}%, the value is 100/(r−g)={v:,.0f}. Raising g by a quarter of a percentage point changes the value by {100*(v2/v-1):.3g}%. '+('With a 4 point spread between r and g, the estimate is fairly robust.' if p<.02 else ('Compared with g=1%, halving the spread to 2 points doubles the value and makes it about twice as sensitive to g.' if p<.04 else 'With only half a point of spread, a tiny change in assumed growth doubles the value, so the number is mostly a guess about g. At g≥r the formula gives no finite value at all.'))\n", "\n", "#### chapter_19\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_18(d,p):\n", " if d==1:\n", " # Lumped model diagnostic; properties explicitly assumed.\n", " r=np.logspace(-4,-1,100);k=200;h=p;bi=h*r/(3*k);fig,ax=canvas('Sphere radius (m)','Biot number','Screen a lumped thermal approximation');ax.loglog(r,bi,label='Biot number');ax.axhline(.1,linestyle='--',label='Common small-Bi screen');ax.axvline(.01,color='#a26913',linestyle=':',label='Selected radius .01 m');b=h*.01/(3*k);tau=2700*900*.01/(3*h);m={'Radius (m)':.01,'Conductivity (W/m/K)':k,'Density (kg/m³)':2700,'Specific heat (J/kg/K)':900,'Heat transfer h (W/m²/K)':h,'Biot number':b,'Screen Bi < .1 passed':b<.1,'Lumped time constant (s)':tau};t=f'Lc=r/3 gives Bi={b:.6g}. '+(f'The screen passes, so the lumped time constant τ=ρcLc/h={tau:.6g} s is a reasonable estimate under assumed aluminium-like properties.' if b<.1 else f'This fails the .1 screen: internal gradients matter, so the lumped τ={tau:.6g} s should not be trusted; use a conduction model.')+' The .1 screen is a rule of thumb; it does not validate real material properties or external heat transfer.'\n", " elif d==2:\n", " length=np.logspace(-3,0,100);diff=length**2/.01;adv=length/p;fig,ax=canvas('Length L (m)','Transport time (s)','Compare diffusion and advection scales');ax.loglog(length,diff,label='Diffusion L²/D');ax.loglog(length,adv,label='Advection L/U');ax.axvline(.1,color='#a26913',linestyle=':',label='L=.1 m (reported)');m={'Speed U (m/s)':p,'Diffusivity D (m²/s)':.01,'Peclet at L=.1m':p*.1/.01,'Equal-time length (m)':.01/p};t=f'At L=.1 m, Pe=UL/D={10*p:g}. '+('Diffusion is faster here, so spreading dominates.' if p*10<1 else ('Flow and diffusion take equal time here.' if p*10==1 else 'Flow carries material across before it diffuses, so advection dominates.'))+' Boundaries and geometry still shape the details.'\n", " elif d==3:\n", " speed=np.logspace(-3,1,100);re=1000*speed*.01/.001;fig,ax=canvas('Speed U (m/s)','Reynolds number','A dimensionless ratio compares inertia and viscosity');ax.loglog(speed,re);m={'Density (kg/m³)':1000,'Length (m)':.01,'Dynamic viscosity (Pa s)':.001,'Selected Reynolds number':10000*p};t=f'With the disclosed density, viscosity and length, U={p:g} m/s gives Re={10000*p:g}. '+('Viscosity dominates, so the flow is smooth and orderly.' if p<.01 else ('Inertia outweighs viscosity, yet many flows are still smooth at this size; pipe flow, for example, usually stays laminar below about 2000.' if p<.5 else 'Inertia dominates; turbulence is likely in most geometries.'))+' The exact switch point depends on geometry, so no single cutoff fits every flow.'\n", " elif d==4:\n", " a=1e-5;L=np.linspace(.002,.05,200);fig,ax=canvas('Slab thickness L (cm)','Diffusion time L²/α (s)','Double the thickness, quadruple the wait');ax.plot(100*L,L*L/a,label='t = L²/α, α=1e-5 m²/s');tt=p*p/a;ax.scatter([100*p],[tt],color='#a26913',zorder=3,label=f'Selected L={100*p:g} cm');m={'Thickness (cm)':100*p,'Thermal diffusivity (m²/s)':a,'Penetration time (s)':tt,'Time vs 2 cm slab':tt/40};t=f'Heat diffuses through {100*p:g} cm in about L²/α={tt:.3g} s (Fourier number 1). '+('Half the thickness takes a quarter of the time.' if p<.02 else ('This is the reference slab.' if p==.02 else 'Twice the thickness takes four times as long, not twice.'))+' Time grows with the square of distance because diffusion is a random walk.'\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_19(d,p):\n", " if d==1:\n", " state=np.array([2.,2.]);values=[];norms=[]\n", " for _ in range(31):\n", " values.append(.5*(state[0]**2+10*state[1]**2));norms.append(np.linalg.norm([state[0],10*state[1]]));state-=p*np.array([state[0],10*state[1]])\n", " fig,ax=canvas('Iteration','Objective','A step can shrink or amplify the stiff direction');ax.semilogy(range(31),np.maximum(values,1e-18));m={'Step size':p,'Initial objective':values[0],'Objective after 30 steps':values[-1],'Final gradient norm':norms[-1]};t=f'For f=(x²+10y²)/2 the largest Hessian eigenvalue is 10. Step {p:g} '+((('is exactly 1/L, the safe default: it wipes out the stiff y-direction in one step, and x then shrinks by 0.9 per step.' if p==.1 else 'contracts both directions, but the slow x-direction shrinks by only 0.95 per step.') if 0opt*10 else ('rounding dominates, so a smaller step makes it worse' if pec*3 else 'At low degree both are rough; the gap opens as degree rises.')\n", " elif d==5:\n", " tiny=1e-16;checks=sorted(set(np.unique(np.logspace(1,math.log10(p),40).astype(int))));naive=1.;s=1.;comp=0.;en=[];ek=[];k=0\n", " for target in checks:\n", " while k1, so this step is unstable: the numerical solution grows while the true solution decays.' if abs(g)>1 else ('The factor is negative, so the stable trajectory oscillates in sign; stability does not guarantee accuracy.' if g<0 else 'The positive factor below one gives a stable, monotone decay.'))\n", " elif d==2:\n", " hs=1/2**np.arange(1,8);errors=[]\n", " for h in hs:\n", " y=1.;z=-h;factor=1+z+z*z/2+z**3/6+z**4/24\n", " for _ in range(round(1/h)):y*=factor\n", " errors.append(abs(y-math.exp(-1)))\n", " i=list(hs).index(p);fig,ax=canvas('Step size h','Endpoint error at t=1','Halving the step cuts RK4 error about sixteenfold');ax.loglog(hs,errors,'o-',label='Computed RK4 error');ax.loglog(hs,errors[-1]*(hs/hs[-1])**4,'--',label='Fourth-order comparison');m={'Selected step':p,'Endpoint absolute error':errors[i],'Coarser / selected error':errors[i-1]/errors[i] if i else 'No coarser step'};t='These trajectories solve y′=−y, y(0)=1 to t=1. Halving h approaches a factor-of-sixteen global error reduction. Roundoff eventually limits such a trend.'\n", " elif d==3:\n", " h=p;n=round(40/h);t=np.arange(n+1)*h;qe=1.;pe=0.;qs=1.;ps=0.;ee=[];es=[]\n", " for _ in t:\n", " ee.append((qe*qe+pe*pe)/2);es.append((qs*qs+ps*ps)/2);qe,pe=qe+h*pe,pe-h*qe;ps-=h*qs;qs+=h*ps\n", " fig,ax=canvas('Time','Oscillator energy','An invariant reveals integration drift');ax.plot(t,ee,label='Explicit Euler');ax.plot(t,es,label='Symplectic Euler');ax.axhline(.5,linestyle='--',label='Exact energy');m={'Step':h,'Explicit final energy':ee[-1],'Symplectic final energy':es[-1]};t=f'The normalized oscillator q′=p, p′=−q has exact energy .5. Explicit Euler gains energy every step and ends at {ee[-1]:.4g}, about {ee[-1]/.5:,.0f} times too much. Symplectic Euler stays within {max(abs(np.array(es)-.5)):.2g} of .5. That bounded error is why long orbit and molecule runs use symplectic methods. It still does not prove the timing (phase) is right.'\n", " elif d==4:\n", " h=.025;n=round(2/h);ts=np.arange(n+1)*h;ye=[0.];yi=[0.]\n", " for k in range(n):ye.append(ye[-1]+h*(-p*(ye[-1]-math.cos(ts[k]))));yi.append((yi[-1]+h*p*math.cos(ts[k+1]))/(1+h*p))\n", " ye=np.array(ye);yi=np.array(yi);dense=np.linspace(0,2,400);ref=lambda s:(p*p*np.cos(s)+p*np.sin(s)-p*p*np.exp(-p*s))/(p*p+1)\n", " fig,ax=canvas('Time (s)','State y',f'Stiffness: decay rate λ={p:g} per second, step h={h} s');ax.plot(dense,ref(dense),'k',lw=1,label='Exact solution');ax.plot(ts,np.clip(ye,-3,3),'o-',ms=3,label='Explicit Euler (clipped at ±3)');ax.plot(ts,yi,'s-',ms=3,label='Implicit (backward) Euler');ax.set_ylim(-3,3)\n", " g=1-h*p;m={'Decay rate λ (1/s)':p,'Step h (s)':h,'Explicit factor 1−hλ':g,'Explicit stable step limit 2/λ (s)':2/p,'Explicit steps needed on [0,2]':math.ceil(2/(2/p)),'Explicit max error':float(abs(ye-ref(ts)).max()),'Implicit max error':float(abs(yi-ref(ts)).max())}\n", " t=f'The solution just follows cos t, which a step of {h} s resolves easily. Explicit Euler, though, needs h below 2/λ={2/p:.3g} s to stay stable. '+(f'At λ={p:g} that limit is loose, so both methods track the curve.' if abs(g)<=1 and g>=0 else (f'At λ={p:g} the step is stable but the factor {g:g} is negative, so explicit Euler overshoots and zigzags around the true curve for the first few steps, until repeated factors of −0.5 die out; implicit Euler does not.' if abs(g)<=1 else f'At λ={p:g} the factor is {g:g}, so explicit Euler explodes even though the true curve is smooth. That is stiffness: stability, not accuracy, forces about {math.ceil(p):d} tiny steps. An implicit method takes the large step safely.'))\n", " elif d==5:\n", " h=2*math.pi/p;n=10*p;q=1.;v=0.;qs=[q]\n", " f=lambda q,v:(v,-q)\n", " for _ in range(n):\n", " k1=f(q,v);k2=f(q+h/2*k1[0],v+h/2*k1[1]);k3=f(q+h/2*k2[0],v+h/2*k2[1]);k4=f(q+h*k3[0],v+h*k3[1]);q,v=q+h/6*(k1[0]+2*k2[0]+2*k3[0]+k4[0]),v+h/6*(k1[1]+2*k2[1]+2*k3[1]+k4[1]);qs.append(q)\n", " ts=np.arange(n+1)*h;amp=math.hypot(q,v);ph=math.degrees(math.atan2(-v,q));ph=(ph+180)%360-180\n", " fig,ax=canvas('Time (periods)','Position q',f'RK4 with {p} steps per period, after 10 periods');dense=np.linspace(0,ts[-1],2000);ax.plot(dense/(2*math.pi),np.cos(dense),'k',lw=1,label='Exact cos t');ax.plot(ts/(2*math.pi),qs,'o-',ms=3,label='RK4 steps');ax.set_xlim(8,10)\n", " m={'Steps per period':p,'Step h':h,'Amplitude after 10 periods':amp,'Amplitude loss (%)':100*(1-amp),'Phase error after 10 periods (degrees)':ph}\n", " t=f'With {p} steps per period, after 10 periods RK4 keeps {100*amp:.4g}% of the amplitude and is {abs(ph):.3g}° off in phase. '+('That is far too coarse: the steps barely sketch the wave, and the amplitude has visibly decayed.' if p<6 else ('That is usable for a few periods, but the errors grow every cycle, so long runs need more steps.' if 100*(1-amp)>.1 or abs(ph)>1 else 'The steps sit on the exact curve; at this resolution RK4 error is far below what the plot can show.'))+' Count steps per shortest period before trusting any oscillation.'\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def diffusion_solution(n,ratio,end=.02):\n", " x=np.linspace(0,1,n+1);dx=1/n;steps=math.ceil(end/(ratio*dx*dx));dt=end/steps;u=np.sin(np.pi*x);u[0]=u[-1]=0\n", " for _ in range(steps):\n", " v=u.copy();v[1:-1]=u[1:-1]+dt/dx**2*(u[:-2]-2*u[1:-1]+u[2:]);u=v\n", " exact=np.exp(-np.pi**2*end)*np.sin(np.pi*x)\n", " return x,u,exact,dt/dx**2,float(np.sqrt(np.mean((u-exact)**2)))\n", "\n", "\n", "def chapter_23(d,p):\n", " if d==1:\n", " n=80;dx=1/n;x=np.arange(n)*dx;initial=np.exp(-((x-.3)/.07)**2);u=initial.copy();steps=20\n", " for _ in range(steps):u=u-p*(u-np.roll(u,1))\n", " shift=steps*p*dx;wrapped=(x-shift-.3+.5)%1-.5;exact=np.exp(-(wrapped/.07)**2);fig,ax=canvas('Periodic x','Transported value','Upwind transport evolves an actual profile');ax.plot(x,exact,label='Shifted analytic profile');ax.plot(x,u,'o-',markersize=2,label='Upwind');m={'Courant number':p,'Steps':steps,'Initial discrete mass':float(initial.sum()*dx),'Final discrete mass':float(u.sum()*dx),'Minimum value':float(u.min())};t=f'The upwind scheme conserves total mass exactly: whatever leaves one cell enters its neighbor. At CFL={p:g}, '+('numerical diffusion spreads and lowers the peak; at CFL=1 the scheme would be an exact grid shift.' if p<1 else 'upwind is an exact grid shift: each step moves the profile one cell, matching the analytic curve.' if p==1 else 'the monotone stability condition fails; conserved mass alone does not establish a usable solution.')\n", " elif d==2:\n", " x,u,exact,ratio,error=diffusion_solution(40,p);fig,ax=canvas('Rod position x','Normalized temperature','Compare computed diffusion with an exact solution');ax.plot(x,exact,label='Exact sine decay');ax.plot(x,u,'o-',markersize=3,label='Explicit finite difference');m={'Grid intervals':40,'Actual dt/dx²':ratio,'RMS error at t=.02':error,'Maximum magnitude':float(abs(u).max())};t=f'Zero endpoints and a sine initial state provide a known heat solution. The actual ratio is {ratio:.6g}; the scheme is stable only when it is ≤.5.'+(' Above .5 it is unstable, yet this plot still looks fine: the sine start holds almost no jagged high-frequency content for the instability to amplify. Run the same ratio to t=.2 and the RMS error explodes to about 10⁶⁰.' if ratio>.5 else ' At or below .5 every mode decays, so the computed curve stays on the exact one.')\n", " elif d==3:\n", " ns=[10,20,40,80];errors=[diffusion_solution(n,.4)[4] for n in ns];fig,ax=canvas('Grid intervals','RMS solution error','Mesh refinement checks the solver');ax.loglog(ns,errors,'o-',label='Executed heat solves');ax.loglog(ns,errors[0]*(np.array(ns[0])/np.array(ns,dtype=float))**2,'--',label='Second-order comparison');i=ns.index(p);m={'Selected intervals':p,'RMS error':errors[i],'Observed order from previous mesh':math.log(errors[i-1]/errors[i],2) if i else 'No previous mesh'};t='The known sine heat solution checks this finite-difference implementation. Holding dt/dx² near .4 makes temporal error decrease with dx² alongside spatial error. This coupled study does not separately measure time and space orders.'\n", " elif d==4:\n", " N=np.linspace(3,40,300);fig,ax=canvas('Grid cells per wavelength','Numerical / true wave speed','Too few cells make waves travel at the wrong speed',two=True);ax[0].plot(N,np.sin(2*np.pi/N)/(2*np.pi/N),label='Centered second-order derivative');ax[0].axhline(1,color='k',lw=.8,linestyle='dashed',label='Exact speed');ax[0].axvline(p,color='#a26913',linestyle=':',label='Selected input')\n", " r=math.sin(2*math.pi/p)/(2*math.pi/p);x=np.linspace(0,3,600);ax[1].plot(x,np.sin(2*np.pi*(x-5)),'k',label='Exact wave after 5 wavelengths');ax[1].plot(x,np.sin(2*np.pi*(x-5*r)),label='Computed wave');ax[1].set(xlabel='Position (wavelengths)',ylabel='Wave height',title=f'{p} cells per wavelength')\n", " lag=5*(1-r)*360;m={'Cells per wavelength':p,'Speed ratio':r,'Speed error (%)':100*(1-r),'Phase lag after 5 wavelengths (degrees)':lag}\n", " t=f'With {p} cells per wavelength the computed wave moves at {100*r:.3g}% of the true speed. After traveling 5 wavelengths it lags by {lag:.3g}°. '+('The crest is more than a full wavelength behind (because the wave repeats, the plot makes it look slightly ahead): the computed wave is useless.' if lag>360 else ('The speed looks close, yet the crest is now a third of a wavelength late. Ten cells is a floor for short trips, not long ones.' if lag>90 else 'The crest arrives only slightly late, good enough for short runs.'))+' Phase error grows with distance traveled, so long runs need more cells or a higher-order scheme.'\n", " elif d==5:\n", " n=20;dx=1/n;a=1.;D=a*dx/p;x=np.linspace(0,1,n+1);A=np.zeros((n-1,n-1));b=np.zeros(n-1)\n", " lo=-D/dx**2-a/(2*dx);di=2*D/dx**2;up=-D/dx**2+a/(2*dx)\n", " for i in range(n-1):\n", " A[i,i]=di\n", " if i>0:A[i,i-1]=lo\n", " if i500 else f'{p:g} Hz is below the 500 Hz Nyquist limit (half the sample rate), so it appears where it belongs.')\n", " elif d==2:\n", " fs=1000;n=int(fs*p);t=np.arange(n)/fs;y=np.sin(2*np.pi*100*t)+np.sin(2*np.pi*100.2*t);window=np.hanning(n);nfft=8*n;f=np.fft.rfftfreq(nfft,1/fs);amp=2*abs(np.fft.rfft(y*window,nfft))/window.sum();fig,ax=canvas('Frequency (Hz)','Hann-windowed amplitude','Longer records change the two-tone spectrum');ax.plot(f,amp,label='8× padded FFT');ax.axvline(100,color='#a26913',linestyle=':',label='True tones');ax.axvline(100.2,color='#a26913',linestyle=':');ax.set_xlim(99,101.2)\n", " band=(f>99.5)&(f<100.7);fb=f[band];ab=amp[band];peaks=[float(fb[i]) for i in range(1,len(ab)-1) if ab[i]>ab[i-1] and ab[i]>=ab[i+1] and ab[i]>.3*ab.max()];resolved=.2>=4/p\n", " m={'Duration (s)':p,'Hann main-lobe half-width 2/T (Hz)':2/p,'Padded bin spacing (Hz)':fs/nfft,'Tone separation (Hz)':.2,'Spectral peaks found (Hz)':', '.join(f'{a:.4g}' for a in peaks)};t=f'The {p:g}-second record contains tones at 100 and 100.2 Hz (dotted lines). '+(f'The Hann main lobe (half-width {2/p:g} Hz) is wider than the 0.2 Hz separation, so the tones are not resolved. '+('The two peaks shown sit at the wrong frequencies: they come from phase interference, not resolution.' if len(peaks)>1 else 'They merge into one lobe.') if not resolved else 'The main lobes are now narrow enough that the peaks land on the true tone frequencies.')+' Zero padding only refines the plotted grid; duration and window govern resolution.'\n", " elif d==3:\n", " fs=1000;n=256;t=np.arange(n)/fs;y=np.sin(2*np.pi*103.3*t);window=np.ones(n) if p=='rectangular' else np.hanning(n);f=np.fft.rfftfreq(8192,1/fs);amp=2*abs(np.fft.rfft(y*window,8192))/window.sum();fig,ax=canvas('Frequency (Hz)','Amplitude (dB relative to 1)','Windows trade sidelobes against main-lobe width');ax.plot(f,20*np.log10(np.maximum(amp,1e-12)));ax.set(xlim=(50,160),ylim=(-100,5));m={'Window':p,'Samples':n,'Tone (Hz)':103.3,'Window average (amplitude correction)':float(window.mean())};t=('With no window, leakage is still at about −24 dB twenty hertz from the tone. ' if p=='rectangular' else 'The Hann window drops leakage twenty hertz away to about −49 dB, but its central peak is twice as wide. ')+'The tone is not coherent with the 256-sample record. A Hann window reduces distant leakage while widening its main lobe. Dividing by the window sum corrects coherent gain; it does not remove every off-bin amplitude bias.'\n", " elif d==4:\n", " fs=1000;n=3000;t_=np.arange(n)/fs;y=np.sin(2*np.pi*50*t_)+np.sin(2*np.pi*380*t_);fs2=fs/p;nyq=fs2/2\n", " k=np.arange(-100,101);cut=.8*nyq/fs;h=2*cut*np.sinc(2*cut*k)*np.hanning(len(k));h/=h.sum();yf=np.convolve(y,h,mode='same')\n", " fig,ax=canvas('Frequency (Hz)','One-sided amplitude',f'Downsample 1000 Hz by {p}: new Nyquist {nyq:.4g} Hz')\n", " for sig,lab,lw in [(y[::p],'Keep every sample (no filter)',3),(yf[::p],'Low-pass first, then keep',1.2)]:\n", " a=2*abs(np.fft.rfft(sig*np.hanning(len(sig))))/np.hanning(len(sig)).sum();ax.plot(np.fft.rfftfreq(len(sig),1/fs2),a,lw=lw,label=lab)\n", " ax.axvline(50,color='k',linestyle=':',label='Real 50 Hz tone');ax.set_xlim(0,nyq)\n", " al=abs((380+fs2/2)%fs2-fs2/2);m={'Downsampling factor':p,'New sample rate (Hz)':fs2,'New Nyquist (Hz)':nyq,'380 Hz tone appears at (Hz)':al if 380>nyq else 380.}\n", " t=('At factor 1 nothing is thrown away, so both tones appear where they belong: 50 and 380 Hz.' if p==1 else f'The new Nyquist limit is {nyq:.4g} Hz, below the 380 Hz tone. Without a filter that tone folds down to a fake {al:.3g} Hz peak'+(', right beside the real 50 Hz tone, where nobody could tell them apart.' if al<80 else ' that looks just like a real signal.')+' Filtering first removes it, leaving only the true 50 Hz.')+' Once aliasing happens, no later processing can undo it.'\n", " return result(fig,ax,m,t)\n", "\n", "\n", "def chapter_25(d,p):\n", " if d==1:\n", " t=np.linspace(0,2,501);y=1-np.exp(-2*np.pi*p*t);fig,ax=canvas('Time (s)','Unit-step response','A first-order loop connects bandwidth and rise time');ax.plot(t,y);rise=math.log(9)/(2*math.pi*p);m={'Bandwidth (Hz)':p,'Exact 10–90% rise time (s)':rise,'Rule .35 / bandwidth (s)':.35/p};t=f'For this normalized first-order closed-loop model, 10–90% rise time is ln(9)/(2πf)={rise:.6g} s. The .35/f rule agrees closely here, but different pole patterns need separate verification.'\n", " elif d==2:\n", " f=np.logspace(-1,2,200);lag=360*f*p;fig,ax=canvas('Frequency (Hz)','Delay phase lag (degrees)','Latency consumes phase margin');ax.semilogx(f,lag);ax.axvline(5,color='#a26913',label='Assumed crossover 5 Hz');m={'Delay (s)':p,'Lag at 5 Hz (degrees)':1800*p,'Nominal margin (degrees)':60,'Fixed-crossover remaining margin':60-1800*p};t=f'Delay {p:g} s contributes {1800*p:g}° lag at 5 Hz. Subtracting it from a nominal 60° margin leaves {60-1800*p:g}°. '+('A negative margin means the loop would likely oscillate or go unstable: cut the delay or lower the crossover.' if 60-1800*p<0 else ('That is below the usual 45° floor, so expect overshoot and ringing.' if 60-1800*p<45 else 'That is still comfortable.'))+' This fixed-crossover screen is not a full stability proof.'\n", " elif d==3:\n", " dt=.005;t=np.arange(0,12+dt,dt);y=0.;integral=0.;ys=[];us=[];zs=[]\n", " for time in t:\n", " target=2. if time<4 else .5;error=target-y;raw=2*error+integral;u=np.clip(raw,-1,1)\n", " if p=='off' or abs(raw-u)<1e-12 or error*(raw-u)<0:integral+=dt*error\n", " y+=dt*(-y+u);ys.append(y);us.append(u);zs.append(integral)\n", " fig,ax=canvas('Time (s)','Plant output','Saturation exposes integral windup',two=True);ax[0].plot(t,ys,label='Plant output');ax[0].plot(t,np.where(t<4,2.,.5),'--',label='Requested setpoint');ax[1].plot(t,zs,label='Integral state');ax[1].plot(t,us,label='Clipped actuator');ax[1].set(ylabel='Controller states',title=f'Conditional integration: {p}');m={'Anti-windup':p,'Actuator limits':'[−1,1]','Final output':ys[-1],'Integral state just before t=4':zs[round(4/dt)-1]};t='A normalized first-order plant uses PI gains Kp=2, Ki=1 and actuator limits ±1. The setpoint is unreachable for four seconds, then drops to .5. '+(f'With anti-windup off, the integral stores {zs[round(4/dt)-1]:.3g} units of unusable push, so at t=12 s the output is still {ys[-1]:.3g} instead of .5.' if p=='off' else f'With conditional integration on, the integral stops growing while the actuator is pinned, so the output reaches {ys[-1]:.3g}, close to the .5 target.')+' Any controller with integral action and a limited actuator needs this guard.'\n", " elif d==4:\n", " dt=.005;ts=np.arange(0,10+dt,dt);y=0.;I=0.;ys=[]\n", " for s in ts:\n", " e=1-y;u=2*e+p*I;dist=-.5 if s>=5 else 0.;I+=dt*e;y+=dt*(-y+u+dist);ys.append(y)\n", " fig,ax=canvas('Time (s)','Plant output',f'Constant disturbance at t=5 s, integral gain Ki={p:g}');ax.plot(ts,ys,label='Plant output');ax.axhline(1,color='k',linestyle='dashed',label='Setpoint');ax.axvline(5,color='#a26913',linestyle=':',label='Disturbance −0.5 starts')\n", " m={'Integral gain Ki':p,'Output before disturbance (t=5 s)':ys[round(5/dt)-1],'Final output (t=10 s)':ys[-1],'Final error':1-ys[-1]}\n", " t=(f'With no integral action the output settles at {ys[-1]:.3g}, short of the setpoint by {1-ys[-1]:.3g}. A proportional controller needs a leftover error to keep pushing, and the disturbance makes that gap bigger.' if p==0 else f'Integral action keeps adding up the error until it is gone. Final error is {1-ys[-1]:.2g}'+(', but the slow integral takes seconds to clean up the disturbance.' if p<2 else ', and a larger Ki removes it faster. The price is already visible: the output overshoots the setpoint by about 8% at the start, and a still larger Ki would ring more.'))\n", " elif d==5:\n", " pole=math.tan(math.radians(p));k=math.hypot(1,pole);dt=.002;ts=np.arange(0,20+dt,dt);y=0.;v=0.;ys=[]\n", " for _ in ts:\n", " ys.append(y);acc=k*(1-y)-pole*v;v+=dt*acc;y+=dt*v\n", " ys=np.array(ys);os_=100*(ys.max()-1);fig,ax=canvas('Time (s)','Output',f'Step response with {p:g}° phase margin, crossover 1 rad/s');ax.plot(ts,ys,label='Closed-loop output');ax.axhline(1,color='k',linestyle='dashed',label='Setpoint')\n", " m={'Phase margin (degrees)':p,'Open-loop pole (rad/s)':pole,'Loop gain':k,'Overshoot (%)':float(os_),'Peak output':float(ys.max())}\n", " t=f'The loop L(s)=k/(s(s+a)) crosses unity gain at 1 rad/s with {p:g}° of phase margin. Its step response overshoots by {os_:.3g}%. '+('With only 30°, the output rings for several cycles before settling: a small extra delay could make it unstable.' if p<40 else ('45° gives a modest overshoot and quick settling, a common working compromise.' if p<55 else '60° gives little overshoot at the cost of a slightly slower rise.'))+' Margin is a starting screen; check the actual response.'\n", " return result(fig,ax,m,t)\n", "\n", "plt.rcParams.update({'font.family': 'DejaVu Sans', 'font.size': 11, 'axes.spines.top': False, 'axes.spines.right': False, 'axes.labelcolor': '#172a3b', 'text.color': '#172a3b', 'svg.fonttype': 'none'})\n", "plt.rcParams['axes.prop_cycle']=cycler(color=['#136f75', '#b77518', '#334c72', '#aa4e37'])\n", "print('Calculation definitions loaded; all inputs are constructed.')\n" ] }, { "cell_type": "markdown", "id": "ch20-cell02", "metadata": {}, "source": [ "## C20-D01: Turn a bracket into a numerical certificate\n", "\n", "What does one extra halving buy?\n", "\n", "Actually bisect x²−2 on [1,2], then compare the observed error with the guaranteed midpoint ceiling.\n", "\n", "$$\n", "|x_{mid}-x_*|\\leq\\frac{b_0-a_0}{2^{k+1}}\n", "$$\n", "\n", "**Symbols and inputs:** Bisection halvings k. Continuous function and a sign-changing bracket containing the positive root.\n", "\n", "**Predict:** What does one extra halving buy?" ] }, { "cell_type": "code", "execution_count": 2, "id": "ch20-cell03", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:58:17.432032Z", "iopub.status.busy": "2026-10-03T00:58:17.431975Z", "iopub.status.idle": "2026-10-03T00:58:17.603872Z", "shell.execute_reply": "2026-10-03T00:58:17.603811Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Turn a bracket into a numerical certificate" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Halvings:** 10\n", "- **Midpoint:** 1.41455078125\n", "- **Actual error:** 0.0003372188769048545\n", "- **Certified error ceiling:** 0.00048828125" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "10 halvings reduce a width-one bracket to 0.000976562. Continuity and a valid root bracket give the midpoint error ceiling 0.000488281." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(20,1,10)\n", "buffer=io.BytesIO()\n", "figure.savefig(buffer,format='png',dpi=140,bbox_inches='tight',pad_inches=.16)\n", "display(Image(data=buffer.getvalue(),alt='Turn a bracket into a numerical certificate'))\n", "plt.close(figure)\n", "display(Markdown('\\n'.join('- **'+str(k)+':** '+str(v) for k,v in metrics.items())))\n", "display(Markdown(interpretation))\n" ] }, { "cell_type": "markdown", "id": "ch20-cell04", "metadata": {}, "source": [ "**Use the idea:** Use rule 20.3.5 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** Continuous function and a sign-changing bracket containing the positive root.\n", "\n", "
What does one extra halving buy?\n", "\n", "It halves the bracket width and the midpoint error ceiling.\n", "\n", "
\n", "\n", "**Book source:** [Rule 20.3.5: Budget bisection iterations from the bracket width](source.html)." ] }, { "cell_type": "markdown", "id": "ch20-cell05", "metadata": {}, "source": [ "## C20-D02: Find where a smaller derivative step stops helping\n", "\n", "Why does extremely tiny h fail?\n", "\n", "Forward and centered differences encounter both truncation and floating subtraction errors.\n", "\n", "$$\n", "f^{\\prime}(x)\\approx\\frac{f(x+h)-f(x-h)}{2h}\n", "$$\n", "\n", "**Symbols and inputs:** Difference step h. Differentiate exp(x) at x=1 in binary64. Function scale and derivatives influence the best step.\n", "\n", "**Predict:** Why does extremely tiny h fail?" ] }, { "cell_type": "code", "execution_count": 3, "id": "ch20-cell06", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:58:17.604912Z", "iopub.status.busy": "2026-10-03T00:58:17.604845Z", "iopub.status.idle": "2026-10-03T00:58:17.726637Z", "shell.execute_reply": "2026-10-03T00:58:17.726576Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Find where a smaller derivative step stops helping" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Step h:** 1e-08\n", "- **Forward error:** 6.60275079056305e-09\n", "- **Centered error:** 6.60275079056305e-09" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "At h=1e-08, forward difference: it is near its best step; centered difference: rounding dominates, so a smaller step makes it worse. Optimal step scales depend on precision, derivative size and function implementation, not a universally best constant." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(20,2,1e-08)\n", "buffer=io.BytesIO()\n", "figure.savefig(buffer,format='png',dpi=140,bbox_inches='tight',pad_inches=.16)\n", "display(Image(data=buffer.getvalue(),alt='Find where a smaller derivative step stops helping'))\n", "plt.close(figure)\n", "display(Markdown('\\n'.join('- **'+str(k)+':** '+str(v) for k,v in metrics.items())))\n", "display(Markdown(interpretation))\n" ] }, { "cell_type": "markdown", "id": "ch20-cell07", "metadata": {}, "source": [ "**Use the idea:** Use rule 20.2.2 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** Differentiate exp(x) at x=1 in binary64. Function scale and derivatives influence the best step.\n", "\n", "
Why does extremely tiny h fail?\n", "\n", "The nearby function values round before subtraction, so dividing by tiny h amplifies rounding error.\n", "\n", "
\n", "\n", "**Book source:** [Rule 20.2.2: Use a cube-root-epsilon step for centered differences](source.html)." ] }, { "cell_type": "markdown", "id": "ch20-cell08", "metadata": {}, "source": [ "## C20-D03: Measure trapezoid convergence\n", "\n", "What error ratio should step halving approach?\n", "\n", "Compute the integral on successive meshes and compare with the known exact value.\n", "\n", "$$\n", "\\int_0^1e^x dx=e-1,\\quad E(h)=O(h^2)\n", "$$\n", "\n", "**Symbols and inputs:** Subinterval count n. Smooth integrand, uniform composite trapezoid rule.\n", "\n", "**Predict:** What error ratio should step halving approach?" ] }, { "cell_type": "code", "execution_count": 4, "id": "ch20-cell09", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:58:17.727754Z", "iopub.status.busy": "2026-10-03T00:58:17.727689Z", "iopub.status.idle": "2026-10-03T00:58:17.854718Z", "shell.execute_reply": "2026-10-03T00:58:17.854667Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Measure trapezoid convergence" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Subintervals:** 32\n", "- **Absolute error:** 0.00013983185728161374\n", "- **Error ratio when n doubles (previous / selected):** 3.999804707041844" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "The smooth integral of exp(x) on [0,1] is e−1. Doubling the subinterval count decreases trapezoid error by about four; nonsmooth integrands need separate analysis." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(20,3,32)\n", "buffer=io.BytesIO()\n", "figure.savefig(buffer,format='png',dpi=140,bbox_inches='tight',pad_inches=.16)\n", "display(Image(data=buffer.getvalue(),alt='Measure trapezoid convergence'))\n", "plt.close(figure)\n", "display(Markdown('\\n'.join('- **'+str(k)+':** '+str(v) for k,v in metrics.items())))\n", "display(Markdown(interpretation))\n" ] }, { "cell_type": "markdown", "id": "ch20-cell10", "metadata": {}, "source": [ "**Use the idea:** Use rule 20.3.1 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** Smooth integrand, uniform composite trapezoid rule.\n", "\n", "
What error ratio should step halving approach?\n", "\n", "About four in the second-order regime, before roundoff dominates.\n", "\n", "
\n", "\n", "**Book source:** [Rule 20.3.1: Expect a factor of four from halving trapezoid spacing](source.html)." ] }, { "cell_type": "markdown", "id": "ch20-cell11", "metadata": {}, "source": [ "## C20-D04: Watch equal spacing blow up\n", "\n", "Does raising the degree always help?\n", "\n", "Interpolate the same smooth bump with equally spaced points and with Chebyshev points.\n", "\n", "$$\n", "f(x)=\\frac{1}{1+25x^2},\\quad x_j=\\cos\\frac{(2j+1)\\pi}{2n+2}\n", "$$\n", "\n", "**Symbols and inputs:** Polynomial degree n. Exact data, one global polynomial on [-1,1] through n+1 nodes, binary64.\n", "\n", "**Predict:** Does raising the degree always help?" ] }, { "cell_type": "code", "execution_count": 5, "id": "ch20-cell12", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:58:17.855687Z", "iopub.status.busy": "2026-10-03T00:58:17.855628Z", "iopub.status.idle": "2026-10-03T00:58:17.931922Z", "shell.execute_reply": "2026-10-03T00:58:17.931863Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Watch equal spacing blow up" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Degree:** 12\n", "- **Max error, equispaced:** 3.663262143306584\n", "- **Max error, Chebyshev:** 0.06921570780775665" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "Degree 12: worst error 3.66 with equal spacing, 0.0692 with Chebyshev nodes. Raising the degree makes equal spacing worse while Chebyshev keeps improving." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(20,4,12)\n", "buffer=io.BytesIO()\n", "figure.savefig(buffer,format='png',dpi=140,bbox_inches='tight',pad_inches=.16)\n", "display(Image(data=buffer.getvalue(),alt='Watch equal spacing blow up'))\n", "plt.close(figure)\n", "display(Markdown('\\n'.join('- **'+str(k)+':** '+str(v) for k,v in metrics.items())))\n", "display(Markdown(interpretation))\n" ] }, { "cell_type": "markdown", "id": "ch20-cell13", "metadata": {}, "source": [ "**Use the idea:** Use rule 20.2.4 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** Exact data, one global polynomial on [-1,1] through n+1 nodes, binary64.\n", "\n", "
Does raising the degree always help?\n", "\n", "Not with equal spacing: worst error grows from .62 to 29. Chebyshev nodes shrink it from .26 to .022.\n", "\n", "
\n", "\n", "**Book source:** [Rule 20.2.4: Use Chebyshev-like nodes for high-degree global interpolation](source.html)." ] }, { "cell_type": "markdown", "id": "ch20-cell14", "metadata": {}, "source": [ "## C20-D05: Recover small terms with compensated summation\n", "\n", "Does adding a million copies of 1e-16 to 1 in plain floating point change the total?\n", "\n", "Add many tiny terms to 1. A plain running sum rounds each one away; a compensated sum keeps a correction term and recovers them.\n", "\n", "$$\n", "\\text{Kahan: } y=a_k-c,\\ t=s+y,\\ c=(t-s)-y,\\ s=t\n", "$$\n", "\n", "**Symbols and inputs:** Number of 1e-16 terms. Binary64, round to nearest, terms below half an ulp of the running total.\n", "\n", "**Predict:** Does adding a million copies of 1e-16 to 1 in plain floating point change the total?" ] }, { "cell_type": "code", "execution_count": 6, "id": "ch20-cell15", "metadata": { "collapsed": true, "execution": { "iopub.execute_input": "2026-10-03T00:58:17.932932Z", "iopub.status.busy": "2026-10-03T00:58:17.932867Z", "iopub.status.idle": "2026-10-03T00:58:18.042224Z", "shell.execute_reply": "2026-10-03T00:58:18.042166Z" }, "jupyter": { "source_hidden": true }, "tags": [ "hide-input", "illustration" ] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "" ] }, "metadata": { "image/png": { "alt": "Recover small terms with compensated summation" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "- **Tiny terms added:** 100,000\n", "- **Exact sum minus 1:** 1e-11\n", "- **Plain sum minus 1:** 0.0\n", "- **Kahan sum minus 1:** 1.000000082740371e-11" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/markdown": [ "Start at 1 and add 100,000 copies of 1e-16. The exact total grows by 1e-11, but each 1e-16 is below half the spacing of doubles near 1, so the plain sum rounds every one away and stays exactly 1. The compensated sum carries the lost bits forward and gets 1e-11. The plain total is off by 1e-11 in relative terms, and the gap grows with every term; Kahan stays at rounding level." ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure, metrics, interpretation=illustrate(20,5,100000)\n", "buffer=io.BytesIO()\n", "figure.savefig(buffer,format='png',dpi=140,bbox_inches='tight',pad_inches=.16)\n", "display(Image(data=buffer.getvalue(),alt='Recover small terms with compensated summation'))\n", "plt.close(figure)\n", "display(Markdown('\\n'.join('- **'+str(k)+':** '+str(v) for k,v in metrics.items())))\n", "display(Markdown(interpretation))\n" ] }, { "cell_type": "markdown", "id": "ch20-cell16", "metadata": {}, "source": [ "**Use the idea:** Use rule 20.1.3 when its stated conditions fit. Compare the calculation with your own decision threshold; retain the relevant error or uncertainty.\n", "\n", "**Assumptions and limits:** Binary64, round to nearest, terms below half an ulp of the running total.\n", "\n", "
Does adding a million copies of 1e-16 to 1 in plain floating point change the total?\n", "\n", "No. Each addition rounds back to exactly 1, losing the whole 1e-10. Kahan summation recovers it.\n", "\n", "
\n", "\n", "**Book source:** [Rule 20.1.3: Use compensated summation for long mixed-scale sums](source.html)." ] }, { "cell_type": "markdown", "id": "ch20-cell17", "metadata": {}, "source": [ "## Continue with the chapter workbook\n", "\n", "The original decision worksheet, additional calculation, exercises and solutions follow." ] }, { "cell_type": "markdown", "id": "ch20-cell18", "metadata": {}, "source": [ "# Chapter 20 notebook: Numerical Methods: Approximation You Can Trust\n", "\n", "**Goal:** Budget a numerical computation and verify its accuracy with an independent check.\n", "\n", "**Start with:** Rules 20.3.4, 20.3.5, 20.3.7. Use a calculator or the optional Python lab. Programming is optional for the workbook; the Jupyter version requires a Python 3 kernel. All lab numbers are constructed practice inputs, not observed data.\n", "\n", "**Source:** [Finished Chapter 20](source.html) from *Mathematical Rules of Thumb*. Numbered rules, classifications, and the decision path come from the book. The lab, exercises, answer key, and worksheet prompts are companion additions.\n", "\n", "## 1. Frame your decision\n", "\n", "Write a question in which an answer would change something you do. Gather: Function or data; domain; root bracket or integration interval; smoothness; conditioning; precision and tolerance; coupled error sources.\n", "\n", "- My question and intended decision:\n", "- Known inputs and units:\n", "- Required accuracy or threshold:\n", "- What I expect before calculating:\n", "- What I still need to find out:\n", "\n", "Use the lab as a worked starting point if you do not yet have your own problem. For notation or prerequisites, ask the chapter skill to explain only the concept blocking the next step.\n", "\n", "## 2. Choose a route\n", "\n", "- **Does a small residual support the claimed answer?** Normalize it, estimate conditioning, and check the quantity of interest before inferring forward accuracy.\n", "- **Is the algorithm itself stable?** Compute a backward error in a structure and scale that represent scientifically acceptable input perturbations.\n", "- **Is arithmetic representation losing information?** Use compensated reduction, Horner nesting, or barycentric interpolation before increasing precision.\n", "- **Is a numerical derivative needed?** Scale the input, choose forward or centered differences from domain access, sweep nearby steps, and use complex-step only through analytic code.\n", "- **Are interpolation samples selectable?** Use Chebyshev-like nodes for a global polynomial; otherwise prefer a representation suited to fixed, noisy, or nonsmooth data.\n", "- **Is an integral smooth and freely sampled?** Use an appropriate Gaussian family; split at known nonsmooth locations and audit adaptive error estimates.\n", "- **Is a convergence order advertised?** Run at least three resolutions with controlled coupled errors and estimate the observed rate before extrapolating.\n", "- **Is a scalar root bracketed?** Budget bisection first, then permit secant or Newton acceleration without surrendering containment.\n", "- **Can a root solver stop safely?** Require a meaningful residual plus location, correction, or bracket evidence, with condition checks near singular roots.\n", "\n", "**Chapter-specific stop check:** Convergence order, residual size, and solver success flags require interpretation. Establish continuity before treating a sign change as a root bracket.\n", "\n", "## 3. Work the lab\n", "\n", "Find sqrt(2) as the root of x^2-2 on [1,2]. Require a final bracket width at most 1e-6. Bisection needs ceil(log2(1/1e-6))=20 interval halvings. The midpoint of the final bracket is then within 0.5e-6 of the root. This location certificate follows from continuity and a preserved sign-changing bracket, not from a small residual alone.\n", "\n", "Predict the sign and scale before running the code. Then change one input and explain why the result moves. The code checks the constructed example; it does not prove the rule for every possible input. Code assertions may describe the example's chosen regime, so inspect them before changing that regime." ] }, { "cell_type": "code", "execution_count": 7, "id": "ch20-cell19", "metadata": { "execution": { "iopub.execute_input": "2026-10-03T00:58:18.043252Z", "iopub.status.busy": "2026-10-03T00:58:18.043184Z", "iopub.status.idle": "2026-10-03T00:58:18.045528Z", "shell.execute_reply": "2026-10-03T00:58:18.045473Z" }, "jupyter": { "source_hidden": true }, "tags": [ "practice-lab", "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Halvings: 20; final width: 9.53674316e-07; answer: 1.414213657\n", "Certified midpoint error <= 4.76837158e-07\n" ] } ], "source": [ "import math\n", "left, right, width_tolerance = 1.0, 2.0, 1e-6\n", "def f(x):\n", " return x*x-2\n", "assert f(left)*f(right) < 0 and width_tolerance > 0\n", "budget = max(0, math.ceil(math.log2((right-left)/width_tolerance)))\n", "for iteration in range(budget):\n", " midpoint = (left+right)/2\n", " if f(left)*f(midpoint) <= 0:\n", " right = midpoint\n", " else:\n", " left = midpoint\n", "answer = (left+right)/2\n", "print(f\"Halvings: {budget}; final width: {right-left:.9g}; answer: {answer:.9f}\")\n", "print(f\"Certified midpoint error <= {(right-left)/2:.9g}\")\n", "assert left <= math.sqrt(2) <= right and right-left <= width_tolerance" ] }, { "cell_type": "markdown", "id": "ch20-cell20", "metadata": {}, "source": [ "**My prediction, observed result, and explanation:**\n", "\n", "_Record your work here._\n", "\n", "## 4. Practise without the answers\n", "\n", "### Exercise 1\n", "\n", "Errors on grids h, h/2, h/4 are 0.04, 0.01, 0.0025. What observed order do they suggest?\n", "\n", "**My approach, assumptions, calculation, and check:**\n", "\n", "_Write your attempt here._\n", "\n", "### Exercise 2\n", "\n", "A root solver reports |f(x)|=1e-8 with local |f'(x)|≈1e-6. What is the local correction scale?\n", "\n", "**My approach, assumptions, calculation, and check:**\n", "\n", "_Write your attempt here._\n", "\n", "### Exercise 3\n", "\n", "Can a sign change across x=0 certify a zero of f(x)=1/x on [-1,1]?\n", "\n", "**My approach, assumptions, calculation, and check:**\n", "\n", "_Write your attempt here._\n", "\n", "**Coaching prompt:** “Use the Chapter 20 skill to help me with Exercise 2. Ask for my attempt, give one useful hint if I need it, and help me check the assumptions before showing the answer.”\n", "\n", "## 5. Answer key and reasoning\n", "\n", "Read this after attempting the exercises, or use it immediately if you prefer a complete walkthrough. An answer is complete only when its assumptions and stopping point are clear.\n", "\n", "### Answer 1\n", "\n", "Each halving reduces error by four, giving log2(4)=2. This supports second order in the tested regime, assuming other errors are controlled.\n", "\n", "### Answer 2\n", "\n", "|f/f'|≈0.01. A small residual may correspond to a substantial location error near a flat root; inspect a bracket or other location evidence.\n", "\n", "### Answer 3\n", "\n", "No. Continuity fails at zero, so the intermediate-value argument behind the bracket is invalid. Split the domain at singularities.\n", "\n", "## 6. Build the complete chapter toolkit\n", "\n", "The new lab samples the chapter; the following checklist covers all 19 rules. Study one thematic group at a time. A large group can take several sessions.\n", "\n", "- **Separate Problem Difficulty From Algorithm Failure:** work with rules 20.1.1, 20.1.2, 20.1.3, 20.1.4, 20.1.5.\n", "- **Choose Nodes and Steps That Balance Error:** work with rules 20.2.1, 20.2.2, 20.2.3, 20.2.4, 20.2.5, 20.2.6.\n", "- **Budget Iterations and Verify Convergence:** work with rules 20.3.1, 20.3.2, 20.3.3, 20.3.4, 20.3.5, 20.3.6, 20.3.7, 20.3.8.\n", "\n", "For each selected rule, read its equation, explanation, and worked use in the source. Reproduce that example; change one input; then change one assumption so the rule is no longer justified. Record the result and what check catches the failure. Historical examples remain labeled and qualified as in the source.\n", "\n", "Read each complete numbered profile in the [chapter reference](source.html) before applying it. The cues below abbreviate the graph metadata; they are not complete conditions. Change the status only after doing the practice described below.\n", "\n", "| Rule | Book role | First assumptions to inspect | Practice status |\n", "|---|---|---|---|\n", "| 20.1.1: Interpret a residual through conditioning | Workflow | compatible condition measure; scale aware residual | new |\n", "| 20.1.2: Use backward error to distinguish stability from conditioning | Workflow | meaningful nearby problem; compatible condition measure | new |\n", "| 20.1.3: Use compensated summation for long mixed-scale sums | Workflow | floating point model; finite nonoverflowing terms | new |\n", "| 20.1.4: Use Horner's rule for polynomial evaluation | Workflow | floating point model; well scaled inputs | new |\n", "| 20.1.5: Evaluate interpolating polynomials in barycentric form | Workflow | floating point model; well scaled inputs | new |\n", "| 20.2.1: Use a square-root-epsilon step for forward differences | Workflow | floating point model; well scaled inputs | new |\n", "| 20.2.2: Use a cube-root-epsilon step for centered differences | Workflow | floating point model; well scaled inputs | new |\n", "| 20.2.3: Use complex-step differentiation when the code is analytic | Workflow | floating point model; well scaled inputs | new |\n", "| 20.2.4: Use Chebyshev-like nodes for high-degree global interpolation | Workflow | floating point model; well scaled inputs | new |\n", "| 20.2.5: An n-point Gauss rule integrates degree 2n-1 polynomials exactly | Independent | floating point model; well scaled inputs | new |\n", "| 20.2.6: Split adaptive quadrature where the integrand is difficult | Specialized | floating point model; well scaled inputs | new |\n", "| 20.3.1: Expect a factor of four from halving trapezoid spacing | Workflow | floating point model; well scaled inputs | new |\n", "| 20.3.2: Expect a factor of sixteen from halving Simpson spacing | Workflow | floating point model; well scaled inputs | new |\n", "| 20.3.3: Use step halving to extrapolate away leading error | Workflow | floating point model; well scaled inputs | new |\n", "| 20.3.4: Verify a claimed discretization order on three resolutions | Workflow | floating point model; well scaled inputs | new |\n", "| 20.3.5: Budget bisection iterations from the bracket width | Independent | floating point model; well scaled inputs | new |\n", "| 20.3.6: Expect secant convergence of order about 1.62 | Independent | floating point model; well scaled inputs | new |\n", "| 20.3.7: Safeguard Newton with a bracket | Specialized | floating point model; well scaled inputs | new |\n", "| 20.3.8: Stop Newton using the correction as well as the residual | Workflow | reliable newton correction; scale aware residual | new |\n", "\n", "For a completed row, record: **rule number / my new input / mathematical claim type / verified assumptions / calculation / check / valid use / rejected use / next step**. “Practised” means you worked an example. “Demonstrated” means you can explain a valid use, transfer it, and reject a misuse without the answer key.\n", "\n", "## 7. Apply it to your own problem\n", "\n", "Return to your opening question. Choose the smallest rule set that can settle it. Use the book's independent/workflow/specialized classification separately from the claim type (exact, approximate, bound, diagnostic, or heuristic).\n", "\n", "- Selected rule number(s) and reason:\n", "- Assumptions that hold, fail, or remain uncertain:\n", "- Substitution with units:\n", "- Result and error, uncertainty, or bound:\n", "- Independent check or limiting case:\n", "- Decision this supports:\n", "- Stop here, do a named next calculation, or gather missing information:\n", "\n", "## 8. Transfer and continue\n", "\n", "Useful nearby chapters: Chapter 5: analysis; Chapter 7: linear algebra; Chapter 21: scientific computing. Bring the question, units, assumptions, result type, and uncertainty to the next chapter. Choose a bridge only when it supplies an operation you actually need.\n", "\n", "**Completion check:** Explain this chapter's lab in your own words; solve one changed-input exercise; reject one invalid use; and produce a decision record for your own problem. If one check fails, revisit that part of the chapter rather than marking every rule complete." ] } ], "metadata": { "book_companion": { "calculation_sha256": "221161ba9a522041cf179f6a7f727cf915bbab1c2c633f469e54196e069a2d89", "chapter": 20, "example_data": "constructed", "execution": "All cells executed in order in a fresh process with a new in-process Python kernel. This is not socket-based Jupyter execution.", "reader": "reader.html", "source_sha256": "a496ef523a331bda7699a642ddfe2d1033d70bec06b1db77ff1d28f91b3d97b3", "version": "2.0.0" }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.14.4" } }, "nbformat": 4, "nbformat_minor": 5 }