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-% !TeX root = ./thuthesis-example.tex
-
-% Adapted for use with thuthesis.
-% Original code is at https://github.com/goodfeli/dlbook_notation/blob/master/math_commands.tex
-
-%%%%% NEW MATH DEFINITIONS %%%%%
-
-\newcommand\ceil[1]{\lceil #1 \rceil}
-\newcommand\floor[1]{\lfloor #1 \rfloor}
-
-
-% Vectors
-\newcommand\Vector[1]{\symbf{#1}}
-
-\newcommand\0{{\Vector{0}}}
-\newcommand\vzero{{\Vector{0}}}
-\newcommand\1{{\Vector{1}}}
-\newcommand\vone{{\Vector{1}}}
-
-\newcommand\va{{\Vector{a}}}
-\newcommand\vb{{\Vector{b}}}
-\newcommand\vc{{\Vector{c}}}
-\newcommand\vd{{\Vector{d}}}
-\newcommand\ve{{\Vector{e}}}
-\newcommand\vf{{\Vector{f}}}
-\newcommand\vg{{\Vector{g}}}
-\newcommand\vh{{\Vector{h}}}
-\newcommand\vi{{\Vector{i}}}
-\newcommand\vj{{\Vector{j}}}
-\newcommand\vk{{\Vector{k}}}
-\newcommand\vl{{\Vector{l}}}
-\newcommand\vm{{\Vector{m}}}
-\newcommand\vn{{\Vector{n}}}
-\newcommand\vo{{\Vector{o}}}
-\newcommand\vp{{\Vector{p}}}
-\newcommand\vq{{\Vector{q}}}
-\newcommand\vr{{\Vector{r}}}
-\newcommand\vs{{\Vector{s}}}
-\newcommand\vt{{\Vector{t}}}
-\newcommand\vu{{\Vector{u}}}
-\newcommand\vv{{\Vector{v}}}
-\newcommand\vw{{\Vector{w}}}
-\newcommand\vx{{\Vector{x}}}
-\newcommand\vy{{\Vector{y}}}
-\newcommand\vz{{\Vector{z}}}
-
-\newcommand\valpha{{\Vector{\alpha}}}
-\newcommand\vbeta{{\Vector{\beta}}}
-\newcommand\vgamma{{\Vector{\gamma}}}
-\newcommand\vdelta{{\Vector{\delta}}}
-\newcommand\vepsilon{{\Vector{\epsilon}}}
-\newcommand\vtheta{{\Vector{\theta}}}
-\newcommand\viota{{\Vector{\iota}}}
-\newcommand\vkappa{{\Vector{\kappa}}}
-\newcommand\vlambda{{\Vector{\lambda}}}
-\newcommand\vmu{{\Vector{\mu}}}
-\newcommand\vnu{{\Vector{\nu}}}
-\newcommand\vxi{{\Vector{\xi}}}
-\newcommand\vpi{{\Vector{\pi}}}
-\newcommand\vrho{{\Vector{\rho}}}
-\newcommand\vsigma{{\Vector{\sigma}}}
-\newcommand\vtau{{\Vector{\tau}}}
-\newcommand\vupsilon{{\Vector{\upsilon}}}
-\newcommand\vphi{{\Vector{\phi}}}
-\newcommand\vchi{{\Vector{\chi}}}
-\newcommand\vpsi{{\Vector{\psi}}}
-\newcommand\vomega{{\Vector{\omega}}}
-
-
-% Matrix
-\newcommand\MATRIX[1]{\symbf{#1}}
-
-\newcommand\mA{{\MATRIX{A}}}
-\newcommand\mB{{\MATRIX{B}}}
-\newcommand\mC{{\MATRIX{C}}}
-\newcommand\mD{{\MATRIX{D}}}
-\newcommand\mE{{\MATRIX{E}}}
-\newcommand\mF{{\MATRIX{F}}}
-\newcommand\mG{{\MATRIX{G}}}
-\newcommand\mH{{\MATRIX{H}}}
-\newcommand\mI{{\MATRIX{I}}}
-\newcommand\mJ{{\MATRIX{J}}}
-\newcommand\mK{{\MATRIX{K}}}
-\newcommand\mL{{\MATRIX{L}}}
-\newcommand\mM{{\MATRIX{M}}}
-\newcommand\mN{{\MATRIX{N}}}
-\newcommand\mO{{\MATRIX{O}}}
-\newcommand\mP{{\MATRIX{P}}}
-\newcommand\mQ{{\MATRIX{Q}}}
-\newcommand\mR{{\MATRIX{R}}}
-\newcommand\mS{{\MATRIX{S}}}
-\newcommand\mT{{\MATRIX{T}}}
-\newcommand\mU{{\MATRIX{U}}}
-\newcommand\mV{{\MATRIX{V}}}
-\newcommand\mW{{\MATRIX{W}}}
-\newcommand\mX{{\MATRIX{X}}}
-\newcommand\mY{{\MATRIX{Y}}}
-\newcommand\mZ{{\MATRIX{Z}}}
-
-\newcommand\mGamma{{\MATRIX{\Gamma}}}
-\newcommand\mDelta{{\MATRIX{\Delta}}}
-\newcommand\mTheta{{\MATRIX{\Theta}}}
-\newcommand\mLambda{{\MATRIX{\Lambda}}}
-\newcommand\mXi{{\MATRIX{\Xi}}}
-\newcommand\mPi{{\MATRIX{\Pi}}}
-\newcommand\mSigma{{\MATRIX{\Sigma}}}
-\newcommand\mUpsilon{{\MATRIX{\Upsilon}}}
-\newcommand\mPhi{{\MATRIX{\Phi}}}
-\newcommand\mPsi{{\MATRIX{\Psi}}}
-\newcommand\mOmega{{\MATRIX{\Omega}}}
-
-
-% Tensor
-\newcommand\tens[1]{\symbfsf{#1}}
-\newcommand\tA{{\tens{A}}}
-\newcommand\tB{{\tens{B}}}
-\newcommand\tC{{\tens{C}}}
-\newcommand\tD{{\tens{D}}}
-\newcommand\tE{{\tens{E}}}
-\newcommand\tF{{\tens{F}}}
-\newcommand\tG{{\tens{G}}}
-\newcommand\tH{{\tens{H}}}
-\newcommand\tI{{\tens{I}}}
-\newcommand\tJ{{\tens{J}}}
-\newcommand\tK{{\tens{K}}}
-\newcommand\tL{{\tens{L}}}
-\newcommand\tM{{\tens{M}}}
-\newcommand\tN{{\tens{N}}}
-\newcommand\tO{{\tens{O}}}
-\newcommand\tP{{\tens{P}}}
-\newcommand\tQ{{\tens{Q}}}
-\newcommand\tR{{\tens{R}}}
-\newcommand\tS{{\tens{S}}}
-\newcommand\tT{{\tens{T}}}
-\newcommand\tU{{\tens{U}}}
-\newcommand\tV{{\tens{V}}}
-\newcommand\tW{{\tens{W}}}
-\newcommand\tX{{\tens{X}}}
-\newcommand\tY{{\tens{Y}}}
-\newcommand\tZ{{\tens{Z}}}
-
-
-% Graph
-\newcommand\gA{{\mathcal{A}}}
-\newcommand\gB{{\mathcal{B}}}
-\newcommand\gC{{\mathcal{C}}}
-\newcommand\gD{{\mathcal{D}}}
-\newcommand\gE{{\mathcal{E}}}
-\newcommand\gF{{\mathcal{F}}}
-\newcommand\gG{{\mathcal{G}}}
-\newcommand\gH{{\mathcal{H}}}
-\newcommand\gI{{\mathcal{I}}}
-\newcommand\gJ{{\mathcal{J}}}
-\newcommand\gK{{\mathcal{K}}}
-\newcommand\gL{{\mathcal{L}}}
-\newcommand\gM{{\mathcal{M}}}
-\newcommand\gN{{\mathcal{N}}}
-\newcommand\gO{{\mathcal{O}}}
-\newcommand\gP{{\mathcal{P}}}
-\newcommand\gQ{{\mathcal{Q}}}
-\newcommand\gR{{\mathcal{R}}}
-\newcommand\gS{{\mathcal{S}}}
-\newcommand\gT{{\mathcal{T}}}
-\newcommand\gU{{\mathcal{U}}}
-\newcommand\gV{{\mathcal{V}}}
-\newcommand\gW{{\mathcal{W}}}
-\newcommand\gX{{\mathcal{X}}}
-\newcommand\gY{{\mathcal{Y}}}
-\newcommand\gZ{{\mathcal{Z}}}
-
-
-% Sets
-\newcommand\sA{{\mathbb{A}}}
-\newcommand\sB{{\mathbb{B}}}
-\newcommand\sC{{\mathbb{C}}}
-\newcommand\sD{{\mathbb{D}}}
-% Don't use a set called E, because this would be the same as our symbol
-% for expectation.
-\newcommand\sF{{\mathbb{F}}}
-\newcommand\sG{{\mathbb{G}}}
-\newcommand\sH{{\mathbb{H}}}
-\newcommand\sI{{\mathbb{I}}}
-\newcommand\sJ{{\mathbb{J}}}
-\newcommand\sK{{\mathbb{K}}}
-\newcommand\sL{{\mathbb{L}}}
-\newcommand\sM{{\mathbb{M}}}
-\newcommand\sN{{\mathbb{N}}}
-\newcommand\sO{{\mathbb{O}}}
-\newcommand\sP{{\mathbb{P}}}
-\newcommand\sQ{{\mathbb{Q}}}
-\newcommand\sR{{\mathbb{R}}}
-\newcommand\sS{{\mathbb{S}}}
-\newcommand\sT{{\mathbb{T}}}
-\newcommand\sU{{\mathbb{U}}}
-\newcommand\sV{{\mathbb{V}}}
-\newcommand\sW{{\mathbb{W}}}
-\newcommand\sX{{\mathbb{X}}}
-\newcommand\sY{{\mathbb{Y}}}
-\newcommand\sZ{{\mathbb{Z}}}
-
-
-% Random variables
-\newcommand\RandomVariable[1]{\symit{#1}}
-
-\newcommand\rA{{\RandomVariable{A}}}
-\newcommand\rB{{\RandomVariable{B}}}
-\newcommand\rC{{\RandomVariable{C}}}
-\newcommand\rD{{\RandomVariable{D}}}
-\newcommand\rE{{\RandomVariable{E}}}
-\newcommand\rF{{\RandomVariable{F}}}
-\newcommand\rG{{\RandomVariable{G}}}
-\newcommand\rH{{\RandomVariable{H}}}
-\newcommand\rI{{\RandomVariable{I}}}
-\newcommand\rJ{{\RandomVariable{J}}}
-\newcommand\rK{{\RandomVariable{K}}}
-\newcommand\rL{{\RandomVariable{L}}}
-\newcommand\rM{{\RandomVariable{M}}}
-\newcommand\rN{{\RandomVariable{N}}}
-\newcommand\rO{{\RandomVariable{O}}}
-\newcommand\rP{{\RandomVariable{P}}}
-\newcommand\rQ{{\RandomVariable{Q}}}
-\newcommand\rR{{\RandomVariable{R}}}
-\newcommand\rS{{\RandomVariable{S}}}
-\newcommand\rT{{\RandomVariable{T}}}
-\newcommand\rU{{\RandomVariable{U}}}
-\newcommand\rV{{\RandomVariable{V}}}
-\newcommand\rW{{\RandomVariable{W}}}
-\newcommand\rX{{\RandomVariable{X}}}
-\newcommand\rY{{\RandomVariable{Y}}}
-\newcommand\rZ{{\RandomVariable{Z}}}
-
-% Random vectors
-\newcommand\RandomVector[1]{\symbf{#1}}
-
-\newcommand\rvA{{\RandomVector{A}}}
-\newcommand\rvB{{\RandomVector{B}}}
-\newcommand\rvC{{\RandomVector{C}}}
-\newcommand\rvD{{\RandomVector{D}}}
-\newcommand\rvE{{\RandomVector{E}}}
-\newcommand\rvF{{\RandomVector{F}}}
-\newcommand\rvG{{\RandomVector{G}}}
-\newcommand\rvH{{\RandomVector{H}}}
-\newcommand\rvI{{\RandomVector{I}}}
-\newcommand\rvJ{{\RandomVector{J}}}
-\newcommand\rvK{{\RandomVector{K}}}
-\newcommand\rvL{{\RandomVector{L}}}
-\newcommand\rvM{{\RandomVector{M}}}
-\newcommand\rvN{{\RandomVector{N}}}
-\newcommand\rvO{{\RandomVector{O}}}
-\newcommand\rvP{{\RandomVector{P}}}
-\newcommand\rvQ{{\RandomVector{Q}}}
-\newcommand\rvR{{\RandomVector{R}}}
-\newcommand\rvS{{\RandomVector{S}}}
-\newcommand\rvT{{\RandomVector{T}}}
-\newcommand\rvU{{\RandomVector{U}}}
-\newcommand\rvV{{\RandomVector{V}}}
-\newcommand\rvW{{\RandomVector{W}}}
-\newcommand\rvX{{\RandomVector{X}}}
-\newcommand\rvY{{\RandomVector{Y}}}
-\newcommand\rvZ{{\RandomVector{Z}}}
-
-\newcommand\laplace{\mathrm{Laplace}} % Laplace distribution
-
-\newcommand\E{\mathbb{E}}
-\newcommand\Ls{\mathcal{L}}
-\newcommand\R{\mathbb{R}}
-\newcommand\emp{\tilde{p}}
-\newcommand\lr{\alpha}
-\newcommand\reg{\lambda}
-\newcommand\rect{\mathrm{rectifier}}
-\newcommand\softmax{\mathrm{softmax}}
-\newcommand\sigmoid{\sigma}
-\newcommand\softplus{\zeta}
-\newcommand\KL{D_{\mathrm{KL}}}
-\newcommand\Var{\mathrm{Var}}
-\newcommand\standarderror{\mathrm{SE}}
-\newcommand\Cov{\mathrm{Cov}}
-% Wolfram Mathworld says $L^2$ is for function spaces and $\ell^2$ is for vectors
-% But then they seem to use $L^2$ for vectors throughout the site, and so does
-% wikipedia.
-\newcommand\normlzero{L^0}
-\newcommand\normlone{L^1}
-\newcommand\normltwo{L^2}
-\newcommand\normlp{L^p}
-\newcommand\normmax{L^\infty}
-
-\DeclareMathOperator*{\argmax}{arg\,max}
-\DeclareMathOperator*{\argmin}{arg\,min}
-
-\DeclareMathOperator{\sign}{sign}
-\DeclareMathOperator{\Tr}{Tr}
-\let\ab\allowbreak