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