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author | Norbert Preining <norbert@preining.info> | 2020-06-18 03:02:56 +0000 |
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committer | Norbert Preining <norbert@preining.info> | 2020-06-18 03:02:56 +0000 |
commit | 7a78c3b8b21b6842d27bb48f37197f8c380ccc5e (patch) | |
tree | aaa0da455d5784ca3b21e12a88b6a739bb543e84 /macros/latex/contrib/mlmath/mlmath.sty | |
parent | da248962ebaf9445ca3c9dde54c05c3baa8715ab (diff) |
CTAN sync 202006180302
Diffstat (limited to 'macros/latex/contrib/mlmath/mlmath.sty')
-rw-r--r-- | macros/latex/contrib/mlmath/mlmath.sty | 622 |
1 files changed, 622 insertions, 0 deletions
diff --git a/macros/latex/contrib/mlmath/mlmath.sty b/macros/latex/contrib/mlmath/mlmath.sty new file mode 100644 index 0000000000..1faa04de0a --- /dev/null +++ b/macros/latex/contrib/mlmath/mlmath.sty @@ -0,0 +1,622 @@ +%% mlmath.sty +%% Copyright 2020 by Zheng Ma, Zhiqin Xu, Tao Luo and Yaoyu Zhang +% +% This work may be distributed and/or modified under the +% conditions of the LaTeX Project Public License, either version 1.3c +% of this license or (at your option) any later version. +% The latest version of this license is in +% http://www.latex-project.org/lppl.txt +% and version 1.3c or later is part of all distributions of LaTeX +% version 2005/12/01 or later. +% +% This work has the LPPL maintenance status `maintained'. +% +% The Current Maintainer of this work is Zheng Ma. +% +% This work consists of the main source files mlmath.sty, mlmath.tex, mlmath.md, +% and the derived documentation mlmath.pdf, README.md as well as the resource +% files (they are svg file) of README.md under the folder svgs/. + +\ProvidesPackage{mlmath}[2020/06/15 v1.0.0 zyboys] + +\RequirePackage{amsmath} +\RequirePackage{amsthm} +\RequirePackage{amssymb} +\RequirePackage{bm} +\RequirePackage{bbm} + + +\newcommand{\mat}[1]{\bm{#1}} +\renewcommand{\vec}[1]{\bm{#1}} +\newcommand{\D}{\mathrm{d}} +\newcommand{\I}{\mathrm{i}} +\newcommand{\E}{\mathrm{e}} +\newcommand{\eps}{\varepsilon} +\newcommand{\sgn}{\mathrm{sgn}} +\newcommand{\cc}{\mathrm{c.c.}} +\newcommand{\T}{\intercal} +\newcommand{\Exp}{\mathbb{E}} +\newcommand{\Prob}{\mathbb{P}} +\newcommand*\diff{\mathop{}\!\D} +\newcommand*\Diff[1]{\mathop{}\!\mathrm{d^#1}} +\newcommand{\abs}[1]{\lvert#1\rvert} +\newcommand{\Abs}[1]{\left\lvert#1\right\rvert} +\newcommand{\norm}[1]{\lVert#1\rVert} +\newcommand{\Norm}[1]{\left\lVert#1\right\rVert} +\newcommand{\ceil}[1]{\lceil#1\rceil} +\newcommand{\floor}[1]{\lfloor#1\rfloor} +\newcommand{\lsim}{\lesssim} +\newcommand{\gsim}{\gtrsim} + +% Random variables +\newcommand{\ralpha}{\textnormal{\alpha}} +\newcommand{\rbeta}{\textnormal{\beta}} +\newcommand{\rgamma}{\textnormal{\gamma}} +\newcommand{\rdelta}{\textnormal{\delta}} +\newcommand{\repsilon}{\textnormal{\epsilon}} +\newcommand{\reps}{\textnormal{\varepsilon}} +\newcommand{\rzeta}{\textnormal{\zeta}} +\newcommand{\reta}{\textnormal{\eta}} +\newcommand{\rtheta}{\textnormal{\theta}} +\newcommand{\rvartheta}{\textnormal{\vartheta}} +\newcommand{\riota}{\textnormal{\iota}} +\newcommand{\rkappa}{\textnormal{\kappa}} +\newcommand{\rlambda}{\textnormal{\lambda}} +\newcommand{\rmu}{\textnormal{\mu}} +\newcommand{\rnu}{\textnormal{\nu}} +\newcommand{\rxi}{\textnormal{\xi}} +\newcommand{\rpi}{\textnormal{\pi}} +\newcommand{\rrho}{\textnormal{\rho}} +\newcommand{\rsigma}{\textnormal{\sigma}} +\newcommand{\rtau}{\textnormal{\tau}} +\newcommand{\rupsilon}{\textnormal{\upsilon}} +\newcommand{\rphi}{\textnormal{\phi}} +\newcommand{\rvarphi}{\textnormal{\varphi}} +\newcommand{\rchi}{\textnormal{\chi}} +\newcommand{\rpsi}{\textnormal{\psi}} +\newcommand{\romega}{\textnormal{\omega}} +\newcommand{\rGamma}{\textnormal{\Gamma}} +\newcommand{\rDelta}{\textnormal{\Delta}} +\newcommand{\rTheta}{\textnormal{\Theta}} +\newcommand{\rLambda}{\textnormal{\Lambda}} +\newcommand{\rXi}{\textnormal{\Xi}} +\newcommand{\rPi}{\textnormal{\Pi}} +\newcommand{\rSigma}{\textnormal{\Sigma}} +\newcommand{\rUpsilon}{\textnormal{\Upsilon}} +\newcommand{\rPhi}{\textnormal{\Phi}} +\newcommand{\rPsi}{\textnormal{\Psi}} +\newcommand{\rOmega}{\textnormal{\Omega}} +\newcommand{\ra}{\textnormal{a}} +\newcommand{\rb}{\textnormal{b}} +\newcommand{\rc}{\textnormal{c}} +\newcommand{\rd}{\textnormal{d}} +\newcommand{\re}{\textnormal{e}} +\newcommand{\rf}{\textnormal{f}} +\newcommand{\rg}{\textnormal{g}} +\newcommand{\rh}{\textnormal{h}} +\newcommand{\ri}{\textnormal{i}} +\newcommand{\rj}{\textnormal{j}} +\newcommand{\rk}{\textnormal{k}} +\newcommand{\rl}{\textnormal{l}} +% rm is already a command, just don't name any random variables m +\newcommand{\rn}{\textnormal{n}} +\newcommand{\ro}{\textnormal{o}} +\newcommand{\rp}{\textnormal{p}} +\newcommand{\rqq}{\textnormal{q}} +\newcommand{\rr}{\textnormal{r}} +\newcommand{\rs}{\textnormal{s}} +\newcommand{\rt}{\textnormal{t}} +\newcommand{\ru}{\textnormal{u}} +\newcommand{\rv}{\textnormal{v}} +\newcommand{\rw}{\textnormal{w}} +\newcommand{\rx}{\textnormal{x}} +\newcommand{\ry}{\textnormal{y}} +\newcommand{\rz}{\textnormal{z}} +\newcommand{\rA}{\textnormal{A}} +\newcommand{\rB}{\textnormal{B}} +\newcommand{\rC}{\textnormal{C}} +\newcommand{\rD}{\textnormal{D}} +\newcommand{\rE}{\textnormal{E}} +\newcommand{\rF}{\textnormal{F}} +\newcommand{\rG}{\textnormal{G}} +\newcommand{\rH}{\textnormal{H}} +\newcommand{\rI}{\textnormal{I}} +\newcommand{\rJ}{\textnormal{J}} +\newcommand{\rK}{\textnormal{K}} +\newcommand{\rL}{\textnormal{L}} +\newcommand{\rM}{\textnormal{M}} +\newcommand{\rN}{\textnormal{N}} +\newcommand{\rO}{\textnormal{O}} +\newcommand{\rP}{\textnormal{P}} +\newcommand{\rQ}{\textnormal{Q}} +\newcommand{\rR}{\textnormal{R}} +\newcommand{\rS}{\textnormal{S}} +\newcommand{\rT}{\textnormal{T}} +\newcommand{\rU}{\textnormal{U}} +\newcommand{\rV}{\textnormal{V}} +\newcommand{\rW}{\textnormal{W}} +\newcommand{\rX}{\textnormal{X}} +\newcommand{\rY}{\textnormal{Y}} +\newcommand{\rZ}{\textnormal{Z}} + +% Random vectors +\newcommand{\rvalpha}{\mathbf{\alpha}} +\newcommand{\rvbeta}{\mathbf{\beta}} +\newcommand{\rvgamma}{\mathbf{\gamma}} +\newcommand{\rvdelta}{\mathbf{\delta}} +\newcommand{\rvepsilon}{\mathbf{\epsilon}} +\newcommand{\rveps}{\mathbf{\varepsilon}} +\newcommand{\rvzeta}{\mathbf{\zeta}} +\newcommand{\rveta}{\mathbf{\eta}} +\newcommand{\rvtheta}{\mathbf{\theta}} +\newcommand{\rvvartheta}{\mathbf{\vartheta}} +\newcommand{\rviota}{\mathbf{\iota}} +\newcommand{\rvkappa}{\mathbf{\kappa}} +\newcommand{\rvlambda}{\mathbf{\lambda}} +\newcommand{\rvmu}{\mathbf{\mu}} +\newcommand{\rvnu}{\mathbf{\nu}} +\newcommand{\rvxi}{\mathbf{\xi}} +\newcommand{\rvpi}{\mathbf{\pi}} +\newcommand{\rvrho}{\mathbf{\rho}} +\newcommand{\rvsigma}{\mathbf{\sigma}} +\newcommand{\rvtau}{\mathbf{\tau}} +\newcommand{\rvupsilon}{\mathbf{\upsilon}} +\newcommand{\rvphi}{\mathbf{\phi}} +\newcommand{\rvvarphi}{\mathbf{\varphi}} +\newcommand{\rvchi}{\mathbf{\chi}} +\newcommand{\rvpsi}{\mathbf{\psi}} +\newcommand{\rvomega}{\mathbf{\omega}} +\newcommand{\rva}{\mathbf{a}} +\newcommand{\rvb}{\mathbf{b}} +\newcommand{\rvc}{\mathbf{c}} +\newcommand{\rvd}{\mathbf{d}} +\newcommand{\rve}{\mathbf{e}} +\newcommand{\rvf}{\mathbf{f}} +\newcommand{\rvg}{\mathbf{g}} +\newcommand{\rvh}{\mathbf{h}} +\newcommand{\rvi}{\mathbf{i}} +\newcommand{\rvj}{\mathbf{j}} +\newcommand{\rvk}{\mathbf{k}} +\newcommand{\rvl}{\mathbf{l}} +\newcommand{\rvm}{\mathbf{m}} +\newcommand{\rvo}{\mathbf{o}} +\newcommand{\rvp}{\mathbf{p}} +\newcommand{\rvq}{\mathbf{q}} +\newcommand{\rvr}{\mathbf{r}} +\newcommand{\rvs}{\mathbf{s}} +\newcommand{\rvt}{\mathbf{t}} +\newcommand{\rvu}{\mathbf{u}} +\newcommand{\rvv}{\mathbf{v}} +\newcommand{\rvw}{\mathbf{w}} +\newcommand{\rvx}{\mathbf{x}} +\newcommand{\rvy}{\mathbf{y}} +\newcommand{\rvz}{\mathbf{z}} + +% Random matrices +\newcommand{\rmGamma}{\mathbf{\Gamma}} +\newcommand{\rmDelta}{\mathbf{\Delta}} +\newcommand{\rmTheta}{\mathbf{\Theta}} +\newcommand{\rmLambda}{\mathbf{\Lambda}} +\newcommand{\rmXi}{\mathbf{\Xi}} +\newcommand{\rmPi}{\mathbf{\Pi}} +\newcommand{\rmSigma}{\mathbf{\Sigma}} +\newcommand{\rmUpsilon}{\mathbf{\Upsilon}} +\newcommand{\rmPhi}{\mathbf{\Phi}} +\newcommand{\rmPsi}{\mathbf{\Psi}} +\newcommand{\rmOmega}{\mathbf{\Omega}} +\newcommand{\rmA}{\mathbf{A}} +\newcommand{\rmB}{\mathbf{B}} +\newcommand{\rmC}{\mathbf{C}} +\newcommand{\rmD}{\mathbf{D}} +\newcommand{\rmE}{\mathbf{E}} +\newcommand{\rmF}{\mathbf{F}} +\newcommand{\rmG}{\mathbf{G}} +\newcommand{\rmH}{\mathbf{H}} +\newcommand{\rmI}{\mathbf{I}} +\newcommand{\rmJ}{\mathbf{J}} +\newcommand{\rmK}{\mathbf{K}} +\newcommand{\rmL}{\mathbf{L}} +\newcommand{\rmM}{\mathbf{M}} +\newcommand{\rmN}{\mathbf{N}} +\newcommand{\rmO}{\mathbf{O}} +\newcommand{\rmP}{\mathbf{P}} +\newcommand{\rmQ}{\mathbf{Q}} +\newcommand{\rmR}{\mathbf{R}} +\newcommand{\rmS}{\mathbf{S}} +\newcommand{\rmT}{\mathbf{T}} +\newcommand{\rmU}{\mathbf{U}} +\newcommand{\rmV}{\mathbf{V}} +\newcommand{\rmW}{\mathbf{W}} +\newcommand{\rmX}{\mathbf{X}} +\newcommand{\rmY}{\mathbf{Y}} +\newcommand{\rmZ}{\mathbf{Z}} + +% Vectors +\newcommand{\vzero}{\bm{0}} +\newcommand{\vone}{\bm{1}} +\newcommand{\valpha}{\bm{\alpha}} +\newcommand{\vbeta}{\bm{\beta}} +\newcommand{\vgamma}{\bm{\gamma}} +\newcommand{\vdelta}{\bm{\delta}} +\newcommand{\vepsilon}{\bm{\epsilon}} +\newcommand{\veps}{\bm{\varepsilon}} +\newcommand{\vzeta}{\bm{\zeta}} +\newcommand{\veta}{\bm{\eta}} +\newcommand{\vtheta}{\bm{\theta}} +\newcommand{\vvartheta}{\bm{\vartheta}} +\newcommand{\viota}{\bm{\iota}} +\newcommand{\vkappa}{\bm{\kappa}} +\newcommand{\vlambda}{\bm{\lambda}} +\newcommand{\vmu}{\bm{\mu}} +\newcommand{\vnu}{\bm{\nu}} +\newcommand{\vxi}{\bm{\xi}} +\newcommand{\vpi}{\bm{\pi}} +\newcommand{\vrho}{\bm{\rho}} +\newcommand{\vsigma}{\bm{\sigma}} +\newcommand{\vtau}{\bm{\tau}} +\newcommand{\vupsilon}{\bm{\upsilon}} +\newcommand{\vphi}{\bm{\phi}} +\newcommand{\vvarphi}{\bm{\varphi}} +\newcommand{\vchi}{\bm{\chi}} +\newcommand{\vpsi}{\bm{\psi}} +\newcommand{\vomega}{\bm{\omega}} +\newcommand{\vGamma}{\bm{\Gamma}} +\newcommand{\vDelta}{\bm{\Delta}} +\newcommand{\vTheta}{\bm{\Theta}} +\newcommand{\vLambda}{\bm{\Lambda}} +\newcommand{\vXi}{\bm{\Xi}} +\newcommand{\vPi}{\bm{\Pi}} +\newcommand{\vSigma}{\bm{\Sigma}} +\newcommand{\vUpsilon}{\bm{\Upsilon}} +\newcommand{\vPhi}{\bm{\Phi}} +\newcommand{\vPsi}{\bm{\Psi}} +\newcommand{\vOmega}{\bm{\Omega}} +\newcommand{\va}{\bm{a}} +\newcommand{\vb}{\bm{b}} +\newcommand{\vc}{\bm{c}} +\newcommand{\vd}{\bm{d}} +\newcommand{\ve}{\bm{e}} +\newcommand{\vf}{\bm{f}} +\newcommand{\vg}{\bm{g}} +\newcommand{\vh}{\bm{h}} +\newcommand{\vi}{\bm{i}} +\newcommand{\vj}{\bm{j}} +\newcommand{\vk}{\bm{k}} +\newcommand{\vl}{\bm{l}} +\newcommand{\vm}{\bm{m}} +\newcommand{\vn}{\bm{n}} +\newcommand{\vo}{\bm{o}} +\newcommand{\vp}{\bm{p}} +\newcommand{\vq}{\bm{q}} +\newcommand{\vr}{\bm{r}} +\newcommand{\vs}{\bm{s}} +\newcommand{\vt}{\bm{t}} +\newcommand{\vu}{\bm{u}} +\newcommand{\vv}{\bm{v}} +\newcommand{\vw}{\bm{w}} +\newcommand{\vx}{\bm{x}} +\newcommand{\vy}{\bm{y}} +\newcommand{\vz}{\bm{z}} +\newcommand{\vA}{\bm{A}} +\newcommand{\vB}{\bm{B}} +\newcommand{\vC}{\bm{C}} +\newcommand{\vD}{\bm{D}} +\newcommand{\vE}{\bm{E}} +\newcommand{\vF}{\bm{F}} +\newcommand{\vG}{\bm{G}} +\newcommand{\vH}{\bm{H}} +\newcommand{\vI}{\bm{I}} +\newcommand{\vJ}{\bm{J}} +\newcommand{\vK}{\bm{K}} +\newcommand{\vL}{\bm{L}} +\newcommand{\vM}{\bm{M}} +\newcommand{\vN}{\bm{N}} +\newcommand{\vO}{\bm{O}} +\newcommand{\vP}{\bm{P}} +\newcommand{\vQ}{\bm{Q}} +\newcommand{\vR}{\bm{R}} +\newcommand{\vS}{\bm{S}} +\newcommand{\vT}{\bm{T}} +\newcommand{\vU}{\bm{U}} +\newcommand{\vV}{\bm{V}} +\newcommand{\vW}{\bm{W}} +\newcommand{\vX}{\bm{X}} +\newcommand{\vY}{\bm{Y}} +\newcommand{\vZ}{\bm{Z}} + +% Matrices +\newcommand{\mzero}{\bm{0}} +\newcommand{\malpha}{\bm{\alpha}} +\newcommand{\mbeta}{\bm{\beta}} +\newcommand{\mgamma}{\bm{\gamma}} +\newcommand{\mdelta}{\bm{\delta}} +\newcommand{\mepsilon}{\bm{\epsilon}} +\newcommand{\meps}{\bm{\varepsilon}} +\newcommand{\mzeta}{\bm{\zeta}} +\newcommand{\meta}{\bm{\eta}} +\newcommand{\mtheta}{\bm{\theta}} +\newcommand{\mvartheta}{\bm{\vartheta}} +\newcommand{\miota}{\bm{\iota}} +\newcommand{\mkappa}{\bm{\kappa}} +\newcommand{\mlambda}{\bm{\lambda}} +\newcommand{\mmu}{\bm{\mu}} +\newcommand{\mnu}{\bm{\nu}} +\newcommand{\mxi}{\bm{\xi}} +\newcommand{\mpi}{\bm{\pi}} +\newcommand{\mrho}{\bm{\rho}} +\newcommand{\msigma}{\bm{\sigma}} +\newcommand{\mtau}{\bm{\tau}} +\newcommand{\mupsilon}{\bm{\upsilon}} +\newcommand{\mphi}{\bm{\phi}} +\newcommand{\mvarphi}{\bm{\varphi}} +\newcommand{\mchi}{\bm{\chi}} +\newcommand{\mpsi}{\bm{\psi}} +\newcommand{\momega}{\bm{\omega}} +\newcommand{\mGamma}{\bm{\Gamma}} +\newcommand{\mDelta}{\bm{\Delta}} +\newcommand{\mTheta}{\bm{\Theta}} +\newcommand{\mLambda}{\bm{\Lambda}} +\newcommand{\mXi}{\bm{\Xi}} +\newcommand{\mPi}{\bm{\Pi}} +\newcommand{\mSigma}{\bm{\Sigma}} +\newcommand{\mUpsilon}{\bm{\Upsilon}} +\newcommand{\mPhi}{\bm{\Phi}} +\newcommand{\mPsi}{\bm{\Psi}} +\newcommand{\mOmega}{\bm{\Omega}} +\newcommand{\mA}{\bm{A}} +\newcommand{\mB}{\bm{B}} +\newcommand{\mC}{\bm{C}} +\newcommand{\mD}{\bm{D}} +\newcommand{\mE}{\bm{E}} +\newcommand{\mF}{\bm{F}} +\newcommand{\mG}{\bm{G}} +\newcommand{\mH}{\bm{H}} +\newcommand{\mI}{\bm{I}} +\newcommand{\mJ}{\bm{J}} +\newcommand{\mK}{\bm{K}} +\newcommand{\mL}{\bm{L}} +\newcommand{\mM}{\bm{M}} +\newcommand{\mN}{\bm{N}} +\newcommand{\mO}{\bm{O}} +\newcommand{\mP}{\bm{P}} +\newcommand{\mQ}{\bm{Q}} +\newcommand{\mR}{\bm{R}} +\newcommand{\mS}{\bm{S}} +\newcommand{\mT}{\bm{T}} +\newcommand{\mU}{\bm{U}} +\newcommand{\mV}{\bm{V}} +\newcommand{\mW}{\bm{W}} +\newcommand{\mX}{\bm{X}} +\newcommand{\mY}{\bm{Y}} +\newcommand{\mZ}{\bm{Z}} + +% Tensor +\DeclareMathAlphabet{\mathsfit}{\encodingdefault}{\sfdefault}{m}{sl} +\SetMathAlphabet{\mathsfit}{bold}{\encodingdefault}{\sfdefault}{bx}{n} +\newcommand{\tens}[1]{\bm{\mathsfit{#1}}} +\newcommand{\talpha}{\tens{\alpha}} +\newcommand{\tbeta}{\tens{\beta}} +\newcommand{\tgamma}{\tens{\gamma}} +\newcommand{\tdelta}{\tens{\delta}} +\newcommand{\tepsilon}{\tens{\epsilon}} +\newcommand{\teps}{\tens{\varepsilon}} +\newcommand{\tzeta}{\tens{\zeta}} +\newcommand{\teta}{\tens{\eta}} +\newcommand{\ttheta}{\tens{\theta}} +\newcommand{\tvartheta}{\tens{\vartheta}} +\newcommand{\tiota}{\tens{\iota}} +\newcommand{\tkappa}{\tens{\kappa}} +\newcommand{\tlambda}{\tens{\lambda}} +\newcommand{\tmu}{\tens{\mu}} +\newcommand{\tnu}{\tens{\nu}} +\newcommand{\txi}{\tens{\xi}} +\newcommand{\tpi}{\tens{\pi}} +\newcommand{\trho}{\tens{\rho}} +\newcommand{\tsigma}{\tens{\sigma}} +\newcommand{\ttau}{\tens{\tau}} +\newcommand{\tupsilon}{\tens{\upsilon}} +\newcommand{\tphi}{\tens{\phi}} +\newcommand{\tvarphi}{\tens{\varphi}} +\newcommand{\tchi}{\tens{\chi}} +\newcommand{\tpsi}{\tens{\psi}} +\newcommand{\tomega}{\tens{\omega}} +\newcommand{\tGamma}{\tens{\Gamma}} +\newcommand{\tDelta}{\tens{\Delta}} +\newcommand{\tTheta}{\tens{\Theta}} +\newcommand{\tLambda}{\tens{\Lambda}} +\newcommand{\tXi}{\tens{\Xi}} +\newcommand{\tPi}{\tens{\Pi}} +\newcommand{\tSigma}{\tens{\Sigma}} +\newcommand{\tUpsilon}{\tens{\Upsilon}} +\newcommand{\tPhi}{\tens{\Phi}} +\newcommand{\tPsi}{\tens{\Psi}} +\newcommand{\tOmega}{\tens{\Omega}} +\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}} + +% entries of a tensor +% Same font as tensor, without \bm wrapper +\newcommand{\etens}[1]{\mathsfit{#1}} +\newcommand{\etalpha}{\etens{\alpha}} +\newcommand{\etbeta}{\etens{\beta}} +\newcommand{\etgamma}{\etens{\gamma}} +\newcommand{\etdelta}{\etens{\delta}} +\newcommand{\etepsilon}{\etens{\epsilon}} +\newcommand{\eteps}{\etens{\varepsilon}} +\newcommand{\etzeta}{\etens{\zeta}} +\newcommand{\eteta}{\etens{\eta}} +\newcommand{\ettheta}{\etens{\theta}} +\newcommand{\etvartheta}{\etens{\vartheta}} +\newcommand{\etiota}{\etens{\iota}} +\newcommand{\etkappa}{\etens{\kappa}} +\newcommand{\etlambda}{\etens{\lambda}} +\newcommand{\etmu}{\etens{\mu}} +\newcommand{\etnu}{\etens{\nu}} +\newcommand{\etxi}{\etens{\xi}} +\newcommand{\etpi}{\etens{\pi}} +\newcommand{\etrho}{\etens{\rho}} +\newcommand{\etsigma}{\etens{\sigma}} +\newcommand{\ettau}{\etens{\tau}} +\newcommand{\etupsilon}{\etens{\upsilon}} +\newcommand{\etphi}{\etens{\phi}} +\newcommand{\etvarphi}{\etens{\varphi}} +\newcommand{\etchi}{\etens{\chi}} +\newcommand{\etpsi}{\etens{\psi}} +\newcommand{\etomega}{\etens{\omega}} +\newcommand{\etGamma}{\etens{\Gamma}} +\newcommand{\etDelta}{\etens{\Delta}} +\newcommand{\etTheta}{\etens{\Theta}} +\newcommand{\etLambda}{\etens{\Lambda}} +\newcommand{\etXi}{\etens{\Xi}} +\newcommand{\etPi}{\etens{\Pi}} +\newcommand{\etSigma}{\etens{\Sigma}} +\newcommand{\etUpsilon}{\etens{\Upsilon}} +\newcommand{\etPhi}{\etens{\Phi}} +\newcommand{\etPsi}{\etens{\Psi}} +\newcommand{\etOmega}{\etens{\Omega}} +\newcommand{\etA}{\etens{A}} +\newcommand{\etB}{\etens{B}} +\newcommand{\etC}{\etens{C}} +\newcommand{\etD}{\etens{D}} +\newcommand{\etE}{\etens{E}} +\newcommand{\etF}{\etens{F}} +\newcommand{\etG}{\etens{G}} +\newcommand{\etH}{\etens{H}} +\newcommand{\etI}{\etens{I}} +\newcommand{\etJ}{\etens{J}} +\newcommand{\etK}{\etens{K}} +\newcommand{\etL}{\etens{L}} +\newcommand{\etM}{\etens{M}} +\newcommand{\etN}{\etens{N}} +\newcommand{\etO}{\etens{O}} +\newcommand{\etP}{\etens{P}} +\newcommand{\etQ}{\etens{Q}} +\newcommand{\etR}{\etens{R}} +\newcommand{\etS}{\etens{S}} +\newcommand{\etT}{\etens{T}} +\newcommand{\etU}{\etens{U}} +\newcommand{\etV}{\etens{V}} +\newcommand{\etW}{\etens{W}} +\newcommand{\etX}{\etens{X}} +\newcommand{\etY}{\etens{Y}} +\newcommand{\etZ}{\etens{Z}} + +% Sets +\newcommand{\sone}{\mathbbm{1}} +\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}} +% Don't use a set called P, because this would be the same as our symbol for probability. +\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}} + +% Function class, spaces, operator, etc. +\newcommand{\fA}{\mathcal{A}} +\newcommand{\fB}{\mathcal{B}} +\newcommand{\fC}{\mathcal{C}} +\newcommand{\fD}{\mathcal{D}} +\newcommand{\fE}{\mathcal{E}} +\newcommand{\fF}{\mathcal{F}} +\newcommand{\fG}{\mathcal{G}} +\newcommand{\fH}{\mathcal{H}} +\newcommand{\fI}{\mathcal{I}} +\newcommand{\fJ}{\mathcal{J}} +\newcommand{\fK}{\mathcal{K}} +\newcommand{\fL}{\mathcal{L}} +\newcommand{\fM}{\mathcal{M}} +\newcommand{\fN}{\mathcal{N}} +\newcommand{\fO}{\mathcal{O}} +\newcommand{\fP}{\mathcal{P}} +\newcommand{\fQ}{\mathcal{Q}} +\newcommand{\fR}{\mathcal{R}} +\newcommand{\fS}{\mathcal{S}} +\newcommand{\fT}{\mathcal{T}} +\newcommand{\fU}{\mathcal{U}} +\newcommand{\fV}{\mathcal{V}} +\newcommand{\fW}{\mathcal{W}} +\newcommand{\fX}{\mathcal{X}} +\newcommand{\fY}{\mathcal{Y}} +\newcommand{\fZ}{\mathcal{Z}} + +%neural networks +\newcommand{\LS}{L_S} +\newcommand{\LD}{L_\fD} +\newcommand{\RS}{R_S} +\newcommand{\Rn}{R_n} +\newcommand{\RD}{R_\fD} +\newcommand{\diam}{\mathrm{diam}} +\newcommand{\diag}{\mathrm{diag}} +\newcommand{\dist}{\mathrm{dist}} +\newcommand{\ERM}{\mathrm{ERM}} +\newcommand{\Lip}{\mathrm{Lip}} +\newcommand{\ReLU}{\mathrm{ReLU}} +\newcommand{\Rep}{\mathrm{Rep}} +\newcommand{\Var}{\mathrm{Var}} +\newcommand{\Rad}{\mathrm{Rad}} +\newcommand{\DKL}{\mathrm{D}_{KL}} +\newcommand{\conv}{\mathrm{conv}} +\newcommand{\csch}{\mathrm{csch}} +\newcommand{\sech}{\mathrm{sech}} +\newcommand{\Sigmoid}{\mathrm{Sigmoid}} + + + + +%define theorems +\newtheorem{thm}{Theorem} +\newtheorem{cor}{Corollary} +\newtheorem{defi}{Definition} +\newtheorem{lem}{Lemma} +\newtheorem{prop}{Proposition} +\newtheorem{rmk}{Remark} +\newtheorem{assump}{Assumption} +\newtheorem{exam}{Example} +\newtheorem{conj}{Conjecture} +\newtheorem{algo}{Algorithm} + +% +\renewcommand{\abstractname}{Summary}
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