emacs.d

math_macros.sty (11546B)

 \newcommand{\E}{\mathrm{e}}
 \newcommand{\I}{\mathrm{i}}
 % Scientific numbers
 \newcommand{\Em}{\text{e-}}
 \newcommand{\Ep}{\text{e+}}
 
 \newcommand{\Alpha}{A}
 \newcommand{\Beta}{B}
 \newcommand{\Epsilon}{E}
 
 \newcommand{\abs}[1]{\lvert#1\rvert}
 \newcommand{\ceil}[1]{\lceil#1\rceil}
 \newcommand{\floor}[1]{\lfloor#1\rfloor}
 \newcommand{\norm}[1]{\lVert#1\rVert}
 \newcommand{\mean}[1]{\bar{#1}}
 \newcommand{\conj}[1]{\overline{#1}}
 
 % Shorthands for mean.
 \newcommand{\ba}{\mean{a}}
 \newcommand{\bb}{\mean{b}}
 \newcommand{\bc}{\mean{c}}
 \newcommand{\bd}{\mean{d}}
 \newcommand{\be}{\mean{e}}
 % \newcommand{\bf}{\mean{f}}
 \newcommand{\bg}{\mean{g}}
 \newcommand{\bh}{\mean{h}}
 \newcommand{\bi}{\mean{i}}
 \newcommand{\bj}{\mean{j}}
 \newcommand{\bk}{\mean{k}}
 \newcommand{\bl}{\mean{l}}
 % \newcommand{\bm}{\mean{m}}
 \newcommand{\bn}{\mean{n}}
 \newcommand{\bo}{\mean{o}}
 \newcommand{\bp}{\mean{p}}
 \newcommand{\bq}{\mean{q}}
 \newcommand{\br}{\mean{r}}
 \newcommand{\bs}{\mean{s}}
 \newcommand{\bt}{\mean{t}}
 \newcommand{\bu}{\mean{u}}
 \newcommand{\bv}{\mean{v}}
 \newcommand{\bw}{\mean{w}}
 \newcommand{\bx}{\mean{x}}
 \newcommand{\by}{\mean{y}}
 \newcommand{\bz}{\mean{z}}
 
 \newcommand{\bA}{\mean{A}}
 \newcommand{\bB}{\mean{B}}
 \newcommand{\bC}{\mean{C}}
 \newcommand{\bD}{\mean{D}}
 \newcommand{\bE}{\mean{E}}
 \newcommand{\bF}{\mean{F}}
 \newcommand{\bG}{\mean{G}}
 \newcommand{\bH}{\mean{H}}
 \newcommand{\bI}{\mean{I}}
 \newcommand{\bJ}{\mean{J}}
 \newcommand{\bK}{\mean{K}}
 \newcommand{\bL}{\mean{L}}
 \newcommand{\bM}{\mean{M}}
 \newcommand{\bN}{\mean{N}}
 \newcommand{\bO}{\mean{O}}
 \newcommand{\bP}{\mean{P}}
 \newcommand{\bQ}{\mean{Q}}
 \newcommand{\bR}{\mean{R}}
 \newcommand{\bS}{\mean{S}}
 \newcommand{\bT}{\mean{T}}
 \newcommand{\bU}{\mean{U}}
 \newcommand{\bV}{\mean{V}}
 \newcommand{\bW}{\mean{W}}
 \newcommand{\bX}{\mean{X}}
 \newcommand{\bY}{\mean{Y}}
 \newcommand{\bZ}{\mean{Z}}
 
 \newcommand{\dd}{\mathop{}\,\mathrm{d}}
 \newcommand{\der}[2][]{\frac{\mathrm{d}#1}{\mathrm{d}#2}}
 \newcommand{\pder}[2][]{\frac{\partial#1}{\partial#2}}
 
 \newcommand{\geqst}{\geq_{\text{st}}}
 \newcommand{\leqst}{\leq_{\text{st}}}
 
 \newcommand{\pto}{\overset{p}\to}
 \newcommand{\lpto}{\overset{p}\longrightarrow}
 \newcommand{\dto}{\overset{d}\to}
 \newcommand{\ldto}{\overset{d}\longrightarrow}
 \newcommand{\asto}{\overset{\text{a.s.}}\longrightarrow}
 
 \newcommand{\sign}{\operatorname{sign}}
 \newcommand{\im}{\operatorname{Im}}
 \newcommand{\re}{\operatorname{Re}}
 \newcommand{\rank}{\operatorname{rank}}
 \newcommand{\trace}{\operatorname{trace}}
 \newcommand{\diag}{\operatorname{diag}}
 \newcommand{\col}{\operatorname{col}}
 \newcommand{\row}{\operatorname{row}}
 \newcommand{\arcsinh}{\operatorname{arcsinh}}
 \newcommand{\arccosh}{\operatorname{arccosh}}
 \newcommand{\arctanh}{\operatorname{arctanh}}
 \newcommand{\argmax}{\mathop{\arg\max}}
 \newcommand{\argmin}{\mathop{\arg\min}}
 
 \newcommand{\As}{\text{ as }}
 % \newcommand{\And}{\text{ and }}
 \newcommand{\To}{\text{ to }}
 \newcommand{\Or}{\text{ or }}
 \newcommand{\If}{\text{ if }}
 \newcommand{\Otherwise}{\text{ otherwise}}
 \newcommand{\ForAll}{\text{ for all }}
 \newcommand{\For}{\text{ for }}
 \newcommand{\Yes}{\text{Yes}}
 \newcommand{\No}{\text{No}}
 \newcommand{\Num}{\text{\# }}
 
 \newcommand{\vctr}[1]{\boldsymbol{#1}}
 \newcommand{\mtrx}[1]{\bm{#1}}
 
 % Special
 \newcommand{\vzero}{\vctr{0}}
 \newcommand{\vone}{\vctr{1}}
 % Greek
 \newcommand{\valpha}{\vctr{\alpha}}
 \newcommand{\vbeta}{\vctr{\beta}}
 \newcommand{\vgamma}{\vctr{\gamma}}
 \newcommand{\vdelta}{\vctr{\delta}}
 \newcommand{\vepsilon}{\vctr{\epsilon}}
 \newcommand{\vvarepsilon}{\vctr{\varepsilon}}
 \newcommand{\vzeta}{\vctr{\zeta}}
 \newcommand{\veta}{\vctr{\eta}}
 \newcommand{\vtheta}{\vctr{\theta}}
 \newcommand{\vvartheta}{\vctr{\vartheta}}
 \newcommand{\vkappa}{\vctr{\kappa}}
 \newcommand{\vlambda}{\vctr{\lambda}}
 \newcommand{\vmu}{\vctr{\mu}}
 \newcommand{\vnu}{\vctr{\nu}}
 \newcommand{\vxi}{\vctr{\xi}}
 \newcommand{\vpi}{\vctr{\pi}}
 \newcommand{\vvarpi}{\vctr{\varpi}}
 \newcommand{\vrho}{\vctr{\rho}}
 \newcommand{\vvarrho}{\vctr{\varrho}}
 \newcommand{\vsigma}{\vctr{\sigma}}
 \newcommand{\vvarsigma}{\vctr{\varsigma}}
 \newcommand{\vtau}{\vctr{\tau}}
 \newcommand{\vupsilon}{\vctr{\upsilon}}
 \newcommand{\vphi}{\vctr{\phi}}
 \newcommand{\vvarphi}{\vctr{\varphi}}
 \newcommand{\vchi}{\vctr{\chi}}
 \newcommand{\vpsi}{\vctr{\psi}}
 \newcommand{\vomega}{\vctr{\omega}}
 % Latin
 \newcommand{\va}{\vctr{a}}
 \newcommand{\vb}{\vctr{b}}
 \newcommand{\vc}{\vctr{c}}
 \newcommand{\vd}{\vctr{d}}
 \newcommand{\ve}{\vctr{e}}
 \newcommand{\vf}{\vctr{f}}
 \newcommand{\vg}{\vctr{g}}
 \newcommand{\vh}{\vctr{h}}
 \newcommand{\vi}{\vctr{i}}
 \newcommand{\vj}{\vctr{j}}
 \newcommand{\vk}{\vctr{k}}
 \newcommand{\vl}{\vctr{l}}
 \newcommand{\vm}{\vctr{m}}
 \newcommand{\vn}{\vctr{n}}
 \newcommand{\vo}{\vctr{o}}
 \newcommand{\vp}{\vctr{p}}
 \newcommand{\vq}{\vctr{q}}
 \newcommand{\vr}{\vctr{r}}
 \newcommand{\vs}{\vctr{s}}
 \newcommand{\vt}{\vctr{t}}
 \newcommand{\vu}{\vctr{u}}
 \newcommand{\vv}{\vctr{v}}
 \newcommand{\vw}{\vctr{w}}
 \newcommand{\vx}{\vctr{x}}
 \newcommand{\vy}{\vctr{y}}
 \newcommand{\vz}{\vctr{z}}
 
 % Special
 \newcommand{\mZero}{\mtrx{0}}
 \newcommand{\mOne}{\mtrx{1}}
 % Greek
 \newcommand{\mGamma}{\mtrx{\Gamma}}
 \newcommand{\mDelta}{\mtrx{\Delta}}
 \newcommand{\mTheta}{\mtrx{\Theta}}
 \newcommand{\mLambda}{\mtrx{\Lambda}}
 \newcommand{\mXi}{\mtrx{\Xi}}
 \newcommand{\mPi}{\mtrx{\Pi}}
 \newcommand{\mSigma}{\mtrx{\Sigma}}
 \newcommand{\mUpsilon}{\mtrx{\Upsilon}}
 \newcommand{\mPhi}{\mtrx{\Phi}}
 \newcommand{\mPsi}{\mtrx{\Psi}}
 \newcommand{\mOmega}{\mtrx{\Omega}}
 % Latin
 \newcommand{\mA}{\mtrx{A}}
 \newcommand{\mB}{\mtrx{B}}
 \newcommand{\mC}{\mtrx{C}}
 \newcommand{\mD}{\mtrx{D}}
 \newcommand{\mE}{\mtrx{E}}
 \newcommand{\mF}{\mtrx{F}}
 \newcommand{\mG}{\mtrx{G}}
 \newcommand{\mH}{\mtrx{H}}
 \newcommand{\mI}{\mtrx{I}}
 \newcommand{\mJ}{\mtrx{J}}
 \newcommand{\mK}{\mtrx{K}}
 \newcommand{\mL}{\mtrx{L}}
 \newcommand{\mM}{\mtrx{M}}
 \newcommand{\mN}{\mtrx{N}}
 \newcommand{\mO}{\mtrx{O}}
 \newcommand{\mP}{\mtrx{P}}
 \newcommand{\mQ}{\mtrx{Q}}
 \newcommand{\mR}{\mtrx{R}}
 \newcommand{\mS}{\mtrx{S}}
 \newcommand{\mT}{\mtrx{T}}
 \newcommand{\mU}{\mtrx{U}}
 \newcommand{\mV}{\mtrx{V}}
 \newcommand{\mW}{\mtrx{W}}
 \newcommand{\mX}{\mtrx{X}}
 \newcommand{\mY}{\mtrx{Y}}
 \newcommand{\mZ}{\mtrx{Z}}
 
 \newcommand{\tr}{^{\mathsf{T}}}
 \newcommand{\ip}[1]{\langle#1\rangle}
 
 \newcommand{\set}[1]{\mathbb{#1}}
 \newcommand{\field}[1]{\mathcal{#1}}
 \renewcommand{\emptyset}{\varnothing}
 
 % Latin
 \newcommand{\sA}{\set{A}}
 \newcommand{\sB}{\set{B}}
 \newcommand{\sC}{\set{C}}
 \newcommand{\sD}{\set{D}}
 \newcommand{\sE}{\set{E}}
 \newcommand{\sF}{\set{F}}
 \newcommand{\sG}{\set{G}}
 \newcommand{\sH}{\set{H}}
 \newcommand{\sI}{\set{I}}
 \newcommand{\sJ}{\set{J}}
 \newcommand{\sK}{\set{K}}
 \newcommand{\sL}{\set{L}}
 \newcommand{\sM}{\set{M}}
 \newcommand{\sN}{\set{N}}
 \newcommand{\sO}{\set{O}}
 \newcommand{\sP}{\set{P}}
 \newcommand{\sQ}{\set{Q}}
 \newcommand{\sR}{\set{R}}
 \newcommand{\sS}{\set{S}}
 \newcommand{\sT}{\set{T}}
 \newcommand{\sU}{\set{U}}
 \newcommand{\sV}{\set{V}}
 \newcommand{\sW}{\set{W}}
 \newcommand{\sX}{\set{X}}
 \newcommand{\sY}{\set{Y}}
 \newcommand{\sZ}{\set{Z}}
 
 % Latin
 \newcommand{\fA}{\field{A}}
 \newcommand{\fB}{\field{B}}
 \newcommand{\fC}{\field{C}}
 \newcommand{\fD}{\field{D}}
 \newcommand{\fE}{\field{E}}
 \newcommand{\fF}{\field{F}}
 \newcommand{\fG}{\field{G}}
 \newcommand{\fH}{\field{H}}
 \newcommand{\fI}{\field{I}}
 \newcommand{\fJ}{\field{J}}
 \newcommand{\fK}{\field{K}}
 \newcommand{\fL}{\field{L}}
 \newcommand{\fM}{\field{M}}
 \newcommand{\fN}{\field{N}}
 \newcommand{\fO}{\field{O}}
 \newcommand{\fP}{\field{P}}
 \newcommand{\fQ}{\field{Q}}
 \newcommand{\fR}{\field{R}}
 \newcommand{\fS}{\field{S}}
 \newcommand{\fT}{\field{T}}
 \newcommand{\fU}{\field{U}}
 \newcommand{\fV}{\field{V}}
 \newcommand{\fW}{\field{W}}
 \newcommand{\fX}{\field{X}}
 \newcommand{\fY}{\field{Y}}
 \newcommand{\fZ}{\field{Z}}
 
 \renewcommand{\subseteq}{\subset}
 
 \newcommand{\rInd}{\mathbf{1}}
 \newcommand{\rPoi}{\operatorname{Poisson}}
 \newcommand{\rBern}{\operatorname{Bern}}
 \newcommand{\rNorm}{\mathcal{N}}
 
 % Probability
 \newcommand{\pr}{\mathbb{P}}
 % Expectation
 \newcommand{\ev}{\mathbb{E}}
 % Variance
 \newcommand{\var}{\operatorname{Var}}
 % Covariance
 \newcommand{\cov}{\operatorname{Cov}}
 % Correlation
 \newcommand{\corr}{\operatorname{Cor}}
 % Skewness
 \newcommand{\skw}{\operatorname{Skw}}
 % Kurtosis
 \newcommand{\kur}{\operatorname{Kur}}
 
 % Random Vectors
 \newcommand{\randvctr}[1]{\mathbf{#1}}
 % Random Scalars
 \newcommand{\rind}{\bm{1}}
 \newcommand{\randvar}[1]{#1}
 
 \newcommand{\rX}{\randvar{X}}
 \newcommand{\rY}{\randvar{Y}}
 \newcommand{\rZ}{\randvar{Z}}
 \newcommand{\rvX}{\randvctr{X}}
 \newcommand{\rvY}{\randvctr{Y}}
 \newcommand{\rvZ}{\randvctr{Z}}
 
 \newcommand{\estm}[1]{\hat{#1}}
 
 % Special
 \newcommand{\hsigmasq}{\estm{\sigma^{2}}}
 % Greek
 \newcommand{\halpha}{\estm{\alpha}}
 \newcommand{\hbeta}{\estm{\beta}}
 \newcommand{\hgamma}{\estm{\gamma}}
 \newcommand{\hdelta}{\estm{\delta}}
 \newcommand{\hepsilon}{\estm{\epsilon}}
 \newcommand{\hvarepsilon}{\estm{\varepsilon}}
 \newcommand{\hzeta}{\estm{\zeta}}
 \newcommand{\heta}{\estm{\eta}}
 \newcommand{\htheta}{\estm{\theta}}
 \newcommand{\hvartheta}{\estm{\vartheta}}
 \newcommand{\hkappa}{\estm{\kappa}}
 \newcommand{\hlambda}{\estm{\lambda}}
 \newcommand{\hmu}{\estm{\mu}}
 \newcommand{\hnu}{\estm{\nu}}
 \newcommand{\hxi}{\estm{\xi}}
 \newcommand{\hpi}{\estm{\pi}}
 \newcommand{\hvarpi}{\estm{\varpi}}
 \newcommand{\hrho}{\estm{\rho}}
 \newcommand{\hvarrho}{\estm{\varrho}}
 \newcommand{\hsigma}{\estm{\sigma}}
 \newcommand{\hvarsigma}{\estm{\varsigma}}
 \newcommand{\htau}{\estm{\tau}}
 \newcommand{\hupsilon}{\estm{\upsilon}}
 \newcommand{\hphi}{\estm{\phi}}
 \newcommand{\hvarphi}{\estm{\varphi}}
 \newcommand{\hchi}{\estm{\chi}}
 \newcommand{\hpsi}{\estm{\psi}}
 \newcommand{\homega}{\estm{\omega}}
 
 \newcommand{\hGamma}{\estm{\Gamma}}
 \newcommand{\hDelta}{\estm{\Delta}}
 \newcommand{\hTheta}{\estm{\Theta}}
 \newcommand{\hLambda}{\estm{\Lambda}}
 \newcommand{\hXi}{\estm{\Xi}}
 \newcommand{\hPi}{\estm{\Pi}}
 \newcommand{\hSigma}{\estm{\Sigma}}
 \newcommand{\hUpsilon}{\estm{\Upsilon}}
 \newcommand{\hPhi}{\estm{\Phi}}
 \newcommand{\hPsi}{\estm{\Psi}}
 \newcommand{\hOmega}{\estm{\Omega}}
 
 % Latin
 \newcommand{\ha}{\estm{a}}
 \newcommand{\hb}{\estm{b}}
 \newcommand{\hc}{\estm{c}}
 \newcommand{\hd}{\estm{d}}
 \newcommand{\he}{\estm{e}}
 \newcommand{\hf}{\estm{f}}
 \newcommand{\hg}{\estm{g}}
 \newcommand{\hh}{\estm{h}}
 \newcommand{\hi}{\estm{i}}
 \newcommand{\hj}{\estm{j}}
 \newcommand{\hk}{\estm{k}}
 \newcommand{\hl}{\estm{l}}
 %\newcommand{\hm}{\estm{m}}
 \newcommand{\hn}{\estm{n}}
 \newcommand{\ho}{\estm{o}}
 \newcommand{\hp}{\estm{p}}
 \newcommand{\hq}{\estm{q}}
 \newcommand{\hr}{\estm{r}}
 \newcommand{\hs}{\estm{s}}
 %\newcommand{\ht}{\estm{t}}
 \newcommand{\hu}{\estm{u}}
 \newcommand{\hv}{\estm{v}}
 \newcommand{\hw}{\estm{w}}
 \newcommand{\hx}{\estm{x}}
 \newcommand{\hy}{\estm{y}}
 \newcommand{\hz}{\estm{z}}
 
 \newcommand{\hA}{\estm{A}}
 \newcommand{\hB}{\estm{B}}
 \newcommand{\hC}{\estm{C}}
 \newcommand{\hD}{\estm{D}}
 \newcommand{\hE}{\estm{E}}
 \newcommand{\hF}{\estm{F}}
 \newcommand{\hG}{\estm{G}}
 \newcommand{\hH}{\estm{H}}
 \newcommand{\hI}{\estm{I}}
 \newcommand{\hJ}{\estm{J}}
 \newcommand{\hK}{\estm{K}}
 \newcommand{\hL}{\estm{L}}
 \newcommand{\hM}{\estm{M}}
 \newcommand{\hN}{\estm{N}}
 \newcommand{\hO}{\estm{O}}
 \newcommand{\hP}{\estm{P}}
 \newcommand{\hQ}{\estm{Q}}
 \newcommand{\hR}{\estm{R}}
 \newcommand{\hS}{\estm{S}}
 \newcommand{\hT}{\estm{T}}
 \newcommand{\hU}{\estm{U}}
 \newcommand{\hV}{\estm{V}}
 \newcommand{\hW}{\estm{W}}
 \newcommand{\hX}{\estm{X}}
 \newcommand{\hY}{\estm{Y}}
 \newcommand{\hZ}{\estm{Z}}