Test
https://zhuanlan.zhihu.com/p/24709748 矩阵求导术
$$x = (d-As)^TN^{-1}(d-As)$$
$$\delta M^{-1} = -M^{-1}(\delta M)M^{-1}$$
$$dx (scalar)=(-Ads)^TN^{-1}(d-As) + (d-As)^TN^{-1}(-Ads) =-2(d-As)^TN^{-1}(Ads)$$
$$dx = (\frac{\partial x}{\partial s} )^T ds$$
$$\frac{\partial x}{\partial s} = -2 A^TN^{-1}(d-As) = 0$$
$$s = (A^TN^{-1}A)^{-1}A^TN^{-1}d$$
\begin{array}{|r|l|l|}
\hline
No. &Method &Specification\\
Paper&\text{Map-making methods} &Tegmark 1997 \\
\hline
1&Generalized COBE &W=[A^tMA]^{-1}A^tM\\
2&Bin averaging &W=[A^tA]^{-1}A^t\\
3&COBE &W=[A^tN^{-1}A]^{-1}A^tN^{-1}\\
4&Wiener 1 &W=SA^t[ASA^t+N]^{-1}\\
5&Wiener 2 &W=[S^{-1}+A^tN^{-1}A]^{-1}A^tN^{-1}\\
6&Saskatoon &W=[\eta S^{-1}+A^tN^{-1}A]^{-1}A^tN^{-1}\\
7&TE96 &W={\bf{\Lambda}} SA^t[ASA^t+N]^{-1},\>\>(WA)_{ii}=1\\
8&TE97 &W={\bf{\Lambda}}[\eta S^{-1}+A^tN^{-1}A]^{-1}A^tN^{-1},\>\>(WA)_{ii}=1\\
9&\text{Maximum probability} &\text{Nonlinear method if non-Gaussian}\\
10&\text{Maximum entropy} &\text{Nonlinear method}\\
\hline
\label{MethodsTable}
\end{array}