root/doc/html/formula.repository @ 164

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Oprava dokumentace

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1\form#0:$A=\frac{df}{dx}|_{x0,u0}$
2\form#1:$A=\frac{d}{dx}f(x,u)|_{x0,u0}$
3\form#2:$A=\frac{d}{du}f(x,u)|_{x0,u0}$
4\form#3:$x \sim epdf(rv)$
5\form#4:\[ f(x|a,b) = \prod f(x_i|a_i,b_i) \]
6\form#5:\[M = L'DL\]
7\form#6:\[ x_t = A x_{t-1} + B u_t + Q^{1/2} e_t \]
8\form#7:\[ y_t = C x_{t-1} + C u_t + Q^{1/2} w_t. \]
9\form#8:\[ f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) \]
10\form#9:$x^{(i)}, i=1..n$
11\form#10:$x \sim epdf(rv|cond)$
12\form#11:$\alpha=k$
13\form#12:$\beta=k/\mu$
14\form#13:$\mu/\sqrt(k)$
15\form#14:$\mu$
16\form#15:$\alpha$
17\form#16:$\beta$
18\form#17:\[ \left[\begin{array}{cc} R^{0.5}\\ P_{t|t-1}^{0.5}C' & P_{t|t-1}^{0.5}CA'\\ & Q^{0.5}\end{array}\right]<\mathrm{orth.oper.}>=\left[\begin{array}{cc} R_{y}^{0.5} & KA'\\ & P_{t+1|t}^{0.5}\\ \\\end{array}\right]\]
19\form#18:\[ \mu = \mu_{t-1} ^{l} p^{1-l}\]
20\form#19:$A=Ch' Ch$
21\form#20:$Ch$
22\form#21:$L$
23\form#22:$D$
24\form#23:$V = V + w v v'$
25\form#24:$C$
26\form#25:$V = C*V*C'$
27\form#26:$V = C'*V*C$
28\form#27:$V$
29\form#28:$x$
30\form#29:$x= v'*V*v$
31\form#30:$x= v'*inv(V)*v$
32\form#31:$U$
33\form#32:$A'D0 A$
34\form#33:$L'DL$
35\form#34:$A'*diag(D)*A = self.L'*diag(self.D)*self.L$
36\form#35:$f(x)$
37\form#36:$f(rv|rvc,data)$
38\form#37:$x=$
39\form#38:$t$
40\form#39:$t+1$
41\form#40:$mu=A*rvc$
42\form#41:$k$
43\form#42:$p$
44\form#43:$l$
45\form#44:$w$
46\form#45:$f(x) = a$
47\form#46:$f(x) = Ax+B$
48\form#47:$f(x,u)$
49\form#48:$f(x,u) = Ax+Bu$
50\form#49:$f(x0,u0)$
51\form#50:$u$
52\form#51:$[\theta r]$
53\form#52:$\psi=\psi(y_{1:t},u_{1:t})$
54\form#53:$u_t$
55\form#54:$e_t$
56\form#55:$\theta_t,r_t$
57\form#56:$\in <0,1>$
58\form#57:$\theta,r$
59\form#58:$dt = [y_t psi_t] $
60\form#59:$epdf(rv)$
61\form#60:$\mathcal{I}$
62\form#61:\[ y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t \]
63\form#62:\[ e_t \sim \mathcal{N}(0,1). \]
64\form#63:\[ f(x) = \sum_{i=1}^{n} w_{i} f_i(x), \quad \sum_{i=1}^n w_i = 1. \]
65\form#64:$f_i(x)$
66\form#65:$\omega$
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