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Diffstat (limited to 'doc/html/formula.repository')
| -rw-r--r-- | doc/html/formula.repository | 15 |
1 files changed, 15 insertions, 0 deletions
diff --git a/doc/html/formula.repository b/doc/html/formula.repository index b50a0ed..bfa1d28 100644 --- a/doc/html/formula.repository +++ b/doc/html/formula.repository @@ -48,3 +48,18 @@ \form#47:\[ R \times \left[ \begin{array}{c} \frac{x_1}{L} \\ \frac{x_2}{L} \\ \frac{x_3}{L} \\ . \\ . \\ . \\ \frac{x_N}{L} \\ \end{array} \right] \] \form#48:\[ f \times \left[ \begin{array}{ccccc} \frac{-1}{x_N} & 0 & 0 & ... & \frac{1}{x_N^2} \\ 0 & \frac{-1}{x_N} & 0 & ... & \frac{1}{x_N^2} \\ 0 & 0 & \frac{-1}{x_N} & ... & \frac{1}{x_N^2} \\ . & . & . & & . \\ . & . & . & & . \\ . & . & . & & . \\ 0 & 0 & 0 & ... & 0 \\ \end{array} \right] \] \form#49:\[ f \times \left[ \begin{array}{c} \frac{-x_1}{x_N} \\ \frac{-x_2}{x_N} \\ \frac{-x_3}{x_N} \\ . \\ . \\ . \\ -1 \\ \end{array} \right] \] +\form#50:\[ v_{output} = H(h_1, G(g_1, g_2, g_3, F(f_1, v_{input}))) \] +\form#51:$ v_{input}(x,y,z), v_{output} $ +\form#52:$ y $ +\form#53:\[ m_{jacobian} = \frac{\partial H(h_1, G(g_1, g_2, g_3, F(f_1, v_{input})))} {\partial G(g_1, g_2, g_3, F(f_1, v_{input})) } \frac{\partial G(g_1, g_2, g_3, F(f_1, v_{input}))} {\partial F(f_1, v_{input}) } \frac{\partial F(f_1, v_{input})} {\partial v_{input} } \frac{\partial v_{input}} {\partial y} \] +\form#54:\[ \frac{\partial v_{input}}{\partial y} = \left[ \begin{array}{c} 0 \\ 1 \\ 0 \\ \end{array} \right] \] +\form#55:\[ v_{output} = H(h_1, h_2, G(g_1, g_2, g_3, F(f_1, v_{input}))) \] +\form#56:$ f_1, g_1, g_2, g_3, h_1, h_2 $ +\form#57:$ F, G, H $ +\form#58:\[ M_{jacobian} = \frac{\partial H(h_1, h_2, G(g_1, g_2, g_3, F(f_1, v_{input})))} {\partial G(g_1, g_2, g_3, F(f_1, v_{input})) } \frac{\partial G(g_1, g_2, g_3, F(f_1, v_{input})) } {\partial F(f_1, v_{input}) } \frac{\partial F(f_1, v_{input}) } {\partial v_{input} } \frac{\partial v_{input} } {\partial y } \] +\form#59:\[ v_{output} = I(i_1,i_2, H(h_1,h_2, G(g_1,g_2,g_3, F(f_1, v_{input})))) \] +\form#60:$ f_1, g_1,g_2,g_3, h_1,h_2, i_1,i_2 $ +\form#61:$ F, G, H, I $ +\form#62:$ g_2 $ +\form#63:\[ M_{jacobian} = \frac{\partial I(i_1,i_2, H(h_1,h_2, G(g_1,g_2,g_3, F(f_1, v_{input}))))} {\partial H(h_1,h_2, G(g_1,g_2,g_3, F(f_1, v_{input}))) } \frac{\partial H(h_1,h_2, G(g_1,g_2,g_3, F(f_1, v_{input}))) } {\partial G(g_1,g_2,g_3, F(f_1, v_{input})) } \frac{\partial G(g_1,g_2,g_3, F(f_1, v_{input})) } {\partial g_2 } \] +\form#64:$ f_1, g_1, g_2, g_3, h_1, h_2, i_1, i_2 $ |