misc
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misc [2022/02/22 10:21] – [another statement] potthast | misc [2023/03/28 09:14] (current) – external edit 127.0.0.1 | ||
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where you can quickly type some ideas in LaTeX and the other | where you can quickly type some ideas in LaTeX and the other | ||
person with internet connection can read it ... | person with internet connection can read it ... | ||
+ | |||
+ | ===== Da Redesign 1 ===== | ||
+ | |||
+ | $a$: all information on bonds, spots or collections or records of observations | ||
+ | |||
+ | $dim_a$: dimension of bonds | ||
+ | |||
+ | $y$: Observation vector, List of observation values | ||
+ | |||
+ | $dim_y$: dimenension of obs | ||
+ | |||
+ | $is$: Ispace, Interpolation space, list of interpolation points and variables | ||
+ | |||
+ | $dim_i$: dimension of interpolation space | ||
+ | |||
+ | $y-i-list$: values needed for y from $is$, this is a vector of some dimension $dim_{yi}$, referenced by vectors yii and yil of integers, where yii(jy) is the starting index and yil(jy) is the number of points needed for the observation with index jy. | ||
+ | ===== Da Redesign 2 ===== | ||
+ | ==== Maths Notation ==== | ||
+ | |||
+ | Linearisierung | ||
+ | $$ | ||
+ | f(x) = f(x_0) + df*(x-x_0), \hspace{1cm} | ||
+ | q_i(t,q) = q_i(t_0, | ||
+ | $$ | ||
+ | |||
+ | $$ | ||
+ | A = \left( \begin{array}{cc} | ||
+ | 1 & 0 \\ | ||
+ | 0 & 1 \\ | ||
+ | v_1 & v_2 | ||
+ | \end{array} \right), \hspace{1cm} | ||
+ | A^{T} = \left( \begin{array}{cc} | ||
+ | 1 & 0 & v_1\\ | ||
+ | 0 & 1 & v_2 | ||
+ | \end{array} \right) | ||
+ | $$ | ||
+ | |||
+ | $$ | ||
+ | x = \left( \begin{array}{c} t \\ q \end{array}\right), | ||
+ | A * x = \left( \begin{array}{c} t \\ q \\ q_i \end{array} \right) | ||
+ | $$ | ||
+ | |||
+ | $z$ be the reflectance using $H_{s}$ MFASIS, then: | ||
+ | $$ | ||
+ | H_{s} = (\alpha_1, \alpha_2, \alpha_3), | ||
+ | \hspace{1cm} \left( \begin{array}{c} t \\ q \\ q_i \end{array} \right) = | ||
+ | \left( \begin{array}{c} \alpha_1 z \\ \alpha_2 z \\ \alpha_3 z \end{array} \right) = H_s^T z | ||
+ | $$ | ||
+ | |||
+ | $$ | ||
+ | A^T H^T z = A^T \left( \begin{array}{c} \alpha_1 z \\ \alpha_2 z \\ \alpha_3 z \end{array} \right) | ||
+ | = \left( \begin{array}{c} (\alpha_1 | ||
+ | (\alpha_2 | ||
+ | \end{array} \right) \hspace{1cm} | ||
+ | H_s * A = \left( \begin{array}{cc} (\alpha_1 | ||
+ | \end{array} \right) | ||
+ | $$ | ||
+ | |||
+ | |||
+ | |||
==== Maths Notation ==== | ==== Maths Notation ==== |
misc.1645521674.txt.gz · Last modified: 2023/03/28 09:14 (external edit)