added html files

2018-08-24 06:35:38 +02:00
parent 3a6bdf1450
commit dc7ce90ee7
20 changed files with 159 additions and 2504 deletions
@@ -393,9 +393,10 @@ and
 !bblock

 For a linear fit we don't need to invert a matrix!!  
+Defining
 !bt
 \[
-\gamma =  \sum_{i=0}^{n-1}\frac{n-1}{\sigma_i^2},
+\gamma =  \sum_{i=0}^{n-1}\frac{1}{\sigma_i^2},
 \]
 !et

@@ -419,7 +420,7 @@ For a linear fit we don't need to invert a matrix!!
 \gamma_{xy} = \sum_{i=0}^{n-1}\frac{y_ix_{i}}{\sigma_i^2},
 \]
 !et
-and show that
+we obtain
 !bt
 \[
 \beta_0 = \frac{\gamma_{xx}\gamma_y-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2},
@@ -431,7 +432,7 @@ and show that
 \]
 !et

-The LSM suffers often from both being underdetermined and overdetermined in the unknown coefficients $\beta_i$.  A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
+This approach (different linear and non-linear regression) suffers often from both being underdetermined and overdetermined in the unknown coefficients $\beta_i$.  A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
 !eblock


@@ -332,9 +332,9 @@ while $P(x)$ is the cumulative probability.
 | Domain                                     | $\left\{x_1, x_2, x_3, \dots, x_N\right\}$ | $[a,b]$                                    |
 | Probability                                | $p(x_i)$                                   | $p(x)dx$                                   |
 | Cumulative                                 | $P_i=\sum_{l=1}^ip(x_l)$                   | $P(x)=\int_a^xp(t)dt$                      |
-| Positivity                                 | $ 0\le p(x_i)\le 1$                      | $ p(x) \ge 0$                              |
-| Positivity                                 | $ 0\le P_i\le 1$                         | $ 0\le P(x)\le 1$                        |
-| Monotonic                                  | $P_i\ge P_j$ if $x_i\ge x_j$             | $P(x_i)\ge P(x_j)$ if $x_i\ge x_j$       |
+| Positivity                                 | $ 0 \le p(x_i) \le 1$                      | $ p(x) \ge 0$                              |
+| Positivity                                 | $ 0 \le P_i \le 1$                         | $ 0 \le P(x) \le 1$                        |
+| Monotonic                                  | $P_i \ge P_j$ if $x_i \ge x_j$             | $P(x_i) \ge P(x_j)$ if $x_i \ge x_j$       |
 | Normalization                              | $P_N=1$                                    | $P(b)=1$                                   |
 |--------------------------------------------------------------------------------------------------------------------------------------|

@@ -44,7 +44,7 @@ system doconce split_html $html.html --method=space10
 # Bootstrap style
 html=${name}-bs
 system doconce format html $name --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=$html $opt
-#system doconce split_html $html.html --method=split --pagination --nav_button=bottom
+system doconce split_html $html.html --method=split --pagination --nav_button=bottom

 # IPython notebook
 system doconce format ipynb $name $opt