-
diff --git a/doc/pub/Regression/html/._Regression-bs018.html b/doc/pub/Regression/html/._Regression-bs018.html index 002c1bf37..0f9e135d9 100644 --- a/doc/pub/Regression/html/._Regression-bs018.html +++ b/doc/pub/Regression/html/._Regression-bs018.html @@ -444,6 +444,14 @@ and finally the relative error as return abs((y_data-y_model)/y_data) print(RelativeError(Energies, ytilde)) +
+We could also add the so-called Huber norm, which we defined as +$$ +H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}, +$$ + +with \( a=\boldsymbol{y} - \boldsymbol{\tilde{y}} \). +
diff --git a/doc/pub/Regression/html/Regression-bs.html b/doc/pub/Regression/html/Regression-bs.html index 1301e7d98..383bb6110 100644 --- a/doc/pub/Regression/html/Regression-bs.html +++ b/doc/pub/Regression/html/Regression-bs.html @@ -425,7 +425,7 @@ MathJax.Hub.Config({
-
diff --git a/doc/pub/Regression/html/Regression-reveal.html b/doc/pub/Regression/html/Regression-reveal.html index 2f47cbeb6..2b88651f8 100644 --- a/doc/pub/Regression/html/Regression-reveal.html +++ b/doc/pub/Regression/html/Regression-reveal.html @@ -148,7 +148,7 @@ MathJax.Hub.Config({
-
@@ -852,6 +852,15 @@ and finally the relative error as return abs((y_data-y_model)/y_data) print(RelativeError(Energies, ytilde)) +
+We could also add the so-called Huber norm, which we defined as +
+$$
+H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}},
+$$
+
+
+with \( a=\boldsymbol{y} - \boldsymbol{\tilde{y}} \).
diff --git a/doc/pub/Regression/html/Regression-solarized.html b/doc/pub/Regression/html/Regression-solarized.html
index b0e916ea2..648f5afa1 100644
--- a/doc/pub/Regression/html/Regression-solarized.html
+++ b/doc/pub/Regression/html/Regression-solarized.html
@@ -305,7 +305,7 @@ MathJax.Hub.Config({
-
@@ -955,6 +955,14 @@ and finally the relative error as
return abs((y_data-y_model)/y_data)
print(RelativeError(Energies, ytilde))
+
+We could also add the so-called Huber norm, which we defined as +$$ +H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}, +$$ + +with \( a=\boldsymbol{y} - \boldsymbol{\tilde{y}} \). +
diff --git a/doc/pub/Regression/html/Regression.html b/doc/pub/Regression/html/Regression.html
index 2ab82a188..9b2aa14dd 100644
--- a/doc/pub/Regression/html/Regression.html
+++ b/doc/pub/Regression/html/Regression.html
@@ -310,7 +310,7 @@ MathJax.Hub.Config({
-
@@ -960,6 +960,14 @@ and finally the relative error as
return abs((y_data-y_model)/y_data)
print(RelativeError(Energies, ytilde))
+
+We could also add the so-called Huber norm, which we defined as +$$ +H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}}, +$$ + +with \( a=\boldsymbol{y} - \boldsymbol{\tilde{y}} \). +
diff --git a/doc/pub/Regression/ipynb/Regression.ipynb b/doc/pub/Regression/ipynb/Regression.ipynb
index 148636282..04601b404 100644
--- a/doc/pub/Regression/ipynb/Regression.ipynb
+++ b/doc/pub/Regression/ipynb/Regression.ipynb
@@ -10,7 +10,7 @@
" \n",
"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
"\n",
- "Date: **Dec 21, 2019**\n",
+ "Date: **Dec 24, 2019**\n",
"\n",
"Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
"\n",
@@ -1031,6 +1031,25 @@
"cell_type": "markdown",
"metadata": {},
"source": [
+ "We could also add the so-called Huber norm, which we defined as"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\n",
+ "H_{\\delta}(a)={\\begin{cases}{\\frac {1}{2}}{a^{2}}&{\\text{for }}|a|\\leq \\delta ,\\\\\\delta (|a|-{\\frac {1}{2}}\\delta ),&{\\text{otherwise.}}\\end{cases}}},\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "with $a=\\boldsymbol{y} - \\boldsymbol{\\tilde{y}}$.\n",
+ "\n",
+ "\n",
"## The $\\chi^2$ function\n",
"\n",
"Normally, the response (dependent or outcome) variable $y_i$ is the\n",
@@ -3374,7 +3393,7 @@
"source": [
"1\n",
"1\n",
- "2\n",
+ "3\n",
" \n",
"<\n",
"<\n",
@@ -6103,7 +6122,7 @@
"source": [
"1\n",
"7\n",
- "6\n",
+ "7\n",
" \n",
"<\n",
"<\n",
diff --git a/doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz b/doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz
index 6c8581ac0..f1210c14e 100644
Binary files a/doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz and b/doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz differ
diff --git a/doc/pub/Regression/pdf/Regression-minted.pdf b/doc/pub/Regression/pdf/Regression-minted.pdf
index 7dcbd1e87..448081daa 100644
Binary files a/doc/pub/Regression/pdf/Regression-minted.pdf and b/doc/pub/Regression/pdf/Regression-minted.pdf differ
diff --git a/doc/src/Regression/Regression.do.txt b/doc/src/Regression/Regression.do.txt
index 357bc9a4f..9a09f6c77 100644
--- a/doc/src/Regression/Regression.do.txt
+++ b/doc/src/Regression/Regression.do.txt
@@ -575,7 +575,13 @@ print(RelativeError(Energies, ytilde))
!ec
-
+We could also add the so-called Huber norm, which we defined as
+!bt
+\[
+H_{\delta}(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta (|a|-{\frac {1}{2}}\delta ),&{\text{otherwise.}}\end{cases}}},
+\]
+!et
+with $a=\bm{y} - \bm{\tilde{y}}$.
!split