From a001e514eb23b34988141c75f087fb6806db36b8 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Tue, 24 Dec 2019 15:28:49 +0100 Subject: [PATCH] regression add --- .../Regression/html/._Regression-bs000.html | 2 +- .../Regression/html/._Regression-bs018.html | 8 ++++++ doc/pub/Regression/html/Regression-bs.html | 2 +- .../Regression/html/Regression-reveal.html | 11 +++++++- .../Regression/html/Regression-solarized.html | 10 ++++++- doc/pub/Regression/html/Regression.html | 10 ++++++- doc/pub/Regression/ipynb/Regression.ipynb | 25 +++++++++++++++--- .../ipynb/ipynb-Regression-src.tar.gz | Bin 193 -> 193 bytes doc/pub/Regression/pdf/Regression-minted.pdf | Bin 455651 -> 456319 bytes doc/src/Regression/Regression.do.txt | 8 +++++- 10 files changed, 67 insertions(+), 9 deletions(-) diff --git a/doc/pub/Regression/html/._Regression-bs000.html b/doc/pub/Regression/html/._Regression-bs000.html index 1301e7d98..383bb6110 100644 --- a/doc/pub/Regression/html/._Regression-bs000.html +++ b/doc/pub/Regression/html/._Regression-bs000.html @@ -425,7 +425,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Dec 21, 2019

+

Dec 24, 2019


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({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Dec 21, 2019

+

Dec 24, 2019


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({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

 
-

Dec 21, 2019

+

Dec 24, 2019


@@ -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({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Dec 21, 2019

+

Dec 24, 2019












@@ -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({

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Dec 21, 2019

+

Dec 24, 2019












@@ -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 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z@C*65zbRxbv@aApjJWX`pXwi2!~?XfzNm#hET zk-5^;YnOLwx8WUZNcVt?gK!OtfTI!yN|yy#mHBIx1^#-N{t>MhL~ap+{{7`@65_#g y7Nl?%;Z?d;KQ(Rv2#F^k%=jYL;oLqm%4)h 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