From cb232e1001e80c63dde29d963cdcbf3e88c0e453 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Tue, 6 Nov 2018 11:02:04 +0100 Subject: [PATCH] adding more to codes for sim --- doc/pub/svm/html/._svm-bs000.html | 13 +++-- doc/pub/svm/html/._svm-bs001.html | 11 +++-- doc/pub/svm/html/._svm-bs002.html | 11 +++-- doc/pub/svm/html/._svm-bs003.html | 11 +++-- doc/pub/svm/html/._svm-bs004.html | 11 +++-- doc/pub/svm/html/._svm-bs005.html | 11 +++-- doc/pub/svm/html/._svm-bs006.html | 11 +++-- doc/pub/svm/html/._svm-bs007.html | 11 +++-- doc/pub/svm/html/._svm-bs008.html | 11 +++-- doc/pub/svm/html/._svm-bs009.html | 11 +++-- doc/pub/svm/html/._svm-bs010.html | 11 +++-- doc/pub/svm/html/._svm-bs011.html | 11 +++-- doc/pub/svm/html/._svm-bs012.html | 11 +++-- doc/pub/svm/html/._svm-bs013.html | 11 ++++- doc/pub/svm/html/._svm-bs014.html | 10 +++- doc/pub/svm/html/._svm-bs015.html | 10 +++- doc/pub/svm/html/._svm-bs016.html | 10 +++- doc/pub/svm/html/._svm-bs017.html | 10 +++- doc/pub/svm/html/._svm-bs018.html | 10 +++- doc/pub/svm/html/._svm-bs019.html | 10 +++- doc/pub/svm/html/._svm-bs020.html | 10 +++- doc/pub/svm/html/._svm-bs021.html | 10 +++- doc/pub/svm/html/._svm-bs022.html | 66 ++++++++----------------- doc/pub/svm/html/svm-bs.html | 13 +++-- doc/pub/svm/html/svm-reveal.html | 46 +++++++++++++++-- doc/pub/svm/html/svm-solarized.html | 50 +++++++++++++++++-- doc/pub/svm/html/svm.html | 50 +++++++++++++++++-- doc/pub/svm/ipynb/ipynb-svm-src.tar.gz | Bin 206 -> 208 bytes doc/pub/svm/ipynb/svm.ipynb | 49 +++++++++++++++++- doc/pub/svm/pdf/svm-minted.pdf | Bin 298508 -> 322574 bytes doc/src/SupportVMachines/svm.do.txt | 36 ++++++++++++++ 31 files changed, 425 insertions(+), 121 deletions(-) diff --git a/doc/pub/svm/html/._svm-bs000.html b/doc/pub/svm/html/._svm-bs000.html index 9fe71862a..85f83e77f 100644 --- a/doc/pub/svm/html/._svm-bs000.html +++ b/doc/pub/svm/html/._svm-bs000.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -158,7 +163,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Nov 5, 2018

    +

    Nov 6, 2018


    @@ -182,7 +187,7 @@ MathJax.Hub.Config({

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    • -
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    • diff --git a/doc/pub/svm/html/._svm-bs001.html b/doc/pub/svm/html/._svm-bs001.html index 6c0d0f6bf..37297f5b7 100644 --- a/doc/pub/svm/html/._svm-bs001.html +++ b/doc/pub/svm/html/._svm-bs001.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -181,7 +186,7 @@ We distinguish also between linear and non-linear approaches. The latter are the
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    • diff --git a/doc/pub/svm/html/._svm-bs002.html b/doc/pub/svm/html/._svm-bs002.html index c17a6cd20..5db305100 100644 --- a/doc/pub/svm/html/._svm-bs002.html +++ b/doc/pub/svm/html/._svm-bs002.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -172,7 +177,7 @@ circles.
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    • diff --git a/doc/pub/svm/html/._svm-bs003.html b/doc/pub/svm/html/._svm-bs003.html index f159bd84e..109fd8cb1 100644 --- a/doc/pub/svm/html/._svm-bs003.html +++ b/doc/pub/svm/html/._svm-bs003.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -182,7 +187,7 @@ $$
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    • diff --git a/doc/pub/svm/html/._svm-bs004.html b/doc/pub/svm/html/._svm-bs004.html index 79f6ee766..bd6abfe12 100644 --- a/doc/pub/svm/html/._svm-bs004.html +++ b/doc/pub/svm/html/._svm-bs004.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -198,7 +203,7 @@ When we try to separate hyperplanes, if it exists, we can use it to construct a
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    • diff --git a/doc/pub/svm/html/._svm-bs005.html b/doc/pub/svm/html/._svm-bs005.html index fe033d199..8c3337f06 100644 --- a/doc/pub/svm/html/._svm-bs005.html +++ b/doc/pub/svm/html/._svm-bs005.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -184,7 +189,7 @@ for our data sample.
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    • diff --git a/doc/pub/svm/html/._svm-bs006.html b/doc/pub/svm/html/._svm-bs006.html index f67f9ac23..2f72c0129 100644 --- a/doc/pub/svm/html/._svm-bs006.html +++ b/doc/pub/svm/html/._svm-bs006.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -180,7 +185,7 @@ $$
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    • diff --git a/doc/pub/svm/html/._svm-bs007.html b/doc/pub/svm/html/._svm-bs007.html index 685685aef..10ed2ca41 100644 --- a/doc/pub/svm/html/._svm-bs007.html +++ b/doc/pub/svm/html/._svm-bs007.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -184,7 +189,7 @@ $$
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    • diff --git a/doc/pub/svm/html/._svm-bs008.html b/doc/pub/svm/html/._svm-bs008.html index cee105910..08dfd1a31 100644 --- a/doc/pub/svm/html/._svm-bs008.html +++ b/doc/pub/svm/html/._svm-bs008.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -188,7 +193,7 @@ at all.
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    • diff --git a/doc/pub/svm/html/._svm-bs009.html b/doc/pub/svm/html/._svm-bs009.html index 00e3f8aa0..13e415077 100644 --- a/doc/pub/svm/html/._svm-bs009.html +++ b/doc/pub/svm/html/._svm-bs009.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -200,7 +205,7 @@ We have thus defined our margin as the invers of the norm of \( \boldsymbol{w} \
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    • diff --git a/doc/pub/svm/html/._svm-bs010.html b/doc/pub/svm/html/._svm-bs010.html index 9a6b29c06..ff49403d1 100644 --- a/doc/pub/svm/html/._svm-bs010.html +++ b/doc/pub/svm/html/._svm-bs010.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -212,7 +217,7 @@ Then \( dz \) is no longer arbitrary.
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    • diff --git a/doc/pub/svm/html/._svm-bs011.html b/doc/pub/svm/html/._svm-bs011.html index 9941de0ab..9c274b1b3 100644 --- a/doc/pub/svm/html/._svm-bs011.html +++ b/doc/pub/svm/html/._svm-bs011.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -205,7 +210,7 @@ $$
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    • diff --git a/doc/pub/svm/html/._svm-bs012.html b/doc/pub/svm/html/._svm-bs012.html index 98c4ecd16..d5deef96a 100644 --- a/doc/pub/svm/html/._svm-bs012.html +++ b/doc/pub/svm/html/._svm-bs012.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -203,7 +208,7 @@ When \( \lambda_i > 0 \), the vectors \( \boldsymbol{x}_i \) are called support
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    • diff --git a/doc/pub/svm/html/._svm-bs013.html b/doc/pub/svm/html/._svm-bs013.html index 8ad3d9fc5..d67cdc39e 100644 --- a/doc/pub/svm/html/._svm-bs013.html +++ b/doc/pub/svm/html/._svm-bs013.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -185,6 +190,8 @@ subject to \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \). Here we defined the vec
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    • diff --git a/doc/pub/svm/html/._svm-bs014.html b/doc/pub/svm/html/._svm-bs014.html index f4042b91c..d132c80e9 100644 --- a/doc/pub/svm/html/._svm-bs014.html +++ b/doc/pub/svm/html/._svm-bs014.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -194,6 +199,7 @@ Below we discuss how to find the optimal values of \( \lambda_i \). Before we pr
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    • diff --git a/doc/pub/svm/html/._svm-bs015.html b/doc/pub/svm/html/._svm-bs015.html index afa001e3c..b87cc8e72 100644 --- a/doc/pub/svm/html/._svm-bs015.html +++ b/doc/pub/svm/html/._svm-bs015.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -194,6 +199,7 @@ misclassifications.
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    • diff --git a/doc/pub/svm/html/._svm-bs016.html b/doc/pub/svm/html/._svm-bs016.html index 8a915f0c2..ef073b5cf 100644 --- a/doc/pub/svm/html/._svm-bs016.html +++ b/doc/pub/svm/html/._svm-bs016.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -212,6 +217,7 @@ $$
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    • diff --git a/doc/pub/svm/html/._svm-bs017.html b/doc/pub/svm/html/._svm-bs017.html index 5486edbe8..8df569d0b 100644 --- a/doc/pub/svm/html/._svm-bs017.html +++ b/doc/pub/svm/html/._svm-bs017.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -180,6 +185,7 @@ we need to introduce for example a polynomial transformation to a two-dimensiona
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    • diff --git a/doc/pub/svm/html/._svm-bs018.html b/doc/pub/svm/html/._svm-bs018.html index 0a17b8423..dd6ac5476 100644 --- a/doc/pub/svm/html/._svm-bs018.html +++ b/doc/pub/svm/html/._svm-bs018.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -180,6 +185,7 @@ from which we also find \( b \).
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  • »
    • diff --git a/doc/pub/svm/html/._svm-bs019.html b/doc/pub/svm/html/._svm-bs019.html index af36a2942..52686a402 100644 --- a/doc/pub/svm/html/._svm-bs019.html +++ b/doc/pub/svm/html/._svm-bs019.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -160,6 +165,7 @@ MathJax.Hub.Config({
  • 21
  • 22
  • 23
    • +
  • 24
  • »
    • diff --git a/doc/pub/svm/html/._svm-bs020.html b/doc/pub/svm/html/._svm-bs020.html index ddf6ab472..fee529438 100644 --- a/doc/pub/svm/html/._svm-bs020.html +++ b/doc/pub/svm/html/._svm-bs020.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -159,6 +164,7 @@ MathJax.Hub.Config({
  • 21
  • 22
  • 23
    • +
  • 24
  • »
    • diff --git a/doc/pub/svm/html/._svm-bs021.html b/doc/pub/svm/html/._svm-bs021.html index d5d695472..d855421d5 100644 --- a/doc/pub/svm/html/._svm-bs021.html +++ b/doc/pub/svm/html/._svm-bs021.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -158,6 +163,7 @@ MathJax.Hub.Config({
  • 21
  • 22
  • 23
    • +
  • 24
  • »
    • diff --git a/doc/pub/svm/html/._svm-bs022.html b/doc/pub/svm/html/._svm-bs022.html index 0325d756e..2c44ea8be 100644 --- a/doc/pub/svm/html/._svm-bs022.html +++ b/doc/pub/svm/html/._svm-bs022.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -139,60 +144,27 @@ MathJax.Hub.Config({ -

    How do we solve these problems

    +

    Mathematical optimization of convex functions

    -If we use Python as programming language and wish to venture beyond -scikit-learn, tensorflow and similar software which makes our -lives so much easier, we need to dive into the wonderful world of -quadratic programming. We can, if we wish, solve the minimization -problem using say standard gradient methods or conjugate gradient -methods. However, these methods tend to exhibit a rather slow -converge. So, welcome to the promised land of quadratic programming. - -

    -The functions we need are contained in the quadratic programming package CVXOPT and we need to import it -

    - - -

    import numpy
-import cvxopt
-
    -

    -Let us first set up the standard form the of quadratic programming (QP) equations by defining the problem as +A mathematical optimization problem, or just optimization problem, has the form $$ -\mathrm{min} +\mathrm{minimize}\hspace{0.1cm} f(x), $$ -

    -subject to Gx u. Note that x itself is not provided to the solver, since it is an internal -variable being optimized over. In particular, this means that the solver has no explicit knowledge -of x itself; everything is implicity defined by the supplied parameters. It is essential -that the same variable order is maintained for the relevant parameters (e.g., qi -Non-convexity implies the existence of local optima, making it difficult to find global optima. +subject to some constraints \( g(\lambda_i) \leq b_i \) for say a selected set \( i=1,2,\dots, n \). +In our case we are optimizing with respect to the Lagrangian multipliers \( \lambda_i \), and the +vector \( \boldsymbol{\lambda}=[\lambda_1, \lambda_2,\dots, \lambda_n] \) is the optimization variable we are dealing with. +and \( f(x) \) is our objective function while \( g(\lambda_i) \leq b_i \) represents our constraint function.

    -collapsed all inequality constraints into a single G matrix of the standard form. -Since there are no equality constraints, we do not need to provide the empty A, b. Note -that even though y -2 did not appear in the original objective, we had to include it with zero -coefficients in P because the solver parameters must be defined using the full set of variables. -Even if certain variables only appear in constraints, they will still need to be expressed with -zero coefficients in the objective parameters, and vice versa. -Let us first define the above parameters in Python. CVXOPT supplies its own matrix -object; all arguments given to its solvers must be in this matrix type. There are two ways -to do this. The first is to define the matrix directly with (potentially nested) lists: -from cvxopt import matrix -

    +In our case we are particularly interested in a class of optimization problems called convex optmization problems. +In our disussion on gradient descent methods we discussed at length the definition of a convex function. - -

    P = matrix([[1.0,0.0],[0.0,0.0]])
-q = matrix([3.0,4.0])
-G = matrix([[-1.0,0.0,-1.0,2.0,3.0],[0.0,-1.0,-3.0,5.0,4.0]])
-h = matrix([0.0,0.0,-15.0,100.0,80.0])
-

    +Convex optimization problems play a central role in applied mathematics and we recommend strongly Boyd and Vandenberghe's text on the topics. +

    diff --git a/doc/pub/svm/html/svm-bs.html b/doc/pub/svm/html/svm-bs.html index 9fe71862a..85f83e77f 100644 --- a/doc/pub/svm/html/svm-bs.html +++ b/doc/pub/svm/html/svm-bs.html @@ -64,7 +64,11 @@ Automatically generated HTML file from DocOnce source ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -123,7 +127,8 @@ MathJax.Hub.Config({
  • Different kernels
  • Quadratic coefficient matrix
  • Mercer's theorem
    • -
  • How do we solve these problems
    • +
  • Mathematical optimization of convex functions
    • +
  • How do we solve these problems
    • @@ -158,7 +163,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Nov 5, 2018

    +

    Nov 6, 2018


    @@ -182,7 +187,7 @@ MathJax.Hub.Config({

  • 9
  • 10
  • ...
    • -
  • 23
    • +
  • 24
  • »
    • diff --git a/doc/pub/svm/html/svm-reveal.html b/doc/pub/svm/html/svm-reveal.html index dc4886414..77ba1ed41 100644 --- a/doc/pub/svm/html/svm-reveal.html +++ b/doc/pub/svm/html/svm-reveal.html @@ -148,7 +148,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

     
    -

    Nov 5, 2018

    +

    Nov 6, 2018


    @@ -871,7 +871,32 @@ from which we also find \( b \).

    -

    How do we solve these problems

    +

    Mathematical optimization of convex functions

    + +

    +A mathematical optimization problem, or just optimization problem, has the form +

     
    +$$ +\mathrm{minimize}\hspace{0.1cm} f(x), +$$ +

     
    + +subject to some constraints \( g(\lambda_i) \leq b_i \) for say a selected set \( i=1,2,\dots, n \). +In our case we are optimizing with respect to the Lagrangian multipliers \( \lambda_i \), and the +vector \( \boldsymbol{\lambda}=[\lambda_1, \lambda_2,\dots, \lambda_n] \) is the optimization variable we are dealing with. +and \( f(x) \) is our objective function while \( g(\lambda_i) \leq b_i \) represents our constraint function. + +

    +In our case we are particularly interested in a class of optimization problems called convex optmization problems. +In our disussion on gradient descent methods we discussed at length the definition of a convex function. + +

    +Convex optimization problems play a central role in applied mathematics and we recommend strongly Boyd and Vandenberghe's text on the topics. +

    + + +
    +

    How do we solve these problems

    If we use Python as programming language and wish to venture beyond @@ -920,10 +945,25 @@ from cvxopt import matrix

    -

    P = matrix([[1.0,0.0],[0.0,0.0]])
+
    # Import the necessary packages
+import numpy
+from cvxopt import matrix
+from cvxopt import solvers
+# Define QP parameters (directly)
+P = matrix([[1.0,0.0],[0.0,0.0]])
 q = matrix([3.0,4.0])
 G = matrix([[-1.0,0.0,-1.0,2.0,3.0],[0.0,-1.0,-3.0,5.0,4.0]])
 h = matrix([0.0,0.0,-15.0,100.0,80.0])
+# Define QP parameters (with NumPy)
+P = matrix(numpy.diag([1,0]), tc=’d’)
+q = matrix(numpy.array([3,4]), tc=’d’)
+G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’)
+h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’)
+# Construct the QP, invoke solver
+sol = solvers.qp(P,q,G,h)
+# Extract optimal value and solution
+sol[’x’] # [7.13e-07, 5.00e+00]
+sol[’primal objective’]
    diff --git a/doc/pub/svm/html/svm-solarized.html b/doc/pub/svm/html/svm-solarized.html index 9f39b8eff..cf850a809 100644 --- a/doc/pub/svm/html/svm-solarized.html +++ b/doc/pub/svm/html/svm-solarized.html @@ -58,7 +58,11 @@ div { text-align: justify; text-justify: inter-word; } ('Different kernels', 2, None, '___sec18'), ('Quadratic coefficient matrix', 2, None, '___sec19'), ("Mercer's theorem", 2, None, '___sec20'), - ('How do we solve these problems', 2, None, '___sec21')]} + ('Mathematical optimization of convex functions', + 2, + None, + '___sec21'), + ('How do we solve these problems', 2, None, '___sec22')]} end of tocinfo --> @@ -100,7 +104,7 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    Nov 5, 2018

    +

    Nov 6, 2018












    @@ -704,7 +708,30 @@ from which we also find \( b \).











    -

    How do we solve these problems

    +

    Mathematical optimization of convex functions

    + +

    +A mathematical optimization problem, or just optimization problem, has the form +$$ +\mathrm{minimize}\hspace{0.1cm} f(x), +$$ + +subject to some constraints \( g(\lambda_i) \leq b_i \) for say a selected set \( i=1,2,\dots, n \). +In our case we are optimizing with respect to the Lagrangian multipliers \( \lambda_i \), and the +vector \( \boldsymbol{\lambda}=[\lambda_1, \lambda_2,\dots, \lambda_n] \) is the optimization variable we are dealing with. +and \( f(x) \) is our objective function while \( g(\lambda_i) \leq b_i \) represents our constraint function. + +

    +In our case we are particularly interested in a class of optimization problems called convex optmization problems. +In our disussion on gradient descent methods we discussed at length the definition of a convex function. + +

    +Convex optimization problems play a central role in applied mathematics and we recommend strongly Boyd and Vandenberghe's text on the topics. + +

    +









    + +

    How do we solve these problems

    If we use Python as programming language and wish to venture beyond @@ -751,10 +778,25 @@ from cvxopt import matrix

    -

    P = matrix([[1.0,0.0],[0.0,0.0]])
+
    # Import the necessary packages
+import numpy
+from cvxopt import matrix
+from cvxopt import solvers
+# Define QP parameters (directly)
+P = matrix([[1.0,0.0],[0.0,0.0]])
 q = matrix([3.0,4.0])
 G = matrix([[-1.0,0.0,-1.0,2.0,3.0],[0.0,-1.0,-3.0,5.0,4.0]])
 h = matrix([0.0,0.0,-15.0,100.0,80.0])
+# Define QP parameters (with NumPy)
+P = matrix(numpy.diag([1,0]), tc=’d’)
+q = matrix(numpy.array([3,4]), tc=’d’)
+G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’)
+h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’)
+# Construct the QP, invoke solver
+sol = solvers.qp(P,q,G,h)
+# Extract optimal value and solution
+sol[’x’] # [7.13e-07, 5.00e+00]
+sol[’primal objective’]
 
    
 
    
 
diff --git a/doc/pub/svm/html/svm.html b/doc/pub/svm/html/svm.html
index c9aca2c61..6d99d69b8 100644
--- a/doc/pub/svm/html/svm.html
+++ b/doc/pub/svm/html/svm.html
@@ -63,7 +63,11 @@ div { text-align: justify; text-justify: inter-word; }
               ('Different kernels', 2, None, '___sec18'),
               ('Quadratic coefficient matrix', 2, None, '___sec19'),
               ("Mercer's theorem", 2, None, '___sec20'),
-              ('How do we solve these problems', 2, None, '___sec21')]}
+              ('Mathematical optimization of convex functions',
+               2,
+               None,
+               '___sec21'),
+              ('How do we solve these problems', 2, None, '___sec22')]}
 end of tocinfo -->
 
 
@@ -105,7 +109,7 @@ MathJax.Hub.Config({
 
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
    
 
    
 
    
-
    Nov 5, 2018
     
+
    Nov 6, 2018
     
 
    
 
    
 









    
@@ -709,7 +713,30 @@ from which we also find \( b \).
 
    
 









    
 
-
    How do we solve these problems 
    
+
    Mathematical optimization of convex functions 
    
+
+
    
+A mathematical optimization problem, or just optimization problem, has the form
+$$
+\mathrm{minimize}\hspace{0.1cm} f(x),
+$$
+
+subject to some constraints \( g(\lambda_i) \leq  b_i \) for say a selected set \( i=1,2,\dots, n \).
+In our case we are optimizing with respect to the Lagrangian multipliers \( \lambda_i \), and the
+vector \( \boldsymbol{\lambda}=[\lambda_1, \lambda_2,\dots, \lambda_n] \) is the optimization variable we are dealing with.
+and \( f(x) \) is our objective function while \( g(\lambda_i) \leq  b_i \) represents our constraint function.
+
+
    
+In our case we are particularly interested in a class of optimization problems called convex optmization problems. 
+In our disussion on gradient descent methods we discussed at length the definition of a convex function.
+
+
    
+Convex optimization problems play a central role in applied mathematics and we recommend strongly Boyd and Vandenberghe's text on the topics.
+
+
    
+









    
+
+
    How do we solve these problems 
    
 
 
    
 If we use Python as programming language and wish to venture beyond
@@ -756,10 +783,25 @@ from cvxopt import matrix
 
    
 
 
-
    P = matrix([[1.0,0.0],[0.0,0.0]])
+
    # Import the necessary packages
+import numpy
+from cvxopt import matrix
+from cvxopt import solvers
+# Define QP parameters (directly)
+P = matrix([[1.0,0.0],[0.0,0.0]])
 q = matrix([3.0,4.0])
 G = matrix([[-1.0,0.0,-1.0,2.0,3.0],[0.0,-1.0,-3.0,5.0,4.0]])
 h = matrix([0.0,0.0,-15.0,100.0,80.0])
+# Define QP parameters (with NumPy)
+P = matrix(numpy.diag([1,0]), tc=’d’)
+q = matrix(numpy.array([3,4]), tc=’d’)
+G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’)
+h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’)
+# Construct the QP, invoke solver
+sol = solvers.qp(P,q,G,h)
+# Extract optimal value and solution
+sol[’x’] # [7.13e-07, 5.00e+00]
+sol[’primal objective’]
 
    
 
    
 
diff --git a/doc/pub/svm/ipynb/ipynb-svm-src.tar.gz b/doc/pub/svm/ipynb/ipynb-svm-src.tar.gz
index a514400d1bac340f342b9a9c75444fe8be62633a..ff6e50e1a1ab1005dcbb325716e8d06f468adc6b 100644
GIT binary patch
literal 208
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zRES)jT}*}oZHd?CE%Ljtq<&c}e-F2KQ-^p*$rj_RMV?b$-u7Q@
zu&zX1>9gJJ^+H{Xvh4o-nbo)X%VakH#Zy+T_Bv;|%3g0}*X!R(=ebXwE?V+wlU9~$
z?YE;2S3ZaBvOKoLdB4~1+!&L0dGYtRMcK|MwsrmY$yX;zI@RcP(CfJt^UqxR-FxJ+
z-sa!ubeDcqoA+OJ#^H->%C|}v%|52~dhR{G?+4d6-#eP~  \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: **Nov 5, 2018**\n",
+    "Date: **Nov 6, 2018**\n",
     "\n",
     "Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
     "\n",
@@ -1137,6 +1137,36 @@
     "\n",
     "## Mercer's theorem\n",
     "\n",
+    "## Mathematical optimization of convex functions\n",
+    "\n",
+    "A mathematical optimization problem, or just optimization problem, has the form"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\mathrm{minimize}\\hspace{0.1cm} f(x),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "subject to some constraints $g(\\lambda_i) \\leq  b_i$ for say a selected set $i=1,2,\\dots, n$.\n",
+    "In our case we are optimizing with respect to the Lagrangian multipliers $\\lambda_i$, and the\n",
+    "vector $\\boldsymbol{\\lambda}=[\\lambda_1, \\lambda_2,\\dots, \\lambda_n]$ is the optimization variable we are dealing with.\n",
+    "and $f(x)$ is our objective function while $g(\\lambda_i) \\leq  b_i$ represents our constraint function.\n",
+    "\n",
+    "In our case we are particularly interested in a class of optimization problems called convex optmization problems. \n",
+    "In our disussion on gradient descent methods we discussed at length the definition of a convex function. \n",
+    "\n",
+    "Convex optimization problems play a central role in applied mathematics and we recommend strongly [Boyd and Vandenberghe's text on the topics](http://web.stanford.edu/~boyd/cvxbook/).\n",
+    "\n",
+    "\n",
+    "\n",
     "## How do we solve these problems\n",
     "\n",
     "If we use Python as programming language and wish to venture beyond\n",
@@ -1209,10 +1239,25 @@
    },
    "outputs": [],
    "source": [
+    "# Import the necessary packages\n",
+    "import numpy\n",
+    "from cvxopt import matrix\n",
+    "from cvxopt import solvers\n",
+    "# Define QP parameters (directly)\n",
     "P = matrix([[1.0,0.0],[0.0,0.0]])\n",
     "q = matrix([3.0,4.0])\n",
     "G = matrix([[-1.0,0.0,-1.0,2.0,3.0],[0.0,-1.0,-3.0,5.0,4.0]])\n",
-    "h = matrix([0.0,0.0,-15.0,100.0,80.0])"
+    "h = matrix([0.0,0.0,-15.0,100.0,80.0])\n",
+    "# Define QP parameters (with NumPy)\n",
+    "P = matrix(numpy.diag([1,0]), tc=’d’)\n",
+    "q = matrix(numpy.array([3,4]), tc=’d’)\n",
+    "G = matrix(numpy.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’)\n",
+    "h = matrix(numpy.array([0,0,-15,100,80]), tc=’d’)\n",
+    "# Construct the QP, invoke solver\n",
+    "sol = solvers.qp(P,q,G,h)\n",
+    "# Extract optimal value and solution\n",
+    "sol[’x’] # [7.13e-07, 5.00e+00]\n",
+    "sol[’primal objective’]"
    ]
   }
  ],
diff --git a/doc/pub/svm/pdf/svm-minted.pdf b/doc/pub/svm/pdf/svm-minted.pdf
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