From 204804be2385dd4d146f7b0a1f483f893a25ece0 Mon Sep 17 00:00:00 2001
From: mhjensen <morten.hjorth-jensen@fys.uio.no>
Date: Sun, 29 Dec 2019 21:59:45 +0100
Subject: [PATCH] updating

---
 doc/pub/DimRed/html/._DimRed-bs019.html      |   3 +++
 doc/pub/DimRed/html/._DimRed-bs024.html      |   5 ++--
 doc/pub/DimRed/html/._DimRed-bs029.html      |   5 ----
 doc/pub/DimRed/html/DimRed-reveal.html       |   9 ++++---
 doc/pub/DimRed/html/DimRed-solarized.html    |  24 +++++++++----------
 doc/pub/DimRed/html/DimRed.html              |  10 ++++----
 doc/pub/DimRed/ipynb/DimRed.ipynb            |   3 ++-
 doc/pub/DimRed/ipynb/ipynb-DimRed-src.tar.gz | Bin 191 -> 191 bytes
 doc/pub/DimRed/pdf/DimRed-minted.pdf         | Bin 262362 -> 262351 bytes
 doc/src/DimRed/DimRed.do.txt                 |   5 ++--
 10 files changed, 28 insertions(+), 36 deletions(-)

diff --git a/doc/pub/DimRed/html/._DimRed-bs019.html b/doc/pub/DimRed/html/._DimRed-bs019.html
index 0281b99d7..e0a87c053 100644
--- a/doc/pub/DimRed/html/._DimRed-bs019.html
+++ b/doc/pub/DimRed/html/._DimRed-bs019.html
@@ -232,6 +232,9 @@ low-dimensional encoding of the data is then given by a set of vectors
 orthogonal projection of the data onto the columns spanned by the
 eigenvectors of the covariance(correlations matrix).
 
+<p>
+The proof which follows will be updated by mid January 2020.
+
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
diff --git a/doc/pub/DimRed/html/._DimRed-bs024.html b/doc/pub/DimRed/html/._DimRed-bs024.html
index 2be659898..9fd66c361 100644
--- a/doc/pub/DimRed/html/._DimRed-bs024.html
+++ b/doc/pub/DimRed/html/._DimRed-bs024.html
@@ -206,9 +206,8 @@ MathJax.Hub.Config({
 <!-- !split -->
 
 <h2 id="___sec26" class="anchor">Principal Component Analysis </h2>
-<div class="panel panel-default">
-<div class="panel-body">
-<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+
+<p>
 Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.
 First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.
 
diff --git a/doc/pub/DimRed/html/._DimRed-bs029.html b/doc/pub/DimRed/html/._DimRed-bs029.html
index 1c29effce..8a4f7a1fd 100644
--- a/doc/pub/DimRed/html/._DimRed-bs029.html
+++ b/doc/pub/DimRed/html/._DimRed-bs029.html
@@ -213,11 +213,6 @@ algorithm that quickly finds an approximation of the first d principal component
 complexity is \( O(m \times d^2)+O(d^3) \), instead of \( O(m \times n^2) + O(n^3) \), so it is dramatically faster than the
 previous algorithms when \( d \) is much smaller than \( n \).
 
-<p>
-</div>
-</div>
-
-
 <p>
 <p>
 <!-- navigation buttons at the bottom of the page -->
diff --git a/doc/pub/DimRed/html/DimRed-reveal.html b/doc/pub/DimRed/html/DimRed-reveal.html
index 9c2731ba5..d27980dab 100644
--- a/doc/pub/DimRed/html/DimRed-reveal.html
+++ b/doc/pub/DimRed/html/DimRed-reveal.html
@@ -1143,6 +1143,9 @@ low-dimensional encoding of the data is then given by a set of vectors
 \( \boldsymbol{z}_i \) with at most \( l \) vectors, with \( l < < p \), defined by the
 orthogonal projection of the data onto the columns spanned by the
 eigenvectors of the covariance(correlations matrix).
+
+<p>
+The proof which follows will be updated by mid January 2020.
 </section>
 
 
@@ -1298,8 +1301,7 @@ This material will be added by mid January 2020.
 
 <section>
 <h2 id="___sec26">Principal Component Analysis </h2>
-<div class="alert alert-block alert-block alert-text-normal">
-<b></b>
+
 <p>
 Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.
 First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.
@@ -1477,9 +1479,6 @@ Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. Th
 algorithm that quickly finds an approximation of the first d principal components. Its computational
 complexity is \( O(m \times d^2)+O(d^3) \), instead of \( O(m \times n^2) + O(n^3) \), so it is dramatically faster than the
 previous algorithms when \( d \) is much smaller than \( n \).
-
-
-</div>
 </section>
 
 
diff --git a/doc/pub/DimRed/html/DimRed-solarized.html b/doc/pub/DimRed/html/DimRed-solarized.html
index af3fb6759..f34ee2991 100644
--- a/doc/pub/DimRed/html/DimRed-solarized.html
+++ b/doc/pub/DimRed/html/DimRed-solarized.html
@@ -1115,6 +1115,9 @@ low-dimensional encoding of the data is then given by a set of vectors
 orthogonal projection of the data onto the columns spanned by the
 eigenvectors of the covariance(correlations matrix).
 
+<p>
+The proof which follows will be updated by mid January 2020.
+
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
@@ -1245,8 +1248,7 @@ This material will be added by mid January 2020.
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
 <h2 id="___sec26">Principal Component Analysis </h2>
-<div class="alert alert-block alert-block alert-text-normal">
-<b></b>
+
 <p>
 Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.
 First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.
@@ -1257,7 +1259,7 @@ training set, then extracts the first two principal components. First we center
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eee8d5"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">IPython.display</span> <span style="color: #8B008B; font-weight: bold">import</span> display
 np.random.seed(<span style="color: #B452CD">100</span>)
@@ -1294,7 +1296,7 @@ Selecting this hyperplane ensures that the projection will preserve as much vari
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eee8d5"><pre style="line-height: 125%"><span></span>W2 = V.T[:, :<span style="color: #B452CD">2</span>]
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>W2 = V.T[:, :<span style="color: #B452CD">2</span>]
 X2D = X_centered.dot(W2)
 </pre></div>
 <p>
@@ -1309,7 +1311,7 @@ that it automatically takes care of centering the data):
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eee8d5"><pre style="line-height: 125%"><span></span><span style="color: #228B22">#thereafter we do a PCA with Scikit-learn</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22">#thereafter we do a PCA with Scikit-learn</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.decomposition</span> <span style="color: #8B008B; font-weight: bold">import</span> PCA
 pca = PCA(n_components = <span style="color: #B452CD">2</span>)
 X2D = pca.fit_transform(X)
@@ -1322,7 +1324,7 @@ principal component is equal to
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eee8d5"><pre style="line-height: 125%"><span></span>pca.components_.T[:, <span style="color: #B452CD">0</span>].
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>pca.components_.T[:, <span style="color: #B452CD">0</span>].
 </pre></div>
 <p>
 Another very useful piece of information is the explained variance ratio of each principal component,
@@ -1338,7 +1340,7 @@ Here we compute performance scores on the training data using logistic regressio
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eee8d5"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
 <span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span>  train_test_split 
 <span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.datasets</span> <span style="color: #8B008B; font-weight: bold">import</span> load_breast_cancer
@@ -1385,7 +1387,7 @@ of dimensions required to preserve 95% of the training set&#8217;s variance:
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eee8d5"><pre style="line-height: 125%"><span></span>pca = PCA()
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>pca = PCA()
 pca.fit(X)
 cumsum = np.cumsum(pca.explained_variance_ratio_)
 d = np.argmax(cumsum &gt;= <span style="color: #B452CD">0.95</span>) + <span style="color: #B452CD">1</span>
@@ -1397,7 +1399,7 @@ a float between 0.0 and 1.0, indicating the ratio of variance you wish to preser
 <p>
 
 <!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
-<div class="highlight" style="background: #eee8d5"><pre style="line-height: 125%"><span></span>pca = PCA(n_components=<span style="color: #B452CD">0.95</span>)
+<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>pca = PCA(n_components=<span style="color: #B452CD">0.95</span>)
 X_reduced = pca.fit_transform(X)
 </pre></div>
 <p>
@@ -1423,10 +1425,6 @@ algorithm that quickly finds an approximation of the first d principal component
 complexity is \( O(m \times d^2)+O(d^3) \), instead of \( O(m \times n^2) + O(n^3) \), so it is dramatically faster than the
 previous algorithms when \( d \) is much smaller than \( n \).
 
-
-</div>
-
-
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
diff --git a/doc/pub/DimRed/html/DimRed.html b/doc/pub/DimRed/html/DimRed.html
index e9a79a081..e5348ddef 100644
--- a/doc/pub/DimRed/html/DimRed.html
+++ b/doc/pub/DimRed/html/DimRed.html
@@ -1120,6 +1120,9 @@ low-dimensional encoding of the data is then given by a set of vectors
 orthogonal projection of the data onto the columns spanned by the
 eigenvectors of the covariance(correlations matrix).
 
+<p>
+The proof which follows will be updated by mid January 2020.
+
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
@@ -1250,8 +1253,7 @@ This material will be added by mid January 2020.
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
 <h2 id="___sec26">Principal Component Analysis </h2>
-<div class="alert alert-block alert-block alert-text-normal">
-<b></b>
+
 <p>
 Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.
 First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.
@@ -1428,10 +1430,6 @@ algorithm that quickly finds an approximation of the first d principal component
 complexity is \( O(m \times d^2)+O(d^3) \), instead of \( O(m \times n^2) + O(n^3) \), so it is dramatically faster than the
 previous algorithms when \( d \) is much smaller than \( n \).
 
-
-</div>
-
-
 <p>
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 
diff --git a/doc/pub/DimRed/ipynb/DimRed.ipynb b/doc/pub/DimRed/ipynb/DimRed.ipynb
index ec03b06a5..da58c850c 100644
--- a/doc/pub/DimRed/ipynb/DimRed.ipynb
+++ b/doc/pub/DimRed/ipynb/DimRed.ipynb
@@ -1253,7 +1253,7 @@
     "orthogonal projection of the data onto the columns spanned by the\n",
     "eigenvectors of the covariance(correlations matrix).\n",
     "\n",
-    "\n",
+    "The proof which follows will be updated by mid January 2020.\n",
     "\n",
     "## Proof of the PCA Theorem\n",
     "\n",
@@ -1492,6 +1492,7 @@
     "\n",
     "\n",
     "## Principal Component Analysis\n",
+    "\n",
     "Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.\n",
     "First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.\n",
     "\n",
diff --git a/doc/pub/DimRed/ipynb/ipynb-DimRed-src.tar.gz b/doc/pub/DimRed/ipynb/ipynb-DimRed-src.tar.gz
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diff --git a/doc/pub/DimRed/pdf/DimRed-minted.pdf b/doc/pub/DimRed/pdf/DimRed-minted.pdf
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z^>?RU%dzw*-24Z?1SnAR=7eJUsjEADK81b2;w&22{9gw&r3DHVo`ns8l2Tkz0^xrF
D;PCL_

diff --git a/doc/src/DimRed/DimRed.do.txt b/doc/src/DimRed/DimRed.do.txt
index 621e66422..d347bf325 100644
--- a/doc/src/DimRed/DimRed.do.txt
+++ b/doc/src/DimRed/DimRed.do.txt
@@ -872,7 +872,7 @@ $\bm{z}_i$ with at most $l$ vectors, with $l << p$, defined by the
 orthogonal projection of the data onto the columns spanned by the
 eigenvectors of the covariance(correlations matrix).
 
-
+The proof which follows will be updated by mid January 2020.
 
 !split
 ===== Proof of the PCA Theorem  =====
@@ -1001,7 +1001,7 @@ This material will be added by mid January 2020.
 
 !split
 ===== Principal Component Analysis =====
-!bblock
+
 Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.
 First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.
 
@@ -1148,7 +1148,6 @@ complexity is $O(m \times d^2)+O(d^3)$, instead of $O(m \times n^2) + O(n^3)$, s
 previous algorithms when $d$ is much smaller than $n$.
 
 
-!eblock
 
 
 !split