From 40b80b0ba09993992c966047b0adfef121f4ae2b Mon Sep 17 00:00:00 2001
From: leosoccio <lss5473@psu.edu>
Date: Sun, 29 Jan 2023 01:33:12 -0500
Subject: [PATCH] finished version of the assignment

---
 .gitignore        |   4 +
 hw-1-soccio.Rproj |  13 ++
 index.html        | 362 ++++++++++++++++++++++++++++++++++------------
 index.pdf         | Bin 175623 -> 184392 bytes
 index.qmd         | 269 ++++++++++++++++++++--------------
 5 files changed, 452 insertions(+), 196 deletions(-)
 create mode 100644 .gitignore
 create mode 100644 hw-1-soccio.Rproj
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..5b6a065
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,4 @@
+.Rproj.user
+.Rhistory
+.RData
+.Ruserdata
diff --git a/hw-1-soccio.Rproj b/hw-1-soccio.Rproj
new file mode 100644
index 0000000..8e3c2eb
--- /dev/null
+++ b/hw-1-soccio.Rproj
@@ -0,0 +1,13 @@
+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
+
+RnwWeave: Sweave
+LaTeX: pdfLaTeX
diff --git a/index.html b/index.html
index 3a108ac..e8899ee 100644
--- a/index.html
+++ b/index.html
@@ -2,11 +2,11 @@
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head>
 
 <meta charset="utf-8">
-<meta name="generator" content="quarto-1.2.313">
+<meta name="generator" content="quarto-1.2.269">
 
 <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
 
-<meta name="author" content="Insert your name here">
+<meta name="author" content="Leo Soccio">
 
 <title>Homework 1</title>
 <style>
@@ -117,7 +117,7 @@ <h1 class="title">Homework 1</h1>
       <div>
       <div class="quarto-title-meta-heading">Author</div>
       <div class="quarto-title-meta-contents">
-               <p><span style="background-color: yellow;">Insert your name here</span> </p>
+               <p><span style="background-color: yellow;">Leo Soccio</span> </p>
             </div>
     </div>
       
@@ -132,7 +132,8 @@ <h1 class="title">Homework 1</h1>
     <h2 id="toc-title">Table of contents</h2>
    
   <ul>
-  <li><a href="#question-1" id="toc-question-1" class="nav-link active" data-scroll-target="#question-1">Question 1</a></li>
+  <li><a href="#section" id="toc-section" class="nav-link active" data-scroll-target="#section"><br><br><br><br></a></li>
+  <li><a href="#question-1" id="toc-question-1" class="nav-link" data-scroll-target="#question-1">Question 1</a></li>
   <li><a href="#question-2" id="toc-question-2" class="nav-link" data-scroll-target="#question-2">Question 2</a></li>
   <li><a href="#question-3" id="toc-question-3" class="nav-link" data-scroll-target="#question-3">Question 3</a></li>
   <li><a href="#appendix" id="toc-appendix" class="nav-link" data-scroll-target="#appendix">Appendix</a></li>
@@ -144,7 +145,7 @@ <h2 id="toc-title">Table of contents</h2>
 
 
 
-<p><a href="https://github.com/psu-stat380/hw-1">Link to the Github repository</a></p>
+<p><a href="https://github.com/leosoccio/hw-1-soccio">Link to the Github repository</a></p>
 <hr>
 <div class="callout-important callout callout-style-default callout-captioned">
 <div class="callout-header d-flex align-content-center">
@@ -169,8 +170,9 @@ <h2 id="toc-title">Table of contents</h2>
 <p>⚠️ Please add your name to the the author information in the frontmatter before submitting your assignment.</p>
 </div>
 </div>
-<p><br><br><br><br></p>
-<hr>
+<section id="section" class="level2">
+<h2 class="anchored" data-anchor-id="section"><br><br><br><br></h2>
+</section>
 <section id="question-1" class="level2">
 <h2 class="anchored" data-anchor-id="question-1">Question 1</h2>
 <div class="callout-tip callout callout-style-default callout-captioned">
@@ -211,8 +213,7 @@ <h2 class="anchored" data-anchor-id="question-1">Question 1</h2>
 <p>Remember to <strong>include your name</strong> in the pull request information!</p></li>
 </ol>
 <p>If you’re stuck at any step along the way, you can refer to the <a href="https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/proposing-changes-to-your-work-with-pull-requests/creating-a-pull-request-from-a-fork">official Github docs here</a></p>
-<p><br><br><br><br> <br><br><br><br></p>
-<hr>
+<p><br><br><br><br> <br><br><br><br> —</p>
 </section>
 <section id="question-2" class="level2">
 <h2 class="anchored" data-anchor-id="question-2">Question 2</h2>
@@ -246,18 +247,61 @@ <h2 class="anchored" data-anchor-id="question-2">Question 2</h2>
 </div>
 <p>For the following questions, provide your answers in a code cell.</p>
 <ol type="1">
-<li><p>What data type does the vector contain?</p></li>
-<li><p>Create two new vectors called <code>my_vec_double</code> and <code>my_vec_int</code> which converts <code>my_vec</code> to Double &amp; Integer types, respectively,</p></li>
+<li>What data type does the vector contain?</li>
+</ol>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="fu">typeof</span>(my_vec)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>[1] "character"</code></pre>
+</div>
+<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="co"># the vector contains character data</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<ol start="2" type="1">
+<li>Create two new vectors called <code>my_vec_double</code> and <code>my_vec_int</code> which converts <code>my_vec</code> to Double &amp; Integer types, respectively,</li>
+</ol>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>my_vec_double <span class="ot">&lt;-</span> <span class="fu">as.double</span>(my_vec)</span>
+<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>my_vec_double</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code> [1]  0.07 -0.07  0.25 -0.84  0.32 -0.24 -0.97 -0.36  1.76 -0.36</code></pre>
+</div>
+<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>my_vec_int <span class="ot">&lt;-</span> <span class="fu">as.integer</span>(my_vec)</span>
+<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>my_vec_int</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code> [1] 0 0 0 0 0 0 0 0 1 0</code></pre>
+</div>
+</div>
+<ol start="3" type="1">
 <li><p>Create a new vector <code>my_vec_bool</code> which comprises of:</p>
 <ul>
-<li><code>TRUE</code>if an element in <code>my_vec_double</code> is <span class="math inline">\(\le 0\)</span></li>
-<li><code>FALSE</code> if an element in <code>my_vec_double</code> is <span class="math inline">\(\ge 0\)</span></li>
+<li>TRUEif an element in <code>my_vec_double</code> is <span class="math inline">\(\le 0\)</span></li>
+<li>FALSE if an element in <code>my_vec_double</code> is <span class="math inline">\(\ge 0\)</span></li>
 </ul>
 <p>How many elements of <code>my_vec_double</code> are greater than zero?</p></li>
-<li><p>Sort the values of <code>my_vec_double</code> in ascending order.</p></li>
 </ol>
-<p><br><br><br><br> <br><br><br><br></p>
-<hr>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>my_vec_bool <span class="ot">&lt;-</span> <span class="fu">ifelse</span>(my_vec_double<span class="sc">&lt;=</span><span class="dv">0</span>,<span class="cn">TRUE</span>,<span class="cn">FALSE</span>)</span>
+<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a>my_vec_bool</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code> [1] FALSE  TRUE FALSE  TRUE FALSE  TRUE  TRUE  TRUE FALSE  TRUE</code></pre>
+</div>
+<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="fu">length</span>(my_vec_bool)<span class="sc">-</span><span class="fu">sum</span>(my_vec_bool)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>[1] 4</code></pre>
+</div>
+<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="co"># while I could also simply count it, this command shows that there are </span></span>
+<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a><span class="co"># 4 values in my_vec_double that are greater than 0.</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<ol start="4" type="1">
+<li>Sort the values of <code>my_vec_double</code> in ascending order.</li>
+</ol>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb16"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="fu">sort</span>(my_vec_double)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code> [1] -0.97 -0.84 -0.36 -0.36 -0.24 -0.07  0.07  0.25  0.32  1.76</code></pre>
+</div>
+</div>
+<p><br><br><br><br> <br><br><br><br> —</p>
 </section>
 <section id="question-3" class="level2">
 <h2 class="anchored" data-anchor-id="question-3">Question 3</h2>
@@ -302,84 +346,157 @@ <h2 class="anchored" data-anchor-id="question-3">Question 3</h2>
 <p>Recall the discussion in class on how <code>R</code> fills in matrices</p>
 </div>
 </div>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>m1 <span class="ot">&lt;-</span><span class="fu">matrix</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">9</span>, <span class="at">nrow=</span><span class="dv">3</span>, <span class="at">byrow =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a>m1</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>     [,1] [,2] [,3]
+[1,]    1    2    3
+[2,]    4    5    6
+[3,]    7    8    9</code></pre>
+</div>
+<div class="sourceCode cell-code" id="cb20"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>m2 <span class="ot">&lt;-</span> <span class="fu">matrix</span>(<span class="fu">c</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">100</span>,(<span class="dv">1</span><span class="sc">:</span><span class="dv">100</span>)<span class="sc">^</span><span class="dv">2</span>), <span class="at">nrow=</span><span class="dv">2</span>, <span class="at">byrow=</span><span class="cn">TRUE</span>)</span>
+<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a>m2</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
+[1,]    1    2    3    4    5    6    7    8    9    10    11    12    13    14
+[2,]    1    4    9   16   25   36   49   64   81   100   121   144   169   196
+     [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
+[1,]    15    16    17    18    19    20    21    22    23    24    25    26
+[2,]   225   256   289   324   361   400   441   484   529   576   625   676
+     [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
+[1,]    27    28    29    30    31    32    33    34    35    36    37    38
+[2,]   729   784   841   900   961  1024  1089  1156  1225  1296  1369  1444
+     [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49] [,50]
+[1,]    39    40    41    42    43    44    45    46    47    48    49    50
+[2,]  1521  1600  1681  1764  1849  1936  2025  2116  2209  2304  2401  2500
+     [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61] [,62]
+[1,]    51    52    53    54    55    56    57    58    59    60    61    62
+[2,]  2601  2704  2809  2916  3025  3136  3249  3364  3481  3600  3721  3844
+     [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73] [,74]
+[1,]    63    64    65    66    67    68    69    70    71    72    73    74
+[2,]  3969  4096  4225  4356  4489  4624  4761  4900  5041  5184  5329  5476
+     [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85] [,86]
+[1,]    75    76    77    78    79    80    81    82    83    84    85    86
+[2,]  5625  5776  5929  6084  6241  6400  6561  6724  6889  7056  7225  7396
+     [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97] [,98]
+[1,]    87    88    89    90    91    92    93    94    95    96    97    98
+[2,]  7569  7744  7921  8100  8281  8464  8649  8836  9025  9216  9409  9604
+     [,99] [,100]
+[1,]    99    100
+[2,]  9801  10000</code></pre>
+</div>
+</div>
 <p>In the next part, we will discover how knowledge of the way in which a matrix is stored in memory can inform better code choices. To this end, the following function takes an input <span class="math inline">\(n\)</span> and creates an <span class="math inline">\(n \times n\)</span> matrix with random entries.</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>generate_matrix <span class="ot">&lt;-</span> <span class="cf">function</span>(n){</span>
-<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>    <span class="fu">return</span>(</span>
-<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>        <span class="fu">matrix</span>(</span>
-<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a>            <span class="fu">rnorm</span>(n<span class="sc">^</span><span class="dv">2</span>),</span>
-<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a>            <span class="at">nrow=</span>n</span>
-<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a>        )</span>
-<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a>    )</span>
-<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb22"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a>generate_matrix <span class="ot">&lt;-</span> <span class="cf">function</span>(n){</span>
+<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a>    <span class="fu">return</span>(</span>
+<span id="cb22-3"><a href="#cb22-3" aria-hidden="true" tabindex="-1"></a>        <span class="fu">matrix</span>(</span>
+<span id="cb22-4"><a href="#cb22-4" aria-hidden="true" tabindex="-1"></a>            <span class="fu">rnorm</span>(n<span class="sc">^</span><span class="dv">2</span>),</span>
+<span id="cb22-5"><a href="#cb22-5" aria-hidden="true" tabindex="-1"></a>            <span class="at">nrow=</span>n</span>
+<span id="cb22-6"><a href="#cb22-6" aria-hidden="true" tabindex="-1"></a>        )</span>
+<span id="cb22-7"><a href="#cb22-7" aria-hidden="true" tabindex="-1"></a>    )</span>
+<span id="cb22-8"><a href="#cb22-8" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>For example:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="fu">generate_matrix</span>(<span class="dv">4</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb23"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="fu">generate_matrix</span>(<span class="dv">4</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>           [,1]       [,2]       [,3]        [,4]
-[1,]  0.6398861 0.35207981 -0.6863098 -0.01839937
-[2,]  0.7613301 0.72302916  1.5097731  0.48976233
-[3,] -0.2608060 0.53979026 -1.0638331 -0.42020192
-[4,]  0.6602682 0.08892854  2.3460769  0.03895466</code></pre>
+<pre><code>           [,1]       [,2]        [,3]       [,4]
+[1,]  1.0544098  0.6387515  0.03942737  0.8625123
+[2,] -1.4516515 -0.5373230 -0.09179662  0.5565093
+[3,] -1.5693012  0.2786405  0.07841723  0.4738225
+[4,] -0.0407414 -1.4366085 -0.66828431 -0.7313053</code></pre>
 </div>
 </div>
 <p>Let <code>M</code> be a fixed <span class="math inline">\(50 \times 50\)</span> matrix</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>M <span class="ot">&lt;-</span> <span class="fu">generate_matrix</span>(<span class="dv">50</span>)</span>
-<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="fu">mean</span>(M)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb25"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a>M <span class="ot">&lt;-</span> <span class="fu">generate_matrix</span>(<span class="dv">50</span>)</span>
+<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a><span class="fu">mean</span>(M)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>[1] 0.03185503</code></pre>
+<pre><code>[1] 0.01104578</code></pre>
 </div>
 </div>
 <ol start="2" type="1">
 <li>Write a function <code>row_wise_scan</code> which scans the entries of <code>M</code> one row after another and outputs the number of elements whose value is <span class="math inline">\(\ge 0\)</span>. You can use the following <strong>starter code</strong></li>
 </ol>
-<div class="sourceCode" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>row_wise_scan <span class="ot">&lt;-</span> <span class="cf">function</span>(x){</span>
-<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>    n <span class="ot">&lt;-</span> <span class="fu">nrow</span>(x)</span>
-<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a>    m <span class="ot">&lt;-</span> <span class="fu">ncol</span>(x)</span>
-<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Insert your code here</span></span>
-<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a>    count <span class="ot">&lt;-</span> <span class="dv">0</span></span>
-<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a>    <span class="cf">for</span>(...){</span>
-<span id="cb9-8"><a href="#cb9-8" aria-hidden="true" tabindex="-1"></a>        <span class="cf">for</span>(...){</span>
-<span id="cb9-9"><a href="#cb9-9" aria-hidden="true" tabindex="-1"></a>            <span class="cf">if</span>(...){</span>
-<span id="cb9-10"><a href="#cb9-10" aria-hidden="true" tabindex="-1"></a>                count <span class="ot">&lt;-</span> count <span class="sc">+</span> <span class="dv">1</span> </span>
-<span id="cb9-11"><a href="#cb9-11" aria-hidden="true" tabindex="-1"></a>            }</span>
-<span id="cb9-12"><a href="#cb9-12" aria-hidden="true" tabindex="-1"></a>        }</span>
-<span id="cb9-13"><a href="#cb9-13" aria-hidden="true" tabindex="-1"></a>    }</span>
-<span id="cb9-14"><a href="#cb9-14" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb9-15"><a href="#cb9-15" aria-hidden="true" tabindex="-1"></a>    <span class="fu">return</span>(count)</span>
-<span id="cb9-16"><a href="#cb9-16" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb27"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a>row_wise_scan <span class="ot">&lt;-</span> <span class="cf">function</span>(x){</span>
+<span id="cb27-2"><a href="#cb27-2" aria-hidden="true" tabindex="-1"></a>    n <span class="ot">&lt;-</span> <span class="fu">nrow</span>(x)</span>
+<span id="cb27-3"><a href="#cb27-3" aria-hidden="true" tabindex="-1"></a>    m <span class="ot">&lt;-</span> <span class="fu">ncol</span>(x)</span>
+<span id="cb27-4"><a href="#cb27-4" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb27-5"><a href="#cb27-5" aria-hidden="true" tabindex="-1"></a>    count <span class="ot">&lt;-</span> <span class="dv">0</span></span>
+<span id="cb27-6"><a href="#cb27-6" aria-hidden="true" tabindex="-1"></a>    <span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span>n){</span>
+<span id="cb27-7"><a href="#cb27-7" aria-hidden="true" tabindex="-1"></a>        <span class="cf">for</span>(j <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span>m){</span>
+<span id="cb27-8"><a href="#cb27-8" aria-hidden="true" tabindex="-1"></a>            <span class="cf">if</span>(x[i,j]<span class="sc">&gt;=</span><span class="dv">0</span>){</span>
+<span id="cb27-9"><a href="#cb27-9" aria-hidden="true" tabindex="-1"></a>                count <span class="ot">&lt;-</span> count <span class="sc">+</span> <span class="dv">1</span> </span>
+<span id="cb27-10"><a href="#cb27-10" aria-hidden="true" tabindex="-1"></a>            }</span>
+<span id="cb27-11"><a href="#cb27-11" aria-hidden="true" tabindex="-1"></a>        }</span>
+<span id="cb27-12"><a href="#cb27-12" aria-hidden="true" tabindex="-1"></a>    }</span>
+<span id="cb27-13"><a href="#cb27-13" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb27-14"><a href="#cb27-14" aria-hidden="true" tabindex="-1"></a>    <span class="fu">return</span>(count)</span>
+<span id="cb27-15"><a href="#cb27-15" aria-hidden="true" tabindex="-1"></a>}</span>
+<span id="cb27-16"><a href="#cb27-16" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb27-17"><a href="#cb27-17" aria-hidden="true" tabindex="-1"></a>test <span class="ot">&lt;-</span> <span class="fu">matrix</span>(my_vec_double, <span class="at">nrow=</span><span class="dv">2</span>)</span>
+<span id="cb27-18"><a href="#cb27-18" aria-hidden="true" tabindex="-1"></a><span class="fu">row_wise_scan</span>(test)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>[1] 4</code></pre>
+</div>
+<div class="sourceCode cell-code" id="cb29"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a><span class="co"># seems to be working, I've never used for loops before so this took a bit of googling</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
 <ol start="3" type="1">
 <li>Similarly, write a function <code>col_wise_scan</code> which does exactly the same thing but scans the entries of <code>M</code> one column after another</li>
 </ol>
-<div class="sourceCode" id="cb10"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>col_wise_scan <span class="ot">&lt;-</span> <span class="cf">function</span>(x){</span>
-<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>    count <span class="ot">&lt;-</span> <span class="dv">0</span></span>
-<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>    </span>
-<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a>    ... <span class="co"># Insert your code here</span></span>
-<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb10-6"><a href="#cb10-6" aria-hidden="true" tabindex="-1"></a>    <span class="fu">return</span>(count)</span>
-<span id="cb10-7"><a href="#cb10-7" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb30"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a>col_wise_scan <span class="ot">&lt;-</span> <span class="cf">function</span>(x){</span>
+<span id="cb30-2"><a href="#cb30-2" aria-hidden="true" tabindex="-1"></a>    n <span class="ot">&lt;-</span> <span class="fu">nrow</span>(x)</span>
+<span id="cb30-3"><a href="#cb30-3" aria-hidden="true" tabindex="-1"></a>    m <span class="ot">&lt;-</span> <span class="fu">ncol</span>(x)</span>
+<span id="cb30-4"><a href="#cb30-4" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb30-5"><a href="#cb30-5" aria-hidden="true" tabindex="-1"></a>    count <span class="ot">&lt;-</span> <span class="dv">0</span></span>
+<span id="cb30-6"><a href="#cb30-6" aria-hidden="true" tabindex="-1"></a>    <span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span>m){</span>
+<span id="cb30-7"><a href="#cb30-7" aria-hidden="true" tabindex="-1"></a>        <span class="cf">for</span>(j <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span>n){</span>
+<span id="cb30-8"><a href="#cb30-8" aria-hidden="true" tabindex="-1"></a>            <span class="cf">if</span>(x[j,i]<span class="sc">&gt;=</span><span class="dv">0</span>){</span>
+<span id="cb30-9"><a href="#cb30-9" aria-hidden="true" tabindex="-1"></a>                count <span class="ot">&lt;-</span> count <span class="sc">+</span> <span class="dv">1</span> </span>
+<span id="cb30-10"><a href="#cb30-10" aria-hidden="true" tabindex="-1"></a>            }</span>
+<span id="cb30-11"><a href="#cb30-11" aria-hidden="true" tabindex="-1"></a>        }</span>
+<span id="cb30-12"><a href="#cb30-12" aria-hidden="true" tabindex="-1"></a>    }</span>
+<span id="cb30-13"><a href="#cb30-13" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb30-14"><a href="#cb30-14" aria-hidden="true" tabindex="-1"></a>    <span class="fu">return</span>(count)</span>
+<span id="cb30-15"><a href="#cb30-15" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
 <p>You can check if your code is doing what it’s supposed to using the function here<a href="#fn1" class="footnote-ref" id="fnref1" role="doc-noteref"><sup>1</sup></a></p>
 <ol start="4" type="1">
-<li><p>Between <code>col_wise_scan</code> and <code>row_wise_scan</code>, which function do you expect to take shorter to run? Why?</p></li>
-<li><p>Write a function <code>time_scan</code> which takes in a method <code>f</code> and a matrix <code>M</code> and outputs the amount of time taken to run <code>f(M)</code></p></li>
+<li>Between <code>col_wise_scan</code> and <code>row_wise_scan</code>, which function do you expect to take shorter to run? Why?</li>
 </ol>
-<div class="sourceCode" id="cb12"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>time_scan <span class="ot">&lt;-</span> <span class="cf">function</span>(f, M){</span>
-<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>    initial_time <span class="ot">&lt;-</span> ... <span class="co"># Write your code here</span></span>
-<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a>    <span class="fu">f</span>(M)</span>
-<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a>    final_time <span class="ot">&lt;-</span> ...  <span class="co"># Write your code here</span></span>
-<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a>    </span>
-<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a>    total_time_taken <span class="ot">&lt;-</span> final_time <span class="sc">-</span> initial_time</span>
-<span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a>    <span class="fu">return</span>(total_time_taken)</span>
-<span id="cb12-8"><a href="#cb12-8" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<p>I expect col_wise_scan to take a shorter amount of time. As discussed in class, R stores all entries of a column at one point in memory, so it can very quickly move from one entry in a column to another. However, because the data is organized by column, moving across a row means that R must jump around between different points in memory, causing the function to take much longer.</p>
+<ol start="5" type="1">
+<li>Write a function <code>time_scan</code> which takes in a method <code>f</code> and a matrix <code>M</code> and outputs the amount of time taken to run <code>f(M)</code></li>
+</ol>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb37"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb37-1"><a href="#cb37-1" aria-hidden="true" tabindex="-1"></a>time_scan <span class="ot">&lt;-</span> <span class="cf">function</span>(f, M){</span>
+<span id="cb37-2"><a href="#cb37-2" aria-hidden="true" tabindex="-1"></a>    initial_time <span class="ot">&lt;-</span> <span class="fu">Sys.time</span>()</span>
+<span id="cb37-3"><a href="#cb37-3" aria-hidden="true" tabindex="-1"></a>    <span class="fu">f</span>(M)</span>
+<span id="cb37-4"><a href="#cb37-4" aria-hidden="true" tabindex="-1"></a>    final_time <span class="ot">&lt;-</span> <span class="fu">Sys.time</span>()</span>
+<span id="cb37-5"><a href="#cb37-5" aria-hidden="true" tabindex="-1"></a>    </span>
+<span id="cb37-6"><a href="#cb37-6" aria-hidden="true" tabindex="-1"></a>    total_time_taken <span class="ot">&lt;-</span> final_time <span class="sc">-</span> initial_time</span>
+<span id="cb37-7"><a href="#cb37-7" aria-hidden="true" tabindex="-1"></a>    <span class="fu">return</span>(total_time_taken)</span>
+<span id="cb37-8"><a href="#cb37-8" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
 <p>Provide your output to</p>
-<div class="sourceCode" id="cb13"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="fu">list</span>(</span>
-<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>    <span class="at">row_wise_time =</span> <span class="fu">time_scan</span>(row_wise_scan, M),</span>
-<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a>    <span class="at">col_wise_time =</span> <span class="fu">time_scan</span>(row_wise_scan, M)</span>
-<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
-<p>Which took longer to run?</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb38"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb38-1"><a href="#cb38-1" aria-hidden="true" tabindex="-1"></a><span class="fu">list</span>(</span>
+<span id="cb38-2"><a href="#cb38-2" aria-hidden="true" tabindex="-1"></a>    <span class="at">row_wise_time =</span> <span class="fu">time_scan</span>(row_wise_scan, M),</span>
+<span id="cb38-3"><a href="#cb38-3" aria-hidden="true" tabindex="-1"></a>    <span class="at">col_wise_time =</span> <span class="fu">time_scan</span>(row_wise_scan, M)</span>
+<span id="cb38-4"><a href="#cb38-4" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>$row_wise_time
+Time difference of 0.0001490116 secs
+
+$col_wise_time
+Time difference of 0.0001502037 secs</code></pre>
+</div>
+</div>
+<p>Which took longer to run? row_wise_time() took longer to run as I expected.</p>
 <ol start="6" type="1">
 <li>Repeat this experiment now when:
 <ul>
@@ -388,36 +505,81 @@ <h2 class="anchored" data-anchor-id="question-3">Question 3</h2>
 <li><code>M</code> is a <span class="math inline">\(5000 \times 5000\)</span> matrix</li>
 </ul></li>
 </ol>
-<p>What can you conclude?</p>
-<p><br><br><br><br> <br><br><br><br></p>
-<hr>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb40"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb40-1"><a href="#cb40-1" aria-hidden="true" tabindex="-1"></a>M100 <span class="ot">&lt;-</span> <span class="fu">generate_matrix</span>(<span class="dv">100</span>)</span>
+<span id="cb40-2"><a href="#cb40-2" aria-hidden="true" tabindex="-1"></a><span class="fu">list</span>(</span>
+<span id="cb40-3"><a href="#cb40-3" aria-hidden="true" tabindex="-1"></a>    <span class="at">row_wise_time =</span> <span class="fu">time_scan</span>(row_wise_scan, M100),</span>
+<span id="cb40-4"><a href="#cb40-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">col_wise_time =</span> <span class="fu">time_scan</span>(row_wise_scan, M100)</span>
+<span id="cb40-5"><a href="#cb40-5" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>$row_wise_time
+Time difference of 0.0009231567 secs
+
+$col_wise_time
+Time difference of 0.0006430149 secs</code></pre>
+</div>
+<div class="sourceCode cell-code" id="cb42"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb42-1"><a href="#cb42-1" aria-hidden="true" tabindex="-1"></a>M1000 <span class="ot">&lt;-</span> <span class="fu">generate_matrix</span>(<span class="dv">1000</span>)</span>
+<span id="cb42-2"><a href="#cb42-2" aria-hidden="true" tabindex="-1"></a><span class="fu">list</span>(</span>
+<span id="cb42-3"><a href="#cb42-3" aria-hidden="true" tabindex="-1"></a>    <span class="at">row_wise_time =</span> <span class="fu">time_scan</span>(row_wise_scan, M1000),</span>
+<span id="cb42-4"><a href="#cb42-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">col_wise_time =</span> <span class="fu">time_scan</span>(row_wise_scan, M1000)</span>
+<span id="cb42-5"><a href="#cb42-5" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>$row_wise_time
+Time difference of 0.06362605 secs
+
+$col_wise_time
+Time difference of 0.06419706 secs</code></pre>
+</div>
+<div class="sourceCode cell-code" id="cb44"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb44-1"><a href="#cb44-1" aria-hidden="true" tabindex="-1"></a>M5000 <span class="ot">&lt;-</span> <span class="fu">generate_matrix</span>(<span class="dv">5000</span>)</span>
+<span id="cb44-2"><a href="#cb44-2" aria-hidden="true" tabindex="-1"></a><span class="fu">list</span>(</span>
+<span id="cb44-3"><a href="#cb44-3" aria-hidden="true" tabindex="-1"></a>    <span class="at">row_wise_time =</span> <span class="fu">time_scan</span>(row_wise_scan, M5000),</span>
+<span id="cb44-4"><a href="#cb44-4" aria-hidden="true" tabindex="-1"></a>    <span class="at">col_wise_time =</span> <span class="fu">time_scan</span>(row_wise_scan, M5000)</span>
+<span id="cb44-5"><a href="#cb44-5" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>$row_wise_time
+Time difference of 1.836015 secs
+
+$col_wise_time
+Time difference of 1.690508 secs</code></pre>
+</div>
+</div>
+<p>What can you conclude? In general, it appears that looking at a matrix column-wise is slightly faster than looking at a matrix row-wise in R. Sometimes certain runs take longer column-wise than row-wise but I think this is attributed to variability in runtime of every function due to the amount of computing power available at any time fluctuating as my computer runs other processes outside of RStudio. If I were to run these functions many times over, column-wise functions would generally take less time than row-wise functions for the same matrix.</p>
+<p><br><br><br><br> <br><br><br><br> —</p>
 </section>
 <section id="appendix" class="level1">
 <h1>Appendix</h1>
 <p>Print your <code>R</code> session information using the following command</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="fu">sessionInfo</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb46"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb46-1"><a href="#cb46-1" aria-hidden="true" tabindex="-1"></a><span class="fu">sessionInfo</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>R version 4.2.2 (2022-10-31)
-Platform: x86_64-apple-darwin22.1.0 (64-bit)
-Running under: macOS Ventura 13.1
+<pre><code>R version 4.2.2 (2022-10-31 ucrt)
+Platform: x86_64-w64-mingw32/x64 (64-bit)
+Running under: Windows 10 x64 (build 22000)
 
 Matrix products: default
-BLAS:   /usr/local/Cellar/openblas/0.3.21/lib/libopenblasp-r0.3.21.dylib
-LAPACK: /usr/local/Cellar/r/4.2.2_1/lib/R/lib/libRlapack.dylib
 
 locale:
-[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
+[1] LC_COLLATE=English_United States.utf8 
+[2] LC_CTYPE=English_United States.utf8   
+[3] LC_MONETARY=English_United States.utf8
+[4] LC_NUMERIC=C                          
+[5] LC_TIME=English_United States.utf8    
 
 attached base packages:
 [1] stats     graphics  grDevices datasets  utils     methods   base     
 
+other attached packages:
+[1] dplyr_1.0.10
+
 loaded via a namespace (and not attached):
- [1] digest_0.6.31   lifecycle_1.0.3 jsonlite_1.8.4  magrittr_2.0.3 
- [5] evaluate_0.20   rlang_1.0.6     stringi_1.7.12  cli_3.6.0      
- [9] renv_0.16.0-53  vctrs_0.5.1     rmarkdown_2.20  tools_4.2.2    
-[13] stringr_1.5.0   glue_1.6.2      xfun_0.36       yaml_2.3.6     
-[17] fastmap_1.1.0   compiler_4.2.2  htmltools_0.5.4 knitr_1.41     </code></pre>
+ [1] rstudioapi_0.14  knitr_1.41       magrittr_2.0.3   tidyselect_1.2.0
+ [5] R6_2.5.1         rlang_1.0.6      fastmap_1.1.0    fansi_1.0.3     
+ [9] stringr_1.5.0    tools_4.2.2      xfun_0.36        utf8_1.2.2      
+[13] DBI_1.1.3        cli_3.6.0        htmltools_0.5.4  assertthat_0.2.1
+[17] yaml_2.3.6       digest_0.6.31    tibble_3.1.8     lifecycle_1.0.3 
+[21] vctrs_0.5.1      glue_1.6.2       evaluate_0.20    rmarkdown_2.20  
+[25] stringi_1.7.12   compiler_4.2.2   pillar_1.8.1     generics_0.1.3  
+[29] jsonlite_1.8.4   renv_0.16.0-53   pkgconfig_2.0.3 </code></pre>
 </div>
 </div>
 </section>
@@ -427,10 +589,30 @@ <h1>Appendix</h1>
 
 <ol>
 <li id="fn1"><p>If your code is right, the following code should evaluate to be <code>TRUE</code></p>
-<div class="sourceCode" id="cb11"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">sapply</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">100</span>, <span class="cf">function</span>(i) {</span>
-<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a>    x <span class="ot">&lt;-</span> <span class="fu">generate_matrix</span>(<span class="dv">100</span>)</span>
-<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a>    <span class="fu">row_wise_scan</span>(x) <span class="sc">==</span> <span class="fu">col_wise_scan</span>(x)</span>
-<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a>}) <span class="sc">%&gt;%</span> sum <span class="sc">==</span> <span class="dv">100</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb31"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(dplyr)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stderr">
+<pre><code>
+Attaching package: 'dplyr'</code></pre>
+</div>
+<div class="cell-output cell-output-stderr">
+<pre><code>The following objects are masked from 'package:stats':
+
+    filter, lag</code></pre>
+</div>
+<div class="cell-output cell-output-stderr">
+<pre><code>The following objects are masked from 'package:base':
+
+    intersect, setdiff, setequal, union</code></pre>
+</div>
+<div class="sourceCode cell-code" id="cb35"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb35-1"><a href="#cb35-1" aria-hidden="true" tabindex="-1"></a><span class="fu">sapply</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">100</span>, <span class="cf">function</span>(i) {</span>
+<span id="cb35-2"><a href="#cb35-2" aria-hidden="true" tabindex="-1"></a>    x <span class="ot">&lt;-</span> <span class="fu">generate_matrix</span>(<span class="dv">100</span>)</span>
+<span id="cb35-3"><a href="#cb35-3" aria-hidden="true" tabindex="-1"></a>    <span class="fu">row_wise_scan</span>(x) <span class="sc">==</span> <span class="fu">col_wise_scan</span>(x)</span>
+<span id="cb35-4"><a href="#cb35-4" aria-hidden="true" tabindex="-1"></a>}) <span class="sc">%&gt;%</span> sum <span class="sc">==</span> <span class="dv">100</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>[1] TRUE</code></pre>
+</div>
+</div>
 <a href="#fnref1" class="footnote-back" role="doc-backlink">↩︎</a></li>
 </ol>
 </section></div></main>
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diff --git a/index.qmd b/index.qmd
index 8fd36ac..da7c1a2 100644
--- a/index.qmd
+++ b/index.qmd
@@ -1,88 +1,84 @@
 ---
 title: "Homework 1"
-author: "[Insert your name here]{style='background-color: yellow;'}"
+author: "[Leo Soccio]{style='background-color: yellow;'}"
 toc: true
 title-block-banner: true
 title-block-style: default
-# format: html
-format: pdf
+format: html
+#format: pdf
 ---
 
-[Link to the Github repository](https://github.com/psu-stat380/hw-1)
-
----
-
-::: {.callout-important}
-## Due: Sun, Jan 29, 2023 @ 11:59pm
+[Link to the Github repository](https://github.com/leosoccio/hw-1-soccio)
 
+------------------------------------------------------------------------
 
+::: callout-important
+## Due: Sun, Jan 29, 2023 \@ 11:59pm
 
-Please read the instructions carefully before submitting your assignment. 
+Please read the instructions carefully before submitting your assignment.
 
-1. This assignment requires you to:
-    - Upload your Quarto markdown files to a `git` repository
-    - Upload a `PDF` file on Canvas
+1.  This assignment requires you to:
 
-1. Don't collapse any code cells before submitting. 
+    -   Upload your Quarto markdown files to a `git` repository
+    -   Upload a `PDF` file on Canvas
 
-1. Remember to make sure all your code output is rendered properly before uploading your submission.
+2.  Don't collapse any code cells before submitting.
 
+3.  Remember to make sure all your code output is rendered properly before uploading your submission.
 
-⚠️ Please add your name to the the author information in the frontmatter before submitting your assignment. 
+⚠️ Please add your name to the the author information in the frontmatter before submitting your assignment.
 :::
 
-<br><br><br><br>
----
+## <br><br><br><br>
 
 ## Question 1
-::: {.callout-tip}
+
+::: callout-tip
 ## 20 points
 :::
 
+In this question, we will walk through the process of *forking* a `git` repository and submitting a *pull request*.
 
-In this question, we will walk through the process of _forking_ a `git` repository and submitting a _pull request_. 
-
-1. Navigate to the Github repository [here](https://github.com/psu-stat380/hw-1) and fork it by clicking on the icon in the top right
+1.  Navigate to the Github repository [here](https://github.com/psu-stat380/hw-1) and fork it by clicking on the icon in the top right
 
 ![](images/fork.png)
 
-> Provide a sensible name for your forked repository when prompted. 
+> Provide a sensible name for your forked repository when prompted.
 
-2. Clone your Github repository on your local machine
+2.  Clone your Github repository on your local machine
 
-    ```bash
+    ``` bash
     $ git clone <<insert your repository url here>>
     $ cd hw-1
     ```
 
     Alternatively, you can use Github codespaces to get started from your repository directly.
 
-3. In order to activate the `R` environment for the homework, make sure you have `renv` installed beforehand. To activate the `renv` environment for this assignment, open an instance of the `R` console from within the directory and type
-    
-    ```R
+3.  In order to activate the `R` environment for the homework, make sure you have `renv` installed beforehand. To activate the `renv` environment for this assignment, open an instance of the `R` console from within the directory and type
+
+    ``` r
     renv::activate()
     ```
-    Follow the instrutions in order to make sure that `renv` is configured correctly. 
 
-4. Work on the _reminaing part_ of this assignment as a `.qmd` file.
+    Follow the instrutions in order to make sure that `renv` is configured correctly.
 
-    - Create a `PDF` and `HTML` file for your output by modifying the YAML frontmatter for the Quarto `.qmd` document
+4.  Work on the *reminaing part* of this assignment as a `.qmd` file.
 
-5. When you're done working on your assignment, push the changes to your github repository.
+    -   Create a `PDF` and `HTML` file for your output by modifying the YAML frontmatter for the Quarto `.qmd` document
+
+5.  When you're done working on your assignment, push the changes to your github repository.
+
+6.  Navigate to the original Github repository [here](https://github.com/psu-stat380/hw-1) and submit a pull request linking to your repository.
 
-6. Navigate to the original Github repository [here](https://github.com/psu-stat380/hw-1) and submit a pull request linking to your repository. 
-    
     Remember to **include your name** in the pull request information!
 
 If you're stuck at any step along the way, you can refer to the [official Github docs here](https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/proposing-changes-to-your-work-with-pull-requests/creating-a-pull-request-from-a-fork)
 
-
-<br><br><br><br>
-<br><br><br><br>
----
+<br><br><br><br> <br><br><br><br> ---
 
 ## Question 2
-::: {.callout-tip}
+
+::: callout-tip
 ## 30 points
 :::
 
@@ -103,54 +99,85 @@ my_vec <- c(
 )
 ```
 
-
 For the following questions, provide your answers in a code cell.
 
-1. What data type does the vector contain?
+1.  What data type does the vector contain?
+
+```{R}
+typeof(my_vec)
+# the vector contains character data
+```
+
+2.  Create two new vectors called `my_vec_double` and `my_vec_int` which converts `my_vec` to Double & Integer types, respectively,
 
-1. Create two new vectors called `my_vec_double` and `my_vec_int` which converts `my_vec` to Double & Integer types, respectively, 
+```{R}
+my_vec_double <- as.double(my_vec)
+my_vec_double
+
+my_vec_int <- as.integer(my_vec)
+my_vec_int
+```
 
-1. Create a new vector `my_vec_bool` which comprises of:
-    * ```r TRUE```if an element in `my_vec_double` is $\le 0$
-    * ```r FALSE``` if an element in `my_vec_double` is $\ge 0$
+3.  Create a new vector `my_vec_bool` which comprises of:
+
+    -   `r TRUE`if an element in `my_vec_double` is $\le 0$
+    -   `r FALSE` if an element in `my_vec_double` is $\ge 0$
 
     How many elements of `my_vec_double` are greater than zero?
 
-1. Sort the values of `my_vec_double` in ascending order. 
+```{R}
+my_vec_bool <- ifelse(my_vec_double<=0,TRUE,FALSE)
+my_vec_bool
+length(my_vec_bool)-sum(my_vec_bool)
+# while I could also simply count it, this command shows that there are 
+# 4 values in my_vec_double that are greater than 0.
+```
+
+4.  Sort the values of `my_vec_double` in ascending order.
 
+```{R}
+sort(my_vec_double)
+```
 
-<br><br><br><br>
-<br><br><br><br>
----
+<br><br><br><br> <br><br><br><br> ---
 
 ## Question 3
-::: {.callout-tip}
+
+::: callout-tip
 ## 50 points
 :::
 
-In this question we will get a better understanding of how `R` handles large data structures in memory. 
-
-1. Provide `R` code to construct the following matrices:
-$$
-\begin{bmatrix} 
-1 & 2 & 3\\
-4 & 5 & 6\\
-7 & 8 & 9\\
-\end{bmatrix}
-\quad \text{ and } \quad
-\begin{bmatrix} 
-1 & 2 & 3 & 4 & 5 & \dots & 100\\
-1 & 4 & 9 & 16 & 25 & \dots & 10000\\
-\end{bmatrix}
-$$
-
-::: {.callout-warning}
+In this question we will get a better understanding of how `R` handles large data structures in memory.
+
+1.  Provide `R` code to construct the following matrices: $$
+    \begin{bmatrix} 
+    1 & 2 & 3\\
+    4 & 5 & 6\\
+    7 & 8 & 9\\
+    \end{bmatrix}
+    \quad \text{ and } \quad
+    \begin{bmatrix} 
+    1 & 2 & 3 & 4 & 5 & \dots & 100\\
+    1 & 4 & 9 & 16 & 25 & \dots & 10000\\
+    \end{bmatrix}
+    $$
+
+::: callout-warning
 ## Tip
 
 Recall the discussion in class on how `R` fills in matrices
 :::
 
-In the next part, we will discover how knowledge of the way in which a matrix is stored in memory can inform better code choices. To this end, the following function takes an input $n$ and creates an $n \times n$ matrix with random entries. 
+```{R}
+m1 <-matrix(1:9, nrow=3, byrow = TRUE)
+m1
+
+m2 <- matrix(c(1:100,(1:100)^2), nrow=2, byrow=TRUE)
+m2
+```
+
+
+In the next part, we will discover how knowledge of the way in which a matrix is stored in memory can inform better code choices. To this end, the following function takes an input $n$ and creates an $n \times n$ matrix with random entries.
 
 ```{R}
 generate_matrix <- function(n){
@@ -169,7 +196,6 @@ For example:
 generate_matrix(4)
 ```
 
-
 Let `M` be a fixed $50 \times 50$ matrix
 
 ```{R}
@@ -177,19 +203,17 @@ M <- generate_matrix(50)
 mean(M)
 ```
 
+2.  Write a function `row_wise_scan` which scans the entries of `M` one row after another and outputs the number of elements whose value is $\ge 0$. You can use the following **starter code**
 
-2. Write a function `row_wise_scan` which scans the entries of `M` one row after another and outputs the number of elements whose value is $\ge 0$. You can use the following **starter code**
-
-```R
+``` {R}
 row_wise_scan <- function(x){
     n <- nrow(x)
     m <- ncol(x)
 
-    # Insert your code here
     count <- 0
-    for(...){
-        for(...){
-            if(...){
+    for(i in 1:n){
+        for(j in 1:m){
+            if(x[i,j]>=0){
                 count <- count + 1 
             }
         }
@@ -197,31 +221,56 @@ row_wise_scan <- function(x){
 
     return(count)
 }
-```
 
+test <- matrix(my_vec_double, nrow=2)
+row_wise_scan(test)
+# seems to be working, I've never used for loops before so this took a bit of googling
+```
 
-3. Similarly, write a function `col_wise_scan` which does exactly the same thing but scans the entries of `M` one column after another
+3.  Similarly, write a function `col_wise_scan` which does exactly the same thing but scans the entries of `M` one column after another
 
-```R
+``` {R}
 col_wise_scan <- function(x){
+    n <- nrow(x)
+    m <- ncol(x)
+
     count <- 0
-    
-    ... # Insert your code here
+    for(i in 1:m){
+        for(j in 1:n){
+            if(x[j,i]>=0){
+                count <- count + 1 
+            }
+        }
+    }
 
     return(count)
 }
 ```
-You can check if your code is doing what it's supposed to using the function here[^footnote]
 
-4. Between `col_wise_scan` and `row_wise_scan`, which function do you expect to take shorter to run? Why?
+You can check if your code is doing what it's supposed to using the function here[^1]
+
+[^1]: If your code is right, the following code should evaluate to be `TRUE`
+
+    ``` {R}
+    library(dplyr)
+    sapply(1:100, function(i) {
+        x <- generate_matrix(100)
+        row_wise_scan(x) == col_wise_scan(x)
+    }) %>% sum == 100
+    ```
+
+4.  Between `col_wise_scan` and `row_wise_scan`, which function do you expect to take shorter to run? Why?
+
+I expect col_wise_scan to take a shorter amount of time. As discussed in class, R stores all entries of a column at one point in memory, so it can very quickly move from one entry in a column to another. However, because the data is organized by column, moving across a row means that R must jump around between different points in memory, causing the function to take much longer.
+
 
-5. Write a function `time_scan` which takes in a method `f` and a matrix `M` and outputs the amount of time taken to run `f(M)`
+5.  Write a function `time_scan` which takes in a method `f` and a matrix `M` and outputs the amount of time taken to run `f(M)`
 
-```R
+``` {R}
 time_scan <- function(f, M){
-    initial_time <- ... # Write your code here
+    initial_time <- Sys.time()
     f(M)
-    final_time <- ...  # Write your code here
+    final_time <- Sys.time()
     
     total_time_taken <- final_time - initial_time
     return(total_time_taken)
@@ -230,24 +279,41 @@ time_scan <- function(f, M){
 
 Provide your output to
 
-```R
+``` {R}
 list(
     row_wise_time = time_scan(row_wise_scan, M),
     col_wise_time = time_scan(row_wise_scan, M)
 )
 ```
-Which took longer to run? 
 
-6. Repeat this experiment now when:
-    * `M` is a $100 \times 100$ matrix
-    * `M` is a $1000 \times 1000$ matrix
-    * `M` is a $5000 \times 5000$ matrix
+Which took longer to run? row_wise_time() took longer to run as I expected.
 
-What can you conclude?
+6.  Repeat this experiment now when:
+    -   `M` is a $100 \times 100$ matrix
+    -   `M` is a $1000 \times 1000$ matrix
+    -   `M` is a $5000 \times 5000$ matrix
+    
+```{R}
+M100 <- generate_matrix(100)
+list(
+    row_wise_time = time_scan(row_wise_scan, M100),
+    col_wise_time = time_scan(row_wise_scan, M100)
+)
+M1000 <- generate_matrix(1000)
+list(
+    row_wise_time = time_scan(row_wise_scan, M1000),
+    col_wise_time = time_scan(row_wise_scan, M1000)
+)
+M5000 <- generate_matrix(5000)
+list(
+    row_wise_time = time_scan(row_wise_scan, M5000),
+    col_wise_time = time_scan(row_wise_scan, M5000)
+)
+```
 
-<br><br><br><br>
-<br><br><br><br>
----
+What can you conclude? In general, it appears that looking at a matrix column-wise is slightly faster than looking at a matrix row-wise in R. Sometimes certain runs take longer column-wise than row-wise but I think this is attributed to variability in runtime of every function due to the amount of computing power available at any time fluctuating as my computer runs other processes outside of RStudio. If I were to run these functions many times over, column-wise functions would generally take less time than row-wise functions for the same matrix.
+
+<br><br><br><br> <br><br><br><br> ---
 
 # Appendix
 
@@ -256,12 +322,3 @@ Print your `R` session information using the following command
 ```{R}
 sessionInfo()
 ```
-
-[^footnote]: If your code is right, the following code should evaluate to be `TRUE`
-
-    ```R
-    sapply(1:100, function(i) {
-        x <- generate_matrix(100)
-        row_wise_scan(x) == col_wise_scan(x)
-    }) %>% sum == 100
-    ```
