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1257 lines
113 KiB
HTML
1257 lines
113 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<html>
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<head>
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<meta http-equiv="content-type" content="text/html; charset=utf-8">
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<title></title>
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<meta name="generator" content="LibreOffice 4.2.5.2 (MacOSX)">
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<meta name="created" content="0;0">
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<meta name="changed" content="20140718;140930381877000">
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<style type="text/css">
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<!--
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td p { color: #000000; font-family: "Verdana"; font-size: 12pt }
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p { color: #000000; font-family: "Verdana"; font-size: 12pt }
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-->
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</style>
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</head>
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<body lang="en-US" text="#000000" dir="ltr" style="background: transparent">
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<table width="948" cellpadding="2" cellspacing="0" style="page-break-before: always">
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<col width="171">
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<col width="174">
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<col width="128">
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<col width="136">
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<col width="126">
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<col width="188">
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<tr>
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<td width="171" height="60" bgcolor="#0066cc" style="border: none; padding: 0in">
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<p align="center"><font color="#ffffff"><font face="Arial"><font size="5" style="font-size: 18pt"><b>Task</b></font></font></font></p>
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</td>
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<td width="174" bgcolor="#0066cc" style="border: none; padding: 0in">
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<p align="center"><font color="#ffffff"><font face="monospace"><font size="5" style="font-size: 18pt"><b>MATLAB/Octave</b></font></font></font></p>
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</td>
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<td width="128" bgcolor="#0066cc" style="border: none; padding: 0in">
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<p align="center"><font color="#ffffff"><font face="monospace"><font size="5" style="font-size: 18pt"><b>Python
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NumPy</b></font></font></font></p>
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</td>
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<td width="136" bgcolor="#0066cc" style="border: none; padding: 0in">
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<p align="center"><font color="#ffffff"><font face="monospace"><font size="5" style="font-size: 18pt"><b>R</b></font></font></font></p>
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</td>
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<td width="126" bgcolor="#0066cc" style="border: none; padding: 0in">
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<p align="center"><font color="#ffffff"><font face="monospace"><font size="5" style="font-size: 18pt"><b>Julia</b></font></font></font></p>
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</td>
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<td width="188" bgcolor="#0066cc" style="border: none; padding: 0in">
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<p align="center"><font color="#ffffff"><font face="Arial"><font size="5" style="font-size: 18pt"><b>Task</b></font></font></font></p>
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</td>
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</tr>
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<tr>
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<td colspan="6" width="944" height="70" bgcolor="#ffffff" style="border: none; padding: 0in">
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<p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>CREATING
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MATRICES</b></font></font></p>
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</td>
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</tr>
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<tr valign="top">
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<td width="171" height="158" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
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<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
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Matrices <br>(here: 3x3 matrix)</b></font></font></p>
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</td>
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<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
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A = [1 2 3; 4 5 6; 7 8 9]<br>A =<br> 1 2
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3<br> 4 5 6<br> 7 8
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9</font></font></p>
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</td>
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<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
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A = np.array([ [1,2,3], [4,5,6], [7,8,9] ])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
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A<br>array([[1, 2, 3],<br> [4, 5, 6],<br>
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[7, 8, 9]])</font></font></p>
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</td>
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<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
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A = matrix(c(1,2,3,4,5,6,7,8,9),nrow=3,byrow=T)<br><br>
#
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equivalent to
<br># A = matrix(1:9,nrow=3,byrow=T)
<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
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A<br>[,1] [,2] [,3]<br>[1,] 1 2 3<br>[2,] 4 5 6<br>[3,] 7 8 9</font></font></p>
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</td>
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<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
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A=[1 2 3; 4 5 6; 7 8 9]<br>3x3 Array{Int64,2}:<br>1 2 3<br>4 5 6<br>7
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8 9</font></font></p>
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</td>
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<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
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<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
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Matrices <br>(here: 3x3 matrix)</b></font></font></p>
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</td>
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</tr>
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<tr valign="top">
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<td width="171" height="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
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<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
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an 1D column vector</b></font></font></p>
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</td>
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<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
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a = [1; 2; 3]<br>a =<br> 1<br> 2<br>
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3</font></font></p>
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</td>
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<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
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<p align="left"><font color="#ff420e"><font face="monospace"><font size="2" style="font-size: 10pt"><b>P></b></font></font></font>
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<font face="monospace"><font size="1" style="font-size: 8pt">a</font></font><font color="#2fff12">
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</font><font color="#000000"><font face="monospace"><font size="1" style="font-size: 8pt">=
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np.array([1,2,3]).reshape(1,3)</font></font></font></p>
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><br></font></font><font color="#ff420e"><font face="monospace"><font size="2" style="font-size: 10pt"><b>P></b></font></font></font>
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<font color="#000000"><font face="monospace"><font size="1" style="font-size: 8pt">b.shape<br>(1,
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3)</font></font></font></p>
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<p align="left"><br>
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</p>
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</td>
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<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
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a = matrix(c(1,2,3), nrow=3, byrow=T)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
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a<br>[,1]<br>[1,] 1<br>[2,] 2<br>[3,] 3</font></font></p>
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</td>
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<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
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a=[1; 2; 3]<br>3-element Array{Int64,1}: <br>1<br>2<br>3</font></font></p>
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</td>
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<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
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<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
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an 1D column vector</b></font></font></p>
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</td>
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</tr>
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<tr valign="top">
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<td width="171" height="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
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<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
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an<br>1D row vector</b></font></font></p>
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</td>
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<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
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b = [1 2 3]<br>b =<br> 1 2 3</font></font></p>
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</td>
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<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
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b = np.array([1,2,3])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
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b<br>array([1, 2, 3])</font></font></p>
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt">#
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note that numpy doesn't have <br># explicit “row-vectors”, but
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1-D <br># arrays</font></font></p>
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<p style="margin-bottom: 0in"><font face="Liberation Serif, serif"><font size="3" style="font-size: 12pt"><font color="#ff420e"><font face="monospace"><font size="2" style="font-size: 10pt"><b>P></b></font></font></font><font color="#2fff12">
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</font><font color="#000000"><font face="monospace"><font size="1" style="font-size: 8pt">b.shape</font></font></font></font></font></p>
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<p style="margin-bottom: 0in"><font face="monospace"><font size="1" style="font-size: 8pt">(3,)</font></font></p>
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<p align="left"><br>
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</p>
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</td>
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<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
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b = matrix(c(1,2,3), ncol=3)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
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b<br>[,1] [,2] [,3]<br>[1,] 1 2 3</font></font></p>
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</td>
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<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
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b=[1 2 3] <br>1x3 Array{Int64,2}:<br>1 2 3<br><br># note that this
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is a 2D array. <br># vectors in Julia are columns</font></font></p>
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</td>
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<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
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<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
|
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an<br>1D row vector</b></font></font></p>
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</td>
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</tr>
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<tr valign="top">
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<td width="171" height="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
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<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
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a <br>random m x n matrix</b></font></font></p>
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</td>
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<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
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rand(3,2)<br>ans =<br> 0.21977 0.10220<br>
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0.38959 0.69911<br> 0.15624 0.65637</font></font></p>
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</td>
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<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
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np.random.rand(3,2)<br>array([[ 0.29347865, 0.17920462],<br>
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[ 0.51615758, 0.64593471],<br>
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[ 0.01067605, 0.09692771]])</font></font></p>
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</td>
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<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
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matrix(runif(3*2), ncol=2)<br>[,1] [,2]<br>[1,] 0.5675127
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0.7751204<br>[2,] 0.3439412 0.5261893<br>[3,] 0.2273177 0.223438</font></font></p>
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</td>
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<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
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rand(3,2)<br>3x2 Array{Float64,2}:<br>0.36882 0.267725<br>0.571856
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0.601524<br>0.848084 0.858935</font></font></p>
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</td>
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<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
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<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
|
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a <br>random m x n matrix</b></font></font></p>
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</td>
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</tr>
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<tr valign="top">
|
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<td width="171" height="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
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<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
|
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a<br>zero m x n matrix </b></font></font></p>
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</td>
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<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
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zeros(3,2)<br>ans =<br> 0 0<br> 0
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0<br> 0 0</font></font></p>
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</td>
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<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
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np.zeros((3,2))<br>array([[ 0., 0.],<br>
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[ 0., 0.],<br> [ 0.,
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0.]])</font></font></p>
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</td>
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<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
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mat.or.vec(3, 2)<br>[,1] [,2]<br>[1,] 0 0<br>[2,] 0 0<br>[3,] 0 0</font></font></p>
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</td>
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<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
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zeros(3,2)<br>3x2 Array{Float64,2}:<br>0.0 0.0<br>0.0 0.0<br>0.0
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0.0</font></font></p>
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</td>
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<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
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<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
|
||
a<br>zero m x n matrix </b></font></font></p>
|
||
</td>
|
||
</tr>
|
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<tr valign="top">
|
||
<td width="171" height="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
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<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
|
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an<br>m x n matrix of ones</b></font></font></p>
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||
</td>
|
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<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
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<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
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ones(3,2)<br>ans =<br> 1 1<br> 1
|
||
1<br> 1 1</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
np.ones((3,2))<br>array([[ 1., 1.],<br>
|
||
[ 1., 1.],<br> [ 1., 1.]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font color="#0000ff"><font face="monospace"><font size="2" style="font-size: 10pt"><b>R></b></font></font></font><font face="monospace"><font size="1" style="font-size: 8pt">
|
||
</font></font><font color="#000000"><font face="AndaleMono, serif"><font size="1" style="font-size: 8pt">matrix(1L,
|
||
3, 2)<br></font></font></font><font face="monospace"><font size="1" style="font-size: 8pt"><br>[,1]
|
||
[,2]<br>[1,] 1 1<br>[2,] 1 1<br>[3,] 1 1</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
ones(3,2)<br>3x2 Array{Float64,2}:<br>1.0 1.0<br>1.0 1.0<br>1.0
|
||
1.0</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
|
||
an<br>m x n matrix of ones</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
|
||
an<br>identity matrix</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
eye(3)<br>ans =<br>Diagonal Matrix<br> 1 0
|
||
0<br> 0 1 0<br> 0 0
|
||
1</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
np.eye(3)<br>array([[ 1., 0., 0.],<br>
|
||
[ 0., 1., 0.],<br> [
|
||
0., 0., 1.]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
diag(3)<br>[,1] [,2] [,3]<br>[1,] 1 0 0<br>[2,] 0 1 0<br>[3,] 0 0
|
||
1</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
eye(3)<br>3x3 Array{Float64,2}:<br>1.0 0.0 0.0<br>0.0 1.0 0.0<br>0.0
|
||
0.0 1.0</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
|
||
an<br>identity matrix</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="217" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
|
||
a<br>diagonal matrix</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
a = [1 2 3]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
diag(a)<br>ans =<br>Diagonal Matrix<br> 1 0
|
||
0<br> 0 2 0<br> 0 0
|
||
3</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
a = np.array([1,2,3])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
np.diag(a)<br>array([[1, 0, 0],<br> [0,
|
||
2, 0],<br> [0, 0, 3]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
diag(1:3)<br>[,1] [,2] [,3]<br>[1,] 1 0 0<br>[2,] 0 2 0<br>[3,] 0
|
||
0 3</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
a=[1, 2, 3] <br><br># added commas because julia<br># vectors are
|
||
columnar<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
diagm(a)<br>3x3 Array{Int64,2}:<br>1 0 0<br>0 2 0<br>0 0 3</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Creating
|
||
a<br>diagonal matrix</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="6" width="944" height="128" bgcolor="#ffffff" style="border: none; padding: 0in">
|
||
<p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>ACCESSING
|
||
MATRIX ELEMENTS</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="159" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Getting
|
||
the dimension<br>of a matrix<br>(here: 2D, rows x cols)</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A = [1 2 3; 4 5 6]<br>A =<br> 1 2 3<br>
|
||
4 5 6<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
size(A)<br>ans =<br> 2 3</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([ [1,2,3], [4,5,6] ])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A<br>array([[1, 2, 3],<br> [4, 5,
|
||
6]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A.shape<br>(2, 3)</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:6,nrow=2,byrow=T)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A<br>[,1] [,2] [,3]<br>[1,] 1 2 3<br>[2,] 4 5 6
</font></font></p>
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
dim(A)<br>[1] 2 3</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6]<br>2x3 Array{Int64,2}:<br>1 2 3<br>4 5 6<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
size(A)<br>(2,3)</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Getting
|
||
the dimension<br>of a matrix<br>(here: 2D, rows x cols)</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="240" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Selecting
|
||
rows </b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A = [1 2 3; 4 5 6; 7 8 9]<br><br>% 1st row<br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A(1,:)<br>ans =<br> 1 2 3<br><br>% 1st 2
|
||
rows<br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A(1:2,:)<br>ans =<br> 1 2 3<br>
|
||
4 5 6</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([ [1,2,3], [4,5,6], [7,8,9] ])<br><br># 1st row<br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A[0,:]<br>array([1, 2, 3])<br><br># 1st 2 rows<br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A[0:2,:]<br>array([[1, 2, 3], [4, 5, 6]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:9,nrow=3,byrow=T)
<br><br># 1st row<br>
<font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A[1,]<br>[1] 1 2 3<br><br>
# 1st 2 rows
<br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A[1:2,]<br>[,1] [,2] [,3]<br>[1,] 1 2 3<br>[2,] 4 5 6</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6; 7 8 9]; <br>#semicolon suppresses output<br><br>#1st
|
||
row<br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A[1,:] <br>1x3 Array{Int64,2}:<br>1 2 3<br><br>#1st 2 rows<br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A[1:2,:] <br>2x3 Array{Int64,2}:<br>1 2 3<br>4 5 6</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Selecting
|
||
rows </b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="304" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Selecting
|
||
columns</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A = [1 2 3; 4 5 6; 7 8 9]<br><br>% 1st column<br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A(:,1)<br>ans =<br> 1<br> 4<br>
|
||
7<br><br>% 1st 2 columns<br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A(:,1:2)<br>ans =<br> 1 2<br> 4
|
||
5<br> 7 8</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([ [1,2,3], [4,5,6], [7,8,9] ])<br><br># 1st column
|
||
(as row vector)<br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A[:,0]<br>array([1, 4, 7])<br><br># 1st column (as column
|
||
vector)<br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A[:,[0]]<br>array([[1],<br> [4],<br>
|
||
[7]])<br><br># 1st 2 columns<br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A[:,0:2]<br>array([[1, 2], <br> [4,
|
||
5], <br> [7, 8]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:9,nrow=3,byrow=T)
<br><br># 1st column as row
|
||
vector
<br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
t(A[,1])<br>[,1] [,2] [,3]<br>[1,] 1 4 7
<br><br># 1st column
|
||
as column vector
<br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A[,1]<br>[1] 1 4 7
<br><br># 1st 2 columns
<br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A[,1:2]<br>[,1] [,2]<br>[1,] 1 2<br>[2,] 4 5<br>[3,] 7 8</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6; 7 8 9];<br><br>#1st column<br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A[:,1] <br>3-element Array{Int64,1}:<br>1<br>4<br>7<br><br>#1st 2
|
||
columns<br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A[:,1:2] <br>3x2 Array{Int64,2}:<br>1 2<br>4 5<br>7 8</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Selecting
|
||
columns</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="260" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Extracting
|
||
rows and columns by criteria<br><br>(here: get rows that have
|
||
value 9 in column 3)</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A = [1 2 3; 4 5 9; 7 8 9]<br>A =<br> 1 2
|
||
3<br> 4 5 9<br> 7 8
|
||
9<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A(A(:,3) == 9,:)<br>ans =<br> 4 5 9<br>
|
||
7 8 9</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([ [1,2,3], [4,5,9], [7,8,9]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A<br>array([[1, 2, 3],<br> [4, 5, 9],<br>
|
||
[7, 8, 9]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A[A[:,2] == 9]<br>array([[4, 5, 9],<br>
|
||
[7, 8, 9]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font color="#0000ff"><font face="monospace"><font size="2" style="font-size: 10pt"><b>R></b></font></font></font><font face="monospace"><font size="1" style="font-size: 8pt">
|
||
A = matrix(1:9,nrow=3,byrow=T)
<br><br></font></font><font color="#0000ff"><font face="monospace"><font size="2" style="font-size: 10pt"><b>R></b></font></font></font><font face="monospace"><font size="1" style="font-size: 8pt">
|
||
A<br>[,1] [,2] [,3]<br>[1,] 1 2 3<br>[2,] 4 5 9<br>[3,] 7 8
|
||
9
<br><br></font></font><font color="#0000ff"><font face="monospace"><font size="2" style="font-size: 10pt"><b>R></b></font></font></font><font face="monospace"><font size="1" style="font-size: 8pt">
|
||
</font></font><font color="#000000"><font face="monospace"><font size="1" style="font-size: 8pt">A[A[,3]==9,]</font></font></font></p>
|
||
<p align="left" style="margin-bottom: 0in"><font face="monospace"><font size="1" style="font-size: 8pt">[1]
|
||
7 8 9</font></font></p>
|
||
<p align="left"><br>
|
||
</p>
|
||
</td>
|
||
<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 9; 7 8 9]<br>3x3 Array{Int64,2}:<br>1 2 3<br>4 5 9<br>7
|
||
8 9<br><br># use '.==' for<br># element-wise check<br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A[ A[:,3] .==9, :] <br>2x3 Array{Int64,2}:<br>4 5 9<br>7 8 9</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Extracting
|
||
rows and columns by criteria<br><br>(here: get rows that have
|
||
value 9 in column 3)</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="118" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Accessing
|
||
elements<br>(here: 1st element)</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A = [1 2 3; 4 5 6; 7 8 9]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A(1,1)<br>ans = 1</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([ [1,2,3], [4,5,6], [7,8,9] ])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A[0,0]<br>1</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(c(1,2,3,4,5,9,7,8,9),nrow=3,byrow=T)
<br><br>
<font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A[1,1]<br>[1] 1</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6; 7 8 9];<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A[1,1]<br>1</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Accessing
|
||
elements<br>(here: 1st element)</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="6" width="944" height="128" bgcolor="#ffffff" style="border: none; padding: 0in">
|
||
<p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>MANIPULATING
|
||
SHAPE AND DIMENSIONS</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="173" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Converting <br>a
|
||
matrix into a row vector (by column)</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A = [1 2 3; 4 5 6; 7 8 9]</font></font></p>
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A(:)</font></font></p>
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt">ans
|
||
= </font></font>
|
||
</p>
|
||
<p><font face="Liberation Serif, serif"><font size="1" style="font-size: 8pt"><font face="AndaleMono, serif">1
|
||
<br>4 <br>7<br>2<br>5<br>8<br>3<br>6<br></font><font face="AndaleMono, serif">9</font></font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([[1,2,3],[4,5,6],[7,8,9]])</font></font></p>
|
||
<p align="left"><font color="#ff420e"><font face="monospace"><font size="2" style="font-size: 10pt"><b>P></b></font></font></font><font face="monospace"><font size="1" style="font-size: 8pt">
|
||
</font></font><font color="#000000"><font face="AndaleMono, serif"><font size="1" style="font-size: 8pt">A.flatten(1)</font></font></font></p>
|
||
<p align="left" style="margin-bottom: 0in"><font face="monospace"><font size="1" style="font-size: 8pt"><font face="AndaleMono, serif">array([1,
|
||
4, 7, 2, 5, 8, 3, 6, 9])</font></font></font></p>
|
||
<p align="left"><br>
|
||
</p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:9,nrow=3,byrow=T)</font></font></p>
|
||
<p align="left" style="margin-bottom: 0in"><br>
|
||
</p>
|
||
<p align="left" style="margin-bottom: 0in"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R>
|
||
</b></font></font><font face="AndaleMono, serif">as.vector(A)</font></font></font></p>
|
||
<p align="left" style="margin-bottom: 0in"><br>
|
||
</p>
|
||
<p style="margin-bottom: 0in"><font face="Liberation Serif, serif"><font size="1" style="font-size: 8pt"><font face="AndaleMono, serif">[1]
|
||
1 4 7 2 5 8 3 6 9</font></font></font></p>
|
||
<p align="left"><br>
|
||
</p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6; 7 8 9]</font></font></p>
|
||
<p align="left" style="margin-bottom: 0in"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font><font color="#2fb41d"><font face="AndaleMono, serif"><font size="3" style="font-size: 12pt">
|
||
</font></font></font><font color="#000000"><font face="AndaleMono, serif">vec(A)</font></font></font></font></p>
|
||
<p style="margin-bottom: 0in"><font face="Liberation Serif, serif"><font size="1" style="font-size: 8pt"><font face="AndaleMono, serif">9-element
|
||
Array{Int64,1}:</font></font></font></p>
|
||
<p><font face="Liberation Serif, serif"><font size="1" style="font-size: 8pt"><font color="#000000"><font face="AndaleMono, serif">1<br>4<br>7<br>2<br>5<br>8<br>3<br>6<br>9</font></font></font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Converting <br>a
|
||
matrix into a row vector (by column)</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="173" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Converting <br>row
|
||
to column vectors</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
b = [1 2 3]
<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
b = b'<br>b =<br> 1<br> 2<br>
|
||
3</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
b = np.array([1, 2, 3])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
b = b[np.newaxis].T<br># alternatively <br># b =
|
||
b[:,np.newaxis]<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
b<br>array([[1],<br> [2],<br>
|
||
[3]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
b = matrix(c(1,2,3), ncol=3)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
t(b)<br>[,1]<br>[1,] 1<br>[2,] 2<br>[3,] 3</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
b=vec([1 2 3])<br>3-element Array{Int64,1}:<br>1<br>2<br>3</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Converting <br>row
|
||
to column vectors</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="275" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Reshaping
|
||
Matrices<br><br>(here: 3x3 matrix to row vector)</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A = [1 2 3; 4 5 6; 7 8 9]<br>A =<br> 1 2
|
||
3<br> 4 5 6<br> 7 8
|
||
9<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
total_elements = numel(A)<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
B = reshape(A,1,total_elements) <br>% or reshape(A,1,9)<br>B
|
||
=<br> 1 4 7 2 5 8
|
||
3 6 9</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([[1,2,3],[4,5,6],[7,8,9]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A<br>array([[1, 2, 3],<br> [4, 5, 9],<br>
|
||
[7, 8, 9]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
total_elements = np.prod(A.shape)</font></font></p>
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
B = A.reshape(1, total_elements) <br><br># alternative
|
||
shortcut:<br># A.reshape(1,-1)<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
B<br>array([[1, 2, 3, 4, 5, 6, 7, 8, 9]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:9,nrow=3,byrow=T)
<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A<br>[,1] [,2] [,3]<br>[1,] 1 2 3<br>[2,] 4 5 6<br>[3,] 7 8 9
<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
total_elements = dim(A)[1] * dim(A)[2]<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
B = matrix(A, ncol=total_elements)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
B<br>[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]<br>[1,] 1 4 7 2
|
||
5 8 3 6 9</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6; 7 8 9]<br>3x3 Array{Int64,2}:<br>1 2 3<br>4 5 6<br>7
|
||
8 9<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
total_elements=length(A)<br>9<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>B=reshape(A,1,total_elements)<br>1x9
|
||
Array{Int64,2}:<br>1 4 7 2 5 8 3 6 9</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Reshaping
|
||
Matrices<br><br>(here: 3x3 matrix to row vector)</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="240" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Concatenating
|
||
matrices</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A = [1 2 3; 4 5 6]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
B = [7 8 9; 10 11 12]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
C = [A; B]<br> 1 2 3<br>
|
||
4 5 6<br> 7
|
||
8 9<br> 10 11 12</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([[1, 2, 3], [4, 5, 6]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
B = np.array([[7, 8, 9],[10,11,12]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
C = np.concatenate((A, B), axis=0)<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
C<br>array([[ 1, 2, 3], <br> [ 4,
|
||
5, 6], <br> [ 7, 8, 9], <br>
|
||
[10, 11, 12]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:6,nrow=2,byrow=T)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
B = matrix(7:12,nrow=2,byrow=T)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
C = rbind(A,B)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
C<br>[,1] [,2] [,3]<br>[1,] 1 2 3<br>[2,] 4 5 6<br>[3,] 7 8 9<br>[4,]
|
||
10 11 12</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6];<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
B=[7 8 9; 10 11 12];<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
C=[A; B]<br>4x3 Array{Int64,2}:<br>1 2 3<br>4 5 6<br>7 8 9<br>10
|
||
11 12</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Concatenating
|
||
matrices</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="256" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Stacking <br>vectors
|
||
and matrices</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
a = [1 2 3]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
b = [4 5 6]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
c = [a' b']<br>c =<br> 1 4<br> 2
|
||
5<br> 3 6<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
c = [a; b]<br>c =<br> 1 2 3<br>
|
||
4 5 6</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
a = np.array([1,2,3])<br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
b = np.array([4,5,6])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
np.c_[a,b]<br>array([[1, 4],<br> [2,
|
||
5],<br> [3, 6]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
np.r_[a,b]<br>array([[1, 2, 3],<br> [4,
|
||
5, 6]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
a = matrix(1:3, ncol=3)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
b = matrix(4:6, ncol=3)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
matrix(rbind(A, B), ncol=2)<br>[,1] [,2]<br>[1,] 1 5<br>[2,] 4
|
||
3
<br><br>
<font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
rbind(A,B)<br>[,1] [,2] [,3]<br>[1,] 1 2 3<br>[2,] 4 5 6</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
a=[1 2 3];<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
b=[4 5 6];<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
c=[a' b']<br>3x2 Array{Int64,2}:<br>1 4<br>2 5<br>3 6<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
c=[a; b]<br>2x3 Array{Int64,2}:<br>1 2 3<br>4 5 6</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Stacking <br>vectors
|
||
and matrices</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="6" width="944" height="114" bgcolor="#ffffff" style="border: none; padding: 0in">
|
||
<p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>BASIC
|
||
MATRIX OPERATIONS</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="253" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Matrix-scalar<br>operations</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font> A
|
||
= [1 2 3; 4 5 6; 7 8 9]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A * 2<br>ans =<br> 2 4 6<br>
|
||
8 10 12<br> 14 16
|
||
18<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A + 2<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A - 2<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A / 2</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([ [1,2,3], [4,5,6], [7,8,9] ])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A * 2<br>array([[ 2, 4, 6],<br>
|
||
[ 8, 10, 12],<br> [14, 16, 18]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A + 2<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A - 2<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A / 2</font></font></p>
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt">#
|
||
Note that NumPy was optimized for<br># in-place assignments<br>#
|
||
e.g., A += A instead of <br># A = A + A</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:9, nrow=3, byrow=T)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A * 2<br>[,1] [,2] [,3]<br>[1,] 2 4 6<br>[2,] 8 10 12<br>[3,] 14
|
||
16 18
</font></font></p>
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A + 2<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A - 2<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A / 2</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6; 7 8 9];<br><br># elementwise operator<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A .* 2 <br>3x3 Array{Int64,2}:<br>2 4 6<br>8 10 12<br>14 16 18
|
||
<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A .+ 2;<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A .- 2;<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A ./ 2;</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Matrix-scalar<br>operations</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="165" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Matrix-matrix<br>multiplication</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font> A
|
||
= [1 2 3; 4 5 6; 7 8 9]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A * A<br>ans =<br> 30 36
|
||
42<br> 66 81 96<br>
|
||
102 126 150</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([ [1,2,3], [4,5,6], [7,8,9] ])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
np.dot(A,A) # or A.dot(A)<br>array([[ 30, 36, 42],<br>
|
||
[ 66, 81, 96],<br>
|
||
[102, 126, 150]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:9, nrow=3, byrow=T)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A %*% A<br>[,1] [,2] [,3]<br>[1,] 30 36 42<br>[2,] 66 81 96<br>[3,]
|
||
102 126 150</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6; 7 8 9];<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A * A<br>3x3 Array{Int64,2}:<br>30 36 42<br>66 81 96<br>102 126
|
||
150</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Matrix-matrix<br>multiplication</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="190" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Matrix-vector<br>multiplication</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A = [1 2 3; 4 5 6; 7 8 9]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
b = [ 1; 2; 3 ]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A * b<br>ans =<br> 14<br> 32<br>
|
||
50</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([ [1,2,3], [4,5,6], [7,8,9] ])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
b = np.array([ [1], [2], [3] ])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
np.dot(A,b) # or A.dot(b)<br><br>array([[14], [32], [50]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:9, ncol=3)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
b = matrix(1:3, nrow=3)<br><br>
<font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
t(b %*% A)<br>[,1]<br>[1,] 14<br>[2,] 32<br>[3,] 50</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6; 7 8 9];<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
b=[1; 2; 3];<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A*b<br>3-element Array{Int64,1}:<br>14<br>32<br>50</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Matrix-vector<br>multiplication</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="240" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Element-wise <br>matrix-matrix operations</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font> A
|
||
= [1 2 3; 4 5 6; 7 8 9]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A .* A<br>ans =<br> 1 4
|
||
9<br> 16 25 36<br> 49
|
||
64 81<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A .+ A<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A .- A<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A ./ A</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([ [1,2,3], [4,5,6], [7,8,9] ])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A * A<br>array([[ 1, 4, 9],<br>
|
||
[16, 25, 36],<br> [49, 64, 81]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A + A<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A - A<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A / A</font></font></p>
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt">#
|
||
Note that NumPy was optimized for<br># in-place assignments<br>#
|
||
e.g., A += A instead of <br># A = A + A</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:9, nrow=3, byrow=T)
<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A * A<br>[,1] [,2] [,3]<br>[1,] 1 4 9<br>[2,] 16 25 36<br>[3,] 49
|
||
64 81
<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A + A<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A - A<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A / A</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6; 7 8 9];<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A .* A<br>3x3 Array{Int64,2}:<br>1 4 9<br>16 25 36<br>49 64 81
|
||
<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A .+ A; <br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A .- A; <br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A ./ A;</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Element-wise <br>matrix-matrix operations</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="164" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Matrix
|
||
elements to power n <br><br>(here: individual elements
|
||
squared)</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font> A
|
||
= [1 2 3; 4 5 6; 7 8 9]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A.^2<br>ans =<br> 1 4 9<br>
|
||
16 25 36<br> 49 64 81</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([ [1,2,3], [4,5,6], [7,8,9] ])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
np.power(A,2)<br>array([[ 1, 4, 9],<br>
|
||
[16, 25, 36],<br> [49, 64, 81]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:9, nrow=3, byrow=T)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A ^ 2<br>[,1] [,2] [,3]<br>[1,] 1 4 9<br>[2,] 16 25 36<br>[3,] 49
|
||
64 81</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6; 7 8 9];<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A .^ 2<br>3x3 Array{Int64,2}:<br>1 4 9<br>16 25 36<br>49 64 81</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Matrix
|
||
elements to power n <br><br>(here: individual elements
|
||
squared)</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="225" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Matrix
|
||
to power n<br><br>(here: matrix-matrix multiplication with
|
||
itself)</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font> A
|
||
= [1 2 3; 4 5 6; 7 8 9]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A ^ 2<br>ans =<br> 30 36
|
||
42<br> 66 81 96<br>
|
||
102 126 150</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([ [1,2,3], [4,5,6], [7,8,9] ])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
np.linalg.matrix_power(A,2)<br>array([[ 30, 36,
|
||
42],<br> [ 66, 81, 96],<br>
|
||
[102, 126, 150]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:9, ncol=3)<br><br>
# requires the ‘expm’
|
||
package
<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
install.packages('expm')
<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
library(expm)
<br><br>
<font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A %^% 2<br>[,1] [,2] [,3]<br>[1,] 30 66 102<br>[2,] 36 81 126<br>[3,]
|
||
42 96 150</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6; 7 8 9];<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A ^ 2<br>3x3 Array{Int64,2}:<br>30 36 42<br>66 81 96<br>102 126
|
||
150</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Matrix
|
||
to power n<br><br>(here: matrix-matrix multiplication with
|
||
itself)</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="172" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Matrix
|
||
transpose</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font> A
|
||
= [1 2 3; 4 5 6; 7 8 9]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A'<br>ans =<br> 1 4 7<br> 2
|
||
5 8<br> 3 6 9</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([ [1,2,3], [4,5,6], [7,8,9] ])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A.T<br>array([[1, 4, 7],<br> [2, 5,
|
||
8],<br> [3, 6, 9]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(1:9, nrow=3, byrow=T)
<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
t(A)<br>[,1] [,2] [,3]<br>[1,] 1 4 7<br>[2,] 2 5 8<br>[3,] 3 6 9</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[1 2 3; 4 5 6; 7 8 9]<br>3x3 Array{Int64,2}:<br>1 2 3<br>4 5 6<br>7
|
||
8 9<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A'<br>3x3 Array{Int64,2}:<br>1 4 7<br>2 5 8<br>3 6 9</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Matrix
|
||
transpose</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="176" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Determinant
|
||
of a matrix:<br> A -> |A|</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A = [6 1 1; 4 -2 5; 2 8 7]<br>A =<br> 6 1
|
||
1<br> 4 -2 5<br> 2 8
|
||
7<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
det(A)<br>ans = -306</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font> A
|
||
= np.array([[6,1,1],[4,-2,5],[2,8,7]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A<br>array([[ 6, 1, 1],<br>
|
||
[ 4, -2, 5],<br> [ 2, 8,
|
||
7]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
np.linalg.det(A)<br>-306.0</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(c(6,1,1,4,-2,5,2,8,7), nrow=3, byrow=T)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A<br>[,1] [,2] [,3]<br>[1,] 6 1 1<br>[2,] 4 -2 5<br>[3,] 2 8 7<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
det(A)<br>[1] -306</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[6 1 1; 4 -2 5; 2 8 7]<br>3x3 Array{Int64,2}:<br>6 1 1<br>4 -2
|
||
5<br>2 8 7<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
det(A)<br>-306.0</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Determinant
|
||
of a matrix:<br> A -> |A|</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="202" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Inverse
|
||
of a matrix</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A = [4 7; 2 6]<br>A =<br> 4 7<br> 2
|
||
6<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A_inv = inv(A)<br>A_inv =<br> 0.60000 -0.70000<br>
|
||
-0.20000 0.40000</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([[4, 7], [2, 6]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A<br>array([[4, 7], <br> [2,
|
||
6]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A_inverse = np.linalg.inv(A)<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A_inverse<br>array([[ 0.6, -0.7], <br>
|
||
[-0.2, 0.4]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(c(4,7,2,6), nrow=2, byrow=T)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A<br>[,1] [,2]<br>[1,] 4 7<br>[2,] 2 6<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
solve(A)<br>[,1] [,2]<br>[1,] 0.6 -0.7<br>[2,] -0.2 0.4</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[4 7; 2 6]<br>2x2 Array{Int64,2}:<br>4 7<br>2 6<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A_inv=inv(A)<br>2x2 Array{Float64,2}:<br>0.6 -0.7<br>-0.2 0.4</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Inverse
|
||
of a matrix</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="6" width="944" height="202" bgcolor="#ffffff" style="border: none; padding: 0in">
|
||
<p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>ADVANCED
|
||
MATRIX OPERATIONS</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="311" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Calculating
|
||
the covariance matrix <br>of 3 random variables <br><br>(here:
|
||
covariances of the means <br>of x1, x2, and x3)</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
x1 = [4.0000 4.2000 3.9000 4.3000 4.1000]’<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
x2 = [2.0000 2.1000 2.0000 2.1000 2.2000]'<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
x3 = [0.60000 0.59000 0.58000 0.62000 0.63000]’<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
cov( [x1,x2,x3] )<br>ans =<br> 2.5000e-02
|
||
7.5000e-03 1.7500e-03<br> 7.5000e-03
|
||
7.0000e-03 1.3500e-03<br> 1.7500e-03
|
||
1.3500e-03 4.3000e-04</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
x1 = np.array([ 4, 4.2, 3.9, 4.3, 4.1])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
x2 = np.array([ 2, 2.1, 2, 2.1, 2.2])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
x3 = np.array([ 0.6, 0.59, 0.58, 0.62, 0.63])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
np.cov([x1, x2, x3])<br>Array([[ 0.025 , 0.0075 ,
|
||
0.00175],<br> [ 0.0075 , 0.007
|
||
, 0.00135],<br> [ 0.00175,
|
||
0.00135, 0.00043]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
x1 = matrix(c(4, 4.2, 3.9, 4.3, 4.1), ncol=5)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
x2 = matrix(c(2, 2.1, 2, 2.1, 2.2), ncol=5)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
x3 = matrix(c(0.6, 0.59, 0.58, 0.62, 0.63), ncol=5)
<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
cov(matrix(c(x1, x2, x3), ncol=3))<br>[,1] [,2] [,3]<br>[1,]
|
||
0.02500 0.00750 0.00175<br>[2,] 0.00750 0.00700 0.00135<br>[3,]
|
||
0.00175 0.00135 0.00043</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
x1=[4.0 4.2 3.9 4.3 4.1]';<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
x2=[2. 2.1 2. 2.1 2.2]';<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
x3=[0.6 .59 .58 .62 .63]';<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
cov([x1 x2 x3])<br>3x3 Array{Float64,2}:<br>0.025 0.0075
|
||
0.00175<br>0.0075 0.007 0.00135<br>0.00175 0.00135 0.00043</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Calculating
|
||
the covariance matrix <br>of 3 random variables <br><br>(here:
|
||
covariances of the means <br>of x1, x2, and x3)</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="309" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Calculating <br>eigenvectors
|
||
and eigenvalues</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
A = [3 1; 1 3]<br>A =<br> 3 1<br> 1
|
||
3<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
[eig_vec,eig_val] = eig(A)<br>eig_vec =<br> -0.70711
|
||
0.70711<br> 0.70711 0.70711<br>eig_val
|
||
=<br>Diagonal Matrix<br> 2 0<br> 0
|
||
4</font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A = np.array([[3, 1], [1, 3]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
A<br>array([[3, 1],<br> [1, 3]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
eig_val, eig_vec = np.linalg.eig(A)<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
eig_val<br>array([ 4., 2.])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
|
||
eig_vec<br>Array([[ 0.70710678, -0.70710678],<br>
|
||
[ 0.70710678, 0.70710678]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A = matrix(c(3,1,1,3), ncol=2)<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
A<br>[,1] [,2]<br>[1,] 3 1<br>[2,] 1 3<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
eigen(A)<br>$values<br>[1] 4 2<br><br>$vectors<br>[,1] [,2]<br>[1,]
|
||
0.7071068 -0.7071068<br>[2,] 0.7071068 0.7071068</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
A=[3 1; 1 3]<br>2x2 Array{Int64,2}:<br>3 1<br>1 3<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
(eig_vec,eig_val)=eig(a)<br>([2.0,4.0],<br>2x2
|
||
Array{Float64,2}:<br>-0.707107 0.707107<br>0.707107 0.707107)</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Calculating <br>eigenvectors
|
||
and eigenvalues</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
<tr valign="top">
|
||
<td width="171" height="542" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px solid #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Generating
|
||
a Gaussian dataset:<br><br>creating random vectors from the
|
||
multivariate normal<br>distribution given mean and covariance
|
||
matrix<br><br>(here: 5 random vectors with <br>mean 0, covariance
|
||
= 0, variance = 2)</b></font></font></p>
|
||
</td>
|
||
<td width="174" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: none; border-right: 1px dotted #000000; padding-top: 0in; padding-bottom: 0in; padding-left: 0in; padding-right: 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt">%
|
||
requires statistics toolbox package<br>% how to install and load
|
||
it in Octave:<br><br>% download the package from: <br>%
|
||
http://octave.sourceforge.net/packages.php<br>% pkg install <br>%
|
||
~/Desktop/io-2.0.2.tar.gz <br>% pkg install <br>%
|
||
~/Desktop/statistics-1.2.3.tar.gz<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
pkg load statistics<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
mean = [0 0]<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
cov = [2 0; 0 2]<br>cov =<br> 2 0<br> 0
|
||
2<br><br><font color="#006699"><font size="2" style="font-size: 10pt"><b>M></b></font></font>
|
||
mvnrnd(mean,cov,5)<br> 2.480150 -0.559906<br>
|
||
-2.933047 0.560212<br> 0.098206
|
||
3.055316<br> -0.985215 -0.990936<br> 1.122528
|
||
0.686977<br> </font></font></p>
|
||
</td>
|
||
<td width="128" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
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||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
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||
mean = np.array([0,0])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
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cov = np.array([[2,0],[0,2]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P></b></font></font>
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||
np.random.multivariate_normal(mean, cov, 5)<br><br>Array([[
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||
1.55432624, -1.17972629], <br>
|
||
[-2.01185294, 1.96081908], <br>
|
||
[-2.11810813, 1.45784216], <br>
|
||
[-2.93207591, -0.07369322], <br>
|
||
[-1.37031244, -1.18408792]])</font></font></p>
|
||
</td>
|
||
<td width="136" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt">#
|
||
requires the ‘mass’ package<br><br>
<font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
install.packages('MASS')<br><br>
<font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
library(MASS)
<br><br><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R></b></font></font>
|
||
mvrnorm(n=10, mean, cov)<br>[,1] [,2]<br>[1,] -0.8407830
|
||
-0.1882706<br>[2,] 0.8496822 -0.7889329<br>[3,] -0.1564171
|
||
0.8422177<br>[4,] -0.6288779 1.0618688<br>[5,] -0.5103879
|
||
0.1303697<br>[6,] 0.8413189 -0.1623758<br>[7,] -1.0495466
|
||
-0.4161082<br>[8,] -1.3236339 0.7755572<br>[9,] 0.2771013
|
||
1.4900494<br>[10,] -1.3536268 0.2338913</font></font></p>
|
||
</td>
|
||
<td width="126" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: none; padding-top: 0in; padding-bottom: 0in; padding-left: 0.02in; padding-right: 0in">
|
||
<p align="left"><font face="monospace"><font size="1" style="font-size: 8pt">#
|
||
requires the Distributions package from
|
||
https://github.com/JuliaStats/Distributions.jl<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
using Distributions<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
mean=[0., 0.]<br>2-element Array{Float64,1}:<br>0.0<br>0.0<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
cov=[2. 0.; 0. 2.]<br>2x2 Array{Float64,2}:<br>2.0 0.0<br>0.0
|
||
2.0<br><br><font color="#9966cc"><font size="2" style="font-size: 10pt"><b>J></b></font></font>
|
||
rand( MvNormal(mean, cov), 5)<br>2x5 Array{Float64,2}:<br>-0.527634
|
||
0.370725 -0.761928 -3.91747 1.47516<br>-0.448821 2.21904 2.24561
|
||
0.692063 0.390495</font></font></p>
|
||
</td>
|
||
<td width="188" bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0in 0.02in">
|
||
<p align="left"><font face="Arial"><font size="2" style="font-size: 10pt"><b>Generating
|
||
a Gaussian dataset:<br><br>creating random vectors from the
|
||
multivariate normal<br>distribution given mean and covariance
|
||
matrix<br><br>(here: 5 random vectors with <br>mean 0, covariance
|
||
= 0, variance = 2)</b></font></font></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
<p><!-- ************************************************************************** --><br><br>
|
||
</p>
|
||
</body>
|
||
</html> |