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note about numpy in-place ops

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tutorials/matrix_cheatsheet.md
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@ -235,6 +235,8 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
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@ -243,7 +245,7 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
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<td height="57" bgcolor="#0066cc" style="border: none; padding: 0in"> <td height="59" bgcolor="#0066cc" style="border: none; padding: 0in">
<p align="center"><font color="#ffffff"><font face="Arial"><font size="5" style="font-size: 18pt"><b>Task</b></font></font></font></p> <p align="center"><font color="#ffffff"><font face="Arial"><font size="5" style="font-size: 18pt"><b>Task</b></font></font></font></p>
</td> </td>
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@ -264,9 +266,9 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
</td> </td>
</tr> </tr>
<tr> <tr>
<td colspan="6" height="70" bgcolor="#ffffff" style="border: none; padding: 0in" id="creating"> <td colspan="6" height="70" bgcolor="#ffffff" style="border: none; padding: 0in">
<p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>CREATING <p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>CREATING
MATRICES </b></font></font><br>[<a href='#cheat_overview'>back to cheat sheet overview</a>]</p> MATRICES</b></font></font></p>
</td> </td>
</tr> </tr>
<tr valign="top"> <tr valign="top">
@ -313,10 +315,15 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
3</font></font></p> 3</font></font></p>
</td> </td>
<td bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in"> <td 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="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> <p align="left"><font color="#ff420e"><font face="Andale Mono"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font></font>
a = np.array([[1],[2],[3]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> <font face="Andale Mono"><font size="1" style="font-size: 8pt">a</font></font><font color="#2fff12">
a<br>array([[1],<br>&nbsp;&nbsp; &nbsp; &nbsp; [2],<br>&nbsp;&nbsp; </font><font color="#000000"><font face="Andale Mono"><font size="1" style="font-size: 8pt">=
&nbsp; &nbsp; [3]])</font></font></p> np.array([1,2,3]).reshape(1,3)</font></font></font></p>
<p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><br></font></font><font color="#ff420e"><font face="Andale Mono"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font></font>
<font color="#000000"><font face="Andale Mono"><font size="1" style="font-size: 8pt">b.shape<br>(1,
3)</font></font></font></p>
<p align="left"><br>
</p>
</td> </td>
<td bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in"> <td 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="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R&gt;</b></font></font> <p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R&gt;</b></font></font>
@ -345,6 +352,14 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
<p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> <p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
b = np.array([1,2,3])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> b = np.array([1,2,3])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
b<br>array([1, 2, 3])</font></font></p> b<br>array([1, 2, 3])</font></font></p>
<p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt">#
note that numpy doesn't have <br># explicit “row-vectors”, but
1-D <br># arrays</font></font></p>
<p style="margin-bottom: 0in"><font face="Liberation Serif, serif"><font size="3" style="font-size: 12pt"><font color="#ff420e"><font face="Andale Mono"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font></font><font color="#2fff12">
</font><font color="#000000"><font face="Andale Mono"><font size="1" style="font-size: 8pt">b.shape</font></font></font></font></font></p>
<p style="margin-bottom: 0in"><font face="Andale Mono"><font size="1" style="font-size: 8pt">(3,)</font></font></p>
<p align="left"><br>
</p>
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<p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R&gt;</b></font></font> <p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R&gt;</b></font></font>
@ -434,7 +449,7 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
</td> </td>
<td bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in"> <td 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="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> <p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
np.ones([3,2])<br>array([[ 1.,&nbsp; 1.],<br>&nbsp;&nbsp; &nbsp; &nbsp; np.ones((3,2))<br>array([[ 1.,&nbsp; 1.],<br>&nbsp;&nbsp; &nbsp; &nbsp;
[ 1.,&nbsp; 1.],<br>&nbsp;&nbsp; &nbsp; &nbsp; [ 1.,&nbsp; 1.]])</font></font></p> [ 1.,&nbsp; 1.],<br>&nbsp;&nbsp; &nbsp; &nbsp; [ 1.,&nbsp; 1.]])</font></font></p>
</td> </td>
<td bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in"> <td bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
@ -519,9 +534,9 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
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<td colspan="6" height="128" bgcolor="#ffffff" style="border: none; padding: 0in" id='accessing'> <td colspan="6" height="128" bgcolor="#ffffff" style="border: none; padding: 0in">
<p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>ACCESSING <p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>ACCESSING
MATRIX ELEMENTS</b></font></font><br>[<a href='#cheat_overview'>back to cheat sheet overview</a>]</p> MATRIX ELEMENTS</b></font></font></p>
</td> </td>
</tr> </tr>
<tr valign="top"> <tr valign="top">
@ -714,9 +729,9 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
</td> </td>
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<tr> <tr>
<td colspan="6" height="128" bgcolor="#ffffff" style="border: none; padding: 0in" id="manipulating"> <td colspan="6" height="128" bgcolor="#ffffff" style="border: none; padding: 0in">
<p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>MANIPULATING <p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>MANIPULATING
SHAPE AND DIMENSIONS</b></font></font><br>[<a href='#cheat_overview'>back to cheat sheet overview</a>]</p> SHAPE AND DIMENSIONS</b></font></font></p>
</td> </td>
</tr> </tr>
<tr valign="top"> <tr valign="top">
@ -772,10 +787,10 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
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&gt;</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&gt;</b></font></font>
A<br>array([[1, 2, 3],<br>&nbsp;&nbsp; &nbsp; &nbsp; [4, 5, 9],<br>&nbsp;&nbsp; A<br>array([[1, 2, 3],<br>&nbsp;&nbsp; &nbsp; &nbsp; [4, 5, 9],<br>&nbsp;&nbsp;
&nbsp; &nbsp; [7, 8, 9]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> &nbsp; &nbsp; [7, 8, 9]])<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
total_elements = A.shape[0] * A.shape[1]<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> total_elements = np.prod(A.shape)</font></font></p>
B = A.reshape(1, total_elements)&nbsp;<br><br># or <p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
A.reshape(1,9)<br># Alternative: A.shape = (1,9)&nbsp;<br># B = A.reshape(1, total_elements)&nbsp;<br><br># alternative
to&nbsp;change the array in place<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> shortcut:<br># A.reshape(1,-1)<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
B<br>array([[1, 2, 3, 4, 5, 6, 7, 8, 9]])</font></font></p> B<br>array([[1, 2, 3, 4, 5, 6, 7, 8, 9]])</font></font></p>
</td> </td>
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@ -885,9 +900,9 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
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<tr> <tr>
<td colspan="6" height="114" bgcolor="#ffffff" style="border: none; padding: 0in" id='basic_ops'> <td colspan="6" height="114" bgcolor="#ffffff" style="border: none; padding: 0in">
<p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>BASIC <p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>BASIC
MATRIX OPERATIONS</b></font></font><br>[<a href='#cheat_overview'>back to cheat sheet overview</a>]</p> MATRIX OPERATIONS</b></font></font></p>
</td> </td>
</tr> </tr>
<tr valign="top"> <tr valign="top">
@ -912,6 +927,9 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
A + 2<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> A + 2<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
A - 2<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> A - 2<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
A / 2</font></font></p> A / 2</font></font></p>
<p align="left"><font face="Andale Mono"><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>
<td bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in"> <td 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="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R&gt;</b></font></font> <p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R&gt;</b></font></font>
@ -1025,6 +1043,9 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
A + A<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> A + A<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
A - A<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> A - A<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
A / A</font></font></p> A / A</font></font></p>
<p align="left"><font face="Andale Mono"><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>
<td bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in"> <td 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="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R&gt;</b></font></font> <p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R&gt;</b></font></font>
@ -1232,9 +1253,9 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
</td> </td>
</tr> </tr>
<tr> <tr>
<td colspan="6" height="202" bgcolor="#ffffff" style="border: none; padding: 0in" id='advanced_ops'> <td colspan="6" height="202" bgcolor="#ffffff" style="border: none; padding: 0in">
<p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>ADVANCED <p align="center"><font face="Arial"><font size="4" style="font-size: 14pt"><b>ADVANCED
MATRIX OPERATIONS</b></font></font><br>[<a href='#cheat_overview'>back to cheat sheet overview</a>]</p> MATRIX OPERATIONS</b></font></font></p>
</td> </td>
</tr> </tr>
<tr valign="top"> <tr valign="top">
@ -1328,7 +1349,7 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
</td> </td>
</tr> </tr>
<tr valign="top"> <tr valign="top">
<td height="539" 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"> <td height="541" 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 <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 a Gaussian dataset:<br><br>creating random vectors from the
multivariate normal<br>distribution given mean and covariance multivariate normal<br>distribution given mean and covariance
@ -1395,6 +1416,8 @@ Bezanson, J., Karpinski, S., Shah, V.B. and Edelman, A. (2012), “Julia: A fast
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<title></title> <title></title>
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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> <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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3</font></font></p> 3</font></font></p>
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<td bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in"> <td 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="#ff420e"><font face="Andale Mono"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font></font><font face="Andale Mono"><font size="1" style="font-size: 8pt"> <p align="left"><font color="#ff420e"><font face="Andale Mono"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font></font>
</font></font><font face="Andale Mono"><font size="1" style="font-size: 8pt">a</font></font><font color="#2fff12"><font face="AndaleMono, serif"><font size="4" style="font-size: 14pt"> <font face="Andale Mono"><font size="1" style="font-size: 8pt">a</font></font><font color="#2fff12">
</font></font></font><font color="#000000"><font face="Andale Mono"><font size="1" style="font-size: 8pt">= </font><font color="#000000"><font face="Andale Mono"><font size="1" style="font-size: 8pt">=
np.array([1,2,3]).reshape(1,3)</font></font></font></p> np.array([1,2,3]).reshape(1,3)</font></font></font></p>
<p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><br></font></font><font color="#ff420e"><font face="Andale Mono"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font></font><font face="Andale Mono"><font size="1" style="font-size: 8pt"> <p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><br></font></font><font color="#ff420e"><font face="Andale Mono"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font></font>
</font></font><font color="#000000"><font face="Andale Mono"><font size="1" style="font-size: 8pt">b.shape<br>(1, <font color="#000000"><font face="Andale Mono"><font size="1" style="font-size: 8pt">b.shape<br>(1,
3)</font></font></font></p> 3)</font></font></font></p>
<p align="left"><br> <p align="left"><br>
</p> </p>
@ -132,10 +132,10 @@
<p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"># <p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt">#
note that numpy doesn't have <br># explicit “row-vectors”, but note that numpy doesn't have <br># explicit “row-vectors”, but
1-D <br># arrays</font></font></p> 1-D <br># arrays</font></font></p>
<p style="margin-bottom: 0in"><font face="Liberation Serif, serif"><font size="3" style="font-size: 12pt"><font color="#ff420e"><font face="Andale Mono"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font></font><font color="#2fff12"><font face="AndaleMono, serif"><font size="4" style="font-size: 14pt"><b> <p style="margin-bottom: 0in"><font face="Liberation Serif, serif"><font size="3" style="font-size: 12pt"><font color="#ff420e"><font face="Andale Mono"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font></font><font color="#2fff12">
</b></font></font></font><font color="#000000"><font face="Andale Mono"><font size="1" style="font-size: 8pt">b.shape</font></font></font></font></font></p> </font><font color="#000000"><font face="Andale Mono"><font size="1" style="font-size: 8pt">b.shape</font></font></font></font></font></p>
<p style="margin-bottom: 0in"><font face="Andale Mono"><font size="1" style="font-size: 8pt">(3,)</font></font></p> <p style="margin-bottom: 0in"><font face="Andale Mono"><font size="1" style="font-size: 8pt">(3,)</font></font></p>
<p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><br></font></font><br> <p align="left"><br>
</p> </p>
</td> </td>
<td bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in"> <td bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in">
@ -704,6 +704,9 @@
A + 2<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> A + 2<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
A - 2<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> A - 2<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
A / 2</font></font></p> A / 2</font></font></p>
<p align="left"><font face="Andale Mono"><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>
<td bgcolor="#cfe7f5" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in"> <td 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="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R&gt;</b></font></font> <p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R&gt;</b></font></font>
@ -817,6 +820,9 @@
A + A<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> A + A<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
A - A<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font> A - A<br><br><font color="#ff420e"><font size="2" style="font-size: 10pt"><b>P&gt;</b></font></font>
A / A</font></font></p> A / A</font></font></p>
<p align="left"><font face="Andale Mono"><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>
<td bgcolor="#ffffff" style="border-top: none; border-bottom: none; border-left: 1px dotted #000000; border-right: 1px dotted #000000; padding: 0in 0.02in"> <td 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="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R&gt;</b></font></font> <p align="left"><font face="Andale Mono"><font size="1" style="font-size: 8pt"><font color="#0000ff"><font size="2" style="font-size: 10pt"><b>R&gt;</b></font></font>
@ -1120,7 +1126,7 @@
</td> </td>
</tr> </tr>
<tr valign="top"> <tr valign="top">
<td height="540" 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"> <td height="541" 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 <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 a Gaussian dataset:<br><br>creating random vectors from the
multivariate normal<br>distribution given mean and covariance multivariate normal<br>distribution given mean and covariance