📄 numbers.mht
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<FONT color=3D#ffa500>local</FONT> <FONT =
color=3D#9ac0cd>$_</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>foreach</FONT> <FONT =
color=3D#00ffff>(</FONT><FONT color=3D#98fb98>values</FONT> <FONT =
color=3D#cdcd00>%weights</FONT><FONT color=3D#00ffff>)</FONT> <FONT =
color=3D#00ffff>{</FONT>
$total +=3D $_<FONT color=3D#00ffff>;</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#ffa500>while</FONT> <FONT color=3D#00ffff>(</FONT> =
<FONT color=3D#00ffff>(</FONT>$key, $weight<FONT =
color=3D#00ffff>)</FONT> =3D <FONT color=3D#ff7f50>each</FONT> <FONT =
color=3D#cdcd00>%weights</FONT> <FONT color=3D#00ffff>)</FONT> <FONT =
color=3D#00ffff>{</FONT>
<FONT color=3D#cdcd00>$dist</FONT><FONT =
color=3D#00ffff>{</FONT>$key<FONT color=3D#00ffff>}</FONT> =3D =
$weight/$total<FONT color=3D#00ffff>;</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#ffa500>return</FONT> <FONT =
color=3D#cdcd00>%dist</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#bebebe># weighted_rand: takes a hash mapping key to =
probability, and
# returns the corresponding element
</FONT><FONT color=3D#ffa500>sub</FONT> weighted_<FONT =
color=3D#98fb98>rand</FONT> <FONT color=3D#00ffff>{</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT color=3D#cdcd00>%dist</FONT> =
=3D <FONT color=3D#cdad00>@_</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT color=3D#00ffff>(</FONT><FONT =
color=3D#9ac0cd>$key</FONT>, <FONT color=3D#9ac0cd>$weight</FONT><FONT =
color=3D#00ffff>);</FONT>
<FONT color=3D#ffa500>while</FONT> <FONT =
color=3D#00ffff>(</FONT><FONT color=3D#cdcd00>1</FONT><FONT =
color=3D#00ffff>)</FONT> <FONT color=3D#00ffff>{</FONT> =
<FONT color=3D#bebebe># to avoid floating point inaccuracies
</FONT> <FONT color=3D#ffa500>my</FONT> <FONT =
color=3D#9ac0cd>$rand</FONT> =3D <FONT color=3D#98fb98>rand</FONT><FONT =
color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>while</FONT> <FONT =
color=3D#00ffff>(</FONT> <FONT color=3D#00ffff>(</FONT>$key, =
$weight<FONT color=3D#00ffff>)</FONT> =3D <FONT =
color=3D#ff7f50>each</FONT> <FONT color=3D#cdcd00>%dist</FONT> <FONT =
color=3D#00ffff>)</FONT> <FONT color=3D#00ffff>{</FONT>
<FONT color=3D#ffa500>return</FONT> $key <FONT =
color=3D#ffa500>if</FONT> <FONT color=3D#00ffff>(</FONT>$rand -=3D =
$weight<FONT color=3D#00ffff>)</FONT> < <FONT =
color=3D#cdcd00>0</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#bebebe>#-----------------------------
# gaussian_rand as above
</FONT>$mean =3D <FONT color=3D#cdcd00>25</FONT><FONT =
color=3D#00ffff>;</FONT>
$sdev =3D <FONT color=3D#cdcd00>2</FONT><FONT color=3D#00ffff>;</FONT>
$salary =3D gaussian_<FONT color=3D#98fb98>rand</FONT><FONT =
color=3D#00ffff>()</FONT> * $sdev + $mean<FONT color=3D#00ffff>;</FONT>
<FONT color=3D#ff7f50>printf</FONT><FONT color=3D#00ffff>(</FONT><FONT =
color=3D#00cd00>"You have been hired at \$%.2f\n"</FONT>, $salary<FONT =
color=3D#00ffff>);</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT></PRE></FONT></TD></TR></TBODY></TABLE></DIV>
<DIV class=3DSECT2>
<H2 class=3DSECT2><A name=3DAEN103>Doing Trigonometry in Degrees, not=20
Radians</A></H2>
<TABLE width=3D"100%" bgColor=3D#2f4f4f border=3D0>
<TBODY>
<TR>
<TD><PRE class=3DSCREEN><FONT color=3D#f5deb3 size=3D+1><FONT =
color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>BEGIN</FONT> <FONT color=3D#00ffff>{</FONT>
<FONT color=3D#ffa500>use</FONT> <FONT =
color=3D#b2dfee>constant</FONT> <FONT color=3D#00cd00>PI</FONT> =3D> =
<FONT color=3D#cdcd00>3.14159265358979</FONT><FONT =
color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>sub</FONT> <FONT =
color=3D#b2dfee>deg2rad</FONT> <FONT color=3D#00ffff>{</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT =
color=3D#9ac0cd>$degrees</FONT> =3D <FONT =
color=3D#ff7f50>shift</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>return</FONT> <FONT =
color=3D#00ffff>(</FONT>$degrees / <FONT color=3D#cdcd00>180</FONT><FONT =
color=3D#00ffff>)</FONT> * PI<FONT color=3D#00ffff>;</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#ffa500>sub</FONT> <FONT =
color=3D#b2dfee>rad2deg</FONT> <FONT color=3D#00ffff>{</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT =
color=3D#9ac0cd>$radians</FONT> =3D <FONT =
color=3D#ff7f50>shift</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>return</FONT> <FONT =
color=3D#00ffff>(</FONT>$radians / PI<FONT color=3D#00ffff>)</FONT> * =
<FONT color=3D#cdcd00>180</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>use</FONT> <FONT =
color=3D#b2dfee>Math::Trig</FONT><FONT color=3D#00ffff>;</FONT>
$radians =3D deg2rad<FONT color=3D#00ffff>(</FONT>$degrees<FONT =
color=3D#00ffff>);</FONT>
$degrees =3D rad2deg<FONT color=3D#00ffff>(</FONT>$radians<FONT =
color=3D#00ffff>);</FONT>
<FONT color=3D#bebebe>#-----------------------------
# deg2rad and rad2deg defined either as above or from Math::Trig
</FONT><FONT color=3D#ffa500>sub</FONT> <FONT =
color=3D#b2dfee>degree_sine</FONT> <FONT color=3D#00ffff>{</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT =
color=3D#9ac0cd>$degrees</FONT> =3D <FONT =
color=3D#ff7f50>shift</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT =
color=3D#9ac0cd>$radians</FONT> =3D deg2rad<FONT =
color=3D#00ffff>(</FONT>$degrees<FONT color=3D#00ffff>);</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT color=3D#9ac0cd>$result</FONT> =
=3D <FONT color=3D#98fb98>sin</FONT><FONT =
color=3D#00ffff>(</FONT>$radians<FONT color=3D#00ffff>);</FONT>
<FONT color=3D#ffa500>return</FONT> $result<FONT =
color=3D#00ffff>;</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT></PRE></FONT></TD></TR></TBODY></TABLE></DIV>
<DIV class=3DSECT2>
<H2 class=3DSECT2><A name=3DAEN106>Calculating More Trigonometric =
Functions</A></H2>
<TABLE width=3D"100%" bgColor=3D#2f4f4f border=3D0>
<TBODY>
<TR>
<TD><PRE class=3DSCREEN><FONT color=3D#f5deb3 size=3D+1><FONT =
color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>sub</FONT> <FONT color=3D#b2dfee>tan</FONT> =
<FONT color=3D#00ffff>{</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT color=3D#9ac0cd>$theta</FONT> =
=3D <FONT color=3D#ff7f50>shift</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>return</FONT> <FONT =
color=3D#98fb98>sin</FONT><FONT color=3D#00ffff>(</FONT>$theta<FONT =
color=3D#00ffff>)</FONT>/<FONT color=3D#98fb98>cos</FONT><FONT =
color=3D#00ffff>(</FONT>$theta<FONT color=3D#00ffff>);</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>use</FONT> <FONT =
color=3D#b2dfee>POSIX</FONT><FONT color=3D#00ffff>;</FONT>
$y =3D acos<FONT color=3D#00ffff>(</FONT><FONT =
color=3D#cdcd00>3.7</FONT><FONT color=3D#00ffff>);</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>use</FONT> <FONT =
color=3D#b2dfee>Math::Trig</FONT><FONT color=3D#00ffff>;</FONT>
$y =3D acos<FONT color=3D#00ffff>(</FONT><FONT =
color=3D#cdcd00>3.7</FONT><FONT color=3D#00ffff>);</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>eval</FONT> <FONT color=3D#00ffff>{</FONT>
$y =3D tan<FONT color=3D#00ffff>(</FONT>$pi/<FONT =
color=3D#cdcd00>2</FONT><FONT color=3D#00ffff>);</FONT>
<FONT color=3D#00ffff>}</FONT> <FONT color=3D#98fb98>or</FONT> <FONT =
color=3D#ffa500>return</FONT> <FONT color=3D#ff7f50>undef</FONT><FONT =
color=3D#00ffff>;</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT></PRE></FONT></TD></TR></TBODY></TABLE></DIV>
<DIV class=3DSECT2>
<H2 class=3DSECT2><A name=3DAEN109>Taking Logarithms</A></H2>
<TABLE width=3D"100%" bgColor=3D#2f4f4f border=3D0>
<TBODY>
<TR>
<TD><PRE class=3DSCREEN><FONT color=3D#f5deb3 size=3D+1><FONT =
color=3D#bebebe>#-----------------------------
</FONT>$log_e =3D <FONT color=3D#98fb98>log</FONT><FONT =
color=3D#00ffff>(</FONT>VALUE<FONT color=3D#00ffff>);</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>use</FONT> <FONT =
color=3D#b2dfee>POSIX</FONT> <FONT color=3D#ff7f50>qw</FONT><FONT =
color=3D#00ffff>(</FONT>log10<FONT color=3D#00ffff>);</FONT>
$log_<FONT color=3D#cdcd00>10</FONT> =3D log10<FONT =
color=3D#00ffff>(</FONT>VALUE<FONT color=3D#00ffff>);</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>sub</FONT> <FONT =
color=3D#98fb98>log</FONT>_base <FONT color=3D#00ffff>{</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT color=3D#00ffff>(</FONT><FONT =
color=3D#9ac0cd>$base</FONT>, <FONT color=3D#9ac0cd>$value</FONT><FONT =
color=3D#00ffff>)</FONT> =3D <FONT color=3D#cdad00>@_</FONT><FONT =
color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>return</FONT> <FONT =
color=3D#98fb98>log</FONT><FONT color=3D#00ffff>(</FONT>$value<FONT =
color=3D#00ffff>)</FONT>/<FONT color=3D#98fb98>log</FONT><FONT =
color=3D#00ffff>(</FONT>$base<FONT color=3D#00ffff>);</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#bebebe>#-----------------------------
# log_base defined as above
</FONT>$answer =3D <FONT color=3D#98fb98>log</FONT>_base<FONT =
color=3D#00ffff>(</FONT><FONT color=3D#cdcd00>10</FONT>, <FONT =
color=3D#cdcd00>10</FONT>_<FONT color=3D#cdcd00>000</FONT><FONT =
color=3D#00ffff>);</FONT>
<FONT color=3D#ff7f50>print</FONT> <FONT color=3D#00cd00>"log10(10,000) =
=3D $answer\n"</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#bebebe># log10(10,000) =3D 4
#-----------------------------
</FONT><FONT color=3D#ffa500>use</FONT> <FONT =
color=3D#b2dfee>Math::Complex</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#ff7f50>printf</FONT> <FONT color=3D#00cd00>"log2(1024) =
=3D </FONT><FONT color=3D#cdcd00>%lf</FONT><FONT =
color=3D#00cd00>\n"</FONT>, logn<FONT color=3D#00ffff>(</FONT><FONT =
color=3D#cdcd00>1024</FONT>, <FONT color=3D#cdcd00>2</FONT><FONT =
color=3D#00ffff>);</FONT> <FONT color=3D#bebebe># watch out for argument =
order!
# log2(1024) =3D 10.000000
#-----------------------------
</FONT></PRE></FONT></TD></TR></TBODY></TABLE></DIV>
<DIV class=3DSECT2>
<H2 class=3DSECT2><A name=3DAEN112>Multiplying Matrices</A></H2>
<TABLE width=3D"100%" bgColor=3D#2f4f4f border=3D0>
<TBODY>
<TR>
<TD><PRE class=3DSCREEN><FONT color=3D#f5deb3 size=3D+1><FONT =
color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>use</FONT> <FONT =
color=3D#b2dfee>PDL</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#bebebe># $a and $b are both pdl objects
</FONT>$c =3D $a * $b<FONT color=3D#00ffff>;</FONT>
<FONT color=3D#bebebe>#-----------------------------
</FONT><FONT color=3D#ffa500>sub</FONT> <FONT =
color=3D#b2dfee>mmult</FONT> <FONT color=3D#00ffff>{</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT color=3D#00ffff>(</FONT><FONT =
color=3D#9ac0cd>$m1</FONT>,<FONT color=3D#9ac0cd>$m2</FONT><FONT =
color=3D#00ffff>)</FONT> =3D <FONT color=3D#cdad00>@_</FONT><FONT =
color=3D#00ffff>;</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT color=3D#00ffff>(</FONT><FONT =
color=3D#9ac0cd>$m1rows</FONT>,<FONT color=3D#9ac0cd>$m1cols</FONT><FONT =
color=3D#00ffff>)</FONT> =3D matdim<FONT =
color=3D#00ffff>(</FONT>$m1<FONT color=3D#00ffff>);</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT color=3D#00ffff>(</FONT><FONT =
color=3D#9ac0cd>$m2rows</FONT>,<FONT color=3D#9ac0cd>$m2cols</FONT><FONT =
color=3D#00ffff>)</FONT> =3D matdim<FONT =
color=3D#00ffff>(</FONT>$m2<FONT color=3D#00ffff>);</FONT>
<FONT color=3D#ffa500>unless</FONT> <FONT =
color=3D#00ffff>(</FONT>$m1cols =3D=3D $m2rows<FONT =
color=3D#00ffff>)</FONT> <FONT color=3D#00ffff>{</FONT> <FONT =
color=3D#bebebe># raise exception
</FONT> <FONT color=3D#ffa500>die</FONT> <FONT =
color=3D#00cd00>"IndexError: matrices don't match: $m1cols !=3D =
$m2rows"</FONT><FONT color=3D#00ffff>;</FONT>
<FONT color=3D#00ffff>}</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT color=3D#9ac0cd>$result</FONT> =
=3D <FONT color=3D#00ffff>[];</FONT>
<FONT color=3D#ffa500>my</FONT> <FONT color=3D#00ffff>(</FONT><FONT =
color=3D#9ac0cd>$i</FONT>, <FONT color=3D#9ac0cd>$j</FONT>, <FONT =
color=3D#9ac0cd>$k</FONT><FONT color=3D#00ffff>);</FONT>
<FONT color=3D#ffa500>for</FONT> <FONT color=3D#9ac0cd>$i</FONT> =
<FONT color=3D#00ffff>(</FONT>range<FONT =
color=3D#00ffff>(</FONT>$m1rows<FONT color=3D#00ffff>))</FONT> <FONT =
color=3D#00ffff>{</FONT>
<FONT color=3D#ffa500>for</FONT> <FONT color=3D#9ac0cd>$j</FONT> =
<FONT color=3D#00ffff>(</FONT>range<FONT =
color=3D#00ffff>(</FONT>$m2cols<FONT color=3D#00ffff>))</FONT> <FONT =
color=3D#00ffff>{</FONT>
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