Fun with y=mx+b

In the beginning, there were two dots. And I needed to find the line between these two dots, so I could find where a third dot would be if it were on that same line somewhere in between.

But wait. It gets worse. There aren't two dots in the beginning. There are two proto-dots, and first I must run them through some complex equations to find the two dots. (Said equations being deeply and obscurely buried in someone's paper, where they obviously didn't want them found.)

But wait. It gets worse. The line they're on isn't a simple straight line. It's all curvy, so I have to invoke logarithms.

But wait. It gets worse. Because there aren't just two proto-dots. There are several gazillion pairs of these dots, each of which has a separate curvy line to find.

And so I wrote some Matlab code. And lo, I saw that it was good.

B1=data(:,1);
B2=data(:,2);

negsB1=find(B1<=0);
adj_B1=B1;
adj_B1(negsB1)=NaN;

ratio=adj_B1./B2;
A323=log(.904*(.781*(ratio.^-1.07))-.00714);
A338=log(.858*(.604*(ratio.^-1.12))-.019);

slope=(A323-A338)/(323-338);
intercept=A323-slope*323;
RESULT=exp(slope*443+intercept);

But wait. My boss doesn't want it in Matlab. He wants it in IDL!

And so I wrote some more code. And lo, it was also good.

OK = WHERE(B1 GT 0.0)
SIZEB = SIZE(B1)
SX = SIZEB(1)
SY = SIZEB(2)
A323 = ALOG(0.904*(0.781*[B1/B2]^(-1.07))-0.00714)
A338 = ALOG(0.858*(0.604*[B1/B2]^(-1.12))-0.019)

SLOPE=[A323-A338]/(323-338)
INTERCEPT=A323-(SLOPE*323)
RESULT = REPLICATE(0.0,SX,SY)
RESULT(OK) = EXP((SLOPE(OK)*443)+INTERCEPT(OK))

Then when I was done with that, instead of doing any more real work I got carried away writing versions of the same code...

PHP style:

$data=explode("\n",$input);
$numrows=count($data);
$RESULT = array();

foreach ($data as $row) {
$columns = explode("\t", $row);
$B1=$columns[0];
$B2=$columns[1];

if ($B1 > 0) {
$A323 = log(0.904*(0.781*($B1/$B2)^(-1.07))-0.00714);
$A338 = log(0.858*(0.604*($B1/$B2)^(-1.12))-0.019);
$slope = ($A323-$A338)/(323-338);
$intercept = $A323-slope*323;
$RESULT[] = exp($slope*443+$intercept);
} #ends if loop

else {
$RESULT[] = 'NaN';
} #ends else

} #ends for loop

SQL style:

SELECT ln(0.904*(0.781*(B1/B2)^(-1.07))-0.00714) AS A323,
ln(0.858*(0.604*(B1/B2)^(-1.12))-0.019) AS A338,
(A323-A338)/(323-338) AS slope,
(A323-slope*323) AS intercept,
exp(slope*443+intercept) AS result
FROM data_table WHERE B1>0;

(Technically I don't know if these latter two work or not. They may not be so good.)

In the end, I've managed to solve for every variable in y=mx+b (x=(y-b)/m, b=y-mx, m=(y-b)/x, e^y=e^(mx+b), ...) and graphed slopes as if they were dots themselves. And that's about half of what I've been doing for the past month. Now the boss is successfully off to his conference with all the pretty pictures I made for him, and I'm back to wrangling with the last part of the Saga of the Three PHP Scripts.


Disclaimer: This version of events is highly fictionalized. I didn't do all that by myself - there was mucho input from my boss, a colleague, and a random guy in an IRC chatroom. No dots were harmed in the writing of this documentary.