** Using WeBWorK **

I'm baffled.

-Tom

Software Error

WeBWorK has encountered a software error while attempting to process this problem. It is likely that there is an error in the problem itself. If you are a student, contact your professor to have the error corrected. If you are a professor, please consut the error output below for more informaiton.
Error messages

Can't take sqrt of -4.44089e-16 at (eval 1491073) line 31.
Error context

Problem1
ERROR caught by Translator while processing problem file:setHagedorn/WeirdError.pg
*
Can't take sqrt of -4.44089e-16 at (eval 1491073) line 31.

*

------Input Read
1 ##DESCRIPTION
2 ##KEYWORDS('linear algebra', 'inner product', 'dot product', 'angle')
3 ##
4 ##ENDDESCRIPTION
5
6 DOCUMENT(); # This should be the first executable line in the problem.
7
8 loadMacros(
9 PG.pl,
10 PGbasicmacros.pl,
11 PGchoicemacros.pl,
12 PGanswermacros.pl,
13 PGgraphmacros.pl,
14 PGnumericalmacros.pl,
15 PGstatisticsmacros.pl,
16 PGauxiliaryFunctions.pl,
17 PGmatrixmacros.pl
18 );
19
20 TEXT(beginproblem());
21 $showPartialCorrectAnswers = 1;
22
23 $prod = 0;
24 $norm_x = 0;
25 $norm_y = 0;
26
27 foreach $i (0..1) {
28 $x[$i] = non_zero_random(-5,5,1);
29 $y[$i] = non_zero_random(-5,5,1);
30 if ($y[$i] == $x[$i]) {
31 $y[$i] = 6;
32 }
33 $prod = $prod + $x[$i] * $y[$i];
34 $norm_x = $norm_x + $x[$i] * $x[$i];
35 $norm_y = $norm_y + $y[$i] * $y[$i];
36
37 }
38
39 if($norm_x <0){$norm_x= -$norm_x};
40 if($norm_y <0){$norm_y= -$norm_y};
41
42 $norm_x = sqrt($norm_x);
43 $norm_y = sqrt($norm_y);
44
45 $angle = arccos( $prod / $norm_x / $norm_y);
46
47 BEGIN_TEXT
48
49 Find the angle ( alpha ) between the vectors
50 { mbox( display_matrix([[$x[0]], [$x[1]]]), ' and ', display_matrix([[$y[0]], [$y[1]]]), '.' ) }
51 $BR
52 ( alpha = ) {ans_rule(20)}.
53
54 END_TEXT
55
56 ANS(num_cmp($angle));
57 ANS($norm_x);
58 ANS($norm_y);
59 ANS($x[1]);
60 ANS($x[0]);
61 ANS($y[0]);
62 ANS($y[1]);
63
64
65 ENDDOCUMENT(); # This should be the last executable line in the problem.

--

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The error comes from the arccos call. It is trying to take arccos(-1), but with round off error, it is arccos of something slightly less than -1. The result is not defined, but only shows up in the internal compuation of arccos (which involves a square root).

John

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This is now fixed in the CVS. The fix involved replacing a segment of code by

$norm_x = sqrt($norm_x);
$norm_y = sqrt($norm_y);

$value = $prod / $norm_x / $norm_y;

if ($value > 1) {$value = 1;}
if ($value < -1) {$value = -1;} ## avoid round off errors

$angle = arccos( $value );

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-Tom

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