# Difference between revisions of "FormulaTestPoints"

Paultpearson (talk | contribs) (added info about evaluating functions only at integers) |
(Added paragraph about functions only of one of the variables, and the "are" command) |
||

Line 48: | Line 48: | ||

(Using <code>test_at</code> adds the specified points to those already chosen from the continuous domain while with <code>test_points</code> only the specified test points are used.) |
(Using <code>test_at</code> adds the specified points to those already chosen from the continuous domain while with <code>test_points</code> only the specified test points are used.) |
||

If the function were a function of two variables, then we might use something like <code>$formula->{test_points} = [[-3,-2],[-2,0],[2,0],[3,2],[4,5]]</code>. <em>Note that the test points are given in alphabetical order by variable name! Thus, if the variables in the formula are specified as x and C, the test point [3,2] is C=3 and x=2.</em> |
If the function were a function of two variables, then we might use something like <code>$formula->{test_points} = [[-3,-2],[-2,0],[2,0],[3,2],[4,5]]</code>. <em>Note that the test points are given in alphabetical order by variable name! Thus, if the variables in the formula are specified as x and C, the test point [3,2] is C=3 and x=2.</em> |
||

+ | </p> |
||

+ | <p> |
||

+ | Also note that your test points must contain one value per variable, even if it doesn't appear in the formula; for instance, if <code>$gunc</code> is a function only of y, then you need to include values for x <em>and</em> y, not just y. The alternative is to use the command |
||

+ | <code>Context() -> variables -> are (y => 'Real')</code> which will remove the (default) variable x from the problem. |
||

</p> |
</p> |
||

<p> |
<p> |

## Revision as of 22:09, 31 May 2014

## Formula Test Points for Evaluation: PG Code Snippet

*This code snippet shows the essential PG code to specify the points on which a formula is evaluated when a student's answer is checked. Note that these are insertions, not a complete PG file. This code will have to be incorporated into the problem file on which you are working.*

This can, of course, be done with new and old-style answer evaluators. An example of the latter appears below. Also note that we may want to do this in two different ways: either by setting the *domain* on which the formula is evaluated (that is, the *limits of evaluation*), or by setting specific *test points* on which the formula should be considered. These are both shown below.

PG problem file | Explanation |
---|---|

Context("Numeric"); Context()->variables->set(x=>{limits=>[-1,1]}); $func = Compute("sqrt(x+1)"); ## Alternately: Context()->flags->set(limits=>[2,5]); # $func = Compute("sqrt(x-1)"); ## Or, setting the limits only for the given ## formula, we don't need to reset the Context, ## and just include # $func = Compute("sqrt(x-1)"); # $func->{limits} = [2,5]; $gunc = Compute("sqrt(x^2 - 4)"); $gunc->{test_points} = [[-3],[-2],[2],[3],[4]]; #$gunc->{test_at} = [[-3],[-2],[2],[3],[4]]; |
We don't have to change anything in the documentation and tagging or initialization sections of the PG file. In the problem set-up, we can specify the limits on which all Formulas are evaluated by setting the
It is also possible to specify the actual points on which the Formula will be evaluated. This is an attribute of the Formula itself; the call is shown for our formula
Also note that your test points must contain one value per variable, even if it doesn't appear in the formula; for instance, if
Note: if the formula is a function of more than one variable and we're specifying limits in the formula, we need to specify the limits for all variables. Thus, we'd have something like
If you are trying to set test points for a function you have added to the context (e.g., using loadMacros("parserFunction.pl"); Context("Numeric"); parserFunction("m(x)" => "log(x/2)" ); $h = Formula("5 m(x)+2"); $answer = $h->with(test_at => [[1],[2]]);
If you want to add a variable Context()->variables->add(n => ['Real', limits=>[1,20], resolution=>1]); |

BEGIN_TEXT Enter \( $func \): \{ ans_rule(35) \} $BR Enter \( $gunc \): \{ ans_rule(35) \} END_TEXT |
The text portion of the file is the same as usual. |

ANS( $func->cmp() ); ANS( $gunc->cmp() ); |
And the answer evaluation is as we'd expect. |

With old-style answer evaluators, we can do the same thing:

PG problem file | Explanation |
---|---|

$func = "sqrt(x+1)"; $gunc = "sqrt(x^2 - 4)"; |
We define the functions as expected in the problem set-up section of the file. |

BEGIN_TEXT Enter \( \sqrt{x+1} \): \{ ans_rule(35) \} $BR Enter \( \sqrt{x^2 - 4} \): \{ ans_rule(35) \} END_TEXT |
And the text portion of the file is similarly mundane. |

ANS(fun_cmp($func, limits=>[-1,1])); ANS(fun_cmp($gunc, test_points=>[-3,-2,2,3,4])); |
The limits or test points are specified in the |