Annotation of /trunk/webwork/system/courseScripts/PGanswermacros.pl

Revision 22 - (view) (download) (as text)

1 :	chris	22	#!/usr/local/bin/perl
2 :	sam	2
3 :			# This file is PGanswermacros.pl
4 :			# This includes the subroutines for the ANS macros, that
5 :			# is, macros allowing a more flexible answer checking
6 :			####################################################################
7 :			# Copyright @ 1995-2000 University of Rochester
8 :			# All Rights Reserved
9 :			####################################################################
10 :
11 :	chris	22
12 :	sam	2	=head1 NAME
13 :
14 :			PGanswermacros.pl -- located in the courseScripts directory
15 :
16 :			=head1 SYNPOSIS
17 :
18 :			Number Answer Evaluators:
19 :			num_cmp() -- uses an input hash to determine parameters
20 :			std_num_cmp(), std_num_cmp_list(), std_num_cmp_abs, std_num_cmp_abs_list()
21 :			frac_num_cmp(), frac_num_cmp_list(), frac_num_cmp_abs, frac_num_cmp_abs_list()
22 :			arith_num_cmp(), arith_num_cmp_list(), arith_num_cmp_abs, arith_num_cmp_abs_list()
23 :			strict_num_cmp(), strict_num_cmp_list(), strict_num_cmp_abs, strict_num_cmp_abs_list()
24 :			numerical_compare_with_units() -- requires units as part of the answer
25 :			std_num_str_cmp() -- also accepts a set of strings as possible answers
26 :
27 :			Function Answer Evaluators:
28 :			fun_cmp() -- uses an input hash to determine parameters
29 :			function_cmp(), function_cmp_abs()
30 :			function_cmp_up_to_constant(), function_cmp_up_to_constant_abs()
31 :			multivar_function_cmp()
32 :
33 :			String Answer Evaluators:
34 :			str_cmp() -- uses an input hash to determine parameters
35 :			std_str_cmp(), std_str_cmp_list(), std_cs_str_cmp(), std_cs_str_cmp_list()
36 :			strict_str_cmp(), strict_str_cmp_list()
37 :			ordered_str_cmp(), ordered_str_cmp_list(), ordered_cs_str_cmp(), ordered_cs_str_cmp_list()
38 :			unordered_str_cmp(), unordered_str_cmp_list(), unordered_cs_str_cmp(), unordered_cs_str_cmp_list()
39 :
40 :			Miscellaneous Answer Evaluators:
41 :			checkbox_cmp()
42 :			radio_cmp()
43 :
44 :			=cut
45 :
46 :			=head1 DESCRIPTION
47 :
48 :			This file adds subroutines which create "answer evaluators" for checking
49 :			answers. Each answer evaluator accepts a single input from a student answer,
50 :			checks it and creates an output hash %ans_hash with seven or eight entries
51 :			(the preview_latex_string is optional). The output hash is now being created
52 :			with the AnswerHash package "class", which is located at the end of this file.
53 :			This class is currently just a wrapper for the hash, but this might change in
54 :			the future as new capabilities are added.
55 :
56 :			score => $correctQ,
57 :			correct_ans => $originalCorrEqn,
58 :			student_ans => $modified_student_ans
59 :			original_student_ans => $original_student_answer,
60 :			ans_message => $PGanswerMessage,
61 :			type => 'typeString',
62 :			preview_text_string => $preview_text_string,
63 :			preview_latex_string => $preview_latex_string
64 :
65 :
66 :			$ans_hash{score} -- a number between 0 and 1 indicating
67 :			whether the answer is correct. Fractions
68 :			allow the implementation of partial
69 :			credit for incorrect answers.
70 :			$ans_hash{correct_ans} -- The correct answer, as supplied by the
71 :			instructor and then formatted. This can
72 :			be viewed by the student after the answer date.
73 :			$ans_hash{student_ans} -- This is the student answer, after reformatting;
74 :			for example the answer might be forced
75 :			to capital letters for comparison with
76 :			the instructors answer. For a numerical
77 :			answer, it gives the evaluated answer.
78 :			This is displayed in the section reporting
79 :			the results of checking the student answers.
80 :			$ans_hash{original_student_ans} -- This is the original student answer. This is displayed
81 :			on the preview page and may be used for sticky answers.
82 :			$ans_hash{ans_message} -- Any error message, or hint provided by the answer evaluator.
83 :			This is also displayed in the section reporting
84 :			the results of checking the student answers.
85 :			$ans_hash{type} -- A string indicating the type of answer evaluator. This
86 :			helps in preprocessing the student answer for errors.
87 :			Some examples:
88 :			'number_with_units'
89 :			'function'
90 :			'frac_number'
91 :			'arith_number'
92 :			$ans_hash{preview_text_string} -- This typically shows how the student answer was parsed. It is
93 :			displayed on the preview page. For a student answer of 2sin(3x)
94 :			this would be 2sin(3x). For string answers it is typically the
95 :			same as $ans_hash{student_ans}.
96 :			$ans_hash{preview_latex_string -- THIS IS OPTIONAL. This is latex version of the student answer
97 :			which is used to show a typeset view on the answer on the preview
98 :			page. For a student answer of 2/3, this would be \frac{2}{3}.
99 :
100 :			Technical note: the routines in this file are not actually answer evaluators. Instead, they create
101 :			answer evaluators. An answer evaluator is an anonymous subroutine, referenced by a named scalar. The
102 :			routines in this file build the subroutine and return a reference to it. Later, when the student
103 :			actually enters an answer, the problem processor feeds that answer to the referenced subroutine, which
104 :			evaluates it and returns a score (usually 0 or 1). For most users, this distinction is unimportant, but
105 :			if you plan on writing your own answer evaluators, you should understand this point.
106 :
107 :			=cut
108 :
109 :			BEGIN {
110 :			be_strict(); # an alias for use strict. This means that all global variable must contain main:: as a prefix.
111 :			}
112 :
113 :	chris	22	my $BR = $main::BR; # convenient localizations.
114 :			my $PAR = $main::PAR;
115 :	sam	2
116 :	chris	22	# import defaults
117 :			# these are now imported from the %envir variable
118 :			my $numRelPercentTolDefault = $main::numRelPercentTolDefault;
119 :			my $numZeroLevelDefault = $main::numZeroLevelDefault;
120 :			my $numZeroLevelTolDefault = $main::numZeroLevelTolDefault;
121 :			my $numAbsTolDefault = $main::numAbsTolDefault;
122 :			my $numFormatDefault = $main::numFormatDefault;
123 :	sam	2
124 :	chris	22	my $functRelPercentTolDefault = $main::functRelPercentTolDefault;
125 :			my $functZeroLevelDefault = $main::functZeroLevelDefault;
126 :			my $functZeroLevelTolDefault = $main::functZeroLevelTolDefault;
127 :			my $functAbsTolDefault = $main::functAbsTolDefault;
128 :			my $functNumOfPoints = $main::functNumOfPoints;
129 :			my $functVarDefault = $main::functVarDefault;
130 :			my $functLLimitDefault = $main::functLLimitDefault;
131 :			my $functULimitDefault = $main::functULimitDefault;
132 :			my $functMaxConstantOfIntegration = $main::functMaxConstantOfIntegration;
133 :	sam	2
134 :	chris	22
135 :
136 :	sam	2	##########################################################################
137 :			##########################################################################
138 :			## Number answer evaluators
139 :
140 :			=head2 Number Answer Evaluators
141 :
142 :			Number answer evaluators take in a numerical answer, compare it to the correct answer,
143 :			and return a score. In addition, they can choose to accept or reject an answer based on
144 :			its format, closeness to the correct answer, and other criteria. There are two types
145 :			of numerical answer evaluators: num_cmp(), which takes a hash of named options as parameters,
146 :			and the "mode"_num_cmp() variety, which use different functions to access different sets of
147 :			options. In addition, there is the special case of std_num_str_cmp(), which can evaluate
148 :			both numbers and strings.
149 :
150 :			Numerical Comparison Options
151 :
152 :			correctAnswer -- This is the correct answer that the student answer will
153 :			be compared to. However, this does not mean that the
154 :			student answer must match this exactly. How close the
155 :			student answer must be is determined by the other
156 :			options, especially tolerance and format.
157 :
158 :			tolerance -- These options determine how close the student answer
159 :			must be to the correct answer to qualify. There are two
160 :			types of tolerance: relative and absolute. Relative
161 :			tolerances are given in percentages. A relative
162 :			tolerance of 1 indicates that the student answer must
163 :			be within 1% of the correct answer to qualify as correct.
164 :			In other words, a student answer is correct when
165 :			abs(studentAnswer - correctAnswer) <= abs(.01relpercentTolcorrectAnswer)
166 :			Using absolute tolerance, the student answer must be a
167 :			fixed distance from the correct answer to qualify.
168 :			For example, an absolute tolerance of 5 means that any
169 :			number which is +-5 of the correct answer qualifies as correct.
170 :			Final (rarely used) tolerance options are zeroLevel
171 :			and zeroLevelTol, used in conjunction with relative
172 :			tolerance. if correctAnswer has absolute value less than
173 :			or equal to zeroLevel, then the student answer must be,
174 :			in absolute terms, within zeroLevelTol of correctAnswer, i.e.,
175 :			abs(studentAnswer - correctAnswer) <= zeroLevelTol.
176 :			In other words, if the correct answer is very near zero,
177 :			an absolute tolerance will be used. One must do this to
178 :			handle floating point answers very near zero, because of
179 :			the inaccuracy of floating point arithmetic. However, the
180 :			default values are almost always adequate.
181 :
182 :			mode -- This determines the allowable methods for entering an
183 :			answer. Answers which do not meet this requirement will
184 :			be graded as incorrect, regardless of their numerical
185 :			value. The recognized modes are:
186 :			'std' (default) -- allows any expression which evaluates
187 :			to a number, including those using
188 :			elementary functions like sin() and
189 :			exp(), as well as the operations of
190 :			arithmetic (+, -, *, /, ^)
191 :			'strict' -- only decimal numbers are allowed
192 :			'frac' -- whole numbers and fractions are allowed
193 :			'arith' -- arithmetic expressions are allowed, but
194 :			no functions
195 :			Note that all modes allow the use of "pi" and "e" as
196 :			constants, and also the use of "E" to represent scientific
197 :			notation.
198 :
199 :			format -- The format to use when displaying the correct and
200 :			submitted answers. This has no effect on how answers are
201 :			evaluated; it is only for cosmetic purposes. The
202 :			formatting syntax is the same as Perl uses for the sprintf()
203 :			function. Format strings are of the form '%m.nx' or '%m.nx#',
204 :			where m and n are described below, and x is a formatter.
205 :			Esentially, m is the minimum length of the field
206 :			(make this negative to left-justify). Note that the decimal
207 :			point counts as a character when determining the field width.
208 :			If m begins with a zero, the number will be padded with zeros
209 :			instead of spaces to fit the field.
210 :			The precision specifier (n) works differently, depending
211 :			on which formatter you are using. For d, i, o, u, x and X
212 :			formatters (non-floating point formatters), n is the minimum
213 :			number of digits to display. For e and f, it is the number of
214 :			digits that appear after the decimal point (extra digits will
215 :			be rounded; insufficient digits will be padded with spaces--see
216 :			'#' below). For g, it is the number of significant digits to
217 :			display.
218 :			The full list of formatters can be found in the manpage
219 :			for printf(3), or by typing "perldoc -f sprintf" at a
220 :			terminal prompt. The following is a brief summary of the
221 :			most frequent formatters:
222 :			d -- decimal number
223 :			ld -- long decimal number
224 :			u -- unsigned decimal number
225 :			lu -- long unsigned decimal number
226 :			x -- hexadecimal number
227 :			o -- octal number
228 :			e -- floating point number in scientific notation
229 :			f -- floating point number
230 :			g -- either e or f, whichever takes less space
231 :			Technically, g will use e if the exponent is less than -4 or
232 :			greater than or equal to the precision. Trailing zeros are
233 :			removed in this mode.
234 :			If the format string ends in '#', trailing zeros will be
235 :			removed in the decimal part. Note that this is not a standard
236 :			syntax; it is handled internally by WeBWorK and not by Perl
237 :			(although this should not be a concern to end users).
238 :			The default format is '%0.5f#', which displays as a floating
239 :			point number with 5 digits of precision and no trailing zeros.
240 :			Other useful format strings might be '%0.2f' for displaying
241 :			dollar amounts, or '%010d' to display an integer with leading
242 :			zeros. Setting format to an empty string ( '' ) means no
243 :			formatting will be used; this will show 'arbitrary' precision
244 :			floating points.
245 :
246 :			Default Values (As of 7/24/2000) (Option -- Variable Name -- Value)
247 :
248 :			Format -- $numFormatDefault -- "%0.5f#"
249 :			Relative Tolerance -- $numRelPercentTolDefault -- .1
250 :			Absolute Tolerance -- $numAbsTolDefault -- .001
251 :			Zero Level -- $numZeroLevelDefault -- 1E-14
252 :			Zero Level Tolerance -- $numZeroLevelTolDefault -- 1E-12
253 :
254 :			=cut
255 :
256 :			=head3 "mode"_num_cmp() functions
257 :
258 :			There are 16 functions total, 4 for each mode (std, frac, strict, arith). Each mode has
259 :			one "normal" function, one which accepts a list of answers, one which uses absolute
260 :			rather than relative tolerance, and one which uses absolute tolerance and accepts a list.
261 :			The "std" family is documented below; all others work precisely the same.
262 :
263 :			std_num_cmp($correctAnswer) OR
264 :			std_num_cmp($correctAnswer, $relPercentTol) OR
265 :			std_num_cmp($correctAnswer, $relPercentTol, $format) OR
266 :			std_num_cmp($correctAnswer, $relPercentTol, $format, $zeroLevel) OR
267 :			std_num_cmp($correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol)
268 :
269 :			$correctAnswer -- the correct answer
270 :			$relPercentTol -- the tolerance, as a percentage (optional)
271 :			$format -- the format of the displayed answer (optional)
272 :			$zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies (optional)
273 :			$zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero (optional)
274 :
275 :			std_num_cmp() uses standard mode (arithmetic operations and elementary
276 :			functions allowed) and relative tolerance. Options are specified by
277 :			one or more parameters. Note that if you wish to set an option which
278 :			is later in the parameter list, you must set all previous options.
279 :
280 :			std_num_cmp_abs($correctAnswer) OR
281 :			std_num_cmp_abs($correctAnswer, $absTol) OR
282 :			std_num_cmp_abs($correctAnswer, $absTol, $format)
283 :
284 :			$correctAnswer -- the correct answer
285 :			$absTol -- an absolute tolerance (optional)
286 :			$format -- the format of the displayed answer (optional)
287 :
288 :			std_num_cmp_abs() uses standard mode and absolute tolerance. Options
289 :			are set as with std_num_cmp(). Note that $zeroLevel and $zeroLevelTol
290 :			do not apply with absolute tolerance.
291 :
292 :			std_num_cmp_list($relPercentTol, $format, @answerList)
293 :
294 :			$relPercentTol -- the tolerance, as a percentage
295 :			$format -- the format of the displayed answer(s)
296 :			@answerList -- a list of one or more correct answers
297 :
298 :			std_num_cmp_list() uses standard mode and relative tolerance. There
299 :			is no way to set $zeroLevel or $zeroLevelTol. Note that no
300 :			parameters are optional. All answers in the list will be
301 :			evaluated with the same set of parameters.
302 :
303 :			std_num_cmp_abs_list($absTol, $format, @answerList)
304 :
305 :			$absTol -- an absolute tolerance
306 :			$format -- the format of the displayed answer(s)
307 :			@answerList -- a list of one or more correct answers
308 :
309 :			std_num_cmp_abs_list() uses standard mode and absolute tolerance.
310 :			Note that no parameters are optional. All answers in the list will be
311 :			evaluated with the same set of parameters.
312 :
313 :			arith_num_cmp(), arith_num_cmp_list(), arith_num_cmp_abs(), arith_num_cmp_abs_list()
314 :			strict_num_cmp(), strict_num_cmp_list(), strict_num_cmp_abs(), strict_num_cmp_abs_list()
315 :			frac_num_cmp(), frac_num_cmp_list(), frac_num_cmp_abs(), frac_num_cmp_abs_list()
316 :
317 :			Examples:
318 :
319 :			ANS( strict_num_cmp( 3.14159 ) ) -- The student answer must be a number
320 :			in decimal or scientific notation which is within .1 percent of 3.14159.
321 :			This assumes $numRelPercentTolDefault has been set to .1.
322 :			ANS( strict_num_cmp( $answer, .01 ) ) -- The student answer must be a
323 :			number within .01 percent of $answer (e.g. 3.14159 if $answer is 3.14159
324 :			or $answer is "pi" or $answer is 4*atan(1)).
325 :			ANS( frac_num_cmp( $answer) ) or ANS( frac_num_cmp( $answer,.01 )) --
326 :			The student answer can be a number or fraction, e.g. 2/3.
327 :			ANS( arith_num_cmp( $answer) ) or ANS( arith_num_cmp( $answer,.01 )) --
328 :			The student answer can be an arithmetic expression, e.g. (2+3)/7-2^.5 .
329 :			ANS( std_num_cmp( $answer) ) or ANS( std_num_cmp( $answer,.01 )) --
330 :			The student answer can contain elementary functions, e.g. sin(.3+pi/2)
331 :
332 :			=cut
333 :
334 :			sub std_num_cmp { # compare numbers allowing use of elementary functions
335 :	chris	22	my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
336 :	sam	2
337 :	chris	22	my %options = ( 'tolerance' => $relPercentTol,
338 :			'format' => $format,
339 :			'zeroLevel' => $zeroLevel,
340 :			'zeroLevelTol' => $zeroLevelTol
341 :			);
342 :
343 :			set_default_options( \%options,
344 :			'tolType' => 'relative',
345 :			'tolerance' => $numRelPercentTolDefault,
346 :			'mode' => 'std',
347 :			'format' => $numFormatDefault,
348 :			'relTol' => $numRelPercentTolDefault,
349 :			'zeroLevel' => $numZeroLevelDefault,
350 :			'zeroLevelTol' => $numZeroLevelTolDefault,
351 :			'debug' => 0,
352 :			);
353 :
354 :			num_cmp([$correctAnswer], %options);
355 :	sam	2	}
356 :
357 :			## Similar to std_num_cmp but accepts a list of numbers in the form
358 :			## std_num_cmp_list(relpercentTol,format,ans1,ans2,ans3,...)
359 :			## format is of the form "%10.3g" or "", i.e., a format suitable for sprintf(). Use "" for default
360 :			## You must enter a format and tolerance
361 :			sub std_num_cmp_list {
362 :			my ( $relPercentTol, $format, @answerList) = @_;
363 :
364 :	chris	22	my %options = ( 'tolerance' => $relPercentTol,
365 :			'format' => $format,
366 :			);
367 :
368 :			set_default_options( \%options,
369 :			'tolType' => 'relative',
370 :			'tolerance' => $numRelPercentTolDefault,
371 :			'mode' => 'std',
372 :			'format' => $numFormatDefault,
373 :			'relTol' => $numRelPercentTolDefault,
374 :			'zeroLevel' => $numZeroLevelDefault,
375 :			'zeroLevelTol' => $numZeroLevelTolDefault,
376 :			'debug' => 0,
377 :			);
378 :
379 :			num_cmp(\@answerList, %options);
380 :
381 :	sam	2	}
382 :
383 :	chris	22	sub std_num_cmp_abs { # compare numbers allowing use of elementary functions with absolute tolerance
384 :	sam	2	my ( $correctAnswer, $absTol, $format) = @_;
385 :	chris	22	my %options = ( 'tolerance' => $absTol,
386 :			'format' => $format);
387 :
388 :			set_default_options (\%options,
389 :			'tolType' => 'absolute',
390 :			'tolerance' => $absTol,
391 :			'mode' => 'std',
392 :			'format' => $numFormatDefault,
393 :			'zeroLevel' => 0,
394 :			'zeroLevelTol' => 0,
395 :			'debug' => 0,
396 :			);
397 :	sam	2
398 :	chris	22	num_cmp([$correctAnswer], %options);
399 :	sam	2	}
400 :
401 :			## See std_num_cmp_list for usage
402 :	chris	22
403 :	sam	2	sub std_num_cmp_abs_list {
404 :			my ( $absTol, $format, @answerList ) = @_;
405 :
406 :	chris	22	my %options = ( 'tolerance' => $absTol,
407 :			'format' => $format,
408 :			);
409 :
410 :			set_default_options( \%options,
411 :			'tolType' => 'absolute',
412 :			'tolerance' => $absTol,
413 :			'mode' => 'std',
414 :			'format' => $numFormatDefault,
415 :			'zeroLevel' => 0,
416 :			'zeroLevelTol' => 0,
417 :			'debug' => 0,
418 :			);
419 :
420 :			num_cmp(\@answerList, %options);
421 :
422 :	sam	2	}
423 :
424 :			sub frac_num_cmp { # only allow fractions and numbers as submitted answer
425 :
426 :	chris	22	my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
427 :
428 :			my %options = ( 'tolerance' => $relPercentTol,
429 :			'format' => $format,
430 :			'zeroLevel' => $zeroLevel,
431 :			'zeroLevelTol' => $zeroLevelTol
432 :			);
433 :
434 :			set_default_options( \%options,
435 :			'tolType' => 'relative',
436 :			'tolerance' => $relPercentTol,
437 :			'mode' => 'frac',
438 :			'format' => $numFormatDefault,
439 :			'zeroLevel' => $numZeroLevelDefault,
440 :			'zeroLevelTol' => $numZeroLevelTolDefault,
441 :			'relTol' => $numRelPercentTolDefault,
442 :			'debug' => 0,
443 :			);
444 :
445 :			num_cmp([$correctAnswer], %options);
446 :	sam	2	}
447 :
448 :			## See std_num_cmp_list for usage
449 :			sub frac_num_cmp_list {
450 :	chris	22	my ( $relPercentTol, $format, @answerList ) = @_;
451 :
452 :			my %options = ( 'tolerance' => $relPercentTol,
453 :			'format' => $format
454 :			);
455 :
456 :			set_default_options( \%options,
457 :			'tolType' => 'relative',
458 :			'tolerance' => $relPercentTol,
459 :			'mode' => 'frac',
460 :			'format' => $numFormatDefault,
461 :			'zeroLevel' => $numZeroLevelDefault,
462 :			'zeroLevelTol' => $numZeroLevelTolDefault,
463 :			'relTol' => $numRelPercentTolDefault,
464 :			'debug' => 0,
465 :			);
466 :
467 :			num_cmp(\@answerList, %options);
468 :
469 :	sam	2	}
470 :
471 :	chris	22	sub frac_num_cmp_abs { # only allow fraction expressions as submitted answer with absolute tolerance
472 :			my ( $correctAnswer, $absTol, $format ) = @_;
473 :
474 :			my %options = ( 'tolerance' => $absTol,
475 :			'format' => $format
476 :			);
477 :
478 :			set_default_options (\%options,
479 :			'tolType' => 'absolute',
480 :			'tolerance' => $absTol,
481 :			'mode' => 'frac',
482 :			'format' => $numFormatDefault,
483 :			'zeroLevel' => 0,
484 :			'zeroLevelTol' => 0,
485 :			'debug' => 0,
486 :			);
487 :			num_cmp([$correctAnswer], %options);
488 :
489 :	sam	2	}
490 :	chris	22
491 :	sam	2	## See std_num_cmp_list for usage
492 :			sub frac_num_cmp_abs_list {
493 :	chris	22	my ( $absTol, $format, @answerList ) = @_;
494 :
495 :			my %options = ( 'tolerance' => $absTol,
496 :			'format' => $format
497 :			);
498 :
499 :			set_default_options (\%options,
500 :			'tolType' => 'absolute',
501 :			'tolerance' => $absTol,
502 :			'mode' => 'frac',
503 :			'format' => $numFormatDefault,
504 :			'zeroLevel' => 0,
505 :			'zeroLevelTol' => 0,
506 :			'debug' => 0,
507 :			);
508 :
509 :			num_cmp(\@answerList, %options);
510 :	sam	2	}
511 :
512 :
513 :			sub arith_num_cmp { # only allow arithmetic expressions as submitted answer
514 :	chris	22
515 :			my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
516 :
517 :			my %options = ( 'tolerance' => $relPercentTol,
518 :			'format' => $format,
519 :			'zeroLevel' => $zeroLevel,
520 :			'zeroLevelTol' => $zeroLevelTol
521 :			);
522 :
523 :			set_default_options( \%options,
524 :			'tolType' => 'relative',
525 :			'tolerance' => $relPercentTol,
526 :			'mode' => 'arith',
527 :			'format' => $numFormatDefault,
528 :			'zeroLevel' => $numZeroLevelDefault,
529 :			'zeroLevelTol' => $numZeroLevelTolDefault,
530 :			'relTol' => $numRelPercentTolDefault,
531 :			'debug' => 0,
532 :			);
533 :	sam	2
534 :	chris	22	num_cmp([$correctAnswer], %options);
535 :	sam	2	}
536 :
537 :			## See std_num_cmp_list for usage
538 :			sub arith_num_cmp_list {
539 :	chris	22	my ( $relPercentTol, $format, @answerList ) = @_;
540 :	sam	2
541 :	chris	22	my %options = ( 'tolerance' => $relPercentTol,
542 :			'format' => $format,
543 :			);
544 :
545 :			set_default_options( \%options,
546 :			'tolType' => 'relative',
547 :			'tolerance' => $relPercentTol,
548 :			'mode' => 'arith',
549 :			'format' => $numFormatDefault,
550 :			'zeroLevel' => $numZeroLevelDefault,
551 :			'zeroLevelTol' => $numZeroLevelTolDefault,
552 :			'relTol' => $numRelPercentTolDefault,
553 :			'debug' => 0,
554 :			);
555 :			num_cmp(\@answerList, %options);
556 :	sam	2	}
557 :
558 :	chris	22	sub arith_num_cmp_abs { # only allow arithmetic expressions as submitted answer with absolute tolerance
559 :			my ( $correctAnswer, $absTol, $format ) = @_;
560 :
561 :			my %options = ( 'tolerance' => $absTol,
562 :			'format' => $format
563 :			);
564 :
565 :			set_default_options (\%options,
566 :			'tolType' => 'absolute',
567 :			'tolerance' => $absTol,
568 :			'mode' => 'arith',
569 :			'format' => $numFormatDefault,
570 :			'zeroLevel' => 0,
571 :			'zeroLevelTol' => 0,
572 :			'debug' => 0,
573 :			);
574 :			num_cmp([$correctAnswer], %options);
575 :	sam	2
576 :	chris	22
577 :	sam	2	}
578 :
579 :			## See std_num_cmp_list for usage
580 :			sub arith_num_cmp_abs_list {
581 :	chris	22	my ( $absTol, $format, @answerList ) = @_;
582 :
583 :			my %options = ( 'tolerance' => $absTol,
584 :			'format' => $format
585 :			);
586 :
587 :			set_default_options (\%options,
588 :			'tolType' => 'absolute',
589 :			'tolerance' => $absTol,
590 :			'mode' => 'arith',
591 :			'format' => $numFormatDefault,
592 :			'zeroLevel' => 0,
593 :			'zeroLevelTol' => 0,
594 :			'debug' => 0,
595 :			);
596 :			num_cmp(\@answerList, %options);
597 :
598 :	sam	2	}
599 :
600 :			sub strict_num_cmp { # only allow numbers as submitted answer
601 :	chris	22
602 :			my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
603 :
604 :			my %options = ( 'tolerance' => $relPercentTol,
605 :			'format' => $format,
606 :			'zeroLevel' => $zeroLevel,
607 :			'zeroLevelTol' => $zeroLevelTol
608 :			);
609 :
610 :			set_default_options( \%options,
611 :			'tolType' => 'relative',
612 :			'tolerance' => $relPercentTol,
613 :			'mode' => 'strict',
614 :			'format' => $numFormatDefault,
615 :			'zeroLevel' => $numZeroLevelDefault,
616 :			'zeroLevelTol' => $numZeroLevelTolDefault,
617 :			'relTol' => $numRelPercentTolDefault,
618 :			'debug' => 0,
619 :			);
620 :
621 :			num_cmp([$correctAnswer], %options);
622 :	sam	2
623 :			}
624 :
625 :			## See std_num_cmp_list for usage
626 :			sub strict_num_cmp_list { # compare numbers
627 :			my ( $relPercentTol, $format, @answerList ) = @_;
628 :	chris	22
629 :			my %options = ( 'tolerance' => $relPercentTol,
630 :			'format' => $format,
631 :			);
632 :
633 :			set_default_options( \%options,
634 :			'tolType' => 'relative',
635 :			'tolerance' => $relPercentTol,
636 :			'mode' => 'strict',
637 :			'format' => $numFormatDefault,
638 :			'zeroLevel' => $numZeroLevelDefault,
639 :			'zeroLevelTol' => $numZeroLevelTolDefault,
640 :			'relTol' => $numRelPercentTolDefault,
641 :			'debug' => 0,
642 :			);
643 :	sam	2
644 :	chris	22	num_cmp(\@answerList, %options);
645 :			}
646 :	sam	2
647 :	chris	22
648 :	sam	2	sub strict_num_cmp_abs { # only allow numbers as submitted answer with absolute tolerance
649 :
650 :	chris	22	my ( $correctAnswer, $absTol, $format ) = @_;
651 :
652 :			my %options = ( 'tolerance' => $absTol,
653 :			'format' => $format
654 :			);
655 :
656 :			set_default_options (\%options,
657 :			'tolType' => 'absolute',
658 :			'tolerance' => $absTol,
659 :			'mode' => 'strict',
660 :			'format' => $numFormatDefault,
661 :			'zeroLevel' => 0,
662 :			'zeroLevelTol' => 0,
663 :			'debug' => 0,
664 :			);
665 :
666 :			num_cmp([$correctAnswer], %options);
667 :
668 :	sam	2	}
669 :
670 :			## See std_num_cmp_list for usage
671 :			sub strict_num_cmp_abs_list { # compare numbers
672 :	chris	22	my ( $absTol, $format, @answerList ) = @_;
673 :	sam	2
674 :	chris	22	my %options = ( 'tolerance' => $absTol,
675 :			'format' => $format
676 :			);
677 :
678 :			set_default_options (\%options,
679 :			'tolType' => 'absolute',
680 :			'tolerance' => $absTol,
681 :			'mode' => 'strict',
682 :			'format' => $numFormatDefault,
683 :			'zeroLevel' => 0,
684 :			'zeroLevelTol' => 0,
685 :			'debug' => 0,
686 :			);
687 :
688 :			num_cmp(\@answerList, %options);
689 :
690 :	sam	2	}
691 :
692 :			## Compares a number with units
693 :			## Deprecated; use num_cmp()
694 :			##
695 :			## IN: a string which includes the numerical answer and the units
696 :			## a hash with the following keys (all optional):
697 :			## mode -- 'std', 'frac', 'arith', or 'strict'
698 :			## format -- the format to use when displaying the answer
699 :			## tol -- an absolute tolerance, or
700 :			## relTol -- a relative tolerance
701 :			## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
702 :			## zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero
703 :
704 :
705 :	chris	22	sub check_units {
706 :			my ($rh_ans, %options) = @_;
707 :
708 :			my %correct_units = %{$rh_ans-> {rh_correct_units}};
709 :
710 :			my $ans = $rh_ans->{student_ans};
711 :			# $ans = '' unless defined ($ans);
712 :			my $original_student_ans = $ans;
713 :
714 :			# $ans = str_filters ($ans, 'trim_whitespace');
715 :			$rh_ans->{original_student_ans} = $original_student_ans;
716 :
717 :			# it surprises me that the match below works since the first .* is greedy.
718 :			my ($num_answer, $units) = $ans =~ /^(.)\s+([^\s])$/;
719 :
720 :			unless ( defined($num_answer) && $units ) {
721 :			# there is an error reading the input
722 :			if ( $ans =~ /\S/ ) { # the answer is not blank
723 :			$rh_ans -> setKeys( 'ans_message' => "The answer \"$ans\" could not be interpreted " .
724 :			"as a number or an arithmetic expression followed by a unit specification. " .
725 :			"Your answer must contain units." );
726 :			$rh_ans->throw_error('UNITS', "The answer \"$ans\" could not be interpreted " .
727 :			"as a number or an arithmetic expression followed by a unit specification. " .
728 :			"Your answer must contain units." );
729 :			}
730 :	sam	2
731 :	chris	22	return $rh_ans;
732 :	sam	2	}
733 :
734 :	chris	22	# we have been able to parse the answer into a numerical part and a unit part
735 :	sam	2
736 :	chris	22	# $num_answer = $1; #$1 and $2 from the regular expression above
737 :			# $units = $2;
738 :	sam	2
739 :	chris	22	my %units = Units::evaluate_units($units);
740 :			if ( defined( $units{'ERROR'} ) ) {
741 :			# handle error condition
742 :			$units{'ERROR'} = clean_up_error_msg($units{'ERROR'});
743 :			$rh_ans -> setKeys( 'ans_message' => "$units{'ERROR'}" );
744 :			return $rh_ans;
745 :	sam	2	}
746 :
747 :	chris	22	my $units_match = 1;
748 :			my $fund_unit;
749 :			foreach $fund_unit (keys %correct_units) {
750 :			next if $fund_unit eq 'factor';
751 :			$units_match = 0 unless $correct_units{$fund_unit} == $units{$fund_unit};
752 :			}
753 :
754 :			if ( $units_match ) {
755 :			# units are ok. Evaluate the numerical part of the answer
756 :			$rh_ans->{'tolerance'} = $rh_ans->{'tolerance'}* $correct_units{'factor'}/$units{'factor'} if
757 :			$rh_ans->{'tolType'} eq 'absolute'; # the tolerance is in the units specified by the instructor.
758 :			$rh_ans->{correct_ans} = prfmt($rh_ans->{correct_ans}*$correct_units{'factor'}/$units{'factor'});
759 :	sam	2
760 :	chris	22
761 :	sam	2
762 :
763 :	chris	22	$rh_ans->{student_ans} = $num_answer;
764 :			# return $rh_ans;
765 :			# my $numerical_answer_evaluator = NUM_CMP( 'correctAnswer' => $correct_num_answer*$correct_units{'factor'}/$units{'factor'},
766 :			# 'tolerance' => $rh_ans->{'tolerance'},
767 :			# 'tolType' => $rh_ans->{'tolType'},
768 :			# 'format' => $options{'format'},
769 :			# 'mode' => $options{'mode'},
770 :			# 'zeroLevel' => $options{'zeroLevel'},
771 :			# 'zeroLevelTol' => $options{'zeroLevelTol'} );
772 :			#
773 :			# # because num_answer may contain an arithmetic expression rather than
774 :			# # a number we can't multiply it by the $units{'factor'}
775 :			# # instead we divide the correctanswer by this amount;
776 :			# # this is also why the numerical_answer_evaluator is not defined outside this subroutine.
777 :			#
778 :			# # $ans_hash = &$numerical_answer_evaluator($num_answer);
779 :			#
780 :			# # now we need to doctor the correct answer in order to add units
781 :			# # to it and correct for the division we did before
782 :			# $ans_hash -> {correct_ans} =
783 :			# prfmt( ( $ans_hash->{'correct_ans'} )*$units{'factor'}/$correct_units{'factor'},
784 :			# $options{'format'} ) . " $correct_units";
785 :			# # we also need to doctor the submitted answer to get it back in its original format.
786 :			#
787 :			# # we don't add the units on if there is an error message from numerical_answer_evaluator
788 :			# if ( ( $ans_hash -> {ans_message} ) =~ /^\s*$/ ) {
789 :			# $ans_hash -> {student_ans} = $ans_hash -> {student_ans} . " $units";
790 :			# $ans_hash -> setKeys( original_student_ans => $ans );
791 :			# }
792 :			# else {
793 :			# # error message from numerical_answer_evaluator doesn't have units tacked on
794 :			# $ans_hash -> setKeys( original_student_ans => $ans );
795 :			# }
796 :			} else {
797 :			$rh_ans -> setKeys( ans_message => 'There is an error in the units for this answer.' );
798 :			$rh_ans -> throw_error ( 'UNITS', 'There is an error in the units for this answer.' );
799 :	sam	2	}
800 :	chris	22
801 :			return $rh_ans;
802 :			}
803 :	sam	2
804 :	chris	22	sub numerical_compare_with_units {
805 :			my $correct_answer = shift; # the answer is a string which includes both the numerical answer and the units.
806 :			my %options = @_; # all of the other inputs are (key value) pairs
807 :	sam	2
808 :	chris	22	# Prepare the correct answer
809 :			$correct_answer = str_filters( $correct_answer, 'trim_whitespace' );
810 :	sam	2
811 :	chris	22	# it surprises me that the match below works since the first .* is greedy.
812 :			my ($correct_num_answer, $correct_units) = $correct_answer =~ /^(.)\s+([^\s])$/;
813 :	sam	2
814 :	chris	22	$options{units} = $correct_units;
815 :
816 :
817 :			num_cmp($correct_num_answer, %options);
818 :	sam	2	}
819 :	chris	22
820 :			#sub numerical_compare_with_units {
821 :			# my $correct_answer = shift; # the answer is a string which includes both the numerical answer and the units.
822 :			# my %options = @_; # all of the other inputs are (key value) pairs
823 :			#
824 :			# # handle the defaults
825 :			# $options{'mode'} = 'std' unless defined( $options{'mode'} );
826 :			# $options{'format'} = $numFormatDefault unless defined( $options{'format'} );
827 :			# $options{'zeroLevel'} = $numZeroLevelDefault unless defined( $options{'zeroLevel'} );
828 :			# $options{'zeroLevelTol'} = $numZeroLevelTolDefault unless defined( $options{'zeroLevelTol'} );
829 :			#
830 :			# # both spellings are maintained for backward compatibility
831 :			# # relTol is preferred
832 :			# if( defined $options{'reltol'} ) {
833 :			# $options{'relTol'} = $options{'reltol'};
834 :			# delete $options{'reltol'};
835 :			# }
836 :			#
837 :			# my ($tol, $tolerance_mode);
838 :			# if ( defined $options{'tol'} ) {
839 :			# $tol = $options{'tol'};
840 :			# $tolerance_mode = 'absolute';
841 :			# }
842 :			# elsif( defined $options{'relTol'} ) {
843 :			# $tol = $options{'relTol'};
844 :			# $tolerance_mode = 'relative';
845 :			# }
846 :			# else { #the default is a relative tolerance
847 :			# $tol = $numRelPercentTolDefault;
848 :			# $tolerance_mode = 'relative';
849 :			# }
850 :			#
851 :			# # Prepare the correct answer
852 :			# $correct_answer = str_filters( $correct_answer, 'trim_whitespace' );
853 :			#
854 :			# # it surprises me that the match below works since the first .* is greedy.
855 :			# my ($correct_num_answer, $correct_units) = $correct_answer =~ /^(.)\s+([^\s])$/;
856 :			#
857 :			# my %correct_units = Units::evaluate_units($correct_units);
858 :			# if ( defined( $correct_units{'ERROR'} ) ) {
859 :			# die "ERROR: The answer \"$correct_answer\" in the problem definition cannot be parsed:\n" .
860 :			# "$correct_units{'ERROR'}\n";
861 :			# }
862 :			#
863 :			# my $ans_evaluator = sub {
864 :			#
865 :			# my $ans = shift;
866 :			# $ans = '' unless defined($ans);
867 :			# my $original_student_ans = $ans;
868 :			#
869 :			# $ans = str_filters( $ans, 'trim_whitespace' );
870 :			#
871 :			# my $ans_hash = new AnswerHash(
872 :			# 'score' => 0,
873 :			# 'correct_ans' => spf($correct_num_answer,$options{'format'}) . " $correct_units",
874 :			# 'student_ans' => $ans,
875 :			# 'ans_message' => '',
876 :			# 'type' => 'num_cmp_with_units',
877 :			# 'preview_text_string' => '',
878 :			# 'original_student_ans' => $original_student_ans
879 :			# );
880 :			#
881 :			# # it surprises me that the match below works since the first .* is greedy.
882 :			# my ($num_answer, $units) = $ans =~ /^(.)\s+([^\s])$/;
883 :			#
884 :			# unless ( defined($num_answer) && $units ) {
885 :			# # there is an error reading the input
886 :			# if ( $ans =~ /\S/ ) { # the answer is not blank
887 :			# $ans_hash -> setKeys( 'ans_message' => "The answer \"$ans\" could not be interpreted " .
888 :			# "as a number or an arithmetic expression followed by a unit specification. " .
889 :			# "Your answer must contain units." );
890 :			# }
891 :			#
892 :			# return $ans_hash;
893 :			# }
894 :			#
895 :			# # we have been able to parse the answer into a numerical part and a unit part
896 :			#
897 :			# $num_answer = $1; #$1 and $2 from the regular expression above
898 :			# $units = $2;
899 :			#
900 :			# my %units = Units::evaluate_units($units);
901 :			# if ( defined( $units{'ERROR'} ) ) {
902 :			# # handle error condition
903 :			# $units{'ERROR'} = clean_up_error_msg($units{'ERROR'});
904 :			#
905 :			# $ans_hash -> setKeys( 'ans_message' => "$units{'ERROR'}" );
906 :			#
907 :			# return $ans_hash;
908 :			# }
909 :			#
910 :			# my $units_match = 1;
911 :			# my $fund_unit;
912 :			# foreach $fund_unit (keys %correct_units) {
913 :			# next if $fund_unit eq 'factor';
914 :			# $units_match = 0 unless $correct_units{$fund_unit} == $units{$fund_unit};
915 :			# }
916 :			#
917 :			# if ( $units_match ) {
918 :			#
919 :			# # units are ok. Evaluate the numerical part of the answer
920 :			# $tol = $tol * $correct_units{'factor'}/$units{'factor'} if
921 :			# $tolerance_mode eq 'absolute'; # the tolerance is in the units specified by the instructor.
922 :			#
923 :			# my $numerical_answer_evaluator = NUM_CMP( 'correctAnswer' => $correct_num_answer*$correct_units{'factor'}/$units{'factor'},
924 :			# 'tolerance' => $tol,
925 :			# 'tolType' => $tolerance_mode,
926 :			# 'format' => $options{'format'},
927 :			# 'mode' => $options{'mode'},
928 :			# 'zeroLevel' => $options{'zeroLevel'},
929 :			# 'zeroLevelTol' => $options{'zeroLevelTol'} );
930 :			#
931 :			# # because num_answer may contain an arithmetic expression rather than
932 :			# # a number we can't multiply it by the $units{'factor'}
933 :			# # instead we divide the correct answer by this amount;
934 :			# # this is also why the numerical_answer_evaluator is not defined outside this subroutine.
935 :			#
936 :			# $ans_hash = &$numerical_answer_evaluator($num_answer);
937 :			#
938 :			# # now we need to doctor the correct answer in order to add units
939 :			# # to it and correct for the division we did before
940 :			# $ans_hash -> {correct_ans} =
941 :			# prfmt( ( $ans_hash->{'correct_ans'} )*$units{'factor'}/$correct_units{'factor'},
942 :			# $options{'format'} ) . " $correct_units";
943 :			# # we also need to doctor the submitted answer to get it back in its original format.
944 :			#
945 :			# # we don't add the units on if there is an error message from numerical_answer_evaluator
946 :			# if ( ( $ans_hash -> {ans_message} ) =~ /^\s*$/ ) {
947 :			# $ans_hash -> {student_ans} = $ans_hash -> {student_ans} . " $units";
948 :			# $ans_hash -> setKeys( original_student_ans => $ans );
949 :			# }
950 :			# else {
951 :			# # error message from numerical_answer_evaluator doesn't have units tacked on
952 :			# $ans_hash -> setKeys( original_student_ans => $ans );
953 :			# }
954 :			# }
955 :			# else {
956 :			# $ans_hash -> setKeys( ans_message => 'There is an error in the units for this answer.' );
957 :			# }
958 :			#
959 :			# return $ans_hash;
960 :			# };
961 :			#
962 :			# $ans_evaluator;
963 :			# }
964 :	sam	2
965 :			=head3 std_num_str_cmp()
966 :	chris	22
967 :	sam	2	NOTE: This function is maintained for compatibility. num_cmp() with the
968 :			'strings' parameter is slightly preferred.
969 :
970 :			std_num_str_cmp() is used when the correct answer could be either a number or a
971 :			string. For example, if you wanted the student to evaluate a function at number
972 :			of points, but write "Inf" or "Minf" if the function is unbounded. This routine
973 :			will provide error messages that do not give a hint as to whether the correct
974 :			answer is a string or a number. For numerical comparisons, std_num_cmp() is
975 :			used internally; for string comparisons, std_str_cmp() is used.
976 :
977 :			std_num_str_cmp( $correctAnswer ) OR
978 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings ) OR
979 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol ) OR
980 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format ) OR
981 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format, $zeroLevel ) OR
982 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format,
983 :			$zeroLevel, $zeroLevelTol )
984 :
985 :			$correctAnswer -- the correct answer
986 :			$ra_legalStrings -- a reference to an array of legal strings, e.g. ["str1", "str2"]
987 :			$relPercentTol -- the error tolerance as a percentage
988 :			$format -- the display format
989 :			$zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
990 :			$zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero
991 :
992 :			Example:
993 :			ANS( std_num_str_cmp( $ans, ["Inf", "Minf", "NaN"] ) );
994 :
995 :			=cut
996 :
997 :			sub std_num_str_cmp {
998 :			my ( $correctAnswer, $ra_legalStrings, $relpercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
999 :
1000 :			$ra_legalStrings = [''] unless defined $ra_legalStrings;
1001 :			my @legalStrings = @{$ra_legalStrings};
1002 :
1003 :			my $ans_evaluator = sub {
1004 :
1005 :			my $ans = shift;
1006 :			my $ans_hash;
1007 :			my $corrAnswerIsString = 0;
1008 :			# my $studAnswerIsString = 0; ## uses new incorrect logic
1009 :			my $studAnswerIsString = 1;
1010 :
1011 :			my $legalString = '';
1012 :			foreach $legalString (@legalStrings) {
1013 :			if ( uc($correctAnswer) eq uc($legalString) ) {
1014 :			$corrAnswerIsString = 1;
1015 :			last;
1016 :			}
1017 :			} ## at this point $corrAnswerIsString = 0 iff correct answer is numeric
1018 :
1019 :			# Neither of these is perfect; the first is more general, but
1020 :			# has problems with certain special strings like "ee", while the
1021 :			# second doesn't support arithmetic expressions.
1022 :			#
1023 :			# if( $ans !~ m/^\s([\+\-\\/\^\[\]\{\}\s\d\.Ee]\|e\|pi)\s$/ ) {
1024 :			# $studAnswerIsString = 1;
1025 :			# }
1026 :			#if( $ans !~ m/^\s([\d+\-\/^()]\|e\|pi)\s*$/ ) {
1027 :			# $studAnswerIsString = 1;
1028 :			#}
1029 :
1030 :			## Both the above new versions are incorrect. We replace this by the original logic namely that
1031 :			## an answer that contain any of the symbols
1032 :			## a digit(0-9), +, -, *, /, ^, (, ), {, }, [, ]
1033 :			## or an answer that consists of "pi" or "e" alone
1034 :			## will be considered an arithmetic expression rather than a string answer.
1035 :
1036 :			if ($ans =~ m/[\d+\-\/^(){}\[\]]\|^\se\s$\|^\spi\s*$/) {$studAnswerIsString = 0;}
1037 :
1038 :
1039 :			## at this point $studAnswerIsString = 0 iff correct answer is numeric
1040 :
1041 :			if( $studAnswerIsString ) {
1042 :			$ans = str_filters( $ans, 'compress_whitespace' )
1043 :			}
1044 :
1045 :			if ( ($corrAnswerIsString == 1) and ($studAnswerIsString == 1) ) {
1046 :			my $string_answer_evaluator = std_str_cmp( $correctAnswer );
1047 :			$ans_hash = &$string_answer_evaluator( $ans );
1048 :
1049 :			if( ($ans_hash -> {score}) != 1 ) { ## find out if string makes sense
1050 :			my $sensibleAnswer = 0;
1051 :			foreach $legalString (@legalStrings) {
1052 :			if ( uc($ans) eq uc($legalString) ) {
1053 :			$sensibleAnswer = 1;
1054 :			last;
1055 :			}
1056 :			}
1057 :			$sensibleAnswer = 1 unless $ans =~ /\S/; ## empty answers are sensible
1058 :
1059 :			$ans_hash -> setKeys( 'ans_message' => 'Your answer is not a recognized answer' )
1060 :			unless ($sensibleAnswer);
1061 :			$ans_hash -> setKeys( 'student_ans' => uc($ans) );
1062 :			}
1063 :			}
1064 :			elsif ( ($corrAnswerIsString == 0) and ($studAnswerIsString == 0) ) {
1065 :			my $numeric_answer_evaluator = std_num_cmp($correctAnswer,$relpercentTol,$format,$zeroLevel,$zeroLevelTol);
1066 :			$ans_hash = &$numeric_answer_evaluator($ans);
1067 :			}
1068 :			elsif ( ($corrAnswerIsString == 1) and ($studAnswerIsString == 0) ) {
1069 :			my $numeric_answer_evaluator = std_num_cmp(1);
1070 :			$ans_hash = &$numeric_answer_evaluator($ans);
1071 :			$ans_hash -> setKeys( 'score' => 0,
1072 :			'correct_ans' => $correctAnswer
1073 :			);
1074 :			}
1075 :			elsif ( ($corrAnswerIsString == 0) and ($studAnswerIsString == 1) ) {
1076 :			my $string_answer_evaluator = std_str_cmp('bad');
1077 :			$ans_hash = &$string_answer_evaluator($ans);
1078 :
1079 :			$ans_hash -> setKeys( 'score' => 0,
1080 :			'correct_ans' => $correctAnswer
1081 :			);
1082 :
1083 :			## find out if string makes sense
1084 :			my $sensibleAnswer = 0;
1085 :			foreach $legalString (@legalStrings) {
1086 :			if ( uc($ans) eq uc($legalString) ) {
1087 :			$sensibleAnswer = 1;
1088 :			last;
1089 :			}
1090 :			}
1091 :			$sensibleAnswer = 1 unless $ans =~ /\S/; ## empty answers are sensible
1092 :
1093 :			$ans_hash -> setKeys( 'ans_message' => "Your answer is not a recognized answer" )
1094 :			unless $sensibleAnswer;
1095 :			}
1096 :
1097 :			return $ans_hash;
1098 :			};
1099 :
1100 :			return $ans_evaluator;
1101 :			}
1102 :
1103 :			=head3 num_cmp()
1104 :
1105 :			Compares a number or a list of numbers, using a named hash of options to set
1106 :			parameters. This can make for more readable code than using the "mode"_num_cmp()
1107 :			style, but some people find one or the other easier to remember.
1108 :
1109 :			ANS( num_cmp( answer or answer_array_ref, options_hash ) );
1110 :
1111 :			1. the correct answer, or a reference to an array of correct answers
1112 :			2. a hash with the following keys (all optional):
1113 :			mode -- 'std' (default) (allows any expression evaluating to a number)
1114 :			'strict' (only numbers are allowed)
1115 :			'frac' (fractions are allowed)
1116 :			'arith' (arithmetic expressions allowed)
1117 :			format -- '%0.5f#' (default); defines formatting for the correct answer
1118 :			tol -- an absolute tolerance, or
1119 :			relTol -- a relative tolerance
1120 :			units -- the units to use for the answer(s)
1121 :			strings -- a reference to an array of strings which are valid
1122 :			answers (works like std_num_str_cmp() )
1123 :			zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
1124 :			zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1125 :
1126 :			Returns an answer evaluator, or (if given a reference to an array of
1127 :			answers), a list of answer evaluators. Note that a reference to an array of
1128 :			answers results is just a shortcut to writing a separate cum_cmp() for each
1129 :			answer. It does not mean that any of those answers are considered correct
1130 :			for one question.
1131 :
1132 :			EXAMPLES:
1133 :
1134 :			num_cmp( 5 ) -- correct answer is 5, using defaults for all options
1135 :			num_cmp( [5,6,7] ) -- correct answers are 5, 6, and 7, using defaults for all options
1136 :			num_cmp( 5, mode => 'strict' ) -- correct answer is 5, mode is strict
1137 :			num_cmp( [5,6], relTol => 5 ) -- correct answers are 5 and 6, both with 5% relative tolerance
1138 :			num_cmp( 6, strings => ["Inf", "Minf", "NaN"] ) -- correct answer is 6, "Inf", "Minf", and "NaN"
1139 :			recognized as valid answers
1140 :
1141 :			=cut
1142 :
1143 :			sub num_cmp {
1144 :			my $correctAnswer = shift @_;
1145 :			my @opt = @_;
1146 :	chris	22	my %out_options;
1147 :	sam	2
1148 :	chris	22	#########################################################################
1149 :			# Retain this first check for backword compatibility. Allows input of the form
1150 :			# num_cmp($ans, 1, '%0.5f') but warns against it
1151 :			#########################################################################
1152 :
1153 :	sam	2	my %known_options = ( 'mode' => 'std',
1154 :	chris	22	'format' => $numFormatDefault,
1155 :			'tol' => $numAbsTolDefault,
1156 :			'relTol' => $numRelPercentTolDefault,
1157 :			'units' => undef,
1158 :			'strings' => undef,
1159 :			'zeroLevel' => $numZeroLevelDefault,
1160 :			'zeroLevelTol' => $numZeroLevelTolDefault,
1161 :			'tolType' => 'relative',
1162 :			'tolerance' => 1,
1163 :			'reltol' => undef, #alternate spelling
1164 :			'unit' => undef); #alternate spelling
1165 :
1166 :	sam	2	my @output_list;
1167 :	chris	22
1168 :	sam	2	unless( ref($correctAnswer) eq 'ARRAY' \|\| scalar( @opt ) == 0 \|\|
1169 :			( defined($opt[0]) and exists $known_options{$opt[0]} ) ) {
1170 :			# unless the first parameter is a list of arrays
1171 :			# or the second parameter is a known option or
1172 :			# no options were used,
1173 :			# use the old num_cmp which does not use options, but has inputs
1174 :			# $relPercentTol,$format,$zeroLevel,$zeroLevelTol
1175 :			warn "This method of using num_cmp() is deprecated. Please rewrite this" .
1176 :			" problem using the options style of parameter passing (or" .
1177 :			" check that your first option is spelled correctly).";
1178 :			my( $relPercentTol, $format, $zeroLevel, $zeroLevelTol) = @opt;
1179 :
1180 :	chris	22	@opt = ( 'relTol' => $relPercentTol,
1181 :			'format' => $format,
1182 :			'zeroLevel' => $numZeroLevelDefault,
1183 :			'zeroLevelTol' => $numZeroLevelTolDefault,
1184 :			'mode' => 'std'
1185 :			);
1186 :			}
1187 :			#########################################################################
1188 :			# Now handle the options assuming they are entered in the form
1189 :			# num_cmp($ans, relTol=>1, format=>'%0.5f')
1190 :			#########################################################################
1191 :			%out_options = @opt;
1192 :			assign_option_aliases( \%out_options,
1193 :			'reltol' => 'relTol',
1194 :			'unit' => 'units',
1195 :			);
1196 :	sam	2
1197 :
1198 :	chris	22	set_default_options( \%out_options,
1199 :			'tolType' => (defined($out_options{tol}) ) ? 'absolute' : 'relative',
1200 :			'tolerance' => (defined($out_options{tol}) ) ? $numAbsTolDefault : $numRelPercentTolDefault,
1201 :			'mode' => 'std',
1202 :			'format' => $numFormatDefault,
1203 :			'tol' => $numAbsTolDefault,
1204 :			'relTol' => $numRelPercentTolDefault,
1205 :			'units' => undef,
1206 :			'strings' => undef,
1207 :			'zeroLevel' => $numZeroLevelDefault,
1208 :			'zeroLevelTol' => $numZeroLevelTolDefault,
1209 :			'debug' => 0,
1210 :
1211 :			);
1212 :	sam	2
1213 :
1214 :
1215 :	chris	22	# can't use both units and strings
1216 :			if( defined( $out_options{'units'} ) && defined( $out_options{'strings'} ) ) {
1217 :			warn "Can't use both 'units' and 'strings' in the same problem " .
1218 :			"(check your parameters to num_cmp() )";
1219 :	sam	2	}
1220 :
1221 :
1222 :	chris	22	# my ($tolType, $tol);
1223 :			if ($out_options{tolType} eq 'absolute') {
1224 :			# $tolType = 'absolute';
1225 :			# $out_options{tolType} = 'absolute';
1226 :			# $tol = $out_options{'tol'};
1227 :			$out_options{'tolerance'}=$out_options{'tol'};
1228 :			delete($out_options{'relTol'}) if exists( $out_options{'relTol'} );
1229 :			} else {
1230 :			# $tolType = 'relative';
1231 :			# $out_options{tolType} = 'relative';
1232 :			# $tol = $out_options{'relTol'};
1233 :			# $out_options{'tolType'} = $out_options{'relative'};
1234 :			$out_options{'tolerance'}=$out_options{'relTol'};
1235 :			# delete($out_options{'tol'}) if exists( $out_options{'tol'} );
1236 :	sam	2	}
1237 :
1238 :	chris	22
1239 :	sam	2	# thread over lists
1240 :			my @ans_list = ();
1241 :
1242 :			if ( ref($correctAnswer) eq 'ARRAY' ) {
1243 :			@ans_list = @{$correctAnswer};
1244 :			}
1245 :			else {
1246 :			push( @ans_list, $correctAnswer );
1247 :			}
1248 :	chris	22
1249 :	sam	2	# produce answer evaluators
1250 :			foreach my $ans (@ans_list) {
1251 :	chris	22	if( defined( $out_options{'units'} ) ) {
1252 :			$ans = "$ans $out_options{'units'}";
1253 :
1254 :			push( @output_list, NUM_CMP( 'correctAnswer' => $ans,
1255 :			'tolerance' => $out_options{tolerance},
1256 :			'tolType' => $out_options{tolType},
1257 :			'format' => $out_options{'format'},
1258 :			'mode' => $out_options{'mode'},
1259 :			'zeroLevel' => $out_options{'zeroLevel'},
1260 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
1261 :			'debug' => $out_options{'debug'},
1262 :			'units' => $out_options{'units'},
1263 :			)
1264 :			);
1265 :			}
1266 :			elsif( defined( $out_options{'strings'} ) ) {
1267 :			if( defined $out_options{'tol'} ) {
1268 :			warn "You are using 'tol' (for absolute tolerance) with a num/str " .
1269 :			"compare, which currently only uses relative tolerance. The default " .
1270 :			"tolerance will be used.";
1271 :	sam	2	}
1272 :	chris	22
1273 :			push( @output_list, std_num_str_cmp( $ans, $out_options{'strings'},
1274 :			$out_options{'relTol'},
1275 :			$out_options{'format'},
1276 :			$out_options{'zeroLevel'},
1277 :			$out_options{'zeroLevelTol'}
1278 :			)
1279 :			);
1280 :			}
1281 :			else {
1282 :
1283 :	sam	2	push(@output_list,
1284 :	chris	22	NUM_CMP( 'correctAnswer' => $ans,
1285 :			'tolerance' => $out_options{tolerance},
1286 :			'tolType' => $out_options{tolType},
1287 :			'format' => $out_options{'format'},
1288 :			'mode' => $out_options{'mode'},
1289 :			'zeroLevel' => $out_options{'zeroLevel'},
1290 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
1291 :			'debug' => $out_options{'debug'}
1292 :			),
1293 :			);
1294 :			}
1295 :	sam	2	}
1296 :	chris	22
1297 :	sam	2	return @output_list;
1298 :	chris	22	}
1299 :	sam	2
1300 :			#legacy code for compatability purposes
1301 :			sub num_rel_cmp { # compare numbers
1302 :	chris	22	std_num_cmp( @_ );
1303 :	sam	2	}
1304 :
1305 :			## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
1306 :			##
1307 :			## IN: a hash containing the following items (error-checking to be added later?):
1308 :			## correctAnswer -- the correct answer
1309 :			## tolerance -- the allowable margin of error
1310 :			## tolType -- 'relative' or 'absolute'
1311 :			## format -- the display format of the answer
1312 :			## mode -- one of 'std', 'strict', 'arith', or 'frac';
1313 :			## determines allowable formats for the input
1314 :			## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
1315 :			## zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1316 :	chris	22	#sub NUM_CMP { # low level numeric compare
1317 :			# my %num_params = @_;
1318 :			#
1319 :			# my @keys = qw ( correctAnswer tolerance tolType format mode zeroLevel zeroLevelTol );
1320 :			# foreach my $key (@keys) {
1321 :			# warn "$key must be defined in options when calling NUM_CMP" unless defined ($num_params{$key});
1322 :			# }
1323 :			#
1324 :			#
1325 :			# my $correctAnswer = $num_params{'correctAnswer'};
1326 :			# my $tol = $num_params{'tolerance'};
1327 :			# my $tolType = $num_params{'tolType'};
1328 :			# my $format = $num_params{'format'};
1329 :			# my $mode = $num_params{'mode'};
1330 :			# my $zeroLevel = $num_params{'zeroLevel'};
1331 :			# my $zeroLevelTol = $num_params{'zeroLevelTol'};
1332 :			#
1333 :			# if( $tolType eq 'relative' ) {
1334 :			# # $tol = $numRelPercentTolDefault unless defined $tol;
1335 :			# $tol *= .01;
1336 :			# }
1337 :			## else {
1338 :			## $tol = $numAbsTolDefault unless defined $tol;
1339 :			## }
1340 :			#
1341 :			# #$format = $numFormatDefault unless defined $format;
1342 :			# #$mode = 'std' unless defined $mode;
1343 :			# #$zeroLevel = $numZeroLevelDefault unless defined $zeroLevel;
1344 :			# #$zeroLevelTol = $numZeroLevelTolDefault unless defined $zeroLevelTol;
1345 :			#
1346 :			# my $formattedCorrectAnswer = prfmt( $correctAnswer, $format );
1347 :			#
1348 :			# my $answer_evaluator = sub {
1349 :			# my $in = shift @_;
1350 :			# $in = '' unless defined $in;
1351 :			# my $score = 0;
1352 :			# my $original_student_answer = $in;
1353 :			# my $parser = new AlgParserWithImplicitExpand;
1354 :			# my $ret = $parser -> parse($in);
1355 :			# my $preview_text_string = '';
1356 :			# my $preview_latex_string = '';
1357 :			#
1358 :			# if ( ref($ret) ) { ## parsed successfully
1359 :			# $parser -> tostring();
1360 :			# $parser -> normalize();
1361 :			# $in = $parser -> tostring();
1362 :			# $preview_text_string = $in;
1363 :			# $preview_latex_string = $parser -> tolatex();
1364 :			#
1365 :			# }
1366 :			# else { ## error in parsing
1367 :			# my $ans_hash = new AnswerHash(
1368 :			# 'score' => $score,
1369 :			# 'correct_ans' => $formattedCorrectAnswer,
1370 :			# 'student_ans' => "error: $parser->{htmlerror}",
1371 :			# 'ans_message' => $parser -> {error_msg},
1372 :			# 'type' => "${mode}_number",
1373 :			# 'preview_text_string' => $preview_text_string,
1374 :			# 'preview_latex_string' => $preview_latex_string,
1375 :			# 'original_student_ans' => $original_student_answer
1376 :			# );
1377 :			#
1378 :			# return $ans_hash;
1379 :			# }
1380 :			#
1381 :			# my $PGanswerMessage = '';
1382 :			#
1383 :			# my ($inVal,$correctVal,$PG_eval_errors,$PG_full_error_report);
1384 :			#
1385 :			# $inVal = '';
1386 :			# $correctAnswer = math_constants($correctAnswer);
1387 :			# my $formattedSubmittedAnswer = '';
1388 :			#
1389 :			# #special variable $@ holds the last error from a Perl eval statement
1390 :			# $@='';
1391 :			#
1392 :			# if ($correctAnswer =~ /\S/) {
1393 :			# ($correctVal, $PG_eval_errors,$PG_full_error_report) = PG_answer_eval($correctAnswer);
1394 :			# }
1395 :			# else {
1396 :			# $PG_eval_errors = ' ';
1397 :			# }
1398 :			#
1399 :			# if ( $PG_eval_errors or not is_a_number($correctVal) ) { ##error message from eval or above
1400 :			# $formattedSubmittedAnswer = $PG_eval_errors;
1401 :			# $formattedSubmittedAnswer = clean_up_error_msg($formattedSubmittedAnswer);
1402 :			# $PGanswerMessage = 'Tell your professor that there is an error in this problem';
1403 :			# my $ans_hash = new AnswerHash(
1404 :			# 'score' => $score,
1405 :			# 'correct_ans' => $formattedCorrectAnswer,
1406 :			# 'student_ans' => $formattedSubmittedAnswer,
1407 :			# 'ans_message' => $PGanswerMessage,
1408 :			# 'type' => 'number',
1409 :			# 'preview_text_string' => $preview_text_string,
1410 :			# 'preview_latex_string' => $preview_latex_string,
1411 :			# 'original_student_ans' => $original_student_answer
1412 :			# );
1413 :			#
1414 :			# return $ans_hash;
1415 :			# }
1416 :			#
1417 :			# $in = &math_constants($in);
1418 :			#
1419 :			# MODE_CASE: { ## bare block for "case" statement
1420 :			# if ($mode eq 'std') {
1421 :			# last MODE_CASE;
1422 :			# }
1423 :			# elsif ($mode eq 'strict') {
1424 :			# unless (is_a_number($in)) {
1425 :			# $PGanswerMessage = 'You must enter a number, e.g. -6, 5.3, or 6.12E-3';
1426 :			# $formattedSubmittedAnswer = 'Incorrect number format';
1427 :			# }
1428 :			# else {
1429 :			# last MODE_CASE;
1430 :			# }
1431 :			# }
1432 :			# elsif ($mode eq 'arith') {
1433 :			# unless (is_an_arithmetic_expression($in)) {
1434 :			# $PGanswerMessage = 'You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2';
1435 :			# $formattedSubmittedAnswer = 'Not an arithmetic expression';
1436 :			# }
1437 :			# else {
1438 :			# last MODE_CASE;
1439 :			# }
1440 :			# }
1441 :			# elsif ($mode eq 'frac') {
1442 :			# unless (is_a_fraction($in)) {
1443 :			# $PGanswerMessage = 'You must enter a number or fraction , e.g. -6 or 7/13';
1444 :			# $formattedSubmittedAnswer = 'Not a number or fraction';
1445 :			# }
1446 :			# else {
1447 :			# last MODE_CASE;
1448 :			# }
1449 :			# }
1450 :			# else {
1451 :			# $PGanswerMessage = 'Tell your professor that there is an error in his or her answer mechanism. No mode was specified.';
1452 :			# $formattedSubmittedAnswer = $in;
1453 :			# }
1454 :			#
1455 :			# my $ans_hash = new AnswerHash(
1456 :			# score => $score,
1457 :			# correct_ans => $formattedCorrectAnswer,
1458 :			# student_ans => $formattedSubmittedAnswer,
1459 :			# ans_message => $PGanswerMessage,
1460 :			# type => "${mode}_number",
1461 :			# preview_text_string => $preview_text_string,
1462 :			# preview_latex_string => $preview_latex_string,
1463 :			# original_student_ans => $original_student_answer
1464 :			# );
1465 :			#
1466 :			# return $ans_hash;
1467 :			# } # end of MODE_CASES bare block
1468 :			#
1469 :			# $@ = '';
1470 :			# if ($in =~ /\S/) {
1471 :			#
1472 :			# ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($in);
1473 :			# }
1474 :			# else {
1475 :			# $PG_eval_errors = ' ';
1476 :			# }
1477 :			#
1478 :			# if ($PG_eval_errors) { ##error message from eval or above
1479 :			# $formattedSubmittedAnswer = $PG_eval_errors;
1480 :			# $formattedSubmittedAnswer =clean_up_error_msg($formattedSubmittedAnswer);
1481 :			# $PGanswerMessage = 'There is a syntax error in your answer';
1482 :			# $PGanswerMessage = '' if $PG_eval_errors eq ' ';
1483 :			# my $ans_hash = new AnswerHash(
1484 :			# 'score' => $score,
1485 :			# 'correct_ans' => $formattedCorrectAnswer,
1486 :			# 'student_ans' => $formattedSubmittedAnswer,
1487 :			# 'ans_message' => $PGanswerMessage,
1488 :			# 'type' => "${mode}_number",
1489 :			# 'preview_text_string' => $preview_text_string,
1490 :			# 'preview_latex_string' => $preview_latex_string,
1491 :			# 'original_student_ans' => $original_student_answer
1492 :			# );
1493 :			#
1494 :			# return $ans_hash;
1495 :			# }
1496 :			# else {
1497 :			# $formattedSubmittedAnswer = prfmt($inVal,$format);
1498 :			# }
1499 :			#
1500 :			# my $permitted_error;
1501 :			# if (defined($tolType) && $tolType eq 'absolute') {
1502 :			# $permitted_error = $tol;
1503 :			# }
1504 :			# elsif ( abs($correctVal) <= $zeroLevel) {
1505 :			# $permitted_error = $zeroLevelTol; ## want $tol to be non zero
1506 :			# }
1507 :			# else {
1508 :			# $permitted_error = abs($tol*$correctVal);
1509 :			# }
1510 :			#
1511 :			# my $is_a_number = is_a_number($inVal);
1512 :			# $score = 1 if ( ($is_a_number) and
1513 :			# (abs( $inVal - $correctVal ) <= $permitted_error) );
1514 :			# if ($PG_eval_errors) {
1515 :			# $PGanswerMessage = 'There is a syntax error in your answer';
1516 :			# }
1517 :			# elsif (not $is_a_number) {
1518 :			# $PGanswerMessage = 'Your answer does not evaluate to a number';
1519 :			# }
1520 :			#
1521 :			# my $ans_hash = new AnswerHash(
1522 :			# 'score' => $score,
1523 :			# 'correct_ans' => $formattedCorrectAnswer,
1524 :			# 'student_ans' => $formattedSubmittedAnswer,
1525 :			# 'ans_message' => $PGanswerMessage,
1526 :			# 'type' => "${mode}_number",
1527 :			# 'preview_text_string' => $preview_text_string,
1528 :			# 'preview_latex_string' => $preview_latex_string,
1529 :			# 'original_student_ans' => $original_student_answer
1530 :			# );
1531 :			#
1532 :			# return $ans_hash;
1533 :			# };
1534 :			#
1535 :			# return $answer_evaluator;
1536 :	sam	2
1537 :	chris	22	#}
1538 :	sam	2
1539 :	chris	22	sub compare_numbers {
1540 :			my ($rh_ans, %options) = @_;
1541 :			my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($rh_ans->{student_ans});
1542 :			if ($PG_eval_errors) {
1543 :			$rh_ans->throw_error('EVAL','There is a syntax error in your answer');
1544 :			$rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors);
1545 :
1546 :
1547 :	gage	5	} else {
1548 :	chris	22	$rh_ans->{student_ans} = prfmt($inVal,$options{format});
1549 :	sam	2	}
1550 :	chris	22
1551 :			my $permitted_error;
1552 :
1553 :			if ($rh_ans->{tolType} eq 'absolute') {
1554 :			$permitted_error = $rh_ans->{tolerance};
1555 :
1556 :			}
1557 :			elsif ( abs($rh_ans->{correct_ans}) <= $options{zeroLevel}) {
1558 :			$permitted_error = $options{zeroLevelTol}; ## want $tol to be non zero
1559 :			}
1560 :			else {
1561 :			$permitted_error = abs($rh_ans->{tolerance}*$rh_ans->{correct_ans});
1562 :			}
1563 :
1564 :			my $is_a_number = is_a_number($inVal);
1565 :			$rh_ans->{score} = 1 if ( ($is_a_number) and
1566 :			(abs( $inVal - $rh_ans->{correct_ans} ) <= $permitted_error) );
1567 :			if (not $is_a_number) {
1568 :			$rh_ans->throw_error('EVAL','Your answer does not evaluate to a number');
1569 :			}
1570 :
1571 :			$rh_ans;
1572 :			}
1573 :	sam	2
1574 :	chris	22	sub NUM_CMP { # low level numeric compare
1575 :			my %num_params = @_;
1576 :	sam	2
1577 :	chris	22	my @keys = qw ( correctAnswer tolerance tolType format mode zeroLevel zeroLevelTol debug );
1578 :			foreach my $key (@keys) {
1579 :			warn "$key must be defined in options when calling NUM_CMP" unless defined ($num_params{$key});
1580 :			}
1581 :	sam	2
1582 :	chris	22	my $correctAnswer = $num_params{'correctAnswer'};
1583 :			my $format = $num_params{'format'};
1584 :			my $mode = $num_params{'mode'};
1585 :
1586 :			# my $tol = $num_params{'tolerance'};
1587 :			# my $tolType = $num_params{'tolType'};
1588 :			# my $zeroLevel = $num_params{'zeroLevel'};
1589 :			# my $zeroLevelTol = $num_params{'zeroLevelTol'};
1590 :
1591 :			if( $num_params{tolType} eq 'relative' ) {
1592 :			$num_params{'tolerance'} = .01*$num_params{'tolerance'};
1593 :			}
1594 :	sam	2
1595 :	chris	22	#$format = $numFormatDefault unless defined $format;
1596 :			#$mode = 'std' unless defined $mode;
1597 :			#$zeroLevel = $numZeroLevelDefault unless defined $zeroLevel;
1598 :			#$zeroLevelTol = $numZeroLevelTolDefault unless defined $zeroLevelTol;
1599 :
1600 :			my $formattedCorrectAnswer;
1601 :			my $correct_units;
1602 :			my $correct_num_answer;
1603 :			my %correct_units;
1604 :	sam	2
1605 :	chris	22	if (defined($num_params{units}) && $num_params{units}) {
1606 :			$correctAnswer = str_filters( $correctAnswer, 'trim_whitespace' );
1607 :			# units are in form stuff space units where units contains no spaces.
1608 :
1609 :			($correct_num_answer, $correct_units) = $correctAnswer =~ /^(.)\s+([^\s])$/;
1610 :			%correct_units = Units::evaluate_units($correct_units);
1611 :			if ( defined( $correct_units{'ERROR'} ) ) {
1612 :			warn ("ERROR: The answer \"$correctAnswer\" in the problem definition cannot be parsed:\n" .
1613 :			"$correct_units{'ERROR'}\n");
1614 :	sam	2	}
1615 :	chris	22	# $formattedCorrectAnswer = spf($correct_num_answer,$num_params{'format'}) . " $correct_units";
1616 :			$formattedCorrectAnswer = pfmt($correct_num_answer,$num_params{'format'}) . " $correct_units";
1617 :
1618 :			} else {
1619 :			$correct_num_answer = $correctAnswer;
1620 :			$formattedCorrectAnswer = prfmt( $correctAnswer, $num_params{'format'} );
1621 :			}
1622 :	sam	2
1623 :	chris	22	$correct_num_answer = math_constants($correct_num_answer);
1624 :
1625 :			my $PGanswerMessage = '';
1626 :
1627 :			my ($inVal,$correctVal,$PG_eval_errors,$PG_full_error_report);
1628 :
1629 :			if (defined($correct_num_answer) && $correct_num_answer =~ /\S/) {
1630 :			($correctVal, $PG_eval_errors,$PG_full_error_report) = PG_answer_eval($correct_num_answer);
1631 :			}
1632 :			else {
1633 :			$PG_eval_errors = ' ';
1634 :			}
1635 :	sam	2
1636 :	chris	22	if ( $PG_eval_errors or not is_a_number($correctVal) ) { ##error message from eval or above
1637 :			warn "Error in 'correct' answer: $PG_eval_errors<br>
1638 :			The answer $correctAnswer evaluates to $correctVal,
1639 :			which cannot be interpreted as a number. ";
1640 :
1641 :			}
1642 :			#########################################################################
1643 :	sam	2
1644 :	chris	22	#construct the answer evaluator
1645 :			my $answer_evaluator = new AnswerEvaluator;
1646 :			$answer_evaluator->{debug} = $num_params{debug};
1647 :			$answer_evaluator->ans_hash( correct_ans => $correct_num_answer,
1648 :			type => "${mode}_number",
1649 :			tolerance => $num_params{tolerance},
1650 :			tolType => $num_params{tolType},
1651 :			units => $correct_units,
1652 :			original_correct_ans => $formattedCorrectAnswer,
1653 :			rh_correct_units => \%correct_units,
1654 :			);
1655 :			my ($in, $formattedSubmittedAnswer);
1656 :			$answer_evaluator->install_pre_filter(sub {my $rh_ans = shift;
1657 :			$rh_ans->{original_student_ans} = $rh_ans->{student_ans}; $rh_ans;}
1658 :			);
1659 :			if (defined($num_params{units}) && $num_params{units}) {
1660 :			$answer_evaluator->install_pre_filter(\&check_units);
1661 :			}
1662 :
1663 :			$answer_evaluator->install_pre_filter(\&check_syntax);
1664 :
1665 :			$answer_evaluator->install_pre_filter(\&math_constants);
1666 :			if ($mode eq 'std') {
1667 :			# do nothing
1668 :			} elsif ($mode eq 'strict') {
1669 :			$answer_evaluator->install_pre_filter(\&is_a_number);
1670 :			} elsif ($mode eq 'arith') {
1671 :			$answer_evaluator->install_pre_filter(\&is_an_arithmetic_expression);
1672 :			} elsif ($mode eq 'frac') {
1673 :			$answer_evaluator->install_pre_filter(\&is_a_fraction);
1674 :	sam	2
1675 :	chris	22	} else {
1676 :			$PGanswerMessage = 'Tell your professor that there is an error in his or her answer mechanism. No mode was specified.';
1677 :			$formattedSubmittedAnswer = $in;
1678 :	sam	2	}
1679 :	chris	22
1680 :			$answer_evaluator->install_evaluator(\&compare_numbers, %num_params);
1681 :	sam	2
1682 :	chris	22	$answer_evaluator->install_post_filter(sub {my $rh_ans = shift;
1683 :			$rh_ans->{foo} = 'There was one.';
1684 :			$rh_ans->{student_ans} = $rh_ans->{original_student_ans};
1685 :			$rh_ans->{correct_ans} = $rh_ans->{original_correct_ans};
1686 :			$rh_ans;}
1687 :			);
1688 :	sam	2
1689 :	chris	22	$answer_evaluator->install_post_filter(sub {my $rh_ans = shift;
1690 :			return $rh_ans unless $rh_ans->catch_error('EVAL');
1691 :			$rh_ans->{student_ans} = $rh_ans->{original_student_ans}. ' '. $rh_ans->{error_message};
1692 :			$rh_ans->clear_error('EVAL'); } );
1693 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('SYNTAX'); } );
1694 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('UNITS'); } );
1695 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('NUMBER'); } );
1696 :
1697 :
1698 :
1699 :			$answer_evaluator;
1700 :	sam	2	}
1701 :
1702 :
1703 :	chris	22	### LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
1704 :			#sub NUM_CMP_LIST { # low level numeric list compare
1705 :			# my %num_params = @_;
1706 :			#
1707 :			# my @outputList;
1708 :			# my $ans;
1709 :			#
1710 :			# while ( @{$num_params{'answerList'}} ) {
1711 :			# $ans = shift @{$num_params{'answerList'}};
1712 :			# push( @outputList, NUM_CMP( 'correctAnswer' => $ans,
1713 :			# 'tolerance' => $num_params{'tolerance'},
1714 :			# 'tolType' => $num_params{'tolType'},
1715 :			# 'format' => $num_params{'format'},
1716 :			# 'mode' => $num_params{'mode'},
1717 :			# 'zeroLevel' => $num_params{'zeroLevel'},
1718 :			# 'zeroLevelTol' => $num_params{'zeroLevelTol'}
1719 :			# )
1720 :			# );
1721 :			# }
1722 :			#
1723 :			# return @outputList;
1724 :			#}
1725 :	sam	2
1726 :
1727 :
1728 :			##########################################################################
1729 :			##########################################################################
1730 :			## Function answer evaluators
1731 :
1732 :			=head2 Function Answer Evaluators
1733 :
1734 :			Function answer evaluators take in a function, compare it numerically to a
1735 :			correct function, and return a score. They can require an exactly equivalent
1736 :			function, or one that is equal up to a constant. They can accept or reject an
1737 :			answer based on specified tolerances for numerical deviation.
1738 :
1739 :			Function Comparison Options
1740 :
1741 :			correctEqn -- The correct equation, specified as a string. It may include
1742 :			all basic arithmetic operations, as well as elementary
1743 :			functions. Variable usage is described below.
1744 :
1745 :			Variables -- The independent variable(s). When comparing the correct
1746 :			equation to the student equation, each variable will be
1747 :			replaced by a certain number of numerical values. If
1748 :			the student equation agrees numerically with the correct
1749 :			equation, they are considered equal. Note that all
1750 :			comparison is numeric; it is possible (although highly
1751 :			unlikely and never a practical concern) for two unequal
1752 :			functions to yield the same numerical results.
1753 :
1754 :			Limits -- The limits of evaluation for the independent variables.
1755 :			Each variable is evaluated only in the half-open interval
1756 :			[lower_limit, upper_limit). This is useful if the function
1757 :			has a singularity or is not defined in a certain range.
1758 :			For example, the function "sqrt(-1-x)" could be evaluated
1759 :			in [-2,-1).
1760 :
1761 :			Tolerance -- Tolerance in function comparisons works exactly as in
1762 :			numerical comparisons; see the numerical comparison
1763 :			documentation for a complete description. Note that the
1764 :			tolerance does applies to the function as a whole, not
1765 :			each point individually.
1766 :
1767 :			Number of -- Specifies how many points to evaluate each variable at. This
1768 :			Points is typically 3, but can be set higher if it is felt that
1769 :			there is a strong possibility of "false positives."
1770 :
1771 :			Maximum -- Sets the maximum size of the constant of integration. For
1772 :			Constant of technical reasons concerning floating point arithmetic, if
1773 :			Integration the additive constant, i.e., the constant of integration, is
1774 :			greater (in absolute value) than maxConstantOfIntegration
1775 :			AND is greater than maxConstantOfIntegration times the
1776 :			correct value, WeBWorK will give an error message saying
1777 :			that it can not handle such a large constant of integration.
1778 :			This is to prevent e.g. cos(x) + 1E20 or even 1E20 as being
1779 :			accepted as a correct antiderivatives of sin(x) since
1780 :			floating point arithmetic cannot tell the difference
1781 :			between cos(x) + 1E20, 1E20, and -cos(x) + 1E20.
1782 :
1783 :			Technical note: if you examine the code for the function routines, you will see
1784 :			that most subroutines are simply doing some basic error-checking and then
1785 :			passing the parameters on to the low-level FUNCTION_CMP(). Because this routine
1786 :			is set up to handle multivariable functions, with single-variable functions as
1787 :			a special case, it is possible to pass multivariable parameters to single-
1788 :			variable functions. This usage is strongly discouraged as unnecessarily
1789 :			confusing. Avoid it.
1790 :
1791 :			Default Values (As of 7/24/2000) (Option -- Variable Name -- Value)
1792 :
1793 :			Variable -- $functVarDefault -- 'x'
1794 :			Relative Tolerance -- $functRelPercentTolDefault -- .1
1795 :			Absolute Tolerance -- $functAbsTolDefault -- .001
1796 :			Lower Limit -- $functLLimitDefault -- .0000001
1797 :			Upper Limit -- $functULimitDefault -- 1
1798 :			Number of Points -- $functNumOfPoints -- 3
1799 :			Zero Level -- $functZeroLevelDefault -- 1E-14
1800 :			Zero Level Tolerance -- $functZeroLevelTolDefault -- 1E-12
1801 :			Maximum Constant -- $functMaxConstantOfIntegration -- 1E8
1802 :			of Integration
1803 :
1804 :			=cut
1805 :
1806 :			=head3 Single-variable Function Comparisons
1807 :
1808 :			There are four single-variable function answer evaluators: "normal," absolute
1809 :			tolerance, antiderivative, and antiderivative with absolute tolerance. All
1810 :			parameters (other than the correct equation) are optional.
1811 :
1812 :			function_cmp( $correctEqn ) OR
1813 :			function_cmp( $correctEqn, $var ) OR
1814 :			function_cmp( $correctEqn, $var, $llimit, $ulimit ) OR
1815 :			function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol ) OR
1816 :			function_cmp( $correctEqn, $var, $llimit, $ulimit,
1817 :			$relPercentTol, $numPoints ) OR
1818 :			function_cmp( $correctEqn, $var, $llimit, $ulimit,
1819 :			$relPercentTol, $numPoints, $zeroLevel ) OR
1820 :			function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol, $numPoints,
1821 :			$zeroLevel,$zeroLevelTol )
1822 :
1823 :			$correctEqn -- the correct equation, as a string
1824 :			$var -- the string representing the variable (optional)
1825 :			$llimit -- the lower limit of the interval to evaluate the
1826 :			variable in (optional)
1827 :			$ulimit -- the upper limit of the interval to evaluate the
1828 :			variable in (optional)
1829 :			$relPercentTol -- the error tolerance as a percentage (optional)
1830 :			$numPoints -- the number of points at which to evaluate the
1831 :			variable (optional)
1832 :			$zeroLevel -- if the correct answer is this close to zero, then
1833 :			zeroLevelTol applies (optional)
1834 :			$zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1835 :
1836 :			function_cmp() uses standard comparison and relative tolerance. It takes a
1837 :			string representing a single-variable function and compares the student
1838 :			answer to that function numerically.
1839 :
1840 :			function_cmp_up_to_constant( $correctEqn ) OR
1841 :			function_cmp_up_to_constant( $correctEqn, $var ) OR
1842 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit ) OR
1843 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1844 :			$relpercentTol ) OR
1845 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1846 :			$relpercentTol, $numOfPoints ) OR
1847 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1848 :			$relpercentTol, $numOfPoints,
1849 :			$maxConstantOfIntegration ) OR
1850 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1851 :			$relpercentTol, $numOfPoints,
1852 :			$maxConstantOfIntegration, $zeroLevel) OR
1853 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1854 :			$relpercentTol, $numOfPoints,
1855 :			$maxConstantOfIntegration,
1856 :			$zeroLevel, $zeroLevelTol )
1857 :
1858 :			$maxConstantOfIntegration -- the maximum size of the constant of
1859 :			integration
1860 :
1861 :			function_cmp_up_to_constant() uses antiderivative compare and relative
1862 :			tolerance. All options work exactly like function_cmp(), except of course
1863 :			$maxConstantOfIntegration. It will accept as correct any function which
1864 :			differs from $correctEqn by at most a constant; that is, if
1865 :			$studentEqn = $correctEqn + C
1866 :			the answer is correct.
1867 :
1868 :			function_cmp_abs( $correctFunction ) OR
1869 :			function_cmp_abs( $correctFunction, $var ) OR
1870 :			function_cmp_abs( $correctFunction, $var, $llimit, $ulimit ) OR
1871 :			function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol ) OR
1872 :			function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol,
1873 :			$numOfPoints )
1874 :
1875 :			$absTol -- the tolerance as an absolute value
1876 :
1877 :			function_cmp_abs() uses standard compare and absolute tolerance. All
1878 :			other options work exactly as for function_cmp().
1879 :
1880 :			function_cmp_up_to_constant_abs( $correctFunction ) OR
1881 :			function_cmp_up_to_constant_abs( $correctFunction, $var ) OR
1882 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit ) OR
1883 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit,
1884 :			$absTol ) OR
1885 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit,
1886 :			$absTol, $numOfPoints ) OR
1887 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit,
1888 :			$absTol, $numOfPoints,
1889 :			$maxConstantOfIntegration )
1890 :
1891 :			function_cmp_up_to_constant_abs() uses antiderivative compare
1892 :			and absolute tolerance. All other options work exactly as with
1893 :			function_cmp_up_to_constant().
1894 :
1895 :			Examples:
1896 :
1897 :			ANS( function_cmp( "cos(x)" ) ) -- Accepts cos(x), sin(x+pi/2),
1898 :			sin(x)^2 + cos(x) + cos(x)^2 -1, etc. This assumes
1899 :			$functVarDefault has been set to "x".
1900 :			ANS( function_cmp( $answer, "t" ) ) -- Assuming $answer is "cos(t)",
1901 :			accepts cos(t), etc.
1902 :			ANS( function_cmp_up_to_constant( "cos(x)" ) ) -- Accepts any
1903 :			antiderivative of sin(x), e.g. cos(x) + 5.
1904 :			ANS( function_cmp_up_to_constant( "cos(z)", "z" ) ) -- Accepts any
1905 :			antiderivative of sin(z), e.g. sin(z+pi/2) + 5.
1906 :
1907 :			=cut
1908 :			sub adaptive_function_cmp {
1909 :			my $correctEqn = shift;
1910 :			my %options = @_;
1911 :			set_default_options( \%options,
1912 :			'vars' => [qw( x y )],
1913 :			'params' => [],
1914 :			'limits' => [ [0,1], [0,1]],
1915 :			'reltol' => $main::functRelPercentTolDefault,
1916 :			'numPoints' => $main::functNumOfPoints,
1917 :			'zeroLevel' => $main::functZeroLevelDefault,
1918 :	chris	22	'zeroLevelTol' => $main::functZeroLevelTolDefault,
1919 :	sam	2	'debug' => 0,
1920 :			);
1921 :
1922 :			my $var_ref = $options{'vars'};
1923 :			my $ra_params = $options{ 'params'};
1924 :			my $limit_ref = $options{'limits'};
1925 :			my $relPercentTol= $options{'reltol'};
1926 :			my $numPoints = $options{'numPoints'};
1927 :			my $zeroLevel = $options{'zeroLevel'};
1928 :			my $zeroLevelTol = $options{'zeroLevelTol'};
1929 :
1930 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1931 :			'var' => $var_ref,
1932 :			'limits' => $limit_ref,
1933 :			'tolerance' => $relPercentTol,
1934 :			'tolType' => 'relative',
1935 :			'numPoints' => $numPoints,
1936 :			'mode' => 'std',
1937 :			'maxConstantOfIntegration' => 10**100,
1938 :			'zeroLevel' => $zeroLevel,
1939 :			'zeroLevelTol' => $zeroLevelTol,
1940 :			'scale_norm' => 1,
1941 :			'params' => $ra_params,
1942 :			'debug' => $options{debug} ,
1943 :	sam	2	);
1944 :
1945 :			}
1946 :
1947 :			sub function_cmp {
1948 :			my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_;
1949 :
1950 :			if ( (scalar(@_) == 3) or (scalar(@_) > 8) or (scalar(@_) == 0) ) {
1951 :			function_invalid_params( $correctEqn );
1952 :			}
1953 :			else {
1954 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1955 :			'var' => $var,
1956 :			'limits' => [$llimit, $ulimit],
1957 :			'tolerance' => $relPercentTol,
1958 :			'tolType' => 'relative',
1959 :			'numPoints' => $numPoints,
1960 :			'mode' => 'std',
1961 :			'maxConstantOfIntegration' => 0,
1962 :			'zeroLevel' => $zeroLevel,
1963 :			'zeroLevelTol' => $zeroLevelTol
1964 :	sam	2	);
1965 :			}
1966 :			}
1967 :
1968 :			sub function_cmp_up_to_constant { ## for antiderivative problems
1969 :			my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$maxConstantOfIntegration,$zeroLevel,$zeroLevelTol) = @_;
1970 :
1971 :			if ( (scalar(@_) == 3) or (scalar(@_) > 9) or (scalar(@_) == 0) ) {
1972 :			function_invalid_params( $correctEqn );
1973 :			}
1974 :			else {
1975 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1976 :			'var' => $var,
1977 :			'limits' => [$llimit, $ulimit],
1978 :			'tolerance' => $relPercentTol,
1979 :			'tolType' => 'relative',
1980 :			'numPoints' => $numPoints,
1981 :			'mode' => 'antider',
1982 :			'maxConstantOfIntegration' => $maxConstantOfIntegration,
1983 :			'zeroLevel' => $zeroLevel,
1984 :			'zeroLevelTol' => $zeroLevelTol
1985 :	sam	2	);
1986 :			}
1987 :			}
1988 :
1989 :			sub function_cmp_abs { ## similar to function_cmp but uses absolute tolerance
1990 :			my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints) = @_;
1991 :
1992 :			if ( (scalar(@_) == 3) or (scalar(@_) > 6) or (scalar(@_) == 0) ) {
1993 :			function_invalid_params( $correctEqn );
1994 :			}
1995 :			else {
1996 :			FUNCTION_CMP( 'correctEqn' => $correctEqn,
1997 :			'var' => $var,
1998 :			'limits' => [$llimit, $ulimit],
1999 :			'tolerance' => $absTol,
2000 :			'tolType' => 'absolute',
2001 :			'numPoints' => $numPoints,
2002 :			'mode' => 'std',
2003 :			'maxConstantOfIntegration' => 0,
2004 :			'zeroLevel' => 0,
2005 :			'zeroLevelTol' => 0
2006 :			);
2007 :			}
2008 :			}
2009 :
2010 :
2011 :			sub function_cmp_up_to_constant_abs { ## for antiderivative problems
2012 :			## similar to function_cmp_up_to_constant
2013 :			## but uses absolute tolerance
2014 :			my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints,$maxConstantOfIntegration) = @_;
2015 :
2016 :			if ( (scalar(@_) == 3) or (scalar(@_) > 7) or (scalar(@_) == 0) ) {
2017 :			function_invalid_params( $correctEqn );
2018 :			}
2019 :
2020 :			else {
2021 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
2022 :			'var' => $var,
2023 :			'limits' => [$llimit, $ulimit],
2024 :			'tolerance' => $absTol,
2025 :			'tolType' => 'absolute',
2026 :			'numPoints' => $numPoints,
2027 :			'mode' => 'antider',
2028 :			'maxConstantOfIntegration' => $maxConstantOfIntegration,
2029 :			'zeroLevel' => 0,
2030 :			'zeroLevelTol' => 0
2031 :	sam	2	);
2032 :			}
2033 :			}
2034 :
2035 :			## The following answer evaluator for comparing multivarable functions was
2036 :			## contributed by Professor William K. Ziemer
2037 :			## (Note: most of the multivariable functionality provided by Professor Ziemer
2038 :			## has now been integrated into fun_cmp and FUNCTION_CMP)
2039 :			############################
2040 :			# W.K. Ziemer, Sep. 1999
2041 :			# Math Dept. CSULB
2042 :			# email: wziemer@csulb.edu
2043 :			############################
2044 :
2045 :			=head3 multivar_function_cmp
2046 :
2047 :			NOTE: this function is maintained for compatibility. fun_cmp() is
2048 :			slightly preferred.
2049 :
2050 :			usage:
2051 :
2052 :			multivar_function_cmp( $answer, $var_reference, options)
2053 :			$answer -- string, represents function of several variables
2054 :			$var_reference -- number (of variables), or list reference (e.g. ["var1","var2"] )
2055 :			options:
2056 :			$limit_reference -- reference to list of lists (e.g. [[1,2],[3,4]])
2057 :			$relPercentTol -- relative percent tolerance in answer
2058 :			$numPoints -- number of points to sample in for each variable
2059 :			$zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
2060 :			$zeroLevelTol -- absolute tolerance to allow when answer is close to zero
2061 :
2062 :			=cut
2063 :
2064 :			sub multivar_function_cmp {
2065 :			my ($correctEqn,$var_ref,$limit_ref,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_;
2066 :
2067 :			if ( (scalar(@_) > 7) or (scalar(@_) < 2) ) {
2068 :			function_invalid_params( $correctEqn );
2069 :			}
2070 :
2071 :			FUNCTION_CMP( 'correctEqn' => $correctEqn,
2072 :			'var' => $var_ref,
2073 :			'limits' => $limit_ref,
2074 :			'tolerance' => $relPercentTol,
2075 :			'tolType' => 'relative',
2076 :			'numPoints' => $numPoints,
2077 :			'mode' => 'std',
2078 :			'maxConstantOfIntegration' => 0,
2079 :			'zeroLevel' => $zeroLevel,
2080 :			'zeroLevelTol' => $zeroLevelTol
2081 :			);
2082 :			}
2083 :
2084 :			=head3 fun_cmp()
2085 :
2086 :			Compares a function or a list of functions, using a named hash of options to set
2087 :			parameters. This can make for more readable code than using the function_cmp()
2088 :			style, but some people find one or the other easier to remember.
2089 :
2090 :			ANS( fun_cmp( answer or answer_array_ref, options_hash ) );
2091 :
2092 :			1. a string containing the correct function, or a reference to an
2093 :			array of correct functions
2094 :			2. a hash containing the following items (all optional):
2095 :			var -- either the number of variables or a reference to an
2096 :			array of variable names (see below)
2097 :			limits -- reference to an array of arrays of limits (see below), or:
2098 :			mode -- 'std' (default) (function must match exactly), or:
2099 :			'antider' (function must match up to a constant)
2100 :			relTol -- (default) a relative tolerance (as a percentage), or:
2101 :			tol -- an absolute tolerance for error
2102 :			numPoints -- the number of points to evaluate the function at
2103 :			maxConstantOfIntegration -- maximum size of the constant of integration
2104 :			zeroLevel -- if the correct answer is this close to zero, then
2105 :			zeroLevelTol applies
2106 :			zeroLevelTol -- absolute tolerance to allow when answer is close to zero
2107 :			params -- an array of "free" parameters which can be used to adapt
2108 :			-- the correct answer to the submitted answer. (e.g. ['c'] for
2109 :			-- a constant of integration in the answer x^3/3 + c.
2110 :			debug -- when set to 1 this provides extra information while checking the
2111 :			-- the answer.
2112 :
2113 :			Returns an answer evaluator, or (if given a reference to an array
2114 :			of answers), a list of answer evaluators
2115 :
2116 :			ANSWER:
2117 :
2118 :			The answer must be in the form of a string. The answer can contain
2119 :			functions, pi, e, and arithmetic operations. However, the correct answer
2120 :			string follows a slightly stricter syntax than student answers; specifically,
2121 :			there is no implicit multiplication. So the correct answer must be "3*x" rather
2122 :			than "3 x". Students can still enter "3 x".
2123 :
2124 :			VARIABLES:
2125 :
2126 :			The var parameter can contain either a number or a reference to an array of
2127 :			variable names. If it contains a number, the variables are named automatically
2128 :			as follows: 1 variable -- x
2129 :			2 variables -- x, y
2130 :			3 variables -- x, y, z
2131 :			4 or more -- x_1, x_2, x_3, etc.
2132 :			If the var parameter contains a reference to an array of variable names, then
2133 :			the number of variables is determined by the number of items in the array. A
2134 :			reference to an array is created with brackets, e.g. "var => ['r', 's', 't']".
2135 :			If only one variable is being used, you can write either "var => ['t']" for
2136 :			consistency or "var => 't'" as a shortcut. The default is one variable, x.
2137 :
2138 :			LIMITS:
2139 :
2140 :			Limits are specified with the limits parameter. You may NOT use llimit/ulimit.
2141 :			If you specify limits for one variable, you must specify them for all variables.
2142 :			The limit parameter must be a reference to an array of arrays of the form
2143 :			[lower_limit. upper_limit], each array corresponding to the lower and upper
2144 :			endpoints of the (half-open) domain of one variable. For example,
2145 :			"vars => 2, limits => [[0,2], [-3,8]]" would cause x to be evaluated in [0,2) and
2146 :			y to be evaluated in [-3,8). If only one variable is being used, you can write
2147 :			either "limits => [[0,3]]" for consistency or "limits => [0,3]" as a shortcut.
2148 :
2149 :			EXAMPLES:
2150 :
2151 :			fun_cmp( "3*x" ) -- standard compare, variable is x
2152 :			fun_cmp( ["3x", "4x+3", "3x*2"] ) -- standard compare, defaults used for all three functions
2153 :			fun_cmp( "3*t", var => 't' ) -- standard compare, variable is t
2154 :			fun_cmp( "5xy*z", var => 3 ) -- x, y and z are the variables
2155 :			fun_cmp( "5*x", mode => 'antider' ) -- student answer must match up to constant (i.e., 5x+C)
2156 :			fun_cmp( ["3xy", "4xy"], limits => [[0,2], [5,7]] ) -- x evaluated in [0,2)
2157 :			y evaluated in [5,7)
2158 :
2159 :			=cut
2160 :
2161 :			sub fun_cmp {
2162 :			my $correctAnswer = shift @_;
2163 :			my %opt = @_;
2164 :
2165 :			assign_option_aliases( \%opt,
2166 :	chris	22	'vars' => 'var', # set the standard option 'var' to the one specified as vars
2167 :			'domain' => 'limits', # set the standard option 'limits' to the one specified as domain
2168 :			'reltol' => 'relTol',
2169 :	sam	2	'param' => 'params',
2170 :			);
2171 :
2172 :			set_default_options( \%opt,
2173 :	chris	22	'var' => $functVarDefault,
2174 :			'params' => [],
2175 :			'limits' => [[$functLLimitDefault, $functULimitDefault]],
2176 :			'mode' => 'std',
2177 :			'tolType' => (defined($opt{tol}) ) ? 'absolute' : 'relative',
2178 :			'tol' => .01, # default mode should be relative, to obtain this tol must not be defined
2179 :			'relTol' => $functRelPercentTolDefault,
2180 :			'numPoints' => $functNumOfPoints,
2181 :	sam	2	'maxConstantOfIntegration' => $functMaxConstantOfIntegration,
2182 :	chris	22	'zeroLevel' => $functZeroLevelDefault,
2183 :			'zeroLevelTol' => $functZeroLevelTolDefault,
2184 :			'debug' => 0,
2185 :	sam	2	);
2186 :
2187 :
2188 :
2189 :			# allow var => 'x' as an abbreviation for var => ['x']
2190 :			my %out_options = %opt;
2191 :			unless ( ref($out_options{var}) eq 'ARRAY' ) {
2192 :			$out_options{var} = [$out_options{var}];
2193 :			}
2194 :			# allow params => 'c' as an abbreviation for params => ['c']
2195 :			unless ( ref($out_options{params}) eq 'ARRAY' ) {
2196 :			$out_options{params} = [$out_options{params}];
2197 :			}
2198 :			my ($tolType, $tol);
2199 :			if ($out_options{tolType} eq 'absolute') {
2200 :			$tolType = 'absolute';
2201 :			$tol = $out_options{'tol'};
2202 :			delete($out_options{'relTol'}) if exists( $out_options{'relTol'} );
2203 :			} else {
2204 :			$tolType = 'relative';
2205 :			$tol = $out_options{'relTol'};
2206 :			delete($out_options{'tol'}) if exists( $out_options{'tol'} );
2207 :			}
2208 :
2209 :			my @output_list = ();
2210 :			# thread over lists
2211 :			my @ans_list = ();
2212 :
2213 :			if ( ref($correctAnswer) eq 'ARRAY' ) {
2214 :			@ans_list = @{$correctAnswer};
2215 :			}
2216 :			else {
2217 :			push( @ans_list, $correctAnswer );
2218 :			}
2219 :
2220 :			# produce answer evaluators
2221 :			foreach my $ans (@ans_list) {
2222 :			push(@output_list,
2223 :	chris	22	FUNCTION_CMP( 'correctEqn' => $ans,
2224 :			'var' => $out_options{'var'},
2225 :			'limits' => $out_options{'limits'},
2226 :			'tolerance' => $tol,
2227 :			'tolType' => $tolType,
2228 :			'numPoints' => $out_options{'numPoints'},
2229 :			'mode' => $out_options{'mode'},
2230 :			'maxConstantOfIntegration' => $out_options{'maxConstantOfIntegration'},
2231 :			'zeroLevel' => $out_options{'zeroLevel'},
2232 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
2233 :			'params' => $out_options{'params'},
2234 :			'debug' => $out_options{'debug'},
2235 :	sam	2	),
2236 :			);
2237 :			}
2238 :
2239 :			return @output_list;
2240 :			}
2241 :
2242 :			## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
2243 :			## NOTE: PG_answer_eval is used instead of PG_restricted_eval in order to insure that the answer
2244 :			## evaluated within the context of the package the problem was originally defined in.
2245 :			## Includes multivariable modifications contributed by Professor William K. Ziemer
2246 :			##
2247 :			## IN: a hash consisting of the following keys (error checking to be added later?)
2248 :			## correctEqn -- the correct equation as a string
2249 :			## var -- the variable name as a string,
2250 :			## or a reference to an array of variables
2251 :			## limits -- reference to an array of arrays of type [lower,upper]
2252 :			## tolerance -- the allowable margin of error
2253 :			## tolType -- 'relative' or 'absolute'
2254 :			## numPoints -- the number of points to evaluate the function at
2255 :			## mode -- 'std' or 'antider'
2256 :			## maxConstantOfIntegration -- maximum size of the constant of integration
2257 :			## zeroLevel -- if the correct answer is this close to zero,
2258 :			## then zeroLevelTol applies
2259 :			## zeroLevelTol -- absolute tolerance to allow when answer is close to zero
2260 :
2261 :
2262 :			sub FUNCTION_CMP {
2263 :			my %func_params = @_;
2264 :
2265 :			my $correctEqn = $func_params{'correctEqn'};
2266 :	chris	22	my $var = $func_params{'var'};
2267 :	sam	2	my $ra_limits = $func_params{'limits'};
2268 :	chris	22	my $tol = $func_params{'tolerance'};
2269 :			my $tolType = $func_params{'tolType'};
2270 :	sam	2	my $numPoints = $func_params{'numPoints'};
2271 :	chris	22	my $mode = $func_params{'mode'};
2272 :			my $maxConstantOfIntegration = $func_params{'maxConstantOfIntegration'};
2273 :	sam	2	my $zeroLevel = $func_params{'zeroLevel'};
2274 :			my $zeroLevelTol = $func_params{'zeroLevelTol'};
2275 :
2276 :
2277 :			# Check that everything is defined:
2278 :			$func_params{debug} = 0 unless defined($func_params{debug});
2279 :			$mode = 'std' unless defined($mode);
2280 :			my @VARS = get_var_array( $var );
2281 :			my @limits = get_limits_array( $ra_limits );
2282 :			my @PARAMS = ();
2283 :			@PARAMS = @{$func_params{'params'}} if defined($func_params{'params'});
2284 :
2285 :			if ($mode eq 'antider' ) {
2286 :			# doctor the equation to allow addition of a constant
2287 :			my $CONSTANT_PARAM = 'Q'; # unfortunately parameters must be single letters.
2288 :			# There is the possibility of conflict here.
2289 :			# 'Q' seemed less dangerous than 'C'.
2290 :			$correctEqn = "( $correctEqn ) + $CONSTANT_PARAM";
2291 :			push(@PARAMS, $CONSTANT_PARAM);
2292 :			}
2293 :			my $dim_of_param_space = @PARAMS; # dimension of equivalence space
2294 :
2295 :			if( $tolType eq 'relative' ) {
2296 :			$tol = $functRelPercentTolDefault unless defined $tol;
2297 :			$tol *= .01;
2298 :			}
2299 :			else {
2300 :			$tol = $functAbsTolDefault unless defined $tol;
2301 :			}
2302 :
2303 :			#loop ensures that number of limits matches number of variables
2304 :			for( my $i = 0; $i < scalar(@VARS); $i++ ) {
2305 :			$limits[$i][0] = $functLLimitDefault unless defined $limits[$i][0];
2306 :			$limits[$i][1] = $functULimitDefault unless defined $limits[$i][1];
2307 :			}
2308 :			$numPoints = $functNumOfPoints unless defined $numPoints;
2309 :			$maxConstantOfIntegration = $functMaxConstantOfIntegration unless defined $maxConstantOfIntegration;
2310 :			$zeroLevel = $functZeroLevelDefault unless defined $zeroLevel;
2311 :			$zeroLevelTol = $functZeroLevelTolDefault unless defined $zeroLevelTol;
2312 :
2313 :	chris	22	$func_params{'var'} = $var;
2314 :			$func_params{'limits'} = \@limits;
2315 :			$func_params{'tolerance'} = $tol;
2316 :			$func_params{'tolType'} = $tolType;
2317 :			$func_params{'numPoints'} = $numPoints;
2318 :			$func_params{'mode'} = $mode;
2319 :			$func_params{'maxConstantOfIntegration'} = $maxConstantOfIntegration;
2320 :			$func_params{'zeroLevel'} = $zeroLevel;
2321 :			$func_params{'zeroLevelTol'} = $zeroLevelTol;
2322 :
2323 :	gage	5	########################################################
2324 :			# End of cleanup of calling parameters
2325 :			########################################################
2326 :	sam	2	my $i; #for use with loops
2327 :			my $PGanswerMessage = "";
2328 :			my $originalCorrEqn = $correctEqn;
2329 :
2330 :			#prepare the correct answer and check it's syntax
2331 :	chris	22	my $rh_correct_ans = new AnswerHash;
2332 :	sam	2	$rh_correct_ans->input($correctEqn);
2333 :			$rh_correct_ans = check_syntax($rh_correct_ans);
2334 :			warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag};
2335 :			$rh_correct_ans->clear_error();
2336 :			$rh_correct_ans = function_from_string2($rh_correct_ans, ra_vars => [ @VARS, @PARAMS ],
2337 :			store_in =>'rf_correct_ans',
2338 :			debug => $func_params{debug});
2339 :			my $correct_eqn_sub = $rh_correct_ans->{rf_correct_ans};
2340 :			warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag};
2341 :
2342 :			#create the evaluation points
2343 :			my $random_for_answers = new PGrandom($main::PG_original_problemSeed);
2344 :	chris	22	my $NUMBER_OF_STEPS_IN_RANDOM = 1000; # determines the granularity of the random_for_answers number generator
2345 :	sam	2	my (@evaluation_points);
2346 :			for( my $count = 0; $count < @PARAMS+1+$numPoints; $count++ ) {
2347 :			my (@vars,$iteration_limit);
2348 :			for( my $i = 0; $i < @VARS; $i++ ) {
2349 :			my $iteration_limit = 10;
2350 :			while ( 0 < --$iteration_limit ) { # make sure that the endpoints of the interval are not included
2351 :			$vars[$i] = $random_for_answers->random($limits[$i][0], $limits[$i][1], abs($limits[$i][1] - $limits[$i][0])/$NUMBER_OF_STEPS_IN_RANDOM );
2352 :			last if $vars[$i]!=$limits[$i][0] and $vars[$i]!=$limits[$i][1];
2353 :			}
2354 :			warn "Unable to properly choose evaluation points for this function in the interval ( $limits[$i][0] , $limits[$i][1] )"
2355 :			if $iteration_limit == 0;
2356 :			};
2357 :
2358 :			push(@evaluation_points,\@vars);
2359 :			}
2360 :			my $evaluation_points = Matrix->new_from_array_ref(\@evaluation_points);
2361 :
2362 :			#my $COEFFS = determine_param_coeffs($correct_eqn_sub,$evaluation_points[0],$numOfParameters);
2363 :	chris	22	#warn "coeff", join(" \| ", @{$COEFFS});
2364 :	sam	2
2365 :			#construct the answer evaluator
2366 :			my $answer_evaluator = new AnswerEvaluator;
2367 :			$answer_evaluator->{debug} = $func_params{debug};
2368 :			$answer_evaluator->ans_hash( correct_ans => $originalCorrEqn,
2369 :			rf_correct_ans => $rh_correct_ans->{rf_correct_ans},
2370 :			evaluation_points => \@evaluation_points,
2371 :			ra_param_vars => \@PARAMS,
2372 :			ra_vars => \@VARS,
2373 :			type => 'function',
2374 :			);
2375 :
2376 :			$answer_evaluator->install_pre_filter(\&check_syntax);
2377 :			$answer_evaluator->install_pre_filter(\&function_from_string2, ra_vars => \@VARS,debug=>$func_params{debug},); # @VARS has been guaranteed to be an array, $var might be a single string.
2378 :			$answer_evaluator->install_pre_filter(\&best_approx_parameters, %func_params, param_vars => \@PARAMS);
2379 :			$answer_evaluator->install_evaluator(\&calculate_difference_vector, %func_params);
2380 :			$answer_evaluator->install_evaluator(\&is_zero_array, tol => $tol );
2381 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('SYNTAX'); $rh_ans;} );
2382 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift;
2383 :			if ($rh_ans->catch_error('EVAL') ) {
2384 :			$rh_ans->{ans_message} = $rh_ans->{error_message};
2385 :			$rh_ans->clear_error('EVAL');
2386 :			}
2387 :			$rh_ans;
2388 :			});
2389 :			$answer_evaluator;
2390 :			}
2391 :
2392 :			=head4 Filters
2393 :
2394 :			=pod
2395 :
2396 :			is_array($rh_ans)
2397 :			returns: $rh_ans. Throws error "NOTARRAY" if this is not an array
2398 :
2399 :			=cut
2400 :
2401 :			sub is_array{
2402 :			my $rh_ans = shift;
2403 :			# return if the result is an array
2404 :			return($rh_ans) if ref($rh_ans->{student_ans}) eq 'ARRAY' ;
2405 :			$rh_ans->throw_error("NOTARRAY","The answer is not an array");
2406 :			$rh_ans;
2407 :			}
2408 :
2409 :			=pod
2410 :
2411 :			check_syntax( $rh_ans, %options)
2412 :			returns an answer hash.
2413 :
2414 :			latex2html preview code are installed in the answer hash.
2415 :			The input has been transformed, changing 7pi to 7pi or 7x to 7x.
2416 :			Syntax error messages may be generated and stored in student_ans
2417 :			Additional syntax error messages are stored in {ans_message} and duplicated in {error_message}
2418 :
2419 :
2420 :			=cut
2421 :
2422 :			sub check_syntax {
2423 :			my $rh_ans = shift;
2424 :			my %options = @_;
2425 :			unless ( defined( $rh_ans->{student_ans} ) ) {
2426 :			warn "Check_syntax requires an equation in the field {student_ans} or input";
2427 :			$rh_ans->throw_error("1","{student_ans} field not defined");
2428 :			return $rh_ans;
2429 :			}
2430 :			my $in = $rh_ans->{student_ans};
2431 :			my $parser = new AlgParserWithImplicitExpand;
2432 :			my $ret = $parser -> parse($in); #for use with loops
2433 :
2434 :			if ( ref($ret) ) { ## parsed successfully
2435 :			$parser -> tostring();
2436 :			$parser -> normalize();
2437 :			$rh_ans->input( $parser -> tostring() );
2438 :			$rh_ans->{preview_text_string} = $in;
2439 :			$rh_ans->{preview_latex_string} = $parser -> tolatex();
2440 :
2441 :			} else { ## error in parsing
2442 :
2443 :			$rh_ans->{'student_ans'} = 'syntax error:'. $parser->{htmlerror},
2444 :			$rh_ans->{'ans_message'} = $parser -> {error_msg},
2445 :			$rh_ans->{'preview_text_string'} = '',
2446 :			$rh_ans->{'preview_latex_string'} = '',
2447 :			$rh_ans->throw_error('SYNTAX', 'syntax error in answer:'. $parser->{htmlerror} . "$BR" .$parser -> {error_msg});
2448 :			}
2449 :
2450 :
2451 :
2452 :			$rh_ans;
2453 :
2454 :
2455 :			}
2456 :
2457 :			=pod
2458 :
2459 :			std_num_filter($rh_ans, %options)
2460 :			returns $rh_ans
2461 :
2462 :			Replaces some constants using math_constants, then evaluates a perl expression.
2463 :
2464 :
2465 :			=cut
2466 :
2467 :			sub std_num_filter {
2468 :			my $rh_ans = shift;
2469 :			my %options = @_;
2470 :			my $in = $rh_ans->input();
2471 :			$in = math_constants($in);
2472 :			$rh_ans->{type} = 'std_number';
2473 :			my ($inVal,$PG_eval_errors,$PG_full_error_report);
2474 :			if ($in =~ /\S/) {
2475 :			($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($in);
2476 :			} else {
2477 :			$PG_eval_errors = '';
2478 :			}
2479 :
2480 :			if ($PG_eval_errors) { ##error message from eval or above
2481 :			$rh_ans->{ans_message} = 'There is a syntax error in your answer';
2482 :			$rh_ans->{student_ans} = clean_up_error_msg($PG_eval_errors);
2483 :			} else {
2484 :			$rh_ans->{student_ans} = $inVal;
2485 :			}
2486 :			$rh_ans;
2487 :			}
2488 :
2489 :			=pod
2490 :
2491 :			std_num_array_filter($rh_ans, %options)
2492 :			returns $rh_ans
2493 :
2494 :			Assumes the {student_ans} field is a numerical array, and applies BOTH check_syntax and std_num_filter
2495 :			to each element of the array. Does it's best to generate sensible error messages for syntax errors.
2496 :			A typical error message displayed in {studnet_ans} might be ( 56, error message, -4).
2497 :
2498 :			=cut
2499 :
2500 :			sub std_num_array_filter{
2501 :			my $rh_ans= shift;
2502 :			my %options = @_;
2503 :			my @in = @{$rh_ans->{student_ans}};
2504 :			my $temp_hash = new AnswerHash;
2505 :			my @out=();
2506 :			my $PGanswerMessage = '';
2507 :			foreach my $item (@in) { # evaluate each number in the vector
2508 :			$temp_hash->input($item);
2509 :			$temp_hash = check_syntax($temp_hash);
2510 :			if (defined($temp_hash->{error_flag}) and $temp_hash->{error_flag} eq 'SYNTAX') {
2511 :			$PGanswerMessage .= $temp_hash->{ans_message};
2512 :			$temp_hash->{ans_message} = undef;
2513 :			} else {
2514 :			#continue processing
2515 :			$temp_hash = std_num_filter($temp_hash);
2516 :			if (defined($temp_hash->{ans_message}) and $temp_hash->{ans_message} ) {
2517 :			$PGanswerMessage .= $temp_hash->{ans_message};
2518 :			$temp_hash->{ans_message} = undef;
2519 :			}
2520 :			}
2521 :			push(@out, $temp_hash->input());
2522 :
2523 :			}
2524 :			if ($PGanswerMessage) {
2525 :			$rh_ans->input( "( " . join(", ", @out ) . " )" );
2526 :	chris	22	$rh_ans->throw_error('SYNTAX', 'There is a syntax error in your answer.');
2527 :	sam	2	} else {
2528 :			$rh_ans->input( [@out] );
2529 :			}
2530 :			$rh_ans;
2531 :			}
2532 :
2533 :
2534 :
2535 :			sub function_from_string2 {
2536 :			my $rh_ans = shift;
2537 :			my %options = @_;
2538 :			my $eqn = $rh_ans->{student_ans};
2539 :			set_default_options( \%options,
2540 :			'store_in' => 'rf_student_ans',
2541 :			'ra_vars' => [qw( x y )],
2542 :			'debug' => 0,
2543 :			);
2544 :			my @VARS = @{ $options{ 'ra_vars'}};
2545 :			warn "VARS = ", join("<>", @VARS) if defined($options{debug}) and $options{debug} ==1;
2546 :			my $originalEqn = $eqn;
2547 :			$eqn = &math_constants($eqn);
2548 :			for( my $i = 0; $i < @VARS; $i++ ) {
2549 :			$eqn =~ s/\b$VARS[$i]\b/\$VARS[$i]/g;
2550 :			}
2551 :			warn "equation evaluated = $eqn",$rh_ans->pretty_print(), "<br>\noptions<br>\n",
2552 :			pretty_print(\%options)
2553 :			if defined($options{debug}) and $options{debug} ==1;
2554 :			my ($function_sub,$PG_eval_errors, $PG_full_errors) = PG_answer_eval( q!
2555 :			sub {
2556 :			my @VARS = @_;
2557 :			my $input_str = '';
2558 :			for( my $i=0; $i<@VARS; $i++ ) {
2559 :			$input_str .= "\$VARS[$i] = $VARS[$i]; ";
2560 :			}
2561 :			my $PGanswerMessage;
2562 :			$input_str .= '! . $eqn . q!'; # need the single quotes to keep the contents of $eqn from being
2563 :			# evaluated when it is assigned to $input_str;
2564 :			my ($out, $PG_eval_errors, $PG_full_errors) = PG_answer_eval($input_str); #Finally evaluated
2565 :
2566 :			if ( defined($PG_eval_errors) and $PG_eval_errors =~ /\S/ ) {
2567 :			$PGanswerMessage = clean_up_error_msg($PG_eval_errors);
2568 :			# This message seemed too verbose, but it does give extra information, we'll see if it is needed.
2569 :			# "<br> There was an error in evaluating your function <br>
2570 :			# !. $originalEqn . q! <br>
2571 :			# at ( " . join(', ', @VARS) . " ) <br>
2572 :			# $PG_eval_errors
2573 :			# "; # this message appears in the answer section which is not process by Latex2HTML so it must
2574 :			# # be in HTML. That is why $BR is NOT used.
2575 :
2576 :			}
2577 :			(wantarray) ? ($out, $PGanswerMessage): $out; # PGanswerMessage may be undefined.
2578 :			};
2579 :			!);
2580 :
2581 :			if (defined($PG_eval_errors) and $PG_eval_errors =~/\S/ ) {
2582 :			$PG_eval_errors = clean_up_error_msg($PG_eval_errors);
2583 :
2584 :			my $PGanswerMessage = "There was an error in converting the expression
2585 :			$main::BR $originalEqn $main::BR into a function.
2586 :			$main::BR $PG_eval_errors.";
2587 :			$rh_ans->{rf_student_ans} = $function_sub;
2588 :			$rh_ans->{ans_message} = $PGanswerMessage;
2589 :			$rh_ans->{error_message} = $PGanswerMessage;
2590 :			$rh_ans->{error_flag} = 1;
2591 :			# we couldn't compile the equation, we'll return an error message.
2592 :			} else {
2593 :			# if (defined($options{store_in} )) {
2594 :			# $rh_ans ->{$options{store_in}} = $function_sub;
2595 :			# } else {
2596 :			# $rh_ans->{rf_student_ans} = $function_sub;
2597 :			# }
2598 :			$rh_ans ->{$options{store_in}} = $function_sub;
2599 :
2600 :			}
2601 :
2602 :			$rh_ans;
2603 :			}
2604 :
2605 :
2606 :			sub is_zero_array{
2607 :			my $rh_ans = shift;
2608 :			my %options = @_;
2609 :			my $array = $rh_ans -> {ra_differences};
2610 :			my $num = @$array;
2611 :			my $i;
2612 :			my $max = 0; my $mm;
2613 :			for ($i=0; $i< $num; $i++) {
2614 :			$mm = $array->[$i] ;
2615 :			if (not is_a_number($mm) ) {
2616 :			$max = $mm; # break out if one of the elements is not a number
2617 :			last;
2618 :			}
2619 :			$max = abs($mm) if abs($mm) > $max;
2620 :			}
2621 :			if (not is_a_number($max)) {
2622 :			$rh_ans->{score} = 0;
2623 :			my $error = "WeBWorK was unable evaluate your function. Please check that your
2624 :			expression doesn't take roots of negative numbers, or divide by zero.";
2625 :			$rh_ans->throw_error('EVAL',$error);
2626 :			} else {
2627 :			my $tol = $options{tol} if defined($options{tol});
2628 :	gage	5	#$tol = 0.01*$options{reltol} if defined($options{reltol});
2629 :	sam	2	$tol = .000001 unless defined($tol);
2630 :
2631 :			$rh_ans->{score} = ($max <$tol) ? 1: 0; # 1 if the array is close to 0;
2632 :			}
2633 :			$rh_ans;
2634 :			}
2635 :			=pod
2636 :
2637 :			best_approx_parameters($rh_ans,%options);
2638 :			{rf_student_ans} # reference to the test answer
2639 :			{rf_correct_ans} # reference to the comparison answer
2640 :			{evaluation_points}, # an array of row vectors indicating the points
2641 :			# to evaluate when comparing the functions
2642 :			%options # debug => 1 gives more error answers
2643 :			# param_vars => [''] additional parameters used to adapt to function
2644 :			)
2645 :			returns $rh_ans;
2646 :			The parameters for the comparison function which best approximates the test_function are stored
2647 :			in the field {ra_parameters}.
2648 :
2649 :			The last $dim_of_parms_space variables are assumed to be parameters, and it is also
2650 :			assumed that the function \&comparison_fun
2651 :			depends linearly on these variables. This function finds the values for these parameters which minimizes the
2652 :			Euclidean distance (L2 distance) between the test function and the comparison function and the test points specified
2653 :			by the array reference \@rows_of_test_points. This is assumed to be an array of arrays, with the inner arrays
2654 :			determining a test point.
2655 :
2656 :			The comparison function should have $dim_of_params_space more input variables than the test function.
2657 :
2658 :			=cut
2659 :
2660 :
2661 :
2662 :
2663 :
2664 :			# =pod
2665 :			#
2666 :			# Used internally:
2667 :			#
2668 :			# &$determine_param_coeff( $rf_comparison_function # a reference to the correct answer function
2669 :			# $ra_variables # an array of the active input variables to the functions
2670 :			# $dim_of_params_space # indicates the number of parameters upon which the
2671 :			# # the comparison function depends linearly. These are assumed to
2672 :			# # be the last group of inputs to the comparison function.
2673 :			#
2674 :			# %options # $options{debug} gives more error messages
2675 :			#
2676 :			# # A typical function might look like
2677 :			# # f(x,y,z,a,b) = x^2+acos(xz) + bsin(x) with a parameter
2678 :			# # space of dimension 2 and a variable space of dimension 3.
2679 :			# )
2680 :			# # returns a list of coefficients
2681 :			#
2682 :			# =cut
2683 :
2684 :
2685 :			sub best_approx_parameters{
2686 :			my $rh_ans = shift;
2687 :			my %options = @_;
2688 :			my $errors = undef;
2689 :			# This subroutine for the determining the coefficents of the parameters at a given point
2690 :			# is pretty specialized, so it is included here as a sub-subroutine.
2691 :			my $determine_param_coeffs = sub {
2692 :			my ($rf_fun, $ra_variables, $dim_of_params_space, %options) =@_;
2693 :			my @zero_params=();
2694 :			for(my $i=1;$i<=$dim_of_params_space;$i++){push(@zero_params,0); }
2695 :			my @vars = @$ra_variables;
2696 :			my @coeff = ();
2697 :			my @inputs = (@vars,@zero_params);
2698 :			my ($f0, $f1, $err);
2699 :			($f0, $err) = &{$rf_fun}(@inputs);
2700 :			if (defined($err) ) {
2701 :			$errors .= "$err ";
2702 :			} else {
2703 :			for (my $i=@vars;$i<@inputs;$i++) {
2704 :			$inputs[$i]=1; # set one parameter to 1;
2705 :			my($f1,$err) = &$rf_fun(@inputs);
2706 :			if (defined($err) ) {
2707 :			$errors .= " $err ";
2708 :			} else {
2709 :			push(@coeff, $f1-$f0);
2710 :			}
2711 :			$inputs[$i]=0; # set it back
2712 :			}
2713 :			}
2714 :			(\@coeff, $errors);
2715 :			};
2716 :			my $rf_fun = $rh_ans->{rf_student_ans};
2717 :			my $rf_correct_fun = $rh_ans->{rf_correct_ans};
2718 :			my $ra_vars_matrix = $rh_ans->{evaluation_points};
2719 :			my $dim_of_param_space = @{$options{param_vars}};
2720 :			# Short cut. Bail if there are no param_vars
2721 :			unless ($dim_of_param_space >0) {
2722 :	gage	5	$rh_ans ->{ra_parameters} = [];
2723 :	sam	2	return $rh_ans;
2724 :			}
2725 :			# inputs are row arrays in this case.
2726 :			my @zero_params=();
2727 :
2728 :			for(my $i=1;$i<=$dim_of_param_space;$i++){push(@zero_params,0); }
2729 :			my @rows_of_vars = @$ra_vars_matrix;
2730 :			warn "input rows ", pretty_print(\@rows_of_vars) if defined($options{debug}) and $options{debug};
2731 :			my $rows = @rows_of_vars;
2732 :			my $matrix =new Matrix($rows,$dim_of_param_space);
2733 :			my $rhs_vec = new Matrix($rows, 1);
2734 :			my $row_num = 1;
2735 :			my ($ra_coeff,$val2, $val1, $err1,$err2,@inputs,@vars);
2736 :			my $number_of_data_points = $dim_of_param_space +2;
2737 :			while (@rows_of_vars and $row_num <= $number_of_data_points) {
2738 :
2739 :			# get one set of data points from the test function;
2740 :			@vars = @{ shift(@rows_of_vars) };
2741 :			($val2, $err1) = &{$rf_fun}(@vars);
2742 :			$errors .= " $err1 " if defined($err1);
2743 :			@inputs = (@vars,@zero_params);
2744 :			($val1, $err2) = &{$rf_correct_fun}(@inputs);
2745 :			$errors .= " $err2 " if defined($err2);
2746 :
2747 :			unless (defined($err1) or defined($err2) ) {
2748 :			$rhs_vec->assign($row_num,1, $val2-$val1 );
2749 :
2750 :			# warn "rhs data val1=$val1, val2=$val2, val2 - val1 = ", $val2 - $val1 if $options{debug};
2751 :			# warn "vars ", join(" \| ", @vars) if $options{debug};
2752 :
2753 :			($ra_coeff, $err1) = &{$determine_param_coeffs}($rf_correct_fun,\@vars,$dim_of_param_space,%options);
2754 :			if (defined($err1) ) {
2755 :			$errors .= " $err1 ";
2756 :			} else {
2757 :			my @coeff = @$ra_coeff;
2758 :			my $col_num=1;
2759 :			while(@coeff) {
2760 :			$matrix->assign($row_num,$col_num, shift(@coeff) );
2761 :			$col_num++;
2762 :			}
2763 :			}
2764 :	gage	5
2765 :	sam	2	}
2766 :			$row_num++;
2767 :			last if $errors; # break if there are any errors.
2768 :			# This cuts down on the size of error messages.
2769 :			# However it impossible to check for equivalence at 95% of points
2770 :	gage	5	# which might be useful for functions that are not defined at some points.
2771 :	sam	2	}
2772 :			warn "<br> best_approx_parameters: matrix1 <br> ", " $matrix " if $options{debug};
2773 :			warn "<br> best_approx_parameters: vector <br> ", " $rhs_vec " if $options{debug};
2774 :
2775 :			# we have Matrix * parameter = data_vec + perpendicular vector
2776 :			# where the matrix has column vectors defining the span of the parameter space
2777 :			# multiply both sides by Matrix_transpose and solve for the parameters
2778 :			# This is exactly what the method proj_coeff method does.
2779 :			my @array;
2780 :			if (defined($errors) ) {
2781 :			@array = (); # new Matrix($dim_of_param_space,1);
2782 :			} else {
2783 :			@array = $matrix->proj_coeff($rhs_vec)->list();
2784 :			}
2785 :			# check size (hack)
2786 :			my $max = 0;
2787 :			foreach my $val (@array ) {
2788 :			$max = abs($val) if $max < abs($val);
2789 :			if (not is_a_number($val) ) {
2790 :			$max = "NaN: $val";
2791 :			last;
2792 :			}
2793 :			}
2794 :			if ($max =~/NaN/) {
2795 :			$errors .= "WeBWorK was unable evaluate your function. Please check that your
2796 :			expression doesn't take roots of negative numbers, or divide by zero.";
2797 :			} elsif ($max > $options{maxConstantOfIntegration} ) {
2798 :			$errors .= "At least one of the adapting parameters
2799 :			(perhaps the constant of integration) is too large: $max,
2800 :			( the maximum allowed is $options{maxConstantOfIntegration} )";
2801 :			}
2802 :
2803 :			$rh_ans->{ra_parameters} = \@array;
2804 :			$rh_ans->throw_error('EVAL', $errors) if defined($errors);
2805 :			$rh_ans;
2806 :			}
2807 :
2808 :			=pod
2809 :
2810 :			calculate_difference_vector( $ans_hash, %options);
2811 :
2812 :			{rf_student_ans}, # a reference to the test function
2813 :			{rf_correct_ans}, # a reference to the correct answer function
2814 :			{evaluation_points}, # an array of row vectors indicating the points
2815 :			# to evaluate when comparing the functions
2816 :			{ra_parameters} # these are the (optional) additional inputs to
2817 :			# the comparison function which adapt it properly
2818 :			# to the problem at hand.
2819 :
2820 :			%options # mode => 'rel' specifies that each element in the
2821 :			# difference matrix is divided by the correct answer.
2822 :			# unless the correct answer is nearly 0.
2823 :			)
2824 :
2825 :			=cut
2826 :
2827 :
2828 :			sub calculate_difference_vector {
2829 :			my $rh_ans = shift;
2830 :			my %options = @_;
2831 :			# initialize
2832 :			my $rf_fun = $rh_ans -> {rf_student_ans};
2833 :			my $rf_correct_fun = $rh_ans -> {rf_correct_ans};
2834 :			my $ra_parameters = $rh_ans ->{ra_parameters};
2835 :			my @evaluation_points = @{$rh_ans->{evaluation_points} };
2836 :			my @parameters = ();
2837 :			@parameters = @$ra_parameters if defined($ra_parameters) and ref($ra_parameters) eq 'ARRAY';
2838 :			my $errors = undef;
2839 :	gage	5	my @zero_params=();
2840 :			for(my $i=1;$i<=@{$ra_parameters};$i++){push(@zero_params,0); }
2841 :	sam	2	my @differences = ();
2842 :	gage	5	my @student_values;
2843 :			my @correct_values;
2844 :			my @tol_values;
2845 :			my ($diff,$tol_val);
2846 :	sam	2	# calculate the vector of differences between the test function and the comparison function.
2847 :			while (@evaluation_points) {
2848 :	gage	5	my ($err1, $err2,$err3);
2849 :	sam	2	my @vars = @{ shift(@evaluation_points) };
2850 :			my @inputs = (@vars, @parameters);
2851 :			my ($inVal, $correctVal);
2852 :			($inVal, $err1) = &{$rf_fun}(@vars);
2853 :			$errors .= " $err1 " if defined($err1);
2854 :	gage	5	$errors .= " Error detected evaluating student input at (".join(' , ',@vars) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err1);
2855 :	sam	2	($correctVal, $err2) =&{$rf_correct_fun}(@inputs);
2856 :			$errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err2 " if defined($err2);
2857 :	gage	5	$errors .= " Error detected evaluating correct answer at (".join(' , ',@inputs) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err2);
2858 :			($tol_val,$err3)= &$rf_correct_fun(@vars, @zero_params);
2859 :			$errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err3 " if defined($err3);
2860 :			$errors .= " Error detected evaluating correct answer at (".join(' , ',@vars, @zero_params) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err3);
2861 :			unless (defined($err1) or defined($err2) or defined($err3) ) {
2862 :			$diff = ( $inVal - ($correctVal -$tol_val ) ) - $tol_val; #prevents entering too high a number?
2863 :	sam	2	#warn "taking the difference of ", $inVal, " and ", $correctVal, " is ", $diff;
2864 :
2865 :			if (defined($options{tolType}) and $options{tolType} eq 'relative' ) { #relative tolerance
2866 :	gage	5	#warn "diff = $diff";
2867 :
2868 :	chris	22	$diff = ( $inVal - ($correctVal-$tol_val ) )/abs($tol_val) -1 if abs($tol_val) > $options{zeroLevel};
2869 :	gage	5	#$diff = ( $inVal - ($correctVal-$tol_val- $tol_val ) )/abs($tol_val) if abs($tol_val) > $options{zeroLevel};
2870 :			#warn "diff = $diff, ", abs( &$rf_correct_fun(@inputs) ) , "-- $correctVal";
2871 :	sam	2	}
2872 :			}
2873 :			last if $errors; # break if there are any errors.
2874 :			# This cuts down on the size of error messages.
2875 :			# However it impossible to check for equivalence at 95% of points
2876 :	gage	5	# which might be useful for functions that are not defined at some points.
2877 :			push(@student_values,$inVal);
2878 :			push(@correct_values,( $inVal - ($correctVal-$tol_val ) ));
2879 :	sam	2	push(@differences, $diff);
2880 :	gage	5	push(@tol_values,$tol_val);
2881 :	sam	2	}
2882 :			$rh_ans ->{ra_differences} = \@differences;
2883 :	chris	22	$rh_ans ->{ra_student_values} = \@student_values;
2884 :			$rh_ans ->{ra_adjusted_student_values} = \@correct_values;
2885 :			$rh_ans->{ra_tol_values}=\@tol_values;
2886 :	sam	2	$rh_ans->throw_error('EVAL', $errors) if defined($errors);
2887 :			$rh_ans;
2888 :			}
2889 :
2890 :
2891 :			##########################################################################
2892 :			##########################################################################
2893 :			## String answer evaluators
2894 :
2895 :			=head2 String Answer Evaluators
2896 :
2897 :			String answer evaluators compare a student string to the correct string.
2898 :			Different filters can be applied to allow various degrees of variation.
2899 :			Both the student and correct answers are subject to the same filters, to
2900 :			ensure that there are no unexpected matches or rejections.
2901 :
2902 :			String Filters
2903 :
2904 :			remove_whitespace -- Removes all whitespace from the string.
2905 :			It applies the following substitution
2906 :			to the string:
2907 :			$filteredAnswer =~ s/\s+//g;
2908 :
2909 :			compress_whitespace -- Removes leading and trailing whitespace, and
2910 :			replaces all other blocks of whitespace by a
2911 :			single space. Applies the following substitutions:
2912 :			$filteredAnswer =~ s/^\s*//;
2913 :			$filteredAnswer =~ s/\s*$//;
2914 :			$filteredAnswer =~ s/\s+/ /g;
2915 :
2916 :			trim_whitespace -- Removes leading and trailing whitespace.
2917 :			Applies the following substitutions:
2918 :			$filteredAnswer =~ s/^\s*//;
2919 :			$filteredAnswer =~ s/\s*$//;
2920 :
2921 :			ignore_case -- Ignores the case of the string. More accurately,
2922 :			it converts the string to uppercase (by convention).
2923 :			Applies the following function:
2924 :			$filteredAnswer = uc $filteredAnswer;
2925 :
2926 :			ignore_order -- Ignores the order of the letters in the string.
2927 :			This is used for problems of the form "Choose all
2928 :			that apply." Specifically, it removes all
2929 :			whitespace and lexically sorts the letters in
2930 :			ascending alphabetical order. Applies the following
2931 :			functions:
2932 :			$filteredAnswer = join( "", lex_sort(
2933 :			split( /\s*/, $filteredAnswer ) ) );
2934 :
2935 :			=cut
2936 :
2937 :			################################
2938 :			## STRING ANSWER FILTERS
2939 :
2940 :			## IN: --the string to be filtered
2941 :			## --a list of the filters to use
2942 :			##
2943 :			## OUT: --the modified string
2944 :			##
2945 :			## Use this subroutine instead of the
2946 :			## individual filters below it
2947 :			sub str_filters {
2948 :			my $stringToFilter = shift @_;
2949 :			my @filters_to_use = @_;
2950 :			my %known_filters = ( 'remove_whitespace' => undef,
2951 :			'compress_whitespace' => undef,
2952 :			'trim_whitespace' => undef,
2953 :			'ignore_case' => undef,
2954 :			'ignore_order' => undef
2955 :			);
2956 :
2957 :			#test for unknown filters
2958 :			my $filter;
2959 :			foreach $filter (@filters_to_use) {
2960 :			die "Unknown string filter $filter (try checking the parameters to str_cmp() )"
2961 :			unless exists $known_filters{$filter};
2962 :			}
2963 :
2964 :			if( grep( /remove_whitespace/i, @filters_to_use ) ) {
2965 :			$stringToFilter = remove_whitespace( $stringToFilter );
2966 :			}
2967 :			if( grep( /compress_whitespace/i, @filters_to_use ) ) {
2968 :			$stringToFilter = compress_whitespace( $stringToFilter );
2969 :			}
2970 :			if( grep( /trim_whitespace/i, @filters_to_use ) ) {
2971 :			$stringToFilter = trim_whitespace( $stringToFilter );
2972 :			}
2973 :			if( grep( /ignore_case/i, @filters_to_use ) ) {
2974 :			$stringToFilter = ignore_case( $stringToFilter );
2975 :			}
2976 :			if( grep( /ignore_order/i, @filters_to_use ) ) {
2977 :			$stringToFilter = ignore_order( $stringToFilter );
2978 :			}
2979 :
2980 :			return $stringToFilter;
2981 :			}
2982 :
2983 :			sub remove_whitespace {
2984 :			my $filteredAnswer = shift;
2985 :
2986 :			$filteredAnswer =~ s/\s+//g; # remove all whitespace
2987 :
2988 :			return $filteredAnswer;
2989 :			}
2990 :
2991 :			sub compress_whitespace {
2992 :			my $filteredAnswer = shift;
2993 :
2994 :			$filteredAnswer =~ s/^\s*//; # remove initial whitespace
2995 :			$filteredAnswer =~ s/\s*$//; # remove trailing whitespace
2996 :			$filteredAnswer =~ s/\s+/ /g; # replace spaces by single space
2997 :
2998 :			return $filteredAnswer;
2999 :			}
3000 :
3001 :			sub trim_whitespace {
3002 :			my $filteredAnswer = shift;
3003 :
3004 :			$filteredAnswer =~ s/^\s*//; # remove initial whitespace
3005 :			$filteredAnswer =~ s/\s*$//; # remove trailing whitespace
3006 :
3007 :			return $filteredAnswer;
3008 :			}
3009 :
3010 :			sub ignore_case {
3011 :			my $filteredAnswer = shift;
3012 :
3013 :			$filteredAnswer = uc $filteredAnswer;
3014 :
3015 :			return $filteredAnswer;
3016 :			}
3017 :
3018 :			sub ignore_order {
3019 :			my $filteredAnswer = shift;
3020 :
3021 :			$filteredAnswer = join( "", lex_sort( split( /\s*/, $filteredAnswer ) ) );
3022 :
3023 :			return $filteredAnswer;
3024 :			}
3025 :			################################
3026 :			## END STRING ANSWER FILTERS
3027 :
3028 :			=head3 "mode"_str_cmp functions
3029 :
3030 :			The functions of the the form "mode"_str_cmp() use different functions to
3031 :			specify which filters to apply. They take no options except the correct
3032 :			string. There are also versions which accept a list of strings.
3033 :
3034 :			std_str_cmp( $correctString )
3035 :			std_str_cmp_list( @correctStringList )
3036 :			Filters: compress_whitespace, ignore_case
3037 :
3038 :			std_cs_str_cmp( $correctString )
3039 :			std_cs_str_cmp_list( @correctStringList )
3040 :			Filters: compress_whitespace
3041 :
3042 :			strict_str_cmp( $correctString )
3043 :			strict_str_cmp_list( @correctStringList )
3044 :			Filters: trim_whitespace
3045 :
3046 :			unordered_str_cmp( $correctString )
3047 :			unordered_str_cmp_list( @correctStringList )
3048 :			Filters: ignore_order, ignore_case
3049 :
3050 :			unordered_cs_str_cmp( $correctString )
3051 :			unordered_cs_str_cmp_list( @correctStringList )
3052 :			Filters: ignore_order
3053 :
3054 :			ordered_str_cmp( $correctString )
3055 :			ordered_str_cmp_list( @correctStringList )
3056 :			Filters: remove_whitespace, ignore_case
3057 :
3058 :			ordered_cs_str_cmp( $correctString )
3059 :			ordered_cs_str_cmp_list( @correctStringList )
3060 :			Filters: remove_whitespace
3061 :
3062 :			Examples
3063 :
3064 :			ANS( std_str_cmp( "W. Mozart" ) ) -- Accepts "W. Mozart", "W. MOZarT",
3065 :			and so forth. Case insensitive. All internal spaces treated
3066 :			as single spaces.
3067 :			ANS( std_cs_str_cmp( "Mozart" ) ) -- Rejects "mozart". Same as
3068 :			std_str_cmp() but case sensitive.
3069 :			ANS( strict_str_cmp( "W. Mozart" ) ) -- Accepts only the exact string.
3070 :			ANS( unordered_str_cmp( "ABC" ) ) -- Accepts "a c B", "CBA" and so forth.
3071 :			Unordered, case insensitive, spaces ignored.
3072 :			ANS( unordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc". Same as
3073 :			unordered_str_cmp() but case sensitive.
3074 :			ANS( ordered_str_cmp( "ABC" ) ) -- Accepts "a b C", "A B C" and so forth.
3075 :			Ordered, case insensitive, spaces ignored.
3076 :			ANS( ordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc", accepts "A BC" and
3077 :			so forth. Same as ordered_str_cmp() but case sensitive.
3078 :
3079 :			=cut
3080 :
3081 :			sub std_str_cmp { # compare strings
3082 :			my $correctAnswer = shift @_;
3083 :			my @filters = ( 'compress_whitespace', 'ignore_case' );
3084 :			my $type = 'std_str_cmp';
3085 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3086 :			'filters' => \@filters,
3087 :			'type' => $type
3088 :			);
3089 :			}
3090 :
3091 :			sub std_str_cmp_list { # alias for std_str_cmp
3092 :			my @answerList = @_;
3093 :			my @output;
3094 :			while (@answerList) {
3095 :			push( @output, std_str_cmp(shift @answerList) );
3096 :			}
3097 :			@output;
3098 :			}
3099 :
3100 :			sub std_cs_str_cmp { # compare strings case sensitive
3101 :			my $correctAnswer = shift @_;
3102 :			my @filters = ( 'compress_whitespace' );
3103 :			my $type = 'std_cs_str_cmp';
3104 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3105 :			'filters' => \@filters,
3106 :			'type' => $type
3107 :			);
3108 :			}
3109 :
3110 :			sub std_cs_str_cmp_list { # alias for std_cs_str_cmp
3111 :			my @answerList = @_;
3112 :			my @output;
3113 :			while (@answerList) {
3114 :			push( @output, std_cs_str_cmp(shift @answerList) );
3115 :			}
3116 :			@output;
3117 :			}
3118 :
3119 :			sub strict_str_cmp { # strict string compare
3120 :			my $correctAnswer = shift @_;
3121 :			my @filters = ( 'trim_whitespace' );
3122 :			my $type = 'strict_str_cmp';
3123 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3124 :			'filters' => \@filters,
3125 :			'type' => $type
3126 :			);
3127 :			}
3128 :
3129 :			sub strict_str_cmp_list { # alias for strict_str_cmp
3130 :			my @answerList = @_;
3131 :			my @output;
3132 :			while (@answerList) {
3133 :			push( @output, strict_str_cmp(shift @answerList) );
3134 :			}
3135 :			@output;
3136 :			}
3137 :
3138 :			sub unordered_str_cmp { # unordered, case insensitive, spaces ignored
3139 :			my $correctAnswer = shift @_;
3140 :			my @filters = ( 'ignore_order', 'ignore_case' );
3141 :			my $type = 'unordered_str_cmp';
3142 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3143 :			'filters' => \@filters,
3144 :			'type' => $type
3145 :			);
3146 :			}
3147 :
3148 :			sub unordered_str_cmp_list { # alias for unordered_str_cmp
3149 :			my @answerList = @_;
3150 :			my @output;
3151 :			while (@answerList) {
3152 :			push( @output, unordered_str_cmp(shift @answerList) );
3153 :			}
3154 :			@output;
3155 :			}
3156 :
3157 :			sub unordered_cs_str_cmp { # unordered, case sensitive, spaces ignored
3158 :			my $correctAnswer = shift @_;
3159 :			my @filters = ( 'ignore_order' );
3160 :			my $type = 'unordered_cs_str_cmp';
3161 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3162 :			'filters' => \@filters,
3163 :			'type' => $type
3164 :			);
3165 :			}
3166 :
3167 :			sub unordered_cs_str_cmp_list { # alias for unordered_cs_str_cmp
3168 :			my @answerList = @_;
3169 :			my @output;
3170 :			while (@answerList) {
3171 :			push( @output, unordered_cs_str_cmp(shift @answerList) );
3172 :			}
3173 :			@output;
3174 :			}
3175 :
3176 :			sub ordered_str_cmp { # ordered, case insensitive, spaces ignored
3177 :			my $correctAnswer = shift @_;
3178 :			my @filters = ( 'remove_whitespace', 'ignore_case' );
3179 :			my $type = 'ordered_str_cmp';
3180 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3181 :			'filters' => \@filters,
3182 :			'type' => $type
3183 :			);
3184 :			}
3185 :
3186 :			sub ordered_str_cmp_list { # alias for ordered_str_cmp
3187 :			my @answerList = @_;
3188 :			my @output;
3189 :			while (@answerList) {
3190 :			push( @output, ordered_str_cmp(shift @answerList) );
3191 :			}
3192 :			@output;
3193 :
3194 :			}
3195 :
3196 :			sub ordered_cs_str_cmp { # ordered, case sensitive, spaces ignored
3197 :			my $correctAnswer = shift @_;
3198 :			my @filters = ( 'remove_whitespace' );
3199 :			my $type = 'ordered_cs_str_cmp';
3200 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3201 :			'filters' => \@filters,
3202 :			'type' => $type
3203 :			);
3204 :			}
3205 :
3206 :			sub ordered_cs_str_cmp_list { # alias for ordered_cs_str_cmp
3207 :			my @answerList = @_;
3208 :			my @output;
3209 :			while (@answerList) {
3210 :			push( @output, ordered_cs_str_cmp(shift @answerList) );
3211 :			}
3212 :			@output;
3213 :			}
3214 :
3215 :			=head3 str_cmp()
3216 :
3217 :			Compares a string or a list of strings, using a named hash of options to set
3218 :			parameters. This can make for more readable code than using the "mode"_str_cmp()
3219 :			style, but some people find one or the other easier to remember.
3220 :
3221 :			ANS( str_cmp( answer or answer_array_ref, options_hash ) );
3222 :
3223 :			1. the correct answer or a reference to an array of answers
3224 :			2. either a list of filters, or:
3225 :			a hash consisting of
3226 :			filters - a reference to an array of filters
3227 :
3228 :			Returns an answer evaluator, or (if given a reference to an array of answers),
3229 :			a list of answer evaluators
3230 :
3231 :			FILTERS:
3232 :
3233 :			remove_whitespace -- removes all whitespace
3234 :			compress_whitespace -- removes whitespace from the beginning and end of the string,
3235 :			and treats one or more whitespace characters in a row as a
3236 :			single space (true by default)
3237 :			trim_whitespace -- removes whitespace from the beginning and end of the string
3238 :			ignore_case -- ignores the case of the letters (true by default)
3239 :			ignore_order -- ignores the order in which letters are entered
3240 :
3241 :			EXAMPLES:
3242 :
3243 :			str_cmp( "Hello" ) -- matches "Hello", " hello" (same as std_str_cmp() )
3244 :			str_cmp( ["Hello", "Goodbye"] ) -- same as std_str_cmp_list()
3245 :			str_cmp( " hello ", trim_whitespace ) -- matches "hello", " hello "
3246 :			str_cmp( "ABC", filters => 'ignore_order' ) -- matches "ACB", "A B C", but not "abc"
3247 :			str_cmp( "D E F", remove_whitespace, ignore_case ) -- matches "def" and "d e f" but not "fed"
3248 :
3249 :			=cut
3250 :
3251 :			sub str_cmp {
3252 :			my $correctAnswer = shift @_;
3253 :			$correctAnswer = '' unless defined($correctAnswer);
3254 :			my @options = @_;
3255 :			my $ra_filters;
3256 :
3257 :			# error-checking for filters occurs in the filters() subroutine
3258 :			if( not defined( $options[0] ) ) { # used with no filters as alias for std_str_cmp()
3259 :			@options = ( 'compress_whitespace', 'ignore_case' );
3260 :			}
3261 :
3262 :			if( $options[0] eq 'filters' ) { # using filters => [f1, f2, ...] notation
3263 :			$ra_filters = $options[1];
3264 :			}
3265 :			else { # using a list of filters
3266 :			$ra_filters = \@options;
3267 :			}
3268 :
3269 :			# thread over lists
3270 :			my @ans_list = ();
3271 :
3272 :			if ( ref($correctAnswer) eq 'ARRAY' ) {
3273 :			@ans_list = @{$correctAnswer};
3274 :			}
3275 :			else {
3276 :			push( @ans_list, $correctAnswer );
3277 :			}
3278 :
3279 :			# final_answer;
3280 :			my @output_list = ();
3281 :
3282 :			foreach my $ans (@ans_list) {
3283 :			push(@output_list, STR_CMP( 'correctAnswer' => $ans,
3284 :			'filters' => $ra_filters,
3285 :			'type' => 'str_cmp'
3286 :			)
3287 :			);
3288 :			}
3289 :
3290 :			return @output_list;
3291 :			}
3292 :
3293 :			## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
3294 :			##
3295 :			## IN: a hashtable with the following entries (error-checking to be added later?):
3296 :			## correctAnswer -- the correct answer, before filtering
3297 :			## filters -- reference to an array containing the filters to be applied
3298 :			## type -- a string containing the type of answer evaluator in use
3299 :			## OUT: a reference to an answer evaluator subroutine
3300 :			sub STR_CMP {
3301 :			my %str_params = @_;
3302 :
3303 :			$str_params{'correctAnswer'} = str_filters( $str_params{'correctAnswer'}, @{$str_params{'filters'}} );
3304 :
3305 :			my $answer_evaluator = sub {
3306 :			my $in = shift @_;
3307 :			$in = '' unless defined $in;
3308 :			my $original_student_ans = $in;
3309 :
3310 :			$in = str_filters( $in, @{$str_params{'filters'}} );
3311 :
3312 :			my $correctQ = ( $in eq $str_params{'correctAnswer'} ) ? 1: 0;
3313 :			my $ans_hash = new AnswerHash(
3314 :			'score' => $correctQ,
3315 :			'correct_ans' => $str_params{'correctAnswer'},
3316 :			'student_ans' => $in,
3317 :			'ans_message' => '',
3318 :			'type' => $str_params{'type'},
3319 :			'preview_text_string' => $in,
3320 :			'preview_latex_string' => $in,
3321 :			'original_student_ans' => $original_student_ans
3322 :			);
3323 :
3324 :			return $ans_hash;
3325 :			};
3326 :
3327 :			return $answer_evaluator;
3328 :			}
3329 :
3330 :
3331 :
3332 :			##########################################################################
3333 :			##########################################################################
3334 :			## Miscellaneous answer evaluators
3335 :
3336 :			=head2 Miscellaneous Answer Evaluators (Checkboxes and Radio Buttons)
3337 :
3338 :			These evaluators do not fit any of the other categories.
3339 :
3340 :			checkbox_cmp( $correctAnswer )
3341 :
3342 :			$correctAnswer -- a string containing the names of the correct boxes,
3343 :			e.g. "ACD". Note that this means that individual
3344 :			checkbox names can only be one character. Internally,
3345 :			this is largely the same as unordered_cs_str_cmp().
3346 :
3347 :			radio_cmp( $correctAnswer )
3348 :
3349 :			$correctAnswer -- a string containing the name of the correct radio
3350 :			button, e.g. "Choice1". This is case sensitive and
3351 :			whitespace sensitive, so the correct answer must match
3352 :			the name of the radio button exactly.
3353 :
3354 :			=cut
3355 :
3356 :			# added 6/14/2000 by David Etlinger
3357 :			# because of the conversion of the answer
3358 :			# string to an array, I thought it better not
3359 :			# to force STR_CMP() to work with this
3360 :			sub checkbox_cmp {
3361 :			my $correctAnswer = shift @_;
3362 :			$correctAnswer = str_filters( $correctAnswer, 'ignore_order' );
3363 :
3364 :			my $answer_evaluator = sub {
3365 :			my $in = shift @_;
3366 :			$in = '' unless defined $in; #in case no boxes checked
3367 :
3368 :			my @temp = split( "\0", $in ); #convert "\0"-delimited string to array...
3369 :			$in = join( "", @temp ); #and then to a single no-delimiter string
3370 :
3371 :			my $original_student_ans = $in; #well, almost original
3372 :			$in = str_filters( $in, 'ignore_order' );
3373 :
3374 :			my $correctQ = ($in eq $correctAnswer) ? 1: 0;
3375 :
3376 :			my $ans_hash = new AnswerHash(
3377 :			'score' => $correctQ,
3378 :			'correct_ans' => $correctAnswer,
3379 :			'student_ans' => $in,
3380 :			'ans_message' => "",
3381 :			'type' => "checkbox_cmp",
3382 :			'preview_text_string' => $in,
3383 :			'original_student_ans' => $original_student_ans
3384 :			);
3385 :
3386 :			return $ans_hash;
3387 :
3388 :			};
3389 :
3390 :			return $answer_evaluator;
3391 :			}
3392 :
3393 :			#added 6/28/2000 by David Etlinger
3394 :			#exactly the same as strict_str_cmp,
3395 :			#but more intuitive to the user
3396 :			sub radio_cmp {
3397 :			strict_str_cmp( @_ );
3398 :			}
3399 :
3400 :
3401 :
3402 :			##########################################################################
3403 :			##########################################################################
3404 :			## Text and e-mail routines
3405 :
3406 :
3407 :			sub store_ans_at {
3408 :			my $answerStringRef = shift;
3409 :			my %options = @_;
3410 :			my $ans_eval= '';
3411 :			if ( ref($answerStringRef) eq 'SCALAR' ) {
3412 :			$ans_eval= sub {
3413 :			my $text = shift;
3414 :			$text = '' unless defined($text);
3415 :			$$answerStringRef = $$answerStringRef . $text;
3416 :			my $ans_hash = new AnswerHash(
3417 :			'score' => 1,
3418 :			'correct_ans' => '',
3419 :			'student_ans' => $text,
3420 :			'ans_message' => '',
3421 :			'type' => 'store_ans_at',
3422 :			'original_student_ans' => $text,
3423 :			'preview_text_string' => ''
3424 :
3425 :			);
3426 :
3427 :			return $ans_hash;
3428 :			};
3429 :			}
3430 :			else {
3431 :			die "Syntax error: \n The argument to store_ans_at() must be a pointer to a scalar.\n(e.g. store_ans_at(~~\$MSG) )\n\n";
3432 :			}
3433 :
3434 :			return $ans_eval;
3435 :			}
3436 :
3437 :
3438 :			#### subroutines used in producing a questionnaire
3439 :			#### these are at least good models for other answers of this type
3440 :
3441 :			my $QUESTIONNAIRE_ANSWERS=''; # stores the answers until it is time to send them
3442 :			# this must be initialized before the answer evaluators are run
3443 :			# but that happens long after all of the text in the problem is
3444 :			# evaluated.
3445 :			# this is a utility script for cleaning up the answer output for display in
3446 :			#the answers.
3447 :
3448 :
3449 :			sub DUMMY_ANSWER {
3450 :			my $num = shift;
3451 :			qq{<INPUT TYPE="HIDDEN" NAME="answer$num" VALUE="">}
3452 :			}
3453 :
3454 :			sub escapeHTML {
3455 :			my $string = shift;
3456 :			$string =~ s/\n/$BR/ge;
3457 :			$string;
3458 :			}
3459 :
3460 :			# these next two subroutines show how to modify the "store_and_at()" answer
3461 :			# evaluator to add extra information before storing the info
3462 :			# They provide a good model for how to tweak answer evaluators in special cases.
3463 :			sub anstext {
3464 :			my $num = shift;
3465 :			my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS);
3466 :			my $ans_eval = sub {
3467 :			my $text = shift;
3468 :			$text = '' unless defined($text);
3469 :			my $new_text = "\n$main::psvnNumber-Problem-$main::probNum-Question-$num:\n $text "; # modify entered text
3470 :			my $out = &$ans_eval_template($new_text); # standard evaluator
3471 :			#warn "$QUESTIONNAIRE_ANSWERS";
3472 :			$out->{student_ans} = escapeHTML($text); # restore original entered text
3473 :			$out->{correct_ans} = "Question $num answered";
3474 :			$out->{original_student_ans} = escapeHTML($text);
3475 :			$out;
3476 :			};
3477 :			$ans_eval;
3478 :			}
3479 :
3480 :			sub ansradio {
3481 :			my $num = shift;
3482 :			my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS);
3483 :			my $ans_eval = sub {
3484 :			my $text = shift;
3485 :			$text = '' unless defined($text);
3486 :			my $new_text = "\n$main::psvnNumber-Problem-$main::probNum-RADIO-$num:\n $text "; # modify entered text
3487 :			my $out = $ans_eval_template->($new_text); # standard evaluator
3488 :			$out->{student_ans} =escapeHTML($text); # restore original entered text
3489 :			$out->{original_student_ans} = escapeHTML($text);
3490 :			$out;
3491 :			};
3492 :
3493 :
3494 :			$ans_eval;
3495 :			}
3496 :
3497 :			# This is another example of how to modify an answer evaluator to obtain
3498 :			# the desired behavior in a special case. Here the object is to have
3499 :			# have the last answer trigger the send_mail_to subroutine which mails
3500 :			# all of the answers to the designated address.
3501 :			# (This address must be listed in PG_environment{'ALLOW_MAIL_TO'} or an error occurs.)
3502 :
3503 :			sub mail_answers_to { #accepts the last answer and mails off the result
3504 :			my $user_address = shift;
3505 :			my $ans_eval = sub {
3506 :
3507 :			# then mail out all of the answers, including this last one.
3508 :
3509 :			send_mail_to( $user_address,
3510 :			'subject' => "$main::courseName WeBWorK questionnaire",
3511 :			'body' => $QUESTIONNAIRE_ANSWERS,
3512 :			'ALLOW_MAIL_TO' => $main::ALLOW_MAIL_TO
3513 :			);
3514 :
3515 :			my $ans_hash = new AnswerHash( 'score' => 1,
3516 :			'correct_ans' => '',
3517 :			'student_ans' => 'Answer recorded',
3518 :			'ans_message' => '',
3519 :			'type' => 'send_mail_to',
3520 :			);
3521 :
3522 :			return $ans_hash;
3523 :			};
3524 :
3525 :			return $ans_eval;
3526 :			}
3527 :			sub mail_answers_to2 { #accepts the last answer and mails off the result
3528 :			my $user_address = shift;
3529 :			my $subject = shift;
3530 :			$subject = "$main::courseName WeBWorK questionnaire" unless defined $subject;
3531 :
3532 :
3533 :			send_mail_to($user_address,
3534 :			'subject' => $subject,
3535 :			'body' => $QUESTIONNAIRE_ANSWERS,
3536 :			'ALLOW_MAIL_TO' => $main::ALLOW_MAIL_TO
3537 :			);
3538 :
3539 :
3540 :			}
3541 :
3542 :
3543 :
3544 :			##########################################################################
3545 :			##########################################################################
3546 :			## Problem Grader Subroutines
3547 :
3548 :
3549 :			#####################################
3550 :			# This is a model for plug-in problem graders
3551 :			#####################################
3552 :			sub install_problem_grader {
3553 :			my $rf_problem_grader = shift;
3554 :			$main::PG_FLAGS{PROBLEM_GRADER_TO_USE} = $rf_problem_grader;
3555 :			}
3556 :
3557 :			#this is called std only for compatability purposes;
3558 :			#almost everyone uses avg_problem_grader
3559 :			sub std_problem_grader{
3560 :			my $rh_evaluated_answers = shift;
3561 :			my $rh_problem_state = shift;
3562 :			my %form_options = @_;
3563 :			my %evaluated_answers = %{$rh_evaluated_answers};
3564 :			# The hash $rh_evaluated_answers typically contains:
3565 :			# 'answer1' => 34, 'answer2'=> 'Mozart', etc.
3566 :
3567 :			# By default the old problem state is simply passed back out again.
3568 :			my %problem_state = %$rh_problem_state;
3569 :
3570 :
3571 :			# %form_options might include
3572 :			# The user login name
3573 :			# The permission level of the user
3574 :			# The studentLogin name for this psvn.
3575 :			# Whether the form is asking for a refresh or is submitting a new answer.
3576 :
3577 :			# initial setup of the answer
3578 :			my %problem_result = ( score => 0,
3579 :			errors => '',
3580 :			type => 'std_problem_grader',
3581 :			msg => '',
3582 :			);
3583 :			# Checks
3584 :
3585 :			my $ansCount = keys %evaluated_answers; # get the number of answers
3586 :			unless ($ansCount > 0 ) {
3587 :			$problem_result{msg} = "This problem did not ask any questions.";
3588 :			return(\%problem_result,\%problem_state);
3589 :			}
3590 :
3591 :			if ($ansCount > 1 ) {
3592 :			$problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ;
3593 :			}
3594 :
3595 :			unless ($form_options{answers_submitted} == 1) {
3596 :			return(\%problem_result,\%problem_state);
3597 :			}
3598 :
3599 :			my $allAnswersCorrectQ=1;
3600 :			foreach my $ans_name (keys %evaluated_answers) {
3601 :			# I'm not sure if this check is really useful.
3602 :			if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) {
3603 :			$allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} );
3604 :			}
3605 :			else {
3606 :			die "Error at file ",__FILE__,"line ", __LINE__,": Answer \|$ans_name\| is not a hash reference\n".
3607 :			$evaluated_answers{$ans_name} .
3608 :			"This probably means that the answer evaluator for this answer\n" .
3609 :			"is not working correctly.";
3610 :			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
3611 :			}
3612 :			}
3613 :			# report the results
3614 :			$problem_result{score} = $allAnswersCorrectQ;
3615 :
3616 :			# I don't like to put in this bit of code.
3617 :			# It makes it hard to construct error free problem graders
3618 :			# I would prefer to know that the problem score was numeric.
3619 :	chris	22	unless ($problem_state{recorded_score} =~ /^([+-]?)(?=\d\|\.\d)\d(\.\d)?([Ee]([+-]?\d+))?$/ ) {
3620 :	sam	2	$problem_state{recorded_score} = 0; # This gets rid of non-numeric scores
3621 :			}
3622 :			#
3623 :			if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) {
3624 :			$problem_state{recorded_score} = 1;
3625 :			}
3626 :			else {
3627 :			$problem_state{recorded_score} = 0;
3628 :			}
3629 :
3630 :			$problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1;
3631 :			$problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0;
3632 :			(\%problem_result, \%problem_state);
3633 :			}
3634 :
3635 :			#the only difference between the two versions
3636 :			#is at the end of the subroutine, where std_problem_grader2
3637 :			#records the attempt only if there have been no syntax errors,
3638 :			#whereas std_problem_grader records it regardless
3639 :			sub std_problem_grader2{
3640 :			my $rh_evaluated_answers = shift;
3641 :			my $rh_problem_state = shift;
3642 :			my %form_options = @_;
3643 :			my %evaluated_answers = %{$rh_evaluated_answers};
3644 :			# The hash $rh_evaluated_answers typically contains:
3645 :			# 'answer1' => 34, 'answer2'=> 'Mozart', etc.
3646 :
3647 :			# By default the old problem state is simply passed back out again.
3648 :			my %problem_state = %$rh_problem_state;
3649 :
3650 :
3651 :			# %form_options might include
3652 :			# The user login name
3653 :			# The permission level of the user
3654 :			# The studentLogin name for this psvn.
3655 :			# Whether the form is asking for a refresh or is submitting a new answer.
3656 :
3657 :			# initial setup of the answer
3658 :			my %problem_result = ( score => 0,
3659 :			errors => '',
3660 :			type => 'std_problem_grader',
3661 :			msg => '',
3662 :			);
3663 :
3664 :			# syntax errors are not counted.
3665 :			my $record_problem_attempt = 1;
3666 :			# Checks
3667 :
3668 :			my $ansCount = keys %evaluated_answers; # get the number of answers
3669 :			unless ($ansCount > 0 ) {
3670 :			$problem_result{msg} = "This problem did not ask any questions.";
3671 :			return(\%problem_result,\%problem_state);
3672 :			}
3673 :
3674 :			if ($ansCount > 1 ) {
3675 :			$problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ;
3676 :			}
3677 :
3678 :			unless ($form_options{answers_submitted} == 1) {
3679 :			return(\%problem_result,\%problem_state);
3680 :			}
3681 :
3682 :			my $allAnswersCorrectQ=1;
3683 :			foreach my $ans_name (keys %evaluated_answers) {
3684 :			# I'm not sure if this check is really useful.
3685 :			if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) {
3686 :			$allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} );
3687 :			}
3688 :			else {
3689 :			die "Error at file ",__FILE__,"line ", __LINE__,": Answer \|$ans_name\| is not a hash reference\n".
3690 :			$evaluated_answers{$ans_name} .
3691 :			"This probably means that the answer evaluator for this answer\n" .
3692 :			"is not working correctly.";
3693 :			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
3694 :			}
3695 :			}
3696 :			# report the results
3697 :			$problem_result{score} = $allAnswersCorrectQ;
3698 :
3699 :			# I don't like to put in this bit of code.
3700 :			# It makes it hard to construct error free problem graders
3701 :			# I would prefer to know that the problem score was numeric.
3702 :			unless ($problem_state{recorded_score} =~ /^([+-]?)(?=\d\|\.\d)\d(\.\d)?([Ee]([+-]?\d+))?$/ ) {
3703 :			$problem_state{recorded_score} = 0; # This gets rid of non-numeric scores
3704 :			}
3705 :			#
3706 :			if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) {
3707 :			$problem_state{recorded_score} = 1;
3708 :			}
3709 :			else {
3710 :			$problem_state{recorded_score} = 0;
3711 :			}
3712 :			# record attempt only if there have been no syntax errors.
3713 :
3714 :			if ($record_problem_attempt == 1) {
3715 :			$problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1;
3716 :			$problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0;
3717 :			}
3718 :			else {
3719 :			$problem_result{show_partial_correct_answers} = 0 ; # prevent partial correct answers from being shown for syntax errors.
3720 :
3721 :			}
3722 :
3723 :			(\%problem_result, \%problem_state);
3724 :			}
3725 :
3726 :
3727 :			sub avg_problem_grader{
3728 :			my $rh_evaluated_answers = shift;
3729 :			my $rh_problem_state = shift;
3730 :			my %form_options = @_;
3731 :			my %evaluated_answers = %{$rh_evaluated_answers};
3732 :			# The hash $rh_evaluated_answers typically contains:
3733 :			# 'answer1' => 34, 'answer2'=> 'Mozart', etc.
3734 :
3735 :			# By default the old problem state is simply passed back out again.
3736 :			my %problem_state = %$rh_problem_state;
3737 :
3738 :
3739 :			# %form_options might include
3740 :			# The user login name
3741 :			# The permission level of the user
3742 :			# The studentLogin name for this psvn.
3743 :			# Whether the form is asking for a refresh or is submitting a new answer.
3744 :
3745 :			# initial setup of the answer
3746 :			my $total=0;
3747 :			my %problem_result = ( score => 0,
3748 :			errors => '',
3749 :			type => 'avg_problem_grader',
3750 :			msg => '',
3751 :			);
3752 :			my $count = keys %evaluated_answers;
3753 :			$problem_result{msg} = 'You can earn partial credit on this problem.' if $count >1;
3754 :			# Return unless answers have been submitted
3755 :			unless ($form_options{answers_submitted} == 1) {
3756 :			return(\%problem_result,\%problem_state);
3757 :			}
3758 :
3759 :			# Answers have been submitted -- process them.
3760 :			foreach my $ans_name (keys %evaluated_answers) {
3761 :			# I'm not sure if this check is really useful.
3762 :			if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) {
3763 :			$total += $evaluated_answers{$ans_name}->{score};
3764 :			}
3765 :			else {
3766 :			die "Error: Answer \|$ans_name\| is not a hash reference\n".
3767 :			$evaluated_answers{$ans_name} .
3768 :			"This probably means that the answer evaluator for this answer\n" .
3769 :			"is not working correctly.";
3770 :			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
3771 :			}
3772 :			}
3773 :			# Calculate score rounded to three places to avoid roundoff problems
3774 :			$problem_result{score} = $total/$count if $count;
3775 :			# increase recorded score if the current score is greater.
3776 :			$problem_state{recorded_score} = $problem_result{score} if $problem_result{score} > $problem_state{recorded_score};
3777 :
3778 :
3779 :			$problem_state{num_of_correct_ans}++ if $total == $count;
3780 :			$problem_state{num_of_incorrect_ans}++ if $total < $count ;
3781 :			warn "Error in grading this problem the total $total is larger than $count" if $total > $count;
3782 :			(\%problem_result, \%problem_state);
3783 :
3784 :			}
3785 :
3786 :
3787 :
3788 :			###########################################################################
3789 :			### THE FOLLOWING ARE LOCAL SUBROUTINES THAT ARE MEANT TO BE CALLED ONLY FROM THIS SCRIPT.
3790 :
3791 :
3792 :			## Internal routine that converts variables into the standard array format
3793 :			##
3794 :			## IN: one of the following:
3795 :			## an undefined value (i.e., no variable was specified)
3796 :			## a reference to an array of variable names -- [var1, var2]
3797 :			## a number (the number of variables desired) -- 3
3798 :			## one or more variable names -- (var1, var2)
3799 :			## OUT: an array of variable names
3800 :			sub get_var_array {
3801 :			my $in = shift @_;
3802 :			my @out;
3803 :
3804 :			if( not defined($in) ) { #if nothing defined, build default array and return
3805 :			@out = ( $functVarDefault );
3806 :			return @out;
3807 :			}
3808 :			elsif( ref( $in ) eq 'ARRAY' ) { #if given an array ref, dereference and return
3809 :			return @{$in};
3810 :			}
3811 :			elsif( $in =~ /^\d+/ ) { #if given a number, set up the array and return
3812 :			if( $in == 1 ) {
3813 :			$out[0] = 'x';
3814 :			}
3815 :			elsif( $in == 2 ) {
3816 :			$out[0] = 'x';
3817 :			$out[1] = 'y';
3818 :			}
3819 :			elsif( $in == 3 ) {
3820 :			$out[0] = 'x';
3821 :			$out[1] = 'y';
3822 :			$out[2] = 'z';
3823 :			}
3824 :			else { #default to the x_1, x_2, ... convention
3825 :			my ($i, $tag);
3826 :			for( $i=0; $i < $in; $i++ ) {
3827 :			## akp the above seems to be off by one 1/4/00
3828 :			$tag = $i + 1; ## akp 1/4/00
3829 :			$out[$i] = "${functVarDefault}_" . $tag; ## akp 1/4/00
3830 :			}
3831 :			}
3832 :
3833 :			return @out;
3834 :			}
3835 :			else { #if given one or more names, return as an array
3836 :			unshift( @_, $in );
3837 :
3838 :			return @_;
3839 :			}
3840 :			}
3841 :
3842 :			## Internal routine that converts limits into the standard array of arrays format
3843 :			## Some of the cases are probably unneccessary, but better safe than sorry
3844 :			##
3845 :			## IN: one of the following:
3846 :			## an undefined value (i.e., no limits were specified)
3847 :			## a reference to an array of arrays of limits -- [[llim,ulim], [llim,ulim]]
3848 :			## a reference to an array of limits -- [llim, ulim]
3849 :			## an array of array references -- ([llim,ulim], [llim,ulim])
3850 :			## an array of limits -- (llim,ulim)
3851 :			## OUT: an array of array references -- ([llim,ulim], [llim,ulim]) or ([llim,ulim])
3852 :	chris	22
3853 :	sam	2	sub get_limits_array {
3854 :			my $in = shift @_;
3855 :			my @out;
3856 :
3857 :			if( not defined($in) ) { #if nothing defined, build default array and return
3858 :			@out = ( [$functLLimitDefault, $functULimitDefault] );
3859 :			return @out;
3860 :			}
3861 :			elsif( ref($in) eq 'ARRAY' ) { #$in is either ref to array, or ref to array of refs
3862 :			my @deref = @{$in};
3863 :
3864 :			if( ref( $in->[0] ) eq 'ARRAY' ) { #$in is a ref to an array of array refs
3865 :			return @deref;
3866 :			}
3867 :			else { #$in was just a ref to an array of numbers
3868 :			@out = ( $in );
3869 :			return @out;
3870 :			}
3871 :			}
3872 :			else { #$in was an array of references or numbers
3873 :			unshift( @_, $in );
3874 :
3875 :			if( ref($_[0]) eq 'ARRAY' ) { #$in was an array of references, so just return it
3876 :			return @_;
3877 :			}
3878 :			else { #$in was an array of numbers
3879 :			@out = ( \@_ );
3880 :			return @out;
3881 :			}
3882 :			}
3883 :			}
3884 :
3885 :			sub check_option_list {
3886 :			my $size = scalar(@_);
3887 :			if( ( $size % 2 ) != 0 ) {
3888 :			warn "ERROR in answer evaluator generator:\n" .
3889 :			"Usage: <CODE>str_cmp([\$ans1, \$ans2],%options)</CODE>
3890 :			or <CODE> num_cmp([\$num1, \$num2], %options)</CODE><BR>
3891 :			A list of inputs must be inclosed in square brackets <CODE>[\$ans1, \$ans2]</CODE>";
3892 :			}
3893 :			}
3894 :
3895 :			# simple subroutine to display an error message when
3896 :			# function compares are called with invalid parameters
3897 :			sub function_invalid_params {
3898 :			my $correctEqn = shift @_;
3899 :			my $error_response = sub {
3900 :			my $PGanswerMessage = "Tell your professor that there is an error with the parameters " .
3901 :			"to the function answer evaluator";
3902 :			return ( 0, $correctEqn, "", $PGanswerMessage );
3903 :			};
3904 :
3905 :			return $error_response;
3906 :			}
3907 :
3908 :
3909 :	chris	22	#########################################################################
3910 :			# Filters for answer evaluators
3911 :			#########################################################################
3912 :
3913 :
3914 :	sam	2	sub is_a_number {
3915 :	chris	22	my ($num,%options) = @_;
3916 :			my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ;
3917 :			my ($rh_ans);
3918 :			if ($process_ans_hash) {
3919 :			$rh_ans = $num;
3920 :			$num = $rh_ans->{student_ans};
3921 :			}
3922 :
3923 :	sam	2	my $is_a_number = 0;
3924 :			return $is_a_number unless defined($num);
3925 :			$num =~ s/^\s*//; ## remove initial spaces
3926 :			$num =~ s/\s*$//; ## remove trailing spaces
3927 :
3928 :			## the following is copied from the online perl manual
3929 :			if ($num =~ /^([+-]?)(?=\d\|\.\d)\d(\.\d)?([Ee]([+-]?\d+))?$/){
3930 :			$is_a_number = 1;
3931 :			}
3932 :	chris	22
3933 :			if ($process_ans_hash) {
3934 :			if ($is_a_number == 1 ) {
3935 :			$rh_ans->{student_ans}=$num;
3936 :			return $rh_ans;
3937 :			} else {
3938 :			$rh_ans->{student_ans} = "Incorrect number format: You must enter a number, e.g. -6, 5.3, or 6.12E-3";
3939 :			$rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3');
3940 :			return $rh_ans;
3941 :			}
3942 :			} else {
3943 :			return $is_a_number;
3944 :			}
3945 :	sam	2	}
3946 :
3947 :			sub is_a_fraction {
3948 :	chris	22	my ($num,%options) = @_;
3949 :			my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ;
3950 :			my ($rh_ans);
3951 :			if ($process_ans_hash) {
3952 :			$rh_ans = $num;
3953 :			$num = $rh_ans->{student_ans};
3954 :			}
3955 :
3956 :			my $is_a_fraction = 0;
3957 :			return $is_a_fraction unless defined($num);
3958 :			$num =~ s/^\s*//; ## remove initial spaces
3959 :			$num =~ s/\s*$//; ## remove trailing spaces
3960 :
3961 :			if ($num =~ /^\s\-?\s[\/\d\.Ee\s]*$/) {
3962 :	sam	2	$is_a_fraction = 1;
3963 :			}
3964 :	chris	22
3965 :			if ($process_ans_hash) {
3966 :			if ($is_a_fraction == 1 ) {
3967 :			$rh_ans->{student_ans}=$num;
3968 :			return $rh_ans;
3969 :			} else {
3970 :			$rh_ans->{student_ans} = "Not a number of fraction: You must enter a number or fraction, e.g. -6 or 7/13";
3971 :			$rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3');
3972 :			return $rh_ans;
3973 :			}
3974 :
3975 :			} else {
3976 :			return $is_a_fraction;
3977 :			}
3978 :	sam	2	}
3979 :
3980 :	chris	22
3981 :			sub is_an_arithmetic_expression {
3982 :			my ($num,%options) = @_;
3983 :			my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ;
3984 :			my ($rh_ans);
3985 :			if ($process_ans_hash) {
3986 :			$rh_ans = $num;
3987 :			$num = $rh_ans->{student_ans};
3988 :			}
3989 :
3990 :			my $is_an_arithmetic_expression = 0;
3991 :			return $is_an_arithmetic_expression unless defined($num);
3992 :			$num =~ s/^\s*//; ## remove initial spaces
3993 :			$num =~ s/\s*$//; ## remove trailing spaces
3994 :
3995 :			if ($num =~ /^[+\-\/\^\[\]\{\}\s\d\.Ee]$/) {
3996 :	sam	2	$is_an_arithmetic_expression = 1;
3997 :			}
3998 :	chris	22
3999 :			if ($process_ans_hash) {
4000 :			if ($is_an_arithmetic_expression == 1 ) {
4001 :			$rh_ans->{student_ans}=$num;
4002 :			return $rh_ans;
4003 :			} else {
4004 :
4005 :			$rh_ans->{student_ans} = "Not an arithmetic expression: You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2";
4006 :			$rh_ans->throw_error('NUMBER', 'You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2');
4007 :			return $rh_ans;
4008 :			}
4009 :
4010 :			} else {
4011 :			return $is_an_arithmetic_expression;
4012 :			}
4013 :	sam	2	}
4014 :
4015 :			#replaces pi, e, and ^ with their Perl equivalents
4016 :			sub math_constants {
4017 :	chris	22	my($in,%options) = @_;
4018 :			my $rh_ans;
4019 :			my $process_ans_hash = ( ref( $in ) eq 'AnswerHash' ) ? 1 : 0 ;
4020 :			if ($process_ans_hash) {
4021 :			$rh_ans = $in;
4022 :			$in = $rh_ans->{student_ans};
4023 :			}
4024 :
4025 :	sam	2	$in =~s/\bpi\b/(4*atan2(1,1))/ge;
4026 :			$in =~s/\be\b/(exp(1))/ge;
4027 :			$in =~s/\^/**/g;
4028 :	chris	22
4029 :			if ($process_ans_hash) {
4030 :			$rh_ans->{student_ans}=$in;
4031 :			return $rh_ans;
4032 :			} else {
4033 :			return $in;
4034 :			}
4035 :	sam	2	}
4036 :
4037 :			sub clean_up_error_msg {
4038 :			my $msg = $_[0];
4039 :			$msg =~ s/^\[[^\]]\][^:]://;
4040 :			$msg =~ s/Unquoted string//g;
4041 :			$msg =~ s/may\s+clash.*/does not make sense here/;
4042 :			$msg =~ s/\sat.line [\d]//g;
4043 :			$msg = 'error: '. $msg;
4044 :
4045 :			return $msg;
4046 :			}
4047 :
4048 :			#formats the student and correct answer as specified
4049 :			#format must be of a form suitable for sprintf (e.g. '%0.5g'),
4050 :			#with the exception that a '#' at the end of the string
4051 :			#will cause trailing zeros in the decimal part to be removed
4052 :			sub prfmt {
4053 :			my($number,$format) = @_; # attention, the order of format and number are reversed
4054 :			my $out;
4055 :			if ($format) {
4056 :			warn "Incorrect format used: $format. <BR> Format should look something like %4.5g<BR>"
4057 :			unless $format =~ /^\s%\d\.?\d\w#?\s$/;
4058 :
4059 :			if( $format =~ s/#\s*$// ) { # remove trailing zeros in the decimal
4060 :			$out = sprintf( $format, $number );
4061 :			$out =~ s/(\.\d*?)0+$/$1/;
4062 :			$out =~ s/\.$//; # in case all decimal digits were zero, remove the decimal
4063 :			}
4064 :			else {
4065 :			$out = sprintf( $format, $number );
4066 :			}
4067 :
4068 :			$out =~ s/e/E/g; # only use capital E's for exponents. Little e is for 2.71828...
4069 :			}
4070 :			else {
4071 :			$out = $number;
4072 :			}
4073 :
4074 :			return $out;
4075 :			}
4076 :
4077 :			=head4
4078 :
4079 :			pretty_print()
4080 :
4081 :
4082 :			=cut
4083 :
4084 :			sub pretty_print {
4085 :			my $r_input = shift;
4086 :			my $out = '';
4087 :			if ( not ref($r_input) ) {
4088 :			$out = $r_input; # not a reference
4089 :			} elsif ("$r_input" =~/hash/i) { # this will pick up objects whose '$self' is hash and so works better than ref($r_iput).
4090 :			local($^W) = 0;
4091 :			$out .= "$r_input " ."<TABLE border = \"2\" cellpadding = \"3\" BGCOLOR = \"#FFFFFF\">";
4092 :			foreach my $key (lex_sort( keys %$r_input )) {
4093 :			$out .= "<tr><TD> $key</TD><TD>=></td><td> ".pretty_print($r_input->{$key}) . "</td></tr>";
4094 :			}
4095 :			$out .="</table>";
4096 :			} elsif (ref($r_input) eq 'ARRAY' ) {
4097 :			my @array = @$r_input;
4098 :			$out .= "( " ;
4099 :			while (@array) {
4100 :			$out .= pretty_print(shift @array) . " , ";
4101 :			}
4102 :			$out .= " )";
4103 :			} elsif (ref($r_input) eq 'CODE') {
4104 :			$out = "$r_input";
4105 :			} else {
4106 :			$out = $r_input;
4107 :			}
4108 :			$out;
4109 :			}
4110 :
4111 :			# Use this to set default options
4112 :			sub set_default_options {
4113 :			my $rh_options = shift;
4114 :			warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH';
4115 :			my %default_options = @_;
4116 :	gage	5	unless ( defined($default_options{allow_unknown_options}) and $default_options{allow_unknown_options} == 1 ) {
4117 :			foreach my $key1 (keys %$rh_options) {
4118 :			warn "This option \|$key1\| is not recognized in this subroutine<br> ", pretty_print($rh_options) unless exists($default_options{$key1});
4119 :			}
4120 :	sam	2	}
4121 :			foreach my $key (keys %default_options) {
4122 :			if ( not defined($rh_options->{$key} ) and defined( $default_options{$key} ) ) {
4123 :	chris	22	$rh_options->{$key} = $default_options{$key}; #this allows tol => undef to allow the tol option, but doesn't define
4124 :	sam	2	# this key unless tol is explicitly defined.
4125 :			}
4126 :			}
4127 :			}
4128 :			# Use this to assign aliases for the standard options
4129 :			sub assign_option_aliases {
4130 :			my $rh_options = shift;
4131 :			warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH';
4132 :			my @option_aliases = @_;
4133 :			while (@option_aliases) {
4134 :			my $alias = shift @option_aliases;
4135 :			my $option_key = shift @option_aliases;
4136 :
4137 :			if (defined($rh_options->{$alias} )) { # if the alias appears in the option list
4138 :			if (not defined($rh_options->{$option_key}) ) { # and the option itself is not defined,
4139 :			$rh_options->{$option_key} = $rh_options->{$alias}; # insert the value defined by the alias into the option value
4140 :			# the FIRST alias for a given option takes precedence
4141 :			# (after the option itself)
4142 :			} else {
4143 :			warn "option $option_key is already defined as", $rh_options->{$option_key}, "<br>\n",
4144 :			"The attempt to override this option with the alias $alias with value ", $rh_options->{$alias},
4145 :			" was ignored.";
4146 :			}
4147 :
4148 :			}
4149 :			delete($rh_options->{$alias}); # remove the alias from the initial list
4150 :			}
4151 :
4152 :			}
4153 :
4154 :
4155 :			1;

aubreyja at gmail dot com	ViewVC Help
Powered by ViewVC 1.0.9