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

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1 :	gage	28	#!/usr/local/bin/webwork-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 :	gage	32	#$Id$
11 :	sam	2
12 :			=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 :	gage	32	sub _PGanswermacros_export {
113 :			my @EXPORT = (
114 :			'&std_num_cmp', '&std_num_cmp_list', '&std_num_cmp_abs',
115 :			'&std_num_cmp_abs_list', '&frac_num_cmp', '&frac_num_cmp_list',
116 :			'&frac_num_cmp_abs', '&frac_num_cmp_abs_list', '&arith_num_cmp',
117 :			'&arith_num_cmp_list', '&arith_num_cmp_abs', '&arith_num_cmp_abs_list',
118 :			'&strict_num_cmp', '&strict_num_cmp_list', '&strict_num_cmp_abs',
119 :			'&strict_num_cmp_abs_list', '&numerical_compare_with_units',
120 :			'&std_num_str_cmp', '&num_cmp', '&num_rel_cmp', '&NUM_CMP',
121 :			'&NUM_CMP_LIST', '&adaptive_function_cmp', '&function_cmp',
122 :			'&function_cmp_up_to_constant', '&function_cmp_abs',
123 :			'&function_cmp_up_to_constant_abs', '&multivar_function_cmp',
124 :			'&fun_cmp', '&FUNCTION_CMP', '&is_array', '&check_syntax',
125 :			'&std_num_filter', '&std_num_array_filter', '&function_from_string2',
126 :			'&is_zero_array', '&best_approx_parameters',
127 :			'&calculate_difference_vector', '&str_filters', '&remove_whitespace',
128 :			'&compress_whitespace', '&trim_whitespace', '&ignore_case',
129 :			'&ignore_order', '&std_str_cmp', '&std_str_cmp_list', '&std_cs_str_cmp',
130 :			'&std_cs_str_cmp_list', '&strict_str_cmp', '&strict_str_cmp_list',
131 :			'&unordered_str_cmp', '&unordered_str_cmp_list',
132 :			'&unordered_cs_str_cmp', '&unordered_cs_str_cmp_list',
133 :			'&ordered_str_cmp', '&ordered_str_cmp_list', '&ordered_cs_str_cmp',
134 :			'&ordered_cs_str_cmp_list', '&str_cmp', '&STR_CMP', '&checkbox_cmp',
135 :			'&radio_cmp', '&store_ans_at', '&DUMMY_ANSWER', '&escapeHTML',
136 :			'&anstext', '&ansradio', '&mail_answers_to', '&mail_answers_to2',
137 :			'&install_problem_grader', '&std_problem_grader',
138 :			'&std_problem_grader2', '&avg_problem_grader', '&get_var_array',
139 :			'&get_limits_array', '&check_option_list', '&function_invalid_params',
140 :			'&is_a_number', '&is_a_fraction', '&is_an_arithmetic_expression',
141 :			'&math_constants', '&clean_up_error_msg', '&prfmt', '&pretty_print',
142 :			'&set_default_options', '&assign_option_aliases',
143 :			);
144 :			@EXPORT;
145 :			}
146 :	sam	2
147 :	gage	32	my ($BR, $PAR,$numRelPercentTolDefault,$numZeroLevelDefault,$numZeroLevelTolDefault,
148 :			$numAbsTolDefault,$numFormatDefault,$functRelPercentTolDefault,$functZeroLevelDefault,
149 :			$functZeroLevelTolDefault,$functAbsTolDefault,$functNumOfPoints,$functVarDefault,
150 :			$functLLimitDefault, $functULimitDefault, $functMaxConstantOfIntegration,
151 :			);
152 :
153 :			sub _PGanswermacros_init {
154 :			PG_restricted_eval(q{
155 :			$BR = $main::BR; # convenient localizations.
156 :			$PAR = $main::PAR;
157 :
158 :			# import defaults
159 :			# these are now imported from the %envir variable
160 :			$numRelPercentTolDefault = $main::numRelPercentTolDefault;
161 :			$numZeroLevelDefault = $main::numZeroLevelDefault;
162 :			$numZeroLevelTolDefault = $main::numZeroLevelTolDefault;
163 :			$numAbsTolDefault = $main::numAbsTolDefault;
164 :			$numFormatDefault = $main::numFormatDefault;
165 :
166 :			$functRelPercentTolDefault = $main::functRelPercentTolDefault;
167 :			$functZeroLevelDefault = $main::functZeroLevelDefault;
168 :			$functZeroLevelTolDefault = $main::functZeroLevelTolDefault;
169 :			$functAbsTolDefault = $main::functAbsTolDefault;
170 :			$functNumOfPoints = $main::functNumOfPoints;
171 :			$functVarDefault = $main::functVarDefault;
172 :			$functLLimitDefault = $main::functLLimitDefault;
173 :			$functULimitDefault = $main::functULimitDefault;
174 :			$functMaxConstantOfIntegration = $main::functMaxConstantOfIntegration;
175 :
176 :			}
177 :			);
178 :	sam	2
179 :	gage	32	}
180 :	sam	2
181 :			##########################################################################
182 :			##########################################################################
183 :			## Number answer evaluators
184 :
185 :			=head2 Number Answer Evaluators
186 :
187 :			Number answer evaluators take in a numerical answer, compare it to the correct answer,
188 :			and return a score. In addition, they can choose to accept or reject an answer based on
189 :			its format, closeness to the correct answer, and other criteria. There are two types
190 :			of numerical answer evaluators: num_cmp(), which takes a hash of named options as parameters,
191 :			and the "mode"_num_cmp() variety, which use different functions to access different sets of
192 :			options. In addition, there is the special case of std_num_str_cmp(), which can evaluate
193 :			both numbers and strings.
194 :
195 :			Numerical Comparison Options
196 :
197 :			correctAnswer -- This is the correct answer that the student answer will
198 :			be compared to. However, this does not mean that the
199 :			student answer must match this exactly. How close the
200 :			student answer must be is determined by the other
201 :			options, especially tolerance and format.
202 :
203 :			tolerance -- These options determine how close the student answer
204 :			must be to the correct answer to qualify. There are two
205 :			types of tolerance: relative and absolute. Relative
206 :			tolerances are given in percentages. A relative
207 :			tolerance of 1 indicates that the student answer must
208 :			be within 1% of the correct answer to qualify as correct.
209 :			In other words, a student answer is correct when
210 :			abs(studentAnswer - correctAnswer) <= abs(.01relpercentTolcorrectAnswer)
211 :			Using absolute tolerance, the student answer must be a
212 :			fixed distance from the correct answer to qualify.
213 :			For example, an absolute tolerance of 5 means that any
214 :			number which is +-5 of the correct answer qualifies as correct.
215 :			Final (rarely used) tolerance options are zeroLevel
216 :			and zeroLevelTol, used in conjunction with relative
217 :			tolerance. if correctAnswer has absolute value less than
218 :			or equal to zeroLevel, then the student answer must be,
219 :			in absolute terms, within zeroLevelTol of correctAnswer, i.e.,
220 :			abs(studentAnswer - correctAnswer) <= zeroLevelTol.
221 :			In other words, if the correct answer is very near zero,
222 :			an absolute tolerance will be used. One must do this to
223 :			handle floating point answers very near zero, because of
224 :			the inaccuracy of floating point arithmetic. However, the
225 :			default values are almost always adequate.
226 :
227 :			mode -- This determines the allowable methods for entering an
228 :			answer. Answers which do not meet this requirement will
229 :			be graded as incorrect, regardless of their numerical
230 :			value. The recognized modes are:
231 :			'std' (default) -- allows any expression which evaluates
232 :			to a number, including those using
233 :			elementary functions like sin() and
234 :			exp(), as well as the operations of
235 :			arithmetic (+, -, *, /, ^)
236 :			'strict' -- only decimal numbers are allowed
237 :			'frac' -- whole numbers and fractions are allowed
238 :			'arith' -- arithmetic expressions are allowed, but
239 :			no functions
240 :			Note that all modes allow the use of "pi" and "e" as
241 :			constants, and also the use of "E" to represent scientific
242 :			notation.
243 :
244 :			format -- The format to use when displaying the correct and
245 :			submitted answers. This has no effect on how answers are
246 :			evaluated; it is only for cosmetic purposes. The
247 :			formatting syntax is the same as Perl uses for the sprintf()
248 :			function. Format strings are of the form '%m.nx' or '%m.nx#',
249 :			where m and n are described below, and x is a formatter.
250 :			Esentially, m is the minimum length of the field
251 :			(make this negative to left-justify). Note that the decimal
252 :			point counts as a character when determining the field width.
253 :			If m begins with a zero, the number will be padded with zeros
254 :			instead of spaces to fit the field.
255 :			The precision specifier (n) works differently, depending
256 :			on which formatter you are using. For d, i, o, u, x and X
257 :			formatters (non-floating point formatters), n is the minimum
258 :			number of digits to display. For e and f, it is the number of
259 :			digits that appear after the decimal point (extra digits will
260 :			be rounded; insufficient digits will be padded with spaces--see
261 :			'#' below). For g, it is the number of significant digits to
262 :			display.
263 :			The full list of formatters can be found in the manpage
264 :			for printf(3), or by typing "perldoc -f sprintf" at a
265 :			terminal prompt. The following is a brief summary of the
266 :			most frequent formatters:
267 :			d -- decimal number
268 :			ld -- long decimal number
269 :			u -- unsigned decimal number
270 :			lu -- long unsigned decimal number
271 :			x -- hexadecimal number
272 :			o -- octal number
273 :			e -- floating point number in scientific notation
274 :			f -- floating point number
275 :			g -- either e or f, whichever takes less space
276 :			Technically, g will use e if the exponent is less than -4 or
277 :			greater than or equal to the precision. Trailing zeros are
278 :			removed in this mode.
279 :			If the format string ends in '#', trailing zeros will be
280 :			removed in the decimal part. Note that this is not a standard
281 :			syntax; it is handled internally by WeBWorK and not by Perl
282 :			(although this should not be a concern to end users).
283 :			The default format is '%0.5f#', which displays as a floating
284 :			point number with 5 digits of precision and no trailing zeros.
285 :			Other useful format strings might be '%0.2f' for displaying
286 :			dollar amounts, or '%010d' to display an integer with leading
287 :			zeros. Setting format to an empty string ( '' ) means no
288 :			formatting will be used; this will show 'arbitrary' precision
289 :			floating points.
290 :
291 :			Default Values (As of 7/24/2000) (Option -- Variable Name -- Value)
292 :
293 :			Format -- $numFormatDefault -- "%0.5f#"
294 :			Relative Tolerance -- $numRelPercentTolDefault -- .1
295 :			Absolute Tolerance -- $numAbsTolDefault -- .001
296 :			Zero Level -- $numZeroLevelDefault -- 1E-14
297 :			Zero Level Tolerance -- $numZeroLevelTolDefault -- 1E-12
298 :
299 :			=cut
300 :
301 :			=head3 "mode"_num_cmp() functions
302 :
303 :			There are 16 functions total, 4 for each mode (std, frac, strict, arith). Each mode has
304 :			one "normal" function, one which accepts a list of answers, one which uses absolute
305 :			rather than relative tolerance, and one which uses absolute tolerance and accepts a list.
306 :			The "std" family is documented below; all others work precisely the same.
307 :
308 :			std_num_cmp($correctAnswer) OR
309 :			std_num_cmp($correctAnswer, $relPercentTol) OR
310 :			std_num_cmp($correctAnswer, $relPercentTol, $format) OR
311 :			std_num_cmp($correctAnswer, $relPercentTol, $format, $zeroLevel) OR
312 :			std_num_cmp($correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol)
313 :
314 :			$correctAnswer -- the correct answer
315 :			$relPercentTol -- the tolerance, as a percentage (optional)
316 :			$format -- the format of the displayed answer (optional)
317 :			$zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies (optional)
318 :			$zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero (optional)
319 :
320 :			std_num_cmp() uses standard mode (arithmetic operations and elementary
321 :			functions allowed) and relative tolerance. Options are specified by
322 :			one or more parameters. Note that if you wish to set an option which
323 :			is later in the parameter list, you must set all previous options.
324 :
325 :			std_num_cmp_abs($correctAnswer) OR
326 :			std_num_cmp_abs($correctAnswer, $absTol) OR
327 :			std_num_cmp_abs($correctAnswer, $absTol, $format)
328 :
329 :			$correctAnswer -- the correct answer
330 :			$absTol -- an absolute tolerance (optional)
331 :			$format -- the format of the displayed answer (optional)
332 :
333 :			std_num_cmp_abs() uses standard mode and absolute tolerance. Options
334 :			are set as with std_num_cmp(). Note that $zeroLevel and $zeroLevelTol
335 :			do not apply with absolute tolerance.
336 :
337 :			std_num_cmp_list($relPercentTol, $format, @answerList)
338 :
339 :			$relPercentTol -- the tolerance, as a percentage
340 :			$format -- the format of the displayed answer(s)
341 :			@answerList -- a list of one or more correct answers
342 :
343 :			std_num_cmp_list() uses standard mode and relative tolerance. There
344 :			is no way to set $zeroLevel or $zeroLevelTol. Note that no
345 :			parameters are optional. All answers in the list will be
346 :			evaluated with the same set of parameters.
347 :
348 :			std_num_cmp_abs_list($absTol, $format, @answerList)
349 :
350 :			$absTol -- an absolute tolerance
351 :			$format -- the format of the displayed answer(s)
352 :			@answerList -- a list of one or more correct answers
353 :
354 :			std_num_cmp_abs_list() uses standard mode and absolute tolerance.
355 :			Note that no parameters are optional. All answers in the list will be
356 :			evaluated with the same set of parameters.
357 :
358 :			arith_num_cmp(), arith_num_cmp_list(), arith_num_cmp_abs(), arith_num_cmp_abs_list()
359 :			strict_num_cmp(), strict_num_cmp_list(), strict_num_cmp_abs(), strict_num_cmp_abs_list()
360 :			frac_num_cmp(), frac_num_cmp_list(), frac_num_cmp_abs(), frac_num_cmp_abs_list()
361 :
362 :			Examples:
363 :
364 :			ANS( strict_num_cmp( 3.14159 ) ) -- The student answer must be a number
365 :			in decimal or scientific notation which is within .1 percent of 3.14159.
366 :			This assumes $numRelPercentTolDefault has been set to .1.
367 :			ANS( strict_num_cmp( $answer, .01 ) ) -- The student answer must be a
368 :			number within .01 percent of $answer (e.g. 3.14159 if $answer is 3.14159
369 :			or $answer is "pi" or $answer is 4*atan(1)).
370 :			ANS( frac_num_cmp( $answer) ) or ANS( frac_num_cmp( $answer,.01 )) --
371 :			The student answer can be a number or fraction, e.g. 2/3.
372 :			ANS( arith_num_cmp( $answer) ) or ANS( arith_num_cmp( $answer,.01 )) --
373 :			The student answer can be an arithmetic expression, e.g. (2+3)/7-2^.5 .
374 :			ANS( std_num_cmp( $answer) ) or ANS( std_num_cmp( $answer,.01 )) --
375 :			The student answer can contain elementary functions, e.g. sin(.3+pi/2)
376 :
377 :			=cut
378 :
379 :			sub std_num_cmp { # compare numbers allowing use of elementary functions
380 :	chris	22	my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
381 :	sam	2
382 :	chris	22	my %options = ( 'tolerance' => $relPercentTol,
383 :			'format' => $format,
384 :			'zeroLevel' => $zeroLevel,
385 :			'zeroLevelTol' => $zeroLevelTol
386 :			);
387 :
388 :			set_default_options( \%options,
389 :			'tolType' => 'relative',
390 :			'tolerance' => $numRelPercentTolDefault,
391 :			'mode' => 'std',
392 :			'format' => $numFormatDefault,
393 :			'relTol' => $numRelPercentTolDefault,
394 :			'zeroLevel' => $numZeroLevelDefault,
395 :			'zeroLevelTol' => $numZeroLevelTolDefault,
396 :			'debug' => 0,
397 :			);
398 :
399 :			num_cmp([$correctAnswer], %options);
400 :	sam	2	}
401 :
402 :			## Similar to std_num_cmp but accepts a list of numbers in the form
403 :			## std_num_cmp_list(relpercentTol,format,ans1,ans2,ans3,...)
404 :			## format is of the form "%10.3g" or "", i.e., a format suitable for sprintf(). Use "" for default
405 :			## You must enter a format and tolerance
406 :			sub std_num_cmp_list {
407 :			my ( $relPercentTol, $format, @answerList) = @_;
408 :
409 :	chris	22	my %options = ( 'tolerance' => $relPercentTol,
410 :			'format' => $format,
411 :			);
412 :
413 :			set_default_options( \%options,
414 :			'tolType' => 'relative',
415 :			'tolerance' => $numRelPercentTolDefault,
416 :			'mode' => 'std',
417 :			'format' => $numFormatDefault,
418 :			'relTol' => $numRelPercentTolDefault,
419 :			'zeroLevel' => $numZeroLevelDefault,
420 :			'zeroLevelTol' => $numZeroLevelTolDefault,
421 :			'debug' => 0,
422 :			);
423 :
424 :			num_cmp(\@answerList, %options);
425 :
426 :	sam	2	}
427 :
428 :	chris	22	sub std_num_cmp_abs { # compare numbers allowing use of elementary functions with absolute tolerance
429 :	sam	2	my ( $correctAnswer, $absTol, $format) = @_;
430 :	chris	22	my %options = ( 'tolerance' => $absTol,
431 :			'format' => $format);
432 :
433 :			set_default_options (\%options,
434 :			'tolType' => 'absolute',
435 :			'tolerance' => $absTol,
436 :			'mode' => 'std',
437 :			'format' => $numFormatDefault,
438 :			'zeroLevel' => 0,
439 :			'zeroLevelTol' => 0,
440 :			'debug' => 0,
441 :			);
442 :	sam	2
443 :	chris	22	num_cmp([$correctAnswer], %options);
444 :	sam	2	}
445 :
446 :			## See std_num_cmp_list for usage
447 :	chris	22
448 :	sam	2	sub std_num_cmp_abs_list {
449 :			my ( $absTol, $format, @answerList ) = @_;
450 :
451 :	chris	22	my %options = ( 'tolerance' => $absTol,
452 :			'format' => $format,
453 :			);
454 :
455 :			set_default_options( \%options,
456 :			'tolType' => 'absolute',
457 :			'tolerance' => $absTol,
458 :			'mode' => 'std',
459 :			'format' => $numFormatDefault,
460 :			'zeroLevel' => 0,
461 :			'zeroLevelTol' => 0,
462 :			'debug' => 0,
463 :			);
464 :
465 :			num_cmp(\@answerList, %options);
466 :
467 :	sam	2	}
468 :
469 :			sub frac_num_cmp { # only allow fractions and numbers as submitted answer
470 :
471 :	chris	22	my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
472 :
473 :			my %options = ( 'tolerance' => $relPercentTol,
474 :			'format' => $format,
475 :			'zeroLevel' => $zeroLevel,
476 :			'zeroLevelTol' => $zeroLevelTol
477 :			);
478 :
479 :			set_default_options( \%options,
480 :			'tolType' => 'relative',
481 :			'tolerance' => $relPercentTol,
482 :			'mode' => 'frac',
483 :			'format' => $numFormatDefault,
484 :			'zeroLevel' => $numZeroLevelDefault,
485 :			'zeroLevelTol' => $numZeroLevelTolDefault,
486 :			'relTol' => $numRelPercentTolDefault,
487 :			'debug' => 0,
488 :			);
489 :
490 :			num_cmp([$correctAnswer], %options);
491 :	sam	2	}
492 :
493 :			## See std_num_cmp_list for usage
494 :			sub frac_num_cmp_list {
495 :	chris	22	my ( $relPercentTol, $format, @answerList ) = @_;
496 :
497 :			my %options = ( 'tolerance' => $relPercentTol,
498 :			'format' => $format
499 :			);
500 :
501 :			set_default_options( \%options,
502 :			'tolType' => 'relative',
503 :			'tolerance' => $relPercentTol,
504 :			'mode' => 'frac',
505 :			'format' => $numFormatDefault,
506 :			'zeroLevel' => $numZeroLevelDefault,
507 :			'zeroLevelTol' => $numZeroLevelTolDefault,
508 :			'relTol' => $numRelPercentTolDefault,
509 :			'debug' => 0,
510 :			);
511 :
512 :			num_cmp(\@answerList, %options);
513 :
514 :	sam	2	}
515 :
516 :	gage	32
517 :	chris	22	sub frac_num_cmp_abs { # only allow fraction expressions as submitted answer with absolute tolerance
518 :			my ( $correctAnswer, $absTol, $format ) = @_;
519 :
520 :			my %options = ( 'tolerance' => $absTol,
521 :			'format' => $format
522 :			);
523 :
524 :			set_default_options (\%options,
525 :			'tolType' => 'absolute',
526 :			'tolerance' => $absTol,
527 :			'mode' => 'frac',
528 :			'format' => $numFormatDefault,
529 :			'zeroLevel' => 0,
530 :			'zeroLevelTol' => 0,
531 :			'debug' => 0,
532 :			);
533 :			num_cmp([$correctAnswer], %options);
534 :
535 :	gage	32
536 :	sam	2	}
537 :	chris	22
538 :	sam	2	## See std_num_cmp_list for usage
539 :			sub frac_num_cmp_abs_list {
540 :	chris	22	my ( $absTol, $format, @answerList ) = @_;
541 :
542 :			my %options = ( 'tolerance' => $absTol,
543 :			'format' => $format
544 :			);
545 :
546 :			set_default_options (\%options,
547 :			'tolType' => 'absolute',
548 :			'tolerance' => $absTol,
549 :			'mode' => 'frac',
550 :			'format' => $numFormatDefault,
551 :			'zeroLevel' => 0,
552 :			'zeroLevelTol' => 0,
553 :			'debug' => 0,
554 :			);
555 :
556 :			num_cmp(\@answerList, %options);
557 :	sam	2	}
558 :
559 :
560 :			sub arith_num_cmp { # only allow arithmetic expressions as submitted answer
561 :	chris	22
562 :			my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
563 :
564 :			my %options = ( 'tolerance' => $relPercentTol,
565 :			'format' => $format,
566 :			'zeroLevel' => $zeroLevel,
567 :			'zeroLevelTol' => $zeroLevelTol
568 :			);
569 :
570 :			set_default_options( \%options,
571 :			'tolType' => 'relative',
572 :			'tolerance' => $relPercentTol,
573 :			'mode' => 'arith',
574 :			'format' => $numFormatDefault,
575 :			'zeroLevel' => $numZeroLevelDefault,
576 :			'zeroLevelTol' => $numZeroLevelTolDefault,
577 :			'relTol' => $numRelPercentTolDefault,
578 :			'debug' => 0,
579 :			);
580 :	sam	2
581 :	chris	22	num_cmp([$correctAnswer], %options);
582 :	sam	2	}
583 :
584 :			## See std_num_cmp_list for usage
585 :			sub arith_num_cmp_list {
586 :	chris	22	my ( $relPercentTol, $format, @answerList ) = @_;
587 :	sam	2
588 :	chris	22	my %options = ( 'tolerance' => $relPercentTol,
589 :			'format' => $format,
590 :			);
591 :
592 :			set_default_options( \%options,
593 :			'tolType' => 'relative',
594 :			'tolerance' => $relPercentTol,
595 :			'mode' => 'arith',
596 :			'format' => $numFormatDefault,
597 :			'zeroLevel' => $numZeroLevelDefault,
598 :			'zeroLevelTol' => $numZeroLevelTolDefault,
599 :			'relTol' => $numRelPercentTolDefault,
600 :			'debug' => 0,
601 :			);
602 :			num_cmp(\@answerList, %options);
603 :	sam	2	}
604 :
605 :	chris	22	sub arith_num_cmp_abs { # only allow arithmetic expressions as submitted answer with absolute tolerance
606 :			my ( $correctAnswer, $absTol, $format ) = @_;
607 :
608 :			my %options = ( 'tolerance' => $absTol,
609 :			'format' => $format
610 :			);
611 :
612 :			set_default_options (\%options,
613 :			'tolType' => 'absolute',
614 :			'tolerance' => $absTol,
615 :			'mode' => 'arith',
616 :			'format' => $numFormatDefault,
617 :			'zeroLevel' => 0,
618 :			'zeroLevelTol' => 0,
619 :			'debug' => 0,
620 :			);
621 :			num_cmp([$correctAnswer], %options);
622 :	sam	2
623 :	chris	22
624 :	sam	2	}
625 :
626 :			## See std_num_cmp_list for usage
627 :			sub arith_num_cmp_abs_list {
628 :	chris	22	my ( $absTol, $format, @answerList ) = @_;
629 :
630 :			my %options = ( 'tolerance' => $absTol,
631 :			'format' => $format
632 :			);
633 :
634 :			set_default_options (\%options,
635 :			'tolType' => 'absolute',
636 :			'tolerance' => $absTol,
637 :			'mode' => 'arith',
638 :			'format' => $numFormatDefault,
639 :			'zeroLevel' => 0,
640 :			'zeroLevelTol' => 0,
641 :			'debug' => 0,
642 :			);
643 :			num_cmp(\@answerList, %options);
644 :
645 :	sam	2	}
646 :
647 :			sub strict_num_cmp { # only allow numbers as submitted answer
648 :	chris	22
649 :			my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
650 :
651 :			my %options = ( 'tolerance' => $relPercentTol,
652 :			'format' => $format,
653 :			'zeroLevel' => $zeroLevel,
654 :			'zeroLevelTol' => $zeroLevelTol
655 :			);
656 :
657 :			set_default_options( \%options,
658 :			'tolType' => 'relative',
659 :			'tolerance' => $relPercentTol,
660 :			'mode' => 'strict',
661 :			'format' => $numFormatDefault,
662 :			'zeroLevel' => $numZeroLevelDefault,
663 :			'zeroLevelTol' => $numZeroLevelTolDefault,
664 :			'relTol' => $numRelPercentTolDefault,
665 :			'debug' => 0,
666 :			);
667 :
668 :			num_cmp([$correctAnswer], %options);
669 :	sam	2
670 :			}
671 :
672 :			## See std_num_cmp_list for usage
673 :			sub strict_num_cmp_list { # compare numbers
674 :			my ( $relPercentTol, $format, @answerList ) = @_;
675 :	chris	22
676 :			my %options = ( 'tolerance' => $relPercentTol,
677 :			'format' => $format,
678 :			);
679 :
680 :			set_default_options( \%options,
681 :			'tolType' => 'relative',
682 :			'tolerance' => $relPercentTol,
683 :			'mode' => 'strict',
684 :			'format' => $numFormatDefault,
685 :			'zeroLevel' => $numZeroLevelDefault,
686 :			'zeroLevelTol' => $numZeroLevelTolDefault,
687 :			'relTol' => $numRelPercentTolDefault,
688 :			'debug' => 0,
689 :			);
690 :	sam	2
691 :	chris	22	num_cmp(\@answerList, %options);
692 :			}
693 :	sam	2
694 :	chris	22
695 :	sam	2	sub strict_num_cmp_abs { # only allow numbers as submitted answer with absolute tolerance
696 :
697 :	chris	22	my ( $correctAnswer, $absTol, $format ) = @_;
698 :
699 :			my %options = ( 'tolerance' => $absTol,
700 :			'format' => $format
701 :			);
702 :
703 :			set_default_options (\%options,
704 :			'tolType' => 'absolute',
705 :			'tolerance' => $absTol,
706 :			'mode' => 'strict',
707 :			'format' => $numFormatDefault,
708 :			'zeroLevel' => 0,
709 :			'zeroLevelTol' => 0,
710 :			'debug' => 0,
711 :			);
712 :
713 :			num_cmp([$correctAnswer], %options);
714 :
715 :	sam	2	}
716 :
717 :			## See std_num_cmp_list for usage
718 :			sub strict_num_cmp_abs_list { # compare numbers
719 :	chris	22	my ( $absTol, $format, @answerList ) = @_;
720 :	sam	2
721 :	gage	32
722 :	chris	22	my %options = ( 'tolerance' => $absTol,
723 :			'format' => $format
724 :			);
725 :
726 :			set_default_options (\%options,
727 :			'tolType' => 'absolute',
728 :			'tolerance' => $absTol,
729 :			'mode' => 'strict',
730 :			'format' => $numFormatDefault,
731 :			'zeroLevel' => 0,
732 :			'zeroLevelTol' => 0,
733 :			'debug' => 0,
734 :			);
735 :
736 :			num_cmp(\@answerList, %options);
737 :
738 :	gage	32
739 :
740 :	sam	2	}
741 :
742 :	gage	32
743 :	sam	2	## Compares a number with units
744 :			## Deprecated; use num_cmp()
745 :			##
746 :			## IN: a string which includes the numerical answer and the units
747 :			## a hash with the following keys (all optional):
748 :			## mode -- 'std', 'frac', 'arith', or 'strict'
749 :			## format -- the format to use when displaying the answer
750 :			## tol -- an absolute tolerance, or
751 :			## relTol -- a relative tolerance
752 :			## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
753 :			## zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero
754 :
755 :
756 :	gage	32
757 :
758 :	chris	22	sub check_units {
759 :			my ($rh_ans, %options) = @_;
760 :
761 :			my %correct_units = %{$rh_ans-> {rh_correct_units}};
762 :
763 :			my $ans = $rh_ans->{student_ans};
764 :			# $ans = '' unless defined ($ans);
765 :			my $original_student_ans = $ans;
766 :
767 :			# $ans = str_filters ($ans, 'trim_whitespace');
768 :			$rh_ans->{original_student_ans} = $original_student_ans;
769 :
770 :			# it surprises me that the match below works since the first .* is greedy.
771 :			my ($num_answer, $units) = $ans =~ /^(.)\s+([^\s])$/;
772 :
773 :			unless ( defined($num_answer) && $units ) {
774 :			# there is an error reading the input
775 :			if ( $ans =~ /\S/ ) { # the answer is not blank
776 :			$rh_ans -> setKeys( 'ans_message' => "The answer \"$ans\" could not be interpreted " .
777 :			"as a number or an arithmetic expression followed by a unit specification. " .
778 :			"Your answer must contain units." );
779 :			$rh_ans->throw_error('UNITS', "The answer \"$ans\" could not be interpreted " .
780 :			"as a number or an arithmetic expression followed by a unit specification. " .
781 :			"Your answer must contain units." );
782 :			}
783 :	sam	2
784 :	chris	22	return $rh_ans;
785 :	sam	2	}
786 :
787 :	chris	22	# we have been able to parse the answer into a numerical part and a unit part
788 :	sam	2
789 :	chris	22	# $num_answer = $1; #$1 and $2 from the regular expression above
790 :			# $units = $2;
791 :	sam	2
792 :	chris	22	my %units = Units::evaluate_units($units);
793 :			if ( defined( $units{'ERROR'} ) ) {
794 :			# handle error condition
795 :			$units{'ERROR'} = clean_up_error_msg($units{'ERROR'});
796 :			$rh_ans -> setKeys( 'ans_message' => "$units{'ERROR'}" );
797 :			return $rh_ans;
798 :	sam	2	}
799 :
800 :	chris	22	my $units_match = 1;
801 :			my $fund_unit;
802 :			foreach $fund_unit (keys %correct_units) {
803 :			next if $fund_unit eq 'factor';
804 :			$units_match = 0 unless $correct_units{$fund_unit} == $units{$fund_unit};
805 :			}
806 :
807 :			if ( $units_match ) {
808 :			# units are ok. Evaluate the numerical part of the answer
809 :			$rh_ans->{'tolerance'} = $rh_ans->{'tolerance'}* $correct_units{'factor'}/$units{'factor'} if
810 :			$rh_ans->{'tolType'} eq 'absolute'; # the tolerance is in the units specified by the instructor.
811 :			$rh_ans->{correct_ans} = prfmt($rh_ans->{correct_ans}*$correct_units{'factor'}/$units{'factor'});
812 :	sam	2
813 :	chris	22
814 :	sam	2
815 :
816 :	chris	22	$rh_ans->{student_ans} = $num_answer;
817 :			# return $rh_ans;
818 :			# my $numerical_answer_evaluator = NUM_CMP( 'correctAnswer' => $correct_num_answer*$correct_units{'factor'}/$units{'factor'},
819 :			# 'tolerance' => $rh_ans->{'tolerance'},
820 :			# 'tolType' => $rh_ans->{'tolType'},
821 :			# 'format' => $options{'format'},
822 :			# 'mode' => $options{'mode'},
823 :			# 'zeroLevel' => $options{'zeroLevel'},
824 :			# 'zeroLevelTol' => $options{'zeroLevelTol'} );
825 :			#
826 :			# # because num_answer may contain an arithmetic expression rather than
827 :			# # a number we can't multiply it by the $units{'factor'}
828 :			# # instead we divide the correctanswer by this amount;
829 :			# # this is also why the numerical_answer_evaluator is not defined outside this subroutine.
830 :			#
831 :			# # $ans_hash = &$numerical_answer_evaluator($num_answer);
832 :			#
833 :			# # now we need to doctor the correct answer in order to add units
834 :			# # to it and correct for the division we did before
835 :			# $ans_hash -> {correct_ans} =
836 :			# prfmt( ( $ans_hash->{'correct_ans'} )*$units{'factor'}/$correct_units{'factor'},
837 :			# $options{'format'} ) . " $correct_units";
838 :			# # we also need to doctor the submitted answer to get it back in its original format.
839 :			#
840 :			# # we don't add the units on if there is an error message from numerical_answer_evaluator
841 :			# if ( ( $ans_hash -> {ans_message} ) =~ /^\s*$/ ) {
842 :			# $ans_hash -> {student_ans} = $ans_hash -> {student_ans} . " $units";
843 :			# $ans_hash -> setKeys( original_student_ans => $ans );
844 :			# }
845 :			# else {
846 :			# # error message from numerical_answer_evaluator doesn't have units tacked on
847 :			# $ans_hash -> setKeys( original_student_ans => $ans );
848 :			# }
849 :			} else {
850 :			$rh_ans -> setKeys( ans_message => 'There is an error in the units for this answer.' );
851 :			$rh_ans -> throw_error ( 'UNITS', 'There is an error in the units for this answer.' );
852 :	sam	2	}
853 :	chris	22
854 :			return $rh_ans;
855 :			}
856 :	sam	2
857 :	chris	22	sub numerical_compare_with_units {
858 :			my $correct_answer = shift; # the answer is a string which includes both the numerical answer and the units.
859 :			my %options = @_; # all of the other inputs are (key value) pairs
860 :	sam	2
861 :	chris	22	# Prepare the correct answer
862 :			$correct_answer = str_filters( $correct_answer, 'trim_whitespace' );
863 :	sam	2
864 :	chris	22	# it surprises me that the match below works since the first .* is greedy.
865 :			my ($correct_num_answer, $correct_units) = $correct_answer =~ /^(.)\s+([^\s])$/;
866 :	sam	2
867 :	chris	22	$options{units} = $correct_units;
868 :
869 :
870 :			num_cmp($correct_num_answer, %options);
871 :	sam	2	}
872 :	chris	22
873 :			#sub numerical_compare_with_units {
874 :			# my $correct_answer = shift; # the answer is a string which includes both the numerical answer and the units.
875 :			# my %options = @_; # all of the other inputs are (key value) pairs
876 :			#
877 :			# # handle the defaults
878 :			# $options{'mode'} = 'std' unless defined( $options{'mode'} );
879 :			# $options{'format'} = $numFormatDefault unless defined( $options{'format'} );
880 :			# $options{'zeroLevel'} = $numZeroLevelDefault unless defined( $options{'zeroLevel'} );
881 :			# $options{'zeroLevelTol'} = $numZeroLevelTolDefault unless defined( $options{'zeroLevelTol'} );
882 :			#
883 :			# # both spellings are maintained for backward compatibility
884 :			# # relTol is preferred
885 :			# if( defined $options{'reltol'} ) {
886 :			# $options{'relTol'} = $options{'reltol'};
887 :			# delete $options{'reltol'};
888 :			# }
889 :			#
890 :			# my ($tol, $tolerance_mode);
891 :			# if ( defined $options{'tol'} ) {
892 :			# $tol = $options{'tol'};
893 :			# $tolerance_mode = 'absolute';
894 :			# }
895 :			# elsif( defined $options{'relTol'} ) {
896 :			# $tol = $options{'relTol'};
897 :			# $tolerance_mode = 'relative';
898 :			# }
899 :			# else { #the default is a relative tolerance
900 :			# $tol = $numRelPercentTolDefault;
901 :			# $tolerance_mode = 'relative';
902 :			# }
903 :			#
904 :			# # Prepare the correct answer
905 :			# $correct_answer = str_filters( $correct_answer, 'trim_whitespace' );
906 :			#
907 :			# # it surprises me that the match below works since the first .* is greedy.
908 :			# my ($correct_num_answer, $correct_units) = $correct_answer =~ /^(.)\s+([^\s])$/;
909 :			#
910 :			# my %correct_units = Units::evaluate_units($correct_units);
911 :			# if ( defined( $correct_units{'ERROR'} ) ) {
912 :			# die "ERROR: The answer \"$correct_answer\" in the problem definition cannot be parsed:\n" .
913 :			# "$correct_units{'ERROR'}\n";
914 :			# }
915 :			#
916 :			# my $ans_evaluator = sub {
917 :			#
918 :			# my $ans = shift;
919 :			# $ans = '' unless defined($ans);
920 :			# my $original_student_ans = $ans;
921 :			#
922 :			# $ans = str_filters( $ans, 'trim_whitespace' );
923 :			#
924 :			# my $ans_hash = new AnswerHash(
925 :			# 'score' => 0,
926 :			# 'correct_ans' => spf($correct_num_answer,$options{'format'}) . " $correct_units",
927 :			# 'student_ans' => $ans,
928 :			# 'ans_message' => '',
929 :			# 'type' => 'num_cmp_with_units',
930 :			# 'preview_text_string' => '',
931 :			# 'original_student_ans' => $original_student_ans
932 :			# );
933 :			#
934 :			# # it surprises me that the match below works since the first .* is greedy.
935 :			# my ($num_answer, $units) = $ans =~ /^(.)\s+([^\s])$/;
936 :			#
937 :			# unless ( defined($num_answer) && $units ) {
938 :			# # there is an error reading the input
939 :			# if ( $ans =~ /\S/ ) { # the answer is not blank
940 :			# $ans_hash -> setKeys( 'ans_message' => "The answer \"$ans\" could not be interpreted " .
941 :			# "as a number or an arithmetic expression followed by a unit specification. " .
942 :			# "Your answer must contain units." );
943 :			# }
944 :			#
945 :			# return $ans_hash;
946 :			# }
947 :			#
948 :			# # we have been able to parse the answer into a numerical part and a unit part
949 :			#
950 :			# $num_answer = $1; #$1 and $2 from the regular expression above
951 :			# $units = $2;
952 :			#
953 :			# my %units = Units::evaluate_units($units);
954 :			# if ( defined( $units{'ERROR'} ) ) {
955 :			# # handle error condition
956 :			# $units{'ERROR'} = clean_up_error_msg($units{'ERROR'});
957 :			#
958 :			# $ans_hash -> setKeys( 'ans_message' => "$units{'ERROR'}" );
959 :			#
960 :			# return $ans_hash;
961 :			# }
962 :			#
963 :			# my $units_match = 1;
964 :			# my $fund_unit;
965 :			# foreach $fund_unit (keys %correct_units) {
966 :			# next if $fund_unit eq 'factor';
967 :			# $units_match = 0 unless $correct_units{$fund_unit} == $units{$fund_unit};
968 :			# }
969 :			#
970 :			# if ( $units_match ) {
971 :			#
972 :			# # units are ok. Evaluate the numerical part of the answer
973 :			# $tol = $tol * $correct_units{'factor'}/$units{'factor'} if
974 :			# $tolerance_mode eq 'absolute'; # the tolerance is in the units specified by the instructor.
975 :			#
976 :			# my $numerical_answer_evaluator = NUM_CMP( 'correctAnswer' => $correct_num_answer*$correct_units{'factor'}/$units{'factor'},
977 :			# 'tolerance' => $tol,
978 :			# 'tolType' => $tolerance_mode,
979 :			# 'format' => $options{'format'},
980 :			# 'mode' => $options{'mode'},
981 :			# 'zeroLevel' => $options{'zeroLevel'},
982 :			# 'zeroLevelTol' => $options{'zeroLevelTol'} );
983 :			#
984 :			# # because num_answer may contain an arithmetic expression rather than
985 :			# # a number we can't multiply it by the $units{'factor'}
986 :			# # instead we divide the correct answer by this amount;
987 :			# # this is also why the numerical_answer_evaluator is not defined outside this subroutine.
988 :			#
989 :			# $ans_hash = &$numerical_answer_evaluator($num_answer);
990 :			#
991 :			# # now we need to doctor the correct answer in order to add units
992 :			# # to it and correct for the division we did before
993 :			# $ans_hash -> {correct_ans} =
994 :			# prfmt( ( $ans_hash->{'correct_ans'} )*$units{'factor'}/$correct_units{'factor'},
995 :			# $options{'format'} ) . " $correct_units";
996 :			# # we also need to doctor the submitted answer to get it back in its original format.
997 :			#
998 :			# # we don't add the units on if there is an error message from numerical_answer_evaluator
999 :			# if ( ( $ans_hash -> {ans_message} ) =~ /^\s*$/ ) {
1000 :			# $ans_hash -> {student_ans} = $ans_hash -> {student_ans} . " $units";
1001 :			# $ans_hash -> setKeys( original_student_ans => $ans );
1002 :			# }
1003 :			# else {
1004 :			# # error message from numerical_answer_evaluator doesn't have units tacked on
1005 :			# $ans_hash -> setKeys( original_student_ans => $ans );
1006 :			# }
1007 :			# }
1008 :			# else {
1009 :			# $ans_hash -> setKeys( ans_message => 'There is an error in the units for this answer.' );
1010 :			# }
1011 :			#
1012 :			# return $ans_hash;
1013 :			# };
1014 :			#
1015 :			# $ans_evaluator;
1016 :			# }
1017 :	sam	2
1018 :			=head3 std_num_str_cmp()
1019 :	chris	22
1020 :	sam	2	NOTE: This function is maintained for compatibility. num_cmp() with the
1021 :			'strings' parameter is slightly preferred.
1022 :
1023 :			std_num_str_cmp() is used when the correct answer could be either a number or a
1024 :			string. For example, if you wanted the student to evaluate a function at number
1025 :			of points, but write "Inf" or "Minf" if the function is unbounded. This routine
1026 :			will provide error messages that do not give a hint as to whether the correct
1027 :			answer is a string or a number. For numerical comparisons, std_num_cmp() is
1028 :			used internally; for string comparisons, std_str_cmp() is used.
1029 :
1030 :			std_num_str_cmp( $correctAnswer ) OR
1031 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings ) OR
1032 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol ) OR
1033 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format ) OR
1034 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format, $zeroLevel ) OR
1035 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format,
1036 :			$zeroLevel, $zeroLevelTol )
1037 :
1038 :			$correctAnswer -- the correct answer
1039 :			$ra_legalStrings -- a reference to an array of legal strings, e.g. ["str1", "str2"]
1040 :			$relPercentTol -- the error tolerance as a percentage
1041 :			$format -- the display format
1042 :			$zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
1043 :			$zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero
1044 :
1045 :			Example:
1046 :			ANS( std_num_str_cmp( $ans, ["Inf", "Minf", "NaN"] ) );
1047 :
1048 :			=cut
1049 :
1050 :			sub std_num_str_cmp {
1051 :			my ( $correctAnswer, $ra_legalStrings, $relpercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
1052 :
1053 :			$ra_legalStrings = [''] unless defined $ra_legalStrings;
1054 :			my @legalStrings = @{$ra_legalStrings};
1055 :
1056 :			my $ans_evaluator = sub {
1057 :
1058 :			my $ans = shift;
1059 :			my $ans_hash;
1060 :			my $corrAnswerIsString = 0;
1061 :			# my $studAnswerIsString = 0; ## uses new incorrect logic
1062 :			my $studAnswerIsString = 1;
1063 :
1064 :			my $legalString = '';
1065 :			foreach $legalString (@legalStrings) {
1066 :			if ( uc($correctAnswer) eq uc($legalString) ) {
1067 :			$corrAnswerIsString = 1;
1068 :			last;
1069 :			}
1070 :			} ## at this point $corrAnswerIsString = 0 iff correct answer is numeric
1071 :
1072 :			# Neither of these is perfect; the first is more general, but
1073 :			# has problems with certain special strings like "ee", while the
1074 :			# second doesn't support arithmetic expressions.
1075 :			#
1076 :			# if( $ans !~ m/^\s([\+\-\\/\^\[\]\{\}\s\d\.Ee]\|e\|pi)\s$/ ) {
1077 :			# $studAnswerIsString = 1;
1078 :			# }
1079 :			#if( $ans !~ m/^\s([\d+\-\/^()]\|e\|pi)\s*$/ ) {
1080 :			# $studAnswerIsString = 1;
1081 :			#}
1082 :
1083 :			## Both the above new versions are incorrect. We replace this by the original logic namely that
1084 :			## an answer that contain any of the symbols
1085 :			## a digit(0-9), +, -, *, /, ^, (, ), {, }, [, ]
1086 :			## or an answer that consists of "pi" or "e" alone
1087 :			## will be considered an arithmetic expression rather than a string answer.
1088 :
1089 :			if ($ans =~ m/[\d+\-\/^(){}\[\]]\|^\se\s$\|^\spi\s*$/) {$studAnswerIsString = 0;}
1090 :
1091 :
1092 :			## at this point $studAnswerIsString = 0 iff correct answer is numeric
1093 :
1094 :			if( $studAnswerIsString ) {
1095 :			$ans = str_filters( $ans, 'compress_whitespace' )
1096 :			}
1097 :
1098 :			if ( ($corrAnswerIsString == 1) and ($studAnswerIsString == 1) ) {
1099 :			my $string_answer_evaluator = std_str_cmp( $correctAnswer );
1100 :			$ans_hash = &$string_answer_evaluator( $ans );
1101 :
1102 :			if( ($ans_hash -> {score}) != 1 ) { ## find out if string makes sense
1103 :			my $sensibleAnswer = 0;
1104 :			foreach $legalString (@legalStrings) {
1105 :			if ( uc($ans) eq uc($legalString) ) {
1106 :			$sensibleAnswer = 1;
1107 :			last;
1108 :			}
1109 :			}
1110 :			$sensibleAnswer = 1 unless $ans =~ /\S/; ## empty answers are sensible
1111 :
1112 :			$ans_hash -> setKeys( 'ans_message' => 'Your answer is not a recognized answer' )
1113 :			unless ($sensibleAnswer);
1114 :			$ans_hash -> setKeys( 'student_ans' => uc($ans) );
1115 :			}
1116 :			}
1117 :			elsif ( ($corrAnswerIsString == 0) and ($studAnswerIsString == 0) ) {
1118 :			my $numeric_answer_evaluator = std_num_cmp($correctAnswer,$relpercentTol,$format,$zeroLevel,$zeroLevelTol);
1119 :			$ans_hash = &$numeric_answer_evaluator($ans);
1120 :			}
1121 :			elsif ( ($corrAnswerIsString == 1) and ($studAnswerIsString == 0) ) {
1122 :			my $numeric_answer_evaluator = std_num_cmp(1);
1123 :			$ans_hash = &$numeric_answer_evaluator($ans);
1124 :			$ans_hash -> setKeys( 'score' => 0,
1125 :			'correct_ans' => $correctAnswer
1126 :			);
1127 :			}
1128 :			elsif ( ($corrAnswerIsString == 0) and ($studAnswerIsString == 1) ) {
1129 :			my $string_answer_evaluator = std_str_cmp('bad');
1130 :			$ans_hash = &$string_answer_evaluator($ans);
1131 :
1132 :			$ans_hash -> setKeys( 'score' => 0,
1133 :			'correct_ans' => $correctAnswer
1134 :			);
1135 :
1136 :			## find out if string makes sense
1137 :			my $sensibleAnswer = 0;
1138 :			foreach $legalString (@legalStrings) {
1139 :			if ( uc($ans) eq uc($legalString) ) {
1140 :			$sensibleAnswer = 1;
1141 :			last;
1142 :			}
1143 :			}
1144 :			$sensibleAnswer = 1 unless $ans =~ /\S/; ## empty answers are sensible
1145 :
1146 :			$ans_hash -> setKeys( 'ans_message' => "Your answer is not a recognized answer" )
1147 :			unless $sensibleAnswer;
1148 :			}
1149 :
1150 :			return $ans_hash;
1151 :			};
1152 :
1153 :			return $ans_evaluator;
1154 :			}
1155 :
1156 :			=head3 num_cmp()
1157 :
1158 :			Compares a number or a list of numbers, using a named hash of options to set
1159 :			parameters. This can make for more readable code than using the "mode"_num_cmp()
1160 :			style, but some people find one or the other easier to remember.
1161 :
1162 :			ANS( num_cmp( answer or answer_array_ref, options_hash ) );
1163 :
1164 :			1. the correct answer, or a reference to an array of correct answers
1165 :			2. a hash with the following keys (all optional):
1166 :			mode -- 'std' (default) (allows any expression evaluating to a number)
1167 :			'strict' (only numbers are allowed)
1168 :			'frac' (fractions are allowed)
1169 :			'arith' (arithmetic expressions allowed)
1170 :			format -- '%0.5f#' (default); defines formatting for the correct answer
1171 :			tol -- an absolute tolerance, or
1172 :			relTol -- a relative tolerance
1173 :			units -- the units to use for the answer(s)
1174 :			strings -- a reference to an array of strings which are valid
1175 :			answers (works like std_num_str_cmp() )
1176 :			zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
1177 :			zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1178 :
1179 :			Returns an answer evaluator, or (if given a reference to an array of
1180 :			answers), a list of answer evaluators. Note that a reference to an array of
1181 :			answers results is just a shortcut to writing a separate cum_cmp() for each
1182 :			answer. It does not mean that any of those answers are considered correct
1183 :			for one question.
1184 :
1185 :			EXAMPLES:
1186 :
1187 :			num_cmp( 5 ) -- correct answer is 5, using defaults for all options
1188 :			num_cmp( [5,6,7] ) -- correct answers are 5, 6, and 7, using defaults for all options
1189 :			num_cmp( 5, mode => 'strict' ) -- correct answer is 5, mode is strict
1190 :			num_cmp( [5,6], relTol => 5 ) -- correct answers are 5 and 6, both with 5% relative tolerance
1191 :			num_cmp( 6, strings => ["Inf", "Minf", "NaN"] ) -- correct answer is 6, "Inf", "Minf", and "NaN"
1192 :			recognized as valid answers
1193 :
1194 :			=cut
1195 :
1196 :			sub num_cmp {
1197 :			my $correctAnswer = shift @_;
1198 :			my @opt = @_;
1199 :	chris	22	my %out_options;
1200 :	sam	2
1201 :	chris	22	#########################################################################
1202 :			# Retain this first check for backword compatibility. Allows input of the form
1203 :			# num_cmp($ans, 1, '%0.5f') but warns against it
1204 :			#########################################################################
1205 :
1206 :	sam	2	my %known_options = ( 'mode' => 'std',
1207 :	chris	22	'format' => $numFormatDefault,
1208 :			'tol' => $numAbsTolDefault,
1209 :			'relTol' => $numRelPercentTolDefault,
1210 :			'units' => undef,
1211 :			'strings' => undef,
1212 :			'zeroLevel' => $numZeroLevelDefault,
1213 :			'zeroLevelTol' => $numZeroLevelTolDefault,
1214 :			'tolType' => 'relative',
1215 :			'tolerance' => 1,
1216 :			'reltol' => undef, #alternate spelling
1217 :			'unit' => undef); #alternate spelling
1218 :
1219 :	sam	2	my @output_list;
1220 :	gage	32	my( $relPercentTol, $format, $zeroLevel, $zeroLevelTol) = @opt;
1221 :	chris	22
1222 :	sam	2	unless( ref($correctAnswer) eq 'ARRAY' \|\| scalar( @opt ) == 0 \|\|
1223 :			( defined($opt[0]) and exists $known_options{$opt[0]} ) ) {
1224 :			# unless the first parameter is a list of arrays
1225 :			# or the second parameter is a known option or
1226 :			# no options were used,
1227 :			# use the old num_cmp which does not use options, but has inputs
1228 :			# $relPercentTol,$format,$zeroLevel,$zeroLevelTol
1229 :			warn "This method of using num_cmp() is deprecated. Please rewrite this" .
1230 :			" problem using the options style of parameter passing (or" .
1231 :			" check that your first option is spelled correctly).";
1232 :	gage	32
1233 :	sam	2
1234 :	gage	32	%out_options = ( 'relTol' => $relPercentTol,
1235 :			'format' => $format,
1236 :			'zeroLevel' => $zeroLevel,
1237 :			'zeroLevelTol' => $zeroLevelTol,
1238 :			'mode' => 'std'
1239 :			);
1240 :			}
1241 :			else {
1242 :			# handle options
1243 :
1244 :
1245 :			@opt = ( 'relTol' => $relPercentTol,
1246 :	chris	22	'format' => $format,
1247 :			'zeroLevel' => $numZeroLevelDefault,
1248 :			'zeroLevelTol' => $numZeroLevelTolDefault,
1249 :			'mode' => 'std'
1250 :			);
1251 :			}
1252 :			#########################################################################
1253 :			# Now handle the options assuming they are entered in the form
1254 :			# num_cmp($ans, relTol=>1, format=>'%0.5f')
1255 :			#########################################################################
1256 :			%out_options = @opt;
1257 :			assign_option_aliases( \%out_options,
1258 :			'reltol' => 'relTol',
1259 :			'unit' => 'units',
1260 :			);
1261 :	sam	2
1262 :
1263 :	gage	32
1264 :
1265 :
1266 :	chris	22	set_default_options( \%out_options,
1267 :			'tolType' => (defined($out_options{tol}) ) ? 'absolute' : 'relative',
1268 :			'tolerance' => (defined($out_options{tol}) ) ? $numAbsTolDefault : $numRelPercentTolDefault,
1269 :			'mode' => 'std',
1270 :			'format' => $numFormatDefault,
1271 :			'tol' => $numAbsTolDefault,
1272 :			'relTol' => $numRelPercentTolDefault,
1273 :			'units' => undef,
1274 :			'strings' => undef,
1275 :			'zeroLevel' => $numZeroLevelDefault,
1276 :			'zeroLevelTol' => $numZeroLevelTolDefault,
1277 :			'debug' => 0,
1278 :
1279 :			);
1280 :	sam	2
1281 :
1282 :
1283 :	gage	32
1284 :
1285 :
1286 :
1287 :	chris	22	# can't use both units and strings
1288 :			if( defined( $out_options{'units'} ) && defined( $out_options{'strings'} ) ) {
1289 :			warn "Can't use both 'units' and 'strings' in the same problem " .
1290 :			"(check your parameters to num_cmp() )";
1291 :	gage	32
1292 :	sam	2	}
1293 :
1294 :
1295 :	chris	22	# my ($tolType, $tol);
1296 :			if ($out_options{tolType} eq 'absolute') {
1297 :			# $tolType = 'absolute';
1298 :			# $out_options{tolType} = 'absolute';
1299 :			# $tol = $out_options{'tol'};
1300 :			$out_options{'tolerance'}=$out_options{'tol'};
1301 :			delete($out_options{'relTol'}) if exists( $out_options{'relTol'} );
1302 :			} else {
1303 :			# $tolType = 'relative';
1304 :			# $out_options{tolType} = 'relative';
1305 :			# $tol = $out_options{'relTol'};
1306 :			# $out_options{'tolType'} = $out_options{'relative'};
1307 :			$out_options{'tolerance'}=$out_options{'relTol'};
1308 :			# delete($out_options{'tol'}) if exists( $out_options{'tol'} );
1309 :	sam	2	}
1310 :
1311 :	chris	22
1312 :	sam	2	# thread over lists
1313 :			my @ans_list = ();
1314 :
1315 :			if ( ref($correctAnswer) eq 'ARRAY' ) {
1316 :			@ans_list = @{$correctAnswer};
1317 :			}
1318 :			else {
1319 :			push( @ans_list, $correctAnswer );
1320 :			}
1321 :	chris	22
1322 :	sam	2	# produce answer evaluators
1323 :			foreach my $ans (@ans_list) {
1324 :	chris	22	if( defined( $out_options{'units'} ) ) {
1325 :			$ans = "$ans $out_options{'units'}";
1326 :
1327 :			push( @output_list, NUM_CMP( 'correctAnswer' => $ans,
1328 :			'tolerance' => $out_options{tolerance},
1329 :			'tolType' => $out_options{tolType},
1330 :			'format' => $out_options{'format'},
1331 :			'mode' => $out_options{'mode'},
1332 :			'zeroLevel' => $out_options{'zeroLevel'},
1333 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
1334 :			'debug' => $out_options{'debug'},
1335 :			'units' => $out_options{'units'},
1336 :			)
1337 :			);
1338 :			}
1339 :			elsif( defined( $out_options{'strings'} ) ) {
1340 :			if( defined $out_options{'tol'} ) {
1341 :			warn "You are using 'tol' (for absolute tolerance) with a num/str " .
1342 :			"compare, which currently only uses relative tolerance. The default " .
1343 :			"tolerance will be used.";
1344 :	sam	2	}
1345 :	chris	22
1346 :			push( @output_list, std_num_str_cmp( $ans, $out_options{'strings'},
1347 :			$out_options{'relTol'},
1348 :			$out_options{'format'},
1349 :			$out_options{'zeroLevel'},
1350 :			$out_options{'zeroLevelTol'}
1351 :			)
1352 :			);
1353 :			}
1354 :			else {
1355 :
1356 :	sam	2	push(@output_list,
1357 :	chris	22	NUM_CMP( 'correctAnswer' => $ans,
1358 :			'tolerance' => $out_options{tolerance},
1359 :			'tolType' => $out_options{tolType},
1360 :			'format' => $out_options{'format'},
1361 :			'mode' => $out_options{'mode'},
1362 :			'zeroLevel' => $out_options{'zeroLevel'},
1363 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
1364 :			'debug' => $out_options{'debug'}
1365 :			),
1366 :			);
1367 :			}
1368 :	sam	2	}
1369 :	chris	22
1370 :	sam	2	return @output_list;
1371 :	chris	22	}
1372 :	sam	2
1373 :			#legacy code for compatability purposes
1374 :			sub num_rel_cmp { # compare numbers
1375 :	chris	22	std_num_cmp( @_ );
1376 :	sam	2	}
1377 :
1378 :			## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
1379 :			##
1380 :			## IN: a hash containing the following items (error-checking to be added later?):
1381 :			## correctAnswer -- the correct answer
1382 :			## tolerance -- the allowable margin of error
1383 :			## tolType -- 'relative' or 'absolute'
1384 :			## format -- the display format of the answer
1385 :			## mode -- one of 'std', 'strict', 'arith', or 'frac';
1386 :			## determines allowable formats for the input
1387 :			## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
1388 :			## zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1389 :	chris	22	#sub NUM_CMP { # low level numeric compare
1390 :			# my %num_params = @_;
1391 :			#
1392 :			# my @keys = qw ( correctAnswer tolerance tolType format mode zeroLevel zeroLevelTol );
1393 :			# foreach my $key (@keys) {
1394 :			# warn "$key must be defined in options when calling NUM_CMP" unless defined ($num_params{$key});
1395 :			# }
1396 :			#
1397 :			#
1398 :			# my $correctAnswer = $num_params{'correctAnswer'};
1399 :			# my $tol = $num_params{'tolerance'};
1400 :			# my $tolType = $num_params{'tolType'};
1401 :			# my $format = $num_params{'format'};
1402 :			# my $mode = $num_params{'mode'};
1403 :			# my $zeroLevel = $num_params{'zeroLevel'};
1404 :			# my $zeroLevelTol = $num_params{'zeroLevelTol'};
1405 :			#
1406 :			# if( $tolType eq 'relative' ) {
1407 :			# # $tol = $numRelPercentTolDefault unless defined $tol;
1408 :			# $tol *= .01;
1409 :			# }
1410 :			## else {
1411 :			## $tol = $numAbsTolDefault unless defined $tol;
1412 :			## }
1413 :			#
1414 :			# #$format = $numFormatDefault unless defined $format;
1415 :			# #$mode = 'std' unless defined $mode;
1416 :			# #$zeroLevel = $numZeroLevelDefault unless defined $zeroLevel;
1417 :			# #$zeroLevelTol = $numZeroLevelTolDefault unless defined $zeroLevelTol;
1418 :			#
1419 :			# my $formattedCorrectAnswer = prfmt( $correctAnswer, $format );
1420 :			#
1421 :			# my $answer_evaluator = sub {
1422 :			# my $in = shift @_;
1423 :			# $in = '' unless defined $in;
1424 :			# my $score = 0;
1425 :			# my $original_student_answer = $in;
1426 :			# my $parser = new AlgParserWithImplicitExpand;
1427 :			# my $ret = $parser -> parse($in);
1428 :			# my $preview_text_string = '';
1429 :			# my $preview_latex_string = '';
1430 :			#
1431 :			# if ( ref($ret) ) { ## parsed successfully
1432 :			# $parser -> tostring();
1433 :			# $parser -> normalize();
1434 :			# $in = $parser -> tostring();
1435 :			# $preview_text_string = $in;
1436 :			# $preview_latex_string = $parser -> tolatex();
1437 :			#
1438 :			# }
1439 :			# else { ## error in parsing
1440 :			# my $ans_hash = new AnswerHash(
1441 :			# 'score' => $score,
1442 :			# 'correct_ans' => $formattedCorrectAnswer,
1443 :			# 'student_ans' => "error: $parser->{htmlerror}",
1444 :			# 'ans_message' => $parser -> {error_msg},
1445 :			# 'type' => "${mode}_number",
1446 :			# 'preview_text_string' => $preview_text_string,
1447 :			# 'preview_latex_string' => $preview_latex_string,
1448 :			# 'original_student_ans' => $original_student_answer
1449 :			# );
1450 :			#
1451 :			# return $ans_hash;
1452 :			# }
1453 :			#
1454 :			# my $PGanswerMessage = '';
1455 :			#
1456 :			# my ($inVal,$correctVal,$PG_eval_errors,$PG_full_error_report);
1457 :			#
1458 :			# $inVal = '';
1459 :			# $correctAnswer = math_constants($correctAnswer);
1460 :			# my $formattedSubmittedAnswer = '';
1461 :			#
1462 :			# #special variable $@ holds the last error from a Perl eval statement
1463 :			# $@='';
1464 :			#
1465 :			# if ($correctAnswer =~ /\S/) {
1466 :			# ($correctVal, $PG_eval_errors,$PG_full_error_report) = PG_answer_eval($correctAnswer);
1467 :			# }
1468 :			# else {
1469 :			# $PG_eval_errors = ' ';
1470 :			# }
1471 :			#
1472 :			# if ( $PG_eval_errors or not is_a_number($correctVal) ) { ##error message from eval or above
1473 :			# $formattedSubmittedAnswer = $PG_eval_errors;
1474 :			# $formattedSubmittedAnswer = clean_up_error_msg($formattedSubmittedAnswer);
1475 :			# $PGanswerMessage = 'Tell your professor that there is an error in this problem';
1476 :			# my $ans_hash = new AnswerHash(
1477 :			# 'score' => $score,
1478 :			# 'correct_ans' => $formattedCorrectAnswer,
1479 :			# 'student_ans' => $formattedSubmittedAnswer,
1480 :			# 'ans_message' => $PGanswerMessage,
1481 :			# 'type' => 'number',
1482 :			# 'preview_text_string' => $preview_text_string,
1483 :			# 'preview_latex_string' => $preview_latex_string,
1484 :			# 'original_student_ans' => $original_student_answer
1485 :			# );
1486 :			#
1487 :			# return $ans_hash;
1488 :			# }
1489 :			#
1490 :			# $in = &math_constants($in);
1491 :			#
1492 :			# MODE_CASE: { ## bare block for "case" statement
1493 :			# if ($mode eq 'std') {
1494 :			# last MODE_CASE;
1495 :			# }
1496 :			# elsif ($mode eq 'strict') {
1497 :			# unless (is_a_number($in)) {
1498 :			# $PGanswerMessage = 'You must enter a number, e.g. -6, 5.3, or 6.12E-3';
1499 :			# $formattedSubmittedAnswer = 'Incorrect number format';
1500 :			# }
1501 :			# else {
1502 :			# last MODE_CASE;
1503 :			# }
1504 :			# }
1505 :			# elsif ($mode eq 'arith') {
1506 :			# unless (is_an_arithmetic_expression($in)) {
1507 :			# $PGanswerMessage = 'You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2';
1508 :			# $formattedSubmittedAnswer = 'Not an arithmetic expression';
1509 :			# }
1510 :			# else {
1511 :			# last MODE_CASE;
1512 :			# }
1513 :			# }
1514 :			# elsif ($mode eq 'frac') {
1515 :			# unless (is_a_fraction($in)) {
1516 :			# $PGanswerMessage = 'You must enter a number or fraction , e.g. -6 or 7/13';
1517 :			# $formattedSubmittedAnswer = 'Not a number or fraction';
1518 :			# }
1519 :			# else {
1520 :			# last MODE_CASE;
1521 :			# }
1522 :			# }
1523 :			# else {
1524 :			# $PGanswerMessage = 'Tell your professor that there is an error in his or her answer mechanism. No mode was specified.';
1525 :			# $formattedSubmittedAnswer = $in;
1526 :			# }
1527 :			#
1528 :			# my $ans_hash = new AnswerHash(
1529 :			# score => $score,
1530 :			# correct_ans => $formattedCorrectAnswer,
1531 :			# student_ans => $formattedSubmittedAnswer,
1532 :			# ans_message => $PGanswerMessage,
1533 :			# type => "${mode}_number",
1534 :			# preview_text_string => $preview_text_string,
1535 :			# preview_latex_string => $preview_latex_string,
1536 :			# original_student_ans => $original_student_answer
1537 :			# );
1538 :			#
1539 :			# return $ans_hash;
1540 :			# } # end of MODE_CASES bare block
1541 :			#
1542 :			# $@ = '';
1543 :			# if ($in =~ /\S/) {
1544 :			#
1545 :			# ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($in);
1546 :			# }
1547 :			# else {
1548 :			# $PG_eval_errors = ' ';
1549 :			# }
1550 :			#
1551 :			# if ($PG_eval_errors) { ##error message from eval or above
1552 :			# $formattedSubmittedAnswer = $PG_eval_errors;
1553 :			# $formattedSubmittedAnswer =clean_up_error_msg($formattedSubmittedAnswer);
1554 :			# $PGanswerMessage = 'There is a syntax error in your answer';
1555 :			# $PGanswerMessage = '' if $PG_eval_errors eq ' ';
1556 :			# my $ans_hash = new AnswerHash(
1557 :			# 'score' => $score,
1558 :			# 'correct_ans' => $formattedCorrectAnswer,
1559 :			# 'student_ans' => $formattedSubmittedAnswer,
1560 :			# 'ans_message' => $PGanswerMessage,
1561 :			# 'type' => "${mode}_number",
1562 :			# 'preview_text_string' => $preview_text_string,
1563 :			# 'preview_latex_string' => $preview_latex_string,
1564 :			# 'original_student_ans' => $original_student_answer
1565 :			# );
1566 :			#
1567 :			# return $ans_hash;
1568 :			# }
1569 :			# else {
1570 :			# $formattedSubmittedAnswer = prfmt($inVal,$format);
1571 :			# }
1572 :			#
1573 :			# my $permitted_error;
1574 :			# if (defined($tolType) && $tolType eq 'absolute') {
1575 :			# $permitted_error = $tol;
1576 :			# }
1577 :			# elsif ( abs($correctVal) <= $zeroLevel) {
1578 :			# $permitted_error = $zeroLevelTol; ## want $tol to be non zero
1579 :			# }
1580 :			# else {
1581 :			# $permitted_error = abs($tol*$correctVal);
1582 :			# }
1583 :			#
1584 :			# my $is_a_number = is_a_number($inVal);
1585 :			# $score = 1 if ( ($is_a_number) and
1586 :			# (abs( $inVal - $correctVal ) <= $permitted_error) );
1587 :			# if ($PG_eval_errors) {
1588 :			# $PGanswerMessage = 'There is a syntax error in your answer';
1589 :			# }
1590 :			# elsif (not $is_a_number) {
1591 :			# $PGanswerMessage = 'Your answer does not evaluate to a number';
1592 :			# }
1593 :			#
1594 :			# my $ans_hash = new AnswerHash(
1595 :			# 'score' => $score,
1596 :			# 'correct_ans' => $formattedCorrectAnswer,
1597 :			# 'student_ans' => $formattedSubmittedAnswer,
1598 :			# 'ans_message' => $PGanswerMessage,
1599 :			# 'type' => "${mode}_number",
1600 :			# 'preview_text_string' => $preview_text_string,
1601 :			# 'preview_latex_string' => $preview_latex_string,
1602 :			# 'original_student_ans' => $original_student_answer
1603 :			# );
1604 :			#
1605 :			# return $ans_hash;
1606 :			# };
1607 :			#
1608 :			# return $answer_evaluator;
1609 :	sam	2
1610 :	chris	22	#}
1611 :	sam	2
1612 :	chris	22	sub compare_numbers {
1613 :			my ($rh_ans, %options) = @_;
1614 :			my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($rh_ans->{student_ans});
1615 :			if ($PG_eval_errors) {
1616 :			$rh_ans->throw_error('EVAL','There is a syntax error in your answer');
1617 :			$rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors);
1618 :
1619 :
1620 :	gage	5	} else {
1621 :	chris	22	$rh_ans->{student_ans} = prfmt($inVal,$options{format});
1622 :	sam	2	}
1623 :	chris	22
1624 :			my $permitted_error;
1625 :
1626 :			if ($rh_ans->{tolType} eq 'absolute') {
1627 :			$permitted_error = $rh_ans->{tolerance};
1628 :
1629 :			}
1630 :			elsif ( abs($rh_ans->{correct_ans}) <= $options{zeroLevel}) {
1631 :			$permitted_error = $options{zeroLevelTol}; ## want $tol to be non zero
1632 :			}
1633 :			else {
1634 :			$permitted_error = abs($rh_ans->{tolerance}*$rh_ans->{correct_ans});
1635 :			}
1636 :
1637 :			my $is_a_number = is_a_number($inVal);
1638 :			$rh_ans->{score} = 1 if ( ($is_a_number) and
1639 :			(abs( $inVal - $rh_ans->{correct_ans} ) <= $permitted_error) );
1640 :			if (not $is_a_number) {
1641 :			$rh_ans->throw_error('EVAL','Your answer does not evaluate to a number');
1642 :			}
1643 :
1644 :			$rh_ans;
1645 :			}
1646 :	sam	2
1647 :	chris	22	sub NUM_CMP { # low level numeric compare
1648 :			my %num_params = @_;
1649 :	sam	2
1650 :	chris	22	my @keys = qw ( correctAnswer tolerance tolType format mode zeroLevel zeroLevelTol debug );
1651 :			foreach my $key (@keys) {
1652 :			warn "$key must be defined in options when calling NUM_CMP" unless defined ($num_params{$key});
1653 :			}
1654 :	sam	2
1655 :	chris	22	my $correctAnswer = $num_params{'correctAnswer'};
1656 :			my $format = $num_params{'format'};
1657 :			my $mode = $num_params{'mode'};
1658 :
1659 :			# my $tol = $num_params{'tolerance'};
1660 :			# my $tolType = $num_params{'tolType'};
1661 :			# my $zeroLevel = $num_params{'zeroLevel'};
1662 :			# my $zeroLevelTol = $num_params{'zeroLevelTol'};
1663 :
1664 :			if( $num_params{tolType} eq 'relative' ) {
1665 :			$num_params{'tolerance'} = .01*$num_params{'tolerance'};
1666 :			}
1667 :	sam	2
1668 :	chris	22	#$format = $numFormatDefault unless defined $format;
1669 :			#$mode = 'std' unless defined $mode;
1670 :			#$zeroLevel = $numZeroLevelDefault unless defined $zeroLevel;
1671 :			#$zeroLevelTol = $numZeroLevelTolDefault unless defined $zeroLevelTol;
1672 :
1673 :			my $formattedCorrectAnswer;
1674 :			my $correct_units;
1675 :			my $correct_num_answer;
1676 :			my %correct_units;
1677 :	sam	2
1678 :	chris	22	if (defined($num_params{units}) && $num_params{units}) {
1679 :			$correctAnswer = str_filters( $correctAnswer, 'trim_whitespace' );
1680 :			# units are in form stuff space units where units contains no spaces.
1681 :
1682 :			($correct_num_answer, $correct_units) = $correctAnswer =~ /^(.)\s+([^\s])$/;
1683 :			%correct_units = Units::evaluate_units($correct_units);
1684 :			if ( defined( $correct_units{'ERROR'} ) ) {
1685 :			warn ("ERROR: The answer \"$correctAnswer\" in the problem definition cannot be parsed:\n" .
1686 :			"$correct_units{'ERROR'}\n");
1687 :	sam	2	}
1688 :	chris	22	# $formattedCorrectAnswer = spf($correct_num_answer,$num_params{'format'}) . " $correct_units";
1689 :			$formattedCorrectAnswer = pfmt($correct_num_answer,$num_params{'format'}) . " $correct_units";
1690 :
1691 :			} else {
1692 :			$correct_num_answer = $correctAnswer;
1693 :			$formattedCorrectAnswer = prfmt( $correctAnswer, $num_params{'format'} );
1694 :			}
1695 :	sam	2
1696 :	chris	22	$correct_num_answer = math_constants($correct_num_answer);
1697 :
1698 :			my $PGanswerMessage = '';
1699 :
1700 :			my ($inVal,$correctVal,$PG_eval_errors,$PG_full_error_report);
1701 :
1702 :			if (defined($correct_num_answer) && $correct_num_answer =~ /\S/) {
1703 :			($correctVal, $PG_eval_errors,$PG_full_error_report) = PG_answer_eval($correct_num_answer);
1704 :			}
1705 :			else {
1706 :			$PG_eval_errors = ' ';
1707 :			}
1708 :	sam	2
1709 :	chris	22	if ( $PG_eval_errors or not is_a_number($correctVal) ) { ##error message from eval or above
1710 :			warn "Error in 'correct' answer: $PG_eval_errors<br>
1711 :			The answer $correctAnswer evaluates to $correctVal,
1712 :			which cannot be interpreted as a number. ";
1713 :
1714 :			}
1715 :			#########################################################################
1716 :	sam	2
1717 :	chris	22	#construct the answer evaluator
1718 :			my $answer_evaluator = new AnswerEvaluator;
1719 :			$answer_evaluator->{debug} = $num_params{debug};
1720 :			$answer_evaluator->ans_hash( correct_ans => $correct_num_answer,
1721 :			type => "${mode}_number",
1722 :			tolerance => $num_params{tolerance},
1723 :			tolType => $num_params{tolType},
1724 :			units => $correct_units,
1725 :			original_correct_ans => $formattedCorrectAnswer,
1726 :			rh_correct_units => \%correct_units,
1727 :			);
1728 :			my ($in, $formattedSubmittedAnswer);
1729 :			$answer_evaluator->install_pre_filter(sub {my $rh_ans = shift;
1730 :			$rh_ans->{original_student_ans} = $rh_ans->{student_ans}; $rh_ans;}
1731 :			);
1732 :			if (defined($num_params{units}) && $num_params{units}) {
1733 :			$answer_evaluator->install_pre_filter(\&check_units);
1734 :			}
1735 :
1736 :			$answer_evaluator->install_pre_filter(\&check_syntax);
1737 :
1738 :			$answer_evaluator->install_pre_filter(\&math_constants);
1739 :			if ($mode eq 'std') {
1740 :			# do nothing
1741 :			} elsif ($mode eq 'strict') {
1742 :			$answer_evaluator->install_pre_filter(\&is_a_number);
1743 :			} elsif ($mode eq 'arith') {
1744 :			$answer_evaluator->install_pre_filter(\&is_an_arithmetic_expression);
1745 :			} elsif ($mode eq 'frac') {
1746 :			$answer_evaluator->install_pre_filter(\&is_a_fraction);
1747 :	sam	2
1748 :	chris	22	} else {
1749 :			$PGanswerMessage = 'Tell your professor that there is an error in his or her answer mechanism. No mode was specified.';
1750 :			$formattedSubmittedAnswer = $in;
1751 :	sam	2	}
1752 :	chris	22
1753 :			$answer_evaluator->install_evaluator(\&compare_numbers, %num_params);
1754 :	sam	2
1755 :	chris	22	$answer_evaluator->install_post_filter(sub {my $rh_ans = shift;
1756 :			$rh_ans->{foo} = 'There was one.';
1757 :			$rh_ans->{student_ans} = $rh_ans->{original_student_ans};
1758 :			$rh_ans->{correct_ans} = $rh_ans->{original_correct_ans};
1759 :			$rh_ans;}
1760 :			);
1761 :	sam	2
1762 :	chris	22	$answer_evaluator->install_post_filter(sub {my $rh_ans = shift;
1763 :			return $rh_ans unless $rh_ans->catch_error('EVAL');
1764 :			$rh_ans->{student_ans} = $rh_ans->{original_student_ans}. ' '. $rh_ans->{error_message};
1765 :			$rh_ans->clear_error('EVAL'); } );
1766 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('SYNTAX'); } );
1767 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('UNITS'); } );
1768 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('NUMBER'); } );
1769 :
1770 :
1771 :
1772 :			$answer_evaluator;
1773 :	sam	2	}
1774 :
1775 :
1776 :	chris	22	### LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
1777 :			#sub NUM_CMP_LIST { # low level numeric list compare
1778 :			# my %num_params = @_;
1779 :			#
1780 :			# my @outputList;
1781 :			# my $ans;
1782 :			#
1783 :			# while ( @{$num_params{'answerList'}} ) {
1784 :			# $ans = shift @{$num_params{'answerList'}};
1785 :			# push( @outputList, NUM_CMP( 'correctAnswer' => $ans,
1786 :			# 'tolerance' => $num_params{'tolerance'},
1787 :			# 'tolType' => $num_params{'tolType'},
1788 :			# 'format' => $num_params{'format'},
1789 :			# 'mode' => $num_params{'mode'},
1790 :			# 'zeroLevel' => $num_params{'zeroLevel'},
1791 :			# 'zeroLevelTol' => $num_params{'zeroLevelTol'}
1792 :			# )
1793 :			# );
1794 :			# }
1795 :			#
1796 :			# return @outputList;
1797 :			#}
1798 :	sam	2
1799 :
1800 :
1801 :			##########################################################################
1802 :			##########################################################################
1803 :			## Function answer evaluators
1804 :
1805 :			=head2 Function Answer Evaluators
1806 :
1807 :			Function answer evaluators take in a function, compare it numerically to a
1808 :			correct function, and return a score. They can require an exactly equivalent
1809 :			function, or one that is equal up to a constant. They can accept or reject an
1810 :			answer based on specified tolerances for numerical deviation.
1811 :
1812 :			Function Comparison Options
1813 :
1814 :			correctEqn -- The correct equation, specified as a string. It may include
1815 :			all basic arithmetic operations, as well as elementary
1816 :			functions. Variable usage is described below.
1817 :
1818 :			Variables -- The independent variable(s). When comparing the correct
1819 :			equation to the student equation, each variable will be
1820 :			replaced by a certain number of numerical values. If
1821 :			the student equation agrees numerically with the correct
1822 :			equation, they are considered equal. Note that all
1823 :			comparison is numeric; it is possible (although highly
1824 :			unlikely and never a practical concern) for two unequal
1825 :			functions to yield the same numerical results.
1826 :
1827 :			Limits -- The limits of evaluation for the independent variables.
1828 :			Each variable is evaluated only in the half-open interval
1829 :			[lower_limit, upper_limit). This is useful if the function
1830 :			has a singularity or is not defined in a certain range.
1831 :			For example, the function "sqrt(-1-x)" could be evaluated
1832 :			in [-2,-1).
1833 :
1834 :			Tolerance -- Tolerance in function comparisons works exactly as in
1835 :			numerical comparisons; see the numerical comparison
1836 :			documentation for a complete description. Note that the
1837 :			tolerance does applies to the function as a whole, not
1838 :			each point individually.
1839 :
1840 :			Number of -- Specifies how many points to evaluate each variable at. This
1841 :			Points is typically 3, but can be set higher if it is felt that
1842 :			there is a strong possibility of "false positives."
1843 :
1844 :			Maximum -- Sets the maximum size of the constant of integration. For
1845 :			Constant of technical reasons concerning floating point arithmetic, if
1846 :			Integration the additive constant, i.e., the constant of integration, is
1847 :			greater (in absolute value) than maxConstantOfIntegration
1848 :			AND is greater than maxConstantOfIntegration times the
1849 :			correct value, WeBWorK will give an error message saying
1850 :			that it can not handle such a large constant of integration.
1851 :			This is to prevent e.g. cos(x) + 1E20 or even 1E20 as being
1852 :			accepted as a correct antiderivatives of sin(x) since
1853 :			floating point arithmetic cannot tell the difference
1854 :			between cos(x) + 1E20, 1E20, and -cos(x) + 1E20.
1855 :
1856 :			Technical note: if you examine the code for the function routines, you will see
1857 :			that most subroutines are simply doing some basic error-checking and then
1858 :			passing the parameters on to the low-level FUNCTION_CMP(). Because this routine
1859 :			is set up to handle multivariable functions, with single-variable functions as
1860 :			a special case, it is possible to pass multivariable parameters to single-
1861 :			variable functions. This usage is strongly discouraged as unnecessarily
1862 :			confusing. Avoid it.
1863 :
1864 :			Default Values (As of 7/24/2000) (Option -- Variable Name -- Value)
1865 :
1866 :			Variable -- $functVarDefault -- 'x'
1867 :			Relative Tolerance -- $functRelPercentTolDefault -- .1
1868 :			Absolute Tolerance -- $functAbsTolDefault -- .001
1869 :			Lower Limit -- $functLLimitDefault -- .0000001
1870 :			Upper Limit -- $functULimitDefault -- 1
1871 :			Number of Points -- $functNumOfPoints -- 3
1872 :			Zero Level -- $functZeroLevelDefault -- 1E-14
1873 :			Zero Level Tolerance -- $functZeroLevelTolDefault -- 1E-12
1874 :			Maximum Constant -- $functMaxConstantOfIntegration -- 1E8
1875 :			of Integration
1876 :
1877 :			=cut
1878 :
1879 :			=head3 Single-variable Function Comparisons
1880 :
1881 :			There are four single-variable function answer evaluators: "normal," absolute
1882 :			tolerance, antiderivative, and antiderivative with absolute tolerance. All
1883 :			parameters (other than the correct equation) are optional.
1884 :
1885 :			function_cmp( $correctEqn ) OR
1886 :			function_cmp( $correctEqn, $var ) OR
1887 :			function_cmp( $correctEqn, $var, $llimit, $ulimit ) OR
1888 :			function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol ) OR
1889 :			function_cmp( $correctEqn, $var, $llimit, $ulimit,
1890 :			$relPercentTol, $numPoints ) OR
1891 :			function_cmp( $correctEqn, $var, $llimit, $ulimit,
1892 :			$relPercentTol, $numPoints, $zeroLevel ) OR
1893 :			function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol, $numPoints,
1894 :			$zeroLevel,$zeroLevelTol )
1895 :
1896 :			$correctEqn -- the correct equation, as a string
1897 :			$var -- the string representing the variable (optional)
1898 :			$llimit -- the lower limit of the interval to evaluate the
1899 :			variable in (optional)
1900 :			$ulimit -- the upper limit of the interval to evaluate the
1901 :			variable in (optional)
1902 :			$relPercentTol -- the error tolerance as a percentage (optional)
1903 :			$numPoints -- the number of points at which to evaluate the
1904 :			variable (optional)
1905 :			$zeroLevel -- if the correct answer is this close to zero, then
1906 :			zeroLevelTol applies (optional)
1907 :			$zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1908 :
1909 :			function_cmp() uses standard comparison and relative tolerance. It takes a
1910 :			string representing a single-variable function and compares the student
1911 :			answer to that function numerically.
1912 :
1913 :			function_cmp_up_to_constant( $correctEqn ) OR
1914 :			function_cmp_up_to_constant( $correctEqn, $var ) OR
1915 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit ) OR
1916 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1917 :			$relpercentTol ) OR
1918 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1919 :			$relpercentTol, $numOfPoints ) OR
1920 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1921 :			$relpercentTol, $numOfPoints,
1922 :			$maxConstantOfIntegration ) OR
1923 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1924 :			$relpercentTol, $numOfPoints,
1925 :			$maxConstantOfIntegration, $zeroLevel) OR
1926 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1927 :			$relpercentTol, $numOfPoints,
1928 :			$maxConstantOfIntegration,
1929 :			$zeroLevel, $zeroLevelTol )
1930 :
1931 :			$maxConstantOfIntegration -- the maximum size of the constant of
1932 :			integration
1933 :
1934 :			function_cmp_up_to_constant() uses antiderivative compare and relative
1935 :			tolerance. All options work exactly like function_cmp(), except of course
1936 :			$maxConstantOfIntegration. It will accept as correct any function which
1937 :			differs from $correctEqn by at most a constant; that is, if
1938 :			$studentEqn = $correctEqn + C
1939 :			the answer is correct.
1940 :
1941 :			function_cmp_abs( $correctFunction ) OR
1942 :			function_cmp_abs( $correctFunction, $var ) OR
1943 :			function_cmp_abs( $correctFunction, $var, $llimit, $ulimit ) OR
1944 :			function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol ) OR
1945 :			function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol,
1946 :			$numOfPoints )
1947 :
1948 :			$absTol -- the tolerance as an absolute value
1949 :
1950 :			function_cmp_abs() uses standard compare and absolute tolerance. All
1951 :			other options work exactly as for function_cmp().
1952 :
1953 :			function_cmp_up_to_constant_abs( $correctFunction ) OR
1954 :			function_cmp_up_to_constant_abs( $correctFunction, $var ) OR
1955 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit ) OR
1956 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit,
1957 :			$absTol ) OR
1958 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit,
1959 :			$absTol, $numOfPoints ) OR
1960 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit,
1961 :			$absTol, $numOfPoints,
1962 :			$maxConstantOfIntegration )
1963 :
1964 :			function_cmp_up_to_constant_abs() uses antiderivative compare
1965 :			and absolute tolerance. All other options work exactly as with
1966 :			function_cmp_up_to_constant().
1967 :
1968 :			Examples:
1969 :
1970 :			ANS( function_cmp( "cos(x)" ) ) -- Accepts cos(x), sin(x+pi/2),
1971 :			sin(x)^2 + cos(x) + cos(x)^2 -1, etc. This assumes
1972 :			$functVarDefault has been set to "x".
1973 :			ANS( function_cmp( $answer, "t" ) ) -- Assuming $answer is "cos(t)",
1974 :			accepts cos(t), etc.
1975 :			ANS( function_cmp_up_to_constant( "cos(x)" ) ) -- Accepts any
1976 :			antiderivative of sin(x), e.g. cos(x) + 5.
1977 :			ANS( function_cmp_up_to_constant( "cos(z)", "z" ) ) -- Accepts any
1978 :			antiderivative of sin(z), e.g. sin(z+pi/2) + 5.
1979 :
1980 :			=cut
1981 :			sub adaptive_function_cmp {
1982 :			my $correctEqn = shift;
1983 :			my %options = @_;
1984 :			set_default_options( \%options,
1985 :			'vars' => [qw( x y )],
1986 :			'params' => [],
1987 :			'limits' => [ [0,1], [0,1]],
1988 :			'reltol' => $main::functRelPercentTolDefault,
1989 :			'numPoints' => $main::functNumOfPoints,
1990 :			'zeroLevel' => $main::functZeroLevelDefault,
1991 :	chris	22	'zeroLevelTol' => $main::functZeroLevelTolDefault,
1992 :	sam	2	'debug' => 0,
1993 :			);
1994 :
1995 :			my $var_ref = $options{'vars'};
1996 :			my $ra_params = $options{ 'params'};
1997 :			my $limit_ref = $options{'limits'};
1998 :			my $relPercentTol= $options{'reltol'};
1999 :			my $numPoints = $options{'numPoints'};
2000 :			my $zeroLevel = $options{'zeroLevel'};
2001 :			my $zeroLevelTol = $options{'zeroLevelTol'};
2002 :
2003 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
2004 :			'var' => $var_ref,
2005 :			'limits' => $limit_ref,
2006 :			'tolerance' => $relPercentTol,
2007 :			'tolType' => 'relative',
2008 :			'numPoints' => $numPoints,
2009 :			'mode' => 'std',
2010 :			'maxConstantOfIntegration' => 10**100,
2011 :			'zeroLevel' => $zeroLevel,
2012 :			'zeroLevelTol' => $zeroLevelTol,
2013 :			'scale_norm' => 1,
2014 :			'params' => $ra_params,
2015 :			'debug' => $options{debug} ,
2016 :	sam	2	);
2017 :
2018 :			}
2019 :
2020 :			sub function_cmp {
2021 :			my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_;
2022 :
2023 :			if ( (scalar(@_) == 3) or (scalar(@_) > 8) or (scalar(@_) == 0) ) {
2024 :			function_invalid_params( $correctEqn );
2025 :			}
2026 :			else {
2027 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
2028 :			'var' => $var,
2029 :			'limits' => [$llimit, $ulimit],
2030 :			'tolerance' => $relPercentTol,
2031 :			'tolType' => 'relative',
2032 :			'numPoints' => $numPoints,
2033 :			'mode' => 'std',
2034 :			'maxConstantOfIntegration' => 0,
2035 :			'zeroLevel' => $zeroLevel,
2036 :			'zeroLevelTol' => $zeroLevelTol
2037 :	sam	2	);
2038 :			}
2039 :			}
2040 :
2041 :			sub function_cmp_up_to_constant { ## for antiderivative problems
2042 :			my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$maxConstantOfIntegration,$zeroLevel,$zeroLevelTol) = @_;
2043 :
2044 :			if ( (scalar(@_) == 3) or (scalar(@_) > 9) or (scalar(@_) == 0) ) {
2045 :			function_invalid_params( $correctEqn );
2046 :			}
2047 :			else {
2048 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
2049 :			'var' => $var,
2050 :			'limits' => [$llimit, $ulimit],
2051 :			'tolerance' => $relPercentTol,
2052 :			'tolType' => 'relative',
2053 :			'numPoints' => $numPoints,
2054 :			'mode' => 'antider',
2055 :			'maxConstantOfIntegration' => $maxConstantOfIntegration,
2056 :			'zeroLevel' => $zeroLevel,
2057 :			'zeroLevelTol' => $zeroLevelTol
2058 :	sam	2	);
2059 :			}
2060 :			}
2061 :
2062 :			sub function_cmp_abs { ## similar to function_cmp but uses absolute tolerance
2063 :			my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints) = @_;
2064 :
2065 :			if ( (scalar(@_) == 3) or (scalar(@_) > 6) or (scalar(@_) == 0) ) {
2066 :			function_invalid_params( $correctEqn );
2067 :			}
2068 :			else {
2069 :			FUNCTION_CMP( 'correctEqn' => $correctEqn,
2070 :			'var' => $var,
2071 :			'limits' => [$llimit, $ulimit],
2072 :			'tolerance' => $absTol,
2073 :			'tolType' => 'absolute',
2074 :			'numPoints' => $numPoints,
2075 :			'mode' => 'std',
2076 :			'maxConstantOfIntegration' => 0,
2077 :			'zeroLevel' => 0,
2078 :			'zeroLevelTol' => 0
2079 :			);
2080 :			}
2081 :			}
2082 :
2083 :
2084 :			sub function_cmp_up_to_constant_abs { ## for antiderivative problems
2085 :			## similar to function_cmp_up_to_constant
2086 :			## but uses absolute tolerance
2087 :			my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints,$maxConstantOfIntegration) = @_;
2088 :
2089 :			if ( (scalar(@_) == 3) or (scalar(@_) > 7) or (scalar(@_) == 0) ) {
2090 :			function_invalid_params( $correctEqn );
2091 :			}
2092 :
2093 :			else {
2094 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
2095 :			'var' => $var,
2096 :			'limits' => [$llimit, $ulimit],
2097 :			'tolerance' => $absTol,
2098 :			'tolType' => 'absolute',
2099 :			'numPoints' => $numPoints,
2100 :			'mode' => 'antider',
2101 :			'maxConstantOfIntegration' => $maxConstantOfIntegration,
2102 :			'zeroLevel' => 0,
2103 :			'zeroLevelTol' => 0
2104 :	sam	2	);
2105 :			}
2106 :			}
2107 :
2108 :			## The following answer evaluator for comparing multivarable functions was
2109 :			## contributed by Professor William K. Ziemer
2110 :			## (Note: most of the multivariable functionality provided by Professor Ziemer
2111 :			## has now been integrated into fun_cmp and FUNCTION_CMP)
2112 :			############################
2113 :			# W.K. Ziemer, Sep. 1999
2114 :			# Math Dept. CSULB
2115 :			# email: wziemer@csulb.edu
2116 :			############################
2117 :
2118 :			=head3 multivar_function_cmp
2119 :
2120 :			NOTE: this function is maintained for compatibility. fun_cmp() is
2121 :			slightly preferred.
2122 :
2123 :			usage:
2124 :
2125 :			multivar_function_cmp( $answer, $var_reference, options)
2126 :			$answer -- string, represents function of several variables
2127 :			$var_reference -- number (of variables), or list reference (e.g. ["var1","var2"] )
2128 :			options:
2129 :			$limit_reference -- reference to list of lists (e.g. [[1,2],[3,4]])
2130 :			$relPercentTol -- relative percent tolerance in answer
2131 :			$numPoints -- number of points to sample in for each variable
2132 :			$zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
2133 :			$zeroLevelTol -- absolute tolerance to allow when answer is close to zero
2134 :
2135 :			=cut
2136 :
2137 :			sub multivar_function_cmp {
2138 :			my ($correctEqn,$var_ref,$limit_ref,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_;
2139 :
2140 :			if ( (scalar(@_) > 7) or (scalar(@_) < 2) ) {
2141 :			function_invalid_params( $correctEqn );
2142 :			}
2143 :
2144 :			FUNCTION_CMP( 'correctEqn' => $correctEqn,
2145 :			'var' => $var_ref,
2146 :			'limits' => $limit_ref,
2147 :			'tolerance' => $relPercentTol,
2148 :			'tolType' => 'relative',
2149 :			'numPoints' => $numPoints,
2150 :			'mode' => 'std',
2151 :			'maxConstantOfIntegration' => 0,
2152 :			'zeroLevel' => $zeroLevel,
2153 :			'zeroLevelTol' => $zeroLevelTol
2154 :			);
2155 :			}
2156 :
2157 :			=head3 fun_cmp()
2158 :
2159 :			Compares a function or a list of functions, using a named hash of options to set
2160 :			parameters. This can make for more readable code than using the function_cmp()
2161 :			style, but some people find one or the other easier to remember.
2162 :
2163 :			ANS( fun_cmp( answer or answer_array_ref, options_hash ) );
2164 :
2165 :			1. a string containing the correct function, or a reference to an
2166 :			array of correct functions
2167 :			2. a hash containing the following items (all optional):
2168 :			var -- either the number of variables or a reference to an
2169 :			array of variable names (see below)
2170 :			limits -- reference to an array of arrays of limits (see below), or:
2171 :			mode -- 'std' (default) (function must match exactly), or:
2172 :			'antider' (function must match up to a constant)
2173 :			relTol -- (default) a relative tolerance (as a percentage), or:
2174 :			tol -- an absolute tolerance for error
2175 :			numPoints -- the number of points to evaluate the function at
2176 :			maxConstantOfIntegration -- maximum size of the constant of integration
2177 :			zeroLevel -- if the correct answer is this close to zero, then
2178 :			zeroLevelTol applies
2179 :			zeroLevelTol -- absolute tolerance to allow when answer is close to zero
2180 :			params -- an array of "free" parameters which can be used to adapt
2181 :			-- the correct answer to the submitted answer. (e.g. ['c'] for
2182 :			-- a constant of integration in the answer x^3/3 + c.
2183 :			debug -- when set to 1 this provides extra information while checking the
2184 :			-- the answer.
2185 :
2186 :			Returns an answer evaluator, or (if given a reference to an array
2187 :			of answers), a list of answer evaluators
2188 :
2189 :			ANSWER:
2190 :
2191 :			The answer must be in the form of a string. The answer can contain
2192 :			functions, pi, e, and arithmetic operations. However, the correct answer
2193 :			string follows a slightly stricter syntax than student answers; specifically,
2194 :			there is no implicit multiplication. So the correct answer must be "3*x" rather
2195 :			than "3 x". Students can still enter "3 x".
2196 :
2197 :			VARIABLES:
2198 :
2199 :			The var parameter can contain either a number or a reference to an array of
2200 :			variable names. If it contains a number, the variables are named automatically
2201 :			as follows: 1 variable -- x
2202 :			2 variables -- x, y
2203 :			3 variables -- x, y, z
2204 :			4 or more -- x_1, x_2, x_3, etc.
2205 :			If the var parameter contains a reference to an array of variable names, then
2206 :			the number of variables is determined by the number of items in the array. A
2207 :			reference to an array is created with brackets, e.g. "var => ['r', 's', 't']".
2208 :			If only one variable is being used, you can write either "var => ['t']" for
2209 :			consistency or "var => 't'" as a shortcut. The default is one variable, x.
2210 :
2211 :			LIMITS:
2212 :
2213 :			Limits are specified with the limits parameter. You may NOT use llimit/ulimit.
2214 :			If you specify limits for one variable, you must specify them for all variables.
2215 :			The limit parameter must be a reference to an array of arrays of the form
2216 :			[lower_limit. upper_limit], each array corresponding to the lower and upper
2217 :			endpoints of the (half-open) domain of one variable. For example,
2218 :			"vars => 2, limits => [[0,2], [-3,8]]" would cause x to be evaluated in [0,2) and
2219 :			y to be evaluated in [-3,8). If only one variable is being used, you can write
2220 :			either "limits => [[0,3]]" for consistency or "limits => [0,3]" as a shortcut.
2221 :
2222 :			EXAMPLES:
2223 :
2224 :			fun_cmp( "3*x" ) -- standard compare, variable is x
2225 :			fun_cmp( ["3x", "4x+3", "3x*2"] ) -- standard compare, defaults used for all three functions
2226 :			fun_cmp( "3*t", var => 't' ) -- standard compare, variable is t
2227 :			fun_cmp( "5xy*z", var => 3 ) -- x, y and z are the variables
2228 :			fun_cmp( "5*x", mode => 'antider' ) -- student answer must match up to constant (i.e., 5x+C)
2229 :			fun_cmp( ["3xy", "4xy"], limits => [[0,2], [5,7]] ) -- x evaluated in [0,2)
2230 :			y evaluated in [5,7)
2231 :
2232 :			=cut
2233 :
2234 :			sub fun_cmp {
2235 :			my $correctAnswer = shift @_;
2236 :			my %opt = @_;
2237 :
2238 :			assign_option_aliases( \%opt,
2239 :	chris	22	'vars' => 'var', # set the standard option 'var' to the one specified as vars
2240 :			'domain' => 'limits', # set the standard option 'limits' to the one specified as domain
2241 :			'reltol' => 'relTol',
2242 :	sam	2	'param' => 'params',
2243 :			);
2244 :
2245 :			set_default_options( \%opt,
2246 :	chris	22	'var' => $functVarDefault,
2247 :			'params' => [],
2248 :			'limits' => [[$functLLimitDefault, $functULimitDefault]],
2249 :			'mode' => 'std',
2250 :			'tolType' => (defined($opt{tol}) ) ? 'absolute' : 'relative',
2251 :			'tol' => .01, # default mode should be relative, to obtain this tol must not be defined
2252 :			'relTol' => $functRelPercentTolDefault,
2253 :			'numPoints' => $functNumOfPoints,
2254 :	sam	2	'maxConstantOfIntegration' => $functMaxConstantOfIntegration,
2255 :	chris	22	'zeroLevel' => $functZeroLevelDefault,
2256 :			'zeroLevelTol' => $functZeroLevelTolDefault,
2257 :			'debug' => 0,
2258 :	sam	2	);
2259 :
2260 :
2261 :
2262 :			# allow var => 'x' as an abbreviation for var => ['x']
2263 :			my %out_options = %opt;
2264 :			unless ( ref($out_options{var}) eq 'ARRAY' ) {
2265 :			$out_options{var} = [$out_options{var}];
2266 :			}
2267 :			# allow params => 'c' as an abbreviation for params => ['c']
2268 :			unless ( ref($out_options{params}) eq 'ARRAY' ) {
2269 :			$out_options{params} = [$out_options{params}];
2270 :			}
2271 :			my ($tolType, $tol);
2272 :			if ($out_options{tolType} eq 'absolute') {
2273 :			$tolType = 'absolute';
2274 :			$tol = $out_options{'tol'};
2275 :			delete($out_options{'relTol'}) if exists( $out_options{'relTol'} );
2276 :			} else {
2277 :			$tolType = 'relative';
2278 :			$tol = $out_options{'relTol'};
2279 :			delete($out_options{'tol'}) if exists( $out_options{'tol'} );
2280 :			}
2281 :
2282 :			my @output_list = ();
2283 :			# thread over lists
2284 :			my @ans_list = ();
2285 :
2286 :			if ( ref($correctAnswer) eq 'ARRAY' ) {
2287 :			@ans_list = @{$correctAnswer};
2288 :			}
2289 :			else {
2290 :			push( @ans_list, $correctAnswer );
2291 :			}
2292 :
2293 :			# produce answer evaluators
2294 :			foreach my $ans (@ans_list) {
2295 :			push(@output_list,
2296 :	chris	22	FUNCTION_CMP( 'correctEqn' => $ans,
2297 :			'var' => $out_options{'var'},
2298 :			'limits' => $out_options{'limits'},
2299 :			'tolerance' => $tol,
2300 :			'tolType' => $tolType,
2301 :			'numPoints' => $out_options{'numPoints'},
2302 :			'mode' => $out_options{'mode'},
2303 :			'maxConstantOfIntegration' => $out_options{'maxConstantOfIntegration'},
2304 :			'zeroLevel' => $out_options{'zeroLevel'},
2305 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
2306 :			'params' => $out_options{'params'},
2307 :			'debug' => $out_options{'debug'},
2308 :	sam	2	),
2309 :			);
2310 :			}
2311 :
2312 :			return @output_list;
2313 :			}
2314 :
2315 :			## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
2316 :			## NOTE: PG_answer_eval is used instead of PG_restricted_eval in order to insure that the answer
2317 :			## evaluated within the context of the package the problem was originally defined in.
2318 :			## Includes multivariable modifications contributed by Professor William K. Ziemer
2319 :			##
2320 :			## IN: a hash consisting of the following keys (error checking to be added later?)
2321 :			## correctEqn -- the correct equation as a string
2322 :			## var -- the variable name as a string,
2323 :			## or a reference to an array of variables
2324 :			## limits -- reference to an array of arrays of type [lower,upper]
2325 :			## tolerance -- the allowable margin of error
2326 :			## tolType -- 'relative' or 'absolute'
2327 :			## numPoints -- the number of points to evaluate the function at
2328 :			## mode -- 'std' or 'antider'
2329 :			## maxConstantOfIntegration -- maximum size of the constant of integration
2330 :			## zeroLevel -- if the correct answer is this close to zero,
2331 :			## then zeroLevelTol applies
2332 :			## zeroLevelTol -- absolute tolerance to allow when answer is close to zero
2333 :
2334 :
2335 :			sub FUNCTION_CMP {
2336 :			my %func_params = @_;
2337 :
2338 :			my $correctEqn = $func_params{'correctEqn'};
2339 :	chris	22	my $var = $func_params{'var'};
2340 :	sam	2	my $ra_limits = $func_params{'limits'};
2341 :	chris	22	my $tol = $func_params{'tolerance'};
2342 :			my $tolType = $func_params{'tolType'};
2343 :	sam	2	my $numPoints = $func_params{'numPoints'};
2344 :	chris	22	my $mode = $func_params{'mode'};
2345 :			my $maxConstantOfIntegration = $func_params{'maxConstantOfIntegration'};
2346 :	sam	2	my $zeroLevel = $func_params{'zeroLevel'};
2347 :			my $zeroLevelTol = $func_params{'zeroLevelTol'};
2348 :
2349 :
2350 :			# Check that everything is defined:
2351 :			$func_params{debug} = 0 unless defined($func_params{debug});
2352 :			$mode = 'std' unless defined($mode);
2353 :			my @VARS = get_var_array( $var );
2354 :			my @limits = get_limits_array( $ra_limits );
2355 :			my @PARAMS = ();
2356 :			@PARAMS = @{$func_params{'params'}} if defined($func_params{'params'});
2357 :
2358 :			if ($mode eq 'antider' ) {
2359 :			# doctor the equation to allow addition of a constant
2360 :			my $CONSTANT_PARAM = 'Q'; # unfortunately parameters must be single letters.
2361 :			# There is the possibility of conflict here.
2362 :			# 'Q' seemed less dangerous than 'C'.
2363 :			$correctEqn = "( $correctEqn ) + $CONSTANT_PARAM";
2364 :			push(@PARAMS, $CONSTANT_PARAM);
2365 :			}
2366 :			my $dim_of_param_space = @PARAMS; # dimension of equivalence space
2367 :
2368 :			if( $tolType eq 'relative' ) {
2369 :			$tol = $functRelPercentTolDefault unless defined $tol;
2370 :			$tol *= .01;
2371 :			}
2372 :			else {
2373 :			$tol = $functAbsTolDefault unless defined $tol;
2374 :			}
2375 :
2376 :			#loop ensures that number of limits matches number of variables
2377 :			for( my $i = 0; $i < scalar(@VARS); $i++ ) {
2378 :			$limits[$i][0] = $functLLimitDefault unless defined $limits[$i][0];
2379 :			$limits[$i][1] = $functULimitDefault unless defined $limits[$i][1];
2380 :			}
2381 :			$numPoints = $functNumOfPoints unless defined $numPoints;
2382 :			$maxConstantOfIntegration = $functMaxConstantOfIntegration unless defined $maxConstantOfIntegration;
2383 :			$zeroLevel = $functZeroLevelDefault unless defined $zeroLevel;
2384 :			$zeroLevelTol = $functZeroLevelTolDefault unless defined $zeroLevelTol;
2385 :
2386 :	chris	22	$func_params{'var'} = $var;
2387 :			$func_params{'limits'} = \@limits;
2388 :			$func_params{'tolerance'} = $tol;
2389 :			$func_params{'tolType'} = $tolType;
2390 :			$func_params{'numPoints'} = $numPoints;
2391 :			$func_params{'mode'} = $mode;
2392 :			$func_params{'maxConstantOfIntegration'} = $maxConstantOfIntegration;
2393 :			$func_params{'zeroLevel'} = $zeroLevel;
2394 :			$func_params{'zeroLevelTol'} = $zeroLevelTol;
2395 :
2396 :	gage	5	########################################################
2397 :			# End of cleanup of calling parameters
2398 :			########################################################
2399 :	sam	2	my $i; #for use with loops
2400 :			my $PGanswerMessage = "";
2401 :			my $originalCorrEqn = $correctEqn;
2402 :
2403 :			#prepare the correct answer and check it's syntax
2404 :	chris	22	my $rh_correct_ans = new AnswerHash;
2405 :	sam	2	$rh_correct_ans->input($correctEqn);
2406 :			$rh_correct_ans = check_syntax($rh_correct_ans);
2407 :			warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag};
2408 :			$rh_correct_ans->clear_error();
2409 :			$rh_correct_ans = function_from_string2($rh_correct_ans, ra_vars => [ @VARS, @PARAMS ],
2410 :			store_in =>'rf_correct_ans',
2411 :			debug => $func_params{debug});
2412 :			my $correct_eqn_sub = $rh_correct_ans->{rf_correct_ans};
2413 :			warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag};
2414 :
2415 :			#create the evaluation points
2416 :			my $random_for_answers = new PGrandom($main::PG_original_problemSeed);
2417 :	chris	22	my $NUMBER_OF_STEPS_IN_RANDOM = 1000; # determines the granularity of the random_for_answers number generator
2418 :	sam	2	my (@evaluation_points);
2419 :			for( my $count = 0; $count < @PARAMS+1+$numPoints; $count++ ) {
2420 :			my (@vars,$iteration_limit);
2421 :			for( my $i = 0; $i < @VARS; $i++ ) {
2422 :			my $iteration_limit = 10;
2423 :			while ( 0 < --$iteration_limit ) { # make sure that the endpoints of the interval are not included
2424 :			$vars[$i] = $random_for_answers->random($limits[$i][0], $limits[$i][1], abs($limits[$i][1] - $limits[$i][0])/$NUMBER_OF_STEPS_IN_RANDOM );
2425 :			last if $vars[$i]!=$limits[$i][0] and $vars[$i]!=$limits[$i][1];
2426 :			}
2427 :			warn "Unable to properly choose evaluation points for this function in the interval ( $limits[$i][0] , $limits[$i][1] )"
2428 :			if $iteration_limit == 0;
2429 :			};
2430 :
2431 :			push(@evaluation_points,\@vars);
2432 :			}
2433 :			my $evaluation_points = Matrix->new_from_array_ref(\@evaluation_points);
2434 :
2435 :			#my $COEFFS = determine_param_coeffs($correct_eqn_sub,$evaluation_points[0],$numOfParameters);
2436 :	chris	22	#warn "coeff", join(" \| ", @{$COEFFS});
2437 :	sam	2
2438 :			#construct the answer evaluator
2439 :			my $answer_evaluator = new AnswerEvaluator;
2440 :			$answer_evaluator->{debug} = $func_params{debug};
2441 :			$answer_evaluator->ans_hash( correct_ans => $originalCorrEqn,
2442 :			rf_correct_ans => $rh_correct_ans->{rf_correct_ans},
2443 :			evaluation_points => \@evaluation_points,
2444 :			ra_param_vars => \@PARAMS,
2445 :			ra_vars => \@VARS,
2446 :			type => 'function',
2447 :			);
2448 :
2449 :			$answer_evaluator->install_pre_filter(\&check_syntax);
2450 :			$answer_evaluator->install_pre_filter(\&function_from_string2, ra_vars => \@VARS,debug=>$func_params{debug},); # @VARS has been guaranteed to be an array, $var might be a single string.
2451 :			$answer_evaluator->install_pre_filter(\&best_approx_parameters, %func_params, param_vars => \@PARAMS);
2452 :			$answer_evaluator->install_evaluator(\&calculate_difference_vector, %func_params);
2453 :			$answer_evaluator->install_evaluator(\&is_zero_array, tol => $tol );
2454 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('SYNTAX'); $rh_ans;} );
2455 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift;
2456 :			if ($rh_ans->catch_error('EVAL') ) {
2457 :			$rh_ans->{ans_message} = $rh_ans->{error_message};
2458 :			$rh_ans->clear_error('EVAL');
2459 :			}
2460 :			$rh_ans;
2461 :			});
2462 :			$answer_evaluator;
2463 :			}
2464 :
2465 :			=head4 Filters
2466 :
2467 :			=pod
2468 :
2469 :			is_array($rh_ans)
2470 :			returns: $rh_ans. Throws error "NOTARRAY" if this is not an array
2471 :
2472 :			=cut
2473 :
2474 :			sub is_array{
2475 :			my $rh_ans = shift;
2476 :			# return if the result is an array
2477 :			return($rh_ans) if ref($rh_ans->{student_ans}) eq 'ARRAY' ;
2478 :			$rh_ans->throw_error("NOTARRAY","The answer is not an array");
2479 :			$rh_ans;
2480 :			}
2481 :
2482 :			=pod
2483 :
2484 :			check_syntax( $rh_ans, %options)
2485 :			returns an answer hash.
2486 :
2487 :			latex2html preview code are installed in the answer hash.
2488 :			The input has been transformed, changing 7pi to 7pi or 7x to 7x.
2489 :			Syntax error messages may be generated and stored in student_ans
2490 :			Additional syntax error messages are stored in {ans_message} and duplicated in {error_message}
2491 :
2492 :
2493 :			=cut
2494 :
2495 :			sub check_syntax {
2496 :			my $rh_ans = shift;
2497 :			my %options = @_;
2498 :			unless ( defined( $rh_ans->{student_ans} ) ) {
2499 :			warn "Check_syntax requires an equation in the field {student_ans} or input";
2500 :			$rh_ans->throw_error("1","{student_ans} field not defined");
2501 :			return $rh_ans;
2502 :			}
2503 :			my $in = $rh_ans->{student_ans};
2504 :			my $parser = new AlgParserWithImplicitExpand;
2505 :			my $ret = $parser -> parse($in); #for use with loops
2506 :
2507 :			if ( ref($ret) ) { ## parsed successfully
2508 :			$parser -> tostring();
2509 :			$parser -> normalize();
2510 :			$rh_ans->input( $parser -> tostring() );
2511 :			$rh_ans->{preview_text_string} = $in;
2512 :			$rh_ans->{preview_latex_string} = $parser -> tolatex();
2513 :
2514 :			} else { ## error in parsing
2515 :
2516 :			$rh_ans->{'student_ans'} = 'syntax error:'. $parser->{htmlerror},
2517 :			$rh_ans->{'ans_message'} = $parser -> {error_msg},
2518 :			$rh_ans->{'preview_text_string'} = '',
2519 :			$rh_ans->{'preview_latex_string'} = '',
2520 :			$rh_ans->throw_error('SYNTAX', 'syntax error in answer:'. $parser->{htmlerror} . "$BR" .$parser -> {error_msg});
2521 :			}
2522 :
2523 :
2524 :
2525 :			$rh_ans;
2526 :
2527 :
2528 :			}
2529 :
2530 :			=pod
2531 :
2532 :			std_num_filter($rh_ans, %options)
2533 :			returns $rh_ans
2534 :
2535 :			Replaces some constants using math_constants, then evaluates a perl expression.
2536 :
2537 :
2538 :			=cut
2539 :
2540 :			sub std_num_filter {
2541 :			my $rh_ans = shift;
2542 :			my %options = @_;
2543 :			my $in = $rh_ans->input();
2544 :			$in = math_constants($in);
2545 :			$rh_ans->{type} = 'std_number';
2546 :			my ($inVal,$PG_eval_errors,$PG_full_error_report);
2547 :			if ($in =~ /\S/) {
2548 :			($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($in);
2549 :			} else {
2550 :			$PG_eval_errors = '';
2551 :			}
2552 :
2553 :			if ($PG_eval_errors) { ##error message from eval or above
2554 :			$rh_ans->{ans_message} = 'There is a syntax error in your answer';
2555 :			$rh_ans->{student_ans} = clean_up_error_msg($PG_eval_errors);
2556 :			} else {
2557 :			$rh_ans->{student_ans} = $inVal;
2558 :			}
2559 :			$rh_ans;
2560 :			}
2561 :
2562 :			=pod
2563 :
2564 :			std_num_array_filter($rh_ans, %options)
2565 :			returns $rh_ans
2566 :
2567 :			Assumes the {student_ans} field is a numerical array, and applies BOTH check_syntax and std_num_filter
2568 :			to each element of the array. Does it's best to generate sensible error messages for syntax errors.
2569 :			A typical error message displayed in {studnet_ans} might be ( 56, error message, -4).
2570 :
2571 :			=cut
2572 :
2573 :			sub std_num_array_filter{
2574 :			my $rh_ans= shift;
2575 :			my %options = @_;
2576 :			my @in = @{$rh_ans->{student_ans}};
2577 :			my $temp_hash = new AnswerHash;
2578 :			my @out=();
2579 :			my $PGanswerMessage = '';
2580 :			foreach my $item (@in) { # evaluate each number in the vector
2581 :			$temp_hash->input($item);
2582 :			$temp_hash = check_syntax($temp_hash);
2583 :			if (defined($temp_hash->{error_flag}) and $temp_hash->{error_flag} eq 'SYNTAX') {
2584 :			$PGanswerMessage .= $temp_hash->{ans_message};
2585 :			$temp_hash->{ans_message} = undef;
2586 :			} else {
2587 :			#continue processing
2588 :			$temp_hash = std_num_filter($temp_hash);
2589 :			if (defined($temp_hash->{ans_message}) and $temp_hash->{ans_message} ) {
2590 :			$PGanswerMessage .= $temp_hash->{ans_message};
2591 :			$temp_hash->{ans_message} = undef;
2592 :			}
2593 :			}
2594 :			push(@out, $temp_hash->input());
2595 :
2596 :			}
2597 :			if ($PGanswerMessage) {
2598 :			$rh_ans->input( "( " . join(", ", @out ) . " )" );
2599 :	chris	22	$rh_ans->throw_error('SYNTAX', 'There is a syntax error in your answer.');
2600 :	sam	2	} else {
2601 :			$rh_ans->input( [@out] );
2602 :			}
2603 :			$rh_ans;
2604 :			}
2605 :
2606 :
2607 :
2608 :			sub function_from_string2 {
2609 :			my $rh_ans = shift;
2610 :			my %options = @_;
2611 :			my $eqn = $rh_ans->{student_ans};
2612 :			set_default_options( \%options,
2613 :			'store_in' => 'rf_student_ans',
2614 :			'ra_vars' => [qw( x y )],
2615 :			'debug' => 0,
2616 :			);
2617 :			my @VARS = @{ $options{ 'ra_vars'}};
2618 :			warn "VARS = ", join("<>", @VARS) if defined($options{debug}) and $options{debug} ==1;
2619 :			my $originalEqn = $eqn;
2620 :			$eqn = &math_constants($eqn);
2621 :			for( my $i = 0; $i < @VARS; $i++ ) {
2622 :			$eqn =~ s/\b$VARS[$i]\b/\$VARS[$i]/g;
2623 :			}
2624 :			warn "equation evaluated = $eqn",$rh_ans->pretty_print(), "<br>\noptions<br>\n",
2625 :			pretty_print(\%options)
2626 :			if defined($options{debug}) and $options{debug} ==1;
2627 :			my ($function_sub,$PG_eval_errors, $PG_full_errors) = PG_answer_eval( q!
2628 :			sub {
2629 :			my @VARS = @_;
2630 :			my $input_str = '';
2631 :			for( my $i=0; $i<@VARS; $i++ ) {
2632 :			$input_str .= "\$VARS[$i] = $VARS[$i]; ";
2633 :			}
2634 :			my $PGanswerMessage;
2635 :			$input_str .= '! . $eqn . q!'; # need the single quotes to keep the contents of $eqn from being
2636 :			# evaluated when it is assigned to $input_str;
2637 :			my ($out, $PG_eval_errors, $PG_full_errors) = PG_answer_eval($input_str); #Finally evaluated
2638 :
2639 :			if ( defined($PG_eval_errors) and $PG_eval_errors =~ /\S/ ) {
2640 :			$PGanswerMessage = clean_up_error_msg($PG_eval_errors);
2641 :			# This message seemed too verbose, but it does give extra information, we'll see if it is needed.
2642 :			# "<br> There was an error in evaluating your function <br>
2643 :			# !. $originalEqn . q! <br>
2644 :			# at ( " . join(', ', @VARS) . " ) <br>
2645 :			# $PG_eval_errors
2646 :			# "; # this message appears in the answer section which is not process by Latex2HTML so it must
2647 :			# # be in HTML. That is why $BR is NOT used.
2648 :
2649 :			}
2650 :			(wantarray) ? ($out, $PGanswerMessage): $out; # PGanswerMessage may be undefined.
2651 :			};
2652 :			!);
2653 :
2654 :			if (defined($PG_eval_errors) and $PG_eval_errors =~/\S/ ) {
2655 :			$PG_eval_errors = clean_up_error_msg($PG_eval_errors);
2656 :
2657 :			my $PGanswerMessage = "There was an error in converting the expression
2658 :			$main::BR $originalEqn $main::BR into a function.
2659 :			$main::BR $PG_eval_errors.";
2660 :			$rh_ans->{rf_student_ans} = $function_sub;
2661 :			$rh_ans->{ans_message} = $PGanswerMessage;
2662 :			$rh_ans->{error_message} = $PGanswerMessage;
2663 :			$rh_ans->{error_flag} = 1;
2664 :			# we couldn't compile the equation, we'll return an error message.
2665 :			} else {
2666 :			# if (defined($options{store_in} )) {
2667 :			# $rh_ans ->{$options{store_in}} = $function_sub;
2668 :			# } else {
2669 :			# $rh_ans->{rf_student_ans} = $function_sub;
2670 :			# }
2671 :			$rh_ans ->{$options{store_in}} = $function_sub;
2672 :
2673 :			}
2674 :
2675 :			$rh_ans;
2676 :			}
2677 :
2678 :
2679 :			sub is_zero_array{
2680 :			my $rh_ans = shift;
2681 :			my %options = @_;
2682 :			my $array = $rh_ans -> {ra_differences};
2683 :			my $num = @$array;
2684 :			my $i;
2685 :			my $max = 0; my $mm;
2686 :			for ($i=0; $i< $num; $i++) {
2687 :			$mm = $array->[$i] ;
2688 :			if (not is_a_number($mm) ) {
2689 :			$max = $mm; # break out if one of the elements is not a number
2690 :			last;
2691 :			}
2692 :			$max = abs($mm) if abs($mm) > $max;
2693 :			}
2694 :			if (not is_a_number($max)) {
2695 :			$rh_ans->{score} = 0;
2696 :			my $error = "WeBWorK was unable evaluate your function. Please check that your
2697 :			expression doesn't take roots of negative numbers, or divide by zero.";
2698 :			$rh_ans->throw_error('EVAL',$error);
2699 :			} else {
2700 :			my $tol = $options{tol} if defined($options{tol});
2701 :	gage	5	#$tol = 0.01*$options{reltol} if defined($options{reltol});
2702 :	sam	2	$tol = .000001 unless defined($tol);
2703 :
2704 :			$rh_ans->{score} = ($max <$tol) ? 1: 0; # 1 if the array is close to 0;
2705 :			}
2706 :			$rh_ans;
2707 :			}
2708 :			=pod
2709 :
2710 :			best_approx_parameters($rh_ans,%options);
2711 :			{rf_student_ans} # reference to the test answer
2712 :			{rf_correct_ans} # reference to the comparison answer
2713 :			{evaluation_points}, # an array of row vectors indicating the points
2714 :			# to evaluate when comparing the functions
2715 :			%options # debug => 1 gives more error answers
2716 :			# param_vars => [''] additional parameters used to adapt to function
2717 :			)
2718 :			returns $rh_ans;
2719 :			The parameters for the comparison function which best approximates the test_function are stored
2720 :			in the field {ra_parameters}.
2721 :
2722 :			The last $dim_of_parms_space variables are assumed to be parameters, and it is also
2723 :			assumed that the function \&comparison_fun
2724 :			depends linearly on these variables. This function finds the values for these parameters which minimizes the
2725 :			Euclidean distance (L2 distance) between the test function and the comparison function and the test points specified
2726 :			by the array reference \@rows_of_test_points. This is assumed to be an array of arrays, with the inner arrays
2727 :			determining a test point.
2728 :
2729 :			The comparison function should have $dim_of_params_space more input variables than the test function.
2730 :
2731 :			=cut
2732 :
2733 :
2734 :
2735 :
2736 :
2737 :			# =pod
2738 :			#
2739 :			# Used internally:
2740 :			#
2741 :			# &$determine_param_coeff( $rf_comparison_function # a reference to the correct answer function
2742 :			# $ra_variables # an array of the active input variables to the functions
2743 :			# $dim_of_params_space # indicates the number of parameters upon which the
2744 :			# # the comparison function depends linearly. These are assumed to
2745 :			# # be the last group of inputs to the comparison function.
2746 :			#
2747 :			# %options # $options{debug} gives more error messages
2748 :			#
2749 :			# # A typical function might look like
2750 :			# # f(x,y,z,a,b) = x^2+acos(xz) + bsin(x) with a parameter
2751 :			# # space of dimension 2 and a variable space of dimension 3.
2752 :			# )
2753 :			# # returns a list of coefficients
2754 :			#
2755 :			# =cut
2756 :
2757 :
2758 :			sub best_approx_parameters{
2759 :			my $rh_ans = shift;
2760 :			my %options = @_;
2761 :			my $errors = undef;
2762 :			# This subroutine for the determining the coefficents of the parameters at a given point
2763 :			# is pretty specialized, so it is included here as a sub-subroutine.
2764 :			my $determine_param_coeffs = sub {
2765 :			my ($rf_fun, $ra_variables, $dim_of_params_space, %options) =@_;
2766 :			my @zero_params=();
2767 :			for(my $i=1;$i<=$dim_of_params_space;$i++){push(@zero_params,0); }
2768 :			my @vars = @$ra_variables;
2769 :			my @coeff = ();
2770 :			my @inputs = (@vars,@zero_params);
2771 :			my ($f0, $f1, $err);
2772 :			($f0, $err) = &{$rf_fun}(@inputs);
2773 :			if (defined($err) ) {
2774 :			$errors .= "$err ";
2775 :			} else {
2776 :			for (my $i=@vars;$i<@inputs;$i++) {
2777 :			$inputs[$i]=1; # set one parameter to 1;
2778 :			my($f1,$err) = &$rf_fun(@inputs);
2779 :			if (defined($err) ) {
2780 :			$errors .= " $err ";
2781 :			} else {
2782 :			push(@coeff, $f1-$f0);
2783 :			}
2784 :			$inputs[$i]=0; # set it back
2785 :			}
2786 :			}
2787 :			(\@coeff, $errors);
2788 :			};
2789 :			my $rf_fun = $rh_ans->{rf_student_ans};
2790 :			my $rf_correct_fun = $rh_ans->{rf_correct_ans};
2791 :			my $ra_vars_matrix = $rh_ans->{evaluation_points};
2792 :			my $dim_of_param_space = @{$options{param_vars}};
2793 :			# Short cut. Bail if there are no param_vars
2794 :			unless ($dim_of_param_space >0) {
2795 :	gage	5	$rh_ans ->{ra_parameters} = [];
2796 :	sam	2	return $rh_ans;
2797 :			}
2798 :			# inputs are row arrays in this case.
2799 :			my @zero_params=();
2800 :
2801 :			for(my $i=1;$i<=$dim_of_param_space;$i++){push(@zero_params,0); }
2802 :			my @rows_of_vars = @$ra_vars_matrix;
2803 :			warn "input rows ", pretty_print(\@rows_of_vars) if defined($options{debug}) and $options{debug};
2804 :			my $rows = @rows_of_vars;
2805 :			my $matrix =new Matrix($rows,$dim_of_param_space);
2806 :			my $rhs_vec = new Matrix($rows, 1);
2807 :			my $row_num = 1;
2808 :			my ($ra_coeff,$val2, $val1, $err1,$err2,@inputs,@vars);
2809 :			my $number_of_data_points = $dim_of_param_space +2;
2810 :			while (@rows_of_vars and $row_num <= $number_of_data_points) {
2811 :
2812 :			# get one set of data points from the test function;
2813 :			@vars = @{ shift(@rows_of_vars) };
2814 :			($val2, $err1) = &{$rf_fun}(@vars);
2815 :			$errors .= " $err1 " if defined($err1);
2816 :			@inputs = (@vars,@zero_params);
2817 :			($val1, $err2) = &{$rf_correct_fun}(@inputs);
2818 :			$errors .= " $err2 " if defined($err2);
2819 :
2820 :			unless (defined($err1) or defined($err2) ) {
2821 :			$rhs_vec->assign($row_num,1, $val2-$val1 );
2822 :
2823 :			# warn "rhs data val1=$val1, val2=$val2, val2 - val1 = ", $val2 - $val1 if $options{debug};
2824 :			# warn "vars ", join(" \| ", @vars) if $options{debug};
2825 :
2826 :			($ra_coeff, $err1) = &{$determine_param_coeffs}($rf_correct_fun,\@vars,$dim_of_param_space,%options);
2827 :			if (defined($err1) ) {
2828 :			$errors .= " $err1 ";
2829 :			} else {
2830 :			my @coeff = @$ra_coeff;
2831 :			my $col_num=1;
2832 :			while(@coeff) {
2833 :			$matrix->assign($row_num,$col_num, shift(@coeff) );
2834 :			$col_num++;
2835 :			}
2836 :			}
2837 :	gage	5
2838 :	sam	2	}
2839 :			$row_num++;
2840 :			last if $errors; # break if there are any errors.
2841 :			# This cuts down on the size of error messages.
2842 :			# However it impossible to check for equivalence at 95% of points
2843 :	gage	5	# which might be useful for functions that are not defined at some points.
2844 :	sam	2	}
2845 :			warn "<br> best_approx_parameters: matrix1 <br> ", " $matrix " if $options{debug};
2846 :			warn "<br> best_approx_parameters: vector <br> ", " $rhs_vec " if $options{debug};
2847 :
2848 :			# we have Matrix * parameter = data_vec + perpendicular vector
2849 :			# where the matrix has column vectors defining the span of the parameter space
2850 :			# multiply both sides by Matrix_transpose and solve for the parameters
2851 :			# This is exactly what the method proj_coeff method does.
2852 :			my @array;
2853 :			if (defined($errors) ) {
2854 :			@array = (); # new Matrix($dim_of_param_space,1);
2855 :			} else {
2856 :			@array = $matrix->proj_coeff($rhs_vec)->list();
2857 :			}
2858 :			# check size (hack)
2859 :			my $max = 0;
2860 :			foreach my $val (@array ) {
2861 :			$max = abs($val) if $max < abs($val);
2862 :			if (not is_a_number($val) ) {
2863 :			$max = "NaN: $val";
2864 :			last;
2865 :			}
2866 :			}
2867 :			if ($max =~/NaN/) {
2868 :			$errors .= "WeBWorK was unable evaluate your function. Please check that your
2869 :			expression doesn't take roots of negative numbers, or divide by zero.";
2870 :			} elsif ($max > $options{maxConstantOfIntegration} ) {
2871 :			$errors .= "At least one of the adapting parameters
2872 :			(perhaps the constant of integration) is too large: $max,
2873 :			( the maximum allowed is $options{maxConstantOfIntegration} )";
2874 :			}
2875 :
2876 :			$rh_ans->{ra_parameters} = \@array;
2877 :			$rh_ans->throw_error('EVAL', $errors) if defined($errors);
2878 :			$rh_ans;
2879 :			}
2880 :
2881 :			=pod
2882 :
2883 :			calculate_difference_vector( $ans_hash, %options);
2884 :
2885 :			{rf_student_ans}, # a reference to the test function
2886 :			{rf_correct_ans}, # a reference to the correct answer function
2887 :			{evaluation_points}, # an array of row vectors indicating the points
2888 :			# to evaluate when comparing the functions
2889 :			{ra_parameters} # these are the (optional) additional inputs to
2890 :			# the comparison function which adapt it properly
2891 :			# to the problem at hand.
2892 :
2893 :			%options # mode => 'rel' specifies that each element in the
2894 :			# difference matrix is divided by the correct answer.
2895 :			# unless the correct answer is nearly 0.
2896 :			)
2897 :
2898 :			=cut
2899 :
2900 :
2901 :			sub calculate_difference_vector {
2902 :			my $rh_ans = shift;
2903 :			my %options = @_;
2904 :			# initialize
2905 :			my $rf_fun = $rh_ans -> {rf_student_ans};
2906 :			my $rf_correct_fun = $rh_ans -> {rf_correct_ans};
2907 :			my $ra_parameters = $rh_ans ->{ra_parameters};
2908 :			my @evaluation_points = @{$rh_ans->{evaluation_points} };
2909 :			my @parameters = ();
2910 :			@parameters = @$ra_parameters if defined($ra_parameters) and ref($ra_parameters) eq 'ARRAY';
2911 :			my $errors = undef;
2912 :	gage	5	my @zero_params=();
2913 :			for(my $i=1;$i<=@{$ra_parameters};$i++){push(@zero_params,0); }
2914 :	sam	2	my @differences = ();
2915 :	gage	5	my @student_values;
2916 :			my @correct_values;
2917 :			my @tol_values;
2918 :			my ($diff,$tol_val);
2919 :	sam	2	# calculate the vector of differences between the test function and the comparison function.
2920 :			while (@evaluation_points) {
2921 :	gage	5	my ($err1, $err2,$err3);
2922 :	sam	2	my @vars = @{ shift(@evaluation_points) };
2923 :			my @inputs = (@vars, @parameters);
2924 :			my ($inVal, $correctVal);
2925 :			($inVal, $err1) = &{$rf_fun}(@vars);
2926 :			$errors .= " $err1 " if defined($err1);
2927 :	gage	5	$errors .= " Error detected evaluating student input at (".join(' , ',@vars) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err1);
2928 :	sam	2	($correctVal, $err2) =&{$rf_correct_fun}(@inputs);
2929 :			$errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err2 " if defined($err2);
2930 :	gage	5	$errors .= " Error detected evaluating correct answer at (".join(' , ',@inputs) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err2);
2931 :			($tol_val,$err3)= &$rf_correct_fun(@vars, @zero_params);
2932 :			$errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err3 " if defined($err3);
2933 :			$errors .= " Error detected evaluating correct answer at (".join(' , ',@vars, @zero_params) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err3);
2934 :			unless (defined($err1) or defined($err2) or defined($err3) ) {
2935 :			$diff = ( $inVal - ($correctVal -$tol_val ) ) - $tol_val; #prevents entering too high a number?
2936 :	sam	2	#warn "taking the difference of ", $inVal, " and ", $correctVal, " is ", $diff;
2937 :
2938 :			if (defined($options{tolType}) and $options{tolType} eq 'relative' ) { #relative tolerance
2939 :	gage	5	#warn "diff = $diff";
2940 :
2941 :	chris	22	$diff = ( $inVal - ($correctVal-$tol_val ) )/abs($tol_val) -1 if abs($tol_val) > $options{zeroLevel};
2942 :	gage	5	#$diff = ( $inVal - ($correctVal-$tol_val- $tol_val ) )/abs($tol_val) if abs($tol_val) > $options{zeroLevel};
2943 :			#warn "diff = $diff, ", abs( &$rf_correct_fun(@inputs) ) , "-- $correctVal";
2944 :	sam	2	}
2945 :			}
2946 :			last if $errors; # break if there are any errors.
2947 :			# This cuts down on the size of error messages.
2948 :			# However it impossible to check for equivalence at 95% of points
2949 :	gage	5	# which might be useful for functions that are not defined at some points.
2950 :			push(@student_values,$inVal);
2951 :			push(@correct_values,( $inVal - ($correctVal-$tol_val ) ));
2952 :	sam	2	push(@differences, $diff);
2953 :	gage	5	push(@tol_values,$tol_val);
2954 :	sam	2	}
2955 :			$rh_ans ->{ra_differences} = \@differences;
2956 :	chris	22	$rh_ans ->{ra_student_values} = \@student_values;
2957 :			$rh_ans ->{ra_adjusted_student_values} = \@correct_values;
2958 :			$rh_ans->{ra_tol_values}=\@tol_values;
2959 :	sam	2	$rh_ans->throw_error('EVAL', $errors) if defined($errors);
2960 :			$rh_ans;
2961 :			}
2962 :
2963 :
2964 :			##########################################################################
2965 :			##########################################################################
2966 :			## String answer evaluators
2967 :
2968 :			=head2 String Answer Evaluators
2969 :
2970 :			String answer evaluators compare a student string to the correct string.
2971 :			Different filters can be applied to allow various degrees of variation.
2972 :			Both the student and correct answers are subject to the same filters, to
2973 :			ensure that there are no unexpected matches or rejections.
2974 :
2975 :			String Filters
2976 :
2977 :			remove_whitespace -- Removes all whitespace from the string.
2978 :			It applies the following substitution
2979 :			to the string:
2980 :			$filteredAnswer =~ s/\s+//g;
2981 :
2982 :			compress_whitespace -- Removes leading and trailing whitespace, and
2983 :			replaces all other blocks of whitespace by a
2984 :			single space. Applies the following substitutions:
2985 :			$filteredAnswer =~ s/^\s*//;
2986 :			$filteredAnswer =~ s/\s*$//;
2987 :			$filteredAnswer =~ s/\s+/ /g;
2988 :
2989 :			trim_whitespace -- Removes leading and trailing whitespace.
2990 :			Applies the following substitutions:
2991 :			$filteredAnswer =~ s/^\s*//;
2992 :			$filteredAnswer =~ s/\s*$//;
2993 :
2994 :			ignore_case -- Ignores the case of the string. More accurately,
2995 :			it converts the string to uppercase (by convention).
2996 :			Applies the following function:
2997 :			$filteredAnswer = uc $filteredAnswer;
2998 :
2999 :			ignore_order -- Ignores the order of the letters in the string.
3000 :			This is used for problems of the form "Choose all
3001 :			that apply." Specifically, it removes all
3002 :			whitespace and lexically sorts the letters in
3003 :			ascending alphabetical order. Applies the following
3004 :			functions:
3005 :			$filteredAnswer = join( "", lex_sort(
3006 :			split( /\s*/, $filteredAnswer ) ) );
3007 :
3008 :			=cut
3009 :
3010 :			################################
3011 :			## STRING ANSWER FILTERS
3012 :
3013 :			## IN: --the string to be filtered
3014 :			## --a list of the filters to use
3015 :			##
3016 :			## OUT: --the modified string
3017 :			##
3018 :			## Use this subroutine instead of the
3019 :			## individual filters below it
3020 :			sub str_filters {
3021 :			my $stringToFilter = shift @_;
3022 :			my @filters_to_use = @_;
3023 :			my %known_filters = ( 'remove_whitespace' => undef,
3024 :			'compress_whitespace' => undef,
3025 :			'trim_whitespace' => undef,
3026 :			'ignore_case' => undef,
3027 :			'ignore_order' => undef
3028 :			);
3029 :
3030 :			#test for unknown filters
3031 :			my $filter;
3032 :			foreach $filter (@filters_to_use) {
3033 :			die "Unknown string filter $filter (try checking the parameters to str_cmp() )"
3034 :			unless exists $known_filters{$filter};
3035 :			}
3036 :
3037 :			if( grep( /remove_whitespace/i, @filters_to_use ) ) {
3038 :			$stringToFilter = remove_whitespace( $stringToFilter );
3039 :			}
3040 :			if( grep( /compress_whitespace/i, @filters_to_use ) ) {
3041 :			$stringToFilter = compress_whitespace( $stringToFilter );
3042 :			}
3043 :			if( grep( /trim_whitespace/i, @filters_to_use ) ) {
3044 :			$stringToFilter = trim_whitespace( $stringToFilter );
3045 :			}
3046 :			if( grep( /ignore_case/i, @filters_to_use ) ) {
3047 :			$stringToFilter = ignore_case( $stringToFilter );
3048 :			}
3049 :			if( grep( /ignore_order/i, @filters_to_use ) ) {
3050 :			$stringToFilter = ignore_order( $stringToFilter );
3051 :			}
3052 :
3053 :			return $stringToFilter;
3054 :			}
3055 :
3056 :			sub remove_whitespace {
3057 :			my $filteredAnswer = shift;
3058 :
3059 :			$filteredAnswer =~ s/\s+//g; # remove all whitespace
3060 :
3061 :			return $filteredAnswer;
3062 :			}
3063 :
3064 :			sub compress_whitespace {
3065 :			my $filteredAnswer = shift;
3066 :
3067 :			$filteredAnswer =~ s/^\s*//; # remove initial whitespace
3068 :			$filteredAnswer =~ s/\s*$//; # remove trailing whitespace
3069 :			$filteredAnswer =~ s/\s+/ /g; # replace spaces by single space
3070 :
3071 :			return $filteredAnswer;
3072 :			}
3073 :
3074 :			sub trim_whitespace {
3075 :			my $filteredAnswer = shift;
3076 :
3077 :			$filteredAnswer =~ s/^\s*//; # remove initial whitespace
3078 :			$filteredAnswer =~ s/\s*$//; # remove trailing whitespace
3079 :
3080 :			return $filteredAnswer;
3081 :			}
3082 :
3083 :			sub ignore_case {
3084 :			my $filteredAnswer = shift;
3085 :
3086 :			$filteredAnswer = uc $filteredAnswer;
3087 :
3088 :			return $filteredAnswer;
3089 :			}
3090 :
3091 :			sub ignore_order {
3092 :			my $filteredAnswer = shift;
3093 :
3094 :			$filteredAnswer = join( "", lex_sort( split( /\s*/, $filteredAnswer ) ) );
3095 :
3096 :			return $filteredAnswer;
3097 :			}
3098 :			################################
3099 :			## END STRING ANSWER FILTERS
3100 :
3101 :			=head3 "mode"_str_cmp functions
3102 :
3103 :			The functions of the the form "mode"_str_cmp() use different functions to
3104 :			specify which filters to apply. They take no options except the correct
3105 :			string. There are also versions which accept a list of strings.
3106 :
3107 :			std_str_cmp( $correctString )
3108 :			std_str_cmp_list( @correctStringList )
3109 :			Filters: compress_whitespace, ignore_case
3110 :
3111 :			std_cs_str_cmp( $correctString )
3112 :			std_cs_str_cmp_list( @correctStringList )
3113 :			Filters: compress_whitespace
3114 :
3115 :			strict_str_cmp( $correctString )
3116 :			strict_str_cmp_list( @correctStringList )
3117 :			Filters: trim_whitespace
3118 :
3119 :			unordered_str_cmp( $correctString )
3120 :			unordered_str_cmp_list( @correctStringList )
3121 :			Filters: ignore_order, ignore_case
3122 :
3123 :			unordered_cs_str_cmp( $correctString )
3124 :			unordered_cs_str_cmp_list( @correctStringList )
3125 :			Filters: ignore_order
3126 :
3127 :			ordered_str_cmp( $correctString )
3128 :			ordered_str_cmp_list( @correctStringList )
3129 :			Filters: remove_whitespace, ignore_case
3130 :
3131 :			ordered_cs_str_cmp( $correctString )
3132 :			ordered_cs_str_cmp_list( @correctStringList )
3133 :			Filters: remove_whitespace
3134 :
3135 :			Examples
3136 :
3137 :			ANS( std_str_cmp( "W. Mozart" ) ) -- Accepts "W. Mozart", "W. MOZarT",
3138 :			and so forth. Case insensitive. All internal spaces treated
3139 :			as single spaces.
3140 :			ANS( std_cs_str_cmp( "Mozart" ) ) -- Rejects "mozart". Same as
3141 :			std_str_cmp() but case sensitive.
3142 :			ANS( strict_str_cmp( "W. Mozart" ) ) -- Accepts only the exact string.
3143 :			ANS( unordered_str_cmp( "ABC" ) ) -- Accepts "a c B", "CBA" and so forth.
3144 :			Unordered, case insensitive, spaces ignored.
3145 :			ANS( unordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc". Same as
3146 :			unordered_str_cmp() but case sensitive.
3147 :			ANS( ordered_str_cmp( "ABC" ) ) -- Accepts "a b C", "A B C" and so forth.
3148 :			Ordered, case insensitive, spaces ignored.
3149 :			ANS( ordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc", accepts "A BC" and
3150 :			so forth. Same as ordered_str_cmp() but case sensitive.
3151 :
3152 :			=cut
3153 :
3154 :			sub std_str_cmp { # compare strings
3155 :			my $correctAnswer = shift @_;
3156 :			my @filters = ( 'compress_whitespace', 'ignore_case' );
3157 :			my $type = 'std_str_cmp';
3158 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3159 :			'filters' => \@filters,
3160 :			'type' => $type
3161 :			);
3162 :			}
3163 :
3164 :			sub std_str_cmp_list { # alias for std_str_cmp
3165 :			my @answerList = @_;
3166 :			my @output;
3167 :			while (@answerList) {
3168 :			push( @output, std_str_cmp(shift @answerList) );
3169 :			}
3170 :			@output;
3171 :			}
3172 :
3173 :			sub std_cs_str_cmp { # compare strings case sensitive
3174 :			my $correctAnswer = shift @_;
3175 :			my @filters = ( 'compress_whitespace' );
3176 :			my $type = 'std_cs_str_cmp';
3177 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3178 :			'filters' => \@filters,
3179 :			'type' => $type
3180 :			);
3181 :			}
3182 :
3183 :			sub std_cs_str_cmp_list { # alias for std_cs_str_cmp
3184 :			my @answerList = @_;
3185 :			my @output;
3186 :			while (@answerList) {
3187 :			push( @output, std_cs_str_cmp(shift @answerList) );
3188 :			}
3189 :			@output;
3190 :			}
3191 :
3192 :			sub strict_str_cmp { # strict string compare
3193 :			my $correctAnswer = shift @_;
3194 :			my @filters = ( 'trim_whitespace' );
3195 :			my $type = 'strict_str_cmp';
3196 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3197 :			'filters' => \@filters,
3198 :			'type' => $type
3199 :			);
3200 :			}
3201 :
3202 :			sub strict_str_cmp_list { # alias for strict_str_cmp
3203 :			my @answerList = @_;
3204 :			my @output;
3205 :			while (@answerList) {
3206 :			push( @output, strict_str_cmp(shift @answerList) );
3207 :			}
3208 :			@output;
3209 :			}
3210 :
3211 :			sub unordered_str_cmp { # unordered, case insensitive, spaces ignored
3212 :			my $correctAnswer = shift @_;
3213 :			my @filters = ( 'ignore_order', 'ignore_case' );
3214 :			my $type = 'unordered_str_cmp';
3215 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3216 :			'filters' => \@filters,
3217 :			'type' => $type
3218 :			);
3219 :			}
3220 :
3221 :			sub unordered_str_cmp_list { # alias for unordered_str_cmp
3222 :			my @answerList = @_;
3223 :			my @output;
3224 :			while (@answerList) {
3225 :			push( @output, unordered_str_cmp(shift @answerList) );
3226 :			}
3227 :			@output;
3228 :			}
3229 :
3230 :			sub unordered_cs_str_cmp { # unordered, case sensitive, spaces ignored
3231 :			my $correctAnswer = shift @_;
3232 :			my @filters = ( 'ignore_order' );
3233 :			my $type = 'unordered_cs_str_cmp';
3234 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3235 :			'filters' => \@filters,
3236 :			'type' => $type
3237 :			);
3238 :			}
3239 :
3240 :			sub unordered_cs_str_cmp_list { # alias for unordered_cs_str_cmp
3241 :			my @answerList = @_;
3242 :			my @output;
3243 :			while (@answerList) {
3244 :			push( @output, unordered_cs_str_cmp(shift @answerList) );
3245 :			}
3246 :			@output;
3247 :			}
3248 :
3249 :			sub ordered_str_cmp { # ordered, case insensitive, spaces ignored
3250 :			my $correctAnswer = shift @_;
3251 :			my @filters = ( 'remove_whitespace', 'ignore_case' );
3252 :			my $type = 'ordered_str_cmp';
3253 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3254 :			'filters' => \@filters,
3255 :			'type' => $type
3256 :			);
3257 :			}
3258 :
3259 :			sub ordered_str_cmp_list { # alias for ordered_str_cmp
3260 :			my @answerList = @_;
3261 :			my @output;
3262 :			while (@answerList) {
3263 :			push( @output, ordered_str_cmp(shift @answerList) );
3264 :			}
3265 :			@output;
3266 :
3267 :			}
3268 :
3269 :			sub ordered_cs_str_cmp { # ordered, case sensitive, spaces ignored
3270 :			my $correctAnswer = shift @_;
3271 :			my @filters = ( 'remove_whitespace' );
3272 :			my $type = 'ordered_cs_str_cmp';
3273 :			STR_CMP( 'correctAnswer' => $correctAnswer,
3274 :			'filters' => \@filters,
3275 :			'type' => $type
3276 :			);
3277 :			}
3278 :
3279 :			sub ordered_cs_str_cmp_list { # alias for ordered_cs_str_cmp
3280 :			my @answerList = @_;
3281 :			my @output;
3282 :			while (@answerList) {
3283 :			push( @output, ordered_cs_str_cmp(shift @answerList) );
3284 :			}
3285 :			@output;
3286 :			}
3287 :
3288 :			=head3 str_cmp()
3289 :
3290 :			Compares a string or a list of strings, using a named hash of options to set
3291 :			parameters. This can make for more readable code than using the "mode"_str_cmp()
3292 :			style, but some people find one or the other easier to remember.
3293 :
3294 :			ANS( str_cmp( answer or answer_array_ref, options_hash ) );
3295 :
3296 :			1. the correct answer or a reference to an array of answers
3297 :			2. either a list of filters, or:
3298 :			a hash consisting of
3299 :			filters - a reference to an array of filters
3300 :
3301 :			Returns an answer evaluator, or (if given a reference to an array of answers),
3302 :			a list of answer evaluators
3303 :
3304 :			FILTERS:
3305 :
3306 :			remove_whitespace -- removes all whitespace
3307 :			compress_whitespace -- removes whitespace from the beginning and end of the string,
3308 :			and treats one or more whitespace characters in a row as a
3309 :			single space (true by default)
3310 :			trim_whitespace -- removes whitespace from the beginning and end of the string
3311 :			ignore_case -- ignores the case of the letters (true by default)
3312 :			ignore_order -- ignores the order in which letters are entered
3313 :
3314 :			EXAMPLES:
3315 :
3316 :			str_cmp( "Hello" ) -- matches "Hello", " hello" (same as std_str_cmp() )
3317 :			str_cmp( ["Hello", "Goodbye"] ) -- same as std_str_cmp_list()
3318 :			str_cmp( " hello ", trim_whitespace ) -- matches "hello", " hello "
3319 :			str_cmp( "ABC", filters => 'ignore_order' ) -- matches "ACB", "A B C", but not "abc"
3320 :			str_cmp( "D E F", remove_whitespace, ignore_case ) -- matches "def" and "d e f" but not "fed"
3321 :
3322 :			=cut
3323 :
3324 :			sub str_cmp {
3325 :			my $correctAnswer = shift @_;
3326 :			$correctAnswer = '' unless defined($correctAnswer);
3327 :			my @options = @_;
3328 :			my $ra_filters;
3329 :
3330 :			# error-checking for filters occurs in the filters() subroutine
3331 :			if( not defined( $options[0] ) ) { # used with no filters as alias for std_str_cmp()
3332 :			@options = ( 'compress_whitespace', 'ignore_case' );
3333 :			}
3334 :
3335 :			if( $options[0] eq 'filters' ) { # using filters => [f1, f2, ...] notation
3336 :			$ra_filters = $options[1];
3337 :			}
3338 :			else { # using a list of filters
3339 :			$ra_filters = \@options;
3340 :			}
3341 :
3342 :			# thread over lists
3343 :			my @ans_list = ();
3344 :
3345 :			if ( ref($correctAnswer) eq 'ARRAY' ) {
3346 :			@ans_list = @{$correctAnswer};
3347 :			}
3348 :			else {
3349 :			push( @ans_list, $correctAnswer );
3350 :			}
3351 :
3352 :			# final_answer;
3353 :			my @output_list = ();
3354 :
3355 :			foreach my $ans (@ans_list) {
3356 :			push(@output_list, STR_CMP( 'correctAnswer' => $ans,
3357 :			'filters' => $ra_filters,
3358 :			'type' => 'str_cmp'
3359 :			)
3360 :			);
3361 :			}
3362 :
3363 :			return @output_list;
3364 :			}
3365 :
3366 :			## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
3367 :			##
3368 :			## IN: a hashtable with the following entries (error-checking to be added later?):
3369 :			## correctAnswer -- the correct answer, before filtering
3370 :			## filters -- reference to an array containing the filters to be applied
3371 :			## type -- a string containing the type of answer evaluator in use
3372 :			## OUT: a reference to an answer evaluator subroutine
3373 :			sub STR_CMP {
3374 :			my %str_params = @_;
3375 :
3376 :			$str_params{'correctAnswer'} = str_filters( $str_params{'correctAnswer'}, @{$str_params{'filters'}} );
3377 :
3378 :			my $answer_evaluator = sub {
3379 :			my $in = shift @_;
3380 :			$in = '' unless defined $in;
3381 :			my $original_student_ans = $in;
3382 :
3383 :			$in = str_filters( $in, @{$str_params{'filters'}} );
3384 :
3385 :			my $correctQ = ( $in eq $str_params{'correctAnswer'} ) ? 1: 0;
3386 :			my $ans_hash = new AnswerHash(
3387 :			'score' => $correctQ,
3388 :			'correct_ans' => $str_params{'correctAnswer'},
3389 :			'student_ans' => $in,
3390 :			'ans_message' => '',
3391 :			'type' => $str_params{'type'},
3392 :			'preview_text_string' => $in,
3393 :			'preview_latex_string' => $in,
3394 :			'original_student_ans' => $original_student_ans
3395 :			);
3396 :
3397 :			return $ans_hash;
3398 :			};
3399 :
3400 :			return $answer_evaluator;
3401 :			}
3402 :
3403 :
3404 :
3405 :			##########################################################################
3406 :			##########################################################################
3407 :			## Miscellaneous answer evaluators
3408 :
3409 :			=head2 Miscellaneous Answer Evaluators (Checkboxes and Radio Buttons)
3410 :
3411 :			These evaluators do not fit any of the other categories.
3412 :
3413 :			checkbox_cmp( $correctAnswer )
3414 :
3415 :			$correctAnswer -- a string containing the names of the correct boxes,
3416 :			e.g. "ACD". Note that this means that individual
3417 :			checkbox names can only be one character. Internally,
3418 :			this is largely the same as unordered_cs_str_cmp().
3419 :
3420 :			radio_cmp( $correctAnswer )
3421 :
3422 :			$correctAnswer -- a string containing the name of the correct radio
3423 :			button, e.g. "Choice1". This is case sensitive and
3424 :			whitespace sensitive, so the correct answer must match
3425 :			the name of the radio button exactly.
3426 :
3427 :			=cut
3428 :
3429 :			# added 6/14/2000 by David Etlinger
3430 :			# because of the conversion of the answer
3431 :			# string to an array, I thought it better not
3432 :			# to force STR_CMP() to work with this
3433 :			sub checkbox_cmp {
3434 :			my $correctAnswer = shift @_;
3435 :			$correctAnswer = str_filters( $correctAnswer, 'ignore_order' );
3436 :
3437 :			my $answer_evaluator = sub {
3438 :			my $in = shift @_;
3439 :			$in = '' unless defined $in; #in case no boxes checked
3440 :
3441 :			my @temp = split( "\0", $in ); #convert "\0"-delimited string to array...
3442 :			$in = join( "", @temp ); #and then to a single no-delimiter string
3443 :
3444 :			my $original_student_ans = $in; #well, almost original
3445 :			$in = str_filters( $in, 'ignore_order' );
3446 :
3447 :			my $correctQ = ($in eq $correctAnswer) ? 1: 0;
3448 :
3449 :			my $ans_hash = new AnswerHash(
3450 :			'score' => $correctQ,
3451 :			'correct_ans' => $correctAnswer,
3452 :			'student_ans' => $in,
3453 :			'ans_message' => "",
3454 :			'type' => "checkbox_cmp",
3455 :			'preview_text_string' => $in,
3456 :			'original_student_ans' => $original_student_ans
3457 :			);
3458 :
3459 :			return $ans_hash;
3460 :
3461 :			};
3462 :
3463 :			return $answer_evaluator;
3464 :			}
3465 :
3466 :			#added 6/28/2000 by David Etlinger
3467 :			#exactly the same as strict_str_cmp,
3468 :			#but more intuitive to the user
3469 :			sub radio_cmp {
3470 :			strict_str_cmp( @_ );
3471 :			}
3472 :
3473 :
3474 :
3475 :			##########################################################################
3476 :			##########################################################################
3477 :			## Text and e-mail routines
3478 :
3479 :
3480 :			sub store_ans_at {
3481 :			my $answerStringRef = shift;
3482 :			my %options = @_;
3483 :			my $ans_eval= '';
3484 :			if ( ref($answerStringRef) eq 'SCALAR' ) {
3485 :			$ans_eval= sub {
3486 :			my $text = shift;
3487 :			$text = '' unless defined($text);
3488 :			$$answerStringRef = $$answerStringRef . $text;
3489 :			my $ans_hash = new AnswerHash(
3490 :			'score' => 1,
3491 :			'correct_ans' => '',
3492 :			'student_ans' => $text,
3493 :			'ans_message' => '',
3494 :			'type' => 'store_ans_at',
3495 :			'original_student_ans' => $text,
3496 :			'preview_text_string' => ''
3497 :
3498 :			);
3499 :
3500 :			return $ans_hash;
3501 :			};
3502 :			}
3503 :			else {
3504 :			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";
3505 :			}
3506 :
3507 :			return $ans_eval;
3508 :			}
3509 :
3510 :
3511 :			#### subroutines used in producing a questionnaire
3512 :			#### these are at least good models for other answers of this type
3513 :
3514 :			my $QUESTIONNAIRE_ANSWERS=''; # stores the answers until it is time to send them
3515 :			# this must be initialized before the answer evaluators are run
3516 :			# but that happens long after all of the text in the problem is
3517 :			# evaluated.
3518 :			# this is a utility script for cleaning up the answer output for display in
3519 :			#the answers.
3520 :
3521 :
3522 :			sub DUMMY_ANSWER {
3523 :			my $num = shift;
3524 :			qq{<INPUT TYPE="HIDDEN" NAME="answer$num" VALUE="">}
3525 :			}
3526 :
3527 :			sub escapeHTML {
3528 :			my $string = shift;
3529 :			$string =~ s/\n/$BR/ge;
3530 :			$string;
3531 :			}
3532 :
3533 :			# these next two subroutines show how to modify the "store_and_at()" answer
3534 :			# evaluator to add extra information before storing the info
3535 :			# They provide a good model for how to tweak answer evaluators in special cases.
3536 :			sub anstext {
3537 :			my $num = shift;
3538 :			my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS);
3539 :			my $ans_eval = sub {
3540 :			my $text = shift;
3541 :			$text = '' unless defined($text);
3542 :			my $new_text = "\n$main::psvnNumber-Problem-$main::probNum-Question-$num:\n $text "; # modify entered text
3543 :			my $out = &$ans_eval_template($new_text); # standard evaluator
3544 :			#warn "$QUESTIONNAIRE_ANSWERS";
3545 :			$out->{student_ans} = escapeHTML($text); # restore original entered text
3546 :			$out->{correct_ans} = "Question $num answered";
3547 :			$out->{original_student_ans} = escapeHTML($text);
3548 :			$out;
3549 :			};
3550 :			$ans_eval;
3551 :			}
3552 :
3553 :			sub ansradio {
3554 :			my $num = shift;
3555 :			my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS);
3556 :			my $ans_eval = sub {
3557 :			my $text = shift;
3558 :			$text = '' unless defined($text);
3559 :			my $new_text = "\n$main::psvnNumber-Problem-$main::probNum-RADIO-$num:\n $text "; # modify entered text
3560 :			my $out = $ans_eval_template->($new_text); # standard evaluator
3561 :			$out->{student_ans} =escapeHTML($text); # restore original entered text
3562 :			$out->{original_student_ans} = escapeHTML($text);
3563 :			$out;
3564 :			};
3565 :
3566 :
3567 :			$ans_eval;
3568 :			}
3569 :
3570 :			# This is another example of how to modify an answer evaluator to obtain
3571 :			# the desired behavior in a special case. Here the object is to have
3572 :			# have the last answer trigger the send_mail_to subroutine which mails
3573 :			# all of the answers to the designated address.
3574 :			# (This address must be listed in PG_environment{'ALLOW_MAIL_TO'} or an error occurs.)
3575 :
3576 :			sub mail_answers_to { #accepts the last answer and mails off the result
3577 :			my $user_address = shift;
3578 :			my $ans_eval = sub {
3579 :
3580 :			# then mail out all of the answers, including this last one.
3581 :
3582 :			send_mail_to( $user_address,
3583 :			'subject' => "$main::courseName WeBWorK questionnaire",
3584 :			'body' => $QUESTIONNAIRE_ANSWERS,
3585 :			'ALLOW_MAIL_TO' => $main::ALLOW_MAIL_TO
3586 :			);
3587 :
3588 :			my $ans_hash = new AnswerHash( 'score' => 1,
3589 :			'correct_ans' => '',
3590 :			'student_ans' => 'Answer recorded',
3591 :			'ans_message' => '',
3592 :			'type' => 'send_mail_to',
3593 :			);
3594 :
3595 :			return $ans_hash;
3596 :			};
3597 :
3598 :			return $ans_eval;
3599 :			}
3600 :			sub mail_answers_to2 { #accepts the last answer and mails off the result
3601 :			my $user_address = shift;
3602 :			my $subject = shift;
3603 :			$subject = "$main::courseName WeBWorK questionnaire" unless defined $subject;
3604 :
3605 :
3606 :			send_mail_to($user_address,
3607 :			'subject' => $subject,
3608 :			'body' => $QUESTIONNAIRE_ANSWERS,
3609 :			'ALLOW_MAIL_TO' => $main::ALLOW_MAIL_TO
3610 :			);
3611 :
3612 :
3613 :			}
3614 :
3615 :
3616 :
3617 :			##########################################################################
3618 :			##########################################################################
3619 :			## Problem Grader Subroutines
3620 :
3621 :
3622 :			#####################################
3623 :			# This is a model for plug-in problem graders
3624 :			#####################################
3625 :			sub install_problem_grader {
3626 :			my $rf_problem_grader = shift;
3627 :			$main::PG_FLAGS{PROBLEM_GRADER_TO_USE} = $rf_problem_grader;
3628 :			}
3629 :
3630 :			#this is called std only for compatability purposes;
3631 :			#almost everyone uses avg_problem_grader
3632 :			sub std_problem_grader{
3633 :			my $rh_evaluated_answers = shift;
3634 :			my $rh_problem_state = shift;
3635 :			my %form_options = @_;
3636 :			my %evaluated_answers = %{$rh_evaluated_answers};
3637 :			# The hash $rh_evaluated_answers typically contains:
3638 :			# 'answer1' => 34, 'answer2'=> 'Mozart', etc.
3639 :
3640 :			# By default the old problem state is simply passed back out again.
3641 :			my %problem_state = %$rh_problem_state;
3642 :
3643 :
3644 :			# %form_options might include
3645 :			# The user login name
3646 :			# The permission level of the user
3647 :			# The studentLogin name for this psvn.
3648 :			# Whether the form is asking for a refresh or is submitting a new answer.
3649 :
3650 :			# initial setup of the answer
3651 :			my %problem_result = ( score => 0,
3652 :			errors => '',
3653 :			type => 'std_problem_grader',
3654 :			msg => '',
3655 :			);
3656 :			# Checks
3657 :
3658 :			my $ansCount = keys %evaluated_answers; # get the number of answers
3659 :			unless ($ansCount > 0 ) {
3660 :			$problem_result{msg} = "This problem did not ask any questions.";
3661 :			return(\%problem_result,\%problem_state);
3662 :			}
3663 :
3664 :			if ($ansCount > 1 ) {
3665 :			$problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ;
3666 :			}
3667 :
3668 :			unless ($form_options{answers_submitted} == 1) {
3669 :			return(\%problem_result,\%problem_state);
3670 :			}
3671 :
3672 :			my $allAnswersCorrectQ=1;
3673 :			foreach my $ans_name (keys %evaluated_answers) {
3674 :			# I'm not sure if this check is really useful.
3675 :			if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) {
3676 :			$allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} );
3677 :			}
3678 :			else {
3679 :			die "Error at file ",__FILE__,"line ", __LINE__,": Answer \|$ans_name\| is not a hash reference\n".
3680 :			$evaluated_answers{$ans_name} .
3681 :			"This probably means that the answer evaluator for this answer\n" .
3682 :			"is not working correctly.";
3683 :			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
3684 :			}
3685 :			}
3686 :			# report the results
3687 :			$problem_result{score} = $allAnswersCorrectQ;
3688 :
3689 :			# I don't like to put in this bit of code.
3690 :			# It makes it hard to construct error free problem graders
3691 :			# I would prefer to know that the problem score was numeric.
3692 :	chris	22	unless ($problem_state{recorded_score} =~ /^([+-]?)(?=\d\|\.\d)\d(\.\d)?([Ee]([+-]?\d+))?$/ ) {
3693 :	sam	2	$problem_state{recorded_score} = 0; # This gets rid of non-numeric scores
3694 :			}
3695 :			#
3696 :			if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) {
3697 :			$problem_state{recorded_score} = 1;
3698 :			}
3699 :			else {
3700 :			$problem_state{recorded_score} = 0;
3701 :			}
3702 :
3703 :			$problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1;
3704 :			$problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0;
3705 :			(\%problem_result, \%problem_state);
3706 :			}
3707 :
3708 :			#the only difference between the two versions
3709 :			#is at the end of the subroutine, where std_problem_grader2
3710 :			#records the attempt only if there have been no syntax errors,
3711 :			#whereas std_problem_grader records it regardless
3712 :			sub std_problem_grader2{
3713 :			my $rh_evaluated_answers = shift;
3714 :			my $rh_problem_state = shift;
3715 :			my %form_options = @_;
3716 :			my %evaluated_answers = %{$rh_evaluated_answers};
3717 :			# The hash $rh_evaluated_answers typically contains:
3718 :			# 'answer1' => 34, 'answer2'=> 'Mozart', etc.
3719 :
3720 :			# By default the old problem state is simply passed back out again.
3721 :			my %problem_state = %$rh_problem_state;
3722 :
3723 :
3724 :			# %form_options might include
3725 :			# The user login name
3726 :			# The permission level of the user
3727 :			# The studentLogin name for this psvn.
3728 :			# Whether the form is asking for a refresh or is submitting a new answer.
3729 :
3730 :			# initial setup of the answer
3731 :			my %problem_result = ( score => 0,
3732 :			errors => '',
3733 :			type => 'std_problem_grader',
3734 :			msg => '',
3735 :			);
3736 :
3737 :			# syntax errors are not counted.
3738 :			my $record_problem_attempt = 1;
3739 :			# Checks
3740 :
3741 :			my $ansCount = keys %evaluated_answers; # get the number of answers
3742 :			unless ($ansCount > 0 ) {
3743 :			$problem_result{msg} = "This problem did not ask any questions.";
3744 :			return(\%problem_result,\%problem_state);
3745 :			}
3746 :
3747 :			if ($ansCount > 1 ) {
3748 :			$problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ;
3749 :			}
3750 :
3751 :			unless ($form_options{answers_submitted} == 1) {
3752 :			return(\%problem_result,\%problem_state);
3753 :			}
3754 :
3755 :			my $allAnswersCorrectQ=1;
3756 :			foreach my $ans_name (keys %evaluated_answers) {
3757 :			# I'm not sure if this check is really useful.
3758 :			if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) {
3759 :			$allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} );
3760 :			}
3761 :			else {
3762 :			die "Error at file ",__FILE__,"line ", __LINE__,": Answer \|$ans_name\| is not a hash reference\n".
3763 :			$evaluated_answers{$ans_name} .
3764 :			"This probably means that the answer evaluator for this answer\n" .
3765 :			"is not working correctly.";
3766 :			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
3767 :			}
3768 :			}
3769 :			# report the results
3770 :			$problem_result{score} = $allAnswersCorrectQ;
3771 :
3772 :			# I don't like to put in this bit of code.
3773 :			# It makes it hard to construct error free problem graders
3774 :			# I would prefer to know that the problem score was numeric.
3775 :			unless ($problem_state{recorded_score} =~ /^([+-]?)(?=\d\|\.\d)\d(\.\d)?([Ee]([+-]?\d+))?$/ ) {
3776 :			$problem_state{recorded_score} = 0; # This gets rid of non-numeric scores
3777 :			}
3778 :			#
3779 :			if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) {
3780 :			$problem_state{recorded_score} = 1;
3781 :			}
3782 :			else {
3783 :			$problem_state{recorded_score} = 0;
3784 :			}
3785 :			# record attempt only if there have been no syntax errors.
3786 :
3787 :			if ($record_problem_attempt == 1) {
3788 :			$problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1;
3789 :			$problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0;
3790 :			}
3791 :			else {
3792 :			$problem_result{show_partial_correct_answers} = 0 ; # prevent partial correct answers from being shown for syntax errors.
3793 :
3794 :			}
3795 :
3796 :			(\%problem_result, \%problem_state);
3797 :			}
3798 :
3799 :
3800 :			sub avg_problem_grader{
3801 :			my $rh_evaluated_answers = shift;
3802 :			my $rh_problem_state = shift;
3803 :			my %form_options = @_;
3804 :			my %evaluated_answers = %{$rh_evaluated_answers};
3805 :			# The hash $rh_evaluated_answers typically contains:
3806 :			# 'answer1' => 34, 'answer2'=> 'Mozart', etc.
3807 :
3808 :			# By default the old problem state is simply passed back out again.
3809 :			my %problem_state = %$rh_problem_state;
3810 :
3811 :
3812 :			# %form_options might include
3813 :			# The user login name
3814 :			# The permission level of the user
3815 :			# The studentLogin name for this psvn.
3816 :			# Whether the form is asking for a refresh or is submitting a new answer.
3817 :
3818 :			# initial setup of the answer
3819 :			my $total=0;
3820 :			my %problem_result = ( score => 0,
3821 :			errors => '',
3822 :			type => 'avg_problem_grader',
3823 :			msg => '',
3824 :			);
3825 :			my $count = keys %evaluated_answers;
3826 :			$problem_result{msg} = 'You can earn partial credit on this problem.' if $count >1;
3827 :			# Return unless answers have been submitted
3828 :			unless ($form_options{answers_submitted} == 1) {
3829 :			return(\%problem_result,\%problem_state);
3830 :			}
3831 :
3832 :			# Answers have been submitted -- process them.
3833 :			foreach my $ans_name (keys %evaluated_answers) {
3834 :			# I'm not sure if this check is really useful.
3835 :			if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) {
3836 :			$total += $evaluated_answers{$ans_name}->{score};
3837 :			}
3838 :			else {
3839 :			die "Error: Answer \|$ans_name\| is not a hash reference\n".
3840 :			$evaluated_answers{$ans_name} .
3841 :			"This probably means that the answer evaluator for this answer\n" .
3842 :			"is not working correctly.";
3843 :			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
3844 :			}
3845 :			}
3846 :			# Calculate score rounded to three places to avoid roundoff problems
3847 :			$problem_result{score} = $total/$count if $count;
3848 :			# increase recorded score if the current score is greater.
3849 :			$problem_state{recorded_score} = $problem_result{score} if $problem_result{score} > $problem_state{recorded_score};
3850 :
3851 :
3852 :			$problem_state{num_of_correct_ans}++ if $total == $count;
3853 :			$problem_state{num_of_incorrect_ans}++ if $total < $count ;
3854 :			warn "Error in grading this problem the total $total is larger than $count" if $total > $count;
3855 :			(\%problem_result, \%problem_state);
3856 :
3857 :			}
3858 :
3859 :
3860 :
3861 :			###########################################################################
3862 :			### THE FOLLOWING ARE LOCAL SUBROUTINES THAT ARE MEANT TO BE CALLED ONLY FROM THIS SCRIPT.
3863 :
3864 :
3865 :			## Internal routine that converts variables into the standard array format
3866 :			##
3867 :			## IN: one of the following:
3868 :			## an undefined value (i.e., no variable was specified)
3869 :			## a reference to an array of variable names -- [var1, var2]
3870 :			## a number (the number of variables desired) -- 3
3871 :			## one or more variable names -- (var1, var2)
3872 :			## OUT: an array of variable names
3873 :			sub get_var_array {
3874 :			my $in = shift @_;
3875 :			my @out;
3876 :
3877 :			if( not defined($in) ) { #if nothing defined, build default array and return
3878 :			@out = ( $functVarDefault );
3879 :			return @out;
3880 :			}
3881 :			elsif( ref( $in ) eq 'ARRAY' ) { #if given an array ref, dereference and return
3882 :			return @{$in};
3883 :			}
3884 :			elsif( $in =~ /^\d+/ ) { #if given a number, set up the array and return
3885 :			if( $in == 1 ) {
3886 :			$out[0] = 'x';
3887 :			}
3888 :			elsif( $in == 2 ) {
3889 :			$out[0] = 'x';
3890 :			$out[1] = 'y';
3891 :			}
3892 :			elsif( $in == 3 ) {
3893 :			$out[0] = 'x';
3894 :			$out[1] = 'y';
3895 :			$out[2] = 'z';
3896 :			}
3897 :			else { #default to the x_1, x_2, ... convention
3898 :			my ($i, $tag);
3899 :			for( $i=0; $i < $in; $i++ ) {
3900 :			## akp the above seems to be off by one 1/4/00
3901 :			$tag = $i + 1; ## akp 1/4/00
3902 :			$out[$i] = "${functVarDefault}_" . $tag; ## akp 1/4/00
3903 :			}
3904 :			}
3905 :
3906 :			return @out;
3907 :			}
3908 :			else { #if given one or more names, return as an array
3909 :			unshift( @_, $in );
3910 :
3911 :			return @_;
3912 :			}
3913 :			}
3914 :
3915 :			## Internal routine that converts limits into the standard array of arrays format
3916 :			## Some of the cases are probably unneccessary, but better safe than sorry
3917 :			##
3918 :			## IN: one of the following:
3919 :			## an undefined value (i.e., no limits were specified)
3920 :			## a reference to an array of arrays of limits -- [[llim,ulim], [llim,ulim]]
3921 :			## a reference to an array of limits -- [llim, ulim]
3922 :			## an array of array references -- ([llim,ulim], [llim,ulim])
3923 :			## an array of limits -- (llim,ulim)
3924 :			## OUT: an array of array references -- ([llim,ulim], [llim,ulim]) or ([llim,ulim])
3925 :	chris	22
3926 :	sam	2	sub get_limits_array {
3927 :			my $in = shift @_;
3928 :			my @out;
3929 :
3930 :			if( not defined($in) ) { #if nothing defined, build default array and return
3931 :			@out = ( [$functLLimitDefault, $functULimitDefault] );
3932 :			return @out;
3933 :			}
3934 :			elsif( ref($in) eq 'ARRAY' ) { #$in is either ref to array, or ref to array of refs
3935 :			my @deref = @{$in};
3936 :
3937 :			if( ref( $in->[0] ) eq 'ARRAY' ) { #$in is a ref to an array of array refs
3938 :			return @deref;
3939 :			}
3940 :			else { #$in was just a ref to an array of numbers
3941 :			@out = ( $in );
3942 :			return @out;
3943 :			}
3944 :			}
3945 :			else { #$in was an array of references or numbers
3946 :			unshift( @_, $in );
3947 :
3948 :			if( ref($_[0]) eq 'ARRAY' ) { #$in was an array of references, so just return it
3949 :			return @_;
3950 :			}
3951 :			else { #$in was an array of numbers
3952 :			@out = ( \@_ );
3953 :			return @out;
3954 :			}
3955 :			}
3956 :			}
3957 :
3958 :			sub check_option_list {
3959 :			my $size = scalar(@_);
3960 :			if( ( $size % 2 ) != 0 ) {
3961 :			warn "ERROR in answer evaluator generator:\n" .
3962 :			"Usage: <CODE>str_cmp([\$ans1, \$ans2],%options)</CODE>
3963 :			or <CODE> num_cmp([\$num1, \$num2], %options)</CODE><BR>
3964 :			A list of inputs must be inclosed in square brackets <CODE>[\$ans1, \$ans2]</CODE>";
3965 :			}
3966 :			}
3967 :
3968 :			# simple subroutine to display an error message when
3969 :			# function compares are called with invalid parameters
3970 :			sub function_invalid_params {
3971 :			my $correctEqn = shift @_;
3972 :			my $error_response = sub {
3973 :			my $PGanswerMessage = "Tell your professor that there is an error with the parameters " .
3974 :			"to the function answer evaluator";
3975 :			return ( 0, $correctEqn, "", $PGanswerMessage );
3976 :			};
3977 :
3978 :			return $error_response;
3979 :			}
3980 :
3981 :
3982 :	chris	22	#########################################################################
3983 :			# Filters for answer evaluators
3984 :			#########################################################################
3985 :
3986 :
3987 :	sam	2	sub is_a_number {
3988 :	chris	22	my ($num,%options) = @_;
3989 :			my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ;
3990 :			my ($rh_ans);
3991 :			if ($process_ans_hash) {
3992 :			$rh_ans = $num;
3993 :			$num = $rh_ans->{student_ans};
3994 :			}
3995 :
3996 :	sam	2	my $is_a_number = 0;
3997 :			return $is_a_number unless defined($num);
3998 :			$num =~ s/^\s*//; ## remove initial spaces
3999 :			$num =~ s/\s*$//; ## remove trailing spaces
4000 :
4001 :			## the following is copied from the online perl manual
4002 :			if ($num =~ /^([+-]?)(?=\d\|\.\d)\d(\.\d)?([Ee]([+-]?\d+))?$/){
4003 :			$is_a_number = 1;
4004 :			}
4005 :	chris	22
4006 :			if ($process_ans_hash) {
4007 :			if ($is_a_number == 1 ) {
4008 :			$rh_ans->{student_ans}=$num;
4009 :			return $rh_ans;
4010 :			} else {
4011 :			$rh_ans->{student_ans} = "Incorrect number format: You must enter a number, e.g. -6, 5.3, or 6.12E-3";
4012 :			$rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3');
4013 :			return $rh_ans;
4014 :			}
4015 :			} else {
4016 :			return $is_a_number;
4017 :			}
4018 :	sam	2	}
4019 :
4020 :			sub is_a_fraction {
4021 :	chris	22	my ($num,%options) = @_;
4022 :			my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ;
4023 :			my ($rh_ans);
4024 :			if ($process_ans_hash) {
4025 :			$rh_ans = $num;
4026 :			$num = $rh_ans->{student_ans};
4027 :			}
4028 :
4029 :			my $is_a_fraction = 0;
4030 :			return $is_a_fraction unless defined($num);
4031 :			$num =~ s/^\s*//; ## remove initial spaces
4032 :			$num =~ s/\s*$//; ## remove trailing spaces
4033 :
4034 :			if ($num =~ /^\s\-?\s[\/\d\.Ee\s]*$/) {
4035 :	sam	2	$is_a_fraction = 1;
4036 :			}
4037 :	chris	22
4038 :			if ($process_ans_hash) {
4039 :			if ($is_a_fraction == 1 ) {
4040 :			$rh_ans->{student_ans}=$num;
4041 :			return $rh_ans;
4042 :			} else {
4043 :			$rh_ans->{student_ans} = "Not a number of fraction: You must enter a number or fraction, e.g. -6 or 7/13";
4044 :			$rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3');
4045 :			return $rh_ans;
4046 :			}
4047 :
4048 :			} else {
4049 :			return $is_a_fraction;
4050 :			}
4051 :	sam	2	}
4052 :
4053 :	chris	22
4054 :			sub is_an_arithmetic_expression {
4055 :			my ($num,%options) = @_;
4056 :			my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ;
4057 :			my ($rh_ans);
4058 :			if ($process_ans_hash) {
4059 :			$rh_ans = $num;
4060 :			$num = $rh_ans->{student_ans};
4061 :			}
4062 :
4063 :			my $is_an_arithmetic_expression = 0;
4064 :			return $is_an_arithmetic_expression unless defined($num);
4065 :			$num =~ s/^\s*//; ## remove initial spaces
4066 :			$num =~ s/\s*$//; ## remove trailing spaces
4067 :
4068 :			if ($num =~ /^[+\-\/\^\[\]\{\}\s\d\.Ee]$/) {
4069 :	sam	2	$is_an_arithmetic_expression = 1;
4070 :			}
4071 :	chris	22
4072 :			if ($process_ans_hash) {
4073 :			if ($is_an_arithmetic_expression == 1 ) {
4074 :			$rh_ans->{student_ans}=$num;
4075 :			return $rh_ans;
4076 :			} else {
4077 :
4078 :			$rh_ans->{student_ans} = "Not an arithmetic expression: You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2";
4079 :			$rh_ans->throw_error('NUMBER', 'You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2');
4080 :			return $rh_ans;
4081 :			}
4082 :
4083 :			} else {
4084 :			return $is_an_arithmetic_expression;
4085 :			}
4086 :	sam	2	}
4087 :
4088 :			#replaces pi, e, and ^ with their Perl equivalents
4089 :			sub math_constants {
4090 :	chris	22	my($in,%options) = @_;
4091 :			my $rh_ans;
4092 :			my $process_ans_hash = ( ref( $in ) eq 'AnswerHash' ) ? 1 : 0 ;
4093 :			if ($process_ans_hash) {
4094 :			$rh_ans = $in;
4095 :			$in = $rh_ans->{student_ans};
4096 :			}
4097 :
4098 :	sam	2	$in =~s/\bpi\b/(4*atan2(1,1))/ge;
4099 :			$in =~s/\be\b/(exp(1))/ge;
4100 :			$in =~s/\^/**/g;
4101 :	chris	22
4102 :			if ($process_ans_hash) {
4103 :			$rh_ans->{student_ans}=$in;
4104 :			return $rh_ans;
4105 :			} else {
4106 :			return $in;
4107 :			}
4108 :	sam	2	}
4109 :
4110 :			sub clean_up_error_msg {
4111 :			my $msg = $_[0];
4112 :			$msg =~ s/^\[[^\]]\][^:]://;
4113 :			$msg =~ s/Unquoted string//g;
4114 :			$msg =~ s/may\s+clash.*/does not make sense here/;
4115 :			$msg =~ s/\sat.line [\d]//g;
4116 :			$msg = 'error: '. $msg;
4117 :
4118 :			return $msg;
4119 :			}
4120 :
4121 :			#formats the student and correct answer as specified
4122 :			#format must be of a form suitable for sprintf (e.g. '%0.5g'),
4123 :			#with the exception that a '#' at the end of the string
4124 :			#will cause trailing zeros in the decimal part to be removed
4125 :			sub prfmt {
4126 :			my($number,$format) = @_; # attention, the order of format and number are reversed
4127 :			my $out;
4128 :			if ($format) {
4129 :			warn "Incorrect format used: $format. <BR> Format should look something like %4.5g<BR>"
4130 :			unless $format =~ /^\s%\d\.?\d\w#?\s$/;
4131 :
4132 :			if( $format =~ s/#\s*$// ) { # remove trailing zeros in the decimal
4133 :			$out = sprintf( $format, $number );
4134 :			$out =~ s/(\.\d*?)0+$/$1/;
4135 :			$out =~ s/\.$//; # in case all decimal digits were zero, remove the decimal
4136 :			}
4137 :			else {
4138 :			$out = sprintf( $format, $number );
4139 :			}
4140 :
4141 :			$out =~ s/e/E/g; # only use capital E's for exponents. Little e is for 2.71828...
4142 :			}
4143 :			else {
4144 :			$out = $number;
4145 :			}
4146 :
4147 :			return $out;
4148 :			}
4149 :
4150 :			=head4
4151 :
4152 :			pretty_print()
4153 :
4154 :
4155 :			=cut
4156 :
4157 :			sub pretty_print {
4158 :			my $r_input = shift;
4159 :			my $out = '';
4160 :			if ( not ref($r_input) ) {
4161 :			$out = $r_input; # not a reference
4162 :			} elsif ("$r_input" =~/hash/i) { # this will pick up objects whose '$self' is hash and so works better than ref($r_iput).
4163 :			local($^W) = 0;
4164 :			$out .= "$r_input " ."<TABLE border = \"2\" cellpadding = \"3\" BGCOLOR = \"#FFFFFF\">";
4165 :			foreach my $key (lex_sort( keys %$r_input )) {
4166 :			$out .= "<tr><TD> $key</TD><TD>=></td><td> ".pretty_print($r_input->{$key}) . "</td></tr>";
4167 :			}
4168 :			$out .="</table>";
4169 :			} elsif (ref($r_input) eq 'ARRAY' ) {
4170 :			my @array = @$r_input;
4171 :			$out .= "( " ;
4172 :			while (@array) {
4173 :			$out .= pretty_print(shift @array) . " , ";
4174 :			}
4175 :			$out .= " )";
4176 :			} elsif (ref($r_input) eq 'CODE') {
4177 :			$out = "$r_input";
4178 :			} else {
4179 :			$out = $r_input;
4180 :			}
4181 :			$out;
4182 :			}
4183 :
4184 :			# Use this to set default options
4185 :			sub set_default_options {
4186 :			my $rh_options = shift;
4187 :			warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH';
4188 :			my %default_options = @_;
4189 :	gage	5	unless ( defined($default_options{allow_unknown_options}) and $default_options{allow_unknown_options} == 1 ) {
4190 :			foreach my $key1 (keys %$rh_options) {
4191 :			warn "This option \|$key1\| is not recognized in this subroutine<br> ", pretty_print($rh_options) unless exists($default_options{$key1});
4192 :			}
4193 :	sam	2	}
4194 :			foreach my $key (keys %default_options) {
4195 :			if ( not defined($rh_options->{$key} ) and defined( $default_options{$key} ) ) {
4196 :	chris	22	$rh_options->{$key} = $default_options{$key}; #this allows tol => undef to allow the tol option, but doesn't define
4197 :	sam	2	# this key unless tol is explicitly defined.
4198 :			}
4199 :			}
4200 :			}
4201 :			# Use this to assign aliases for the standard options
4202 :			sub assign_option_aliases {
4203 :			my $rh_options = shift;
4204 :			warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH';
4205 :			my @option_aliases = @_;
4206 :			while (@option_aliases) {
4207 :			my $alias = shift @option_aliases;
4208 :			my $option_key = shift @option_aliases;
4209 :
4210 :			if (defined($rh_options->{$alias} )) { # if the alias appears in the option list
4211 :			if (not defined($rh_options->{$option_key}) ) { # and the option itself is not defined,
4212 :			$rh_options->{$option_key} = $rh_options->{$alias}; # insert the value defined by the alias into the option value
4213 :			# the FIRST alias for a given option takes precedence
4214 :			# (after the option itself)
4215 :			} else {
4216 :			warn "option $option_key is already defined as", $rh_options->{$option_key}, "<br>\n",
4217 :			"The attempt to override this option with the alias $alias with value ", $rh_options->{$alias},
4218 :			" was ignored.";
4219 :			}
4220 :
4221 :			}
4222 :			delete($rh_options->{$alias}); # remove the alias from the initial list
4223 :			}
4224 :
4225 :			}
4226 :
4227 :
4228 :			1;

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