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 :	gage	122
21 :	sam	2	std_num_cmp(), std_num_cmp_list(), std_num_cmp_abs, std_num_cmp_abs_list()
22 :			frac_num_cmp(), frac_num_cmp_list(), frac_num_cmp_abs, frac_num_cmp_abs_list()
23 :			arith_num_cmp(), arith_num_cmp_list(), arith_num_cmp_abs, arith_num_cmp_abs_list()
24 :			strict_num_cmp(), strict_num_cmp_list(), strict_num_cmp_abs, strict_num_cmp_abs_list()
25 :			numerical_compare_with_units() -- requires units as part of the answer
26 :			std_num_str_cmp() -- also accepts a set of strings as possible answers
27 :
28 :			Function Answer Evaluators:
29 :			fun_cmp() -- uses an input hash to determine parameters
30 :	gage	122
31 :	sam	2	function_cmp(), function_cmp_abs()
32 :			function_cmp_up_to_constant(), function_cmp_up_to_constant_abs()
33 :			multivar_function_cmp()
34 :
35 :			String Answer Evaluators:
36 :			str_cmp() -- uses an input hash to determine parameters
37 :	gage	122
38 :	sam	2	std_str_cmp(), std_str_cmp_list(), std_cs_str_cmp(), std_cs_str_cmp_list()
39 :			strict_str_cmp(), strict_str_cmp_list()
40 :			ordered_str_cmp(), ordered_str_cmp_list(), ordered_cs_str_cmp(), ordered_cs_str_cmp_list()
41 :			unordered_str_cmp(), unordered_str_cmp_list(), unordered_cs_str_cmp(), unordered_cs_str_cmp_list()
42 :
43 :			Miscellaneous Answer Evaluators:
44 :			checkbox_cmp()
45 :			radio_cmp()
46 :
47 :			=cut
48 :
49 :			=head1 DESCRIPTION
50 :
51 :			This file adds subroutines which create "answer evaluators" for checking
52 :			answers. Each answer evaluator accepts a single input from a student answer,
53 :			checks it and creates an output hash %ans_hash with seven or eight entries
54 :			(the preview_latex_string is optional). The output hash is now being created
55 :			with the AnswerHash package "class", which is located at the end of this file.
56 :			This class is currently just a wrapper for the hash, but this might change in
57 :			the future as new capabilities are added.
58 :
59 :	chris	54	score => $correctQ,
60 :			correct_ans => $originalCorrEqn,
61 :			student_ans => $modified_student_ans
62 :	sam	2	original_student_ans => $original_student_answer,
63 :	chris	54	ans_message => $PGanswerMessage,
64 :			type => 'typeString',
65 :			preview_text_string => $preview_text_string,
66 :	sam	2	preview_latex_string => $preview_latex_string
67 :
68 :
69 :	chris	81	$ans_hash{score} -- a number between 0 and 1 indicating
70 :	sam	2	whether the answer is correct. Fractions
71 :			allow the implementation of partial
72 :			credit for incorrect answers.
73 :			$ans_hash{correct_ans} -- The correct answer, as supplied by the
74 :			instructor and then formatted. This can
75 :			be viewed by the student after the answer date.
76 :			$ans_hash{student_ans} -- This is the student answer, after reformatting;
77 :			for example the answer might be forced
78 :			to capital letters for comparison with
79 :			the instructors answer. For a numerical
80 :			answer, it gives the evaluated answer.
81 :			This is displayed in the section reporting
82 :			the results of checking the student answers.
83 :	chris	81	$ans_hash{original_student_ans} -- This is the original student answer. This is displayed
84 :	sam	2	on the preview page and may be used for sticky answers.
85 :			$ans_hash{ans_message} -- Any error message, or hint provided by the answer evaluator.
86 :			This is also displayed in the section reporting
87 :			the results of checking the student answers.
88 :	chris	81	$ans_hash{type} -- A string indicating the type of answer evaluator. This
89 :	sam	2	helps in preprocessing the student answer for errors.
90 :			Some examples:
91 :			'number_with_units'
92 :			'function'
93 :			'frac_number'
94 :			'arith_number'
95 :	chris	81	$ans_hash{preview_text_string} -- This typically shows how the student answer was parsed. It is
96 :	sam	2	displayed on the preview page. For a student answer of 2sin(3x)
97 :			this would be 2sin(3x). For string answers it is typically the
98 :			same as $ans_hash{student_ans}.
99 :	gage	122	$ans_hash{preview_latex_string} -- THIS IS OPTIONAL. This is latex version of the student answer
100 :	sam	2	which is used to show a typeset view on the answer on the preview
101 :			page. For a student answer of 2/3, this would be \frac{2}{3}.
102 :
103 :			Technical note: the routines in this file are not actually answer evaluators. Instead, they create
104 :			answer evaluators. An answer evaluator is an anonymous subroutine, referenced by a named scalar. The
105 :			routines in this file build the subroutine and return a reference to it. Later, when the student
106 :			actually enters an answer, the problem processor feeds that answer to the referenced subroutine, which
107 :			evaluates it and returns a score (usually 0 or 1). For most users, this distinction is unimportant, but
108 :			if you plan on writing your own answer evaluators, you should understand this point.
109 :
110 :			=cut
111 :
112 :			BEGIN {
113 :			be_strict(); # an alias for use strict. This means that all global variable must contain main:: as a prefix.
114 :			}
115 :	gage	33
116 :
117 :	chris	81	my ($BR , # convenient localizations.
118 :			$PAR ,
119 :	gage	36	$numRelPercentTolDefault ,
120 :			$numZeroLevelDefault ,
121 :			$numZeroLevelTolDefault ,
122 :	chris	81	$numAbsTolDefault ,
123 :			$numFormatDefault ,
124 :	gage	36	$functRelPercentTolDefault ,
125 :			$functZeroLevelDefault ,
126 :			$functZeroLevelTolDefault ,
127 :	chris	81	$functAbsTolDefault ,
128 :			$functNumOfPoints ,
129 :			$functVarDefault ,
130 :			$functLLimitDefault ,
131 :			$functULimitDefault ,
132 :			$functMaxConstantOfIntegration ,
133 :			$CA
134 :	gage	36	);
135 :	gage	103
136 :
137 :
138 :
139 :	gage	32	sub _PGanswermacros_init {
140 :	gage	34
141 :	gage	103	$BR = $main::BR; # convenient localizations.
142 :	gage	32	$PAR = $main::PAR;
143 :	gage	103
144 :	gage	32	# import defaults
145 :			# these are now imported from the %envir variable
146 :	gage	36	$numRelPercentTolDefault = $main::numRelPercentTolDefault;
147 :			$numZeroLevelDefault = $main::numZeroLevelDefault;
148 :			$numZeroLevelTolDefault = $main::numZeroLevelTolDefault;
149 :	chris	54	$numAbsTolDefault = $main::numAbsTolDefault;
150 :			$numFormatDefault = $main::numFormatDefault;
151 :	gage	36	$functRelPercentTolDefault = $main::functRelPercentTolDefault;
152 :			$functZeroLevelDefault = $main::functZeroLevelDefault;
153 :			$functZeroLevelTolDefault = $main::functZeroLevelTolDefault;
154 :			$functAbsTolDefault = $main::functAbsTolDefault;
155 :	chris	54	$functNumOfPoints = $main::functNumOfPoints;
156 :			$functVarDefault = $main::functVarDefault;
157 :	gage	36	$functLLimitDefault = $main::functLLimitDefault;
158 :			$functULimitDefault = $main::functULimitDefault;
159 :	chris	54	$functMaxConstantOfIntegration = $main::functMaxConstantOfIntegration;
160 :	gage	32
161 :	gage	34
162 :
163 :	gage	32	}
164 :	sam	2
165 :			##########################################################################
166 :			##########################################################################
167 :			## Number answer evaluators
168 :
169 :			=head2 Number Answer Evaluators
170 :
171 :			Number answer evaluators take in a numerical answer, compare it to the correct answer,
172 :			and return a score. In addition, they can choose to accept or reject an answer based on
173 :			its format, closeness to the correct answer, and other criteria. There are two types
174 :			of numerical answer evaluators: num_cmp(), which takes a hash of named options as parameters,
175 :			and the "mode"_num_cmp() variety, which use different functions to access different sets of
176 :			options. In addition, there is the special case of std_num_str_cmp(), which can evaluate
177 :			both numbers and strings.
178 :
179 :			Numerical Comparison Options
180 :
181 :	chris	81	correctAnswer -- This is the correct answer that the student answer will
182 :	sam	2	be compared to. However, this does not mean that the
183 :			student answer must match this exactly. How close the
184 :			student answer must be is determined by the other
185 :			options, especially tolerance and format.
186 :
187 :			tolerance -- These options determine how close the student answer
188 :			must be to the correct answer to qualify. There are two
189 :			types of tolerance: relative and absolute. Relative
190 :			tolerances are given in percentages. A relative
191 :			tolerance of 1 indicates that the student answer must
192 :			be within 1% of the correct answer to qualify as correct.
193 :			In other words, a student answer is correct when
194 :			abs(studentAnswer - correctAnswer) <= abs(.01relpercentTolcorrectAnswer)
195 :			Using absolute tolerance, the student answer must be a
196 :			fixed distance from the correct answer to qualify.
197 :			For example, an absolute tolerance of 5 means that any
198 :			number which is +-5 of the correct answer qualifies as correct.
199 :			Final (rarely used) tolerance options are zeroLevel
200 :			and zeroLevelTol, used in conjunction with relative
201 :			tolerance. if correctAnswer has absolute value less than
202 :			or equal to zeroLevel, then the student answer must be,
203 :			in absolute terms, within zeroLevelTol of correctAnswer, i.e.,
204 :			abs(studentAnswer - correctAnswer) <= zeroLevelTol.
205 :			In other words, if the correct answer is very near zero,
206 :			an absolute tolerance will be used. One must do this to
207 :			handle floating point answers very near zero, because of
208 :			the inaccuracy of floating point arithmetic. However, the
209 :			default values are almost always adequate.
210 :
211 :			mode -- This determines the allowable methods for entering an
212 :			answer. Answers which do not meet this requirement will
213 :			be graded as incorrect, regardless of their numerical
214 :			value. The recognized modes are:
215 :			'std' (default) -- allows any expression which evaluates
216 :			to a number, including those using
217 :			elementary functions like sin() and
218 :			exp(), as well as the operations of
219 :			arithmetic (+, -, *, /, ^)
220 :	chris	81	'strict' -- only decimal numbers are allowed
221 :			'frac' -- whole numbers and fractions are allowed
222 :			'arith' -- arithmetic expressions are allowed, but
223 :	sam	2	no functions
224 :			Note that all modes allow the use of "pi" and "e" as
225 :			constants, and also the use of "E" to represent scientific
226 :			notation.
227 :
228 :			format -- The format to use when displaying the correct and
229 :			submitted answers. This has no effect on how answers are
230 :			evaluated; it is only for cosmetic purposes. The
231 :			formatting syntax is the same as Perl uses for the sprintf()
232 :			function. Format strings are of the form '%m.nx' or '%m.nx#',
233 :			where m and n are described below, and x is a formatter.
234 :			Esentially, m is the minimum length of the field
235 :			(make this negative to left-justify). Note that the decimal
236 :			point counts as a character when determining the field width.
237 :			If m begins with a zero, the number will be padded with zeros
238 :			instead of spaces to fit the field.
239 :			The precision specifier (n) works differently, depending
240 :			on which formatter you are using. For d, i, o, u, x and X
241 :			formatters (non-floating point formatters), n is the minimum
242 :			number of digits to display. For e and f, it is the number of
243 :			digits that appear after the decimal point (extra digits will
244 :			be rounded; insufficient digits will be padded with spaces--see
245 :			'#' below). For g, it is the number of significant digits to
246 :			display.
247 :			The full list of formatters can be found in the manpage
248 :			for printf(3), or by typing "perldoc -f sprintf" at a
249 :			terminal prompt. The following is a brief summary of the
250 :			most frequent formatters:
251 :			d -- decimal number
252 :			ld -- long decimal number
253 :			u -- unsigned decimal number
254 :			lu -- long unsigned decimal number
255 :			x -- hexadecimal number
256 :			o -- octal number
257 :			e -- floating point number in scientific notation
258 :			f -- floating point number
259 :			g -- either e or f, whichever takes less space
260 :			Technically, g will use e if the exponent is less than -4 or
261 :			greater than or equal to the precision. Trailing zeros are
262 :			removed in this mode.
263 :			If the format string ends in '#', trailing zeros will be
264 :			removed in the decimal part. Note that this is not a standard
265 :			syntax; it is handled internally by WeBWorK and not by Perl
266 :			(although this should not be a concern to end users).
267 :			The default format is '%0.5f#', which displays as a floating
268 :			point number with 5 digits of precision and no trailing zeros.
269 :			Other useful format strings might be '%0.2f' for displaying
270 :			dollar amounts, or '%010d' to display an integer with leading
271 :			zeros. Setting format to an empty string ( '' ) means no
272 :			formatting will be used; this will show 'arbitrary' precision
273 :			floating points.
274 :
275 :			Default Values (As of 7/24/2000) (Option -- Variable Name -- Value)
276 :
277 :	gage	124	Format -- $numFormatDefault -- "%0.5f#"
278 :			Relative Tolerance -- $numRelPercentTolDefault -- .1
279 :			Absolute Tolerance -- $numAbsTolDefault -- .001
280 :			Zero Level -- $numZeroLevelDefault -- 1E-14
281 :	sam	2	Zero Level Tolerance -- $numZeroLevelTolDefault -- 1E-12
282 :
283 :			=cut
284 :
285 :	gage	122
286 :			=head3 num_cmp()
287 :
288 :			Compares a number or a list of numbers, using a named hash of options to set
289 :			parameters. This can make for more readable code than using the "mode"_num_cmp()
290 :			style, but some people find one or the other easier to remember.
291 :
292 :			ANS( num_cmp( answer or answer_array_ref, options_hash ) );
293 :
294 :			1. the correct answer, or a reference to an array of correct answers
295 :			2. a hash with the following keys (all optional):
296 :	gage	124	mode -- 'std' (default) (allows any expression evaluating to
297 :			a number)
298 :	gage	122	'strict' (only numbers are allowed)
299 :			'frac' (fractions are allowed)
300 :	gage	124	'arith' (arithmetic expressions allowed)
301 :			format -- '%0.5f#' (default); defines formatting for the
302 :			correct answer
303 :			tol -- an absolute tolerance, or
304 :	gage	122	relTol -- a relative tolerance
305 :			units -- the units to use for the answer(s)
306 :			strings -- a reference to an array of strings which are valid
307 :			answers (works like std_num_str_cmp() )
308 :	gage	124	zeroLevel -- if the correct answer is this close to zero,
309 :			then zeroLevelTol applies
310 :			zeroLevelTol -- absolute tolerance to allow when answer is close
311 :			to zero
312 :	gage	122
313 :	gage	124	debug -- if set to 1, provides verbose listing of
314 :			hash entries throughout fliters.
315 :	gage	122
316 :			Returns an answer evaluator, or (if given a reference to an array of
317 :			answers), a list of answer evaluators. Note that a reference to an array of
318 :	gage	124	answers results is just a shortcut for writing a separate <code>num_cmp()</code> for each
319 :			answer.
320 :	gage	122
321 :			EXAMPLES:
322 :
323 :	gage	124	num_cmp( 5 ) -- correct answer is 5, using defaults
324 :			for all options
325 :			num_cmp( [5,6,7] ) -- correct answers are 5, 6, and 7,
326 :			using defaults for all options
327 :	gage	122	num_cmp( 5, mode => 'strict' ) -- correct answer is 5, mode is strict
328 :	gage	124	num_cmp( [5,6], relTol => 5 ) -- correct answers are 5 and 6,
329 :			both with 5% relative tolerance
330 :			num_cmp( 6, strings => ["Inf", "Minf", "NaN"] )
331 :			-- correct answer is 6, "Inf", "Minf",
332 :			and "NaN" recognized as valid, but
333 :			incorrect answers.
334 :	gage	122
335 :			=cut
336 :
337 :			sub num_cmp {
338 :			my $correctAnswer = shift @_;
339 :			$CA = $correctAnswer;
340 :			my @opt = @_;
341 :			my %out_options;
342 :
343 :			#########################################################################
344 :			# Retain this first check for backword compatibility. Allows input of the form
345 :			# num_cmp($ans, 1, '%0.5f') but warns against it
346 :			#########################################################################
347 :	gage	125	my %known_options = (
348 :			'mode' => 'std',
349 :	gage	122	'format' => $numFormatDefault,
350 :			'tol' => $numAbsTolDefault,
351 :			'relTol' => $numRelPercentTolDefault,
352 :			'units' => undef,
353 :			'strings' => undef,
354 :			'zeroLevel' => $numZeroLevelDefault,
355 :	gage	125	'zeroLevelTol' => $numZeroLevelTolDefault,
356 :	gage	274	'tolType' => 'relative',
357 :			'tolerance' => 1,
358 :	gage	122	'reltol' => undef, #alternate spelling
359 :			'unit' => undef, #alternate spelling
360 :			'debug' => 0
361 :			);
362 :
363 :			my @output_list;
364 :			my( $relPercentTol, $format, $zeroLevel, $zeroLevelTol) = @opt;
365 :
366 :			unless( ref($correctAnswer) eq 'ARRAY' \|\| scalar( @opt ) == 0 \|\|
367 :			( defined($opt[0]) and exists $known_options{$opt[0]} ) ) {
368 :			# unless the first parameter is a list of arrays
369 :			# or the second parameter is a known option or
370 :			# no options were used,
371 :			# use the old num_cmp which does not use options, but has inputs
372 :			# $relPercentTol,$format,$zeroLevel,$zeroLevelTol
373 :			warn "This method of using num_cmp() is deprecated. Please rewrite this" .
374 :			" problem using the options style of parameter passing (or" .
375 :			" check that your first option is spelled correctly).";
376 :
377 :			%out_options = ( 'relTol' => $relPercentTol,
378 :			'format' => $format,
379 :			'zeroLevel' => $zeroLevel,
380 :	gage	274	'zeroLevelTol' => $zeroLevelTol,
381 :	gage	122	'mode' => 'std'
382 :			);
383 :			}
384 :
385 :			#########################################################################
386 :			# Now handle the options assuming they are entered in the form
387 :			# num_cmp($ans, relTol=>1, format=>'%0.5f')
388 :			#########################################################################
389 :			%out_options = @opt;
390 :			assign_option_aliases( \%out_options,
391 :			'reltol' => 'relTol',
392 :			'unit' => 'units',
393 :	gage	274	'abstol' => 'tol',
394 :	gage	122	);
395 :
396 :			set_default_options( \%out_options,
397 :	apizer	275	'tolType' => (defined($out_options{'tol'}) ) ? 'absolute' : 'relative', # the existence of "tol" means that we use absolute tolerance mode
398 :			'tolerance' => (defined($out_options{'tolType'}) && $out_options{'tolType'} eq 'absolute' ) ? $numAbsTolDefault : $numRelPercentTolDefault, # relative tolerance is the default
399 :	gage	274	'mode' => 'std',
400 :	gage	122	'format' => $numFormatDefault,
401 :	gage	274	'tol' => undef,
402 :			'relTol' => undef,
403 :	gage	122	'units' => undef,
404 :			'strings' => undef,
405 :			'zeroLevel' => $numZeroLevelDefault,
406 :			'zeroLevelTol' => $numZeroLevelTolDefault,
407 :			'debug' => 0,
408 :			);
409 :
410 :			# can't use both units and strings
411 :			if( defined( $out_options{'units'} ) && defined( $out_options{'strings'} ) ) {
412 :			warn "Can't use both 'units' and 'strings' in the same problem " .
413 :			"(check your parameters to num_cmp() )";
414 :			}
415 :	apizer	275
416 :			# absolute tolType and relTol are incompatible. So are relative tolType and tol
417 :			if( defined( $out_options{'relTol'} ) && $out_options{'tolType'} eq 'absolute' ) {
418 :			warn "The 'tolType' 'absolute' is not compatible with 'relTol' " .
419 :			"(check your parameters to num_cmp() )";
420 :			}
421 :			if( defined( $out_options{'tol'} ) && $out_options{'tolType'} eq 'relative' ) {
422 :			warn "The 'tolType' 'relative' is not compatible with 'tol' " .
423 :			"(check your parameters to num_cmp() )";
424 :			}
425 :
426 :	gage	122
427 :	gage	274	# Handle legacy options
428 :	gage	122	if ($out_options{tolType} eq 'absolute') {
429 :	gage	274	$out_options{'tolerance'}=$out_options{'tol'} if defined($out_options{'tol'});
430 :	gage	122	delete($out_options{'relTol'}) if exists( $out_options{'relTol'} );
431 :			} else {
432 :	gage	274	$out_options{'tolerance'}=$out_options{'relTol'} if defined($out_options{'relTol'});
433 :	gage	122	# delete($out_options{'tol'}) if exists( $out_options{'tol'} );
434 :			}
435 :	gage	274	# end legacy options
436 :
437 :	gage	122	# thread over lists
438 :			my @ans_list = ();
439 :
440 :			if ( ref($correctAnswer) eq 'ARRAY' ) {
441 :			@ans_list = @{$correctAnswer};
442 :			}
443 :			else { push( @ans_list, $correctAnswer );
444 :			}
445 :
446 :			# produce answer evaluators
447 :			foreach my $ans (@ans_list) {
448 :	gage	198	if( defined( $out_options{'units'} ) ) {
449 :			$ans = "$ans $out_options{'units'}";
450 :
451 :			push( @output_list, NUM_CMP( 'correctAnswer' => $ans,
452 :	gage	274	'tolerance' => $out_options{'tolerance'},
453 :			'tolType' => $out_options{'tolType'},
454 :	gage	198	'format' => $out_options{'format'},
455 :			'mode' => $out_options{'mode'},
456 :			'zeroLevel' => $out_options{'zeroLevel'},
457 :	gage	274	'zeroLevelTol' => $out_options{'zeroLevelTol'},
458 :	gage	198	'debug' => $out_options{'debug'},
459 :			'units' => $out_options{'units'},
460 :	gage	274	)
461 :	gage	198	);
462 :			} elsif( defined( $out_options{'strings'} ) ) {
463 :
464 :	gage	274
465 :	gage	198	push( @output_list, NUM_CMP( 'correctAnswer' => $ans,
466 :	gage	274	'tolerance' => $out_options{tolerance},
467 :	gage	198	'tolType' => $out_options{tolType},
468 :			'format' => $out_options{'format'},
469 :			'mode' => $out_options{'mode'},
470 :			'zeroLevel' => $out_options{'zeroLevel'},
471 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
472 :			'debug' => $out_options{'debug'},
473 :			'strings' => $out_options{'strings'},
474 :			)
475 :			);
476 :			} else {
477 :			push(@output_list,
478 :			NUM_CMP( 'correctAnswer' => $ans,
479 :	gage	122	'tolerance' => $out_options{tolerance},
480 :			'tolType' => $out_options{tolType},
481 :			'format' => $out_options{'format'},
482 :			'mode' => $out_options{'mode'},
483 :			'zeroLevel' => $out_options{'zeroLevel'},
484 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
485 :			'debug' => $out_options{'debug'},
486 :	gage	198	),
487 :			);
488 :	gage	122	}
489 :			}
490 :
491 :	gage	172	return (wantarray) ? @output_list : $output_list[0];
492 :	gage	198	}
493 :	gage	122
494 :			#legacy code for compatability purposes
495 :			sub num_rel_cmp { # compare numbers
496 :			std_num_cmp( @_ );
497 :			}
498 :
499 :
500 :	sam	2	=head3 "mode"_num_cmp() functions
501 :
502 :			There are 16 functions total, 4 for each mode (std, frac, strict, arith). Each mode has
503 :			one "normal" function, one which accepts a list of answers, one which uses absolute
504 :			rather than relative tolerance, and one which uses absolute tolerance and accepts a list.
505 :			The "std" family is documented below; all others work precisely the same.
506 :
507 :			std_num_cmp($correctAnswer) OR
508 :			std_num_cmp($correctAnswer, $relPercentTol) OR
509 :			std_num_cmp($correctAnswer, $relPercentTol, $format) OR
510 :			std_num_cmp($correctAnswer, $relPercentTol, $format, $zeroLevel) OR
511 :			std_num_cmp($correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol)
512 :
513 :			$correctAnswer -- the correct answer
514 :			$relPercentTol -- the tolerance, as a percentage (optional)
515 :	chris	54	$format -- the format of the displayed answer (optional)
516 :			$zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies (optional)
517 :	sam	2	$zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero (optional)
518 :
519 :			std_num_cmp() uses standard mode (arithmetic operations and elementary
520 :			functions allowed) and relative tolerance. Options are specified by
521 :			one or more parameters. Note that if you wish to set an option which
522 :			is later in the parameter list, you must set all previous options.
523 :
524 :			std_num_cmp_abs($correctAnswer) OR
525 :			std_num_cmp_abs($correctAnswer, $absTol) OR
526 :			std_num_cmp_abs($correctAnswer, $absTol, $format)
527 :
528 :	chris	54	$correctAnswer -- the correct answer
529 :	sam	2	$absTol -- an absolute tolerance (optional)
530 :			$format -- the format of the displayed answer (optional)
531 :
532 :			std_num_cmp_abs() uses standard mode and absolute tolerance. Options
533 :			are set as with std_num_cmp(). Note that $zeroLevel and $zeroLevelTol
534 :			do not apply with absolute tolerance.
535 :
536 :			std_num_cmp_list($relPercentTol, $format, @answerList)
537 :
538 :	chris	54	$relPercentTol -- the tolerance, as a percentage
539 :	sam	2	$format -- the format of the displayed answer(s)
540 :			@answerList -- a list of one or more correct answers
541 :
542 :			std_num_cmp_list() uses standard mode and relative tolerance. There
543 :			is no way to set $zeroLevel or $zeroLevelTol. Note that no
544 :			parameters are optional. All answers in the list will be
545 :			evaluated with the same set of parameters.
546 :
547 :			std_num_cmp_abs_list($absTol, $format, @answerList)
548 :
549 :			$absTol -- an absolute tolerance
550 :			$format -- the format of the displayed answer(s)
551 :			@answerList -- a list of one or more correct answers
552 :
553 :			std_num_cmp_abs_list() uses standard mode and absolute tolerance.
554 :			Note that no parameters are optional. All answers in the list will be
555 :			evaluated with the same set of parameters.
556 :
557 :			arith_num_cmp(), arith_num_cmp_list(), arith_num_cmp_abs(), arith_num_cmp_abs_list()
558 :			strict_num_cmp(), strict_num_cmp_list(), strict_num_cmp_abs(), strict_num_cmp_abs_list()
559 :			frac_num_cmp(), frac_num_cmp_list(), frac_num_cmp_abs(), frac_num_cmp_abs_list()
560 :
561 :			Examples:
562 :
563 :			ANS( strict_num_cmp( 3.14159 ) ) -- The student answer must be a number
564 :			in decimal or scientific notation which is within .1 percent of 3.14159.
565 :			This assumes $numRelPercentTolDefault has been set to .1.
566 :			ANS( strict_num_cmp( $answer, .01 ) ) -- The student answer must be a
567 :			number within .01 percent of $answer (e.g. 3.14159 if $answer is 3.14159
568 :			or $answer is "pi" or $answer is 4*atan(1)).
569 :			ANS( frac_num_cmp( $answer) ) or ANS( frac_num_cmp( $answer,.01 )) --
570 :			The student answer can be a number or fraction, e.g. 2/3.
571 :			ANS( arith_num_cmp( $answer) ) or ANS( arith_num_cmp( $answer,.01 )) --
572 :			The student answer can be an arithmetic expression, e.g. (2+3)/7-2^.5 .
573 :			ANS( std_num_cmp( $answer) ) or ANS( std_num_cmp( $answer,.01 )) --
574 :			The student answer can contain elementary functions, e.g. sin(.3+pi/2)
575 :
576 :			=cut
577 :
578 :	chris	54	sub std_num_cmp { # compare numbers allowing use of elementary functions
579 :	chris	22	my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
580 :	sam	2
581 :	apizer	237	my %options = ( 'relTol' => $relPercentTol,
582 :	chris	22	'format' => $format,
583 :			'zeroLevel' => $zeroLevel,
584 :			'zeroLevelTol' => $zeroLevelTol
585 :	chris	81	);
586 :	chris	22
587 :			set_default_options( \%options,
588 :			'tolType' => 'relative',
589 :			'tolerance' => $numRelPercentTolDefault,
590 :	chris	54	'mode' => 'std',
591 :			'format' => $numFormatDefault,
592 :			'relTol' => $numRelPercentTolDefault,
593 :	chris	22	'zeroLevel' => $numZeroLevelDefault,
594 :			'zeroLevelTol' => $numZeroLevelTolDefault,
595 :			'debug' => 0,
596 :	chris	81	);
597 :	gage	34
598 :	chris	22	num_cmp([$correctAnswer], %options);
599 :	sam	2	}
600 :
601 :			## Similar to std_num_cmp but accepts a list of numbers in the form
602 :			## std_num_cmp_list(relpercentTol,format,ans1,ans2,ans3,...)
603 :			## format is of the form "%10.3g" or "", i.e., a format suitable for sprintf(). Use "" for default
604 :			## You must enter a format and tolerance
605 :	chris	81
606 :	chris	54	sub std_num_cmp_list {
607 :	sam	2	my ( $relPercentTol, $format, @answerList) = @_;
608 :
609 :	apizer	237	my %options = ( 'relTol' => $relPercentTol,
610 :	chris	54	'format' => $format,
611 :	chris	81	);
612 :	chris	22
613 :			set_default_options( \%options,
614 :			'tolType' => 'relative',
615 :			'tolerance' => $numRelPercentTolDefault,
616 :			'mode' => 'std',
617 :			'format' => $numFormatDefault,
618 :			'relTol' => $numRelPercentTolDefault,
619 :			'zeroLevel' => $numZeroLevelDefault,
620 :			'zeroLevelTol' => $numZeroLevelTolDefault,
621 :			'debug' => 0,
622 :			);
623 :
624 :			num_cmp(\@answerList, %options);
625 :
626 :	sam	2	}
627 :
628 :	chris	54	sub std_num_cmp_abs { # compare numbers allowing use of elementary functions with absolute tolerance
629 :	sam	2	my ( $correctAnswer, $absTol, $format) = @_;
630 :	chris	22	my %options = ( 'tolerance' => $absTol,
631 :	chris	54	'format' => $format
632 :	chris	81	);
633 :	chris	22
634 :			set_default_options (\%options,
635 :			'tolType' => 'absolute',
636 :			'tolerance' => $absTol,
637 :			'mode' => 'std',
638 :			'format' => $numFormatDefault,
639 :			'zeroLevel' => 0,
640 :			'zeroLevelTol' => 0,
641 :			'debug' => 0,
642 :	chris	81	);
643 :	sam	2
644 :	chris	22	num_cmp([$correctAnswer], %options);
645 :	sam	2	}
646 :
647 :			## See std_num_cmp_list for usage
648 :	chris	22
649 :	chris	54	sub std_num_cmp_abs_list {
650 :	sam	2	my ( $absTol, $format, @answerList ) = @_;
651 :
652 :	chris	22	my %options = ( 'tolerance' => $absTol,
653 :			'format' => $format,
654 :	chris	81	);
655 :	chris	22
656 :			set_default_options( \%options,
657 :			'tolType' => 'absolute',
658 :			'tolerance' => $absTol,
659 :			'mode' => 'std',
660 :			'format' => $numFormatDefault,
661 :			'zeroLevel' => 0,
662 :			'zeroLevelTol' => 0,
663 :			'debug' => 0,
664 :	chris	81	);
665 :	chris	22
666 :			num_cmp(\@answerList, %options);
667 :	sam	2	}
668 :
669 :	chris	54	sub frac_num_cmp { # only allow fractions and numbers as submitted answer
670 :	sam	2
671 :	gage	124	my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
672 :
673 :	apizer	237	my %options = ( 'relTol' => $relPercentTol,
674 :			'format' => $format,
675 :			'zeroLevel' => $zeroLevel,
676 :			'zeroLevelTol' => $zeroLevelTol
677 :	gage	124	);
678 :	chris	22
679 :	gage	124	set_default_options( \%options,
680 :			'tolType' => 'relative',
681 :			'tolerance' => $relPercentTol,
682 :			'mode' => 'frac',
683 :			'format' => $numFormatDefault,
684 :			'zeroLevel' => $numZeroLevelDefault,
685 :			'zeroLevelTol' => $numZeroLevelTolDefault,
686 :			'relTol' => $numRelPercentTolDefault,
687 :			'debug' => 0,
688 :			);
689 :	chris	22
690 :	gage	124	num_cmp([$correctAnswer], %options);
691 :	sam	2	}
692 :
693 :			## See std_num_cmp_list for usage
694 :	chris	54	sub frac_num_cmp_list {
695 :	gage	124	my ( $relPercentTol, $format, @answerList ) = @_;
696 :
697 :	apizer	237	my %options = ( 'relTol' => $relPercentTol,
698 :	gage	124	'format' => $format
699 :			);
700 :
701 :			set_default_options( \%options,
702 :			'tolType' => 'relative',
703 :			'tolerance' => $relPercentTol,
704 :			'mode' => 'frac',
705 :			'format' => $numFormatDefault,
706 :			'zeroLevel' => $numZeroLevelDefault,
707 :			'zeroLevelTol' => $numZeroLevelTolDefault,
708 :			'relTol' => $numRelPercentTolDefault,
709 :			'debug' => 0,
710 :			);
711 :
712 :			num_cmp(\@answerList, %options);
713 :	sam	2	}
714 :
715 :	chris	54	sub frac_num_cmp_abs { # only allow fraction expressions as submitted answer with absolute tolerance
716 :	chris	22	my ( $correctAnswer, $absTol, $format ) = @_;
717 :
718 :	chris	54	my %options = ( 'tolerance' => $absTol,
719 :			'format' => $format
720 :	chris	81	);
721 :	gage	124
722 :			set_default_options (\%options,
723 :			'tolType' => 'absolute',
724 :			'tolerance' => $absTol,
725 :			'mode' => 'frac',
726 :			'format' => $numFormatDefault,
727 :			'zeroLevel' => 0,
728 :			'zeroLevelTol' => 0,
729 :			'debug' => 0,
730 :			);
731 :	gage	32
732 :	chris	54	num_cmp([$correctAnswer], %options);
733 :	sam	2	}
734 :	chris	22
735 :	sam	2	## See std_num_cmp_list for usage
736 :	chris	81
737 :	chris	54	sub frac_num_cmp_abs_list {
738 :	chris	22	my ( $absTol, $format, @answerList ) = @_;
739 :
740 :	chris	54	my %options = ( 'tolerance' => $absTol,
741 :			'format' => $format
742 :	chris	81	);
743 :	chris	22
744 :			set_default_options (\%options,
745 :			'tolType' => 'absolute',
746 :			'tolerance' => $absTol,
747 :			'mode' => 'frac',
748 :			'format' => $numFormatDefault,
749 :			'zeroLevel' => 0,
750 :			'zeroLevelTol' => 0,
751 :			'debug' => 0,
752 :	chris	81	);
753 :	chris	22
754 :			num_cmp(\@answerList, %options);
755 :	sam	2	}
756 :
757 :
758 :	chris	54	sub arith_num_cmp { # only allow arithmetic expressions as submitted answer
759 :	chris	22
760 :			my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
761 :
762 :	apizer	237	my %options = ( 'relTol' => $relPercentTol,
763 :	chris	54	'format' => $format,
764 :			'zeroLevel' => $zeroLevel,
765 :			'zeroLevelTol' => $zeroLevelTol
766 :	chris	81	);
767 :	chris	22
768 :			set_default_options( \%options,
769 :	chris	54	'tolType' => 'relative',
770 :			'tolerance' => $relPercentTol,
771 :			'mode' => 'arith',
772 :			'format' => $numFormatDefault,
773 :			'zeroLevel' => $numZeroLevelDefault,
774 :			'zeroLevelTol' => $numZeroLevelTolDefault,
775 :			'relTol' => $numRelPercentTolDefault,
776 :			'debug' => 0,
777 :	chris	81	);
778 :	sam	2
779 :	chris	22	num_cmp([$correctAnswer], %options);
780 :	sam	2	}
781 :
782 :			## See std_num_cmp_list for usage
783 :	chris	54	sub arith_num_cmp_list {
784 :	chris	22	my ( $relPercentTol, $format, @answerList ) = @_;
785 :	sam	2
786 :	apizer	237	my %options = ( 'relTol' => $relPercentTol,
787 :	chris	54	'format' => $format,
788 :	chris	81	);
789 :	chris	22
790 :			set_default_options( \%options,
791 :			'tolType' => 'relative',
792 :			'tolerance' => $relPercentTol,
793 :			'mode' => 'arith',
794 :			'format' => $numFormatDefault,
795 :			'zeroLevel' => $numZeroLevelDefault,
796 :			'zeroLevelTol' => $numZeroLevelTolDefault,
797 :			'relTol' => $numRelPercentTolDefault,
798 :			'debug' => 0,
799 :	chris	81	);
800 :
801 :	chris	22	num_cmp(\@answerList, %options);
802 :	sam	2	}
803 :
804 :	chris	54	sub arith_num_cmp_abs { # only allow arithmetic expressions as submitted answer with absolute tolerance
805 :	chris	22	my ( $correctAnswer, $absTol, $format ) = @_;
806 :
807 :	chris	54	my %options = ( 'tolerance' => $absTol,
808 :			'format' => $format
809 :	chris	81	);
810 :	chris	22
811 :			set_default_options (\%options,
812 :			'tolType' => 'absolute',
813 :			'tolerance' => $absTol,
814 :			'mode' => 'arith',
815 :			'format' => $numFormatDefault,
816 :			'zeroLevel' => 0,
817 :			'zeroLevelTol' => 0,
818 :			'debug' => 0,
819 :	chris	81	);
820 :
821 :	chris	22	num_cmp([$correctAnswer], %options);
822 :	sam	2	}
823 :
824 :			## See std_num_cmp_list for usage
825 :	chris	54	sub arith_num_cmp_abs_list {
826 :	chris	22	my ( $absTol, $format, @answerList ) = @_;
827 :
828 :	chris	54	my %options = ( 'tolerance' => $absTol,
829 :			'format' => $format
830 :	chris	81	);
831 :	chris	22
832 :			set_default_options (\%options,
833 :			'tolType' => 'absolute',
834 :			'tolerance' => $absTol,
835 :			'mode' => 'arith',
836 :			'format' => $numFormatDefault,
837 :			'zeroLevel' => 0,
838 :			'zeroLevelTol' => 0,
839 :			'debug' => 0,
840 :			);
841 :
842 :	chris	81	num_cmp(\@answerList, %options);
843 :	sam	2	}
844 :
845 :	chris	54	sub strict_num_cmp { # only allow numbers as submitted answer
846 :	chris	22	my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
847 :
848 :	apizer	237	my %options = ( 'relTol' => $relPercentTol,
849 :	chris	54	'format' => $format,
850 :			'zeroLevel' => $zeroLevel,
851 :			'zeroLevelTol' => $zeroLevelTol
852 :	chris	22	);
853 :
854 :			set_default_options( \%options,
855 :			'tolType' => 'relative',
856 :			'tolerance' => $relPercentTol,
857 :			'mode' => 'strict',
858 :			'format' => $numFormatDefault,
859 :			'zeroLevel' => $numZeroLevelDefault,
860 :			'zeroLevelTol' => $numZeroLevelTolDefault,
861 :			'relTol' => $numRelPercentTolDefault,
862 :			'debug' => 0,
863 :			);
864 :			num_cmp([$correctAnswer], %options);
865 :	chris	81
866 :	sam	2	}
867 :
868 :			## See std_num_cmp_list for usage
869 :	chris	54	sub strict_num_cmp_list { # compare numbers
870 :	chris	81	my ( $relPercentTol, $format, @answerList ) = @_;
871 :	chris	22
872 :	apizer	237	my %options = ( 'relTol' => $relPercentTol,
873 :	chris	54	'format' => $format,
874 :	chris	81	);
875 :	chris	22
876 :	chris	81	set_default_options( \%options,
877 :	chris	22	'tolType' => 'relative',
878 :			'tolerance' => $relPercentTol,
879 :			'mode' => 'strict',
880 :			'format' => $numFormatDefault,
881 :			'zeroLevel' => $numZeroLevelDefault,
882 :			'zeroLevelTol' => $numZeroLevelTolDefault,
883 :			'relTol' => $numRelPercentTolDefault,
884 :			'debug' => 0,
885 :	chris	81	);
886 :
887 :			num_cmp(\@answerList, %options);
888 :			}
889 :	sam	2
890 :	chris	22
891 :	chris	54	sub strict_num_cmp_abs { # only allow numbers as submitted answer with absolute tolerance
892 :	chris	22	my ( $correctAnswer, $absTol, $format ) = @_;
893 :
894 :	chris	54	my %options = ( 'tolerance' => $absTol,
895 :			'format' => $format
896 :	chris	81	);
897 :	chris	22
898 :			set_default_options (\%options,
899 :			'tolType' => 'absolute',
900 :			'tolerance' => $absTol,
901 :			'mode' => 'strict',
902 :			'format' => $numFormatDefault,
903 :			'zeroLevel' => 0,
904 :			'zeroLevelTol' => 0,
905 :			'debug' => 0,
906 :	chris	81	);
907 :	chris	22	num_cmp([$correctAnswer], %options);
908 :
909 :	sam	2	}
910 :
911 :			## See std_num_cmp_list for usage
912 :	chris	54	sub strict_num_cmp_abs_list { # compare numbers
913 :	chris	22	my ( $absTol, $format, @answerList ) = @_;
914 :	chris	81
915 :	chris	54	my %options = ( 'tolerance' => $absTol,
916 :			'format' => $format
917 :	chris	81	);
918 :	sam	2
919 :	chris	22	set_default_options (\%options,
920 :			'tolType' => 'absolute',
921 :			'tolerance' => $absTol,
922 :			'mode' => 'strict',
923 :			'format' => $numFormatDefault,
924 :			'zeroLevel' => 0,
925 :			'zeroLevelTol' => 0,
926 :			'debug' => 0,
927 :	chris	81	);
928 :	chris	22
929 :			num_cmp(\@answerList, %options);
930 :	sam	2	}
931 :
932 :	chris	81	## sub numerical_compare_with_units
933 :	sam	2	## Compares a number with units
934 :			## Deprecated; use num_cmp()
935 :			##
936 :			## IN: a string which includes the numerical answer and the units
937 :			## a hash with the following keys (all optional):
938 :	chris	81	## mode -- 'std', 'frac', 'arith', or 'strict'
939 :			## format -- the format to use when displaying the answer
940 :			## tol -- an absolute tolerance, or
941 :			## relTol -- a relative tolerance
942 :			## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
943 :	sam	2	## zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero
944 :
945 :	chris	35	# This mode is depricated. send input through num_cmp -- it can handle units.
946 :	chris	54
947 :			sub numerical_compare_with_units {
948 :	chris	81	my $correct_answer = shift; # the answer is a string which includes both the numerical answer and the units.
949 :	chris	22	my %options = @_; # all of the other inputs are (key value) pairs
950 :	sam	2
951 :	chris	22	# Prepare the correct answer
952 :			$correct_answer = str_filters( $correct_answer, 'trim_whitespace' );
953 :	sam	2
954 :	chris	22	# it surprises me that the match below works since the first .* is greedy.
955 :			my ($correct_num_answer, $correct_units) = $correct_answer =~ /^(.)\s+([^\s])$/;
956 :			$options{units} = $correct_units;
957 :
958 :			num_cmp($correct_num_answer, %options);
959 :	sam	2	}
960 :	chris	22
961 :	sam	2
962 :			=head3 std_num_str_cmp()
963 :	chris	22
964 :	sam	2	NOTE: This function is maintained for compatibility. num_cmp() with the
965 :			'strings' parameter is slightly preferred.
966 :
967 :			std_num_str_cmp() is used when the correct answer could be either a number or a
968 :			string. For example, if you wanted the student to evaluate a function at number
969 :			of points, but write "Inf" or "Minf" if the function is unbounded. This routine
970 :			will provide error messages that do not give a hint as to whether the correct
971 :			answer is a string or a number. For numerical comparisons, std_num_cmp() is
972 :			used internally; for string comparisons, std_str_cmp() is used.
973 :
974 :			std_num_str_cmp( $correctAnswer ) OR
975 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings ) OR
976 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol ) OR
977 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format ) OR
978 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format, $zeroLevel ) OR
979 :			std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format,
980 :			$zeroLevel, $zeroLevelTol )
981 :
982 :			$correctAnswer -- the correct answer
983 :			$ra_legalStrings -- a reference to an array of legal strings, e.g. ["str1", "str2"]
984 :			$relPercentTol -- the error tolerance as a percentage
985 :	chris	54	$format -- the display format
986 :			$zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
987 :	sam	2	$zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero
988 :
989 :			Example:
990 :			ANS( std_num_str_cmp( $ans, ["Inf", "Minf", "NaN"] ) );
991 :
992 :			=cut
993 :
994 :	chris	54	sub std_num_str_cmp {
995 :	sam	2	my ( $correctAnswer, $ra_legalStrings, $relpercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_;
996 :	chris	35	# warn ('This method is depreciated. Use num_cmp instead.');
997 :			return num_cmp ($correctAnswer, strings=>$ra_legalStrings, relTol=>$relpercentTol, format=>$format,
998 :			zeroLevel=>$zeroLevel, zeroLevelTol=>$zeroLevelTol);
999 :			}
1000 :	sam	2
1001 :	chris	54	sub NUM_CMP { # low level numeric compare
1002 :	chris	22	my %num_params = @_;
1003 :	gage	34
1004 :	chris	22	my @keys = qw ( correctAnswer tolerance tolType format mode zeroLevel zeroLevelTol debug );
1005 :			foreach my $key (@keys) {
1006 :			warn "$key must be defined in options when calling NUM_CMP" unless defined ($num_params{$key});
1007 :			}
1008 :	sam	2
1009 :	chris	22	my $correctAnswer = $num_params{'correctAnswer'};
1010 :			my $format = $num_params{'format'};
1011 :			my $mode = $num_params{'mode'};
1012 :
1013 :			if( $num_params{tolType} eq 'relative' ) {
1014 :			$num_params{'tolerance'} = .01*$num_params{'tolerance'};
1015 :			}
1016 :
1017 :			my $formattedCorrectAnswer;
1018 :			my $correct_units;
1019 :			my $correct_num_answer;
1020 :			my %correct_units;
1021 :	chris	35	my $corrAnswerIsString = 0;
1022 :
1023 :	sam	2
1024 :	chris	22	if (defined($num_params{units}) && $num_params{units}) {
1025 :			$correctAnswer = str_filters( $correctAnswer, 'trim_whitespace' );
1026 :			# units are in form stuff space units where units contains no spaces.
1027 :
1028 :			($correct_num_answer, $correct_units) = $correctAnswer =~ /^(.)\s+([^\s])$/;
1029 :			%correct_units = Units::evaluate_units($correct_units);
1030 :			if ( defined( $correct_units{'ERROR'} ) ) {
1031 :			warn ("ERROR: The answer \"$correctAnswer\" in the problem definition cannot be parsed:\n" .
1032 :			"$correct_units{'ERROR'}\n");
1033 :	sam	2	}
1034 :	chris	22	# $formattedCorrectAnswer = spf($correct_num_answer,$num_params{'format'}) . " $correct_units";
1035 :	chris	35	$formattedCorrectAnswer = prfmt($correct_num_answer,$num_params{'format'}) . " $correct_units";
1036 :	chris	22
1037 :	chris	35	} elsif (defined($num_params{strings}) && $num_params{strings}) {
1038 :			my $legalString = '';
1039 :			my @legalStrings = @{$num_params{strings}};
1040 :			$correct_num_answer = $correctAnswer;
1041 :			$formattedCorrectAnswer = $correctAnswer;
1042 :			foreach $legalString (@legalStrings) {
1043 :			if ( uc($correctAnswer) eq uc($legalString) ) {
1044 :			$corrAnswerIsString = 1;
1045 :	gage	200
1046 :	chris	35	last;
1047 :			}
1048 :			} ## at this point $corrAnswerIsString = 0 iff correct answer is numeric
1049 :	chris	22	} else {
1050 :			$correct_num_answer = $correctAnswer;
1051 :			$formattedCorrectAnswer = prfmt( $correctAnswer, $num_params{'format'} );
1052 :			}
1053 :	sam	2
1054 :	chris	22	$correct_num_answer = math_constants($correct_num_answer);
1055 :
1056 :			my $PGanswerMessage = '';
1057 :
1058 :			my ($inVal,$correctVal,$PG_eval_errors,$PG_full_error_report);
1059 :
1060 :	chris	35	if (defined($correct_num_answer) && $correct_num_answer =~ /\S/ && $corrAnswerIsString == 0 ) {
1061 :	chris	49	($correctVal, $PG_eval_errors,$PG_full_error_report) = PG_answer_eval($correct_num_answer);
1062 :	gage	200	} else { # case of a string answer
1063 :			$PG_eval_errors = ' ';
1064 :			$correctVal = $correctAnswer;
1065 :	chris	22	}
1066 :	sam	2
1067 :	chris	35	if ( ($PG_eval_errors && $corrAnswerIsString == 0) or ((not is_a_number($correctVal)) && $corrAnswerIsString == 0)) {
1068 :			##error message from eval or above
1069 :	chris	22	warn "Error in 'correct' answer: $PG_eval_errors<br>
1070 :			The answer $correctAnswer evaluates to $correctVal,
1071 :			which cannot be interpreted as a number. ";
1072 :
1073 :			}
1074 :			#########################################################################
1075 :	sam	2
1076 :	chris	22	#construct the answer evaluator
1077 :			my $answer_evaluator = new AnswerEvaluator;
1078 :			$answer_evaluator->{debug} = $num_params{debug};
1079 :	gage	159	$answer_evaluator->ans_hash(
1080 :			correct_ans => $correctVal,
1081 :			type => "${mode}_number",
1082 :			tolerance => $num_params{tolerance},
1083 :			tolType => $num_params{tolType},
1084 :			units => $correct_units,
1085 :			original_correct_ans => $formattedCorrectAnswer,
1086 :			rh_correct_units => \%correct_units,
1087 :			answerIsString => $corrAnswerIsString,
1088 :	chris	22	);
1089 :			my ($in, $formattedSubmittedAnswer);
1090 :			$answer_evaluator->install_pre_filter(sub {my $rh_ans = shift;
1091 :			$rh_ans->{original_student_ans} = $rh_ans->{student_ans}; $rh_ans;}
1092 :			);
1093 :			if (defined($num_params{units}) && $num_params{units}) {
1094 :			$answer_evaluator->install_pre_filter(\&check_units);
1095 :			}
1096 :	chris	35	if (defined($num_params{strings}) && $num_params{strings}) {
1097 :			$answer_evaluator->install_pre_filter(\&check_strings, %num_params);
1098 :			}
1099 :
1100 :	chris	22	$answer_evaluator->install_pre_filter(\&check_syntax);
1101 :
1102 :			$answer_evaluator->install_pre_filter(\&math_constants);
1103 :	chris	44
1104 :	chris	22	if ($mode eq 'std') {
1105 :			# do nothing
1106 :			} elsif ($mode eq 'strict') {
1107 :			$answer_evaluator->install_pre_filter(\&is_a_number);
1108 :			} elsif ($mode eq 'arith') {
1109 :			$answer_evaluator->install_pre_filter(\&is_an_arithmetic_expression);
1110 :			} elsif ($mode eq 'frac') {
1111 :			$answer_evaluator->install_pre_filter(\&is_a_fraction);
1112 :	sam	2
1113 :	chris	22	} else {
1114 :			$PGanswerMessage = 'Tell your professor that there is an error in his or her answer mechanism. No mode was specified.';
1115 :			$formattedSubmittedAnswer = $in;
1116 :	sam	2	}
1117 :	chris	44
1118 :	chris	35	if ($corrAnswerIsString == 0 ){ # avoiding running compare_numbers when correct answer is a string.
1119 :			$answer_evaluator->install_evaluator(\&compare_numbers, %num_params);
1120 :	chris	49	}
1121 :
1122 :
1123 :	gage	40	###############################################################################
1124 :			# We'll leave these next lines out for now, so that the evaluated versions of the student's and professor's
1125 :			# can be displayed in the answer message. This may still cause a few anomolies when strings are used
1126 :			#
1127 :			###############################################################################
1128 :	sam	2
1129 :	chris	41	$answer_evaluator->install_post_filter(\&fix_answers_for_display);
1130 :	sam	2
1131 :	chris	81	$answer_evaluator->install_post_filter(sub {my $rh_ans = shift;
1132 :	chris	22	return $rh_ans unless $rh_ans->catch_error('EVAL');
1133 :			$rh_ans->{student_ans} = $rh_ans->{original_student_ans}. ' '. $rh_ans->{error_message};
1134 :			$rh_ans->clear_error('EVAL'); } );
1135 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('SYNTAX'); } );
1136 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('UNITS'); } );
1137 :			$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('NUMBER'); } );
1138 :	chris	35	$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('STRING'); } );
1139 :	chris	22	$answer_evaluator;
1140 :	sam	2	}
1141 :
1142 :
1143 :	chris	50
1144 :	sam	2	##########################################################################
1145 :			##########################################################################
1146 :			## Function answer evaluators
1147 :
1148 :			=head2 Function Answer Evaluators
1149 :
1150 :			Function answer evaluators take in a function, compare it numerically to a
1151 :			correct function, and return a score. They can require an exactly equivalent
1152 :			function, or one that is equal up to a constant. They can accept or reject an
1153 :			answer based on specified tolerances for numerical deviation.
1154 :
1155 :			Function Comparison Options
1156 :
1157 :			correctEqn -- The correct equation, specified as a string. It may include
1158 :			all basic arithmetic operations, as well as elementary
1159 :			functions. Variable usage is described below.
1160 :
1161 :			Variables -- The independent variable(s). When comparing the correct
1162 :			equation to the student equation, each variable will be
1163 :			replaced by a certain number of numerical values. If
1164 :			the student equation agrees numerically with the correct
1165 :			equation, they are considered equal. Note that all
1166 :			comparison is numeric; it is possible (although highly
1167 :			unlikely and never a practical concern) for two unequal
1168 :			functions to yield the same numerical results.
1169 :
1170 :			Limits -- The limits of evaluation for the independent variables.
1171 :			Each variable is evaluated only in the half-open interval
1172 :			[lower_limit, upper_limit). This is useful if the function
1173 :			has a singularity or is not defined in a certain range.
1174 :			For example, the function "sqrt(-1-x)" could be evaluated
1175 :			in [-2,-1).
1176 :
1177 :			Tolerance -- Tolerance in function comparisons works exactly as in
1178 :			numerical comparisons; see the numerical comparison
1179 :			documentation for a complete description. Note that the
1180 :			tolerance does applies to the function as a whole, not
1181 :			each point individually.
1182 :
1183 :			Number of -- Specifies how many points to evaluate each variable at. This
1184 :			Points is typically 3, but can be set higher if it is felt that
1185 :			there is a strong possibility of "false positives."
1186 :
1187 :			Maximum -- Sets the maximum size of the constant of integration. For
1188 :			Constant of technical reasons concerning floating point arithmetic, if
1189 :			Integration the additive constant, i.e., the constant of integration, is
1190 :			greater (in absolute value) than maxConstantOfIntegration
1191 :			AND is greater than maxConstantOfIntegration times the
1192 :			correct value, WeBWorK will give an error message saying
1193 :			that it can not handle such a large constant of integration.
1194 :			This is to prevent e.g. cos(x) + 1E20 or even 1E20 as being
1195 :			accepted as a correct antiderivatives of sin(x) since
1196 :			floating point arithmetic cannot tell the difference
1197 :			between cos(x) + 1E20, 1E20, and -cos(x) + 1E20.
1198 :
1199 :			Technical note: if you examine the code for the function routines, you will see
1200 :			that most subroutines are simply doing some basic error-checking and then
1201 :			passing the parameters on to the low-level FUNCTION_CMP(). Because this routine
1202 :			is set up to handle multivariable functions, with single-variable functions as
1203 :			a special case, it is possible to pass multivariable parameters to single-
1204 :			variable functions. This usage is strongly discouraged as unnecessarily
1205 :			confusing. Avoid it.
1206 :
1207 :			Default Values (As of 7/24/2000) (Option -- Variable Name -- Value)
1208 :
1209 :	chris	81	Variable -- $functVarDefault -- 'x'
1210 :	sam	2	Relative Tolerance -- $functRelPercentTolDefault -- .1
1211 :	chris	81	Absolute Tolerance -- $functAbsTolDefault -- .001
1212 :			Lower Limit -- $functLLimitDefault -- .0000001
1213 :			Upper Limit -- $functULimitDefault -- 1
1214 :			Number of Points -- $functNumOfPoints -- 3
1215 :			Zero Level -- $functZeroLevelDefault -- 1E-14
1216 :			Zero Level Tolerance -- $functZeroLevelTolDefault -- 1E-12
1217 :			Maximum Constant -- $functMaxConstantOfIntegration -- 1E8
1218 :	sam	2	of Integration
1219 :
1220 :			=cut
1221 :
1222 :	gage	122
1223 :
1224 :			=head3 fun_cmp()
1225 :
1226 :			Compares a function or a list of functions, using a named hash of options to set
1227 :			parameters. This can make for more readable code than using the function_cmp()
1228 :			style, but some people find one or the other easier to remember.
1229 :
1230 :			ANS( fun_cmp( answer or answer_array_ref, options_hash ) );
1231 :
1232 :			1. a string containing the correct function, or a reference to an
1233 :			array of correct functions
1234 :			2. a hash containing the following items (all optional):
1235 :			var -- either the number of variables or a reference to an
1236 :			array of variable names (see below)
1237 :			limits -- reference to an array of arrays of limits (see below), or:
1238 :			mode -- 'std' (default) (function must match exactly), or:
1239 :			'antider' (function must match up to a constant)
1240 :			relTol -- (default) a relative tolerance (as a percentage), or:
1241 :			tol -- an absolute tolerance for error
1242 :			numPoints -- the number of points to evaluate the function at
1243 :			maxConstantOfIntegration -- maximum size of the constant of integration
1244 :			zeroLevel -- if the correct answer is this close to zero, then
1245 :			zeroLevelTol applies
1246 :			zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1247 :			params an array of "free" parameters which can be used to adapt
1248 :			the correct answer to the submitted answer. (e.g. ['c'] for
1249 :			a constant of integration in the answer x^3/3 + c.
1250 :			debug -- when set to 1 this provides extra information while checking the
1251 :			the answer.
1252 :
1253 :			Returns an answer evaluator, or (if given a reference to an array
1254 :			of answers), a list of answer evaluators
1255 :
1256 :			ANSWER:
1257 :
1258 :			The answer must be in the form of a string. The answer can contain
1259 :			functions, pi, e, and arithmetic operations. However, the correct answer
1260 :			string follows a slightly stricter syntax than student answers; specifically,
1261 :			there is no implicit multiplication. So the correct answer must be "3*x" rather
1262 :			than "3 x". Students can still enter "3 x".
1263 :
1264 :			VARIABLES:
1265 :
1266 :			The var parameter can contain either a number or a reference to an array of
1267 :			variable names. If it contains a number, the variables are named automatically
1268 :			as follows: 1 variable -- x
1269 :			2 variables -- x, y
1270 :			3 variables -- x, y, z
1271 :			4 or more -- x_1, x_2, x_3, etc.
1272 :			If the var parameter contains a reference to an array of variable names, then
1273 :			the number of variables is determined by the number of items in the array. A
1274 :			reference to an array is created with brackets, e.g. "var => ['r', 's', 't']".
1275 :			If only one variable is being used, you can write either "var => ['t']" for
1276 :			consistency or "var => 't'" as a shortcut. The default is one variable, x.
1277 :
1278 :			LIMITS:
1279 :
1280 :			Limits are specified with the limits parameter. You may NOT use llimit/ulimit.
1281 :			If you specify limits for one variable, you must specify them for all variables.
1282 :			The limit parameter must be a reference to an array of arrays of the form
1283 :			[lower_limit. upper_limit], each array corresponding to the lower and upper
1284 :			endpoints of the (half-open) domain of one variable. For example,
1285 :			"vars => 2, limits => [[0,2], [-3,8]]" would cause x to be evaluated in [0,2) and
1286 :			y to be evaluated in [-3,8). If only one variable is being used, you can write
1287 :			either "limits => [[0,3]]" for consistency or "limits => [0,3]" as a shortcut.
1288 :
1289 :			EXAMPLES:
1290 :
1291 :			fun_cmp( "3*x" ) -- standard compare, variable is x
1292 :			fun_cmp( ["3x", "4x+3", "3x*2"] ) -- standard compare, defaults used for all three functions
1293 :			fun_cmp( "3*t", var => 't' ) -- standard compare, variable is t
1294 :			fun_cmp( "5xy*z", var => 3 ) -- x, y and z are the variables
1295 :			fun_cmp( "5*x", mode => 'antider' ) -- student answer must match up to constant (i.e., 5x+C)
1296 :			fun_cmp( ["3xy", "4xy"], limits => [[0,2], [5,7]] ) -- x evaluated in [0,2)
1297 :			y evaluated in [5,7)
1298 :
1299 :			=cut
1300 :
1301 :			sub fun_cmp {
1302 :			my $correctAnswer = shift @_;
1303 :			my %opt = @_;
1304 :
1305 :			assign_option_aliases( \%opt,
1306 :			'vars' => 'var', # set the standard option 'var' to the one specified as vars
1307 :			'domain' => 'limits', # set the standard option 'limits' to the one specified as domain
1308 :			'reltol' => 'relTol',
1309 :			'param' => 'params',
1310 :			);
1311 :
1312 :			set_default_options( \%opt,
1313 :			'var' => $functVarDefault,
1314 :			'params' => [],
1315 :			'limits' => [[$functLLimitDefault, $functULimitDefault]],
1316 :			'mode' => 'std',
1317 :			'tolType' => (defined($opt{tol}) ) ? 'absolute' : 'relative',
1318 :			'tol' => .01, # default mode should be relative, to obtain this tol must not be defined
1319 :			'relTol' => $functRelPercentTolDefault,
1320 :			'numPoints' => $functNumOfPoints,
1321 :			'maxConstantOfIntegration' => $functMaxConstantOfIntegration,
1322 :			'zeroLevel' => $functZeroLevelDefault,
1323 :			'zeroLevelTol' => $functZeroLevelTolDefault,
1324 :			'debug' => 0,
1325 :			);
1326 :
1327 :			# allow var => 'x' as an abbreviation for var => ['x']
1328 :			my %out_options = %opt;
1329 :			unless ( ref($out_options{var}) eq 'ARRAY' ) {
1330 :			$out_options{var} = [$out_options{var}];
1331 :			}
1332 :			# allow params => 'c' as an abbreviation for params => ['c']
1333 :			unless ( ref($out_options{params}) eq 'ARRAY' ) {
1334 :			$out_options{params} = [$out_options{params}];
1335 :			}
1336 :			my ($tolType, $tol);
1337 :			if ($out_options{tolType} eq 'absolute') {
1338 :			$tolType = 'absolute';
1339 :			$tol = $out_options{'tol'};
1340 :			delete($out_options{'relTol'}) if exists( $out_options{'relTol'} );
1341 :			} else {
1342 :			$tolType = 'relative';
1343 :			$tol = $out_options{'relTol'};
1344 :			delete($out_options{'tol'}) if exists( $out_options{'tol'} );
1345 :			}
1346 :
1347 :			my @output_list = ();
1348 :			# thread over lists
1349 :			my @ans_list = ();
1350 :
1351 :			if ( ref($correctAnswer) eq 'ARRAY' ) {
1352 :			@ans_list = @{$correctAnswer};
1353 :			}
1354 :			else {
1355 :			push( @ans_list, $correctAnswer );
1356 :			}
1357 :
1358 :			# produce answer evaluators
1359 :			foreach my $ans (@ans_list) {
1360 :			push(@output_list,
1361 :			FUNCTION_CMP(
1362 :			'correctEqn' => $ans,
1363 :			'var' => $out_options{'var'},
1364 :			'limits' => $out_options{'limits'},
1365 :			'tolerance' => $tol,
1366 :			'tolType' => $tolType,
1367 :			'numPoints' => $out_options{'numPoints'},
1368 :			'mode' => $out_options{'mode'},
1369 :			'maxConstantOfIntegration' => $out_options{'maxConstantOfIntegration'},
1370 :			'zeroLevel' => $out_options{'zeroLevel'},
1371 :			'zeroLevelTol' => $out_options{'zeroLevelTol'},
1372 :			'params' => $out_options{'params'},
1373 :			'debug' => $out_options{'debug'},
1374 :			),
1375 :			);
1376 :			}
1377 :
1378 :	gage	172	return (wantarray) ? @output_list : $output_list[0];
1379 :	gage	122	}
1380 :
1381 :	sam	2	=head3 Single-variable Function Comparisons
1382 :
1383 :			There are four single-variable function answer evaluators: "normal," absolute
1384 :			tolerance, antiderivative, and antiderivative with absolute tolerance. All
1385 :			parameters (other than the correct equation) are optional.
1386 :
1387 :			function_cmp( $correctEqn ) OR
1388 :			function_cmp( $correctEqn, $var ) OR
1389 :			function_cmp( $correctEqn, $var, $llimit, $ulimit ) OR
1390 :			function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol ) OR
1391 :			function_cmp( $correctEqn, $var, $llimit, $ulimit,
1392 :			$relPercentTol, $numPoints ) OR
1393 :			function_cmp( $correctEqn, $var, $llimit, $ulimit,
1394 :			$relPercentTol, $numPoints, $zeroLevel ) OR
1395 :			function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol, $numPoints,
1396 :			$zeroLevel,$zeroLevelTol )
1397 :
1398 :			$correctEqn -- the correct equation, as a string
1399 :			$var -- the string representing the variable (optional)
1400 :			$llimit -- the lower limit of the interval to evaluate the
1401 :			variable in (optional)
1402 :			$ulimit -- the upper limit of the interval to evaluate the
1403 :			variable in (optional)
1404 :			$relPercentTol -- the error tolerance as a percentage (optional)
1405 :			$numPoints -- the number of points at which to evaluate the
1406 :			variable (optional)
1407 :			$zeroLevel -- if the correct answer is this close to zero, then
1408 :			zeroLevelTol applies (optional)
1409 :			$zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1410 :
1411 :			function_cmp() uses standard comparison and relative tolerance. It takes a
1412 :			string representing a single-variable function and compares the student
1413 :			answer to that function numerically.
1414 :
1415 :			function_cmp_up_to_constant( $correctEqn ) OR
1416 :			function_cmp_up_to_constant( $correctEqn, $var ) OR
1417 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit ) OR
1418 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1419 :			$relpercentTol ) OR
1420 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1421 :			$relpercentTol, $numOfPoints ) OR
1422 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1423 :			$relpercentTol, $numOfPoints,
1424 :			$maxConstantOfIntegration ) OR
1425 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1426 :			$relpercentTol, $numOfPoints,
1427 :			$maxConstantOfIntegration, $zeroLevel) OR
1428 :			function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit,
1429 :			$relpercentTol, $numOfPoints,
1430 :			$maxConstantOfIntegration,
1431 :			$zeroLevel, $zeroLevelTol )
1432 :
1433 :			$maxConstantOfIntegration -- the maximum size of the constant of
1434 :			integration
1435 :
1436 :			function_cmp_up_to_constant() uses antiderivative compare and relative
1437 :			tolerance. All options work exactly like function_cmp(), except of course
1438 :			$maxConstantOfIntegration. It will accept as correct any function which
1439 :			differs from $correctEqn by at most a constant; that is, if
1440 :			$studentEqn = $correctEqn + C
1441 :			the answer is correct.
1442 :
1443 :			function_cmp_abs( $correctFunction ) OR
1444 :			function_cmp_abs( $correctFunction, $var ) OR
1445 :			function_cmp_abs( $correctFunction, $var, $llimit, $ulimit ) OR
1446 :			function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol ) OR
1447 :			function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol,
1448 :			$numOfPoints )
1449 :
1450 :			$absTol -- the tolerance as an absolute value
1451 :
1452 :			function_cmp_abs() uses standard compare and absolute tolerance. All
1453 :			other options work exactly as for function_cmp().
1454 :
1455 :			function_cmp_up_to_constant_abs( $correctFunction ) OR
1456 :			function_cmp_up_to_constant_abs( $correctFunction, $var ) OR
1457 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit ) OR
1458 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit,
1459 :			$absTol ) OR
1460 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit,
1461 :			$absTol, $numOfPoints ) OR
1462 :			function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit,
1463 :			$absTol, $numOfPoints,
1464 :			$maxConstantOfIntegration )
1465 :
1466 :			function_cmp_up_to_constant_abs() uses antiderivative compare
1467 :			and absolute tolerance. All other options work exactly as with
1468 :			function_cmp_up_to_constant().
1469 :
1470 :			Examples:
1471 :
1472 :			ANS( function_cmp( "cos(x)" ) ) -- Accepts cos(x), sin(x+pi/2),
1473 :			sin(x)^2 + cos(x) + cos(x)^2 -1, etc. This assumes
1474 :			$functVarDefault has been set to "x".
1475 :			ANS( function_cmp( $answer, "t" ) ) -- Assuming $answer is "cos(t)",
1476 :			accepts cos(t), etc.
1477 :			ANS( function_cmp_up_to_constant( "cos(x)" ) ) -- Accepts any
1478 :			antiderivative of sin(x), e.g. cos(x) + 5.
1479 :			ANS( function_cmp_up_to_constant( "cos(z)", "z" ) ) -- Accepts any
1480 :			antiderivative of sin(z), e.g. sin(z+pi/2) + 5.
1481 :
1482 :			=cut
1483 :	gage	122
1484 :	sam	2	sub adaptive_function_cmp {
1485 :			my $correctEqn = shift;
1486 :			my %options = @_;
1487 :			set_default_options( \%options,
1488 :	chris	81	'vars' => [qw( x y )],
1489 :	sam	2	'params' => [],
1490 :			'limits' => [ [0,1], [0,1]],
1491 :			'reltol' => $main::functRelPercentTolDefault,
1492 :			'numPoints' => $main::functNumOfPoints,
1493 :			'zeroLevel' => $main::functZeroLevelDefault,
1494 :	chris	22	'zeroLevelTol' => $main::functZeroLevelTolDefault,
1495 :	sam	2	'debug' => 0,
1496 :			);
1497 :
1498 :	chris	81	my $var_ref = $options{'vars'};
1499 :	sam	2	my $ra_params = $options{ 'params'};
1500 :			my $limit_ref = $options{'limits'};
1501 :			my $relPercentTol= $options{'reltol'};
1502 :			my $numPoints = $options{'numPoints'};
1503 :			my $zeroLevel = $options{'zeroLevel'};
1504 :			my $zeroLevelTol = $options{'zeroLevelTol'};
1505 :
1506 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1507 :			'var' => $var_ref,
1508 :			'limits' => $limit_ref,
1509 :			'tolerance' => $relPercentTol,
1510 :			'tolType' => 'relative',
1511 :			'numPoints' => $numPoints,
1512 :			'mode' => 'std',
1513 :			'maxConstantOfIntegration' => 10**100,
1514 :			'zeroLevel' => $zeroLevel,
1515 :			'zeroLevelTol' => $zeroLevelTol,
1516 :			'scale_norm' => 1,
1517 :			'params' => $ra_params,
1518 :			'debug' => $options{debug} ,
1519 :	chris	81	);
1520 :	sam	2	}
1521 :
1522 :	chris	54	sub function_cmp {
1523 :	sam	2	my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_;
1524 :
1525 :			if ( (scalar(@_) == 3) or (scalar(@_) > 8) or (scalar(@_) == 0) ) {
1526 :			function_invalid_params( $correctEqn );
1527 :			}
1528 :			else {
1529 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1530 :			'var' => $var,
1531 :			'limits' => [$llimit, $ulimit],
1532 :			'tolerance' => $relPercentTol,
1533 :			'tolType' => 'relative',
1534 :			'numPoints' => $numPoints,
1535 :			'mode' => 'std',
1536 :			'maxConstantOfIntegration' => 0,
1537 :			'zeroLevel' => $zeroLevel,
1538 :			'zeroLevelTol' => $zeroLevelTol
1539 :	sam	2	);
1540 :			}
1541 :			}
1542 :
1543 :	chris	54	sub function_cmp_up_to_constant { ## for antiderivative problems
1544 :	sam	2	my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$maxConstantOfIntegration,$zeroLevel,$zeroLevelTol) = @_;
1545 :
1546 :			if ( (scalar(@_) == 3) or (scalar(@_) > 9) or (scalar(@_) == 0) ) {
1547 :			function_invalid_params( $correctEqn );
1548 :			}
1549 :			else {
1550 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1551 :			'var' => $var,
1552 :			'limits' => [$llimit, $ulimit],
1553 :			'tolerance' => $relPercentTol,
1554 :			'tolType' => 'relative',
1555 :			'numPoints' => $numPoints,
1556 :			'mode' => 'antider',
1557 :			'maxConstantOfIntegration' => $maxConstantOfIntegration,
1558 :			'zeroLevel' => $zeroLevel,
1559 :			'zeroLevelTol' => $zeroLevelTol
1560 :	chris	81	);
1561 :	sam	2	}
1562 :			}
1563 :
1564 :	chris	54	sub function_cmp_abs { ## similar to function_cmp but uses absolute tolerance
1565 :	sam	2	my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints) = @_;
1566 :
1567 :			if ( (scalar(@_) == 3) or (scalar(@_) > 6) or (scalar(@_) == 0) ) {
1568 :			function_invalid_params( $correctEqn );
1569 :			}
1570 :			else {
1571 :	chris	54	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1572 :			'var' => $var,
1573 :			'limits' => [$llimit, $ulimit],
1574 :			'tolerance' => $absTol,
1575 :			'tolType' => 'absolute',
1576 :			'numPoints' => $numPoints,
1577 :			'mode' => 'std',
1578 :			'maxConstantOfIntegration' => 0,
1579 :			'zeroLevel' => 0,
1580 :			'zeroLevelTol' => 0
1581 :	chris	81	);
1582 :	sam	2	}
1583 :			}
1584 :
1585 :
1586 :	chris	54	sub function_cmp_up_to_constant_abs { ## for antiderivative problems
1587 :	sam	2	## similar to function_cmp_up_to_constant
1588 :			## but uses absolute tolerance
1589 :			my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints,$maxConstantOfIntegration) = @_;
1590 :
1591 :			if ( (scalar(@_) == 3) or (scalar(@_) > 7) or (scalar(@_) == 0) ) {
1592 :			function_invalid_params( $correctEqn );
1593 :			}
1594 :
1595 :			else {
1596 :	chris	22	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1597 :			'var' => $var,
1598 :			'limits' => [$llimit, $ulimit],
1599 :			'tolerance' => $absTol,
1600 :			'tolType' => 'absolute',
1601 :			'numPoints' => $numPoints,
1602 :			'mode' => 'antider',
1603 :			'maxConstantOfIntegration' => $maxConstantOfIntegration,
1604 :			'zeroLevel' => 0,
1605 :			'zeroLevelTol' => 0
1606 :	chris	81	);
1607 :	sam	2	}
1608 :			}
1609 :
1610 :			## The following answer evaluator for comparing multivarable functions was
1611 :			## contributed by Professor William K. Ziemer
1612 :			## (Note: most of the multivariable functionality provided by Professor Ziemer
1613 :			## has now been integrated into fun_cmp and FUNCTION_CMP)
1614 :			############################
1615 :			# W.K. Ziemer, Sep. 1999
1616 :			# Math Dept. CSULB
1617 :			# email: wziemer@csulb.edu
1618 :			############################
1619 :
1620 :			=head3 multivar_function_cmp
1621 :
1622 :			NOTE: this function is maintained for compatibility. fun_cmp() is
1623 :			slightly preferred.
1624 :
1625 :			usage:
1626 :
1627 :			multivar_function_cmp( $answer, $var_reference, options)
1628 :			$answer -- string, represents function of several variables
1629 :			$var_reference -- number (of variables), or list reference (e.g. ["var1","var2"] )
1630 :			options:
1631 :			$limit_reference -- reference to list of lists (e.g. [[1,2],[3,4]])
1632 :			$relPercentTol -- relative percent tolerance in answer
1633 :			$numPoints -- number of points to sample in for each variable
1634 :			$zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
1635 :			$zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1636 :
1637 :			=cut
1638 :
1639 :			sub multivar_function_cmp {
1640 :			my ($correctEqn,$var_ref,$limit_ref,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_;
1641 :
1642 :			if ( (scalar(@_) > 7) or (scalar(@_) < 2) ) {
1643 :			function_invalid_params( $correctEqn );
1644 :			}
1645 :
1646 :	chris	81	FUNCTION_CMP( 'correctEqn' => $correctEqn,
1647 :			'var' => $var_ref,
1648 :			'limits' => $limit_ref,
1649 :			'tolerance' => $relPercentTol,
1650 :			'tolType' => 'relative',
1651 :			'numPoints' => $numPoints,
1652 :			'mode' => 'std',
1653 :			'maxConstantOfIntegration' => 0,
1654 :			'zeroLevel' => $zeroLevel,
1655 :			'zeroLevelTol' => $zeroLevelTol
1656 :			);
1657 :	sam	2	}
1658 :
1659 :			## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
1660 :			## NOTE: PG_answer_eval is used instead of PG_restricted_eval in order to insure that the answer
1661 :			## evaluated within the context of the package the problem was originally defined in.
1662 :			## Includes multivariable modifications contributed by Professor William K. Ziemer
1663 :			##
1664 :			## IN: a hash consisting of the following keys (error checking to be added later?)
1665 :	chris	81	## correctEqn -- the correct equation as a string
1666 :			## var -- the variable name as a string,
1667 :			## or a reference to an array of variables
1668 :			## limits -- reference to an array of arrays of type [lower,upper]
1669 :			## tolerance -- the allowable margin of error
1670 :			## tolType -- 'relative' or 'absolute'
1671 :			## numPoints -- the number of points to evaluate the function at
1672 :			## mode -- 'std' or 'antider'
1673 :	sam	2	## maxConstantOfIntegration -- maximum size of the constant of integration
1674 :	chris	81	## zeroLevel -- if the correct answer is this close to zero,
1675 :	sam	2	## then zeroLevelTol applies
1676 :	chris	81	## zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1677 :	sam	2
1678 :
1679 :	chris	54	sub FUNCTION_CMP {
1680 :	sam	2	my %func_params = @_;
1681 :
1682 :			my $correctEqn = $func_params{'correctEqn'};
1683 :	chris	22	my $var = $func_params{'var'};
1684 :	sam	2	my $ra_limits = $func_params{'limits'};
1685 :	chris	22	my $tol = $func_params{'tolerance'};
1686 :			my $tolType = $func_params{'tolType'};
1687 :	sam	2	my $numPoints = $func_params{'numPoints'};
1688 :	chris	22	my $mode = $func_params{'mode'};
1689 :			my $maxConstantOfIntegration = $func_params{'maxConstantOfIntegration'};
1690 :	sam	2	my $zeroLevel = $func_params{'zeroLevel'};
1691 :			my $zeroLevelTol = $func_params{'zeroLevelTol'};
1692 :
1693 :
1694 :			# Check that everything is defined:
1695 :			$func_params{debug} = 0 unless defined($func_params{debug});
1696 :			$mode = 'std' unless defined($mode);
1697 :			my @VARS = get_var_array( $var );
1698 :			my @limits = get_limits_array( $ra_limits );
1699 :			my @PARAMS = ();
1700 :			@PARAMS = @{$func_params{'params'}} if defined($func_params{'params'});
1701 :
1702 :			if ($mode eq 'antider' ) {
1703 :			# doctor the equation to allow addition of a constant
1704 :			my $CONSTANT_PARAM = 'Q'; # unfortunately parameters must be single letters.
1705 :			# There is the possibility of conflict here.
1706 :			# 'Q' seemed less dangerous than 'C'.
1707 :			$correctEqn = "( $correctEqn ) + $CONSTANT_PARAM";
1708 :			push(@PARAMS, $CONSTANT_PARAM);
1709 :			}
1710 :			my $dim_of_param_space = @PARAMS; # dimension of equivalence space
1711 :
1712 :			if( $tolType eq 'relative' ) {
1713 :	chris	81	$tol = $functRelPercentTolDefault unless defined $tol;
1714 :	sam	2	$tol *= .01;
1715 :			}
1716 :			else {
1717 :	chris	81	$tol = $functAbsTolDefault unless defined $tol;
1718 :	sam	2	}
1719 :
1720 :			#loop ensures that number of limits matches number of variables
1721 :			for( my $i = 0; $i < scalar(@VARS); $i++ ) {
1722 :	chris	81	$limits[$i][0] = $functLLimitDefault unless defined $limits[$i][0];
1723 :			$limits[$i][1] = $functULimitDefault unless defined $limits[$i][1];
1724 :	sam	2	}
1725 :	chris	81	$numPoints = $functNumOfPoints unless defined $numPoints;
1726 :	sam	2	$maxConstantOfIntegration = $functMaxConstantOfIntegration unless defined $maxConstantOfIntegration;
1727 :	chris	81	$zeroLevel = $functZeroLevelDefault unless defined $zeroLevel;
1728 :			$zeroLevelTol = $functZeroLevelTolDefault unless defined $zeroLevelTol;
1729 :	sam	2
1730 :	chris	22	$func_params{'var'} = $var;
1731 :			$func_params{'limits'} = \@limits;
1732 :			$func_params{'tolerance'} = $tol;
1733 :			$func_params{'tolType'} = $tolType;
1734 :			$func_params{'numPoints'} = $numPoints;
1735 :			$func_params{'mode'} = $mode;
1736 :			$func_params{'maxConstantOfIntegration'} = $maxConstantOfIntegration;
1737 :			$func_params{'zeroLevel'} = $zeroLevel;
1738 :			$func_params{'zeroLevelTol'} = $zeroLevelTol;
1739 :
1740 :	gage	5	########################################################
1741 :			# End of cleanup of calling parameters
1742 :			########################################################
1743 :	sam	2	my $i; #for use with loops
1744 :			my $PGanswerMessage = "";
1745 :			my $originalCorrEqn = $correctEqn;
1746 :
1747 :			#prepare the correct answer and check it's syntax
1748 :	chris	22	my $rh_correct_ans = new AnswerHash;
1749 :	sam	2	$rh_correct_ans->input($correctEqn);
1750 :			$rh_correct_ans = check_syntax($rh_correct_ans);
1751 :			warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag};
1752 :			$rh_correct_ans->clear_error();
1753 :			$rh_correct_ans = function_from_string2($rh_correct_ans, ra_vars => [ @VARS, @PARAMS ],
1754 :			store_in =>'rf_correct_ans',
1755 :			debug => $func_params{debug});
1756 :			my $correct_eqn_sub = $rh_correct_ans->{rf_correct_ans};
1757 :			warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag};
1758 :
1759 :			#create the evaluation points
1760 :			my $random_for_answers = new PGrandom($main::PG_original_problemSeed);
1761 :	chris	22	my $NUMBER_OF_STEPS_IN_RANDOM = 1000; # determines the granularity of the random_for_answers number generator
1762 :	sam	2	my (@evaluation_points);
1763 :			for( my $count = 0; $count < @PARAMS+1+$numPoints; $count++ ) {
1764 :			my (@vars,$iteration_limit);
1765 :			for( my $i = 0; $i < @VARS; $i++ ) {
1766 :			my $iteration_limit = 10;
1767 :			while ( 0 < --$iteration_limit ) { # make sure that the endpoints of the interval are not included
1768 :			$vars[$i] = $random_for_answers->random($limits[$i][0], $limits[$i][1], abs($limits[$i][1] - $limits[$i][0])/$NUMBER_OF_STEPS_IN_RANDOM );
1769 :			last if $vars[$i]!=$limits[$i][0] and $vars[$i]!=$limits[$i][1];
1770 :			}
1771 :			warn "Unable to properly choose evaluation points for this function in the interval ( $limits[$i][0] , $limits[$i][1] )"
1772 :			if $iteration_limit == 0;
1773 :			};
1774 :
1775 :			push(@evaluation_points,\@vars);
1776 :			}
1777 :			my $evaluation_points = Matrix->new_from_array_ref(\@evaluation_points);
1778 :
1779 :			#my $COEFFS = determine_param_coeffs($correct_eqn_sub,$evaluation_points[0],$numOfParameters);
1780 :	chris	22	#warn "coeff", join(" \| ", @{$COEFFS});
1781 :	sam	2
1782 :			#construct the answer evaluator
1783 :			my $answer_evaluator = new AnswerEvaluator;
1784 :			$answer_evaluator->{debug} = $func_params{debug};
1785 :			$answer_evaluator->ans_hash( correct_ans => $originalCorrEqn,
1786 :	chris	54	rf_correct_ans => $rh_correct_ans->{rf_correct_ans},
1787 :			evaluation_points => \@evaluation_points,
1788 :			ra_param_vars => \@PARAMS,
1789 :			ra_vars => \@VARS,
1790 :			type => 'function',
1791 :	sam	2	);
1792 :
1793 :			$answer_evaluator->install_pre_filter(\&check_syntax);
1794 :			$answer_evaluator->install_pre_filter(\&function_from_string2, ra_vars => \@VARS,debug=>$func_params{debug},); # @VARS has been guaranteed to be an array, $var might be a single string.
1795 :			$answer_evaluator->install_pre_filter(\&best_approx_parameters, %func_params, param_vars => \@PARAMS);
1796 :			$answer_evaluator->install_evaluator(\&calculate_difference_vector, %func_params);
1797 :	gage	154	$answer_evaluator->install_evaluator(\&is_zero_array, tolerance => $tol );
1798 :	sam	2	$answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('SYNTAX'); $rh_ans;} );
1799 :	gage	154	$answer_evaluator->install_post_filter(
1800 :			sub {my $rh_ans = shift;
1801 :	chris	81	if ($rh_ans->catch_error('EVAL') ) {
1802 :			$rh_ans->{ans_message} = $rh_ans->{error_message};
1803 :			$rh_ans->clear_error('EVAL');
1804 :			}
1805 :	gage	154	$rh_ans;
1806 :			}
1807 :			);
1808 :	sam	2	$answer_evaluator;
1809 :			}
1810 :
1811 :
1812 :	chris	54	## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
1813 :			##
1814 :			## IN: a hash containing the following items (error-checking to be added later?):
1815 :			## correctAnswer -- the correct answer
1816 :			## tolerance -- the allowable margin of error
1817 :			## tolType -- 'relative' or 'absolute'
1818 :			## format -- the display format of the answer
1819 :			## mode -- one of 'std', 'strict', 'arith', or 'frac';
1820 :			## determines allowable formats for the input
1821 :			## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies
1822 :			## zeroLevelTol -- absolute tolerance to allow when answer is close to zero
1823 :
1824 :
1825 :	sam	2	##########################################################################
1826 :			##########################################################################
1827 :			## String answer evaluators
1828 :
1829 :			=head2 String Answer Evaluators
1830 :
1831 :			String answer evaluators compare a student string to the correct string.
1832 :			Different filters can be applied to allow various degrees of variation.
1833 :			Both the student and correct answers are subject to the same filters, to
1834 :			ensure that there are no unexpected matches or rejections.
1835 :
1836 :			String Filters
1837 :
1838 :			remove_whitespace -- Removes all whitespace from the string.
1839 :	chris	81	It applies the following substitution
1840 :			to the string:
1841 :			$filteredAnswer =~ s/\s+//g;
1842 :	sam	2
1843 :			compress_whitespace -- Removes leading and trailing whitespace, and
1844 :	chris	81	replaces all other blocks of whitespace by a
1845 :			single space. Applies the following substitutions:
1846 :			$filteredAnswer =~ s/^\s*//;
1847 :			$filteredAnswer =~ s/\s*$//;
1848 :			$filteredAnswer =~ s/\s+/ /g;
1849 :	sam	2
1850 :			trim_whitespace -- Removes leading and trailing whitespace.
1851 :	chris	81	Applies the following substitutions:
1852 :			$filteredAnswer =~ s/^\s*//;
1853 :			$filteredAnswer =~ s/\s*$//;
1854 :	sam	2
1855 :			ignore_case -- Ignores the case of the string. More accurately,
1856 :	chris	81	it converts the string to uppercase (by convention).
1857 :			Applies the following function:
1858 :			$filteredAnswer = uc $filteredAnswer;
1859 :	sam	2
1860 :			ignore_order -- Ignores the order of the letters in the string.
1861 :	chris	81	This is used for problems of the form "Choose all
1862 :			that apply." Specifically, it removes all
1863 :			whitespace and lexically sorts the letters in
1864 :			ascending alphabetical order. Applies the following
1865 :			functions:
1866 :			$filteredAnswer = join( "", lex_sort(
1867 :			split( /\s*/, $filteredAnswer ) ) );
1868 :	sam	2
1869 :			=cut
1870 :
1871 :			################################
1872 :			## STRING ANSWER FILTERS
1873 :
1874 :			## IN: --the string to be filtered
1875 :			## --a list of the filters to use
1876 :			##
1877 :			## OUT: --the modified string
1878 :			##
1879 :			## Use this subroutine instead of the
1880 :			## individual filters below it
1881 :	chris	81
1882 :	sam	2	sub str_filters {
1883 :			my $stringToFilter = shift @_;
1884 :			my @filters_to_use = @_;
1885 :			my %known_filters = ( 'remove_whitespace' => undef,
1886 :	chris	35	'compress_whitespace' => undef,
1887 :			'trim_whitespace' => undef,
1888 :			'ignore_case' => undef,
1889 :			'ignore_order' => undef
1890 :	chris	81	);
1891 :	sam	2
1892 :			#test for unknown filters
1893 :			my $filter;
1894 :			foreach $filter (@filters_to_use) {
1895 :			die "Unknown string filter $filter (try checking the parameters to str_cmp() )"
1896 :	chris	81	unless exists $known_filters{$filter};
1897 :	sam	2	}
1898 :
1899 :			if( grep( /remove_whitespace/i, @filters_to_use ) ) {
1900 :			$stringToFilter = remove_whitespace( $stringToFilter );
1901 :			}
1902 :			if( grep( /compress_whitespace/i, @filters_to_use ) ) {
1903 :			$stringToFilter = compress_whitespace( $stringToFilter );
1904 :			}
1905 :			if( grep( /trim_whitespace/i, @filters_to_use ) ) {
1906 :			$stringToFilter = trim_whitespace( $stringToFilter );
1907 :			}
1908 :			if( grep( /ignore_case/i, @filters_to_use ) ) {
1909 :			$stringToFilter = ignore_case( $stringToFilter );
1910 :			}
1911 :			if( grep( /ignore_order/i, @filters_to_use ) ) {
1912 :			$stringToFilter = ignore_order( $stringToFilter );
1913 :			}
1914 :
1915 :			return $stringToFilter;
1916 :			}
1917 :
1918 :			sub remove_whitespace {
1919 :			my $filteredAnswer = shift;
1920 :
1921 :			$filteredAnswer =~ s/\s+//g; # remove all whitespace
1922 :
1923 :			return $filteredAnswer;
1924 :			}
1925 :
1926 :	chris	54	sub compress_whitespace {
1927 :	sam	2	my $filteredAnswer = shift;
1928 :
1929 :			$filteredAnswer =~ s/^\s*//; # remove initial whitespace
1930 :			$filteredAnswer =~ s/\s*$//; # remove trailing whitespace
1931 :			$filteredAnswer =~ s/\s+/ /g; # replace spaces by single space
1932 :
1933 :			return $filteredAnswer;
1934 :			}
1935 :
1936 :			sub trim_whitespace {
1937 :			my $filteredAnswer = shift;
1938 :
1939 :			$filteredAnswer =~ s/^\s*//; # remove initial whitespace
1940 :			$filteredAnswer =~ s/\s*$//; # remove trailing whitespace
1941 :
1942 :			return $filteredAnswer;
1943 :			}
1944 :
1945 :			sub ignore_case {
1946 :			my $filteredAnswer = shift;
1947 :
1948 :			$filteredAnswer = uc $filteredAnswer;
1949 :
1950 :			return $filteredAnswer;
1951 :			}
1952 :
1953 :			sub ignore_order {
1954 :			my $filteredAnswer = shift;
1955 :
1956 :			$filteredAnswer = join( "", lex_sort( split( /\s*/, $filteredAnswer ) ) );
1957 :
1958 :			return $filteredAnswer;
1959 :			}
1960 :			################################
1961 :			## END STRING ANSWER FILTERS
1962 :
1963 :	gage	122
1964 :			=head3 str_cmp()
1965 :
1966 :			Compares a string or a list of strings, using a named hash of options to set
1967 :			parameters. This can make for more readable code than using the "mode"_str_cmp()
1968 :			style, but some people find one or the other easier to remember.
1969 :
1970 :			ANS( str_cmp( answer or answer_array_ref, options_hash ) );
1971 :
1972 :			1. the correct answer or a reference to an array of answers
1973 :			2. either a list of filters, or:
1974 :			a hash consisting of
1975 :			filters - a reference to an array of filters
1976 :
1977 :			Returns an answer evaluator, or (if given a reference to an array of answers),
1978 :			a list of answer evaluators
1979 :
1980 :			FILTERS:
1981 :
1982 :			remove_whitespace -- removes all whitespace
1983 :			compress_whitespace -- removes whitespace from the beginning and end of the string,
1984 :			and treats one or more whitespace characters in a row as a
1985 :			single space (true by default)
1986 :			trim_whitespace -- removes whitespace from the beginning and end of the string
1987 :			ignore_case -- ignores the case of the letters (true by default)
1988 :			ignore_order -- ignores the order in which letters are entered
1989 :
1990 :			EXAMPLES:
1991 :
1992 :			str_cmp( "Hello" ) -- matches "Hello", " hello" (same as std_str_cmp() )
1993 :			str_cmp( ["Hello", "Goodbye"] ) -- same as std_str_cmp_list()
1994 :			str_cmp( " hello ", trim_whitespace ) -- matches "hello", " hello "
1995 :			str_cmp( "ABC", filters => 'ignore_order' ) -- matches "ACB", "A B C", but not "abc"
1996 :			str_cmp( "D E F", remove_whitespace, ignore_case ) -- matches "def" and "d e f" but not "fed"
1997 :
1998 :
1999 :			=cut
2000 :
2001 :			sub str_cmp {
2002 :			my $correctAnswer = shift @_;
2003 :			$correctAnswer = '' unless defined($correctAnswer);
2004 :			my @options = @_;
2005 :			my $ra_filters;
2006 :
2007 :			# error-checking for filters occurs in the filters() subroutine
2008 :			if( not defined( $options[0] ) ) { # used with no filters as alias for std_str_cmp()
2009 :			@options = ( 'compress_whitespace', 'ignore_case' );
2010 :			}
2011 :
2012 :			if( $options[0] eq 'filters' ) { # using filters => [f1, f2, ...] notation
2013 :			$ra_filters = $options[1];
2014 :			}
2015 :			else { # using a list of filters
2016 :			$ra_filters = \@options;
2017 :			}
2018 :
2019 :			# thread over lists
2020 :			my @ans_list = ();
2021 :
2022 :			if ( ref($correctAnswer) eq 'ARRAY' ) {
2023 :			@ans_list = @{$correctAnswer};
2024 :			}
2025 :			else {
2026 :			push( @ans_list, $correctAnswer );
2027 :			}
2028 :
2029 :			# final_answer;
2030 :			my @output_list = ();
2031 :
2032 :			foreach my $ans (@ans_list) {
2033 :			push(@output_list, STR_CMP( 'correctAnswer' => $ans,
2034 :			'filters' => $ra_filters,
2035 :			'type' => 'str_cmp'
2036 :			)
2037 :			);
2038 :			}
2039 :
2040 :	gage	172	return (wantarray) ? @output_list : $output_list[0] ;
2041 :	gage	122	}
2042 :
2043 :	sam	2	=head3 "mode"_str_cmp functions
2044 :
2045 :			The functions of the the form "mode"_str_cmp() use different functions to
2046 :			specify which filters to apply. They take no options except the correct
2047 :			string. There are also versions which accept a list of strings.
2048 :
2049 :			std_str_cmp( $correctString )
2050 :			std_str_cmp_list( @correctStringList )
2051 :			Filters: compress_whitespace, ignore_case
2052 :
2053 :			std_cs_str_cmp( $correctString )
2054 :			std_cs_str_cmp_list( @correctStringList )
2055 :			Filters: compress_whitespace
2056 :
2057 :			strict_str_cmp( $correctString )
2058 :			strict_str_cmp_list( @correctStringList )
2059 :			Filters: trim_whitespace
2060 :
2061 :			unordered_str_cmp( $correctString )
2062 :			unordered_str_cmp_list( @correctStringList )
2063 :			Filters: ignore_order, ignore_case
2064 :
2065 :			unordered_cs_str_cmp( $correctString )
2066 :			unordered_cs_str_cmp_list( @correctStringList )
2067 :			Filters: ignore_order
2068 :
2069 :			ordered_str_cmp( $correctString )
2070 :			ordered_str_cmp_list( @correctStringList )
2071 :			Filters: remove_whitespace, ignore_case
2072 :
2073 :			ordered_cs_str_cmp( $correctString )
2074 :			ordered_cs_str_cmp_list( @correctStringList )
2075 :			Filters: remove_whitespace
2076 :
2077 :			Examples
2078 :
2079 :			ANS( std_str_cmp( "W. Mozart" ) ) -- Accepts "W. Mozart", "W. MOZarT",
2080 :			and so forth. Case insensitive. All internal spaces treated
2081 :			as single spaces.
2082 :			ANS( std_cs_str_cmp( "Mozart" ) ) -- Rejects "mozart". Same as
2083 :			std_str_cmp() but case sensitive.
2084 :			ANS( strict_str_cmp( "W. Mozart" ) ) -- Accepts only the exact string.
2085 :			ANS( unordered_str_cmp( "ABC" ) ) -- Accepts "a c B", "CBA" and so forth.
2086 :			Unordered, case insensitive, spaces ignored.
2087 :			ANS( unordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc". Same as
2088 :			unordered_str_cmp() but case sensitive.
2089 :			ANS( ordered_str_cmp( "ABC" ) ) -- Accepts "a b C", "A B C" and so forth.
2090 :			Ordered, case insensitive, spaces ignored.
2091 :			ANS( ordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc", accepts "A BC" and
2092 :			so forth. Same as ordered_str_cmp() but case sensitive.
2093 :
2094 :			=cut
2095 :
2096 :	chris	54	sub std_str_cmp { # compare strings
2097 :	sam	2	my $correctAnswer = shift @_;
2098 :			my @filters = ( 'compress_whitespace', 'ignore_case' );
2099 :			my $type = 'std_str_cmp';
2100 :			STR_CMP( 'correctAnswer' => $correctAnswer,
2101 :	chris	35	'filters' => \@filters,
2102 :			'type' => $type
2103 :	sam	2	);
2104 :			}
2105 :
2106 :	chris	54	sub std_str_cmp_list { # alias for std_str_cmp
2107 :	sam	2	my @answerList = @_;
2108 :			my @output;
2109 :			while (@answerList) {
2110 :			push( @output, std_str_cmp(shift @answerList) );
2111 :			}
2112 :			@output;
2113 :			}
2114 :
2115 :	chris	54	sub std_cs_str_cmp { # compare strings case sensitive
2116 :	sam	2	my $correctAnswer = shift @_;
2117 :			my @filters = ( 'compress_whitespace' );
2118 :			my $type = 'std_cs_str_cmp';
2119 :			STR_CMP( 'correctAnswer' => $correctAnswer,
2120 :	chris	54	'filters' => \@filters,
2121 :			'type' => $type
2122 :	sam	2	);
2123 :			}
2124 :
2125 :	chris	54	sub std_cs_str_cmp_list { # alias for std_cs_str_cmp
2126 :	sam	2	my @answerList = @_;
2127 :			my @output;
2128 :			while (@answerList) {
2129 :			push( @output, std_cs_str_cmp(shift @answerList) );
2130 :			}
2131 :			@output;
2132 :			}
2133 :
2134 :	chris	54	sub strict_str_cmp { # strict string compare
2135 :	sam	2	my $correctAnswer = shift @_;
2136 :			my @filters = ( 'trim_whitespace' );
2137 :			my $type = 'strict_str_cmp';
2138 :			STR_CMP( 'correctAnswer' => $correctAnswer,
2139 :	chris	54	'filters' => \@filters,
2140 :			'type' => $type
2141 :	sam	2	);
2142 :			}
2143 :
2144 :	chris	54	sub strict_str_cmp_list { # alias for strict_str_cmp
2145 :	sam	2	my @answerList = @_;
2146 :			my @output;
2147 :			while (@answerList) {
2148 :			push( @output, strict_str_cmp(shift @answerList) );
2149 :			}
2150 :			@output;
2151 :			}
2152 :
2153 :	chris	54	sub unordered_str_cmp { # unordered, case insensitive, spaces ignored
2154 :	sam	2	my $correctAnswer = shift @_;
2155 :			my @filters = ( 'ignore_order', 'ignore_case' );
2156 :			my $type = 'unordered_str_cmp';
2157 :	chris	81	STR_CMP( 'correctAnswer' => $correctAnswer,
2158 :			'filters' => \@filters,
2159 :			'type' => $type
2160 :	sam	2	);
2161 :			}
2162 :
2163 :	chris	54	sub unordered_str_cmp_list { # alias for unordered_str_cmp
2164 :	sam	2	my @answerList = @_;
2165 :			my @output;
2166 :			while (@answerList) {
2167 :			push( @output, unordered_str_cmp(shift @answerList) );
2168 :			}
2169 :			@output;
2170 :			}
2171 :
2172 :	chris	54	sub unordered_cs_str_cmp { # unordered, case sensitive, spaces ignored
2173 :	sam	2	my $correctAnswer = shift @_;
2174 :			my @filters = ( 'ignore_order' );
2175 :			my $type = 'unordered_cs_str_cmp';
2176 :	chris	81	STR_CMP( 'correctAnswer' => $correctAnswer,
2177 :			'filters' => \@filters,
2178 :			'type' => $type
2179 :	sam	2	);
2180 :			}
2181 :
2182 :	chris	54	sub unordered_cs_str_cmp_list { # alias for unordered_cs_str_cmp
2183 :	sam	2	my @answerList = @_;
2184 :			my @output;
2185 :			while (@answerList) {
2186 :			push( @output, unordered_cs_str_cmp(shift @answerList) );
2187 :			}
2188 :			@output;
2189 :			}
2190 :
2191 :	chris	54	sub ordered_str_cmp { # ordered, case insensitive, spaces ignored
2192 :	sam	2	my $correctAnswer = shift @_;
2193 :			my @filters = ( 'remove_whitespace', 'ignore_case' );
2194 :			my $type = 'ordered_str_cmp';
2195 :			STR_CMP( 'correctAnswer' => $correctAnswer,
2196 :	chris	54	'filters' => \@filters,
2197 :			'type' => $type
2198 :	sam	2	);
2199 :			}
2200 :
2201 :	chris	54	sub ordered_str_cmp_list { # alias for ordered_str_cmp
2202 :	sam	2	my @answerList = @_;
2203 :			my @output;
2204 :			while (@answerList) {
2205 :			push( @output, ordered_str_cmp(shift @answerList) );
2206 :			}
2207 :			@output;
2208 :			}
2209 :
2210 :	chris	54	sub ordered_cs_str_cmp { # ordered, case sensitive, spaces ignored
2211 :	sam	2	my $correctAnswer = shift @_;
2212 :			my @filters = ( 'remove_whitespace' );
2213 :			my $type = 'ordered_cs_str_cmp';
2214 :			STR_CMP( 'correctAnswer' => $correctAnswer,
2215 :	chris	54	'filters' => \@filters,
2216 :			'type' => $type
2217 :	sam	2	);
2218 :			}
2219 :
2220 :	chris	54	sub ordered_cs_str_cmp_list { # alias for ordered_cs_str_cmp
2221 :	sam	2	my @answerList = @_;
2222 :			my @output;
2223 :			while (@answerList) {
2224 :			push( @output, ordered_cs_str_cmp(shift @answerList) );
2225 :			}
2226 :			@output;
2227 :			}
2228 :
2229 :
2230 :			## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION
2231 :			##
2232 :			## IN: a hashtable with the following entries (error-checking to be added later?):
2233 :			## correctAnswer -- the correct answer, before filtering
2234 :			## filters -- reference to an array containing the filters to be applied
2235 :			## type -- a string containing the type of answer evaluator in use
2236 :			## OUT: a reference to an answer evaluator subroutine
2237 :	chris	35
2238 :	chris	54	sub STR_CMP {
2239 :	sam	2	my %str_params = @_;
2240 :			$str_params{'correctAnswer'} = str_filters( $str_params{'correctAnswer'}, @{$str_params{'filters'}} );
2241 :			my $answer_evaluator = sub {
2242 :			my $in = shift @_;
2243 :			$in = '' unless defined $in;
2244 :			my $original_student_ans = $in;
2245 :			$in = str_filters( $in, @{$str_params{'filters'}} );
2246 :			my $correctQ = ( $in eq $str_params{'correctAnswer'} ) ? 1: 0;
2247 :	chris	35	my $ans_hash = new AnswerHash( 'score' => $correctQ,
2248 :	sam	2	'correct_ans' => $str_params{'correctAnswer'},
2249 :			'student_ans' => $in,
2250 :			'ans_message' => '',
2251 :	chris	35	'type' => $str_params{'type'},
2252 :			'preview_text_string' => $in,
2253 :			'preview_latex_string' => $in,
2254 :			'original_student_ans' => $original_student_ans
2255 :	sam	2	);
2256 :			return $ans_hash;
2257 :			};
2258 :			return $answer_evaluator;
2259 :			}
2260 :
2261 :			##########################################################################
2262 :			##########################################################################
2263 :			## Miscellaneous answer evaluators
2264 :
2265 :			=head2 Miscellaneous Answer Evaluators (Checkboxes and Radio Buttons)
2266 :
2267 :			These evaluators do not fit any of the other categories.
2268 :
2269 :			checkbox_cmp( $correctAnswer )
2270 :
2271 :			$correctAnswer -- a string containing the names of the correct boxes,
2272 :			e.g. "ACD". Note that this means that individual
2273 :			checkbox names can only be one character. Internally,
2274 :			this is largely the same as unordered_cs_str_cmp().
2275 :
2276 :			radio_cmp( $correctAnswer )
2277 :
2278 :			$correctAnswer -- a string containing the name of the correct radio
2279 :			button, e.g. "Choice1". This is case sensitive and
2280 :			whitespace sensitive, so the correct answer must match
2281 :			the name of the radio button exactly.
2282 :
2283 :			=cut
2284 :
2285 :			# added 6/14/2000 by David Etlinger
2286 :			# because of the conversion of the answer
2287 :			# string to an array, I thought it better not
2288 :			# to force STR_CMP() to work with this
2289 :	chris	54	sub checkbox_cmp {
2290 :	sam	2	my $correctAnswer = shift @_;
2291 :			$correctAnswer = str_filters( $correctAnswer, 'ignore_order' );
2292 :
2293 :			my $answer_evaluator = sub {
2294 :			my $in = shift @_;
2295 :			$in = '' unless defined $in; #in case no boxes checked
2296 :
2297 :			my @temp = split( "\0", $in ); #convert "\0"-delimited string to array...
2298 :			$in = join( "", @temp ); #and then to a single no-delimiter string
2299 :
2300 :			my $original_student_ans = $in; #well, almost original
2301 :			$in = str_filters( $in, 'ignore_order' );
2302 :
2303 :			my $correctQ = ($in eq $correctAnswer) ? 1: 0;
2304 :
2305 :			my $ans_hash = new AnswerHash(
2306 :	chris	81	'score' => $correctQ,
2307 :			'correct_ans' => $correctAnswer,
2308 :			'student_ans' => $in,
2309 :			'ans_message' => "",
2310 :			'type' => "checkbox_cmp",
2311 :	sam	2	'preview_text_string' => $in,
2312 :			'original_student_ans' => $original_student_ans
2313 :			);
2314 :			return $ans_hash;
2315 :
2316 :			};
2317 :			return $answer_evaluator;
2318 :			}
2319 :
2320 :			#added 6/28/2000 by David Etlinger
2321 :			#exactly the same as strict_str_cmp,
2322 :			#but more intuitive to the user
2323 :			sub radio_cmp {
2324 :			strict_str_cmp( @_ );
2325 :			}
2326 :
2327 :			##########################################################################
2328 :			##########################################################################
2329 :			## Text and e-mail routines
2330 :
2331 :	chris	54	sub store_ans_at {
2332 :	sam	2	my $answerStringRef = shift;
2333 :			my %options = @_;
2334 :			my $ans_eval= '';
2335 :			if ( ref($answerStringRef) eq 'SCALAR' ) {
2336 :			$ans_eval= sub {
2337 :			my $text = shift;
2338 :			$text = '' unless defined($text);
2339 :			$$answerStringRef = $$answerStringRef . $text;
2340 :			my $ans_hash = new AnswerHash(
2341 :	chris	81	'score' => 1,
2342 :	sam	2	'correct_ans' => '',
2343 :			'student_ans' => $text,
2344 :			'ans_message' => '',
2345 :	chris	81	'type' => 'store_ans_at',
2346 :			'original_student_ans' => $text,
2347 :			'preview_text_string' => ''
2348 :	sam	2	);
2349 :
2350 :	chris	81	return $ans_hash;
2351 :	sam	2	};
2352 :			}
2353 :			else {
2354 :			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";
2355 :			}
2356 :
2357 :			return $ans_eval;
2358 :			}
2359 :
2360 :			#### subroutines used in producing a questionnaire
2361 :			#### these are at least good models for other answers of this type
2362 :
2363 :			my $QUESTIONNAIRE_ANSWERS=''; # stores the answers until it is time to send them
2364 :			# this must be initialized before the answer evaluators are run
2365 :			# but that happens long after all of the text in the problem is
2366 :			# evaluated.
2367 :			# this is a utility script for cleaning up the answer output for display in
2368 :			#the answers.
2369 :
2370 :	chris	54	sub DUMMY_ANSWER {
2371 :	sam	2	my $num = shift;
2372 :			qq{<INPUT TYPE="HIDDEN" NAME="answer$num" VALUE="">}
2373 :			}
2374 :
2375 :	chris	54	sub escapeHTML {
2376 :	sam	2	my $string = shift;
2377 :			$string =~ s/\n/$BR/ge;
2378 :			$string;
2379 :			}
2380 :
2381 :	apizer	206	# these next three subroutines show how to modify the "store_ans_at()" answer
2382 :	sam	2	# evaluator to add extra information before storing the info
2383 :			# They provide a good model for how to tweak answer evaluators in special cases.
2384 :	chris	81
2385 :	chris	54	sub anstext {
2386 :	sam	2	my $num = shift;
2387 :			my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS);
2388 :			my $ans_eval = sub {
2389 :	chris	81	my $text = shift;
2390 :			$text = '' unless defined($text);
2391 :			my $new_text = "\n$main::psvnNumber-Problem-$main::probNum-Question-$num:\n $text "; # modify entered text
2392 :			my $out = &$ans_eval_template($new_text); # standard evaluator
2393 :			#warn "$QUESTIONNAIRE_ANSWERS";
2394 :			$out->{student_ans} = escapeHTML($text); # restore original entered text
2395 :			$out->{correct_ans} = "Question $num answered";
2396 :			$out->{original_student_ans} = escapeHTML($text);
2397 :			$out;
2398 :			};
2399 :	sam	2	$ans_eval;
2400 :			}
2401 :
2402 :	chris	54	sub ansradio {
2403 :	sam	2	my $num = shift;
2404 :			my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS);
2405 :			my $ans_eval = sub {
2406 :	chris	81	my $text = shift;
2407 :			$text = '' unless defined($text);
2408 :			my $new_text = "\n$main::psvnNumber-Problem-$main::probNum-RADIO-$num:\n $text "; # modify entered text
2409 :			my $out = $ans_eval_template->($new_text); # standard evaluator
2410 :			$out->{student_ans} =escapeHTML($text); # restore original entered text
2411 :			$out->{original_student_ans} = escapeHTML($text);
2412 :			$out;
2413 :	sam	2	};
2414 :
2415 :			$ans_eval;
2416 :			}
2417 :
2418 :	apizer	206	sub anstext_non_anonymous {
2419 :			## this emails identifying information
2420 :			my $num = shift;
2421 :			my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS);
2422 :			my $ans_eval = sub {
2423 :			my $text = shift;
2424 :			$text = '' unless defined($text);
2425 :			my $new_text = "\n$main::psvnNumber-Problem-$main::probNum-Question-$num:\n$main::studentLogin $main::studentID $main::studentName\n$text "; # modify entered text
2426 :			my $out = &$ans_eval_template($new_text); # standard evaluator
2427 :			#warn "$QUESTIONNAIRE_ANSWERS";
2428 :			$out->{student_ans} = escapeHTML($text); # restore original entered text
2429 :			$out->{correct_ans} = "Question $num answered";
2430 :			$out->{original_student_ans} = escapeHTML($text);
2431 :			$out;
2432 :			};
2433 :			$ans_eval;
2434 :			}
2435 :
2436 :
2437 :	sam	2	# This is another example of how to modify an answer evaluator to obtain
2438 :			# the desired behavior in a special case. Here the object is to have
2439 :			# have the last answer trigger the send_mail_to subroutine which mails
2440 :			# all of the answers to the designated address.
2441 :			# (This address must be listed in PG_environment{'ALLOW_MAIL_TO'} or an error occurs.)
2442 :
2443 :	chris	54	sub mail_answers_to { #accepts the last answer and mails off the result
2444 :	sam	2	my $user_address = shift;
2445 :			my $ans_eval = sub {
2446 :
2447 :	chris	81	# then mail out all of the answers, including this last one.
2448 :	sam	2
2449 :			send_mail_to( $user_address,
2450 :	chris	81	'subject' => "$main::courseName WeBWorK questionnaire",
2451 :			'body' => $QUESTIONNAIRE_ANSWERS,
2452 :			'ALLOW_MAIL_TO' => $main::ALLOW_MAIL_TO
2453 :			);
2454 :	sam	2
2455 :	chris	81	my $ans_hash = new AnswerHash( 'score' => 1,
2456 :			'correct_ans' => '',
2457 :			'student_ans' => 'Answer recorded',
2458 :			'ans_message' => '',
2459 :			'type' => 'send_mail_to',
2460 :			);
2461 :	sam	2
2462 :			return $ans_hash;
2463 :			};
2464 :
2465 :			return $ans_eval;
2466 :			}
2467 :	chris	54	sub mail_answers_to2 { #accepts the last answer and mails off the result
2468 :	sam	2	my $user_address = shift;
2469 :			my $subject = shift;
2470 :			$subject = "$main::courseName WeBWorK questionnaire" unless defined $subject;
2471 :
2472 :			send_mail_to($user_address,
2473 :			'subject' => $subject,
2474 :			'body' => $QUESTIONNAIRE_ANSWERS,
2475 :			'ALLOW_MAIL_TO' => $main::ALLOW_MAIL_TO
2476 :			);
2477 :			}
2478 :
2479 :			##########################################################################
2480 :			##########################################################################
2481 :	gage	120
2482 :
2483 :	sam	2	###########################################################################
2484 :			### THE FOLLOWING ARE LOCAL SUBROUTINES THAT ARE MEANT TO BE CALLED ONLY FROM THIS SCRIPT.
2485 :
2486 :			## Internal routine that converts variables into the standard array format
2487 :			##
2488 :			## IN: one of the following:
2489 :			## an undefined value (i.e., no variable was specified)
2490 :			## a reference to an array of variable names -- [var1, var2]
2491 :			## a number (the number of variables desired) -- 3
2492 :			## one or more variable names -- (var1, var2)
2493 :			## OUT: an array of variable names
2494 :	chris	54
2495 :	sam	2	sub get_var_array {
2496 :			my $in = shift @_;
2497 :			my @out;
2498 :
2499 :			if( not defined($in) ) { #if nothing defined, build default array and return
2500 :			@out = ( $functVarDefault );
2501 :			return @out;
2502 :			}
2503 :			elsif( ref( $in ) eq 'ARRAY' ) { #if given an array ref, dereference and return
2504 :			return @{$in};
2505 :			}
2506 :			elsif( $in =~ /^\d+/ ) { #if given a number, set up the array and return
2507 :			if( $in == 1 ) {
2508 :			$out[0] = 'x';
2509 :			}
2510 :			elsif( $in == 2 ) {
2511 :			$out[0] = 'x';
2512 :			$out[1] = 'y';
2513 :			}
2514 :			elsif( $in == 3 ) {
2515 :			$out[0] = 'x';
2516 :			$out[1] = 'y';
2517 :			$out[2] = 'z';
2518 :			}
2519 :			else { #default to the x_1, x_2, ... convention
2520 :			my ($i, $tag);
2521 :			for( $i=0; $i < $in; $i++ ) {
2522 :	chris	54	## akp the above seems to be off by one 1/4/00
2523 :	sam	2	$tag = $i + 1; ## akp 1/4/00
2524 :			$out[$i] = "${functVarDefault}_" . $tag; ## akp 1/4/00
2525 :			}
2526 :			}
2527 :			return @out;
2528 :			}
2529 :	chris	54	else { #if given one or more names, return as an array
2530 :	sam	2	unshift( @_, $in );
2531 :			return @_;
2532 :			}
2533 :			}
2534 :
2535 :			## Internal routine that converts limits into the standard array of arrays format
2536 :			## Some of the cases are probably unneccessary, but better safe than sorry
2537 :			##
2538 :			## IN: one of the following:
2539 :			## an undefined value (i.e., no limits were specified)
2540 :			## a reference to an array of arrays of limits -- [[llim,ulim], [llim,ulim]]
2541 :			## a reference to an array of limits -- [llim, ulim]
2542 :			## an array of array references -- ([llim,ulim], [llim,ulim])
2543 :			## an array of limits -- (llim,ulim)
2544 :			## OUT: an array of array references -- ([llim,ulim], [llim,ulim]) or ([llim,ulim])
2545 :	chris	22
2546 :	sam	2	sub get_limits_array {
2547 :			my $in = shift @_;
2548 :			my @out;
2549 :
2550 :	chris	54	if( not defined($in) ) { #if nothing defined, build default array and return
2551 :	sam	2	@out = ( [$functLLimitDefault, $functULimitDefault] );
2552 :			return @out;
2553 :			}
2554 :	chris	54	elsif( ref($in) eq 'ARRAY' ) { #$in is either ref to array, or ref to array of refs
2555 :	sam	2	my @deref = @{$in};
2556 :
2557 :	chris	54	if( ref( $in->[0] ) eq 'ARRAY' ) { #$in is a ref to an array of array refs
2558 :	sam	2	return @deref;
2559 :			}
2560 :	chris	54	else { #$in was just a ref to an array of numbers
2561 :	sam	2	@out = ( $in );
2562 :			return @out;
2563 :			}
2564 :			}
2565 :	chris	54	else { #$in was an array of references or numbers
2566 :	sam	2	unshift( @_, $in );
2567 :
2568 :	chris	54	if( ref($_[0]) eq 'ARRAY' ) { #$in was an array of references, so just return it
2569 :	sam	2	return @_;
2570 :			}
2571 :	chris	54	else { #$in was an array of numbers
2572 :	sam	2	@out = ( \@_ );
2573 :			return @out;
2574 :			}
2575 :			}
2576 :			}
2577 :
2578 :	gage	119	#sub check_option_list {
2579 :			# my $size = scalar(@_);
2580 :			# if( ( $size % 2 ) != 0 ) {
2581 :			# warn "ERROR in answer evaluator generator:\n" .
2582 :			# "Usage: <CODE>str_cmp([\$ans1, \$ans2],%options)</CODE>
2583 :			# or <CODE> num_cmp([\$num1, \$num2], %options)</CODE><BR>
2584 :			# A list of inputs must be inclosed in square brackets <CODE>[\$ans1, \$ans2]</CODE>";
2585 :			# }
2586 :			#}
2587 :	sam	2
2588 :			# simple subroutine to display an error message when
2589 :			# function compares are called with invalid parameters
2590 :			sub function_invalid_params {
2591 :			my $correctEqn = shift @_;
2592 :			my $error_response = sub {
2593 :	chris	54	my $PGanswerMessage = "Tell your professor that there is an error with the parameters " .
2594 :			"to the function answer evaluator";
2595 :	sam	2	return ( 0, $correctEqn, "", $PGanswerMessage );
2596 :			};
2597 :			return $error_response;
2598 :			}
2599 :
2600 :	gage	119	sub clean_up_error_msg {
2601 :			my $msg = $_[0];
2602 :			$msg =~ s/^\[[^\]]\][^:]://;
2603 :			$msg =~ s/Unquoted string//g;
2604 :			$msg =~ s/may\s+clash.*/does not make sense here/;
2605 :			$msg =~ s/\sat.line [\d]//g;
2606 :			$msg = 'error: '. $msg;
2607 :
2608 :			return $msg;
2609 :			}
2610 :
2611 :			#formats the student and correct answer as specified
2612 :			#format must be of a form suitable for sprintf (e.g. '%0.5g'),
2613 :			#with the exception that a '#' at the end of the string
2614 :			#will cause trailing zeros in the decimal part to be removed
2615 :			sub prfmt {
2616 :			my($number,$format) = @_; # attention, the order of format and number are reversed
2617 :			my $out;
2618 :			if ($format) {
2619 :			warn "Incorrect format used: $format. <BR> Format should look something like %4.5g<BR>"
2620 :			unless $format =~ /^\s%\d\.?\d\w#?\s$/;
2621 :
2622 :			if( $format =~ s/#\s*$// ) { # remove trailing zeros in the decimal
2623 :			$out = sprintf( $format, $number );
2624 :			$out =~ s/(\.\d*?)0+$/$1/;
2625 :			$out =~ s/\.$//; # in case all decimal digits were zero, remove the decimal
2626 :	gage	159	$out =~ s/e/E/g; # only use capital E's for exponents. Little e is for 2.71828...
2627 :			} elsif (is_a_number($number) ){
2628 :	gage	119	$out = sprintf( $format, $number );
2629 :	gage	159	$out =~ s/e/E/g; # only use capital E's for exponents. Little e is for 2.71828...
2630 :			} else { # number is probably a string representing an arithmetic expression
2631 :			$out = $number;
2632 :	gage	119	}
2633 :	gage	159
2634 :			} else {
2635 :	apizer	227	if (is_a_number($number)) {# only use capital E's for exponents. Little e is for 2.71828...
2636 :			$out = $number;
2637 :			$out =~ s/e/E/g;
2638 :			} else { # number is probably a string representing an arithmetic expression
2639 :			$out = $number;
2640 :			}
2641 :	gage	119	}
2642 :			return $out;
2643 :			}
2644 :	chris	22	#########################################################################
2645 :			# Filters for answer evaluators
2646 :			#########################################################################
2647 :
2648 :	gage	119	=head2 Filters
2649 :
2650 :			=pod
2651 :
2652 :			A filter is a short subroutine with the following structure. It accepts an
2653 :			AnswerHash, followed by a hash of options. It returns an AnswerHash
2654 :
2655 :			$ans_hash = filter($ans_hash, %options);
2656 :	gage	120
2657 :	gage	119	See the AnswerHash.pm file for a list of entries which can be expected to be found
2658 :	gage	120	in an AnswerHash, such as 'student_ans', 'score' and so forth. Other entries
2659 :	gage	119	may be present for specialized answer evaluators.
2660 :
2661 :			The hope is that a well designed set of filters can easily be combined to form
2662 :			a new answer_evaluator and that this method will produce answer evaluators which are
2663 :			are more robust than the method of copying existing answer evaluators and modifying them.
2664 :
2665 :			Here is an outline of how a filter is constructed:
2666 :
2667 :			sub filter{
2668 :			my $rh_ans = shift;
2669 :			my %options = @_;
2670 :			assign_option_aliases(\%options,
2671 :			'alias1' => 'option5'
2672 :			'alias2' => 'option7'
2673 :			);
2674 :			set_default_options(\%options,
2675 :			'_filter_name' => 'filter',
2676 :			'option5' => .0001,
2677 :			'option7' => 'ascii',
2678 :			'allow_unknown_options => 0,
2679 :			}
2680 :			.... body code of filter .......
2681 :			if ($error) {
2682 :			$rh_ans->throw_error("FILTER_ERROR", "Something went wrong");
2683 :			# see AnswerHash.pm for details on using the throw_error method.
2684 :
2685 :			$rh_ans; #reference to an AnswerHash object is returned.
2686 :			}
2687 :
2688 :			=cut
2689 :
2690 :	gage	120	=head4 compare_numbers
2691 :
2692 :
2693 :			=cut
2694 :
2695 :
2696 :			sub compare_numbers {
2697 :			my ($rh_ans, %options) = @_;
2698 :			my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($rh_ans->{student_ans});
2699 :			if ($PG_eval_errors) {
2700 :			$rh_ans->throw_error('EVAL','There is a syntax error in your answer');
2701 :			$rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors);
2702 :			# return $rh_ans;
2703 :			} else {
2704 :			$rh_ans->{student_ans} = prfmt($inVal,$options{format});
2705 :			}
2706 :
2707 :			my $permitted_error;
2708 :
2709 :			if ($rh_ans->{tolType} eq 'absolute') {
2710 :			$permitted_error = $rh_ans->{tolerance};
2711 :			}
2712 :			elsif ( abs($rh_ans->{correct_ans}) <= $options{zeroLevel}) {
2713 :			$permitted_error = $options{zeroLevelTol}; ## want $tol to be non zero
2714 :			}
2715 :			else {
2716 :			$permitted_error = abs($rh_ans->{tolerance}*$rh_ans->{correct_ans});
2717 :			}
2718 :
2719 :			my $is_a_number = is_a_number($inVal);
2720 :			$rh_ans->{score} = 1 if ( ($is_a_number) and
2721 :			(abs( $inVal - $rh_ans->{correct_ans} ) <= $permitted_error) );
2722 :			if (not $is_a_number) {
2723 :			$rh_ans->{error_message} = "$rh_ans->{error_message}". 'Your answer does not evaluate to a number ';
2724 :			}
2725 :
2726 :			$rh_ans;
2727 :			}
2728 :
2729 :			=head4 std_num_filter
2730 :
2731 :			std_num_filter($rh_ans, %options)
2732 :			returns $rh_ans
2733 :
2734 :			Replaces some constants using math_constants, then evaluates a perl expression.
2735 :
2736 :
2737 :			=cut
2738 :
2739 :			sub std_num_filter {
2740 :			my $rh_ans = shift;
2741 :			my %options = @_;
2742 :			my $in = $rh_ans->input();
2743 :			$in = math_constants($in);
2744 :			$rh_ans->{type} = 'std_number';
2745 :			my ($inVal,$PG_eval_errors,$PG_full_error_report);
2746 :			if ($in =~ /\S/) {
2747 :			($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($in);
2748 :			} else {
2749 :			$PG_eval_errors = '';
2750 :			}
2751 :
2752 :			if ($PG_eval_errors) { ##error message from eval or above
2753 :			$rh_ans->{ans_message} = 'There is a syntax error in your answer';
2754 :			$rh_ans->{student_ans} = clean_up_error_msg($PG_eval_errors);
2755 :			} else {
2756 :			$rh_ans->{student_ans} = $inVal;
2757 :			}
2758 :			$rh_ans;
2759 :			}
2760 :
2761 :			=head std_num_array_filter
2762 :
2763 :			std_num_array_filter($rh_ans, %options)
2764 :			returns $rh_ans
2765 :
2766 :			Assumes the {student_ans} field is a numerical array, and applies BOTH check_syntax and std_num_filter
2767 :			to each element of the array. Does it's best to generate sensible error messages for syntax errors.
2768 :			A typical error message displayed in {studnet_ans} might be ( 56, error message, -4).
2769 :
2770 :			=cut
2771 :
2772 :			sub std_num_array_filter {
2773 :			my $rh_ans= shift;
2774 :			my %options = @_;
2775 :			set_default_options( \%options,
2776 :			'_filter_name' => 'std_num_array_filter',
2777 :			);
2778 :			my @in = @{$rh_ans->{student_ans}};
2779 :			my $temp_hash = new AnswerHash;
2780 :			my @out=();
2781 :			my $PGanswerMessage = '';
2782 :			foreach my $item (@in) { # evaluate each number in the vector
2783 :			$temp_hash->input($item);
2784 :			$temp_hash = check_syntax($temp_hash);
2785 :			if (defined($temp_hash->{error_flag}) and $temp_hash->{error_flag} eq 'SYNTAX') {
2786 :			$PGanswerMessage .= $temp_hash->{ans_message};
2787 :			$temp_hash->{ans_message} = undef;
2788 :			} else {
2789 :			#continue processing
2790 :			$temp_hash = std_num_filter($temp_hash);
2791 :			if (defined($temp_hash->{ans_message}) and $temp_hash->{ans_message} ) {
2792 :			$PGanswerMessage .= $temp_hash->{ans_message};
2793 :			$temp_hash->{ans_message} = undef;
2794 :			}
2795 :			}
2796 :			push(@out, $temp_hash->input());
2797 :
2798 :			}
2799 :			if ($PGanswerMessage) {
2800 :			$rh_ans->input( "( " . join(", ", @out ) . " )" );
2801 :			$rh_ans->throw_error('SYNTAX', 'There is a syntax error in your answer.');
2802 :			} else {
2803 :			$rh_ans->input( [@out] );
2804 :			}
2805 :			$rh_ans;
2806 :			}
2807 :
2808 :			=head4 function_from_string2
2809 :
2810 :
2811 :
2812 :			=cut
2813 :
2814 :			sub function_from_string2 {
2815 :			my $rh_ans = shift;
2816 :			my %options = @_;
2817 :			my $eqn = $rh_ans->{student_ans};
2818 :			assign_option_aliases(\%options,
2819 :			'vars' => 'ra_vars',
2820 :			'var' => 'ra_vars',
2821 :			);
2822 :			set_default_options( \%options,
2823 :			'store_in' => 'rf_student_ans',
2824 :			'ra_vars' => [qw( x y )],
2825 :			'debug' => 0,
2826 :			'_filter_name' => 'function_from_string2',
2827 :			);
2828 :			$rh_ans->{_filter_name} = $options{_filter_name};
2829 :			my @VARS = @{ $options{ 'ra_vars'}};
2830 :			#warn "VARS = ", join("<>", @VARS) if defined($options{debug}) and $options{debug} ==1;
2831 :			my $originalEqn = $eqn;
2832 :			$eqn = &math_constants($eqn);
2833 :			for( my $i = 0; $i < @VARS; $i++ ) {
2834 :			# This next line is a hack required for 5.6.0 -- it doesn't appear to be needed in 5.6.1
2835 :			my ($temp,$er1,$er2) = PG_restricted_eval('"'. $VARS[$i] . '"');
2836 :			#$eqn =~ s/\b$VARS[$i]\b/\$VARS[$i]/g;
2837 :			$eqn =~ s/\b$temp\b/\$VARS[$i]/g;
2838 :
2839 :			}
2840 :			#warn "equation evaluated = $eqn",$rh_ans->pretty_print(), "<br>\noptions<br>\n",
2841 :			# pretty_print(\%options)
2842 :			# if defined($options{debug}) and $options{debug} ==1;
2843 :			my ($function_sub,$PG_eval_errors, $PG_full_errors) = PG_answer_eval( q!
2844 :			sub {
2845 :			my @VARS = @_;
2846 :			my $input_str = '';
2847 :			for( my $i=0; $i<@VARS; $i++ ) {
2848 :			$input_str .= "\$VARS[$i] = $VARS[$i]; ";
2849 :			}
2850 :			my $PGanswerMessage;
2851 :			$input_str .= '! . $eqn . q!'; # need the single quotes to keep the contents of $eqn from being
2852 :			# evaluated when it is assigned to $input_str;
2853 :			my ($out, $PG_eval_errors, $PG_full_errors) = PG_answer_eval($input_str); #Finally evaluated
2854 :
2855 :			if ( defined($PG_eval_errors) and $PG_eval_errors =~ /\S/ ) {
2856 :			$PGanswerMessage = clean_up_error_msg($PG_eval_errors);
2857 :			# This message seemed too verbose, but it does give extra information, we'll see if it is needed.
2858 :			# "<br> There was an error in evaluating your function <br>
2859 :			# !. $originalEqn . q! <br>
2860 :			# at ( " . join(', ', @VARS) . " ) <br>
2861 :			# $PG_eval_errors
2862 :			# "; # this message appears in the answer section which is not process by Latex2HTML so it must
2863 :			# # be in HTML. That is why $BR is NOT used.
2864 :
2865 :			}
2866 :			(wantarray) ? ($out, $PGanswerMessage): $out; # PGanswerMessage may be undefined.
2867 :			};
2868 :			!);
2869 :
2870 :			if (defined($PG_eval_errors) and $PG_eval_errors =~/\S/ ) {
2871 :			$PG_eval_errors = clean_up_error_msg($PG_eval_errors);
2872 :
2873 :			my $PGanswerMessage = "There was an error in converting the expression
2874 :			$main::BR $originalEqn $main::BR into a function.
2875 :			$main::BR $PG_eval_errors.";
2876 :			$rh_ans->{rf_student_ans} = $function_sub;
2877 :			$rh_ans->{ans_message} = $PGanswerMessage;
2878 :			$rh_ans->{error_message} = $PGanswerMessage;
2879 :			$rh_ans->{error_flag} = 1;
2880 :			# we couldn't compile the equation, we'll return an error message.
2881 :			} else {
2882 :			# if (defined($options{store_in} )) {
2883 :			# $rh_ans ->{$options{store_in}} = $function_sub;
2884 :			# } else {
2885 :			# $rh_ans->{rf_student_ans} = $function_sub;
2886 :			# }
2887 :			$rh_ans ->{$options{store_in}} = $function_sub;
2888 :			}
2889 :
2890 :			$rh_ans;
2891 :			}
2892 :
2893 :			=head4 is_zero_array
2894 :
2895 :
2896 :			=cut
2897 :
2898 :
2899 :			sub is_zero_array {
2900 :			my $rh_ans = shift;
2901 :			my %options = @_;
2902 :			set_default_options( \%options,
2903 :	ch003i	135	'_filter_name' => 'is_zero_array',
2904 :	gage	154	'tolerance' => 0.000001,
2905 :	gage	120	);
2906 :			my $array = $rh_ans -> {ra_differences};
2907 :			my $num = @$array;
2908 :			my $i;
2909 :			my $max = 0; my $mm;
2910 :			for ($i=0; $i< $num; $i++) {
2911 :			$mm = $array->[$i] ;
2912 :			if (not is_a_number($mm) ) {
2913 :			$max = $mm; # break out if one of the elements is not a number
2914 :			last;
2915 :			}
2916 :			$max = abs($mm) if abs($mm) > $max;
2917 :			}
2918 :			if (not is_a_number($max)) {
2919 :			$rh_ans->{score} = 0;
2920 :			my $error = "WeBWorK was unable evaluate your function. Please check that your
2921 :			expression doesn't take roots of negative numbers, or divide by zero.";
2922 :			$rh_ans->throw_error('EVAL',$error);
2923 :			} else {
2924 :	gage	154	$rh_ans->{score} = ($max < $options{tolerance} ) ? 1: 0; # 1 if the array is close to 0;
2925 :	gage	120	}
2926 :			$rh_ans;
2927 :			}
2928 :
2929 :			=head4 best_approx_parameters
2930 :
2931 :	gage	122	best_approx_parameters($rh_ans,%options); #requires the following fields in $rh_ans
2932 :	gage	120	{rf_student_ans} # reference to the test answer
2933 :			{rf_correct_ans} # reference to the comparison answer
2934 :	gage	122	{evaluation_points}, # an array of row vectors indicating the points
2935 :			# to evaluate when comparing the functions
2936 :
2937 :			%options # debug => 1 gives more error answers
2938 :			# param_vars => [''] additional parameters used to adapt to function
2939 :	gage	120	)
2940 :	gage	122
2941 :
2942 :			The parameters for the comparison function which best approximates the test_function are stored
2943 :			in the field {ra_parameters}.
2944 :
2945 :
2946 :	gage	120	The last $dim_of_parms_space variables are assumed to be parameters, and it is also
2947 :			assumed that the function \&comparison_fun
2948 :			depends linearly on these variables. This function finds the values for these parameters which minimizes the
2949 :			Euclidean distance (L2 distance) between the test function and the comparison function and the test points specified
2950 :			by the array reference \@rows_of_test_points. This is assumed to be an array of arrays, with the inner arrays
2951 :			determining a test point.
2952 :
2953 :			The comparison function should have $dim_of_params_space more input variables than the test function.
2954 :
2955 :
2956 :
2957 :	gage	122
2958 :	gage	120
2959 :			=cut
2960 :
2961 :	gage	122	# Used internally:
2962 :			#
2963 :			# &$determine_param_coeff( $rf_comparison_function # a reference to the correct answer function
2964 :			# $ra_variables # an array of the active input variables to the functions
2965 :			# $dim_of_params_space # indicates the number of parameters upon which the
2966 :			# # the comparison function depends linearly. These are assumed to
2967 :			# # be the last group of inputs to the comparison function.
2968 :			#
2969 :			# %options # $options{debug} gives more error messages
2970 :			#
2971 :			# # A typical function might look like
2972 :			# # f(x,y,z,a,b) = x^2+acos(xz) + bsin(x) with a parameter
2973 :			# # space of dimension 2 and a variable space of dimension 3.
2974 :			# )
2975 :			# # returns a list of coefficients
2976 :
2977 :	gage	120	sub best_approx_parameters {
2978 :			my $rh_ans = shift;
2979 :			my %options = @_;
2980 :			set_default_options(\%options,
2981 :			'_filter_name' => 'best_approx_paramters',
2982 :			'allow_unknown_options' => 1,
2983 :			);
2984 :			my $errors = undef;
2985 :			# This subroutine for the determining the coefficents of the parameters at a given point
2986 :			# is pretty specialized, so it is included here as a sub-subroutine.
2987 :			my $determine_param_coeffs = sub {
2988 :			my ($rf_fun, $ra_variables, $dim_of_params_space, %options) =@_;
2989 :			my @zero_params=();
2990 :			for(my $i=1;$i<=$dim_of_params_space;$i++){push(@zero_params,0); }
2991 :			my @vars = @$ra_variables;
2992 :			my @coeff = ();
2993 :			my @inputs = (@vars,@zero_params);
2994 :			my ($f0, $f1, $err);
2995 :			($f0, $err) = &{$rf_fun}(@inputs);
2996 :			if (defined($err) ) {
2997 :			$errors .= "$err ";
2998 :			} else {
2999 :			for (my $i=@vars;$i<@inputs;$i++) {
3000 :			$inputs[$i]=1; # set one parameter to 1;
3001 :			my($f1,$err) = &$rf_fun(@inputs);
3002 :			if (defined($err) ) {
3003 :			$errors .= " $err ";
3004 :			} else {
3005 :			push(@coeff, $f1-$f0);
3006 :			}
3007 :			$inputs[$i]=0; # set it back
3008 :			}
3009 :			}
3010 :			(\@coeff, $errors);
3011 :			};
3012 :			my $rf_fun = $rh_ans->{rf_student_ans};
3013 :			my $rf_correct_fun = $rh_ans->{rf_correct_ans};
3014 :			my $ra_vars_matrix = $rh_ans->{evaluation_points};
3015 :			my $dim_of_param_space = @{$options{param_vars}};
3016 :			# Short cut. Bail if there are no param_vars
3017 :			unless ($dim_of_param_space >0) {
3018 :			$rh_ans ->{ra_parameters} = [];
3019 :			return $rh_ans;
3020 :			}
3021 :			# inputs are row arrays in this case.
3022 :			my @zero_params=();
3023 :
3024 :			for(my $i=1;$i<=$dim_of_param_space;$i++){push(@zero_params,0); }
3025 :			my @rows_of_vars = @$ra_vars_matrix;
3026 :			warn "input rows ", pretty_print(\@rows_of_vars) if defined($options{debug}) and $options{debug};
3027 :			my $rows = @rows_of_vars;
3028 :			my $matrix =new Matrix($rows,$dim_of_param_space);
3029 :			my $rhs_vec = new Matrix($rows, 1);
3030 :			my $row_num = 1;
3031 :			my ($ra_coeff,$val2, $val1, $err1,$err2,@inputs,@vars);
3032 :			my $number_of_data_points = $dim_of_param_space +2;
3033 :			while (@rows_of_vars and $row_num <= $number_of_data_points) {
3034 :			# get one set of data points from the test function;
3035 :			@vars = @{ shift(@rows_of_vars) };
3036 :			($val2, $err1) = &{$rf_fun}(@vars);
3037 :			$errors .= " $err1 " if defined($err1);
3038 :			@inputs = (@vars,@zero_params);
3039 :			($val1, $err2) = &{$rf_correct_fun}(@inputs);
3040 :			$errors .= " $err2 " if defined($err2);
3041 :
3042 :			unless (defined($err1) or defined($err2) ) {
3043 :			$rhs_vec->assign($row_num,1, $val2-$val1 );
3044 :
3045 :			# warn "rhs data val1=$val1, val2=$val2, val2 - val1 = ", $val2 - $val1 if $options{debug};
3046 :			# warn "vars ", join(" \| ", @vars) if $options{debug};
3047 :
3048 :			($ra_coeff, $err1) = &{$determine_param_coeffs}($rf_correct_fun,\@vars,$dim_of_param_space,%options);
3049 :			if (defined($err1) ) {
3050 :			$errors .= " $err1 ";
3051 :			} else {
3052 :			my @coeff = @$ra_coeff;
3053 :			my $col_num=1;
3054 :			while(@coeff) {
3055 :			$matrix->assign($row_num,$col_num, shift(@coeff) );
3056 :			$col_num++;
3057 :			}
3058 :			}
3059 :			}
3060 :			$row_num++;
3061 :			last if $errors; # break if there are any errors.
3062 :			# This cuts down on the size of error messages.
3063 :			# However it impossible to check for equivalence at 95% of points
3064 :			# which might be useful for functions that are not defined at some points.
3065 :			}
3066 :			warn "<br> best_approx_parameters: matrix1 <br> ", " $matrix " if $options{debug};
3067 :			warn "<br> best_approx_parameters: vector <br> ", " $rhs_vec " if $options{debug};
3068 :
3069 :			# we have Matrix * parameter = data_vec + perpendicular vector
3070 :			# where the matrix has column vectors defining the span of the parameter space
3071 :			# multiply both sides by Matrix_transpose and solve for the parameters
3072 :			# This is exactly what the method proj_coeff method does.
3073 :			my @array;
3074 :			if (defined($errors) ) {
3075 :			@array = (); # new Matrix($dim_of_param_space,1);
3076 :			} else {
3077 :			@array = $matrix->proj_coeff($rhs_vec)->list();
3078 :			}
3079 :			# check size (hack)
3080 :			my $max = 0;
3081 :			foreach my $val (@array ) {
3082 :			$max = abs($val) if $max < abs($val);
3083 :			if (not is_a_number($val) ) {
3084 :			$max = "NaN: $val";
3085 :			last;
3086 :			}
3087 :			}
3088 :			if ($max =~/NaN/) {
3089 :			$errors .= "WeBWorK was unable evaluate your function. Please check that your
3090 :			expression doesn't take roots of negative numbers, or divide by zero.";
3091 :			} elsif ($max > $options{maxConstantOfIntegration} ) {
3092 :			$errors .= "At least one of the adapting parameters
3093 :			(perhaps the constant of integration) is too large: $max,
3094 :			( the maximum allowed is $options{maxConstantOfIntegration} )";
3095 :			}
3096 :
3097 :			$rh_ans->{ra_parameters} = \@array;
3098 :			$rh_ans->throw_error('EVAL', $errors) if defined($errors);
3099 :			$rh_ans;
3100 :			}
3101 :
3102 :			=head4 calculate_difference_vector
3103 :
3104 :			calculate_difference_vector( $ans_hash, %options);
3105 :
3106 :			{rf_student_ans}, # a reference to the test function
3107 :			{rf_correct_ans}, # a reference to the correct answer function
3108 :			{evaluation_points}, # an array of row vectors indicating the points
3109 :			# to evaluate when comparing the functions
3110 :			{ra_parameters} # these are the (optional) additional inputs to
3111 :			# the comparison function which adapt it properly
3112 :			# to the problem at hand.
3113 :
3114 :			%options # mode => 'rel' specifies that each element in the
3115 :			# difference matrix is divided by the correct answer.
3116 :			# unless the correct answer is nearly 0.
3117 :			)
3118 :
3119 :			=cut
3120 :
3121 :			sub calculate_difference_vector {
3122 :			my $rh_ans = shift;
3123 :			my %options = @_;
3124 :			# initialize
3125 :			my $rf_fun = $rh_ans -> {rf_student_ans};
3126 :			my $rf_correct_fun = $rh_ans -> {rf_correct_ans};
3127 :			my $ra_parameters = $rh_ans ->{ra_parameters};
3128 :			my @evaluation_points = @{$rh_ans->{evaluation_points} };
3129 :			my @parameters = ();
3130 :			@parameters = @$ra_parameters if defined($ra_parameters) and ref($ra_parameters) eq 'ARRAY';
3131 :			my $errors = undef;
3132 :			my @zero_params=();
3133 :			for(my $i=1;$i<=@{$ra_parameters};$i++){push(@zero_params,0); }
3134 :			my @differences = ();
3135 :			my @student_values;
3136 :			my @adjusted_student_values;
3137 :			my @instructorVals;
3138 :			my ($diff,$instructorVal);
3139 :			# calculate the vector of differences between the test function and the comparison function.
3140 :			while (@evaluation_points) {
3141 :			my ($err1, $err2,$err3);
3142 :			my @vars = @{ shift(@evaluation_points) };
3143 :			my @inputs = (@vars, @parameters);
3144 :			my ($inVal, $correctVal);
3145 :			($inVal, $err1) = &{$rf_fun}(@vars);
3146 :			$errors .= " $err1 " if defined($err1);
3147 :			$errors .= " Error detected evaluating student input at (".join(' , ',@vars) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err1);
3148 :			($correctVal, $err2) =&{$rf_correct_fun}(@inputs);
3149 :			$errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err2 " if defined($err2);
3150 :			$errors .= " Error detected evaluating correct adapted answer at (".join(' , ',@inputs) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err2);
3151 :			($instructorVal,$err3)= &$rf_correct_fun(@vars, @zero_params);
3152 :			$errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err3 " if defined($err3);
3153 :			$errors .= " Error detected evaluating instructor answer at (".join(' , ',@vars, @zero_params) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err3);
3154 :			unless (defined($err1) or defined($err2) or defined($err3) ) {
3155 :			$diff = ( $inVal - ($correctVal -$instructorVal ) ) - $instructorVal; #prevents entering too high a number?
3156 :			#warn "taking the difference of ", $inVal, " and ", $correctVal, " is ", $diff;
3157 :			if (defined($options{tolType}) and $options{tolType} eq 'relative' ) { #relative tolerance
3158 :			#warn "diff = $diff";
3159 :			#$diff = ( $inVal - ($correctVal-$instructorVal ) )/abs($instructorVal) -1 if abs($instructorVal) > $options{zeroLevel};
3160 :			$diff = ( $inVal - ($correctVal-$instructorVal ) )/$instructorVal -1 if abs($instructorVal) > $options{zeroLevel};
3161 :			#$diff = ( $inVal - ($correctVal-$instructorVal- $instructorVal ) )/abs($instructorVal) if abs($instructorVal) > $options{zeroLevel};
3162 :			#warn "diff = $diff, ", abs( &$rf_correct_fun(@inputs) ) , "-- $correctVal";
3163 :			}
3164 :			}
3165 :			last if $errors; # break if there are any errors.
3166 :			# This cuts down on the size of error messages.
3167 :			# However it impossible to check for equivalence at 95% of points
3168 :			# which might be useful for functions that are not defined at some points.
3169 :			push(@student_values,$inVal);
3170 :			push(@adjusted_student_values,( $inVal - ($correctVal -$instructorVal) ) );
3171 :			push(@differences, $diff);
3172 :			push(@instructorVals,$instructorVal);
3173 :			}
3174 :			$rh_ans ->{ra_differences} = \@differences;
3175 :			$rh_ans ->{ra_student_values} = \@student_values;
3176 :			$rh_ans ->{ra_adjusted_student_values} = \@adjusted_student_values;
3177 :			$rh_ans->{ra_instructor_values}=\@instructorVals;
3178 :			$rh_ans->throw_error('EVAL', $errors) if defined($errors);
3179 :			$rh_ans;
3180 :			}
3181 :
3182 :	gage	119	=head4 fix_answer_for_display
3183 :
3184 :			=cut
3185 :
3186 :			sub fix_answers_for_display {
3187 :			my ($rh_ans, %options) = @_;
3188 :			if ( $rh_ans->{answerIsString} ==1) {
3189 :			$rh_ans = evaluatesToNumber ($rh_ans, %options);
3190 :			}
3191 :			if (defined ($rh_ans->{student_units})) {
3192 :			$rh_ans->{student_ans} = $rh_ans->{student_ans}. ' '. $rh_ans->{student_units};
3193 :			}
3194 :			$rh_ans->{correct_ans} = $rh_ans->{original_correct_ans};
3195 :
3196 :			$rh_ans;
3197 :			}
3198 :
3199 :			=head4 evaluatesToNumber
3200 :
3201 :			=cut
3202 :
3203 :			sub evaluatesToNumber {
3204 :			my ($rh_ans, %options) = @_;
3205 :			if (is_a_numeric_expression($rh_ans->{student_ans})) {
3206 :			my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($rh_ans->{student_ans});
3207 :			if ($PG_eval_errors) { # this if statement should never be run
3208 :			# change nothing
3209 :			} else {
3210 :			# change this
3211 :			$rh_ans->{student_ans} = prfmt($inVal,$options{format});
3212 :			}
3213 :			}
3214 :			$rh_ans;
3215 :			}
3216 :
3217 :			=head4 is_numeric_expression
3218 :
3219 :			=cut
3220 :
3221 :			sub is_a_numeric_expression {
3222 :			my $testString = shift;
3223 :			my $is_a_numeric_expression = 0;
3224 :			my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($testString);
3225 :			if ($PG_eval_errors) {
3226 :			$is_a_numeric_expression = 0;
3227 :			} else {
3228 :			$is_a_numeric_expression = 1;
3229 :			}
3230 :			$is_a_numeric_expression;
3231 :			}
3232 :
3233 :			=head4 is_a_number
3234 :
3235 :			=cut
3236 :
3237 :	chris	54	sub is_a_number {
3238 :	chris	22	my ($num,%options) = @_;
3239 :			my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ;
3240 :			my ($rh_ans);
3241 :			if ($process_ans_hash) {
3242 :			$rh_ans = $num;
3243 :			$num = $rh_ans->{student_ans};
3244 :			}
3245 :
3246 :	sam	2	my $is_a_number = 0;
3247 :			return $is_a_number unless defined($num);
3248 :			$num =~ s/^\s*//; ## remove initial spaces
3249 :			$num =~ s/\s*$//; ## remove trailing spaces
3250 :
3251 :			## the following is copied from the online perl manual
3252 :			if ($num =~ /^([+-]?)(?=\d\|\.\d)\d(\.\d)?([Ee]([+-]?\d+))?$/){
3253 :			$is_a_number = 1;
3254 :			}
3255 :	chris	22
3256 :			if ($process_ans_hash) {
3257 :			if ($is_a_number == 1 ) {
3258 :			$rh_ans->{student_ans}=$num;
3259 :			return $rh_ans;
3260 :			} else {
3261 :			$rh_ans->{student_ans} = "Incorrect number format: You must enter a number, e.g. -6, 5.3, or 6.12E-3";
3262 :			$rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3');
3263 :			return $rh_ans;
3264 :			}
3265 :			} else {
3266 :			return $is_a_number;
3267 :			}
3268 :	sam	2	}
3269 :
3270 :	gage	119	=head4 is_a_fraction
3271 :
3272 :			=cut
3273 :
3274 :	chris	54	sub is_a_fraction {
3275 :	chris	22	my ($num,%options) = @_;
3276 :			my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ;
3277 :			my ($rh_ans);
3278 :			if ($process_ans_hash) {
3279 :			$rh_ans = $num;
3280 :			$num = $rh_ans->{student_ans};
3281 :			}
3282 :
3283 :			my $is_a_fraction = 0;
3284 :			return $is_a_fraction unless defined($num);
3285 :			$num =~ s/^\s*//; ## remove initial spaces
3286 :			$num =~ s/\s*$//; ## remove trailing spaces
3287 :
3288 :			if ($num =~ /^\s\-?\s[\/\d\.Ee\s]*$/) {
3289 :	sam	2	$is_a_fraction = 1;
3290 :			}
3291 :	chris	22
3292 :			if ($process_ans_hash) {
3293 :			if ($is_a_fraction == 1 ) {
3294 :			$rh_ans->{student_ans}=$num;
3295 :			return $rh_ans;
3296 :			} else {
3297 :			$rh_ans->{student_ans} = "Not a number of fraction: You must enter a number or fraction, e.g. -6 or 7/13";
3298 :			$rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3');
3299 :			return $rh_ans;
3300 :			}
3301 :
3302 :			} else {
3303 :			return $is_a_fraction;
3304 :			}
3305 :	sam	2	}
3306 :
3307 :	gage	119	=head4 is_an_arithemetic_expression
3308 :	chris	22
3309 :	gage	119	=cut
3310 :
3311 :	chris	54	sub is_an_arithmetic_expression {
3312 :	chris	22	my ($num,%options) = @_;
3313 :			my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ;
3314 :			my ($rh_ans);
3315 :			if ($process_ans_hash) {
3316 :			$rh_ans = $num;
3317 :			$num = $rh_ans->{student_ans};
3318 :			}
3319 :
3320 :			my $is_an_arithmetic_expression = 0;
3321 :			return $is_an_arithmetic_expression unless defined($num);
3322 :			$num =~ s/^\s*//; ## remove initial spaces
3323 :			$num =~ s/\s*$//; ## remove trailing spaces
3324 :
3325 :			if ($num =~ /^[+\-\/\^\[\]\{\}\s\d\.Ee]$/) {
3326 :	sam	2	$is_an_arithmetic_expression = 1;
3327 :			}
3328 :	chris	22
3329 :			if ($process_ans_hash) {
3330 :			if ($is_an_arithmetic_expression == 1 ) {
3331 :			$rh_ans->{student_ans}=$num;
3332 :			return $rh_ans;
3333 :			} else {
3334 :
3335 :			$rh_ans->{student_ans} = "Not an arithmetic expression: You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2";
3336 :			$rh_ans->throw_error('NUMBER', 'You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2');
3337 :			return $rh_ans;
3338 :			}
3339 :
3340 :			} else {
3341 :			return $is_an_arithmetic_expression;
3342 :			}
3343 :	sam	2	}
3344 :
3345 :	gage	119	#
3346 :
3347 :			=head4 math_constants
3348 :
3349 :			replaces pi, e, and ^ with their Perl equivalents
3350 :
3351 :			=cut
3352 :
3353 :	chris	54	sub math_constants {
3354 :	chris	22	my($in,%options) = @_;
3355 :			my $rh_ans;
3356 :			my $process_ans_hash = ( ref( $in ) eq 'AnswerHash' ) ? 1 : 0 ;
3357 :			if ($process_ans_hash) {
3358 :			$rh_ans = $in;
3359 :			$in = $rh_ans->{student_ans};
3360 :			}
3361 :	gage	119	# The code fragment above allows this filter to be used when the input is simply a string
3362 :			# as well as when the input is an AnswerHash, and options.
3363 :	sam	2	$in =~s/\bpi\b/(4*atan2(1,1))/ge;
3364 :			$in =~s/\be\b/(exp(1))/ge;
3365 :			$in =~s/\^/**/g;
3366 :	chris	22
3367 :			if ($process_ans_hash) {
3368 :			$rh_ans->{student_ans}=$in;
3369 :			return $rh_ans;
3370 :			} else {
3371 :			return $in;
3372 :			}
3373 :	sam	2	}
3374 :
3375 :
3376 :
3377 :	gage	122	=head4 is_array
3378 :
3379 :			is_array($rh_ans)
3380 :			returns: $rh_ans. Throws error "NOTARRAY" if this is not an array
3381 :
3382 :			=cut
3383 :
3384 :			sub is_array {
3385 :			my $rh_ans = shift;
3386 :			# return if the result is an array
3387 :			return($rh_ans) if ref($rh_ans->{student_ans}) eq 'ARRAY' ;
3388 :			$rh_ans->throw_error("NOTARRAY","The answer is not an array");
3389 :			$rh_ans;
3390 :			}
3391 :
3392 :			=head4 check_syntax
3393 :
3394 :			check_syntax( $rh_ans, %options)
3395 :			returns an answer hash.
3396 :
3397 :			latex2html preview code are installed in the answer hash.
3398 :			The input has been transformed, changing 7pi to 7pi or 7x to 7x.
3399 :			Syntax error messages may be generated and stored in student_ans
3400 :			Additional syntax error messages are stored in {ans_message} and duplicated in {error_message}
3401 :
3402 :
3403 :			=cut
3404 :
3405 :			sub check_syntax {
3406 :			my $rh_ans = shift;
3407 :			my %options = @_;
3408 :			unless ( defined( $rh_ans->{student_ans} ) ) {
3409 :			warn "Check_syntax requires an equation in the field {student_ans} or input";
3410 :			$rh_ans->throw_error("1","{student_ans} field not defined");
3411 :			return $rh_ans;
3412 :			}
3413 :			my $in = $rh_ans->{student_ans};
3414 :			my $parser = new AlgParserWithImplicitExpand;
3415 :			my $ret = $parser -> parse($in); #for use with loops
3416 :
3417 :			if ( ref($ret) ) { ## parsed successfully
3418 :			$parser -> tostring();
3419 :			$parser -> normalize();
3420 :			$rh_ans->input( $parser -> tostring() );
3421 :			$rh_ans->{preview_text_string} = $in;
3422 :			$rh_ans->{preview_latex_string} = $parser -> tolatex();
3423 :
3424 :			} else { ## error in parsing
3425 :
3426 :			$rh_ans->{'student_ans'} = 'syntax error:'. $parser->{htmlerror},
3427 :			$rh_ans->{'ans_message'} = $parser -> {error_msg},
3428 :			$rh_ans->{'preview_text_string'} = '',
3429 :			$rh_ans->{'preview_latex_string'} = '',
3430 :			$rh_ans->throw_error('SYNTAX', 'syntax error in answer:'. $parser->{htmlerror} . "$BR" .$parser -> {error_msg});
3431 :			}
3432 :			$rh_ans;
3433 :
3434 :			}
3435 :
3436 :			=head4 check_strings
3437 :
3438 :			check_strings ($rh_ans, %options)
3439 :			returns $rh_ans
3440 :
3441 :			=cut
3442 :
3443 :			sub check_strings {
3444 :			my ($rh_ans, %options) = @_;
3445 :	sam	2
3446 :	gage	122	# if the student's answer is a number, simply return the answer hash (unchanged).
3447 :
3448 :			if ( $rh_ans->{student_ans} =~ m/[\d+\-\/^(){}\[\]]\|^\se\s$\|^\spi\s*$/) {
3449 :			if ( $rh_ans->{answerIsString} == 1) {
3450 :			#$rh_ans->throw_error('STRING','Incorrect Answer'); # student's answer is a number
3451 :			}
3452 :			return $rh_ans;
3453 :			}
3454 :			# the student's answer is recognized as a string
3455 :			my $ans = $rh_ans->{student_ans};
3456 :	gage	120
3457 :	gage	122	# OVERVIEW of reminder of function:
3458 :			# if answer is correct, return correct. (adjust score to 1)
3459 :			# if answer is incorect:
3460 :			# 1) determine if the answer is sensible. if it is, return incorrect.
3461 :			# 2) if the answer is not sensible (and incorrect), then return an error message indicating so.
3462 :			# no matter what: throw a 'STRING' error to skip numerical evaluations. (error flag skips remainder of pre_filters and evaluators)
3463 :			# last: 'STRING' post_filter will clear the error (avoiding pink screen.)
3464 :
3465 :			my $sensibleAnswer = 0;
3466 :			$ans = str_filters( $ans, 'compress_whitespace' ); # remove trailing, leading, and double spaces.
3467 :			my ($ans_eval) = str_cmp($rh_ans->{correct_ans});
3468 :			my $temp_ans_hash = &$ans_eval($ans);
3469 :			$rh_ans->{test} = $temp_ans_hash;
3470 :			if ($temp_ans_hash->{score} ==1 ) { # students answer matches the correct answer.
3471 :			$rh_ans->{score} = 1;
3472 :			$sensibleAnswer = 1;
3473 :			} else { # students answer does not match the correct answer.
3474 :			my $legalString = ''; # find out if string makes sense
3475 :			my @legalStrings = @{$options{strings}};
3476 :			foreach $legalString (@legalStrings) {
3477 :			if ( uc($ans) eq uc($legalString) ) {
3478 :			$sensibleAnswer = 1;
3479 :			last;
3480 :			}
3481 :			}
3482 :			$sensibleAnswer = 1 unless $ans =~ /\S/; ## empty answers are sensible
3483 :			$rh_ans->throw_error('EVAL', "Your answer is not a recognized answer") unless ($sensibleAnswer);
3484 :			# $temp_ans_hash -> setKeys( 'ans_message' => 'Your answer is not a recognized answer' ) unless ($sensibleAnswer);
3485 :			# $temp_ans_hash -> setKeys( 'student_ans' => uc($ans) );
3486 :			}
3487 :			$rh_ans->{student_ans} = $ans;
3488 :			if ($sensibleAnswer) {
3489 :			$rh_ans->throw_error('STRING', "The student's answer $rh_ans->{student_ans} is interpreted as a string.");
3490 :			}
3491 :			# warn ("\$rh_ans->{answerIsString} = $rh_ans->{answerIsString}");
3492 :			$rh_ans;
3493 :			}
3494 :
3495 :			=head4 check_units
3496 :
3497 :			check_strings ($rh_ans, %options)
3498 :			returns $rh_ans
3499 :
3500 :
3501 :	sam	2	=cut
3502 :
3503 :	gage	122	sub check_units {
3504 :			my ($rh_ans, %options) = @_;
3505 :			my %correct_units = %{$rh_ans-> {rh_correct_units}};
3506 :			my $ans = $rh_ans->{student_ans};
3507 :			# $ans = '' unless defined ($ans);
3508 :			$ans = str_filters ($ans, 'trim_whitespace');
3509 :			my $original_student_ans = $ans;
3510 :			$rh_ans->{original_student_ans} = $original_student_ans;
3511 :
3512 :			# it surprises me that the match below works since the first .* is greedy.
3513 :			my ($num_answer, $units) = $ans =~ /^(.)\s+([^\s])$/;
3514 :
3515 :			unless ( defined($num_answer) && $units ) {
3516 :			# there is an error reading the input
3517 :			if ( $ans =~ /\S/ ) { # the answer is not blank
3518 :			$rh_ans -> setKeys( 'ans_message' => "The answer \"$ans\" could not be interpreted " .
3519 :			"as a number or an arithmetic expression followed by a unit specification. " .
3520 :			"Your answer must contain units." );
3521 :			$rh_ans->throw_error('UNITS', "The answer \"$ans\" could not be interpreted " .
3522 :			"as a number or an arithmetic expression followed by a unit specification. " .
3523 :			"Your answer must contain units." );
3524 :	sam	2	}
3525 :	gage	122	return $rh_ans;
3526 :			}
3527 :
3528 :			# we have been able to parse the answer into a numerical part and a unit part
3529 :
3530 :			# $num_answer = $1; #$1 and $2 from the regular expression above
3531 :			# $units = $2;
3532 :
3533 :			my %units = Units::evaluate_units($units);
3534 :			if ( defined( $units{'ERROR'} ) ) {
3535 :			# handle error condition
3536 :			$units{'ERROR'} = clean_up_error_msg($units{'ERROR'});
3537 :			$rh_ans -> setKeys( 'ans_message' => "$units{'ERROR'}" );
3538 :			$rh_ans -> throw_error('UNITS', "$units{'ERROR'}");
3539 :			return $rh_ans;
3540 :			}
3541 :
3542 :			my $units_match = 1;
3543 :			my $fund_unit;
3544 :			foreach $fund_unit (keys %correct_units) {
3545 :			next if $fund_unit eq 'factor';
3546 :			$units_match = 0 unless $correct_units{$fund_unit} == $units{$fund_unit};
3547 :			}
3548 :
3549 :			if ( $units_match ) {
3550 :			# units are ok. Evaluate the numerical part of the answer
3551 :			$rh_ans->{'tolerance'} = $rh_ans->{'tolerance'}* $correct_units{'factor'}/$units{'factor'} if
3552 :			$rh_ans->{'tolType'} eq 'absolute'; # the tolerance is in the units specified by the instructor.
3553 :			$rh_ans->{correct_ans} = prfmt($rh_ans->{correct_ans}*$correct_units{'factor'}/$units{'factor'});
3554 :			$rh_ans->{student_units} = $units;
3555 :			$rh_ans->{student_ans} = $num_answer;
3556 :
3557 :	sam	2	} else {
3558 :	gage	122	$rh_ans -> setKeys( ans_message => 'There is an error in the units for this answer.' );
3559 :			$rh_ans -> throw_error ( 'UNITS', 'There is an error in the units for this answer.' );
3560 :	sam	2	}
3561 :	gage	122
3562 :			return $rh_ans;
3563 :	sam	2	}
3564 :
3565 :	gage	122
3566 :
3567 :	gage	119	=head2 Filter utilities
3568 :
3569 :			These two subroutines can be used in filters to set default options. They
3570 :			help make filters perform in uniform, predictable ways, and also make it
3571 :			easy to recognize from the code which options a given filter expects.
3572 :
3573 :
3574 :			=head4 assign_option_aliases
3575 :
3576 :			Use this to assign aliases for the standard options. It must come before set_default_options
3577 :			within the subroutine.
3578 :
3579 :			assign_option_aliases(\%options,
3580 :			'alias1' => 'option5'
3581 :			'alias2' => 'option7'
3582 :			);
3583 :	gage	122
3584 :
3585 :	gage	119	If the subroutine is called with an option " alias1 => 23 " it will behave as if it had been
3586 :			called with the option " option5 => 23 "
3587 :
3588 :			=cut
3589 :
3590 :
3591 :
3592 :	sam	2	sub assign_option_aliases {
3593 :			my $rh_options = shift;
3594 :			warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH';
3595 :			my @option_aliases = @_;
3596 :			while (@option_aliases) {
3597 :			my $alias = shift @option_aliases;
3598 :			my $option_key = shift @option_aliases;
3599 :
3600 :			if (defined($rh_options->{$alias} )) { # if the alias appears in the option list
3601 :			if (not defined($rh_options->{$option_key}) ) { # and the option itself is not defined,
3602 :			$rh_options->{$option_key} = $rh_options->{$alias}; # insert the value defined by the alias into the option value
3603 :			# the FIRST alias for a given option takes precedence
3604 :			# (after the option itself)
3605 :			} else {
3606 :			warn "option $option_key is already defined as", $rh_options->{$option_key}, "<br>\n",
3607 :			"The attempt to override this option with the alias $alias with value ", $rh_options->{$alias},
3608 :			" was ignored.";
3609 :			}
3610 :			}
3611 :			delete($rh_options->{$alias}); # remove the alias from the initial list
3612 :			}
3613 :
3614 :			}
3615 :
3616 :	gage	119	=head4 set_default_options
3617 :	sam	2
3618 :	gage	119	set_default_options(\%options,
3619 :			'_filter_name' => 'filter',
3620 :			'option5' => .0001,
3621 :			'option7' => 'ascii',
3622 :			'allow_unknown_options => 0,
3623 :			}
3624 :
3625 :			Note that the first entry is a reference to the options with which the filter was called.
3626 :	gage	122
3627 :	gage	119	The option5 is set to .0001 unless the option is explicitly set when the subroutine is called.
3628 :
3629 :	gage	122	The B<'_filter_name'> option should always be set, although there is no error if it is missing.
3630 :	gage	119	It is used mainly for debugging answer evaluators and allows
3631 :			you to keep track of which filter is currently processing the answer.
3632 :
3633 :	gage	122	If B<'allow_unknown_options'> is set to 0 then if the filter is called with options which do NOT appear in the
3634 :	gage	119	set_default_options list an error will be signaled and a warning message will be printed out. This provides
3635 :			error checking against misspelling an option and is generally what is desired for most filters.
3636 :
3637 :	gage	122	Occasionally one wants to write a filter which accepts a long list of options, not all of which are known in advance,
3638 :			but only uses a subset of the options
3639 :			provided. In this case, setting 'allow_unkown_options' to 1 prevents the error from being signaled.
3640 :	gage	119
3641 :			=cut
3642 :
3643 :			sub set_default_options {
3644 :			my $rh_options = shift;
3645 :			warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH';
3646 :			my %default_options = @_;
3647 :			unless ( defined($default_options{allow_unknown_options}) and $default_options{allow_unknown_options} == 1 ) {
3648 :			foreach my $key1 (keys %$rh_options) {
3649 :			warn "This option \|$key1\| is not recognized in this subroutine<br> ", pretty_print($rh_options) unless exists($default_options{$key1});
3650 :			}
3651 :			}
3652 :			foreach my $key (keys %default_options) {
3653 :			if ( not defined($rh_options->{$key} ) and defined( $default_options{$key} ) ) {
3654 :			$rh_options->{$key} = $default_options{$key}; #this allows tol => undef to allow the tol option, but doesn't define
3655 :			# this key unless tol is explicitly defined.
3656 :			}
3657 :			}
3658 :			}
3659 :
3660 :	gage	122	=head2 Problem Grader Subroutines
3661 :	gage	119
3662 :	gage	122	=cut
3663 :	gage	119
3664 :	gage	122	## Problem Grader Subroutines
3665 :
3666 :			#####################################
3667 :			# This is a model for plug-in problem graders
3668 :			#####################################
3669 :			sub install_problem_grader {
3670 :			my $rf_problem_grader = shift;
3671 :			$main::PG_FLAGS{PROBLEM_GRADER_TO_USE} = $rf_problem_grader;
3672 :			}
3673 :
3674 :			=head4 std_problem_grader
3675 :
3676 :			This is an all-or-nothing grader. A student must get all parts of the problem write
3677 :			before receiving credit. You should make sure to use this grader on multiple choice
3678 :			and true-false questions, otherwise students will be able to deduce how many
3679 :			answers are correct by the grade reported by webwork.
3680 :
3681 :
3682 :			install_problem_grader(~~&std_problem_grader);
3683 :
3684 :			=cut
3685 :
3686 :			sub std_problem_grader {
3687 :			my $rh_evaluated_answers = shift;
3688 :			my $rh_problem_state = shift;
3689 :			my %form_options = @_;
3690 :			my %evaluated_answers = %{$rh_evaluated_answers};
3691 :			# The hash $rh_evaluated_answers typically contains:
3692 :			# 'answer1' => 34, 'answer2'=> 'Mozart', etc.
3693 :
3694 :			# By default the old problem state is simply passed back out again.
3695 :			my %problem_state = %$rh_problem_state;
3696 :
3697 :			# %form_options might include
3698 :			# The user login name
3699 :			# The permission level of the user
3700 :			# The studentLogin name for this psvn.
3701 :			# Whether the form is asking for a refresh or is submitting a new answer.
3702 :
3703 :			# initial setup of the answer
3704 :			my %problem_result = ( score => 0,
3705 :			errors => '',
3706 :			type => 'std_problem_grader',
3707 :			msg => '',
3708 :			);
3709 :			# Checks
3710 :
3711 :			my $ansCount = keys %evaluated_answers; # get the number of answers
3712 :	ch003i	135
3713 :	gage	122	unless ($ansCount > 0 ) {
3714 :	ch003i	135
3715 :	gage	122	$problem_result{msg} = "This problem did not ask any questions.";
3716 :			return(\%problem_result,\%problem_state);
3717 :			}
3718 :
3719 :			if ($ansCount > 1 ) {
3720 :			$problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ;
3721 :			}
3722 :
3723 :			unless ($form_options{answers_submitted} == 1) {
3724 :			return(\%problem_result,\%problem_state);
3725 :			}
3726 :
3727 :			my $allAnswersCorrectQ=1;
3728 :			foreach my $ans_name (keys %evaluated_answers) {
3729 :			# I'm not sure if this check is really useful.
3730 :			if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) {
3731 :			$allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} );
3732 :			}
3733 :			else {
3734 :			die "Error at file ",__FILE__,"line ", __LINE__,": Answer \|$ans_name\| is not a hash reference\n".
3735 :			$evaluated_answers{$ans_name} .
3736 :			"This probably means that the answer evaluator for this answer\n" .
3737 :			"is not working correctly.";
3738 :			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
3739 :			}
3740 :			}
3741 :			# report the results
3742 :			$problem_result{score} = $allAnswersCorrectQ;
3743 :
3744 :			# I don't like to put in this bit of code.
3745 :			# It makes it hard to construct error free problem graders
3746 :			# I would prefer to know that the problem score was numeric.
3747 :			unless (defined($problem_state{recorded_score}) and $problem_state{recorded_score} =~ /^([+-]?)(?=\d\|\.\d)\d(\.\d)?([Ee]([+-]?\d+))?$/ ) {
3748 :			$problem_state{recorded_score} = 0; # This gets rid of non-numeric scores
3749 :			}
3750 :			#
3751 :			if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) {
3752 :			$problem_state{recorded_score} = 1;
3753 :			}
3754 :			else {
3755 :			$problem_state{recorded_score} = 0;
3756 :			}
3757 :
3758 :			$problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1;
3759 :			$problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0;
3760 :			(\%problem_result, \%problem_state);
3761 :			}
3762 :
3763 :			=head4 std_problem_grader2
3764 :
3765 :			This is an all-or-nothing grader. A student must get all parts of the problem write
3766 :			before receiving credit. You should make sure to use this grader on multiple choice
3767 :			and true-false questions, otherwise students will be able to deduce how many
3768 :			answers are correct by the grade reported by webwork.
3769 :
3770 :
3771 :			install_problem_grader(~~&std_problem_grader2);
3772 :
3773 :			The only difference between the two versions
3774 :			is at the end of the subroutine, where std_problem_grader2
3775 :			records the attempt only if there have been no syntax errors,
3776 :			whereas std_problem_grader records it regardless.
3777 :
3778 :			=cut
3779 :
3780 :
3781 :
3782 :			sub std_problem_grader2 {
3783 :			my $rh_evaluated_answers = shift;
3784 :			my $rh_problem_state = shift;
3785 :			my %form_options = @_;
3786 :			my %evaluated_answers = %{$rh_evaluated_answers};
3787 :			# The hash $rh_evaluated_answers typically contains:
3788 :			# 'answer1' => 34, 'answer2'=> 'Mozart', etc.
3789 :
3790 :			# By default the old problem state is simply passed back out again.
3791 :			my %problem_state = %$rh_problem_state;
3792 :
3793 :			# %form_options might include
3794 :			# The user login name
3795 :			# The permission level of the user
3796 :			# The studentLogin name for this psvn.
3797 :			# Whether the form is asking for a refresh or is submitting a new answer.
3798 :
3799 :			# initial setup of the answer
3800 :			my %problem_result = ( score => 0,
3801 :			errors => '',
3802 :			type => 'std_problem_grader',
3803 :			msg => '',
3804 :			);
3805 :
3806 :			# syntax errors are not counted.
3807 :			my $record_problem_attempt = 1;
3808 :			# Checks
3809 :
3810 :			my $ansCount = keys %evaluated_answers; # get the number of answers
3811 :			unless ($ansCount > 0 ) {
3812 :			$problem_result{msg} = "This problem did not ask any questions.";
3813 :			return(\%problem_result,\%problem_state);
3814 :			}
3815 :
3816 :			if ($ansCount > 1 ) {
3817 :			$problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ;
3818 :			}
3819 :
3820 :			unless ($form_options{answers_submitted} == 1) {
3821 :			return(\%problem_result,\%problem_state);
3822 :			}
3823 :
3824 :			my $allAnswersCorrectQ=1;
3825 :			foreach my $ans_name (keys %evaluated_answers) {
3826 :			# I'm not sure if this check is really useful.
3827 :			if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) {
3828 :			$allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} );
3829 :			}
3830 :			else {
3831 :			die "Error at file ",__FILE__,"line ", __LINE__,": Answer \|$ans_name\| is not a hash reference\n".
3832 :			$evaluated_answers{$ans_name} .
3833 :			"This probably means that the answer evaluator for this answer\n" .
3834 :			"is not working correctly.";
3835 :			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
3836 :			}
3837 :			}
3838 :			# report the results
3839 :			$problem_result{score} = $allAnswersCorrectQ;
3840 :
3841 :			# I don't like to put in this bit of code.
3842 :			# It makes it hard to construct error free problem graders
3843 :			# I would prefer to know that the problem score was numeric.
3844 :			unless ($problem_state{recorded_score} =~ /^([+-]?)(?=\d\|\.\d)\d(\.\d)?([Ee]([+-]?\d+))?$/ ) {
3845 :			$problem_state{recorded_score} = 0; # This gets rid of non-numeric scores
3846 :			}
3847 :			#
3848 :			if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) {
3849 :			$problem_state{recorded_score} = 1;
3850 :			}
3851 :			else {
3852 :			$problem_state{recorded_score} = 0;
3853 :			}
3854 :			# record attempt only if there have been no syntax errors.
3855 :
3856 :			if ($record_problem_attempt == 1) {
3857 :			$problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1;
3858 :			$problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0;
3859 :			}
3860 :			else {
3861 :			$problem_result{show_partial_correct_answers} = 0 ; # prevent partial correct answers from being shown for syntax errors.
3862 :			}
3863 :			(\%problem_result, \%problem_state);
3864 :			}
3865 :
3866 :			=head4 avg_problem_grader
3867 :
3868 :			This grader gives a grade depending on how many questions from the problem are correct. (The highest
3869 :			grade is the one that is kept. One can never lower the recorded grade on a problem by repeating it.)
3870 :			Many professors (and almost all students :-) ) prefer this grader.
3871 :
3872 :
3873 :			install_problem_grader(~~&avg_problem_grader);
3874 :
3875 :			=cut
3876 :
3877 :
3878 :			sub avg_problem_grader {
3879 :			my $rh_evaluated_answers = shift;
3880 :			my $rh_problem_state = shift;
3881 :			my %form_options = @_;
3882 :			my %evaluated_answers = %{$rh_evaluated_answers};
3883 :			# The hash $rh_evaluated_answers typically contains:
3884 :			# 'answer1' => 34, 'answer2'=> 'Mozart', etc.
3885 :
3886 :			# By default the old problem state is simply passed back out again.
3887 :			my %problem_state = %$rh_problem_state;
3888 :
3889 :
3890 :			# %form_options might include
3891 :			# The user login name
3892 :			# The permission level of the user
3893 :			# The studentLogin name for this psvn.
3894 :			# Whether the form is asking for a refresh or is submitting a new answer.
3895 :
3896 :			# initial setup of the answer
3897 :			my $total=0;
3898 :			my %problem_result = ( score => 0,
3899 :			errors => '',
3900 :			type => 'avg_problem_grader',
3901 :			msg => '',
3902 :			);
3903 :			my $count = keys %evaluated_answers;
3904 :			$problem_result{msg} = 'You can earn partial credit on this problem.' if $count >1;
3905 :			# Return unless answers have been submitted
3906 :			unless ($form_options{answers_submitted} == 1) {
3907 :			return(\%problem_result,\%problem_state);
3908 :			}
3909 :
3910 :			# Answers have been submitted -- process them.
3911 :			foreach my $ans_name (keys %evaluated_answers) {
3912 :			# I'm not sure if this check is really useful.
3913 :			if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) {
3914 :			$total += $evaluated_answers{$ans_name}->{score};
3915 :			}
3916 :			else {
3917 :			die "Error: Answer \|$ans_name\| is not a hash reference\n".
3918 :			$evaluated_answers{$ans_name} .
3919 :			"This probably means that the answer evaluator for this answer\n" .
3920 :			"is not working correctly.";
3921 :			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
3922 :			}
3923 :			}
3924 :			# Calculate score rounded to three places to avoid roundoff problems
3925 :			$problem_result{score} = $total/$count if $count;
3926 :			# increase recorded score if the current score is greater.
3927 :			$problem_state{recorded_score} = $problem_result{score} if $problem_result{score} > $problem_state{recorded_score};
3928 :
3929 :
3930 :			$problem_state{num_of_correct_ans}++ if $total == $count;
3931 :			$problem_state{num_of_incorrect_ans}++ if $total < $count ;
3932 :			warn "Error in grading this problem the total $total is larger than $count" if $total > $count;
3933 :			(\%problem_result, \%problem_state);
3934 :			}
3935 :
3936 :			=head2 Utility subroutines
3937 :
3938 :			=head4
3939 :
3940 :			warn pretty_print( $rh_hash_input)
3941 :
3942 :			This can be very useful for printing out messages about objects while debugging
3943 :
3944 :			=cut
3945 :
3946 :			sub pretty_print {
3947 :			my $r_input = shift;
3948 :			my $out = '';
3949 :			if ( not ref($r_input) ) {
3950 :			$out = $r_input; # not a reference
3951 :			} elsif ("$r_input" =~/hash/i) { # this will pick up objects whose '$self' is hash and so works better than ref($r_iput).
3952 :			local($^W) = 0;
3953 :			$out .= "$r_input " ."<TABLE border = \"2\" cellpadding = \"3\" BGCOLOR = \"#FFFFFF\">";
3954 :			foreach my $key (lex_sort( keys %$r_input )) {
3955 :			$out .= "<tr><TD> $key</TD><TD>=></td><td> ".pretty_print($r_input->{$key}) . "</td></tr>";
3956 :			}
3957 :			$out .="</table>";
3958 :			} elsif (ref($r_input) eq 'ARRAY' ) {
3959 :			my @array = @$r_input;
3960 :			$out .= "( " ;
3961 :			while (@array) {
3962 :			$out .= pretty_print(shift @array) . " , ";
3963 :			}
3964 :			$out .= " )";
3965 :			} elsif (ref($r_input) eq 'CODE') {
3966 :			$out = "$r_input";
3967 :			} else {
3968 :			$out = $r_input;
3969 :			}
3970 :			$out;
3971 :			}
3972 :
3973 :	sam	2	1;

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