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Corrected a problem with contexts not being reset properly after num_cmp or fun_cmp.
1 # This file is PGanswermacros.pl 2 # This includes the subroutines for the ANS macros, that 3 # is, macros allowing a more flexible answer checking 4 #################################################################### 5 # Copyright @ 1995-2000 University of Rochester 6 # All Rights Reserved 7 #################################################################### 8 #$Id$ 9 10 =head1 NAME 11 12 PGanswermacros.pl -- located in the courseScripts directory 13 14 =head1 SYNPOSIS 15 16 Number Answer Evaluators: 17 num_cmp() -- uses an input hash to determine parameters 18 19 std_num_cmp(), std_num_cmp_list(), std_num_cmp_abs, std_num_cmp_abs_list() 20 frac_num_cmp(), frac_num_cmp_list(), frac_num_cmp_abs, frac_num_cmp_abs_list() 21 arith_num_cmp(), arith_num_cmp_list(), arith_num_cmp_abs, arith_num_cmp_abs_list() 22 strict_num_cmp(), strict_num_cmp_list(), strict_num_cmp_abs, strict_num_cmp_abs_list() 23 numerical_compare_with_units() -- requires units as part of the answer 24 std_num_str_cmp() -- also accepts a set of strings as possible answers 25 26 Function Answer Evaluators: 27 fun_cmp() -- uses an input hash to determine parameters 28 29 function_cmp(), function_cmp_abs() 30 function_cmp_up_to_constant(), function_cmp_up_to_constant_abs() 31 multivar_function_cmp() 32 33 String Answer Evaluators: 34 str_cmp() -- uses an input hash to determine parameters 35 36 std_str_cmp(), std_str_cmp_list(), std_cs_str_cmp(), std_cs_str_cmp_list() 37 strict_str_cmp(), strict_str_cmp_list() 38 ordered_str_cmp(), ordered_str_cmp_list(), ordered_cs_str_cmp(), ordered_cs_str_cmp_list() 39 unordered_str_cmp(), unordered_str_cmp_list(), unordered_cs_str_cmp(), unordered_cs_str_cmp_list() 40 41 Miscellaneous Answer Evaluators: 42 checkbox_cmp() 43 radio_cmp() 44 45 =cut 46 47 =head1 DESCRIPTION 48 49 This file adds subroutines which create "answer evaluators" for checking 50 answers. Each answer evaluator accepts a single input from a student answer, 51 checks it and creates an output hash %ans_hash with seven or eight entries 52 (the preview_latex_string is optional). The output hash is now being created 53 with the AnswerHash package "class", which is located at the end of this file. 54 This class is currently just a wrapper for the hash, but this might change in 55 the future as new capabilities are added. 56 57 score => $correctQ, 58 correct_ans => $originalCorrEqn, 59 student_ans => $modified_student_ans 60 original_student_ans => $original_student_answer, 61 ans_message => $PGanswerMessage, 62 type => 'typeString', 63 preview_text_string => $preview_text_string, 64 preview_latex_string => $preview_latex_string 65 66 67 $ans_hash{score} -- a number between 0 and 1 indicating 68 whether the answer is correct. Fractions 69 allow the implementation of partial 70 credit for incorrect answers. 71 $ans_hash{correct_ans} -- The correct answer, as supplied by the 72 instructor and then formatted. This can 73 be viewed by the student after the answer date. 74 $ans_hash{student_ans} -- This is the student answer, after reformatting; 75 for example the answer might be forced 76 to capital letters for comparison with 77 the instructors answer. For a numerical 78 answer, it gives the evaluated answer. 79 This is displayed in the section reporting 80 the results of checking the student answers. 81 $ans_hash{original_student_ans} -- This is the original student answer. This is displayed 82 on the preview page and may be used for sticky answers. 83 $ans_hash{ans_message} -- Any error message, or hint provided by the answer evaluator. 84 This is also displayed in the section reporting 85 the results of checking the student answers. 86 $ans_hash{type} -- A string indicating the type of answer evaluator. This 87 helps in preprocessing the student answer for errors. 88 Some examples: 89 'number_with_units' 90 'function' 91 'frac_number' 92 'arith_number' 93 $ans_hash{preview_text_string} -- This typically shows how the student answer was parsed. It is 94 displayed on the preview page. For a student answer of 2sin(3x) 95 this would be 2*sin(3*x). For string answers it is typically the 96 same as $ans_hash{student_ans}. 97 $ans_hash{preview_latex_string} -- THIS IS OPTIONAL. This is latex version of the student answer 98 which is used to show a typeset view on the answer on the preview 99 page. For a student answer of 2/3, this would be \frac{2}{3}. 100 101 Technical note: the routines in this file are not actually answer evaluators. Instead, they create 102 answer evaluators. An answer evaluator is an anonymous subroutine, referenced by a named scalar. The 103 routines in this file build the subroutine and return a reference to it. Later, when the student 104 actually enters an answer, the problem processor feeds that answer to the referenced subroutine, which 105 evaluates it and returns a score (usually 0 or 1). For most users, this distinction is unimportant, but 106 if you plan on writing your own answer evaluators, you should understand this point. 107 108 =cut 109 110 BEGIN { 111 be_strict(); # an alias for use strict. This means that all global variable must contain main:: as a prefix. 112 } 113 114 115 my ($BR , # convenient localizations. 116 $PAR , 117 $numRelPercentTolDefault , 118 $numZeroLevelDefault , 119 $numZeroLevelTolDefault , 120 $numAbsTolDefault , 121 $numFormatDefault , 122 $functRelPercentTolDefault , 123 $functZeroLevelDefault , 124 $functZeroLevelTolDefault , 125 $functAbsTolDefault , 126 $functNumOfPoints , 127 $functVarDefault , 128 $functLLimitDefault , 129 $functULimitDefault , 130 $functMaxConstantOfIntegration , 131 $CA , 132 $rh_envir , 133 $useBaseTenLog , 134 $inputs_ref , 135 $QUESTIONNAIRE_ANSWERS , 136 $user_context, 137 $Context, 138 ); 139 140 141 142 143 sub _PGanswermacros_init { 144 145 $BR = main::PG_restricted_eval(q!$main::BR!); 146 $PAR = main::PG_restricted_eval(q!$main::PAR!); 147 148 # import defaults 149 # these are now imported from the %envir variable 150 $numRelPercentTolDefault = main::PG_restricted_eval(q!$main::numRelPercentTolDefault!); 151 $numZeroLevelDefault = main::PG_restricted_eval(q!$main::numZeroLevelDefault!); 152 $numZeroLevelTolDefault = main::PG_restricted_eval(q!$main::numZeroLevelTolDefault!); 153 $numAbsTolDefault = main::PG_restricted_eval(q!$main::numAbsTolDefault!); 154 $numFormatDefault = main::PG_restricted_eval(q!$main::numFormatDefault!); 155 $functRelPercentTolDefault = main::PG_restricted_eval(q!$main::functRelPercentTolDefault!); 156 $functZeroLevelDefault = main::PG_restricted_eval(q!$main::functZeroLevelDefault!); 157 $functZeroLevelTolDefault = main::PG_restricted_eval(q!$main::functZeroLevelTolDefault!); 158 $functAbsTolDefault = main::PG_restricted_eval(q!$main::functAbsTolDefault!); 159 $functNumOfPoints = main::PG_restricted_eval(q!$main::functNumOfPoints!); 160 $functVarDefault = main::PG_restricted_eval(q!$main::functVarDefault!); 161 $functLLimitDefault = main::PG_restricted_eval(q!$main::functLLimitDefault!); 162 $functULimitDefault = main::PG_restricted_eval(q!$main::functULimitDefault!); 163 $functMaxConstantOfIntegration = main::PG_restricted_eval(q!$main::functMaxConstantOfIntegration!); 164 $rh_envir = main::PG_restricted_eval(q!\%main::envir!); 165 $useBaseTenLog = main::PG_restricted_eval(q!$main::useBaseTenLog!); 166 $inputs_ref = main::PG_restricted_eval(q!$main::inputs_ref!); 167 $QUESTIONNAIRE_ANSWERS = ''; 168 169 if (!main::PG_restricted_eval(q!$main::useOldAnswerMacros!)) { 170 $user_context = main::PG_restricted_eval(q!\%context!); 171 $Context = sub {Parser::Context->current($user_context,@_)}; 172 } 173 } 174 175 176 177 ########################################################################## 178 179 #Note use $rh_envir to read environment variables 180 181 ########################################################################## 182 ## Number answer evaluators 183 184 =head2 Number Answer Evaluators 185 186 Number answer evaluators take in a numerical answer, compare it to the correct answer, 187 and return a score. In addition, they can choose to accept or reject an answer based on 188 its format, closeness to the correct answer, and other criteria. There are two types 189 of numerical answer evaluators: num_cmp(), which takes a hash of named options as parameters, 190 and the "mode"_num_cmp() variety, which use different functions to access different sets of 191 options. In addition, there is the special case of std_num_str_cmp(), which can evaluate 192 both numbers and strings. 193 194 Numerical Comparison Options 195 196 correctAnswer -- This is the correct answer that the student answer will 197 be compared to. However, this does not mean that the 198 student answer must match this exactly. How close the 199 student answer must be is determined by the other 200 options, especially tolerance and format. 201 202 tolerance -- These options determine how close the student answer 203 must be to the correct answer to qualify. There are two 204 types of tolerance: relative and absolute. Relative 205 tolerances are given in percentages. A relative 206 tolerance of 1 indicates that the student answer must 207 be within 1% of the correct answer to qualify as correct. 208 In other words, a student answer is correct when 209 abs(studentAnswer - correctAnswer) <= abs(.01*relpercentTol*correctAnswer) 210 Using absolute tolerance, the student answer must be a 211 fixed distance from the correct answer to qualify. 212 For example, an absolute tolerance of 5 means that any 213 number which is +-5 of the correct answer qualifies as correct. 214 Final (rarely used) tolerance options are zeroLevel 215 and zeroLevelTol, used in conjunction with relative 216 tolerance. if correctAnswer has absolute value less than 217 or equal to zeroLevel, then the student answer must be, 218 in absolute terms, within zeroLevelTol of correctAnswer, i.e., 219 abs(studentAnswer - correctAnswer) <= zeroLevelTol. 220 In other words, if the correct answer is very near zero, 221 an absolute tolerance will be used. One must do this to 222 handle floating point answers very near zero, because of 223 the inaccuracy of floating point arithmetic. However, the 224 default values are almost always adequate. 225 226 mode -- This determines the allowable methods for entering an 227 answer. Answers which do not meet this requirement will 228 be graded as incorrect, regardless of their numerical 229 value. The recognized modes are: 230 'std' (default) -- allows any expression which evaluates 231 to a number, including those using 232 elementary functions like sin() and 233 exp(), as well as the operations of 234 arithmetic (+, -, *, /, ^) 235 'strict' -- only decimal numbers are allowed 236 'frac' -- whole numbers and fractions are allowed 237 'arith' -- arithmetic expressions are allowed, but 238 no functions 239 Note that all modes allow the use of "pi" and "e" as 240 constants, and also the use of "E" to represent scientific 241 notation. 242 243 format -- The format to use when displaying the correct and 244 submitted answers. This has no effect on how answers are 245 evaluated; it is only for cosmetic purposes. The 246 formatting syntax is the same as Perl uses for the sprintf() 247 function. Format strings are of the form '%m.nx' or '%m.nx#', 248 where m and n are described below, and x is a formatter. 249 Esentially, m is the minimum length of the field 250 (make this negative to left-justify). Note that the decimal 251 point counts as a character when determining the field width. 252 If m begins with a zero, the number will be padded with zeros 253 instead of spaces to fit the field. 254 The precision specifier (n) works differently, depending 255 on which formatter you are using. For d, i, o, u, x and X 256 formatters (non-floating point formatters), n is the minimum 257 number of digits to display. For e and f, it is the number of 258 digits that appear after the decimal point (extra digits will 259 be rounded; insufficient digits will be padded with spaces--see 260 '#' below). For g, it is the number of significant digits to 261 display. 262 The full list of formatters can be found in the manpage 263 for printf(3), or by typing "perldoc -f sprintf" at a 264 terminal prompt. The following is a brief summary of the 265 most frequent formatters: 266 d -- decimal number 267 ld -- long decimal number 268 u -- unsigned decimal number 269 lu -- long unsigned decimal number 270 x -- hexadecimal number 271 o -- octal number 272 e -- floating point number in scientific notation 273 f -- floating point number 274 g -- either e or f, whichever takes less space 275 Technically, g will use e if the exponent is less than -4 or 276 greater than or equal to the precision. Trailing zeros are 277 removed in this mode. 278 If the format string ends in '#', trailing zeros will be 279 removed in the decimal part. Note that this is not a standard 280 syntax; it is handled internally by WeBWorK and not by Perl 281 (although this should not be a concern to end users). 282 The default format is '%0.5f#', which displays as a floating 283 point number with 5 digits of precision and no trailing zeros. 284 Other useful format strings might be '%0.2f' for displaying 285 dollar amounts, or '%010d' to display an integer with leading 286 zeros. Setting format to an empty string ( '' ) means no 287 formatting will be used; this will show 'arbitrary' precision 288 floating points. 289 290 Default Values (As of 7/24/2000) (Option -- Variable Name -- Value) 291 292 Format -- $numFormatDefault -- "%0.5f#" 293 Relative Tolerance -- $numRelPercentTolDefault -- .1 294 Absolute Tolerance -- $numAbsTolDefault -- .001 295 Zero Level -- $numZeroLevelDefault -- 1E-14 296 Zero Level Tolerance -- $numZeroLevelTolDefault -- 1E-12 297 298 =cut 299 300 301 =head3 num_cmp() 302 303 Compares a number or a list of numbers, using a named hash of options to set 304 parameters. This can make for more readable code than using the "mode"_num_cmp() 305 style, but some people find one or the other easier to remember. 306 307 ANS( num_cmp( answer or answer_array_ref, options_hash ) ); 308 309 1. the correct answer, or a reference to an array of correct answers 310 2. a hash with the following keys (all optional): 311 mode -- 'std' (default) (allows any expression evaluating to 312 a number) 313 'strict' (only numbers are allowed) 314 'frac' (fractions are allowed) 315 'arith' (arithmetic expressions allowed) 316 format -- '%0.5f#' (default); defines formatting for the 317 correct answer 318 tol -- an absolute tolerance, or 319 relTol -- a relative tolerance 320 units -- the units to use for the answer(s) 321 strings -- a reference to an array of strings which are valid 322 answers (works like std_num_str_cmp() ) 323 zeroLevel -- if the correct answer is this close to zero, 324 then zeroLevelTol applies 325 zeroLevelTol -- absolute tolerance to allow when answer is close 326 to zero 327 328 debug -- if set to 1, provides verbose listing of 329 hash entries throughout fliters. 330 331 Returns an answer evaluator, or (if given a reference to an array of 332 answers), a list of answer evaluators. Note that a reference to an array of 333 answers results is just a shortcut for writing a separate <code>num_cmp()</code> for each 334 answer. 335 336 EXAMPLES: 337 338 num_cmp( 5 ) -- correct answer is 5, using defaults 339 for all options 340 num_cmp( [5,6,7] ) -- correct answers are 5, 6, and 7, 341 using defaults for all options 342 num_cmp( 5, mode => 'strict' ) -- correct answer is 5, mode is strict 343 num_cmp( [5,6], relTol => 5 ) -- correct answers are 5 and 6, 344 both with 5% relative tolerance 345 num_cmp( 6, strings => ["Inf", "Minf", "NaN"] ) 346 -- correct answer is 6, "Inf", "Minf", 347 and "NaN" recognized as valid, but 348 incorrect answers. 349 num_cmp( "-INF", strings => ["INF", "-INF"] ) 350 -- correct answer is "-INF", "INF" and 351 numerical expressions recognized as valid, 352 but incorrect answers. 353 354 355 =cut 356 357 sub num_cmp { 358 my $correctAnswer = shift @_; 359 $CA = $correctAnswer; 360 my @opt = @_; 361 my %out_options; 362 363 ######################################################################### 364 # Retain this first check for backword compatibility. Allows input of the form 365 # num_cmp($ans, 1, '%0.5f') but warns against it 366 ######################################################################### 367 my %known_options = ( 368 'mode' => 'std', 369 'format' => $numFormatDefault, 370 'tol' => $numAbsTolDefault, 371 'relTol' => $numRelPercentTolDefault, 372 'units' => undef, 373 'strings' => undef, 374 'zeroLevel' => $numZeroLevelDefault, 375 'zeroLevelTol' => $numZeroLevelTolDefault, 376 'tolType' => 'relative', 377 'tolerance' => 1, 378 'reltol' => undef, #alternate spelling 379 'unit' => undef, #alternate spelling 380 'debug' => 0 381 ); 382 383 my @output_list; 384 my( $relPercentTol, $format, $zeroLevel, $zeroLevelTol) = @opt; 385 386 unless( ref($correctAnswer) eq 'ARRAY' || scalar( @opt ) == 0 || 387 ( defined($opt[0]) and exists $known_options{$opt[0]} ) ) { 388 # unless the first parameter is a list of arrays 389 # or the second parameter is a known option or 390 # no options were used, 391 # use the old num_cmp which does not use options, but has inputs 392 # $relPercentTol,$format,$zeroLevel,$zeroLevelTol 393 warn "This method of using num_cmp() is deprecated. Please rewrite this" . 394 " problem using the options style of parameter passing (or" . 395 " check that your first option is spelled correctly)."; 396 397 %out_options = ( 'relTol' => $relPercentTol, 398 'format' => $format, 399 'zeroLevel' => $zeroLevel, 400 'zeroLevelTol' => $zeroLevelTol, 401 'mode' => 'std' 402 ); 403 } 404 405 ######################################################################### 406 # Now handle the options assuming they are entered in the form 407 # num_cmp($ans, relTol=>1, format=>'%0.5f') 408 ######################################################################### 409 %out_options = @opt; 410 assign_option_aliases( \%out_options, 411 'reltol' => 'relTol', 412 'unit' => 'units', 413 'abstol' => 'tol', 414 ); 415 416 set_default_options( \%out_options, 417 'tolType' => (defined($out_options{'tol'}) ) ? 'absolute' : 'relative', # the existence of "tol" means that we use absolute tolerance mode 418 'tolerance' => (defined($out_options{'tolType'}) && $out_options{'tolType'} eq 'absolute' ) ? $numAbsTolDefault : $numRelPercentTolDefault, # relative tolerance is the default 419 'mode' => 'std', 420 'format' => $numFormatDefault, 421 'tol' => undef, 422 'relTol' => undef, 423 'units' => undef, 424 'strings' => undef, 425 'zeroLevel' => $numZeroLevelDefault, 426 'zeroLevelTol' => $numZeroLevelTolDefault, 427 'debug' => 0, 428 ); 429 430 # can't use both units and strings 431 if( defined( $out_options{'units'} ) && defined( $out_options{'strings'} ) ) { 432 warn "Can't use both 'units' and 'strings' in the same problem " . 433 "(check your parameters to num_cmp() )"; 434 } 435 436 # absolute tolType and relTol are incompatible. So are relative tolType and tol 437 if( defined( $out_options{'relTol'} ) && $out_options{'tolType'} eq 'absolute' ) { 438 warn "The 'tolType' 'absolute' is not compatible with 'relTol' " . 439 "(check your parameters to num_cmp() )"; 440 } 441 if( defined( $out_options{'tol'} ) && $out_options{'tolType'} eq 'relative' ) { 442 warn "The 'tolType' 'relative' is not compatible with 'tol' " . 443 "(check your parameters to num_cmp() )"; 444 } 445 446 447 # Handle legacy options 448 if ($out_options{tolType} eq 'absolute') { 449 $out_options{'tolerance'}=$out_options{'tol'} if defined($out_options{'tol'}); 450 delete($out_options{'relTol'}) if exists( $out_options{'relTol'} ); 451 } else { 452 $out_options{'tolerance'}=$out_options{'relTol'} if defined($out_options{'relTol'}); 453 # delete($out_options{'tol'}) if exists( $out_options{'tol'} ); 454 } 455 # end legacy options 456 457 # thread over lists 458 my @ans_list = (); 459 460 if ( ref($correctAnswer) eq 'ARRAY' ) { 461 @ans_list = @{$correctAnswer}; 462 } 463 else { push( @ans_list, $correctAnswer ); 464 } 465 466 # produce answer evaluators 467 foreach my $ans (@ans_list) { 468 if( defined( $out_options{'units'} ) ) { 469 $ans = "$ans $out_options{'units'}"; 470 471 push( @output_list, NUM_CMP( 'correctAnswer' => $ans, 472 'tolerance' => $out_options{'tolerance'}, 473 'tolType' => $out_options{'tolType'}, 474 'format' => $out_options{'format'}, 475 'mode' => $out_options{'mode'}, 476 'zeroLevel' => $out_options{'zeroLevel'}, 477 'zeroLevelTol' => $out_options{'zeroLevelTol'}, 478 'debug' => $out_options{'debug'}, 479 'units' => $out_options{'units'}, 480 ) 481 ); 482 } elsif( defined( $out_options{'strings'} ) ) { 483 484 485 push( @output_list, NUM_CMP( 'correctAnswer' => $ans, 486 'tolerance' => $out_options{tolerance}, 487 'tolType' => $out_options{tolType}, 488 'format' => $out_options{'format'}, 489 'mode' => $out_options{'mode'}, 490 'zeroLevel' => $out_options{'zeroLevel'}, 491 'zeroLevelTol' => $out_options{'zeroLevelTol'}, 492 'debug' => $out_options{'debug'}, 493 'strings' => $out_options{'strings'}, 494 ) 495 ); 496 } else { 497 push(@output_list, 498 NUM_CMP( 'correctAnswer' => $ans, 499 'tolerance' => $out_options{tolerance}, 500 'tolType' => $out_options{tolType}, 501 'format' => $out_options{'format'}, 502 'mode' => $out_options{'mode'}, 503 'zeroLevel' => $out_options{'zeroLevel'}, 504 'zeroLevelTol' => $out_options{'zeroLevelTol'}, 505 'debug' => $out_options{'debug'}, 506 ), 507 ); 508 } 509 } 510 511 return (wantarray) ? @output_list : $output_list[0]; 512 } 513 514 #legacy code for compatability purposes 515 sub num_rel_cmp { # compare numbers 516 std_num_cmp( @_ ); 517 } 518 519 520 =head3 "mode"_num_cmp() functions 521 522 There are 16 functions total, 4 for each mode (std, frac, strict, arith). Each mode has 523 one "normal" function, one which accepts a list of answers, one which uses absolute 524 rather than relative tolerance, and one which uses absolute tolerance and accepts a list. 525 The "std" family is documented below; all others work precisely the same. 526 527 std_num_cmp($correctAnswer) OR 528 std_num_cmp($correctAnswer, $relPercentTol) OR 529 std_num_cmp($correctAnswer, $relPercentTol, $format) OR 530 std_num_cmp($correctAnswer, $relPercentTol, $format, $zeroLevel) OR 531 std_num_cmp($correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol) 532 533 $correctAnswer -- the correct answer 534 $relPercentTol -- the tolerance, as a percentage (optional) 535 $format -- the format of the displayed answer (optional) 536 $zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies (optional) 537 $zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero (optional) 538 539 std_num_cmp() uses standard mode (arithmetic operations and elementary 540 functions allowed) and relative tolerance. Options are specified by 541 one or more parameters. Note that if you wish to set an option which 542 is later in the parameter list, you must set all previous options. 543 544 std_num_cmp_abs($correctAnswer) OR 545 std_num_cmp_abs($correctAnswer, $absTol) OR 546 std_num_cmp_abs($correctAnswer, $absTol, $format) 547 548 $correctAnswer -- the correct answer 549 $absTol -- an absolute tolerance (optional) 550 $format -- the format of the displayed answer (optional) 551 552 std_num_cmp_abs() uses standard mode and absolute tolerance. Options 553 are set as with std_num_cmp(). Note that $zeroLevel and $zeroLevelTol 554 do not apply with absolute tolerance. 555 556 std_num_cmp_list($relPercentTol, $format, @answerList) 557 558 $relPercentTol -- the tolerance, as a percentage 559 $format -- the format of the displayed answer(s) 560 @answerList -- a list of one or more correct answers 561 562 std_num_cmp_list() uses standard mode and relative tolerance. There 563 is no way to set $zeroLevel or $zeroLevelTol. Note that no 564 parameters are optional. All answers in the list will be 565 evaluated with the same set of parameters. 566 567 std_num_cmp_abs_list($absTol, $format, @answerList) 568 569 $absTol -- an absolute tolerance 570 $format -- the format of the displayed answer(s) 571 @answerList -- a list of one or more correct answers 572 573 std_num_cmp_abs_list() uses standard mode and absolute tolerance. 574 Note that no parameters are optional. All answers in the list will be 575 evaluated with the same set of parameters. 576 577 arith_num_cmp(), arith_num_cmp_list(), arith_num_cmp_abs(), arith_num_cmp_abs_list() 578 strict_num_cmp(), strict_num_cmp_list(), strict_num_cmp_abs(), strict_num_cmp_abs_list() 579 frac_num_cmp(), frac_num_cmp_list(), frac_num_cmp_abs(), frac_num_cmp_abs_list() 580 581 Examples: 582 583 ANS( strict_num_cmp( 3.14159 ) ) -- The student answer must be a number 584 in decimal or scientific notation which is within .1 percent of 3.14159. 585 This assumes $numRelPercentTolDefault has been set to .1. 586 ANS( strict_num_cmp( $answer, .01 ) ) -- The student answer must be a 587 number within .01 percent of $answer (e.g. 3.14159 if $answer is 3.14159 588 or $answer is "pi" or $answer is 4*atan(1)). 589 ANS( frac_num_cmp( $answer) ) or ANS( frac_num_cmp( $answer,.01 )) -- 590 The student answer can be a number or fraction, e.g. 2/3. 591 ANS( arith_num_cmp( $answer) ) or ANS( arith_num_cmp( $answer,.01 )) -- 592 The student answer can be an arithmetic expression, e.g. (2+3)/7-2^.5 . 593 ANS( std_num_cmp( $answer) ) or ANS( std_num_cmp( $answer,.01 )) -- 594 The student answer can contain elementary functions, e.g. sin(.3+pi/2) 595 596 =cut 597 598 sub std_num_cmp { # compare numbers allowing use of elementary functions 599 my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_; 600 601 my %options = ( 'relTol' => $relPercentTol, 602 'format' => $format, 603 'zeroLevel' => $zeroLevel, 604 'zeroLevelTol' => $zeroLevelTol 605 ); 606 607 set_default_options( \%options, 608 'tolType' => 'relative', 609 'tolerance' => $numRelPercentTolDefault, 610 'mode' => 'std', 611 'format' => $numFormatDefault, 612 'relTol' => $numRelPercentTolDefault, 613 'zeroLevel' => $numZeroLevelDefault, 614 'zeroLevelTol' => $numZeroLevelTolDefault, 615 'debug' => 0, 616 ); 617 618 num_cmp([$correctAnswer], %options); 619 } 620 621 ## Similar to std_num_cmp but accepts a list of numbers in the form 622 ## std_num_cmp_list(relpercentTol,format,ans1,ans2,ans3,...) 623 ## format is of the form "%10.3g" or "", i.e., a format suitable for sprintf(). Use "" for default 624 ## You must enter a format and tolerance 625 626 sub std_num_cmp_list { 627 my ( $relPercentTol, $format, @answerList) = @_; 628 629 my %options = ( 'relTol' => $relPercentTol, 630 'format' => $format, 631 ); 632 633 set_default_options( \%options, 634 'tolType' => 'relative', 635 'tolerance' => $numRelPercentTolDefault, 636 'mode' => 'std', 637 'format' => $numFormatDefault, 638 'relTol' => $numRelPercentTolDefault, 639 'zeroLevel' => $numZeroLevelDefault, 640 'zeroLevelTol' => $numZeroLevelTolDefault, 641 'debug' => 0, 642 ); 643 644 num_cmp(\@answerList, %options); 645 646 } 647 648 sub std_num_cmp_abs { # compare numbers allowing use of elementary functions with absolute tolerance 649 my ( $correctAnswer, $absTol, $format) = @_; 650 my %options = ( 'tolerance' => $absTol, 651 'format' => $format 652 ); 653 654 set_default_options (\%options, 655 'tolType' => 'absolute', 656 'tolerance' => $absTol, 657 'mode' => 'std', 658 'format' => $numFormatDefault, 659 'zeroLevel' => 0, 660 'zeroLevelTol' => 0, 661 'debug' => 0, 662 ); 663 664 num_cmp([$correctAnswer], %options); 665 } 666 667 ## See std_num_cmp_list for usage 668 669 sub std_num_cmp_abs_list { 670 my ( $absTol, $format, @answerList ) = @_; 671 672 my %options = ( 'tolerance' => $absTol, 673 'format' => $format, 674 ); 675 676 set_default_options( \%options, 677 'tolType' => 'absolute', 678 'tolerance' => $absTol, 679 'mode' => 'std', 680 'format' => $numFormatDefault, 681 'zeroLevel' => 0, 682 'zeroLevelTol' => 0, 683 'debug' => 0, 684 ); 685 686 num_cmp(\@answerList, %options); 687 } 688 689 sub frac_num_cmp { # only allow fractions and numbers as submitted answer 690 691 my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_; 692 693 my %options = ( 'relTol' => $relPercentTol, 694 'format' => $format, 695 'zeroLevel' => $zeroLevel, 696 'zeroLevelTol' => $zeroLevelTol 697 ); 698 699 set_default_options( \%options, 700 'tolType' => 'relative', 701 'tolerance' => $relPercentTol, 702 'mode' => 'frac', 703 'format' => $numFormatDefault, 704 'zeroLevel' => $numZeroLevelDefault, 705 'zeroLevelTol' => $numZeroLevelTolDefault, 706 'relTol' => $numRelPercentTolDefault, 707 'debug' => 0, 708 ); 709 710 num_cmp([$correctAnswer], %options); 711 } 712 713 ## See std_num_cmp_list for usage 714 sub frac_num_cmp_list { 715 my ( $relPercentTol, $format, @answerList ) = @_; 716 717 my %options = ( 'relTol' => $relPercentTol, 718 'format' => $format 719 ); 720 721 set_default_options( \%options, 722 'tolType' => 'relative', 723 'tolerance' => $relPercentTol, 724 'mode' => 'frac', 725 'format' => $numFormatDefault, 726 'zeroLevel' => $numZeroLevelDefault, 727 'zeroLevelTol' => $numZeroLevelTolDefault, 728 'relTol' => $numRelPercentTolDefault, 729 'debug' => 0, 730 ); 731 732 num_cmp(\@answerList, %options); 733 } 734 735 sub frac_num_cmp_abs { # only allow fraction expressions as submitted answer with absolute tolerance 736 my ( $correctAnswer, $absTol, $format ) = @_; 737 738 my %options = ( 'tolerance' => $absTol, 739 'format' => $format 740 ); 741 742 set_default_options (\%options, 743 'tolType' => 'absolute', 744 'tolerance' => $absTol, 745 'mode' => 'frac', 746 'format' => $numFormatDefault, 747 'zeroLevel' => 0, 748 'zeroLevelTol' => 0, 749 'debug' => 0, 750 ); 751 752 num_cmp([$correctAnswer], %options); 753 } 754 755 ## See std_num_cmp_list for usage 756 757 sub frac_num_cmp_abs_list { 758 my ( $absTol, $format, @answerList ) = @_; 759 760 my %options = ( 'tolerance' => $absTol, 761 'format' => $format 762 ); 763 764 set_default_options (\%options, 765 'tolType' => 'absolute', 766 'tolerance' => $absTol, 767 'mode' => 'frac', 768 'format' => $numFormatDefault, 769 'zeroLevel' => 0, 770 'zeroLevelTol' => 0, 771 'debug' => 0, 772 ); 773 774 num_cmp(\@answerList, %options); 775 } 776 777 778 sub arith_num_cmp { # only allow arithmetic expressions as submitted answer 779 780 my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_; 781 782 my %options = ( 'relTol' => $relPercentTol, 783 'format' => $format, 784 'zeroLevel' => $zeroLevel, 785 'zeroLevelTol' => $zeroLevelTol 786 ); 787 788 set_default_options( \%options, 789 'tolType' => 'relative', 790 'tolerance' => $relPercentTol, 791 'mode' => 'arith', 792 'format' => $numFormatDefault, 793 'zeroLevel' => $numZeroLevelDefault, 794 'zeroLevelTol' => $numZeroLevelTolDefault, 795 'relTol' => $numRelPercentTolDefault, 796 'debug' => 0, 797 ); 798 799 num_cmp([$correctAnswer], %options); 800 } 801 802 ## See std_num_cmp_list for usage 803 sub arith_num_cmp_list { 804 my ( $relPercentTol, $format, @answerList ) = @_; 805 806 my %options = ( 'relTol' => $relPercentTol, 807 'format' => $format, 808 ); 809 810 set_default_options( \%options, 811 'tolType' => 'relative', 812 'tolerance' => $relPercentTol, 813 'mode' => 'arith', 814 'format' => $numFormatDefault, 815 'zeroLevel' => $numZeroLevelDefault, 816 'zeroLevelTol' => $numZeroLevelTolDefault, 817 'relTol' => $numRelPercentTolDefault, 818 'debug' => 0, 819 ); 820 821 num_cmp(\@answerList, %options); 822 } 823 824 sub arith_num_cmp_abs { # only allow arithmetic expressions as submitted answer with absolute tolerance 825 my ( $correctAnswer, $absTol, $format ) = @_; 826 827 my %options = ( 'tolerance' => $absTol, 828 'format' => $format 829 ); 830 831 set_default_options (\%options, 832 'tolType' => 'absolute', 833 'tolerance' => $absTol, 834 'mode' => 'arith', 835 'format' => $numFormatDefault, 836 'zeroLevel' => 0, 837 'zeroLevelTol' => 0, 838 'debug' => 0, 839 ); 840 841 num_cmp([$correctAnswer], %options); 842 } 843 844 ## See std_num_cmp_list for usage 845 sub arith_num_cmp_abs_list { 846 my ( $absTol, $format, @answerList ) = @_; 847 848 my %options = ( 'tolerance' => $absTol, 849 'format' => $format 850 ); 851 852 set_default_options (\%options, 853 'tolType' => 'absolute', 854 'tolerance' => $absTol, 855 'mode' => 'arith', 856 'format' => $numFormatDefault, 857 'zeroLevel' => 0, 858 'zeroLevelTol' => 0, 859 'debug' => 0, 860 ); 861 862 num_cmp(\@answerList, %options); 863 } 864 865 sub strict_num_cmp { # only allow numbers as submitted answer 866 my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_; 867 868 my %options = ( 'relTol' => $relPercentTol, 869 'format' => $format, 870 'zeroLevel' => $zeroLevel, 871 'zeroLevelTol' => $zeroLevelTol 872 ); 873 874 set_default_options( \%options, 875 'tolType' => 'relative', 876 'tolerance' => $relPercentTol, 877 'mode' => 'strict', 878 'format' => $numFormatDefault, 879 'zeroLevel' => $numZeroLevelDefault, 880 'zeroLevelTol' => $numZeroLevelTolDefault, 881 'relTol' => $numRelPercentTolDefault, 882 'debug' => 0, 883 ); 884 num_cmp([$correctAnswer], %options); 885 886 } 887 888 ## See std_num_cmp_list for usage 889 sub strict_num_cmp_list { # compare numbers 890 my ( $relPercentTol, $format, @answerList ) = @_; 891 892 my %options = ( 'relTol' => $relPercentTol, 893 'format' => $format, 894 ); 895 896 set_default_options( \%options, 897 'tolType' => 'relative', 898 'tolerance' => $relPercentTol, 899 'mode' => 'strict', 900 'format' => $numFormatDefault, 901 'zeroLevel' => $numZeroLevelDefault, 902 'zeroLevelTol' => $numZeroLevelTolDefault, 903 'relTol' => $numRelPercentTolDefault, 904 'debug' => 0, 905 ); 906 907 num_cmp(\@answerList, %options); 908 } 909 910 911 sub strict_num_cmp_abs { # only allow numbers as submitted answer with absolute tolerance 912 my ( $correctAnswer, $absTol, $format ) = @_; 913 914 my %options = ( 'tolerance' => $absTol, 915 'format' => $format 916 ); 917 918 set_default_options (\%options, 919 'tolType' => 'absolute', 920 'tolerance' => $absTol, 921 'mode' => 'strict', 922 'format' => $numFormatDefault, 923 'zeroLevel' => 0, 924 'zeroLevelTol' => 0, 925 'debug' => 0, 926 ); 927 num_cmp([$correctAnswer], %options); 928 929 } 930 931 ## See std_num_cmp_list for usage 932 sub strict_num_cmp_abs_list { # compare numbers 933 my ( $absTol, $format, @answerList ) = @_; 934 935 my %options = ( 'tolerance' => $absTol, 936 'format' => $format 937 ); 938 939 set_default_options (\%options, 940 'tolType' => 'absolute', 941 'tolerance' => $absTol, 942 'mode' => 'strict', 943 'format' => $numFormatDefault, 944 'zeroLevel' => 0, 945 'zeroLevelTol' => 0, 946 'debug' => 0, 947 ); 948 949 num_cmp(\@answerList, %options); 950 } 951 952 ## sub numerical_compare_with_units 953 ## Compares a number with units 954 ## Deprecated; use num_cmp() 955 ## 956 ## IN: a string which includes the numerical answer and the units 957 ## a hash with the following keys (all optional): 958 ## mode -- 'std', 'frac', 'arith', or 'strict' 959 ## format -- the format to use when displaying the answer 960 ## tol -- an absolute tolerance, or 961 ## relTol -- a relative tolerance 962 ## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies 963 ## zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero 964 965 # This mode is depricated. send input through num_cmp -- it can handle units. 966 967 sub numerical_compare_with_units { 968 my $correct_answer = shift; # the answer is a string which includes both the numerical answer and the units. 969 my %options = @_; # all of the other inputs are (key value) pairs 970 971 # Prepare the correct answer 972 $correct_answer = str_filters( $correct_answer, 'trim_whitespace' ); 973 974 # it surprises me that the match below works since the first .* is greedy. 975 my ($correct_num_answer, $correct_units) = $correct_answer =~ /^(.*)\s+([^\s]*)$/; 976 $options{units} = $correct_units; 977 978 num_cmp($correct_num_answer, %options); 979 } 980 981 982 =head3 std_num_str_cmp() 983 984 NOTE: This function is maintained for compatibility. num_cmp() with the 985 'strings' parameter is slightly preferred. 986 987 std_num_str_cmp() is used when the correct answer could be either a number or a 988 string. For example, if you wanted the student to evaluate a function at number 989 of points, but write "Inf" or "Minf" if the function is unbounded. This routine 990 will provide error messages that do not give a hint as to whether the correct 991 answer is a string or a number. For numerical comparisons, std_num_cmp() is 992 used internally; for string comparisons, std_str_cmp() is used. String answers 993 must consist entirely of letters except that an initial minus sign is allowed. 994 E.g. "inf" and "-inf" are valid strings where as "too-big" is not. 995 996 std_num_str_cmp( $correctAnswer ) OR 997 std_num_str_cmp( $correctAnswer, $ra_legalStrings ) OR 998 std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol ) OR 999 std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format ) OR 1000 std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format, $zeroLevel ) OR 1001 std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format, 1002 $zeroLevel, $zeroLevelTol ) 1003 1004 $correctAnswer -- the correct answer 1005 $ra_legalStrings -- a reference to an array of legal strings, e.g. ["str1", "str2"] 1006 $relPercentTol -- the error tolerance as a percentage 1007 $format -- the display format 1008 $zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies 1009 $zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero 1010 1011 Examples: 1012 ANS( std_num_str_cmp( $ans, ["Inf", "Minf", "NaN"] ) ); 1013 ANS( std_num_str_cmp( $ans, ["INF", "-INF"] ) ); 1014 1015 =cut 1016 1017 sub std_num_str_cmp { 1018 my ( $correctAnswer, $ra_legalStrings, $relpercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_; 1019 # warn ('This method is depreciated. Use num_cmp instead.'); 1020 return num_cmp ($correctAnswer, strings=>$ra_legalStrings, relTol=>$relpercentTol, format=>$format, 1021 zeroLevel=>$zeroLevel, zeroLevelTol=>$zeroLevelTol); 1022 } 1023 1024 sub NUM_CMP { # low level numeric compare (now uses Parser) 1025 return ORIGINAL_NUM_CMP(@_) 1026 if main::PG_restricted_eval(q!$main::useOldAnswerMacros!); 1027 1028 my %num_params = @_; 1029 1030 # 1031 # check for required parameters 1032 # 1033 my @keys = qw(correctAnswer tolerance tolType format mode zeroLevel zeroLevelTol debug); 1034 foreach my $key (@keys) { 1035 warn "$key must be defined in options when calling NUM_CMP" 1036 unless defined($num_params{$key}); 1037 } 1038 1039 my $correctAnswer = $num_params{correctAnswer}; 1040 my $mode = $num_params{mode}; 1041 my %options = (debug => $num_params{debug}); 1042 1043 # 1044 # Hack to fix up exponential notation in correct answer 1045 # (e.g., perl will pass .0000001 as 1e-07). 1046 # 1047 $correctAnswer = uc($correctAnswer) 1048 if $correctAnswer =~ m/e/ && Value::isNumber($correctAnswer); 1049 1050 # 1051 # Get an apppropriate context based on the mode 1052 # 1053 my $context; 1054 for ($mode) { 1055 /^strict$/i and do { 1056 $context = $Parser::Context::Default::context{LimitedNumeric}->copy; 1057 last; 1058 }; 1059 /^arith$/i and do { 1060 $context = $Parser::Context::Default::context{LegacyNumeric}->copy; 1061 $context->functions->disable('All'); 1062 last; 1063 }; 1064 /^frac$/i and do { 1065 $context = $Parser::Context::Default::context{'LimitedNumeric-Fraction'}->copy; 1066 last; 1067 }; 1068 1069 # default 1070 $context = $Parser::Context::Default::context{LegacyNumeric}->copy; 1071 } 1072 $context->{format}{number} = $num_params{'format'}; 1073 $context->strings->clear; 1074 # FIXME: should clear variables as well? Copy them from the current context? 1075 1076 # 1077 # Add the strings to the context 1078 # 1079 if ($num_params{strings}) { 1080 foreach my $string (@{$num_params{strings}}) { 1081 my %tex = ($string =~ m/^(-?)inf(inity)?$/i)? (TeX => "$1\\infty"): (); 1082 %tex = (TeX => "-\\infty") if uc($string) eq "MINF"; 1083 $context->strings->add(uc($string) => {%tex}); 1084 } 1085 } 1086 1087 # 1088 # Set the tolerances 1089 # 1090 if ($num_params{tolType} eq 'absolute') { 1091 $context->flags->set( 1092 tolerance => $num_params{tolerance}, 1093 tolType => 'absolute', 1094 ); 1095 } else { 1096 $context->flags->set( 1097 tolerance => .01*$num_params{tolerance}, 1098 tolType => 'relative', 1099 ); 1100 } 1101 $context->flags->set( 1102 zeroLevel => $num_params{zeroLevel}, 1103 zeroLevelTol => $num_params{zeroLevelTol}, 1104 ); 1105 1106 # 1107 # Get the proper Parser object for the professor's answer 1108 # using the initialized context 1109 # 1110 my $oldContext = &$Context(); &$Context($context); my $r; 1111 if ($num_params{units}) { 1112 $r = new Parser::Legacy::NumberWithUnits($correctAnswer); 1113 $options{rh_correct_units} = $num_params{units}; 1114 } else { 1115 $r = Value::Formula->new($correctAnswer); 1116 die "The professor's answer can't be a formula" unless $r->isConstant; 1117 $r = $r->eval; $r = new Value::Real($r) unless Value::class($r) eq 'String'; 1118 $r->{correct_ans} = $correctAnswer; 1119 if ($mode eq 'phase_pi') { 1120 my $pi = 4*atan2(1,1); 1121 while ($r > $pi/2) {$r -= $pi} 1122 while ($r < -$pi/2) {$r += $pi} 1123 } 1124 } 1125 # 1126 # Get the answer checker from the parser object 1127 # 1128 my $cmp = $r->cmp(%options); 1129 $cmp->install_pre_filter(sub { 1130 my $rh_ans = shift; 1131 $rh_ans->{original_student_ans} = $rh_ans->{student_ans}; 1132 $rh_ans->{original_correct_ans} = $rh_ans->{correct_ans}; 1133 return $rh_ans; 1134 }); 1135 $cmp->install_post_filter(sub { 1136 my $rh_ans = shift; 1137 $rh_ans->{student_ans} = $rh_ans->{student_value}->string 1138 if ref($rh_ans->{student_value}); 1139 return $rh_ans; 1140 }); 1141 $cmp->{debug} = $num_params{debug}; 1142 &$Context($oldContext); 1143 1144 return $cmp; 1145 } 1146 1147 # 1148 # The original version, for backward compatibility 1149 # (can be removed when the Parser-based version is more fully tested.) 1150 # 1151 sub ORIGINAL_NUM_CMP { # low level numeric compare 1152 my %num_params = @_; 1153 1154 my @keys = qw ( correctAnswer tolerance tolType format mode zeroLevel zeroLevelTol debug ); 1155 foreach my $key (@keys) { 1156 warn "$key must be defined in options when calling NUM_CMP" unless defined ($num_params{$key}); 1157 } 1158 1159 my $correctAnswer = $num_params{'correctAnswer'}; 1160 my $format = $num_params{'format'}; 1161 my $mode = $num_params{'mode'}; 1162 1163 if( $num_params{tolType} eq 'relative' ) { 1164 $num_params{'tolerance'} = .01*$num_params{'tolerance'}; 1165 } 1166 1167 my $formattedCorrectAnswer; 1168 my $correct_units; 1169 my $correct_num_answer; 1170 my %correct_units; 1171 my $corrAnswerIsString = 0; 1172 1173 1174 if (defined($num_params{units}) && $num_params{units}) { 1175 $correctAnswer = str_filters( $correctAnswer, 'trim_whitespace' ); 1176 # units are in form stuff space units where units contains no spaces. 1177 1178 ($correct_num_answer, $correct_units) = $correctAnswer =~ /^(.*)\s+([^\s]*)$/; 1179 %correct_units = Units::evaluate_units($correct_units); 1180 if ( defined( $correct_units{'ERROR'} ) ) { 1181 warn ("ERROR: The answer \"$correctAnswer\" in the problem definition cannot be parsed:\n" . 1182 "$correct_units{'ERROR'}\n"); 1183 } 1184 # $formattedCorrectAnswer = spf($correct_num_answer,$num_params{'format'}) . " $correct_units"; 1185 $formattedCorrectAnswer = prfmt($correct_num_answer,$num_params{'format'}) . " $correct_units"; 1186 1187 } elsif (defined($num_params{strings}) && $num_params{strings}) { 1188 my $legalString = ''; 1189 my @legalStrings = @{$num_params{strings}}; 1190 $correct_num_answer = $correctAnswer; 1191 $formattedCorrectAnswer = $correctAnswer; 1192 foreach $legalString (@legalStrings) { 1193 if ( uc($correctAnswer) eq uc($legalString) ) { 1194 $corrAnswerIsString = 1; 1195 1196 last; 1197 } 1198 } ## at this point $corrAnswerIsString = 0 iff correct answer is numeric 1199 } else { 1200 $correct_num_answer = $correctAnswer; 1201 $formattedCorrectAnswer = prfmt( $correctAnswer, $num_params{'format'} ); 1202 } 1203 1204 $correct_num_answer = math_constants($correct_num_answer); 1205 1206 my $PGanswerMessage = ''; 1207 1208 my ($inVal,$correctVal,$PG_eval_errors,$PG_full_error_report); 1209 1210 if (defined($correct_num_answer) && $correct_num_answer =~ /\S/ && $corrAnswerIsString == 0 ) { 1211 ($correctVal, $PG_eval_errors,$PG_full_error_report) = PG_answer_eval($correct_num_answer); 1212 } else { # case of a string answer 1213 $PG_eval_errors = ' '; 1214 $correctVal = $correctAnswer; 1215 } 1216 1217 if ( ($PG_eval_errors && $corrAnswerIsString == 0) or ((not is_a_number($correctVal)) && $corrAnswerIsString == 0)) { 1218 ##error message from eval or above 1219 warn "Error in 'correct' answer: $PG_eval_errors<br> 1220 The answer $correctAnswer evaluates to $correctVal, 1221 which cannot be interpreted as a number. "; 1222 1223 } 1224 ######################################################################### 1225 1226 #construct the answer evaluator 1227 my $answer_evaluator = new AnswerEvaluator; 1228 $answer_evaluator->{debug} = $num_params{debug}; 1229 $answer_evaluator->ans_hash( 1230 correct_ans => $correctVal, 1231 type => "${mode}_number", 1232 tolerance => $num_params{tolerance}, 1233 tolType => $num_params{tolType}, 1234 units => $correct_units, 1235 original_correct_ans => $formattedCorrectAnswer, 1236 rh_correct_units => \%correct_units, 1237 answerIsString => $corrAnswerIsString, 1238 ); 1239 my ($in, $formattedSubmittedAnswer); 1240 $answer_evaluator->install_pre_filter(sub {my $rh_ans = shift; 1241 $rh_ans->{original_student_ans} = $rh_ans->{student_ans}; $rh_ans;} 1242 ); 1243 1244 1245 1246 if (defined($num_params{units}) && $num_params{units}) { 1247 $answer_evaluator->install_pre_filter(\&check_units); 1248 } 1249 if (defined($num_params{strings}) && $num_params{strings}) { 1250 $answer_evaluator->install_pre_filter(\&check_strings, %num_params); 1251 } 1252 1253 ## FIXME? - this pre filter was moved before check_units to allow 1254 ## for latex preview of answers with no units. 1255 ## seems to work but may have unintended side effects elsewhere. 1256 1257 ## Actually it caused trouble with the check strings package so it has been moved back 1258 # We'll try some other method -- perhaps add code to fix_answer for display 1259 $answer_evaluator->install_pre_filter(\&check_syntax); 1260 1261 $answer_evaluator->install_pre_filter(\&math_constants); 1262 1263 if ($mode eq 'std') { 1264 # do nothing 1265 } elsif ($mode eq 'strict') { 1266 $answer_evaluator->install_pre_filter(\&is_a_number); 1267 } elsif ($mode eq 'arith') { 1268 $answer_evaluator->install_pre_filter(\&is_an_arithmetic_expression); 1269 } elsif ($mode eq 'frac') { 1270 $answer_evaluator->install_pre_filter(\&is_a_fraction); 1271 1272 } elsif ($mode eq 'phase_pi') { 1273 $answer_evaluator->install_pre_filter(\&phase_pi); 1274 1275 } else { 1276 $PGanswerMessage = 'Tell your professor that there is an error in his or her answer mechanism. No mode was specified.'; 1277 $formattedSubmittedAnswer = $in; 1278 } 1279 1280 if ($corrAnswerIsString == 0 ){ # avoiding running compare_numbers when correct answer is a string. 1281 $answer_evaluator->install_evaluator(\&compare_numbers, %num_params); 1282 } 1283 1284 1285 ############################################################################### 1286 # We'll leave these next lines out for now, so that the evaluated versions of the student's and professor's 1287 # can be displayed in the answer message. This may still cause a few anomolies when strings are used 1288 # 1289 ############################################################################### 1290 1291 $answer_evaluator->install_post_filter(\&fix_answers_for_display); 1292 1293 $answer_evaluator->install_post_filter(sub {my $rh_ans = shift; 1294 return $rh_ans unless $rh_ans->catch_error('EVAL'); 1295 $rh_ans->{student_ans} = $rh_ans->{original_student_ans}. ' '. $rh_ans->{error_message}; 1296 $rh_ans->clear_error('EVAL'); } ); 1297 $answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('SYNTAX'); } ); 1298 $answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('UNITS'); } ); 1299 $answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('NUMBER'); } ); 1300 $answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('STRING'); } ); 1301 $answer_evaluator; 1302 } 1303 1304 1305 1306 ########################################################################## 1307 ########################################################################## 1308 ## Function answer evaluators 1309 1310 =head2 Function Answer Evaluators 1311 1312 Function answer evaluators take in a function, compare it numerically to a 1313 correct function, and return a score. They can require an exactly equivalent 1314 function, or one that is equal up to a constant. They can accept or reject an 1315 answer based on specified tolerances for numerical deviation. 1316 1317 Function Comparison Options 1318 1319 correctEqn -- The correct equation, specified as a string. It may include 1320 all basic arithmetic operations, as well as elementary 1321 functions. Variable usage is described below. 1322 1323 Variables -- The independent variable(s). When comparing the correct 1324 equation to the student equation, each variable will be 1325 replaced by a certain number of numerical values. If 1326 the student equation agrees numerically with the correct 1327 equation, they are considered equal. Note that all 1328 comparison is numeric; it is possible (although highly 1329 unlikely and never a practical concern) for two unequal 1330 functions to yield the same numerical results. 1331 1332 Limits -- The limits of evaluation for the independent variables. 1333 Each variable is evaluated only in the half-open interval 1334 [lower_limit, upper_limit). This is useful if the function 1335 has a singularity or is not defined in a certain range. 1336 For example, the function "sqrt(-1-x)" could be evaluated 1337 in [-2,-1). 1338 1339 Tolerance -- Tolerance in function comparisons works exactly as in 1340 numerical comparisons; see the numerical comparison 1341 documentation for a complete description. Note that the 1342 tolerance does applies to the function as a whole, not 1343 each point individually. 1344 1345 Number of -- Specifies how many points to evaluate each variable at. This 1346 Points is typically 3, but can be set higher if it is felt that 1347 there is a strong possibility of "false positives." 1348 1349 Maximum -- Sets the maximum size of the constant of integration. For 1350 Constant of technical reasons concerning floating point arithmetic, if 1351 Integration the additive constant, i.e., the constant of integration, is 1352 greater (in absolute value) than maxConstantOfIntegration 1353 AND is greater than maxConstantOfIntegration times the 1354 correct value, WeBWorK will give an error message saying 1355 that it can not handle such a large constant of integration. 1356 This is to prevent e.g. cos(x) + 1E20 or even 1E20 as being 1357 accepted as a correct antiderivatives of sin(x) since 1358 floating point arithmetic cannot tell the difference 1359 between cos(x) + 1E20, 1E20, and -cos(x) + 1E20. 1360 1361 Technical note: if you examine the code for the function routines, you will see 1362 that most subroutines are simply doing some basic error-checking and then 1363 passing the parameters on to the low-level FUNCTION_CMP(). Because this routine 1364 is set up to handle multivariable functions, with single-variable functions as 1365 a special case, it is possible to pass multivariable parameters to single- 1366 variable functions. This usage is strongly discouraged as unnecessarily 1367 confusing. Avoid it. 1368 1369 Default Values (As of 7/24/2000) (Option -- Variable Name -- Value) 1370 1371 Variable -- $functVarDefault -- 'x' 1372 Relative Tolerance -- $functRelPercentTolDefault -- .1 1373 Absolute Tolerance -- $functAbsTolDefault -- .001 1374 Lower Limit -- $functLLimitDefault -- .0000001 1375 Upper Limit -- $functULimitDefault -- 1 1376 Number of Points -- $functNumOfPoints -- 3 1377 Zero Level -- $functZeroLevelDefault -- 1E-14 1378 Zero Level Tolerance -- $functZeroLevelTolDefault -- 1E-12 1379 Maximum Constant -- $functMaxConstantOfIntegration -- 1E8 1380 of Integration 1381 1382 =cut 1383 1384 1385 1386 =head3 fun_cmp() 1387 1388 Compares a function or a list of functions, using a named hash of options to set 1389 parameters. This can make for more readable code than using the function_cmp() 1390 style, but some people find one or the other easier to remember. 1391 1392 ANS( fun_cmp( answer or answer_array_ref, options_hash ) ); 1393 1394 1. a string containing the correct function, or a reference to an 1395 array of correct functions 1396 2. a hash containing the following items (all optional): 1397 var -- either the number of variables or a reference to an 1398 array of variable names (see below) 1399 limits -- reference to an array of arrays of limits (see below), or: 1400 mode -- 'std' (default) (function must match exactly), or: 1401 'antider' (function must match up to a constant) 1402 relTol -- (default) a relative tolerance (as a percentage), or: 1403 tol -- an absolute tolerance for error 1404 numPoints -- the number of points to evaluate the function at 1405 maxConstantOfIntegration -- maximum size of the constant of integration 1406 zeroLevel -- if the correct answer is this close to zero, then 1407 zeroLevelTol applies 1408 zeroLevelTol -- absolute tolerance to allow when answer is close to zero 1409 test_points -- a list of points to use in checking the function, or a list of lists when there is more than one variable. 1410 params an array of "free" parameters which can be used to adapt 1411 the correct answer to the submitted answer. (e.g. ['c'] for 1412 a constant of integration in the answer x^3/3 + c. 1413 debug -- when set to 1 this provides extra information while checking the 1414 the answer. 1415 1416 Returns an answer evaluator, or (if given a reference to an array 1417 of answers), a list of answer evaluators 1418 1419 ANSWER: 1420 1421 The answer must be in the form of a string. The answer can contain 1422 functions, pi, e, and arithmetic operations. However, the correct answer 1423 string follows a slightly stricter syntax than student answers; specifically, 1424 there is no implicit multiplication. So the correct answer must be "3*x" rather 1425 than "3 x". Students can still enter "3 x". 1426 1427 VARIABLES: 1428 1429 The var parameter can contain either a number or a reference to an array of 1430 variable names. If it contains a number, the variables are named automatically 1431 as follows: 1 variable -- x 1432 2 variables -- x, y 1433 3 variables -- x, y, z 1434 4 or more -- x_1, x_2, x_3, etc. 1435 If the var parameter contains a reference to an array of variable names, then 1436 the number of variables is determined by the number of items in the array. A 1437 reference to an array is created with brackets, e.g. "var => ['r', 's', 't']". 1438 If only one variable is being used, you can write either "var => ['t']" for 1439 consistency or "var => 't'" as a shortcut. The default is one variable, x. 1440 1441 LIMITS: 1442 1443 Limits are specified with the limits parameter. You may NOT use llimit/ulimit. 1444 If you specify limits for one variable, you must specify them for all variables. 1445 The limit parameter must be a reference to an array of arrays of the form 1446 [lower_limit. upper_limit], each array corresponding to the lower and upper 1447 endpoints of the (half-open) domain of one variable. For example, 1448 "vars => 2, limits => [[0,2], [-3,8]]" would cause x to be evaluated in [0,2) and 1449 y to be evaluated in [-3,8). If only one variable is being used, you can write 1450 either "limits => [[0,3]]" for consistency or "limits => [0,3]" as a shortcut. 1451 1452 TEST POINTS: 1453 1454 In some cases, the problem writer may want to specify the points 1455 used to check a particular function. For example, if you want to 1456 use only integer values, they can be specified. With one variable, 1457 you can specify "test_points => [1,4,5,6]" or "test_points => [[1,4,5,6]]". 1458 With more variables, specify the list for the first variable, then the 1459 second, and so on: "vars=>['x','y'], test_points => [[1,4,5],[7,14,29]]". 1460 1461 If the problem writer wants random values which need to meet some special 1462 restrictions (such as being integers), they can be generated in the problem: 1463 "test_points=>[random(1,50), random(1,50), random(1,50), random(1,50)]". 1464 1465 Note that test_points should not be used for function checks which involve 1466 parameters (either explicitly given by "params", or as antiderivatives). 1467 1468 EXAMPLES: 1469 1470 fun_cmp( "3*x" ) -- standard compare, variable is x 1471 fun_cmp( ["3*x", "4*x+3", "3*x**2"] ) -- standard compare, defaults used for all three functions 1472 fun_cmp( "3*t", var => 't' ) -- standard compare, variable is t 1473 fun_cmp( "5*x*y*z", var => 3 ) -- x, y and z are the variables 1474 fun_cmp( "5*x", mode => 'antider' ) -- student answer must match up to constant (i.e., 5x+C) 1475 fun_cmp( ["3*x*y", "4*x*y"], limits => [[0,2], [5,7]] ) -- x evaluated in [0,2) 1476 y evaluated in [5,7) 1477 1478 =cut 1479 1480 sub fun_cmp { 1481 my $correctAnswer = shift @_; 1482 my %opt = @_; 1483 1484 assign_option_aliases( \%opt, 1485 'vars' => 'var', # set the standard option 'var' to the one specified as vars 1486 'domain' => 'limits', # set the standard option 'limits' to the one specified as domain 1487 'reltol' => 'relTol', 1488 'param' => 'params', 1489 ); 1490 1491 set_default_options( \%opt, 1492 'var' => $functVarDefault, 1493 'params' => [], 1494 'limits' => [[$functLLimitDefault, $functULimitDefault]], 1495 'test_points' => undef, 1496 'mode' => 'std', 1497 'tolType' => (defined($opt{tol}) ) ? 'absolute' : 'relative', 1498 'tol' => .01, # default mode should be relative, to obtain this tol must not be defined 1499 'relTol' => $functRelPercentTolDefault, 1500 'numPoints' => $functNumOfPoints, 1501 'maxConstantOfIntegration' => $functMaxConstantOfIntegration, 1502 'zeroLevel' => $functZeroLevelDefault, 1503 'zeroLevelTol' => $functZeroLevelTolDefault, 1504 'debug' => 0, 1505 ); 1506 1507 # allow var => 'x' as an abbreviation for var => ['x'] 1508 my %out_options = %opt; 1509 unless ( ref($out_options{var}) eq 'ARRAY' || $out_options{var} =~ m/^\d+$/) { 1510 $out_options{var} = [$out_options{var}]; 1511 } 1512 # allow params => 'c' as an abbreviation for params => ['c'] 1513 unless ( ref($out_options{params}) eq 'ARRAY' ) { 1514 $out_options{params} = [$out_options{params}]; 1515 } 1516 my ($tolType, $tol); 1517 if ($out_options{tolType} eq 'absolute') { 1518 $tolType = 'absolute'; 1519 $tol = $out_options{'tol'}; 1520 delete($out_options{'relTol'}) if exists( $out_options{'relTol'} ); 1521 } else { 1522 $tolType = 'relative'; 1523 $tol = $out_options{'relTol'}; 1524 delete($out_options{'tol'}) if exists( $out_options{'tol'} ); 1525 } 1526 1527 my @output_list = (); 1528 # thread over lists 1529 my @ans_list = (); 1530 1531 if ( ref($correctAnswer) eq 'ARRAY' ) { 1532 @ans_list = @{$correctAnswer}; 1533 } 1534 else { 1535 push( @ans_list, $correctAnswer ); 1536 } 1537 1538 # produce answer evaluators 1539 foreach my $ans (@ans_list) { 1540 push(@output_list, 1541 FUNCTION_CMP( 1542 'correctEqn' => $ans, 1543 'var' => $out_options{'var'}, 1544 'limits' => $out_options{'limits'}, 1545 'tolerance' => $tol, 1546 'tolType' => $tolType, 1547 'numPoints' => $out_options{'numPoints'}, 1548 'test_points' => $out_options{'test_points'}, 1549 'mode' => $out_options{'mode'}, 1550 'maxConstantOfIntegration' => $out_options{'maxConstantOfIntegration'}, 1551 'zeroLevel' => $out_options{'zeroLevel'}, 1552 'zeroLevelTol' => $out_options{'zeroLevelTol'}, 1553 'params' => $out_options{'params'}, 1554 'debug' => $out_options{'debug'}, 1555 ), 1556 ); 1557 } 1558 1559 return (wantarray) ? @output_list : $output_list[0]; 1560 } 1561 1562 =head3 Single-variable Function Comparisons 1563 1564 There are four single-variable function answer evaluators: "normal," absolute 1565 tolerance, antiderivative, and antiderivative with absolute tolerance. All 1566 parameters (other than the correct equation) are optional. 1567 1568 function_cmp( $correctEqn ) OR 1569 function_cmp( $correctEqn, $var ) OR 1570 function_cmp( $correctEqn, $var, $llimit, $ulimit ) OR 1571 function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol ) OR 1572 function_cmp( $correctEqn, $var, $llimit, $ulimit, 1573 $relPercentTol, $numPoints ) OR 1574 function_cmp( $correctEqn, $var, $llimit, $ulimit, 1575 $relPercentTol, $numPoints, $zeroLevel ) OR 1576 function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol, $numPoints, 1577 $zeroLevel,$zeroLevelTol ) 1578 1579 $correctEqn -- the correct equation, as a string 1580 $var -- the string representing the variable (optional) 1581 $llimit -- the lower limit of the interval to evaluate the 1582 variable in (optional) 1583 $ulimit -- the upper limit of the interval to evaluate the 1584 variable in (optional) 1585 $relPercentTol -- the error tolerance as a percentage (optional) 1586 $numPoints -- the number of points at which to evaluate the 1587 variable (optional) 1588 $zeroLevel -- if the correct answer is this close to zero, then 1589 zeroLevelTol applies (optional) 1590 $zeroLevelTol -- absolute tolerance to allow when answer is close to zero 1591 1592 function_cmp() uses standard comparison and relative tolerance. It takes a 1593 string representing a single-variable function and compares the student 1594 answer to that function numerically. 1595 1596 function_cmp_up_to_constant( $correctEqn ) OR 1597 function_cmp_up_to_constant( $correctEqn, $var ) OR 1598 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit ) OR 1599 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1600 $relpercentTol ) OR 1601 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1602 $relpercentTol, $numOfPoints ) OR 1603 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1604 $relpercentTol, $numOfPoints, 1605 $maxConstantOfIntegration ) OR 1606 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1607 $relpercentTol, $numOfPoints, 1608 $maxConstantOfIntegration, $zeroLevel) OR 1609 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1610 $relpercentTol, $numOfPoints, 1611 $maxConstantOfIntegration, 1612 $zeroLevel, $zeroLevelTol ) 1613 1614 $maxConstantOfIntegration -- the maximum size of the constant of 1615 integration 1616 1617 function_cmp_up_to_constant() uses antiderivative compare and relative 1618 tolerance. All options work exactly like function_cmp(), except of course 1619 $maxConstantOfIntegration. It will accept as correct any function which 1620 differs from $correctEqn by at most a constant; that is, if 1621 $studentEqn = $correctEqn + C 1622 the answer is correct. 1623 1624 function_cmp_abs( $correctFunction ) OR 1625 function_cmp_abs( $correctFunction, $var ) OR 1626 function_cmp_abs( $correctFunction, $var, $llimit, $ulimit ) OR 1627 function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol ) OR 1628 function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol, 1629 $numOfPoints ) 1630 1631 $absTol -- the tolerance as an absolute value 1632 1633 function_cmp_abs() uses standard compare and absolute tolerance. All 1634 other options work exactly as for function_cmp(). 1635 1636 function_cmp_up_to_constant_abs( $correctFunction ) OR 1637 function_cmp_up_to_constant_abs( $correctFunction, $var ) OR 1638 function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit ) OR 1639 function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit, 1640 $absTol ) OR 1641 function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit, 1642 $absTol, $numOfPoints ) OR 1643 function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit, 1644 $absTol, $numOfPoints, 1645 $maxConstantOfIntegration ) 1646 1647 function_cmp_up_to_constant_abs() uses antiderivative compare 1648 and absolute tolerance. All other options work exactly as with 1649 function_cmp_up_to_constant(). 1650 1651 Examples: 1652 1653 ANS( function_cmp( "cos(x)" ) ) -- Accepts cos(x), sin(x+pi/2), 1654 sin(x)^2 + cos(x) + cos(x)^2 -1, etc. This assumes 1655 $functVarDefault has been set to "x". 1656 ANS( function_cmp( $answer, "t" ) ) -- Assuming $answer is "cos(t)", 1657 accepts cos(t), etc. 1658 ANS( function_cmp_up_to_constant( "cos(x)" ) ) -- Accepts any 1659 antiderivative of sin(x), e.g. cos(x) + 5. 1660 ANS( function_cmp_up_to_constant( "cos(z)", "z" ) ) -- Accepts any 1661 antiderivative of sin(z), e.g. sin(z+pi/2) + 5. 1662 1663 =cut 1664 1665 sub adaptive_function_cmp { 1666 my $correctEqn = shift; 1667 my %options = @_; 1668 set_default_options( \%options, 1669 'vars' => [qw( x y )], 1670 'params' => [], 1671 'limits' => [ [0,1], [0,1]], 1672 'reltol' => $functRelPercentTolDefault, 1673 'numPoints' => $functNumOfPoints, 1674 'zeroLevel' => $functZeroLevelDefault, 1675 'zeroLevelTol' => $functZeroLevelTolDefault, 1676 'debug' => 0, 1677 ); 1678 1679 my $var_ref = $options{'vars'}; 1680 my $ra_params = $options{ 'params'}; 1681 my $limit_ref = $options{'limits'}; 1682 my $relPercentTol= $options{'reltol'}; 1683 my $numPoints = $options{'numPoints'}; 1684 my $zeroLevel = $options{'zeroLevel'}; 1685 my $zeroLevelTol = $options{'zeroLevelTol'}; 1686 1687 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1688 'var' => $var_ref, 1689 'limits' => $limit_ref, 1690 'tolerance' => $relPercentTol, 1691 'tolType' => 'relative', 1692 'numPoints' => $numPoints, 1693 'mode' => 'std', 1694 'maxConstantOfIntegration' => 10**100, 1695 'zeroLevel' => $zeroLevel, 1696 'zeroLevelTol' => $zeroLevelTol, 1697 'scale_norm' => 1, 1698 'params' => $ra_params, 1699 'debug' => $options{debug} , 1700 ); 1701 } 1702 1703 sub function_cmp { 1704 my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_; 1705 1706 if ( (scalar(@_) == 3) or (scalar(@_) > 8) or (scalar(@_) == 0) ) { 1707 function_invalid_params( $correctEqn ); 1708 } 1709 else { 1710 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1711 'var' => $var, 1712 'limits' => [$llimit, $ulimit], 1713 'tolerance' => $relPercentTol, 1714 'tolType' => 'relative', 1715 'numPoints' => $numPoints, 1716 'mode' => 'std', 1717 'maxConstantOfIntegration' => 0, 1718 'zeroLevel' => $zeroLevel, 1719 'zeroLevelTol' => $zeroLevelTol 1720 ); 1721 } 1722 } 1723 1724 sub function_cmp_up_to_constant { ## for antiderivative problems 1725 my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$maxConstantOfIntegration,$zeroLevel,$zeroLevelTol) = @_; 1726 1727 if ( (scalar(@_) == 3) or (scalar(@_) > 9) or (scalar(@_) == 0) ) { 1728 function_invalid_params( $correctEqn ); 1729 } 1730 else { 1731 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1732 'var' => $var, 1733 'limits' => [$llimit, $ulimit], 1734 'tolerance' => $relPercentTol, 1735 'tolType' => 'relative', 1736 'numPoints' => $numPoints, 1737 'mode' => 'antider', 1738 'maxConstantOfIntegration' => $maxConstantOfIntegration, 1739 'zeroLevel' => $zeroLevel, 1740 'zeroLevelTol' => $zeroLevelTol 1741 ); 1742 } 1743 } 1744 1745 sub function_cmp_abs { ## similar to function_cmp but uses absolute tolerance 1746 my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints) = @_; 1747 1748 if ( (scalar(@_) == 3) or (scalar(@_) > 6) or (scalar(@_) == 0) ) { 1749 function_invalid_params( $correctEqn ); 1750 } 1751 else { 1752 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1753 'var' => $var, 1754 'limits' => [$llimit, $ulimit], 1755 'tolerance' => $absTol, 1756 'tolType' => 'absolute', 1757 'numPoints' => $numPoints, 1758 'mode' => 'std', 1759 'maxConstantOfIntegration' => 0, 1760 'zeroLevel' => 0, 1761 'zeroLevelTol' => 0 1762 ); 1763 } 1764 } 1765 1766 1767 sub function_cmp_up_to_constant_abs { ## for antiderivative problems 1768 ## similar to function_cmp_up_to_constant 1769 ## but uses absolute tolerance 1770 my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints,$maxConstantOfIntegration) = @_; 1771 1772 if ( (scalar(@_) == 3) or (scalar(@_) > 7) or (scalar(@_) == 0) ) { 1773 function_invalid_params( $correctEqn ); 1774 } 1775 1776 else { 1777 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1778 'var' => $var, 1779 'limits' => [$llimit, $ulimit], 1780 'tolerance' => $absTol, 1781 'tolType' => 'absolute', 1782 'numPoints' => $numPoints, 1783 'mode' => 'antider', 1784 'maxConstantOfIntegration' => $maxConstantOfIntegration, 1785 'zeroLevel' => 0, 1786 'zeroLevelTol' => 0 1787 ); 1788 } 1789 } 1790 1791 ## The following answer evaluator for comparing multivarable functions was 1792 ## contributed by Professor William K. Ziemer 1793 ## (Note: most of the multivariable functionality provided by Professor Ziemer 1794 ## has now been integrated into fun_cmp and FUNCTION_CMP) 1795 ############################ 1796 # W.K. Ziemer, Sep. 1999 1797 # Math Dept. CSULB 1798 # email: wziemer@csulb.edu 1799 ############################ 1800 1801 =head3 multivar_function_cmp 1802 1803 NOTE: this function is maintained for compatibility. fun_cmp() is 1804 slightly preferred. 1805 1806 usage: 1807 1808 multivar_function_cmp( $answer, $var_reference, options) 1809 $answer -- string, represents function of several variables 1810 $var_reference -- number (of variables), or list reference (e.g. ["var1","var2"] ) 1811 options: 1812 $limit_reference -- reference to list of lists (e.g. [[1,2],[3,4]]) 1813 $relPercentTol -- relative percent tolerance in answer 1814 $numPoints -- number of points to sample in for each variable 1815 $zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies 1816 $zeroLevelTol -- absolute tolerance to allow when answer is close to zero 1817 1818 =cut 1819 1820 sub multivar_function_cmp { 1821 my ($correctEqn,$var_ref,$limit_ref,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_; 1822 1823 if ( (scalar(@_) > 7) or (scalar(@_) < 2) ) { 1824 function_invalid_params( $correctEqn ); 1825 } 1826 1827 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1828 'var' => $var_ref, 1829 'limits' => $limit_ref, 1830 'tolerance' => $relPercentTol, 1831 'tolType' => 'relative', 1832 'numPoints' => $numPoints, 1833 'mode' => 'std', 1834 'maxConstantOfIntegration' => 0, 1835 'zeroLevel' => $zeroLevel, 1836 'zeroLevelTol' => $zeroLevelTol 1837 ); 1838 } 1839 1840 ## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION 1841 ## NOTE: PG_answer_eval is used instead of PG_restricted_eval in order to insure that the answer 1842 ## evaluated within the context of the package the problem was originally defined in. 1843 ## Includes multivariable modifications contributed by Professor William K. Ziemer 1844 ## 1845 ## IN: a hash consisting of the following keys (error checking to be added later?) 1846 ## correctEqn -- the correct equation as a string 1847 ## var -- the variable name as a string, 1848 ## or a reference to an array of variables 1849 ## limits -- reference to an array of arrays of type [lower,upper] 1850 ## tolerance -- the allowable margin of error 1851 ## tolType -- 'relative' or 'absolute' 1852 ## numPoints -- the number of points to evaluate the function at 1853 ## mode -- 'std' or 'antider' 1854 ## maxConstantOfIntegration -- maximum size of the constant of integration 1855 ## zeroLevel -- if the correct answer is this close to zero, 1856 ## then zeroLevelTol applies 1857 ## zeroLevelTol -- absolute tolerance to allow when answer is close to zero 1858 ## test_points -- user supplied points to use for testing the 1859 ## function, either array of arrays, or optionally 1860 ## reference to single array (for one variable) 1861 1862 1863 sub FUNCTION_CMP { 1864 return ORIGINAL_FUNCTION_CMP(@_) 1865 if main::PG_restricted_eval(q!$main::useOldAnswerMacros!); 1866 1867 my %func_params = @_; 1868 1869 my $correctEqn = $func_params{'correctEqn'}; 1870 my $var = $func_params{'var'}; 1871 my $ra_limits = $func_params{'limits'}; 1872 my $tol = $func_params{'tolerance'}; 1873 my $tolType = $func_params{'tolType'}; 1874 my $numPoints = $func_params{'numPoints'}; 1875 my $mode = $func_params{'mode'}; 1876 my $maxConstantOfIntegration = $func_params{'maxConstantOfIntegration'}; 1877 my $zeroLevel = $func_params{'zeroLevel'}; 1878 my $zeroLevelTol = $func_params{'zeroLevelTol'}; 1879 my $testPoints = $func_params{'test_points'}; 1880 1881 # 1882 # Check that everything is defined: 1883 # 1884 $func_params{debug} = 0 unless defined $func_params{debug}; 1885 $mode = 'std' unless defined $mode; 1886 my @VARS = get_var_array($var); 1887 my @limits = get_limits_array($ra_limits); 1888 my @PARAMS = @{$func_params{'params'} || []}; 1889 1890 if($tolType eq 'relative') { 1891 $tol = $functRelPercentTolDefault unless defined $tol; 1892 $tol *= .01; 1893 } else { 1894 $tol = $functAbsTolDefault unless defined $tol; 1895 } 1896 1897 # 1898 # Ensure that the number of limits matches number of variables 1899 # 1900 foreach my $i (0..scalar(@VARS)-1) { 1901 $limits[$i][0] = $functLLimitDefault unless defined $limits[$i][0]; 1902 $limits[$i][1] = $functULimitDefault unless defined $limits[$i][1]; 1903 } 1904 1905 # 1906 # Check that the test points are array references with the right number of coordinates 1907 # 1908 if ($testPoints) { 1909 my $n = scalar(@VARS); my $s = ($n != 1)? "s": ""; 1910 foreach my $p (@{$testPoints}) { 1911 $p = [$p] unless ref($p) eq 'ARRAY'; 1912 warn "Test point (".join(',',@{$p}).") should have $n coordiante$s" 1913 unless scalar(@{$p}) == $n; 1914 } 1915 } 1916 1917 $numPoints = $functNumOfPoints unless defined $numPoints; 1918 $maxConstantOfIntegration = $functMaxConstantOfIntegration unless defined $maxConstantOfIntegration; 1919 $zeroLevel = $functZeroLevelDefault unless defined $zeroLevel; 1920 $zeroLevelTol = $functZeroLevelTolDefault unless defined $zeroLevelTol; 1921 1922 $func_params{'var'} = \@VARS; 1923 $func_params{'params'} = \@PARAMS; 1924 $func_params{'limits'} = \@limits; 1925 $func_params{'tolerance'} = $tol; 1926 $func_params{'tolType'} = $tolType; 1927 $func_params{'numPoints'} = $numPoints; 1928 $func_params{'mode'} = $mode; 1929 $func_params{'maxConstantOfIntegration'} = $maxConstantOfIntegration; 1930 $func_params{'zeroLevel'} = $zeroLevel; 1931 $func_params{'zeroLevelTol'} = $zeroLevelTol; 1932 1933 ######################################################## 1934 # End of cleanup of calling parameters 1935 ######################################################## 1936 1937 my %options = (debug => $func_params{'debug'}); 1938 1939 # 1940 # Initialize the context for the formula 1941 # 1942 my $context = $Parser::Context::Default::context{"LegacyNumeric"}->copy; 1943 $context->flags->set( 1944 tolerance => $func_params{'tolerance'}, 1945 tolType => $func_params{'tolType'}, 1946 zeroLevel => $func_params{'zeroLevel'}, 1947 zeroLevelTol => $func_params{'zeroLevelTol'}, 1948 num_points => $func_params{'numPoints'}, 1949 ); 1950 if ($func_params{'mode'} eq 'antider') { 1951 $context->flags->set(max_adapt => $func_params{'maxConstantOfIntegration'}); 1952 $options{upToConstant} = 1; 1953 } 1954 1955 # 1956 # Add the variables and parameters to the context 1957 # 1958 my %variables; my $x; 1959 foreach $x (@{$func_params{'var'}}) { 1960 if (length($x) > 1) { 1961 $context->{_variables}->{pattern} = $context->{_variables}->{namePattern} = 1962 $x . '|' . $context->{_variables}->{pattern}; 1963 $context->update; 1964 } 1965 $variables{$x} = 'Real'; 1966 } 1967 foreach $x (@{$func_params{'params'}}) {$variables{$x} = 'Parameter'} 1968 $context->variables->are(%variables); 1969 1970 # 1971 # Create the Formula object and get its answer checker 1972 # 1973 my $oldContext = &$Context(); &$Context($context); 1974 my $f = new Value::Formula($correctEqn); 1975 $f->{limits} = $func_params{'limits'}; 1976 $f->{test_points} = $func_params{'test_points'}; 1977 my $cmp = $f->cmp(%options); 1978 $cmp->{debug} = 1 if $func_params{'debug'}; 1979 &$Context($oldContext); 1980 1981 # 1982 # Get previous answer from hidden field of form 1983 # 1984 $cmp->install_pre_filter( 1985 sub { 1986 my $rh_ans = shift; 1987 $rh_ans->{_filter_name} = "fetch_previous_answer"; 1988 my $prev_ans_label = "previous_".$rh_ans->{ans_label}; 1989 $rh_ans->{prev_ans} = 1990 (defined $inputs_ref->{$prev_ans_label} and 1991 $inputs_ref->{$prev_ans_label} =~/\S/) ? $inputs_ref->{$prev_ans_label} : undef; 1992 $rh_ans; 1993 } 1994 ); 1995 1996 # 1997 # Parse the previous answer, if any 1998 # 1999 $cmp->install_pre_filter( 2000 sub { 2001 my $rh_ans = shift; 2002 $rh_ans->{_filter_name} = "parse_previous_answer"; 2003 return $rh_ans unless defined $rh_ans->{prev_ans}; 2004 $rh_ans->{prev_formula} = Parser::Formula($rh_ans->{prev_ans}); 2005 $rh_ans; 2006 } 2007 ); 2008 2009 # 2010 # Check if previous answer equals this current one 2011 # 2012 $cmp->install_evaluator( 2013 sub { 2014 my $rh_ans = shift; 2015 $rh_ans->{_filter_name} = "compare_to_previous_answer"; 2016 return $rh_ans unless defined($rh_ans->{prev_formula}) && defined($rh_ans->{student_formula}); 2017 $rh_ans->{prev_equals_current} = 2018 Value::cmp_compare($rh_ans->{student_formula},$rh_ans->{prev_formula},{}); 2019 $rh_ans; 2020 } 2021 ); 2022 2023 # 2024 # Produce a message if the previous answer equals this one 2025 # (and is not correct, and is not specified the same way) 2026 # 2027 $cmp->install_post_filter( 2028 sub { 2029 my $rh_ans = shift; 2030 $rh_ans->{_filter_name} = "produce_equivalence_message"; 2031 return $rh_ans unless $rh_ans->{prev_equals_current} && $rh_ans->{score} == 0; 2032 return $rh_ans if $rh_ans->{prev_ans} eq $rh_ans->{original_student_ans}; 2033 $rh_ans->{ans_message} = "This answer is equivalent to the one you just submitted or previewed."; 2034 $rh_ans; 2035 } 2036 ); 2037 2038 return $cmp; 2039 } 2040 2041 # 2042 # The original version, for backward compatibility 2043 # (can be removed when the Parser-based version is more fully tested.) 2044 # 2045 sub ORIGINAL_FUNCTION_CMP { 2046 my %func_params = @_; 2047 2048 my $correctEqn = $func_params{'correctEqn'}; 2049 my $var = $func_params{'var'}; 2050 my $ra_limits = $func_params{'limits'}; 2051 my $tol = $func_params{'tolerance'}; 2052 my $tolType = $func_params{'tolType'}; 2053 my $numPoints = $func_params{'numPoints'}; 2054 my $mode = $func_params{'mode'}; 2055 my $maxConstantOfIntegration = $func_params{'maxConstantOfIntegration'}; 2056 my $zeroLevel = $func_params{'zeroLevel'}; 2057 my $zeroLevelTol = $func_params{'zeroLevelTol'}; 2058 my $ra_test_points = $func_params{'test_points'}; 2059 2060 # Check that everything is defined: 2061 $func_params{debug} = 0 unless defined $func_params{debug}; 2062 $mode = 'std' unless defined $mode; 2063 my @VARS = get_var_array($var); 2064 my @limits = get_limits_array($ra_limits); 2065 my @PARAMS = (); 2066 @PARAMS = @{$func_params{'params'}} if defined $func_params{'params'}; 2067 2068 my @evaluation_points; 2069 if(defined $ra_test_points) { 2070 # see if this is the standard format 2071 if(ref $ra_test_points->[0] eq 'ARRAY') { 2072 $numPoints = scalar @{$ra_test_points->[0]}; 2073 # now a little sanity check 2074 my $j; 2075 for $j (@{$ra_test_points}) { 2076 warn "Test points do not give the same number of values for each variable" 2077 unless(scalar(@{$j}) == $numPoints); 2078 } 2079 warn "Test points do not match the number of variables" 2080 unless scalar @{$ra_test_points} == scalar @VARS; 2081 } else { # we are got the one-variable format 2082 $ra_test_points = [$ra_test_points]; 2083 $numPoints = scalar $ra_test_points->[0]; 2084 } 2085 # The input format for test points is the transpose of what is used 2086 # internally below, so take care of that now. 2087 my ($j1, $j2); 2088 for ($j1 = 0; $j1 < scalar @{$ra_test_points}; $j1++) { 2089 for ($j2 = 0; $j2 < scalar @{$ra_test_points->[$j1]}; $j2++) { 2090 $evaluation_points[$j2][$j1] = $ra_test_points->[$j1][$j2]; 2091 } 2092 } 2093 } # end of handling of user supplied evaluation points 2094 2095 if ($mode eq 'antider') { 2096 # doctor the equation to allow addition of a constant 2097 my $CONSTANT_PARAM = 'Q'; # unfortunately parameters must be single letters. 2098 # There is the possibility of conflict here. 2099 # 'Q' seemed less dangerous than 'C'. 2100 $correctEqn = "( $correctEqn ) + $CONSTANT_PARAM"; 2101 push @PARAMS, $CONSTANT_PARAM; 2102 } 2103 my $dim_of_param_space = @PARAMS; # dimension of equivalence space 2104 2105 if($tolType eq 'relative') { 2106 $tol = $functRelPercentTolDefault unless defined $tol; 2107 $tol *= .01; 2108 } else { 2109 $tol = $functAbsTolDefault unless defined $tol; 2110 } 2111 2112 #loop ensures that number of limits matches number of variables 2113 for(my $i = 0; $i < scalar @VARS; $i++) { 2114 $limits[$i][0] = $functLLimitDefault unless defined $limits[$i][0]; 2115 $limits[$i][1] = $functULimitDefault unless defined $limits[$i][1]; 2116 } 2117 $numPoints = $functNumOfPoints unless defined $numPoints; 2118 $maxConstantOfIntegration = $functMaxConstantOfIntegration unless defined $maxConstantOfIntegration; 2119 $zeroLevel = $functZeroLevelDefault unless defined $zeroLevel; 2120 $zeroLevelTol = $functZeroLevelTolDefault unless defined $zeroLevelTol; 2121 2122 $func_params{'var'} = $var; 2123 $func_params{'limits'} = \@limits; 2124 $func_params{'tolerance'} = $tol; 2125 $func_params{'tolType'} = $tolType; 2126 $func_params{'numPoints'} = $numPoints; 2127 $func_params{'mode'} = $mode; 2128 $func_params{'maxConstantOfIntegration'} = $maxConstantOfIntegration; 2129 $func_params{'zeroLevel'} = $zeroLevel; 2130 $func_params{'zeroLevelTol'} = $zeroLevelTol; 2131 2132 ######################################################## 2133 # End of cleanup of calling parameters 2134 ######################################################## 2135 2136 my $i; # for use with loops 2137 my $PGanswerMessage = ""; 2138 my $originalCorrEqn = $correctEqn; 2139 2140 ###################################################################### 2141 # prepare the correct answer and check its syntax 2142 ###################################################################### 2143 2144 my $rh_correct_ans = new AnswerHash; 2145 $rh_correct_ans->input($correctEqn); 2146 $rh_correct_ans = check_syntax($rh_correct_ans); 2147 warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag}; 2148 $rh_correct_ans->clear_error(); 2149 $rh_correct_ans = function_from_string2($rh_correct_ans, 2150 ra_vars => [ @VARS, @PARAMS ], 2151 stdout => 'rf_correct_ans', 2152 debug => $func_params{debug} 2153 ); 2154 my $correct_eqn_sub = $rh_correct_ans->{rf_correct_ans}; 2155 warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag}; 2156 2157 ###################################################################### 2158 # define the points at which the functions are to be evaluated 2159 ###################################################################### 2160 2161 if(not defined $ra_test_points) { 2162 #create the evaluation points 2163 my $random_for_answers = new PGrandom($main::PG_original_problemSeed); 2164 my $NUMBER_OF_STEPS_IN_RANDOM = 1000; # determines the granularity of the random_for_answers number generator 2165 for(my $count = 0; $count < @PARAMS+1+$numPoints; $count++) { 2166 my (@vars,$iteration_limit); 2167 for(my $i = 0; $i < @VARS; $i++) { 2168 my $iteration_limit = 10; 2169 while (0 < --$iteration_limit) { # make sure that the endpoints of the interval are not included 2170 $vars[$i] = $random_for_answers->random($limits[$i][0], $limits[$i][1], abs($limits[$i][1] - $limits[$i][0])/$NUMBER_OF_STEPS_IN_RANDOM); 2171 last if $vars[$i]!=$limits[$i][0] and $vars[$i]!=$limits[$i][1]; 2172 } 2173 warn "Unable to properly choose evaluation points for this function in the interval ( $limits[$i][0] , $limits[$i][1] )" 2174 if $iteration_limit == 0; 2175 } 2176 2177 push @evaluation_points, \@vars; 2178 } 2179 } 2180 my $evaluation_points = Matrix->new_from_array_ref(\@evaluation_points); 2181 2182 #my $COEFFS = determine_param_coeffs($correct_eqn_sub,$evaluation_points[0],$numOfParameters); 2183 #warn "coeff", join(" | ", @{$COEFFS}); 2184 2185 #construct the answer evaluator 2186 my $answer_evaluator = new AnswerEvaluator; 2187 $answer_evaluator->{debug} = $func_params{debug}; 2188 $answer_evaluator->ans_hash( 2189 correct_ans => $originalCorrEqn, 2190 rf_correct_ans => $rh_correct_ans->{rf_correct_ans}, 2191 evaluation_points => \@evaluation_points, 2192 ra_param_vars => \@PARAMS, 2193 ra_vars => \@VARS, 2194 type => 'function', 2195 score => 0, 2196 ); 2197 2198 ######################################################### 2199 # Prepare the previous answer for evaluation, discard errors 2200 ######################################################### 2201 2202 $answer_evaluator->install_pre_filter( 2203 sub { 2204 my $rh_ans = shift; 2205 $rh_ans->{_filter_name} = "fetch_previous_answer"; 2206 my $prev_ans_label = "previous_".$rh_ans->{ans_label}; 2207 $rh_ans->{prev_ans} = (defined $inputs_ref->{$prev_ans_label} and $inputs_ref->{$prev_ans_label} =~/\S/) 2208 ? $inputs_ref->{$prev_ans_label} 2209 : undef; 2210 $rh_ans; 2211 } 2212 ); 2213 2214 $answer_evaluator->install_pre_filter( 2215 sub { 2216 my $rh_ans = shift; 2217 return $rh_ans unless defined $rh_ans->{prev_ans}; 2218 check_syntax($rh_ans, 2219 stdin => 'prev_ans', 2220 stdout => 'prev_ans', 2221 error_msg_flag => 0 2222 ); 2223 $rh_ans->{_filter_name} = "check_syntax_of_previous_answer"; 2224 $rh_ans; 2225 } 2226 ); 2227 2228 $answer_evaluator->install_pre_filter( 2229 sub { 2230 my $rh_ans = shift; 2231 return $rh_ans unless defined $rh_ans->{prev_ans}; 2232 function_from_string2($rh_ans, 2233 stdin => 'prev_ans', 2234 stdout => 'rf_prev_ans', 2235 ra_vars => \@VARS, 2236 debug => $func_params{debug} 2237 ); 2238 $rh_ans->{_filter_name} = "compile_previous_answer"; 2239 $rh_ans; 2240 } 2241 ); 2242 2243 ######################################################### 2244 # Prepare the current answer for evaluation 2245 ######################################################### 2246 2247 $answer_evaluator->install_pre_filter(\&check_syntax); 2248 $answer_evaluator->install_pre_filter(\&function_from_string2, 2249 ra_vars => \@VARS, 2250 debug => $func_params{debug} 2251 ); # @VARS has been guaranteed to be an array, $var might be a single string. 2252 2253 ######################################################### 2254 # Compare the previous and current answer. Discard errors 2255 ######################################################### 2256 2257 $answer_evaluator->install_evaluator( 2258 sub { 2259 my $rh_ans = shift; 2260 return $rh_ans unless defined $rh_ans->{rf_prev_ans}; 2261 calculate_difference_vector($rh_ans, 2262 %func_params, 2263 stdin1 => 'rf_student_ans', 2264 stdin2 => 'rf_prev_ans', 2265 stdout => 'ra_diff_with_prev_ans', 2266 error_msg_flag => 0, 2267 ); 2268 $rh_ans->{_filter_name} = "calculate_difference_vector_of_previous_answer"; 2269 $rh_ans; 2270 } 2271 ); 2272 2273 $answer_evaluator->install_evaluator( 2274 sub { 2275 my $rh_ans = shift; 2276 return $rh_ans unless defined $rh_ans->{ra_diff_with_prev_ans}; 2277 ## 2278 ## DPVC -- only give the message if the answer is specified differently 2279 ## 2280 return $rh_ans if $rh_ans->{prev_ans} eq $rh_ans->{student_ans}; 2281 ## 2282 ## /DPVC 2283 ## 2284 is_zero_array($rh_ans, 2285 stdin => 'ra_diff_with_prev_ans', 2286 stdout => 'ans_equals_prev_ans' 2287 ); 2288 } 2289 ); 2290 2291 ######################################################### 2292 # Calculate values for approximation parameters and 2293 # compare the current answer with the correct answer. Keep errors this time. 2294 ######################################################### 2295 2296 $answer_evaluator->install_pre_filter(\&best_approx_parameters, %func_params, param_vars => \@PARAMS); 2297 $answer_evaluator->install_evaluator(\&calculate_difference_vector, %func_params); 2298 $answer_evaluator->install_evaluator(\&is_zero_array, tolerance => $tol ); 2299 2300 $answer_evaluator->install_post_filter( 2301 sub { 2302 my $rh_ans = shift; 2303 $rh_ans->clear_error('SYNTAX'); 2304 $rh_ans; 2305 } 2306 ); 2307 2308 $answer_evaluator->install_post_filter( 2309 sub { 2310 my $rh_ans = shift; 2311 if ($rh_ans->catch_error('EVAL')) { 2312 $rh_ans->{ans_message} = $rh_ans->{error_message}; 2313 $rh_ans->clear_error('EVAL'); 2314 } 2315 $rh_ans; 2316 } 2317 ); 2318 2319 $answer_evaluator->install_post_filter( 2320 sub { 2321 my $rh_ans = shift; 2322 if ( defined($rh_ans->{'ans_equals_prev_ans'}) and $rh_ans->{'ans_equals_prev_ans'} and $rh_ans->{score}==0) { 2323 ## $rh_ans->{ans_message} = "This answer is the same as the one you just submitted or previewed."; 2324 $rh_ans->{ans_message} = "This answer is equivalent to the one you just submitted or previewed."; ## DPVC 2325 } 2326 $rh_ans; 2327 } 2328 ); 2329 2330 $answer_evaluator; 2331 } 2332 2333 2334 ## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION 2335 ## 2336 ## IN: a hash containing the following items (error-checking to be added later?): 2337 ## correctAnswer -- the correct answer 2338 ## tolerance -- the allowable margin of error 2339 ## tolType -- 'relative' or 'absolute' 2340 ## format -- the display format of the answer 2341 ## mode -- one of 'std', 'strict', 'arith', or 'frac'; 2342 ## determines allowable formats for the input 2343 ## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies 2344 ## zeroLevelTol -- absolute tolerance to allow when answer is close to zero 2345 2346 2347 ########################################################################## 2348 ########################################################################## 2349 ## String answer evaluators 2350 2351 =head2 String Answer Evaluators 2352 2353 String answer evaluators compare a student string to the correct string. 2354 Different filters can be applied to allow various degrees of variation. 2355 Both the student and correct answers are subject to the same filters, to 2356 ensure that there are no unexpected matches or rejections. 2357 2358 String Filters 2359 2360 remove_whitespace -- Removes all whitespace from the string. 2361 It applies the following substitution 2362 to the string: 2363 $filteredAnswer =~ s/\s+//g; 2364 2365 compress_whitespace -- Removes leading and trailing whitespace, and 2366 replaces all other blocks of whitespace by a 2367 single space. Applies the following substitutions: 2368 $filteredAnswer =~ s/^\s*//; 2369 $filteredAnswer =~ s/\s*$//; 2370 $filteredAnswer =~ s/\s+/ /g; 2371 2372 trim_whitespace -- Removes leading and trailing whitespace. 2373 Applies the following substitutions: 2374 $filteredAnswer =~ s/^\s*//; 2375 $filteredAnswer =~ s/\s*$//; 2376 2377 ignore_case -- Ignores the case of the string. More accurately, 2378 it converts the string to uppercase (by convention). 2379 Applies the following function: 2380 $filteredAnswer = uc $filteredAnswer; 2381 2382 ignore_order -- Ignores the order of the letters in the string. 2383 This is used for problems of the form "Choose all 2384 that apply." Specifically, it removes all 2385 whitespace and lexically sorts the letters in 2386 ascending alphabetical order. Applies the following 2387 functions: 2388 $filteredAnswer = join( "", lex_sort( 2389 split( /\s*/, $filteredAnswer ) ) ); 2390 2391 =cut 2392 2393 ################################ 2394 ## STRING ANSWER FILTERS 2395 2396 ## IN: --the string to be filtered 2397 ## --a list of the filters to use 2398 ## 2399 ## OUT: --the modified string 2400 ## 2401 ## Use this subroutine instead of the 2402 ## individual filters below it 2403 2404 sub str_filters { 2405 my $stringToFilter = shift @_; 2406 # filters now take an answer hash, so encapsulate the string 2407 # in the answer hash. 2408 my $rh_ans = new AnswerHash; 2409 $rh_ans->{student_ans} = $stringToFilter; 2410 $rh_ans->{correct_ans}=''; 2411 my @filters_to_use = @_; 2412 my %known_filters = ( 2413 'remove_whitespace' => \&remove_whitespace, 2414 'compress_whitespace' => \&compress_whitespace, 2415 'trim_whitespace' => \&trim_whitespace, 2416 'ignore_case' => \&ignore_case, 2417 'ignore_order' => \&ignore_order, 2418 ); 2419 2420 #test for unknown filters 2421 foreach my $filter ( @filters_to_use ) { 2422 #check that filter is known 2423 die "Unknown string filter $filter (try checking the parameters to str_cmp() )" 2424 unless exists $known_filters{$filter}; 2425 $rh_ans = $known_filters{$filter}($rh_ans); # apply filter. 2426 } 2427 # foreach $filter (@filters_to_use) { 2428 # die "Unknown string filter $filter (try checking the parameters to str_cmp() )" 2429 # unless exists $known_filters{$filter}; 2430 # } 2431 # 2432 # if( grep( /remove_whitespace/i, @filters_to_use ) ) { 2433 # $rh_ans = remove_whitespace( $rh_ans ); 2434 # } 2435 # if( grep( /compress_whitespace/i, @filters_to_use ) ) { 2436 # $rh_ans = compress_whitespace( $rh_ans ); 2437 # } 2438 # if( grep( /trim_whitespace/i, @filters_to_use ) ) { 2439 # $rh_ans = trim_whitespace( $rh_ans ); 2440 # } 2441 # if( grep( /ignore_case/i, @filters_to_use ) ) { 2442 # $rh_ans = ignore_case( $rh_ans ); 2443 # } 2444 # if( grep( /ignore_order/i, @filters_to_use ) ) { 2445 # $rh_ans = ignore_order( $rh_ans ); 2446 # } 2447 2448 return $rh_ans->{student_ans}; 2449 } 2450 sub remove_whitespace { 2451 my $rh_ans = shift; 2452 die "expected an answer hash" unless ref($rh_ans)=~/HASH/i; 2453 $rh_ans->{_filter_name} = 'remove_whitespace'; 2454 $rh_ans->{student_ans} =~ s/\s+//g; # remove all whitespace 2455 $rh_ans->{correct_ans} =~ s/\s+//g; # remove all whitespace 2456 return $rh_ans; 2457 } 2458 2459 sub compress_whitespace { 2460 my $rh_ans = shift; 2461 die "expected an answer hash" unless ref($rh_ans)=~/HASH/i; 2462 $rh_ans->{_filter_name} = 'compress_whitespace'; 2463 $rh_ans->{student_ans} =~ s/^\s*//; # remove initial whitespace 2464 $rh_ans->{student_ans} =~ s/\s*$//; # remove trailing whitespace 2465 $rh_ans->{student_ans} =~ s/\s+/ /g; # replace spaces by single space 2466 $rh_ans->{correct_ans} =~ s/^\s*//; # remove initial whitespace 2467 $rh_ans->{correct_ans} =~ s/\s*$//; # remove trailing whitespace 2468 $rh_ans->{correct_ans} =~ s/\s+/ /g; # replace spaces by single space 2469 2470 return $rh_ans; 2471 } 2472 2473 sub trim_whitespace { 2474 my $rh_ans = shift; 2475 die "expected an answer hash" unless ref($rh_ans)=~/HASH/i; 2476 $rh_ans->{_filter_name} = 'trim_whitespace'; 2477 $rh_ans->{student_ans} =~ s/^\s*//; # remove initial whitespace 2478 $rh_ans->{student_ans} =~ s/\s*$//; # remove trailing whitespace 2479 $rh_ans->{correct_ans} =~ s/^\s*//; # remove initial whitespace 2480 $rh_ans->{correct_ans} =~ s/\s*$//; # remove trailing whitespace 2481 2482 return $rh_ans; 2483 } 2484 2485 sub ignore_case { 2486 my $rh_ans = shift; 2487 die "expected an answer hash" unless ref($rh_ans)=~/HASH/i; 2488 $rh_ans->{_filter_name} = 'ignore_case'; 2489 $rh_ans->{student_ans} =~ tr/a-z/A-Z/; 2490 $rh_ans->{correct_ans} =~ tr/a-z/A-Z/; 2491 return $rh_ans; 2492 } 2493 2494 sub ignore_order { 2495 my $rh_ans = shift; 2496 die "expected an answer hash" unless ref($rh_ans)=~/HASH/i; 2497 $rh_ans->{_filter_name} = 'ignore_order'; 2498 $rh_ans->{student_ans} = join( "", lex_sort( split( /\s*/, $rh_ans->{student_ans} ) ) ); 2499 $rh_ans->{correct_ans} = join( "", lex_sort( split( /\s*/, $rh_ans->{correct_ans} ) ) ); 2500 2501 return $rh_ans; 2502 } 2503 # sub remove_whitespace { 2504 # my $filteredAnswer = shift; 2505 # 2506 # $filteredAnswer =~ s/\s+//g; # remove all whitespace 2507 # 2508 # return $filteredAnswer; 2509 # } 2510 # 2511 # sub compress_whitespace { 2512 # my $filteredAnswer = shift; 2513 # 2514 # $filteredAnswer =~ s/^\s*//; # remove initial whitespace 2515 # $filteredAnswer =~ s/\s*$//; # remove trailing whitespace 2516 # $filteredAnswer =~ s/\s+/ /g; # replace spaces by single space 2517 # 2518 # return $filteredAnswer; 2519 # } 2520 # 2521 # sub trim_whitespace { 2522 # my $filteredAnswer = shift; 2523 # 2524 # $filteredAnswer =~ s/^\s*//; # remove initial whitespace 2525 # $filteredAnswer =~ s/\s*$//; # remove trailing whitespace 2526 # 2527 # return $filteredAnswer; 2528 # } 2529 # 2530 # sub ignore_case { 2531 # my $filteredAnswer = shift; 2532 # #warn "filtered answer is ", $filteredAnswer; 2533 # #$filteredAnswer = uc $filteredAnswer; # this didn't work on webwork xmlrpc, but does elsewhere ???? 2534 # $filteredAnswer =~ tr/a-z/A-Z/; 2535 # 2536 # return $filteredAnswer; 2537 # } 2538 # 2539 # sub ignore_order { 2540 # my $filteredAnswer = shift; 2541 # 2542 # $filteredAnswer = join( "", lex_sort( split( /\s*/, $filteredAnswer ) ) ); 2543 # 2544 # return $filteredAnswer; 2545 # } 2546 ################################ 2547 ## END STRING ANSWER FILTERS 2548 2549 2550 =head3 str_cmp() 2551 2552 Compares a string or a list of strings, using a named hash of options to set 2553 parameters. This can make for more readable code than using the "mode"_str_cmp() 2554 style, but some people find one or the other easier to remember. 2555 2556 ANS( str_cmp( answer or answer_array_ref, options_hash ) ); 2557 2558 1. the correct answer or a reference to an array of answers 2559 2. either a list of filters, or: 2560 a hash consisting of 2561 filters - a reference to an array of filters 2562 2563 Returns an answer evaluator, or (if given a reference to an array of answers), 2564 a list of answer evaluators 2565 2566 FILTERS: 2567 2568 remove_whitespace -- removes all whitespace 2569 compress_whitespace -- removes whitespace from the beginning and end of the string, 2570 and treats one or more whitespace characters in a row as a 2571 single space (true by default) 2572 trim_whitespace -- removes whitespace from the beginning and end of the string 2573 ignore_case -- ignores the case of the letters (true by default) 2574 ignore_order -- ignores the order in which letters are entered 2575 2576 EXAMPLES: 2577 2578 str_cmp( "Hello" ) -- matches "Hello", " hello" (same as std_str_cmp() ) 2579 str_cmp( ["Hello", "Goodbye"] ) -- same as std_str_cmp_list() 2580 str_cmp( " hello ", trim_whitespace ) -- matches "hello", " hello " 2581 str_cmp( "ABC", filters => 'ignore_order' ) -- matches "ACB", "A B C", but not "abc" 2582 str_cmp( "D E F", remove_whitespace, ignore_case ) -- matches "def" and "d e f" but not "fed" 2583 2584 2585 =cut 2586 2587 sub str_cmp { 2588 my $correctAnswer = shift @_; 2589 $correctAnswer = '' unless defined($correctAnswer); 2590 my @options = @_; 2591 my %options = (); 2592 # backward compatibility 2593 if (grep /filters|debug|filter/, @options) { # see whether we have hash keys in the input. 2594 %options = @options; 2595 } elsif (@options) { # all options are names of filters. 2596 $options{filters} = [@options]; 2597 } 2598 my $ra_filters; 2599 assign_option_aliases( \%options, 2600 'filter' => 'filters', 2601 ); 2602 set_default_options( \%options, 2603 'filters' => [qw(trim_whitespace compress_whitespace ignore_case)], 2604 'debug' => 0, 2605 'type' => 'str_cmp', 2606 ); 2607 $options{filters} = (ref($options{filters}))?$options{filters}:[$options{filters}]; 2608 # make sure this is a reference to an array. 2609 # error-checking for filters occurs in the filters() subroutine 2610 # if( not defined( $options[0] ) ) { # used with no filters as alias for std_str_cmp() 2611 # @options = ( 'compress_whitespace', 'ignore_case' ); 2612 # } 2613 # 2614 # if( $options[0] eq 'filters' ) { # using filters => [f1, f2, ...] notation 2615 # $ra_filters = $options[1]; 2616 # } 2617 # else { # using a list of filters 2618 # $ra_filters = \@options; 2619 # } 2620 2621 # thread over lists 2622 my @ans_list = (); 2623 2624 if ( ref($correctAnswer) eq 'ARRAY' ) { 2625 @ans_list = @{$correctAnswer}; 2626 } 2627 else { 2628 push( @ans_list, $correctAnswer ); 2629 } 2630 2631 # final_answer; 2632 my @output_list = (); 2633 2634 foreach my $ans (@ans_list) { 2635 push(@output_list, STR_CMP( 2636 'correct_ans' => $ans, 2637 'filters' => $options{filters}, 2638 'type' => $options{type}, 2639 'debug' => $options{debug}, 2640 ) 2641 ); 2642 } 2643 2644 return (wantarray) ? @output_list : $output_list[0] ; 2645 } 2646 2647 =head3 "mode"_str_cmp functions 2648 2649 The functions of the the form "mode"_str_cmp() use different functions to 2650 specify which filters to apply. They take no options except the correct 2651 string. There are also versions which accept a list of strings. 2652 2653 std_str_cmp( $correctString ) 2654 std_str_cmp_list( @correctStringList ) 2655 Filters: compress_whitespace, ignore_case 2656 2657 std_cs_str_cmp( $correctString ) 2658 std_cs_str_cmp_list( @correctStringList ) 2659 Filters: compress_whitespace 2660 2661 strict_str_cmp( $correctString ) 2662 strict_str_cmp_list( @correctStringList ) 2663 Filters: trim_whitespace 2664 2665 unordered_str_cmp( $correctString ) 2666 unordered_str_cmp_list( @correctStringList ) 2667 Filters: ignore_order, ignore_case 2668 2669 unordered_cs_str_cmp( $correctString ) 2670 unordered_cs_str_cmp_list( @correctStringList ) 2671 Filters: ignore_order 2672 2673 ordered_str_cmp( $correctString ) 2674 ordered_str_cmp_list( @correctStringList ) 2675 Filters: remove_whitespace, ignore_case 2676 2677 ordered_cs_str_cmp( $correctString ) 2678 ordered_cs_str_cmp_list( @correctStringList ) 2679 Filters: remove_whitespace 2680 2681 Examples 2682 2683 ANS( std_str_cmp( "W. Mozart" ) ) -- Accepts "W. Mozart", "W. MOZarT", 2684 and so forth. Case insensitive. All internal spaces treated 2685 as single spaces. 2686 ANS( std_cs_str_cmp( "Mozart" ) ) -- Rejects "mozart". Same as 2687 std_str_cmp() but case sensitive. 2688 ANS( strict_str_cmp( "W. Mozart" ) ) -- Accepts only the exact string. 2689 ANS( unordered_str_cmp( "ABC" ) ) -- Accepts "a c B", "CBA" and so forth. 2690 Unordered, case insensitive, spaces ignored. 2691 ANS( unordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc". Same as 2692 unordered_str_cmp() but case sensitive. 2693 ANS( ordered_str_cmp( "ABC" ) ) -- Accepts "a b C", "A B C" and so forth. 2694 Ordered, case insensitive, spaces ignored. 2695 ANS( ordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc", accepts "A BC" and 2696 so forth. Same as ordered_str_cmp() but case sensitive. 2697 2698 =cut 2699 2700 sub std_str_cmp { # compare strings 2701 my $correctAnswer = shift @_; 2702 my @filters = ( 'compress_whitespace', 'ignore_case' ); 2703 my $type = 'std_str_cmp'; 2704 STR_CMP('correct_ans' => $correctAnswer, 2705 'filters' => \@filters, 2706 'type' => $type 2707 ); 2708 } 2709 2710 sub std_str_cmp_list { # alias for std_str_cmp 2711 my @answerList = @_; 2712 my @output; 2713 while (@answerList) { 2714 push( @output, std_str_cmp(shift @answerList) ); 2715 } 2716 @output; 2717 } 2718 2719 sub std_cs_str_cmp { # compare strings case sensitive 2720 my $correctAnswer = shift @_; 2721 my @filters = ( 'compress_whitespace' ); 2722 my $type = 'std_cs_str_cmp'; 2723 STR_CMP( 'correct_ans' => $correctAnswer, 2724 'filters' => \@filters, 2725 'type' => $type 2726 ); 2727 } 2728 2729 sub std_cs_str_cmp_list { # alias for std_cs_str_cmp 2730 my @answerList = @_; 2731 my @output; 2732 while (@answerList) { 2733 push( @output, std_cs_str_cmp(shift @answerList) ); 2734 } 2735 @output; 2736 } 2737 2738 sub strict_str_cmp { # strict string compare 2739 my $correctAnswer = shift @_; 2740 my @filters = ( 'trim_whitespace' ); 2741 my $type = 'strict_str_cmp'; 2742 STR_CMP( 'correct_ans' => $correctAnswer, 2743 'filters' => \@filters, 2744 'type' => $type 2745 ); 2746 } 2747 2748 sub strict_str_cmp_list { # alias for strict_str_cmp 2749 my @answerList = @_; 2750 my @output; 2751 while (@answerList) { 2752 push( @output, strict_str_cmp(shift @answerList) ); 2753 } 2754 @output; 2755 } 2756 2757 sub unordered_str_cmp { # unordered, case insensitive, spaces ignored 2758 my $correctAnswer = shift @_; 2759 my @filters = ( 'ignore_order', 'ignore_case' ); 2760 my $type = 'unordered_str_cmp'; 2761 STR_CMP( 'correct_ans' => $correctAnswer, 2762 'filters' => \@filters, 2763 'type' => $type 2764 ); 2765 } 2766 2767 sub unordered_str_cmp_list { # alias for unordered_str_cmp 2768 my @answerList = @_; 2769 my @output; 2770 while (@answerList) { 2771 push( @output, unordered_str_cmp(shift @answerList) ); 2772 } 2773 @output; 2774 } 2775 2776 sub unordered_cs_str_cmp { # unordered, case sensitive, spaces ignored 2777 my $correctAnswer = shift @_; 2778 my @filters = ( 'ignore_order' ); 2779 my $type = 'unordered_cs_str_cmp'; 2780 STR_CMP( 'correct_ans' => $correctAnswer, 2781 'filters' => \@filters, 2782 'type' => $type 2783 ); 2784 } 2785 2786 sub unordered_cs_str_cmp_list { # alias for unordered_cs_str_cmp 2787 my @answerList = @_; 2788 my @output; 2789 while (@answerList) { 2790 push( @output, unordered_cs_str_cmp(shift @answerList) ); 2791 } 2792 @output; 2793 } 2794 2795 sub ordered_str_cmp { # ordered, case insensitive, spaces ignored 2796 my $correctAnswer = shift @_; 2797 my @filters = ( 'remove_whitespace', 'ignore_case' ); 2798 my $type = 'ordered_str_cmp'; 2799 STR_CMP( 'correct_ans' => $correctAnswer, 2800 'filters' => \@filters, 2801 'type' => $type 2802 ); 2803 } 2804 2805 sub ordered_str_cmp_list { # alias for ordered_str_cmp 2806 my @answerList = @_; 2807 my @output; 2808 while (@answerList) { 2809 push( @output, ordered_str_cmp(shift @answerList) ); 2810 } 2811 @output; 2812 } 2813 2814 sub ordered_cs_str_cmp { # ordered, case sensitive, spaces ignored 2815 my $correctAnswer = shift @_; 2816 my @filters = ( 'remove_whitespace' ); 2817 my $type = 'ordered_cs_str_cmp'; 2818 STR_CMP( 'correct_ans' => $correctAnswer, 2819 'filters' => \@filters, 2820 'type' => $type 2821 ); 2822 } 2823 2824 sub ordered_cs_str_cmp_list { # alias for ordered_cs_str_cmp 2825 my @answerList = @_; 2826 my @output; 2827 while (@answerList) { 2828 push( @output, ordered_cs_str_cmp(shift @answerList) ); 2829 } 2830 @output; 2831 } 2832 2833 2834 ## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION 2835 ## 2836 ## IN: a hashtable with the following entries (error-checking to be added later?): 2837 ## correctAnswer -- the correct answer, before filtering 2838 ## filters -- reference to an array containing the filters to be applied 2839 ## type -- a string containing the type of answer evaluator in use 2840 ## OUT: a reference to an answer evaluator subroutine 2841 sub STR_CMP { 2842 my %str_params = @_; 2843 #my $correctAnswer = str_filters( $str_params{'correct_ans'}, @{$str_params{'filters'}} ); 2844 my $answer_evaluator = new AnswerEvaluator; 2845 $answer_evaluator->{debug} = $str_params{debug}; 2846 $answer_evaluator->ans_hash( 2847 correct_ans => "$str_params{correct_ans}", 2848 type => $str_params{type}||'str_cmp', 2849 score => 0, 2850 2851 ); 2852 my %known_filters = ( 2853 'remove_whitespace' => \&remove_whitespace, 2854 'compress_whitespace' => \&compress_whitespace, 2855 'trim_whitespace' => \&trim_whitespace, 2856 'ignore_case' => \&ignore_case, 2857 'ignore_order' => \&ignore_order, 2858 ); 2859 2860 foreach my $filter ( @{$str_params{filters}} ) { 2861 #check that filter is known 2862 die "Unknown string filter |$filter|. Known filters are ". 2863 join(" ", keys %known_filters) . 2864 "(try checking the parameters to str_cmp() )" 2865 unless exists $known_filters{$filter}; 2866 # install related pre_filter 2867 $answer_evaluator->install_pre_filter( $known_filters{$filter} ); 2868 } 2869 $answer_evaluator->install_evaluator(sub { 2870 my $rh_ans = shift; 2871 $rh_ans->{_filter_name} = "Evaluator: Compare string answers with eq"; 2872 $rh_ans->{score} = ($rh_ans->{student_ans} eq $rh_ans->{correct_ans})?1:0 ; 2873 $rh_ans; 2874 }); 2875 $answer_evaluator->install_post_filter(sub { 2876 my $rh_hash = shift; 2877 $rh_hash->{_filter_name} = "clean up preview strings"; 2878 $rh_hash->{'preview_text_string'} = $rh_hash->{student_ans}; 2879 $rh_hash->{'preview_latex_string'} = "\\text{ ".$rh_hash->{student_ans}." }"; 2880 $rh_hash; 2881 }); 2882 return $answer_evaluator; 2883 } 2884 2885 # sub STR_CMP_old { 2886 # my %str_params = @_; 2887 # $str_params{'correct_ans'} = str_filters( $str_params{'correct_ans'}, @{$str_params{'filters'}} ); 2888 # my $answer_evaluator = sub { 2889 # my $in = shift @_; 2890 # $in = '' unless defined $in; 2891 # my $original_student_ans = $in; 2892 # $in = str_filters( $in, @{$str_params{'filters'}} ); 2893 # my $correctQ = ( $in eq $str_params{'correct_ans'} ) ? 1: 0; 2894 # my $ans_hash = new AnswerHash( 'score' => $correctQ, 2895 # 'correct_ans' => $str_params{'correctAnswer'}, 2896 # 'student_ans' => $in, 2897 # 'ans_message' => '', 2898 # 'type' => $str_params{'type'}, 2899 # 'preview_text_string' => $in, 2900 # 'preview_latex_string' => $in, 2901 # 'original_student_ans' => $original_student_ans 2902 # ); 2903 # return $ans_hash; 2904 # }; 2905 # return $answer_evaluator; 2906 # } 2907 2908 ########################################################################## 2909 ########################################################################## 2910 ## Miscellaneous answer evaluators 2911 2912 =head2 Miscellaneous Answer Evaluators (Checkboxes and Radio Buttons) 2913 2914 These evaluators do not fit any of the other categories. 2915 2916 checkbox_cmp( $correctAnswer ) 2917 2918 $correctAnswer -- a string containing the names of the correct boxes, 2919 e.g. "ACD". Note that this means that individual 2920 checkbox names can only be one character. Internally, 2921 this is largely the same as unordered_cs_str_cmp(). 2922 2923 radio_cmp( $correctAnswer ) 2924 2925 $correctAnswer -- a string containing the name of the correct radio 2926 button, e.g. "Choice1". This is case sensitive and 2927 whitespace sensitive, so the correct answer must match 2928 the name of the radio button exactly. 2929 2930 =cut 2931 2932 # added 6/14/2000 by David Etlinger 2933 # because of the conversion of the answer 2934 # string to an array, I thought it better not 2935 # to force STR_CMP() to work with this 2936 2937 #added 2/26/2003 by Mike Gage 2938 # handled the case where multiple answers are passed as an array reference 2939 # rather than as a \0 delimited string. 2940 sub checkbox_cmp { 2941 my $correctAnswer = shift @_; 2942 my %options = @_; 2943 assign_option_aliases( \%options, 2944 ); 2945 set_default_options( \%options, 2946 'debug' => 0, 2947 'type' => 'checkbox_cmp', 2948 ); 2949 my $answer_evaluator = new AnswerEvaluator( 2950 correct_ans => $correctAnswer, 2951 type => $options{type}, 2952 ); 2953 # pass along debug requests 2954 $answer_evaluator->{debug} = $options{debug}; 2955 2956 # join student answer array into a single string if necessary 2957 $answer_evaluator->install_pre_filter(sub { 2958 my $rh_ans = shift; 2959 $rh_ans->{_filter_name} = 'convert student_ans to string'; 2960 $rh_ans->{student_ans} = join("", @{$rh_ans->{student_ans}}) 2961 if ref($rh_ans->{student_ans}) =~/ARRAY/i; 2962 $rh_ans; 2963 }); 2964 # ignore order of check boxes 2965 $answer_evaluator->install_pre_filter(\&ignore_order); 2966 # compare as strings 2967 $answer_evaluator->install_evaluator(sub { 2968 my $rh_ans = shift; 2969 $rh_ans->{_filter_name} = 'compare strings generated by checked boxes'; 2970 $rh_ans->{score} = ($rh_ans->{student_ans} eq $rh_ans->{correct_ans}) ? 1 : 0; 2971 $rh_ans; 2972 }); 2973 # fix up preview displays 2974 $answer_evaluator->install_post_filter( sub { 2975 my $rh_ans = shift; 2976 $rh_ans->{_filter_name} = 'adjust preview strings'; 2977 $rh_ans->{type} = $options{type}; 2978 $rh_ans->{preview_text_string} = '\\text{'.$rh_ans->{student_ans}.'}', 2979 $rh_ans->{preview_latex_string} = '\\text{'.$rh_ans->{student_ans}.'}', 2980 $rh_ans; 2981 2982 2983 }); 2984 2985 # my $answer_evaluator = sub { 2986 # my $in = shift @_; 2987 # $in = '' unless defined $in; #in case no boxes checked 2988 # # multiple answers could come in two forms 2989 # # either a \0 delimited string or 2990 # # an array reference. We handle both. 2991 # if (ref($in) eq 'ARRAY') { 2992 # $in = join("",@{$in}); # convert array to single no-delimiter string 2993 # } else { 2994 # my @temp = split( "\0", $in ); #convert "\0"-delimited string to array... 2995 # $in = join( "", @temp ); #and then to a single no-delimiter string 2996 # } 2997 # my $original_student_ans = $in; #well, almost original 2998 # $in = str_filters( $in, 'ignore_order' ); 2999 # 3000 # my $correctQ = ($in eq $correctAnswer) ? 1: 0; 3001 # 3002 # my $ans_hash = new AnswerHash( 3003 # 'score' => $correctQ, 3004 # 'correct_ans' => "$correctAnswer", 3005 # 'student_ans' => $in, 3006 # 'ans_message' => "", 3007 # 'type' => "checkbox_cmp", 3008 # 'preview_text_string' => $in, 3009 # 'preview_latex_string' => $in, 3010 # 'original_student_ans' => $original_student_ans 3011 # ); 3012 # return $ans_hash; 3013 # 3014 # }; 3015 return $answer_evaluator; 3016 } 3017 # sub checkbox_cmp { 3018 # my $correctAnswer = shift @_; 3019 # $correctAnswer = str_filters( $correctAnswer, 'ignore_order' ); 3020 # 3021 # my $answer_evaluator = sub { 3022 # my $in = shift @_; 3023 # $in = '' unless defined $in; #in case no boxes checked 3024 # # multiple answers could come in two forms 3025 # # either a \0 delimited string or 3026 # # an array reference. We handle both. 3027 # if (ref($in) eq 'ARRAY') { 3028 # $in = join("",@{$in}); # convert array to single no-delimiter string 3029 # } else { 3030 # my @temp = split( "\0", $in ); #convert "\0"-delimited string to array... 3031 # $in = join( "", @temp ); #and then to a single no-delimiter string 3032 # } 3033 # my $original_student_ans = $in; #well, almost original 3034 # $in = str_filters( $in, 'ignore_order' ); 3035 # 3036 # my $correctQ = ($in eq $correctAnswer) ? 1: 0; 3037 # 3038 # my $ans_hash = new AnswerHash( 3039 # 'score' => $correctQ, 3040 # 'correct_ans' => "$correctAnswer", 3041 # 'student_ans' => $in, 3042 # 'ans_message' => "", 3043 # 'type' => "checkbox_cmp", 3044 # 'preview_text_string' => $in, 3045 # 'preview_latex_string' => $in, 3046 # 'original_student_ans' => $original_student_ans 3047 # ); 3048 # return $ans_hash; 3049 # 3050 # }; 3051 # return $answer_evaluator; 3052 # } 3053 3054 #added 6/28/2000 by David Etlinger 3055 #exactly the same as strict_str_cmp, 3056 #but more intuitive to the user 3057 3058 # check that answer is really a string and not an array 3059 # also use ordinary string compare 3060 sub radio_cmp { 3061 #strict_str_cmp( @_ ); 3062 my $response = shift; # there should be only one item. 3063 warn "Multiple choices -- this should not happen with radio buttons. Have 3064 you used checkboxes perhaps?" if ref($response); #triggered if an ARRAY is passed 3065 str_cmp($response); 3066 } 3067 3068 ########################################################################## 3069 ########################################################################## 3070 ## Text and e-mail routines 3071 3072 sub store_ans_at { 3073 my $answerStringRef = shift; 3074 my %options = @_; 3075 my $ans_eval= ''; 3076 if ( ref($answerStringRef) eq 'SCALAR' ) { 3077 $ans_eval= sub { 3078 my $text = shift; 3079 $text = '' unless defined($text); 3080 $$answerStringRef = $$answerStringRef . $text; 3081 my $ans_hash = new AnswerHash( 3082 'score' => 1, 3083 'correct_ans' => '', 3084 'student_ans' => $text, 3085 'ans_message' => '', 3086 'type' => 'store_ans_at', 3087 'original_student_ans' => $text, 3088 'preview_text_string' => '' 3089 ); 3090 3091 return $ans_hash; 3092 }; 3093 } 3094 else { 3095 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"; 3096 } 3097 3098 return $ans_eval; 3099 } 3100 3101 #### subroutines used in producing a questionnaire 3102 #### these are at least good models for other answers of this type 3103 3104 # my $QUESTIONNAIRE_ANSWERS=''; # stores the answers until it is time to send them 3105 # this must be initialized before the answer evaluators are run 3106 # but that happens long after all of the text in the problem is 3107 # evaluated. 3108 # this is a utility script for cleaning up the answer output for display in 3109 #the answers. 3110 3111 sub DUMMY_ANSWER { 3112 my $num = shift; 3113 qq{<INPUT TYPE="HIDDEN" NAME="answer$num" VALUE="">} 3114 } 3115 3116 sub escapeHTML { 3117 my $string = shift; 3118 $string =~ s/\n/$BR/ge; 3119 $string; 3120 } 3121 3122 # these next three subroutines show how to modify the "store_ans_at()" answer 3123 # evaluator to add extra information before storing the info 3124 # They provide a good model for how to tweak answer evaluators in special cases. 3125 3126 sub anstext { 3127 my $num = shift; 3128 my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS); 3129 my $psvnNumber = PG_restricted_eval(q!$main::psvnNumber!); 3130 my $probNum = PG_restricted_eval(q!$main::probNum!); 3131 my $ans_eval = sub { 3132 my $text = shift; 3133 $text = '' unless defined($text); 3134 my $new_text = "\n$psvnNumber-Problem-$probNum-Question-$num:\n $text "; # modify entered text 3135 my $out = &$ans_eval_template($new_text); # standard evaluator 3136 #warn "$QUESTIONNAIRE_ANSWERS"; 3137 $out->{student_ans} = escapeHTML($text); # restore original entered text 3138 $out->{correct_ans} = "Question $num answered"; 3139 $out->{original_student_ans} = escapeHTML($text); 3140 $out; 3141 }; 3142 $ans_eval; 3143 } 3144 3145 3146 sub ansradio { 3147 my $num = shift; 3148 my $psvnNumber = PG_restricted_eval(q!$main::psvnNumber!); 3149 my $probNum = PG_restricted_eval(q!$main::probNum!); 3150 3151 my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS); 3152 my $ans_eval = sub { 3153 my $text = shift; 3154 $text = '' unless defined($text); 3155 my $new_text = "\n$psvnNumber-Problem-$probNum-RADIO-$num:\n $text "; # modify entered text 3156 my $out = $ans_eval_template->($new_text); # standard evaluator 3157 $out->{student_ans} =escapeHTML($text); # restore original entered text 3158 $out->{original_student_ans} = escapeHTML($text); 3159 $out; 3160 }; 3161 3162 $ans_eval; 3163 } 3164 3165 sub anstext_non_anonymous { 3166 ## this emails identifying information 3167 my $num = shift; 3168 my $psvnNumber = PG_restricted_eval(q!$main::psvnNumber!); 3169 my $probNum = PG_restricted_eval(q!$main::probNum!); 3170 my $studentLogin = PG_restricted_eval(q!$main::studentLogin!); 3171 my $studentID = PG_restricted_eval(q!$main::studentID!); 3172 my $studentName = PG_restricted_eval(q!$main::studentName!); 3173 3174 3175 my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS); 3176 my $ans_eval = sub { 3177 my $text = shift; 3178 $text = '' unless defined($text); 3179 my $new_text = "\n$psvnNumber-Problem-$probNum-Question-$num:\n$studentLogin $main::studentID $studentName\n$text "; # modify entered text 3180 my $out = &$ans_eval_template($new_text); # standard evaluator 3181 #warn "$QUESTIONNAIRE_ANSWERS"; 3182 $out->{student_ans} = escapeHTML($text); # restore original entered text 3183 $out->{correct_ans} = "Question $num answered"; 3184 $out->{original_student_ans} = escapeHTML($text); 3185 $out; 3186 }; 3187 $ans_eval; 3188 } 3189 3190 3191 # This is another example of how to modify an answer evaluator to obtain 3192 # the desired behavior in a special case. Here the object is to have 3193 # have the last answer trigger the send_mail_to subroutine which mails 3194 # all of the answers to the designated address. 3195 # (This address must be listed in PG_environment{'ALLOW_MAIL_TO'} or an error occurs.) 3196 3197 # Fix me?? why is the body hard wired to the string QUESTIONNAIRE_ANSWERS? 3198 3199 sub mail_answers_to { #accepts the last answer and mails off the result 3200 my $user_address = shift; 3201 my $ans_eval = sub { 3202 3203 # then mail out all of the answers, including this last one. 3204 3205 send_mail_to( $user_address, 3206 'subject' => "$main::courseName WeBWorK questionnaire", 3207 'body' => $QUESTIONNAIRE_ANSWERS, 3208 'ALLOW_MAIL_TO' => $rh_envir->{ALLOW_MAIL_TO} 3209 ); 3210 3211 my $ans_hash = new AnswerHash( 'score' => 1, 3212 'correct_ans' => '', 3213 'student_ans' => 'Answer recorded', 3214 'ans_message' => '', 3215 'type' => 'send_mail_to', 3216 ); 3217 3218 return $ans_hash; 3219 }; 3220 3221 return $ans_eval; 3222 } 3223 3224 sub save_answer_to_file { #accepts the last answer and mails off the result 3225 my $fileID = shift; 3226 my $ans_eval = new AnswerEvaluator; 3227 $ans_eval->install_evaluator( 3228 sub { 3229 my $rh_ans = shift; 3230 3231 unless ( defined( $rh_ans->{student_ans} ) ) { 3232 $rh_ans->throw_error("save_answers_to_file","{student_ans} field not defined"); 3233 return $rh_ans; 3234 } 3235 3236 my $error; 3237 my $string = ''; 3238 $string = qq![[<$main::studentLogin> $main::studentName /!. time() . qq!/]]\n!. 3239 $rh_ans->{student_ans}. qq!\n\n============================\n\n!; 3240 3241 if ($error = AnswerIO::saveAnswerToFile('preflight',$string) ) { 3242 $rh_ans->throw_error("save_answers_to_file","Error: $error"); 3243 } else { 3244 $rh_ans->{'student_ans'} = 'Answer saved'; 3245 $rh_ans->{'score'} = 1; 3246 } 3247 $rh_ans; 3248 } 3249 ); 3250 3251 return $ans_eval; 3252 } 3253 3254 sub mail_answers_to2 { #accepts the last answer and mails off the result 3255 my $user_address = shift; 3256 my $subject = shift; 3257 my $ra_allow_mail_to = shift; 3258 $subject = "$main::courseName WeBWorK questionnaire" unless defined $subject; 3259 send_mail_to($user_address, 3260 'subject' => $subject, 3261 'body' => $QUESTIONNAIRE_ANSWERS, 3262 'ALLOW_MAIL_TO' => $rh_envir->{ALLOW_MAIL_TO}, 3263 ); 3264 } 3265 3266 ########################################################################## 3267 ########################################################################## 3268 3269 3270 ########################################################################### 3271 ### THE FOLLOWING ARE LOCAL SUBROUTINES THAT ARE MEANT TO BE CALLED ONLY FROM THIS SCRIPT. 3272 3273 ## Internal routine that converts variables into the standard array format 3274 ## 3275 ## IN: one of the following: 3276 ## an undefined value (i.e., no variable was specified) 3277 ## a reference to an array of variable names -- [var1, var2] 3278 ## a number (the number of variables desired) -- 3 3279 ## one or more variable names -- (var1, var2) 3280 ## OUT: an array of variable names 3281 3282 sub get_var_array { 3283 my $in = shift @_; 3284 my @out; 3285 3286 if( not defined($in) ) { #if nothing defined, build default array and return 3287 @out = ( $functVarDefault ); 3288 return @out; 3289 } 3290 elsif( ref( $in ) eq 'ARRAY' ) { #if given an array ref, dereference and return 3291 return @{$in}; 3292 } 3293 elsif( $in =~ /^\d+/ ) { #if given a number, set up the array and return 3294 if( $in == 1 ) { 3295 $out[0] = 'x'; 3296 } 3297 elsif( $in == 2 ) { 3298 $out[0] = 'x'; 3299 $out[1] = 'y'; 3300 } 3301 elsif( $in == 3 ) { 3302 $out[0] = 'x'; 3303 $out[1] = 'y'; 3304 $out[2] = 'z'; 3305 } 3306 else { #default to the x_1, x_2, ... convention 3307 my ($i, $tag); 3308 for($i = 0; $i < $in; $i++) {$out[$i] = "${functVarDefault}_".($i+1)} 3309 } 3310 return @out; 3311 } 3312 else { #if given one or more names, return as an array 3313 unshift( @_, $in ); 3314 return @_; 3315 } 3316 } 3317 3318 ## Internal routine that converts limits into the standard array of arrays format 3319 ## Some of the cases are probably unneccessary, but better safe than sorry 3320 ## 3321 ## IN: one of the following: 3322 ## an undefined value (i.e., no limits were specified) 3323 ## a reference to an array of arrays of limits -- [[llim,ulim], [llim,ulim]] 3324 ## a reference to an array of limits -- [llim, ulim] 3325 ## an array of array references -- ([llim,ulim], [llim,ulim]) 3326 ## an array of limits -- (llim,ulim) 3327 ## OUT: an array of array references -- ([llim,ulim], [llim,ulim]) or ([llim,ulim]) 3328 3329 sub get_limits_array { 3330 my $in = shift @_; 3331 my @out; 3332 3333 if( not defined($in) ) { #if nothing defined, build default array and return 3334 @out = ( [$functLLimitDefault, $functULimitDefault] ); 3335 return @out; 3336 } 3337 elsif( ref($in) eq 'ARRAY' ) { #$in is either ref to array, or ref to array of refs 3338 my @deref = @{$in}; 3339 3340 if( ref( $in->[0] ) eq 'ARRAY' ) { #$in is a ref to an array of array refs 3341 return @deref; 3342 } 3343 else { #$in was just a ref to an array of numbers 3344 @out = ( $in ); 3345 return @out; 3346 } 3347 } 3348 else { #$in was an array of references or numbers 3349 unshift( @_, $in ); 3350 3351 if( ref($_[0]) eq 'ARRAY' ) { #$in was an array of references, so just return it 3352 return @_; 3353 } 3354 else { #$in was an array of numbers 3355 @out = ( \@_ ); 3356 return @out; 3357 } 3358 } 3359 } 3360 3361 #sub check_option_list { 3362 # my $size = scalar(@_); 3363 # if( ( $size % 2 ) != 0 ) { 3364 # warn "ERROR in answer evaluator generator:\n" . 3365 # "Usage: <CODE>str_cmp([\$ans1, \$ans2],%options)</CODE> 3366 # or <CODE> num_cmp([\$num1, \$num2], %options)</CODE><BR> 3367 # A list of inputs must be inclosed in square brackets <CODE>[\$ans1, \$ans2]</CODE>"; 3368 # } 3369 #} 3370 3371 # simple subroutine to display an error message when 3372 # function compares are called with invalid parameters 3373 sub function_invalid_params { 3374 my $correctEqn = shift @_; 3375 my $error_response = sub { 3376 my $PGanswerMessage = "Tell your professor that there is an error with the parameters " . 3377 "to the function answer evaluator"; 3378 return ( 0, $correctEqn, "", $PGanswerMessage ); 3379 }; 3380 return $error_response; 3381 } 3382 3383 sub clean_up_error_msg { 3384 my $msg = $_[0]; 3385 $msg =~ s/^\[[^\]]*\][^:]*://; 3386 $msg =~ s/Unquoted string//g; 3387 $msg =~ s/may\s+clash.*/does not make sense here/; 3388 $msg =~ s/\sat.*line [\d]*//g; 3389 $msg = 'Error: '. $msg; 3390 3391 return $msg; 3392 } 3393 3394 #formats the student and correct answer as specified 3395 #format must be of a form suitable for sprintf (e.g. '%0.5g'), 3396 #with the exception that a '#' at the end of the string 3397 #will cause trailing zeros in the decimal part to be removed 3398 sub prfmt { 3399 my($number,$format) = @_; # attention, the order of format and number are reversed 3400 my $out; 3401 if ($format) { 3402 warn "Incorrect format used: $format. <BR> Format should look something like %4.5g<BR>" 3403 unless $format =~ /^\s*%\d*\.?\d*\w#?\s*$/; 3404 3405 if( $format =~ s/#\s*$// ) { # remove trailing zeros in the decimal 3406 $out = sprintf( $format, $number ); 3407 $out =~ s/(\.\d*?)0+$/$1/; 3408 $out =~ s/\.$//; # in case all decimal digits were zero, remove the decimal 3409 $out =~ s/e/E/g; # only use capital E's for exponents. Little e is for 2.71828... 3410 } elsif (is_a_number($number) ){ 3411 $out = sprintf( $format, $number ); 3412 $out =~ s/e/E/g; # only use capital E's for exponents. Little e is for 2.71828... 3413 } else { # number is probably a string representing an arithmetic expression 3414 $out = $number; 3415 } 3416 3417 } else { 3418 if (is_a_number($number)) {# only use capital E's for exponents. Little e is for 2.71828... 3419 $out = $number; 3420 $out =~ s/e/E/g; 3421 } else { # number is probably a string representing an arithmetic expression 3422 $out = $number; 3423 } 3424 } 3425 return $out; 3426 } 3427 ######################################################################### 3428 # Filters for answer evaluators 3429 ######################################################################### 3430 3431 =head2 Filters 3432 3433 =pod 3434 3435 A filter is a short subroutine with the following structure. It accepts an 3436 AnswerHash, followed by a hash of options. It returns an AnswerHash 3437 3438 $ans_hash = filter($ans_hash, %options); 3439 3440 See the AnswerHash.pm file for a list of entries which can be expected to be found 3441 in an AnswerHash, such as 'student_ans', 'score' and so forth. Other entries 3442 may be present for specialized answer evaluators. 3443 3444 The hope is that a well designed set of filters can easily be combined to form 3445 a new answer_evaluator and that this method will produce answer evaluators which are 3446 are more robust than the method of copying existing answer evaluators and modifying them. 3447 3448 Here is an outline of how a filter is constructed: 3449 3450 sub filter{ 3451 my $rh_ans = shift; 3452 my %options = @_; 3453 assign_option_aliases(\%options, 3454 'alias1' => 'option5' 3455 'alias2' => 'option7' 3456 ); 3457 set_default_options(\%options, 3458 '_filter_name' => 'filter', 3459 'option5' => .0001, 3460 'option7' => 'ascii', 3461 'allow_unknown_options => 0, 3462 } 3463 .... body code of filter ....... 3464 if ($error) { 3465 $rh_ans->throw_error("FILTER_ERROR", "Something went wrong"); 3466 # see AnswerHash.pm for details on using the throw_error method. 3467 3468 $rh_ans; #reference to an AnswerHash object is returned. 3469 } 3470 3471 =cut 3472 3473 =head4 compare_numbers 3474 3475 3476 =cut 3477 3478 3479 sub compare_numbers { 3480 my ($rh_ans, %options) = @_; 3481 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($rh_ans->{student_ans}); 3482 if ($PG_eval_errors) { 3483 $rh_ans->throw_error('EVAL','There is a syntax error in your answer'); 3484 $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors); 3485 # return $rh_ans; 3486 } else { 3487 $rh_ans->{student_ans} = prfmt($inVal,$options{format}); 3488 } 3489 3490 my $permitted_error; 3491 3492 if ($rh_ans->{tolType} eq 'absolute') { 3493 $permitted_error = $rh_ans->{tolerance}; 3494 } 3495 elsif ( abs($rh_ans->{correct_ans}) <= $options{zeroLevel}) { 3496 $permitted_error = $options{zeroLevelTol}; ## want $tol to be non zero 3497 } 3498 else { 3499 $permitted_error = abs($rh_ans->{tolerance}*$rh_ans->{correct_ans}); 3500 } 3501 3502 my $is_a_number = is_a_number($inVal); 3503 $rh_ans->{score} = 1 if ( ($is_a_number) and 3504 (abs( $inVal - $rh_ans->{correct_ans} ) <= $permitted_error) ); 3505 if (not $is_a_number) { 3506 $rh_ans->{error_message} = "$rh_ans->{error_message}". 'Your answer does not evaluate to a number '; 3507 } 3508 3509 $rh_ans; 3510 } 3511 3512 =head4 std_num_filter 3513 3514 std_num_filter($rh_ans, %options) 3515 returns $rh_ans 3516 3517 Replaces some constants using math_constants, then evaluates a perl expression. 3518 3519 3520 =cut 3521 3522 sub std_num_filter { 3523 my $rh_ans = shift; 3524 my %options = @_; 3525 my $in = $rh_ans->input(); 3526 $in = math_constants($in); 3527 $rh_ans->{type} = 'std_number'; 3528 my ($inVal,$PG_eval_errors,$PG_full_error_report); 3529 if ($in =~ /\S/) { 3530 ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($in); 3531 } else { 3532 $PG_eval_errors = ''; 3533 } 3534 3535 if ($PG_eval_errors) { ##error message from eval or above 3536 $rh_ans->{ans_message} = 'There is a syntax error in your answer'; 3537 $rh_ans->{student_ans} = 3538 clean_up_error_msg($PG_eval_errors); 3539 } else { 3540 $rh_ans->{student_ans} = $inVal; 3541 } 3542 $rh_ans; 3543 } 3544 3545 =head std_num_array_filter 3546 3547 std_num_array_filter($rh_ans, %options) 3548 returns $rh_ans 3549 3550 Assumes the {student_ans} field is a numerical array, and applies BOTH check_syntax and std_num_filter 3551 to each element of the array. Does it's best to generate sensible error messages for syntax errors. 3552 A typical error message displayed in {studnet_ans} might be ( 56, error message, -4). 3553 3554 =cut 3555 3556 sub std_num_array_filter { 3557 my $rh_ans= shift; 3558 my %options = @_; 3559 set_default_options( \%options, 3560 '_filter_name' => 'std_num_array_filter', 3561 ); 3562 my @in = @{$rh_ans->{student_ans}}; 3563 my $temp_hash = new AnswerHash; 3564 my @out=(); 3565 my $PGanswerMessage = ''; 3566 foreach my $item (@in) { # evaluate each number in the vector 3567 $temp_hash->input($item); 3568 $temp_hash = check_syntax($temp_hash); 3569 if (defined($temp_hash->{error_flag}) and $temp_hash->{error_flag} eq 'SYNTAX') { 3570 $PGanswerMessage .= $temp_hash->{ans_message}; 3571 $temp_hash->{ans_message} = undef; 3572 } else { 3573 #continue processing 3574 $temp_hash = std_num_filter($temp_hash); 3575 if (defined($temp_hash->{ans_message}) and $temp_hash->{ans_message} ) { 3576 $PGanswerMessage .= $temp_hash->{ans_message}; 3577 $temp_hash->{ans_message} = undef; 3578 } 3579 } 3580 push(@out, $temp_hash->input()); 3581 3582 } 3583 if ($PGanswerMessage) { 3584 $rh_ans->input( "( " . join(", ", @out ) . " )" ); 3585 $rh_ans->throw_error('SYNTAX', 'There is a syntax error in your answer.'); 3586 } else { 3587 $rh_ans->input( [@out] ); 3588 } 3589 $rh_ans; 3590 } 3591 3592 =head4 function_from_string2 3593 3594 3595 3596 =cut 3597 3598 sub function_from_string2 { 3599 my $rh_ans = shift; 3600 my %options = @_; 3601 assign_option_aliases(\%options, 3602 'vars' => 'ra_vars', 3603 'var' => 'ra_vars', 3604 'store_in' => 'stdout', 3605 ); 3606 set_default_options( \%options, 3607 'stdin' => 'student_ans', 3608 'stdout' => 'rf_student_ans', 3609 'ra_vars' => [qw( x y )], 3610 'debug' => 0, 3611 '_filter_name' => 'function_from_string2', 3612 ); 3613 # initialize 3614 $rh_ans->{_filter_name} = $options{_filter_name}; 3615 3616 my $eqn = $rh_ans->{ $options{stdin} }; 3617 my @VARS = @{ $options{ 'ra_vars'} }; 3618 #warn "VARS = ", join("<>", @VARS) if defined($options{debug}) and $options{debug} ==1; 3619 my $originalEqn = $eqn; 3620 $eqn = &math_constants($eqn); 3621 for( my $i = 0; $i < @VARS; $i++ ) { 3622 # This next line is a hack required for 5.6.0 -- it doesn't appear to be needed in 5.6.1 3623 my ($temp,$er1,$er2) = PG_restricted_eval('"'. $VARS[$i] . '"'); 3624 #$eqn =~ s/\b$VARS[$i]\b/\$VARS[$i]/g; 3625 $eqn =~ s/\b$temp\b/\$VARS[$i]/g; 3626 3627 } 3628 #warn "equation evaluated = $eqn",$rh_ans->pretty_print(), "<br>\noptions<br>\n", 3629 # pretty_print(\%options) 3630 # if defined($options{debug}) and $options{debug} ==1; 3631 my ($function_sub,$PG_eval_errors, $PG_full_errors) = PG_answer_eval( q! 3632 sub { 3633 my @VARS = @_; 3634 my $input_str = ''; 3635 for( my $i=0; $i<@VARS; $i++ ) { 3636 $input_str .= "\$VARS[$i] = $VARS[$i]; "; 3637 } 3638 my $PGanswerMessage; 3639 $input_str .= '! . $eqn . q!'; # need the single quotes to keep the contents of $eqn from being 3640 # evaluated when it is assigned to $input_str; 3641 my ($out, $PG_eval_errors, $PG_full_errors) = PG_answer_eval($input_str); #Finally evaluated 3642 3643 if ( defined($PG_eval_errors) and $PG_eval_errors =~ /\S/ ) { 3644 $PGanswerMessage = clean_up_error_msg($PG_eval_errors); 3645 # This message seemed too verbose, but it does give extra information, we'll see if it is needed. 3646 # "<br> There was an error in evaluating your function <br> 3647 # !. $originalEqn . q! <br> 3648 # at ( " . join(', ', @VARS) . " ) <br> 3649 # $PG_eval_errors 3650 # "; # this message appears in the answer section which is not process by Latex2HTML so it must 3651 # # be in HTML. That is why $BR is NOT used. 3652 3653 } 3654 (wantarray) ? ($out, $PGanswerMessage): $out; # PGanswerMessage may be undefined. 3655 }; 3656 !); 3657 3658 if (defined($PG_eval_errors) and $PG_eval_errors =~/\S/ ) { 3659 $PG_eval_errors = clean_up_error_msg($PG_eval_errors); 3660 3661 my $PGanswerMessage = "There was an error in converting the expression 3662 $BR $originalEqn $BR into a function. 3663 $BR $PG_eval_errors."; 3664 $rh_ans->{rf_student_ans} = $function_sub; 3665 $rh_ans->{ans_message} = $PGanswerMessage; 3666 $rh_ans->{error_message} = $PGanswerMessage; 3667 $rh_ans->{error_flag} = 1; 3668 # we couldn't compile the equation, we'll return an error message. 3669 } else { 3670 # if (defined($options{stdout} )) { 3671 # $rh_ans ->{$options{stdout}} = $function_sub; 3672 # } else { 3673 # $rh_ans->{rf_student_ans} = $function_sub; 3674 # } 3675 $rh_ans ->{$options{stdout}} = $function_sub; 3676 } 3677 3678 $rh_ans; 3679 } 3680 3681 =head4 is_zero_array 3682 3683 3684 =cut 3685 3686 3687 sub is_zero_array { 3688 my $rh_ans = shift; 3689 my %options = @_; 3690 set_default_options( \%options, 3691 '_filter_name' => 'is_zero_array', 3692 'tolerance' => 0.000001, 3693 'stdin' => 'ra_differences', 3694 'stdout' => 'score', 3695 ); 3696 #intialize 3697 $rh_ans->{_filter_name} = $options{_filter_name}; 3698 3699 my $array = $rh_ans -> {$options{stdin}}; # default ra_differences 3700 my $num = @$array; 3701 my $i; 3702 my $max = 0; my $mm; 3703 for ($i=0; $i< $num; $i++) { 3704 $mm = $array->[$i] ; 3705 if (not is_a_number($mm) ) { 3706 $max = $mm; # break out if one of the elements is not a number 3707 last; 3708 } 3709 $max = abs($mm) if abs($mm) > $max; 3710 } 3711 if (not is_a_number($max)) { 3712 $rh_ans->{score} = 0; 3713 my $error = "WeBWorK was unable evaluate your function. Please check that your 3714 expression doesn't take roots of negative numbers, or divide by zero."; 3715 $rh_ans->throw_error('EVAL',$error); 3716 } else { 3717 $rh_ans->{$options{stdout}} = ($max < $options{tolerance} ) ? 1: 0; # set 'score' to 1 if the array is close to 0; 3718 } 3719 $rh_ans; 3720 } 3721 3722 =head4 best_approx_parameters 3723 3724 best_approx_parameters($rh_ans,%options); #requires the following fields in $rh_ans 3725 {rf_student_ans} # reference to the test answer 3726 {rf_correct_ans} # reference to the comparison answer 3727 {evaluation_points}, # an array of row vectors indicating the points 3728 # to evaluate when comparing the functions 3729 3730 %options # debug => 1 gives more error answers 3731 # param_vars => [''] additional parameters used to adapt to function 3732 ) 3733 3734 3735 The parameters for the comparison function which best approximates the test_function are stored 3736 in the field {ra_parameters}. 3737 3738 3739 The last $dim_of_parms_space variables are assumed to be parameters, and it is also 3740 assumed that the function \&comparison_fun 3741 depends linearly on these variables. This function finds the values for these parameters which minimizes the 3742 Euclidean distance (L2 distance) between the test function and the comparison function and the test points specified 3743 by the array reference \@rows_of_test_points. This is assumed to be an array of arrays, with the inner arrays 3744 determining a test point. 3745 3746 The comparison function should have $dim_of_params_space more input variables than the test function. 3747 3748 3749 3750 3751 3752 =cut 3753 3754 # Used internally: 3755 # 3756 # &$determine_param_coeff( $rf_comparison_function # a reference to the correct answer function 3757 # $ra_variables # an array of the active input variables to the functions 3758 # $dim_of_params_space # indicates the number of parameters upon which the 3759 # # the comparison function depends linearly. These are assumed to 3760 # # be the last group of inputs to the comparison function. 3761 # 3762 # %options # $options{debug} gives more error messages 3763 # 3764 # # A typical function might look like 3765 # # f(x,y,z,a,b) = x^2+a*cos(xz) + b*sin(x) with a parameter 3766 # # space of dimension 2 and a variable space of dimension 3. 3767 # ) 3768 # # returns a list of coefficients 3769 3770 sub best_approx_parameters { 3771 my $rh_ans = shift; 3772 my %options = @_; 3773 set_default_options(\%options, 3774 '_filter_name' => 'best_approx_paramters', 3775 'allow_unknown_options' => 1, 3776 ); 3777 my $errors = undef; 3778 # This subroutine for the determining the coefficents of the parameters at a given point 3779 # is pretty specialized, so it is included here as a sub-subroutine. 3780 my $determine_param_coeffs = sub { 3781 my ($rf_fun, $ra_variables, $dim_of_params_space, %options) =@_; 3782 my @zero_params=(); 3783 for(my $i=1;$i<=$dim_of_params_space;$i++){push(@zero_params,0); } 3784 my @vars = @$ra_variables; 3785 my @coeff = (); 3786 my @inputs = (@vars,@zero_params); 3787 my ($f0, $f1, $err); 3788 ($f0, $err) = &{$rf_fun}(@inputs); 3789 if (defined($err) ) { 3790 $errors .= "$err "; 3791 } else { 3792 for (my $i=@vars;$i<@inputs;$i++) { 3793 $inputs[$i]=1; # set one parameter to 1; 3794 my($f1,$err) = &$rf_fun(@inputs); 3795 if (defined($err) ) { 3796 $errors .= " $err "; 3797 } else { 3798 push(@coeff, $f1-$f0); 3799 } 3800 $inputs[$i]=0; # set it back 3801 } 3802 } 3803 (\@coeff, $errors); 3804 }; 3805 my $rf_fun = $rh_ans->{rf_student_ans}; 3806 my $rf_correct_fun = $rh_ans->{rf_correct_ans}; 3807 my $ra_vars_matrix = $rh_ans->{evaluation_points}; 3808 my $dim_of_param_space = @{$options{param_vars}}; 3809 # Short cut. Bail if there are no param_vars 3810 unless ($dim_of_param_space >0) { 3811 $rh_ans ->{ra_parameters} = []; 3812 return $rh_ans; 3813 } 3814 # inputs are row arrays in this case. 3815 my @zero_params=(); 3816 3817 for(my $i=1;$i<=$dim_of_param_space;$i++){push(@zero_params,0); } 3818 my @rows_of_vars = @$ra_vars_matrix; 3819 warn "input rows ", pretty_print(\@rows_of_vars) if defined($options{debug}) and $options{debug}; 3820 my $rows = @rows_of_vars; 3821 my $matrix =new Matrix($rows,$dim_of_param_space); 3822 my $rhs_vec = new Matrix($rows, 1); 3823 my $row_num = 1; 3824 my ($ra_coeff,$val2, $val1, $err1,$err2,@inputs,@vars); 3825 my $number_of_data_points = $dim_of_param_space +2; 3826 while (@rows_of_vars and $row_num <= $number_of_data_points) { 3827 # get one set of data points from the test function; 3828 @vars = @{ shift(@rows_of_vars) }; 3829 ($val2, $err1) = &{$rf_fun}(@vars); 3830 $errors .= " $err1 " if defined($err1); 3831 @inputs = (@vars,@zero_params); 3832 ($val1, $err2) = &{$rf_correct_fun}(@inputs); 3833 $errors .= " $err2 " if defined($err2); 3834 3835 unless (defined($err1) or defined($err2) ) { 3836 $rhs_vec->assign($row_num,1, $val2-$val1 ); 3837 3838 # warn "rhs data val1=$val1, val2=$val2, val2 - val1 = ", $val2 - $val1 if $options{debug}; 3839 # warn "vars ", join(" | ", @vars) if $options{debug}; 3840 3841 ($ra_coeff, $err1) = &{$determine_param_coeffs}($rf_correct_fun,\@vars,$dim_of_param_space,%options); 3842 if (defined($err1) ) { 3843 $errors .= " $err1 "; 3844 } else { 3845 my @coeff = @$ra_coeff; 3846 my $col_num=1; 3847 while(@coeff) { 3848 $matrix->assign($row_num,$col_num, shift(@coeff) ); 3849 $col_num++; 3850 } 3851 } 3852 } 3853 $row_num++; 3854 last if $errors; # break if there are any errors. 3855 # This cuts down on the size of error messages. 3856 # However it impossible to check for equivalence at 95% of points 3857 # which might be useful for functions that are not defined at some points. 3858 } 3859 warn "<br> best_approx_parameters: matrix1 <br> ", " $matrix " if $options{debug}; 3860 warn "<br> best_approx_parameters: vector <br> ", " $rhs_vec " if $options{debug}; 3861 3862 # we have Matrix * parameter = data_vec + perpendicular vector 3863 # where the matrix has column vectors defining the span of the parameter space 3864 # multiply both sides by Matrix_transpose and solve for the parameters 3865 # This is exactly what the method proj_coeff method does. 3866 my @array; 3867 if (defined($errors) ) { 3868 @array = (); # new Matrix($dim_of_param_space,1); 3869 } else { 3870 @array = $matrix->proj_coeff($rhs_vec)->list(); 3871 } 3872 # check size (hack) 3873 my $max = 0; 3874 foreach my $val (@array ) { 3875 $max = abs($val) if $max < abs($val); 3876 if (not is_a_number($val) ) { 3877 $max = "NaN: $val"; 3878 last; 3879 } 3880 } 3881 if ($max =~/NaN/) { 3882 $errors .= "WeBWorK was unable evaluate your function. Please check that your 3883 expression doesn't take roots of negative numbers, or divide by zero."; 3884 } elsif ($max > $options{maxConstantOfIntegration} ) { 3885 $errors .= "At least one of the adapting parameters 3886 (perhaps the constant of integration) is too large: $max, 3887 ( the maximum allowed is $options{maxConstantOfIntegration} )"; 3888 } 3889 3890 $rh_ans->{ra_parameters} = \@array; 3891 $rh_ans->throw_error('EVAL', $errors) if defined($errors); 3892 $rh_ans; 3893 } 3894 3895 =head4 calculate_difference_vector 3896 3897 calculate_difference_vector( $ans_hash, %options); 3898 3899 {rf_student_ans}, # a reference to the test function 3900 {rf_correct_ans}, # a reference to the correct answer function 3901 {evaluation_points}, # an array of row vectors indicating the points 3902 # to evaluate when comparing the functions 3903 {ra_parameters} # these are the (optional) additional inputs to 3904 # the comparison function which adapt it properly 3905 # to the problem at hand. 3906 3907 %options # mode => 'rel' specifies that each element in the 3908 # difference matrix is divided by the correct answer. 3909 # unless the correct answer is nearly 0. 3910 ) 3911 3912 =cut 3913 3914 sub calculate_difference_vector { 3915 my $rh_ans = shift; 3916 my %options = @_; 3917 assign_option_aliases( \%options, 3918 ); 3919 set_default_options( \%options, 3920 allow_unknown_options => 1, 3921 stdin1 => 'rf_student_ans', 3922 stdin2 => 'rf_correct_ans', 3923 stdout => 'ra_differences', 3924 debug => 0, 3925 tolType => 'absolute', 3926 error_msg_flag => 1, 3927 ); 3928 # initialize 3929 $rh_ans->{_filter_name} = 'calculate_difference_vector'; 3930 my $rf_fun = $rh_ans -> {$options{stdin1}}; # rf_student_ans by default 3931 my $rf_correct_fun = $rh_ans -> {$options{stdin2}}; # rf_correct_ans by default 3932 my $ra_parameters = $rh_ans -> {ra_parameters}; 3933 my @evaluation_points = @{$rh_ans->{evaluation_points} }; 3934 my @parameters = (); 3935 @parameters = @$ra_parameters if defined($ra_parameters) and ref($ra_parameters) eq 'ARRAY'; 3936 my $errors = undef; 3937 my @zero_params = (); 3938 for (my $i=1;$i<=@{$ra_parameters};$i++) { 3939 push(@zero_params,0); 3940 } 3941 my @differences = (); 3942 my @student_values; 3943 my @adjusted_student_values; 3944 my @instructorVals; 3945 my ($diff,$instructorVal); 3946 # calculate the vector of differences between the test function and the comparison function. 3947 while (@evaluation_points) { 3948 my ($err1, $err2,$err3); 3949 my @vars = @{ shift(@evaluation_points) }; 3950 my @inputs = (@vars, @parameters); 3951 my ($inVal, $correctVal); 3952 ($inVal, $err1) = &{$rf_fun}(@vars); 3953 $errors .= " $err1 " if defined($err1); 3954 $errors .= " Error detected evaluating student input at (".join(' , ',@vars) ." ) " if defined($options{debug}) and $options{debug}==1 and defined($err1); 3955 ($correctVal, $err2) =&{$rf_correct_fun}(@inputs); 3956 $errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err2 " if defined($err2); 3957 $errors .= " Error detected evaluating correct adapted answer at (".join(' , ',@inputs) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err2); 3958 ($instructorVal,$err3)= &$rf_correct_fun(@vars, @zero_params); 3959 $errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err3 " if defined($err3); 3960 $errors .= " Error detected evaluating instructor answer at (".join(' , ',@vars, @zero_params) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err3); 3961 unless (defined($err1) or defined($err2) or defined($err3) ) { 3962 $diff = ( $inVal - ($correctVal -$instructorVal ) ) - $instructorVal; #prevents entering too high a number? 3963 #warn "taking the difference of ", $inVal, " and ", $correctVal, " is ", $diff; 3964 if ( $options{tolType} eq 'relative' ) { #relative tolerance 3965 #warn "diff = $diff"; 3966 #$diff = ( $inVal - ($correctVal-$instructorVal ) )/abs($instructorVal) -1 if abs($instructorVal) > $options{zeroLevel}; 3967 $diff = ( $inVal - ($correctVal-$instructorVal ) )/$instructorVal -1 if abs($instructorVal) > $options{zeroLevel}; 3968 #$diff = ( $inVal - ($correctVal-$instructorVal- $instructorVal ) )/abs($instructorVal) if abs($instructorVal) > $options{zeroLevel}; 3969 #warn "diff = $diff, ", abs( &$rf_correct_fun(@inputs) ) , "-- $correctVal"; 3970 } 3971 } 3972 last if $errors; # break if there are any errors. 3973 # This cuts down on the size of error messages. 3974 # However it impossible to check for equivalence at 95% of points 3975 # which might be useful for functions that are not defined at some points. 3976 push(@student_values,$inVal); 3977 push(@adjusted_student_values,( $inVal - ($correctVal -$instructorVal) ) ); 3978 push(@differences, $diff); 3979 push(@instructorVals,$instructorVal); 3980 } 3981 if (( not defined($errors) ) or $errors eq '' or $options{error_msg_flag} ) { 3982 $rh_ans ->{$options{stdout}} = \@differences; 3983 $rh_ans ->{ra_student_values} = \@student_values; 3984 $rh_ans ->{ra_adjusted_student_values} = \@adjusted_student_values; 3985 $rh_ans->{ra_instructor_values}=\@instructorVals; 3986 $rh_ans->throw_error('EVAL', $errors) if defined($errors); 3987 } else { 3988 3989 } # no output if error_msg_flag is set to 0. 3990 3991 $rh_ans; 3992 } 3993 3994 =head4 fix_answer_for_display 3995 3996 =cut 3997 3998 sub fix_answers_for_display { 3999 my ($rh_ans, %options) = @_; 4000 if ( $rh_ans->{answerIsString} ==1) { 4001 $rh_ans = evaluatesToNumber ($rh_ans, %options); 4002 } 4003 if (defined ($rh_ans->{student_units})) { 4004 $rh_ans->{student_ans} = $rh_ans->{student_ans}. ' '. $rh_ans->{student_units}; 4005 4006 } 4007 if ( $rh_ans->catch_error('UNITS') ) { # create preview latex string for expressions even if the units are incorrect 4008 my $rh_temp = new AnswerHash; 4009 $rh_temp->{student_ans} = $rh_ans->{student_ans}; 4010 $rh_temp = check_syntax($rh_temp); 4011 $rh_ans->{preview_latex_string} = $rh_temp->{preview_latex_string}; 4012 } 4013 $rh_ans->{correct_ans} = $rh_ans->{original_correct_ans}; 4014 4015 $rh_ans; 4016 } 4017 4018 =head4 evaluatesToNumber 4019 4020 =cut 4021 4022 sub evaluatesToNumber { 4023 my ($rh_ans, %options) = @_; 4024 if (is_a_numeric_expression($rh_ans->{student_ans})) { 4025 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($rh_ans->{student_ans}); 4026 if ($PG_eval_errors) { # this if statement should never be run 4027 # change nothing 4028 } else { 4029 # change this 4030 $rh_ans->{student_ans} = prfmt($inVal,$options{format}); 4031 } 4032 } 4033 $rh_ans; 4034 } 4035 4036 =head4 is_numeric_expression 4037 4038 =cut 4039 4040 sub is_a_numeric_expression { 4041 my $testString = shift; 4042 my $is_a_numeric_expression = 0; 4043 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($testString); 4044 if ($PG_eval_errors) { 4045 $is_a_numeric_expression = 0; 4046 } else { 4047 $is_a_numeric_expression = 1; 4048 } 4049 $is_a_numeric_expression; 4050 } 4051 4052 =head4 is_a_number 4053 4054 =cut 4055 4056 sub is_a_number { 4057 my ($num,%options) = @_; 4058 my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ; 4059 my ($rh_ans); 4060 if ($process_ans_hash) { 4061 $rh_ans = $num; 4062 $num = $rh_ans->{student_ans}; 4063 } 4064 4065 my $is_a_number = 0; 4066 return $is_a_number unless defined($num); 4067 $num =~ s/^\s*//; ## remove initial spaces 4068 $num =~ s/\s*$//; ## remove trailing spaces 4069 4070 ## the following is copied from the online perl manual 4071 if ($num =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/){ 4072 $is_a_number = 1; 4073 } 4074 4075 if ($process_ans_hash) { 4076 if ($is_a_number == 1 ) { 4077 $rh_ans->{student_ans}=$num; 4078 return $rh_ans; 4079 } else { 4080 $rh_ans->{student_ans} = "Incorrect number format: You must enter a number, e.g. -6, 5.3, or 6.12E-3"; 4081 $rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3'); 4082 return $rh_ans; 4083 } 4084 } else { 4085 return $is_a_number; 4086 } 4087 } 4088 4089 =head4 is_a_fraction 4090 4091 =cut 4092 4093 sub is_a_fraction { 4094 my ($num,%options) = @_; 4095 my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ; 4096 my ($rh_ans); 4097 if ($process_ans_hash) { 4098 $rh_ans = $num; 4099 $num = $rh_ans->{student_ans}; 4100 } 4101 4102 my $is_a_fraction = 0; 4103 return $is_a_fraction unless defined($num); 4104 $num =~ s/^\s*//; ## remove initial spaces 4105 $num =~ s/\s*$//; ## remove trailing spaces 4106 4107 if ($num =~ /^\s*\-?\s*[\/\d\.Ee\s]*$/) { 4108 $is_a_fraction = 1; 4109 } 4110 4111 if ($process_ans_hash) { 4112 if ($is_a_fraction == 1 ) { 4113 $rh_ans->{student_ans}=$num; 4114 return $rh_ans; 4115 } else { 4116 $rh_ans->{student_ans} = "Not a number of fraction: You must enter a number or fraction, e.g. -6 or 7/13"; 4117 $rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3'); 4118 return $rh_ans; 4119 } 4120 4121 } else { 4122 return $is_a_fraction; 4123 } 4124 } 4125 4126 =head4 phase_pi 4127 I often discovered that the answers I was getting, when using the arctan function would be off by phases of 4128 pi, which for the tangent function, were equivalent values. This method allows for this. 4129 =cut 4130 4131 sub phase_pi { 4132 my ($num,%options) = @_; 4133 my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ; 4134 my ($rh_ans); 4135 if ($process_ans_hash) { 4136 $rh_ans = $num; 4137 $num = $rh_ans->{correct_ans}; 4138 } 4139 while( ($rh_ans->{correct_ans}) > 3.14159265358979/2 ){ 4140 $rh_ans->{correct_ans} -= 3.14159265358979; 4141 } 4142 while( ($rh_ans->{correct_ans}) <= -3.14159265358979/2 ){ 4143 $rh_ans->{correct_ans} += 3.14159265358979; 4144 } 4145 $rh_ans; 4146 } 4147 4148 =head4 is_an_arithemetic_expression 4149 4150 =cut 4151 4152 sub is_an_arithmetic_expression { 4153 my ($num,%options) = @_; 4154 my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ; 4155 my ($rh_ans); 4156 if ($process_ans_hash) { 4157 $rh_ans = $num; 4158 $num = $rh_ans->{student_ans}; 4159 } 4160 4161 my $is_an_arithmetic_expression = 0; 4162 return $is_an_arithmetic_expression unless defined($num); 4163 $num =~ s/^\s*//; ## remove initial spaces 4164 $num =~ s/\s*$//; ## remove trailing spaces 4165 4166 if ($num =~ /^[+\-*\/\^\(\)\[\]\{\}\s\d\.Ee]*$/) { 4167 $is_an_arithmetic_expression = 1; 4168 } 4169 4170 if ($process_ans_hash) { 4171 if ($is_an_arithmetic_expression == 1 ) { 4172 $rh_ans->{student_ans}=$num; 4173 return $rh_ans; 4174 } else { 4175 4176 $rh_ans->{student_ans} = "Not an arithmetic expression: You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2"; 4177 $rh_ans->throw_error('NUMBER', 'You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2'); 4178 return $rh_ans; 4179 } 4180 4181 } else { 4182 return $is_an_arithmetic_expression; 4183 } 4184 } 4185 4186 # 4187 4188 =head4 math_constants 4189 4190 replaces pi, e, and ^ with their Perl equivalents 4191 if useBaseTenLog is non-zero, convert log to logten 4192 4193 =cut 4194 4195 sub math_constants { 4196 my($in,%options) = @_; 4197 my $rh_ans; 4198 my $process_ans_hash = ( ref( $in ) eq 'AnswerHash' ) ? 1 : 0 ; 4199 if ($process_ans_hash) { 4200 $rh_ans = $in; 4201 $in = $rh_ans->{student_ans}; 4202 } 4203 # The code fragment above allows this filter to be used when the input is simply a string 4204 # as well as when the input is an AnswerHash, and options. 4205 $in =~s/\bpi\b/(4*atan2(1,1))/ge; 4206 $in =~s/\be\b/(exp(1))/ge; 4207 $in =~s/\^/**/g; 4208 if($useBaseTenLog) { 4209 $in =~ s/\blog\b/logten/g; 4210 } 4211 4212 if ($process_ans_hash) { 4213 $rh_ans->{student_ans}=$in; 4214 return $rh_ans; 4215 } else { 4216 return $in; 4217 } 4218 } 4219 4220 4221 4222 =head4 is_array 4223 4224 is_array($rh_ans) 4225 returns: $rh_ans. Throws error "NOTARRAY" if this is not an array 4226 4227 =cut 4228 4229 sub is_array { 4230 my $rh_ans = shift; 4231 # return if the result is an array 4232 return($rh_ans) if ref($rh_ans->{student_ans}) eq 'ARRAY' ; 4233 $rh_ans->throw_error("NOTARRAY","The answer is not an array"); 4234 $rh_ans; 4235 } 4236 4237 =head4 check_syntax 4238 4239 check_syntax( $rh_ans, %options) 4240 returns an answer hash. 4241 4242 latex2html preview code are installed in the answer hash. 4243 The input has been transformed, changing 7pi to 7*pi or 7x to 7*x. 4244 Syntax error messages may be generated and stored in student_ans 4245 Additional syntax error messages are stored in {ans_message} and duplicated in {error_message} 4246 4247 4248 =cut 4249 4250 sub check_syntax { 4251 my $rh_ans = shift; 4252 my %options = @_; 4253 assign_option_aliases(\%options, 4254 ); 4255 set_default_options( \%options, 4256 'stdin' => 'student_ans', 4257 'stdout' => 'student_ans', 4258 'ra_vars' => [qw( x y )], 4259 'debug' => 0, 4260 '_filter_name' => 'check_syntax', 4261 error_msg_flag => 1, 4262 ); 4263 #initialize 4264 $rh_ans->{_filter_name} = $options{_filter_name}; 4265 unless ( defined( $rh_ans->{$options{stdin}} ) ) { 4266 warn "Check_syntax requires an equation in the field '$options{stdin}' or input"; 4267 $rh_ans->throw_error("1","'$options{stdin}' field not defined"); 4268 return $rh_ans; 4269 } 4270 my $in = $rh_ans->{$options{stdin}}; 4271 my $parser = new AlgParserWithImplicitExpand; 4272 my $ret = $parser -> parse($in); #for use with loops 4273 4274 if ( ref($ret) ) { ## parsed successfully 4275 # $parser -> tostring(); # FIXME? was this needed for some reason????? 4276 $parser -> normalize(); 4277 $rh_ans -> {$options{stdout}} = $parser -> tostring(); 4278 $rh_ans -> {preview_text_string} = $in; 4279 $rh_ans -> {preview_latex_string} = $parser -> tolatex(); 4280 4281 } elsif ($options{error_msg_flag} ) { ## error in parsing 4282 4283 $rh_ans->{$options{stdout}} = 'syntax error:'. $parser->{htmlerror}, 4284 $rh_ans->{'ans_message'} = $parser -> {error_msg}, 4285 $rh_ans->{'preview_text_string'} = '', 4286 $rh_ans->{'preview_latex_string'} = '', 4287 $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'. $parser->{htmlerror} . "$BR" .$parser -> {error_msg}); 4288 } # no output is produced if there is an error and the error_msg_flag is set to zero 4289 $rh_ans; 4290 4291 } 4292 4293 =head4 check_strings 4294 4295 check_strings ($rh_ans, %options) 4296 returns $rh_ans 4297 4298 =cut 4299 4300 sub check_strings { 4301 my ($rh_ans, %options) = @_; 4302 4303 # if the student's answer is a number, simply return the answer hash (unchanged). 4304 4305 # we allow constructions like -INF to be treated as a string. Thus we ignore an initial 4306 # - in deciding whether the student's answer is a number or string 4307 4308 my $temp_ans = $rh_ans->{student_ans}; 4309 $temp_ans =~ s/^\s*\-//; # remove an initial - 4310 4311 if ( $temp_ans =~ m/[\d+\-*\/^(){}\[\]]|^\s*e\s*$|^\s*pi\s*$/) { 4312 # if ( $rh_ans->{answerIsString} == 1) { 4313 # #$rh_ans->throw_error('STRING','Incorrect Answer'); # student's answer is a number 4314 # } 4315 return $rh_ans; 4316 } 4317 # the student's answer is recognized as a string 4318 my $ans = $rh_ans->{student_ans}; 4319 4320 # OVERVIEW of reminder of function: 4321 # if answer is correct, return correct. (adjust score to 1) 4322 # if answer is incorect: 4323 # 1) determine if the answer is sensible. if it is, return incorrect. 4324 # 2) if the answer is not sensible (and incorrect), then return an error message indicating so. 4325 # no matter what: throw a 'STRING' error to skip numerical evaluations. (error flag skips remainder of pre_filters and evaluators) 4326 # last: 'STRING' post_filter will clear the error (avoiding pink screen.) 4327 4328 my $sensibleAnswer = 0; 4329 $ans = str_filters( $ans, 'compress_whitespace' ); # remove trailing, leading, and double spaces. 4330 my ($ans_eval) = str_cmp($rh_ans->{correct_ans}); 4331 my $temp_ans_hash = $ans_eval->evaluate($ans); 4332 $rh_ans->{test} = $temp_ans_hash; 4333 4334 if ($temp_ans_hash->{score} ==1 ) { # students answer matches the correct answer. 4335 $rh_ans->{score} = 1; 4336 $sensibleAnswer = 1; 4337 } else { # students answer does not match the correct answer. 4338 my $legalString = ''; # find out if string makes sense 4339 my @legalStrings = @{$options{strings}}; 4340 foreach $legalString (@legalStrings) { 4341 if ( uc($ans) eq uc($legalString) ) { 4342 $sensibleAnswer = 1; 4343 last; 4344 } 4345 } 4346 $sensibleAnswer = 1 unless $ans =~ /\S/; ## empty answers are sensible 4347 $rh_ans->throw_error('EVAL', "Your answer is not a recognized answer") unless ($sensibleAnswer); 4348 # $temp_ans_hash -> setKeys( 'ans_message' => 'Your answer is not a recognized answer' ) unless ($sensibleAnswer); 4349 # $temp_ans_hash -> setKeys( 'student_ans' => uc($ans) ); 4350 } 4351 4352 $rh_ans->{student_ans} = $ans; 4353 4354 if ($sensibleAnswer) { 4355 $rh_ans->throw_error('STRING', "The student's answer $rh_ans->{student_ans} is interpreted as a string."); 4356 } 4357 4358 $rh_ans->{'preview_text_string'} = $ans, 4359 $rh_ans->{'preview_latex_string'} = $ans, 4360 4361 # warn ("\$rh_ans->{answerIsString} = $rh_ans->{answerIsString}"); 4362 $rh_ans; 4363 } 4364 4365 =head4 check_units 4366 4367 check_strings ($rh_ans, %options) 4368 returns $rh_ans 4369 4370 4371 =cut 4372 4373 sub check_units { 4374 my ($rh_ans, %options) = @_; 4375 my %correct_units = %{$rh_ans-> {rh_correct_units}}; 4376 my $ans = $rh_ans->{student_ans}; 4377 # $ans = '' unless defined ($ans); 4378 $ans = str_filters ($ans, 'trim_whitespace'); 4379 my $original_student_ans = $ans; 4380 $rh_ans->{original_student_ans} = $original_student_ans; 4381 4382 # it surprises me that the match below works since the first .* is greedy. 4383 my ($num_answer, $units) = $ans =~ /^(.*)\s+([^\s]*)$/; 4384 4385 unless ( defined($num_answer) && $units ) { 4386 # there is an error reading the input 4387 if ( $ans =~ /\S/ ) { # the answer is not blank 4388 $rh_ans -> setKeys( 'ans_message' => "The answer \"$ans\" could not be interpreted " . 4389 "as a number or an arithmetic expression followed by a unit specification. " . 4390 "Your answer must contain units." ); 4391 $rh_ans->throw_error('UNITS', "The answer \"$ans\" could not be interpreted " . 4392 "as a number or an arithmetic expression followed by a unit specification. " . 4393 "Your answer must contain units." ); 4394 } 4395 return $rh_ans; 4396 } 4397 4398 # we have been able to parse the answer into a numerical part and a unit part 4399 4400 # $num_answer = $1; #$1 and $2 from the regular expression above 4401 # $units = $2; 4402 4403 my %units = Units::evaluate_units($units); 4404 if ( defined( $units{'ERROR'} ) ) { 4405 # handle error condition 4406 $units{'ERROR'} = clean_up_error_msg($units{'ERROR'}); 4407 $rh_ans -> setKeys( 'ans_message' => "$units{'ERROR'}" ); 4408 $rh_ans -> throw_error('UNITS', "$units{'ERROR'}"); 4409 return $rh_ans; 4410 } 4411 4412 my $units_match = 1; 4413 my $fund_unit; 4414 foreach $fund_unit (keys %correct_units) { 4415 next if $fund_unit eq 'factor'; 4416 $units_match = 0 unless $correct_units{$fund_unit} == $units{$fund_unit}; 4417 } 4418 4419 if ( $units_match ) { 4420 # units are ok. Evaluate the numerical part of the answer 4421 $rh_ans->{'tolerance'} = $rh_ans->{'tolerance'}* $correct_units{'factor'}/$units{'factor'} if 4422 $rh_ans->{'tolType'} eq 'absolute'; # the tolerance is in the units specified by the instructor. 4423 $rh_ans->{correct_ans} = prfmt($rh_ans->{correct_ans}*$correct_units{'factor'}/$units{'factor'}); 4424 $rh_ans->{student_units} = $units; 4425 $rh_ans->{student_ans} = $num_answer; 4426 4427 } else { 4428 $rh_ans -> setKeys( ans_message => 'There is an error in the units for this answer.' ); 4429 $rh_ans -> throw_error ( 'UNITS', 'There is an error in the units for this answer.' ); 4430 } 4431 4432 return $rh_ans; 4433 } 4434 4435 4436 4437 =head2 Filter utilities 4438 4439 These two subroutines can be used in filters to set default options. They 4440 help make filters perform in uniform, predictable ways, and also make it 4441 easy to recognize from the code which options a given filter expects. 4442 4443 4444 =head4 assign_option_aliases 4445 4446 Use this to assign aliases for the standard options. It must come before set_default_options 4447 within the subroutine. 4448 4449 assign_option_aliases(\%options, 4450 'alias1' => 'option5' 4451 'alias2' => 'option7' 4452 ); 4453 4454 4455 If the subroutine is called with an option " alias1 => 23 " it will behave as if it had been 4456 called with the option " option5 => 23 " 4457 4458 =cut 4459 4460 4461 4462 sub assign_option_aliases { 4463 my $rh_options = shift; 4464 warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH'; 4465 my @option_aliases = @_; 4466 while (@option_aliases) { 4467 my $alias = shift @option_aliases; 4468 my $option_key = shift @option_aliases; 4469 4470 if (defined($rh_options->{$alias} )) { # if the alias appears in the option list 4471 if (not defined($rh_options->{$option_key}) ) { # and the option itself is not defined, 4472 $rh_options->{$option_key} = $rh_options->{$alias}; # insert the value defined by the alias into the option value 4473 # the FIRST alias for a given option takes precedence 4474 # (after the option itself) 4475 } else { 4476 warn "option $option_key is already defined as", $rh_options->{$option_key}, "<br>\n", 4477 "The attempt to override this option with the alias $alias with value ", $rh_options->{$alias}, 4478 " was ignored."; 4479 } 4480 } 4481 delete($rh_options->{$alias}); # remove the alias from the initial list 4482 } 4483 4484 } 4485 4486 =head4 set_default_options 4487 4488 set_default_options(\%options, 4489 '_filter_name' => 'filter', 4490 'option5' => .0001, 4491 'option7' => 'ascii', 4492 'allow_unknown_options => 0, 4493 } 4494 4495 Note that the first entry is a reference to the options with which the filter was called. 4496 4497 The option5 is set to .0001 unless the option is explicitly set when the subroutine is called. 4498 4499 The B<'_filter_name'> option should always be set, although there is no error if it is missing. 4500 It is used mainly for debugging answer evaluators and allows 4501 you to keep track of which filter is currently processing the answer. 4502 4503 If B<'allow_unknown_options'> is set to 0 then if the filter is called with options which do NOT appear in the 4504 set_default_options list an error will be signaled and a warning message will be printed out. This provides 4505 error checking against misspelling an option and is generally what is desired for most filters. 4506 4507 Occasionally one wants to write a filter which accepts a long list of options, not all of which are known in advance, 4508 but only uses a subset of the options 4509 provided. In this case, setting 'allow_unkown_options' to 1 prevents the error from being signaled. 4510 4511 =cut 4512 4513 sub set_default_options { 4514 my $rh_options = shift; 4515 warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH'; 4516 my %default_options = @_; 4517 unless ( defined($default_options{allow_unknown_options}) and $default_options{allow_unknown_options} == 1 ) { 4518 foreach my $key1 (keys %$rh_options) { 4519 warn "This option |$key1| is not recognized in this subroutine<br> ", pretty_print($rh_options) unless exists($default_options{$key1}); 4520 } 4521 } 4522 foreach my $key (keys %default_options) { 4523 if ( not defined($rh_options->{$key} ) and defined( $default_options{$key} ) ) { 4524 $rh_options->{$key} = $default_options{$key}; #this allows tol => undef to allow the tol option, but doesn't define 4525 # this key unless tol is explicitly defined. 4526 } 4527 } 4528 } 4529 4530 =head2 Problem Grader Subroutines 4531 4532 =cut 4533 4534 ## Problem Grader Subroutines 4535 4536 ##################################### 4537 # This is a model for plug-in problem graders 4538 ##################################### 4539 sub install_problem_grader { 4540 my $rf_problem_grader = shift; 4541 my $rh_flags = PG_restricted_eval(q!\\%main::PG_FLAGS!); 4542 $rh_flags->{PROBLEM_GRADER_TO_USE} = $rf_problem_grader; 4543 } 4544 4545 =head4 std_problem_grader 4546 4547 This is an all-or-nothing grader. A student must get all parts of the problem write 4548 before receiving credit. You should make sure to use this grader on multiple choice 4549 and true-false questions, otherwise students will be able to deduce how many 4550 answers are correct by the grade reported by webwork. 4551 4552 4553 install_problem_grader(~~&std_problem_grader); 4554 4555 =cut 4556 4557 sub std_problem_grader { 4558 my $rh_evaluated_answers = shift; 4559 my $rh_problem_state = shift; 4560 my %form_options = @_; 4561 my %evaluated_answers = %{$rh_evaluated_answers}; 4562 # The hash $rh_evaluated_answers typically contains: 4563 # 'answer1' => 34, 'answer2'=> 'Mozart', etc. 4564 4565 # By default the old problem state is simply passed back out again. 4566 my %problem_state = %$rh_problem_state; 4567 4568 # %form_options might include 4569 # The user login name 4570 # The permission level of the user 4571 # The studentLogin name for this psvn. 4572 # Whether the form is asking for a refresh or is submitting a new answer. 4573 4574 # initial setup of the answer 4575 my %problem_result = ( score => 0, 4576 errors => '', 4577 type => 'std_problem_grader', 4578 msg => '', 4579 ); 4580 # Checks 4581 4582 my $ansCount = keys %evaluated_answers; # get the number of answers 4583 4584 unless ($ansCount > 0 ) { 4585 4586 $problem_result{msg} = "This problem did not ask any questions."; 4587 return(\%problem_result,\%problem_state); 4588 } 4589 4590 if ($ansCount > 1 ) { 4591 $problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ; 4592 } 4593 4594 unless ($form_options{answers_submitted} == 1) { 4595 return(\%problem_result,\%problem_state); 4596 } 4597 4598 my $allAnswersCorrectQ=1; 4599 foreach my $ans_name (keys %evaluated_answers) { 4600 # I'm not sure if this check is really useful. 4601 if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) { 4602 $allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} ); 4603 } 4604 else { 4605 die "Error at file ",__FILE__,"line ", __LINE__,": Answer |$ans_name| is not a hash reference\n". 4606 $evaluated_answers{$ans_name} . 4607 "This probably means that the answer evaluator for this answer\n" . 4608 "is not working correctly."; 4609 $problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}"; 4610 } 4611 } 4612 # report the results 4613 $problem_result{score} = $allAnswersCorrectQ; 4614 4615 # I don't like to put in this bit of code. 4616 # It makes it hard to construct error free problem graders 4617 # I would prefer to know that the problem score was numeric. 4618 unless (defined($problem_state{recorded_score}) and $problem_state{recorded_score} =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/ ) { 4619 $problem_state{recorded_score} = 0; # This gets rid of non-numeric scores 4620 } 4621 # 4622 if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) { 4623 $problem_state{recorded_score} = 1; 4624 } 4625 else { 4626 $problem_state{recorded_score} = 0; 4627 } 4628 4629 $problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1; 4630 $problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0; 4631 4632 $problem_state{state_summary_msg} = ''; # an HTML formatted message printed at the bottom of the problem page 4633 4634 (\%problem_result, \%problem_state); 4635 } 4636 4637 =head4 std_problem_grader2 4638 4639 This is an all-or-nothing grader. A student must get all parts of the problem write 4640 before receiving credit. You should make sure to use this grader on multiple choice 4641 and true-false questions, otherwise students will be able to deduce how many 4642 answers are correct by the grade reported by webwork. 4643 4644 4645 install_problem_grader(~~&std_problem_grader2); 4646 4647 The only difference between the two versions 4648 is at the end of the subroutine, where std_problem_grader2 4649 records the attempt only if there have been no syntax errors, 4650 whereas std_problem_grader records it regardless. 4651 4652 =cut 4653 4654 4655 4656 sub std_problem_grader2 { 4657 my $rh_evaluated_answers = shift; 4658 my $rh_problem_state = shift; 4659 my %form_options = @_; 4660 my %evaluated_answers = %{$rh_evaluated_answers}; 4661 # The hash $rh_evaluated_answers typically contains: 4662 # 'answer1' => 34, 'answer2'=> 'Mozart', etc. 4663 4664 # By default the old problem state is simply passed back out again. 4665 my %problem_state = %$rh_problem_state; 4666 4667 # %form_options might include 4668 # The user login name 4669 # The permission level of the user 4670 # The studentLogin name for this psvn. 4671 # Whether the form is asking for a refresh or is submitting a new answer. 4672 4673 # initial setup of the answer 4674 my %problem_result = ( score => 0, 4675 errors => '', 4676 type => 'std_problem_grader', 4677 msg => '', 4678 ); 4679 4680 # syntax errors are not counted. 4681 my $record_problem_attempt = 1; 4682 # Checks 4683 4684 my $ansCount = keys %evaluated_answers; # get the number of answers 4685 unless ($ansCount > 0 ) { 4686 $problem_result{msg} = "This problem did not ask any questions."; 4687 return(\%problem_result,\%problem_state); 4688 } 4689 4690 if ($ansCount > 1 ) { 4691 $problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ; 4692 } 4693 4694 unless ($form_options{answers_submitted} == 1) { 4695 return(\%problem_result,\%problem_state); 4696 } 4697 4698 my $allAnswersCorrectQ=1; 4699 foreach my $ans_name (keys %evaluated_answers) { 4700 # I'm not sure if this check is really useful. 4701 if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) { 4702 $allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} ); 4703 } 4704 else { 4705 die "Error at file ",__FILE__,"line ", __LINE__,": Answer |$ans_name| is not a hash reference\n". 4706 $evaluated_answers{$ans_name} . 4707 "This probably means that the answer evaluator for this answer\n" . 4708 "is not working correctly."; 4709 $problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}"; 4710 } 4711 } 4712 # report the results 4713 $problem_result{score} = $allAnswersCorrectQ; 4714 4715 # I don't like to put in this bit of code. 4716 # It makes it hard to construct error free problem graders 4717 # I would prefer to know that the problem score was numeric. 4718 unless ($problem_state{recorded_score} =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/ ) { 4719 $problem_state{recorded_score} = 0; # This gets rid of non-numeric scores 4720 } 4721 # 4722 if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) { 4723 $problem_state{recorded_score} = 1; 4724 } 4725 else { 4726 $problem_state{recorded_score} = 0; 4727 } 4728 # record attempt only if there have been no syntax errors. 4729 4730 if ($record_problem_attempt == 1) { 4731 $problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1; 4732 $problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0; 4733 $problem_state{state_summary_msg} = ''; # an HTML formatted message printed at the bottom of the problem page 4734 4735 } 4736 else { 4737 $problem_result{show_partial_correct_answers} = 0 ; # prevent partial correct answers from being shown for syntax errors. 4738 } 4739 (\%problem_result, \%problem_state); 4740 } 4741 4742 =head4 avg_problem_grader 4743 4744 This grader gives a grade depending on how many questions from the problem are correct. (The highest 4745 grade is the one that is kept. One can never lower the recorded grade on a problem by repeating it.) 4746 Many professors (and almost all students :-) ) prefer this grader. 4747 4748 4749 install_problem_grader(~~&avg_problem_grader); 4750 4751 =cut 4752 4753 4754 sub avg_problem_grader { 4755 my $rh_evaluated_answers = shift; 4756 my $rh_problem_state = shift; 4757 my %form_options = @_; 4758 my %evaluated_answers = %{$rh_evaluated_answers}; 4759 # The hash $rh_evaluated_answers typically contains: 4760 # 'answer1' => 34, 'answer2'=> 'Mozart', etc. 4761 4762 # By default the old problem state is simply passed back out again. 4763 my %problem_state = %$rh_problem_state; 4764 4765 4766 # %form_options might include 4767 # The user login name 4768 # The permission level of the user 4769 # The studentLogin name for this psvn. 4770 # Whether the form is asking for a refresh or is submitting a new answer. 4771 4772 # initial setup of the answer 4773 my $total=0; 4774 my %problem_result = ( score => 0, 4775 errors => '', 4776 type => 'avg_problem_grader', 4777 msg => '', 4778 ); 4779 my $count = keys %evaluated_answers; 4780 $problem_result{msg} = 'You can earn partial credit on this problem.' if $count >1; 4781 # Return unless answers have been submitted 4782 unless ($form_options{answers_submitted} == 1) { 4783 return(\%problem_result,\%problem_state); 4784 } 4785 4786 # Answers have been submitted -- process them. 4787 foreach my $ans_name (keys %evaluated_answers) { 4788 # I'm not sure if this check is really useful. 4789 if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) { 4790 $total += $evaluated_answers{$ans_name}->{score}; 4791 } 4792 else { 4793 die "Error: Answer |$ans_name| is not a hash reference\n". 4794 $evaluated_answers{$ans_name} . 4795 "This probably means that the answer evaluator for this answer\n" . 4796 "is not working correctly."; 4797 $problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}"; 4798 } 4799 } 4800 # Calculate score rounded to three places to avoid roundoff problems 4801 $problem_result{score} = $total/$count if $count; 4802 # increase recorded score if the current score is greater. 4803 $problem_state{recorded_score} = $problem_result{score} if $problem_result{score} > $problem_state{recorded_score}; 4804 4805 4806 $problem_state{num_of_correct_ans}++ if $total == $count; 4807 $problem_state{num_of_incorrect_ans}++ if $total < $count ; 4808 4809 $problem_state{state_summary_msg} = ''; # an HTML formatted message printed at the bottom of the problem page 4810 4811 warn "Error in grading this problem the total $total is larger than $count" if $total > $count; 4812 (\%problem_result, \%problem_state); 4813 } 4814 4815 =head2 Utility subroutines 4816 4817 =head4 4818 4819 warn pretty_print( $rh_hash_input) 4820 4821 This can be very useful for printing out messages about objects while debugging 4822 4823 =cut 4824 4825 sub pretty_print { 4826 my $r_input = shift; 4827 my $out = ''; 4828 if ( not ref($r_input) ) { 4829 $out = $r_input; # not a reference 4830 } elsif ("$r_input" =~/hash/i) { # this will pick up objects whose '$self' is hash and so works better than ref($r_iput). 4831 local($^W) = 0; 4832 $out .= "$r_input " ."<TABLE border = \"2\" cellpadding = \"3\" BGCOLOR = \"#FFFFFF\">"; 4833 foreach my $key (lex_sort( keys %$r_input )) { 4834 $out .= "<tr><TD> $key</TD><TD>=></td><td> ".pretty_print($r_input->{$key}) . "</td></tr>"; 4835 } 4836 $out .="</table>"; 4837 } elsif (ref($r_input) eq 'ARRAY' ) { 4838 my @array = @$r_input; 4839 $out .= "( " ; 4840 while (@array) { 4841 $out .= pretty_print(shift @array) . " , "; 4842 } 4843 $out .= " )"; 4844 } elsif (ref($r_input) eq 'CODE') { 4845 $out = "$r_input"; 4846 } else { 4847 $out = $r_input; 4848 } 4849 $out; 4850 } 4851 4852 1;
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