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give answer is equivalent message regardless of correctness. fixes bug #752.
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 unless $context->strings->get(uc($string)); 1085 } 1086 } 1087 1088 # 1089 # Set the tolerances 1090 # 1091 if ($num_params{tolType} eq 'absolute') { 1092 $context->flags->set( 1093 tolerance => $num_params{tolerance}, 1094 tolType => 'absolute', 1095 ); 1096 } else { 1097 $context->flags->set( 1098 tolerance => .01*$num_params{tolerance}, 1099 tolType => 'relative', 1100 ); 1101 } 1102 $context->flags->set( 1103 zeroLevel => $num_params{zeroLevel}, 1104 zeroLevelTol => $num_params{zeroLevelTol}, 1105 ); 1106 1107 # 1108 # Get the proper Parser object for the professor's answer 1109 # using the initialized context 1110 # 1111 my $oldContext = &$Context(); &$Context($context); my $r; 1112 if ($num_params{units}) { 1113 $r = new Parser::Legacy::NumberWithUnits($correctAnswer); 1114 $options{rh_correct_units} = $num_params{units}; 1115 } else { 1116 $r = Value::Formula->new($correctAnswer); 1117 die "The professor's answer can't be a formula" unless $r->isConstant; 1118 $r = $r->eval; $r = new Value::Real($r) unless Value::class($r) eq 'String'; 1119 $r->{correct_ans} = $correctAnswer; 1120 if ($mode eq 'phase_pi') { 1121 my $pi = 4*atan2(1,1); 1122 while ($r > $pi/2) {$r -= $pi} 1123 while ($r < -$pi/2) {$r += $pi} 1124 } 1125 } 1126 # 1127 # Get the answer checker from the parser object 1128 # 1129 my $cmp = $r->cmp(%options); 1130 $cmp->install_pre_filter(sub { 1131 my $rh_ans = shift; 1132 $rh_ans->{original_student_ans} = $rh_ans->{student_ans}; 1133 $rh_ans->{original_correct_ans} = $rh_ans->{correct_ans}; 1134 return $rh_ans; 1135 }); 1136 $cmp->install_post_filter(sub { 1137 my $rh_ans = shift; 1138 $rh_ans->{student_ans} = $rh_ans->{student_value}->string 1139 if ref($rh_ans->{student_value}); 1140 return $rh_ans; 1141 }); 1142 &$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' => $functZeroLevelTolDefault, 1504 'debug' => 0, 1505 'diagnostics' => undef, 1506 ); 1507 1508 # allow var => 'x' as an abbreviation for var => ['x'] 1509 my %out_options = %opt; 1510 unless ( ref($out_options{var}) eq 'ARRAY' || $out_options{var} =~ m/^\d+$/) { 1511 $out_options{var} = [$out_options{var}]; 1512 } 1513 # allow params => 'c' as an abbreviation for params => ['c'] 1514 unless ( ref($out_options{params}) eq 'ARRAY' ) { 1515 $out_options{params} = [$out_options{params}]; 1516 } 1517 my ($tolType, $tol); 1518 if ($out_options{tolType} eq 'absolute') { 1519 $tolType = 'absolute'; 1520 $tol = $out_options{'tol'}; 1521 delete($out_options{'relTol'}) if exists( $out_options{'relTol'} ); 1522 } else { 1523 $tolType = 'relative'; 1524 $tol = $out_options{'relTol'}; 1525 delete($out_options{'tol'}) if exists( $out_options{'tol'} ); 1526 } 1527 1528 my @output_list = (); 1529 # thread over lists 1530 my @ans_list = (); 1531 1532 if ( ref($correctAnswer) eq 'ARRAY' ) { 1533 @ans_list = @{$correctAnswer}; 1534 } 1535 else { 1536 push( @ans_list, $correctAnswer ); 1537 } 1538 1539 # produce answer evaluators 1540 foreach my $ans (@ans_list) { 1541 push(@output_list, 1542 FUNCTION_CMP( 1543 'correctEqn' => $ans, 1544 'var' => $out_options{'var'}, 1545 'limits' => $out_options{'limits'}, 1546 'tolerance' => $tol, 1547 'tolType' => $tolType, 1548 'numPoints' => $out_options{'numPoints'}, 1549 'test_points' => $out_options{'test_points'}, 1550 'mode' => $out_options{'mode'}, 1551 'maxConstantOfIntegration' => $out_options{'maxConstantOfIntegration'}, 1552 'zeroLevel' => $out_options{'zeroLevel'}, 1553 'zeroLevelTol' => $out_options{'zeroLevelTol'}, 1554 'params' => $out_options{'params'}, 1555 'debug' => $out_options{'debug'}, 1556 'diagnostics' => $out_options{'diagnostics'} , 1557 ), 1558 ); 1559 } 1560 1561 return (wantarray) ? @output_list : $output_list[0]; 1562 } 1563 1564 =head3 Single-variable Function Comparisons 1565 1566 There are four single-variable function answer evaluators: "normal," absolute 1567 tolerance, antiderivative, and antiderivative with absolute tolerance. All 1568 parameters (other than the correct equation) are optional. 1569 1570 function_cmp( $correctEqn ) OR 1571 function_cmp( $correctEqn, $var ) OR 1572 function_cmp( $correctEqn, $var, $llimit, $ulimit ) OR 1573 function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol ) OR 1574 function_cmp( $correctEqn, $var, $llimit, $ulimit, 1575 $relPercentTol, $numPoints ) OR 1576 function_cmp( $correctEqn, $var, $llimit, $ulimit, 1577 $relPercentTol, $numPoints, $zeroLevel ) OR 1578 function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol, $numPoints, 1579 $zeroLevel,$zeroLevelTol ) 1580 1581 $correctEqn -- the correct equation, as a string 1582 $var -- the string representing the variable (optional) 1583 $llimit -- the lower limit of the interval to evaluate the 1584 variable in (optional) 1585 $ulimit -- the upper limit of the interval to evaluate the 1586 variable in (optional) 1587 $relPercentTol -- the error tolerance as a percentage (optional) 1588 $numPoints -- the number of points at which to evaluate the 1589 variable (optional) 1590 $zeroLevel -- if the correct answer is this close to zero, then 1591 zeroLevelTol applies (optional) 1592 $zeroLevelTol -- absolute tolerance to allow when answer is close to zero 1593 1594 function_cmp() uses standard comparison and relative tolerance. It takes a 1595 string representing a single-variable function and compares the student 1596 answer to that function numerically. 1597 1598 function_cmp_up_to_constant( $correctEqn ) OR 1599 function_cmp_up_to_constant( $correctEqn, $var ) OR 1600 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit ) OR 1601 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1602 $relpercentTol ) OR 1603 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1604 $relpercentTol, $numOfPoints ) OR 1605 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1606 $relpercentTol, $numOfPoints, 1607 $maxConstantOfIntegration ) OR 1608 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1609 $relpercentTol, $numOfPoints, 1610 $maxConstantOfIntegration, $zeroLevel) OR 1611 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1612 $relpercentTol, $numOfPoints, 1613 $maxConstantOfIntegration, 1614 $zeroLevel, $zeroLevelTol ) 1615 1616 $maxConstantOfIntegration -- the maximum size of the constant of 1617 integration 1618 1619 function_cmp_up_to_constant() uses antiderivative compare and relative 1620 tolerance. All options work exactly like function_cmp(), except of course 1621 $maxConstantOfIntegration. It will accept as correct any function which 1622 differs from $correctEqn by at most a constant; that is, if 1623 $studentEqn = $correctEqn + C 1624 the answer is correct. 1625 1626 function_cmp_abs( $correctFunction ) OR 1627 function_cmp_abs( $correctFunction, $var ) OR 1628 function_cmp_abs( $correctFunction, $var, $llimit, $ulimit ) OR 1629 function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol ) OR 1630 function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol, 1631 $numOfPoints ) 1632 1633 $absTol -- the tolerance as an absolute value 1634 1635 function_cmp_abs() uses standard compare and absolute tolerance. All 1636 other options work exactly as for function_cmp(). 1637 1638 function_cmp_up_to_constant_abs( $correctFunction ) OR 1639 function_cmp_up_to_constant_abs( $correctFunction, $var ) OR 1640 function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit ) OR 1641 function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit, 1642 $absTol ) OR 1643 function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit, 1644 $absTol, $numOfPoints ) OR 1645 function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit, 1646 $absTol, $numOfPoints, 1647 $maxConstantOfIntegration ) 1648 1649 function_cmp_up_to_constant_abs() uses antiderivative compare 1650 and absolute tolerance. All other options work exactly as with 1651 function_cmp_up_to_constant(). 1652 1653 Examples: 1654 1655 ANS( function_cmp( "cos(x)" ) ) -- Accepts cos(x), sin(x+pi/2), 1656 sin(x)^2 + cos(x) + cos(x)^2 -1, etc. This assumes 1657 $functVarDefault has been set to "x". 1658 ANS( function_cmp( $answer, "t" ) ) -- Assuming $answer is "cos(t)", 1659 accepts cos(t), etc. 1660 ANS( function_cmp_up_to_constant( "cos(x)" ) ) -- Accepts any 1661 antiderivative of sin(x), e.g. cos(x) + 5. 1662 ANS( function_cmp_up_to_constant( "cos(z)", "z" ) ) -- Accepts any 1663 antiderivative of sin(z), e.g. sin(z+pi/2) + 5. 1664 1665 =cut 1666 1667 sub adaptive_function_cmp { 1668 my $correctEqn = shift; 1669 my %options = @_; 1670 set_default_options( \%options, 1671 'vars' => [qw( x y )], 1672 'params' => [], 1673 'limits' => [ [0,1], [0,1]], 1674 'reltol' => $functRelPercentTolDefault, 1675 'numPoints' => $functNumOfPoints, 1676 'zeroLevel' => $functZeroLevelDefault, 1677 'zeroLevelTol' => $functZeroLevelTolDefault, 1678 'debug' => 0, 1679 'diagnostics' => undef, 1680 ); 1681 1682 my $var_ref = $options{'vars'}; 1683 my $ra_params = $options{ 'params'}; 1684 my $limit_ref = $options{'limits'}; 1685 my $relPercentTol= $options{'reltol'}; 1686 my $numPoints = $options{'numPoints'}; 1687 my $zeroLevel = $options{'zeroLevel'}; 1688 my $zeroLevelTol = $options{'zeroLevelTol'}; 1689 1690 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1691 'var' => $var_ref, 1692 'limits' => $limit_ref, 1693 'tolerance' => $relPercentTol, 1694 'tolType' => 'relative', 1695 'numPoints' => $numPoints, 1696 'mode' => 'std', 1697 'maxConstantOfIntegration' => 10**100, 1698 'zeroLevel' => $zeroLevel, 1699 'zeroLevelTol' => $zeroLevelTol, 1700 'scale_norm' => 1, 1701 'params' => $ra_params, 1702 'debug' => $options{debug} , 1703 'diagnostics' => $options{diagnostics} , 1704 ); 1705 } 1706 1707 sub function_cmp { 1708 my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_; 1709 1710 if ( (scalar(@_) == 3) or (scalar(@_) > 8) or (scalar(@_) == 0) ) { 1711 function_invalid_params( $correctEqn ); 1712 } 1713 else { 1714 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1715 'var' => $var, 1716 'limits' => [$llimit, $ulimit], 1717 'tolerance' => $relPercentTol, 1718 'tolType' => 'relative', 1719 'numPoints' => $numPoints, 1720 'mode' => 'std', 1721 'maxConstantOfIntegration' => 0, 1722 'zeroLevel' => $zeroLevel, 1723 'zeroLevelTol' => $zeroLevelTol 1724 ); 1725 } 1726 } 1727 1728 sub function_cmp_up_to_constant { ## for antiderivative problems 1729 my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$maxConstantOfIntegration,$zeroLevel,$zeroLevelTol) = @_; 1730 1731 if ( (scalar(@_) == 3) or (scalar(@_) > 9) or (scalar(@_) == 0) ) { 1732 function_invalid_params( $correctEqn ); 1733 } 1734 else { 1735 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1736 'var' => $var, 1737 'limits' => [$llimit, $ulimit], 1738 'tolerance' => $relPercentTol, 1739 'tolType' => 'relative', 1740 'numPoints' => $numPoints, 1741 'mode' => 'antider', 1742 'maxConstantOfIntegration' => $maxConstantOfIntegration, 1743 'zeroLevel' => $zeroLevel, 1744 'zeroLevelTol' => $zeroLevelTol 1745 ); 1746 } 1747 } 1748 1749 sub function_cmp_abs { ## similar to function_cmp but uses absolute tolerance 1750 my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints) = @_; 1751 1752 if ( (scalar(@_) == 3) or (scalar(@_) > 6) or (scalar(@_) == 0) ) { 1753 function_invalid_params( $correctEqn ); 1754 } 1755 else { 1756 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1757 'var' => $var, 1758 'limits' => [$llimit, $ulimit], 1759 'tolerance' => $absTol, 1760 'tolType' => 'absolute', 1761 'numPoints' => $numPoints, 1762 'mode' => 'std', 1763 'maxConstantOfIntegration' => 0, 1764 'zeroLevel' => 0, 1765 'zeroLevelTol' => 0 1766 ); 1767 } 1768 } 1769 1770 1771 sub function_cmp_up_to_constant_abs { ## for antiderivative problems 1772 ## similar to function_cmp_up_to_constant 1773 ## but uses absolute tolerance 1774 my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints,$maxConstantOfIntegration) = @_; 1775 1776 if ( (scalar(@_) == 3) or (scalar(@_) > 7) or (scalar(@_) == 0) ) { 1777 function_invalid_params( $correctEqn ); 1778 } 1779 1780 else { 1781 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1782 'var' => $var, 1783 'limits' => [$llimit, $ulimit], 1784 'tolerance' => $absTol, 1785 'tolType' => 'absolute', 1786 'numPoints' => $numPoints, 1787 'mode' => 'antider', 1788 'maxConstantOfIntegration' => $maxConstantOfIntegration, 1789 'zeroLevel' => 0, 1790 'zeroLevelTol' => 0 1791 ); 1792 } 1793 } 1794 1795 ## The following answer evaluator for comparing multivarable functions was 1796 ## contributed by Professor William K. Ziemer 1797 ## (Note: most of the multivariable functionality provided by Professor Ziemer 1798 ## has now been integrated into fun_cmp and FUNCTION_CMP) 1799 ############################ 1800 # W.K. Ziemer, Sep. 1999 1801 # Math Dept. CSULB 1802 # email: wziemer@csulb.edu 1803 ############################ 1804 1805 =head3 multivar_function_cmp 1806 1807 NOTE: this function is maintained for compatibility. fun_cmp() is 1808 slightly preferred. 1809 1810 usage: 1811 1812 multivar_function_cmp( $answer, $var_reference, options) 1813 $answer -- string, represents function of several variables 1814 $var_reference -- number (of variables), or list reference (e.g. ["var1","var2"] ) 1815 options: 1816 $limit_reference -- reference to list of lists (e.g. [[1,2],[3,4]]) 1817 $relPercentTol -- relative percent tolerance in answer 1818 $numPoints -- number of points to sample in for each variable 1819 $zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies 1820 $zeroLevelTol -- absolute tolerance to allow when answer is close to zero 1821 1822 =cut 1823 1824 sub multivar_function_cmp { 1825 my ($correctEqn,$var_ref,$limit_ref,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_; 1826 1827 if ( (scalar(@_) > 7) or (scalar(@_) < 2) ) { 1828 function_invalid_params( $correctEqn ); 1829 } 1830 1831 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1832 'var' => $var_ref, 1833 'limits' => $limit_ref, 1834 'tolerance' => $relPercentTol, 1835 'tolType' => 'relative', 1836 'numPoints' => $numPoints, 1837 'mode' => 'std', 1838 'maxConstantOfIntegration' => 0, 1839 'zeroLevel' => $zeroLevel, 1840 'zeroLevelTol' => $zeroLevelTol 1841 ); 1842 } 1843 1844 ## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION 1845 ## NOTE: PG_answer_eval is used instead of PG_restricted_eval in order to insure that the answer 1846 ## evaluated within the context of the package the problem was originally defined in. 1847 ## Includes multivariable modifications contributed by Professor William K. Ziemer 1848 ## 1849 ## IN: a hash consisting of the following keys (error checking to be added later?) 1850 ## correctEqn -- the correct equation as a string 1851 ## var -- the variable name as a string, 1852 ## or a reference to an array of variables 1853 ## limits -- reference to an array of arrays of type [lower,upper] 1854 ## tolerance -- the allowable margin of error 1855 ## tolType -- 'relative' or 'absolute' 1856 ## numPoints -- the number of points to evaluate the function at 1857 ## mode -- 'std' or 'antider' 1858 ## maxConstantOfIntegration -- maximum size of the constant of integration 1859 ## zeroLevel -- if the correct answer is this close to zero, 1860 ## then zeroLevelTol applies 1861 ## zeroLevelTol -- absolute tolerance to allow when answer is close to zero 1862 ## test_points -- user supplied points to use for testing the 1863 ## function, either array of arrays, or optionally 1864 ## reference to single array (for one variable) 1865 1866 1867 sub FUNCTION_CMP { 1868 return ORIGINAL_FUNCTION_CMP(@_) 1869 if main::PG_restricted_eval(q!$main::useOldAnswerMacros!); 1870 1871 my %func_params = @_; 1872 1873 my $correctEqn = $func_params{'correctEqn'}; 1874 my $var = $func_params{'var'}; 1875 my $ra_limits = $func_params{'limits'}; 1876 my $tol = $func_params{'tolerance'}; 1877 my $tolType = $func_params{'tolType'}; 1878 my $numPoints = $func_params{'numPoints'}; 1879 my $mode = $func_params{'mode'}; 1880 my $maxConstantOfIntegration = $func_params{'maxConstantOfIntegration'}; 1881 my $zeroLevel = $func_params{'zeroLevel'}; 1882 my $zeroLevelTol = $func_params{'zeroLevelTol'}; 1883 my $testPoints = $func_params{'test_points'}; 1884 1885 # 1886 # Check that everything is defined: 1887 # 1888 $func_params{debug} = 0 unless defined $func_params{debug}; 1889 $mode = 'std' unless defined $mode; 1890 my @VARS = get_var_array($var); 1891 my @limits = get_limits_array($ra_limits); 1892 my @PARAMS = @{$func_params{'params'} || []}; 1893 1894 if($tolType eq 'relative') { 1895 $tol = $functRelPercentTolDefault unless defined $tol; 1896 $tol *= .01; 1897 } else { 1898 $tol = $functAbsTolDefault unless defined $tol; 1899 } 1900 1901 # 1902 # Ensure that the number of limits matches number of variables 1903 # 1904 foreach my $i (0..scalar(@VARS)-1) { 1905 $limits[$i][0] = $functLLimitDefault unless defined $limits[$i][0]; 1906 $limits[$i][1] = $functULimitDefault unless defined $limits[$i][1]; 1907 } 1908 1909 # 1910 # Check that the test points are array references with the right number of coordinates 1911 # 1912 if ($testPoints) { 1913 my $n = scalar(@VARS); my $s = ($n != 1)? "s": ""; 1914 foreach my $p (@{$testPoints}) { 1915 $p = [$p] unless ref($p) eq 'ARRAY'; 1916 warn "Test point (".join(',',@{$p}).") should have $n coordiante$s" 1917 unless scalar(@{$p}) == $n; 1918 } 1919 } 1920 1921 $numPoints = $functNumOfPoints unless defined $numPoints; 1922 $maxConstantOfIntegration = $functMaxConstantOfIntegration unless defined $maxConstantOfIntegration; 1923 $zeroLevel = $functZeroLevelDefault unless defined $zeroLevel; 1924 $zeroLevelTol = $functZeroLevelTolDefault unless defined $zeroLevelTol; 1925 1926 $func_params{'var'} = \@VARS; 1927 $func_params{'params'} = \@PARAMS; 1928 $func_params{'limits'} = \@limits; 1929 $func_params{'tolerance'} = $tol; 1930 $func_params{'tolType'} = $tolType; 1931 $func_params{'numPoints'} = $numPoints; 1932 $func_params{'mode'} = $mode; 1933 $func_params{'maxConstantOfIntegration'} = $maxConstantOfIntegration; 1934 $func_params{'zeroLevel'} = $zeroLevel; 1935 $func_params{'zeroLevelTol'} = $zeroLevelTol; 1936 1937 ######################################################## 1938 # End of cleanup of calling parameters 1939 ######################################################## 1940 1941 my %options = ( 1942 debug => $func_params{'debug'}, 1943 diagnostics => $func_params{'diagnostics'}, 1944 ); 1945 1946 # 1947 # Initialize the context for the formula 1948 # 1949 my $context = $Parser::Context::Default::context{"LegacyNumeric"}->copy; 1950 $context->flags->set( 1951 tolerance => $func_params{'tolerance'}, 1952 tolType => $func_params{'tolType'}, 1953 zeroLevel => $func_params{'zeroLevel'}, 1954 zeroLevelTol => $func_params{'zeroLevelTol'}, 1955 num_points => $func_params{'numPoints'}, 1956 ); 1957 if ($func_params{'mode'} eq 'antider') { 1958 $context->flags->set(max_adapt => $func_params{'maxConstantOfIntegration'}); 1959 $options{upToConstant} = 1; 1960 } 1961 1962 # 1963 # Add the variables and parameters to the context 1964 # 1965 my %variables; my $x; 1966 foreach $x (@{$func_params{'var'}}) { 1967 if (length($x) > 1) { 1968 $context->{_variables}->{pattern} = $context->{_variables}->{namePattern} = 1969 $x . '|' . $context->{_variables}->{pattern}; 1970 $context->update; 1971 } 1972 $variables{$x} = 'Real'; 1973 } 1974 foreach $x (@{$func_params{'params'}}) {$variables{$x} = 'Parameter'} 1975 $context->variables->are(%variables); 1976 1977 # 1978 # Create the Formula object and get its answer checker 1979 # 1980 my $oldContext = &$Context(); &$Context($context); 1981 my $f = new Value::Formula($correctEqn); 1982 $f->{limits} = $func_params{'limits'}; 1983 $f->{test_points} = $func_params{'test_points'}; 1984 my $cmp = $f->cmp(%options); 1985 &$Context($oldContext); 1986 1987 # 1988 # Get previous answer from hidden field of form 1989 # 1990 $cmp->install_pre_filter( 1991 sub { 1992 my $rh_ans = shift; 1993 $rh_ans->{_filter_name} = "fetch_previous_answer"; 1994 my $prev_ans_label = "previous_".$rh_ans->{ans_label}; 1995 $rh_ans->{prev_ans} = 1996 (defined $inputs_ref->{$prev_ans_label} and 1997 $inputs_ref->{$prev_ans_label} =~/\S/) ? $inputs_ref->{$prev_ans_label} : undef; 1998 $rh_ans; 1999 } 2000 ); 2001 2002 # 2003 # Parse the previous answer, if any 2004 # 2005 $cmp->install_evaluator( 2006 sub { 2007 my $rh_ans = shift; 2008 $rh_ans->{_filter_name} = "parse_previous_answer"; 2009 return $rh_ans unless defined $rh_ans->{prev_ans}; 2010 my $oldContext = &$Context(); 2011 &$Context($rh_ans->{correct_value}{context}); 2012 $rh_ans->{prev_formula} = Parser::Formula($rh_ans->{prev_ans}); 2013 &$Context($oldContext); 2014 $rh_ans; 2015 } 2016 ); 2017 2018 # 2019 # Check if previous answer equals this current one 2020 # 2021 $cmp->install_evaluator( 2022 sub { 2023 my $rh_ans = shift; 2024 $rh_ans->{_filter_name} = "compare_to_previous_answer"; 2025 return $rh_ans unless defined($rh_ans->{prev_formula}) && defined($rh_ans->{student_formula}); 2026 $rh_ans->{prev_equals_current} = 2027 Value::cmp_compare($rh_ans->{student_formula},$rh_ans->{prev_formula},{}); 2028 $rh_ans; 2029 } 2030 ); 2031 2032 # 2033 # Produce a message if the previous answer equals this one and is not specified the same way 2034 # 2035 $cmp->install_post_filter( 2036 sub { 2037 my $rh_ans = shift; 2038 $rh_ans->{_filter_name} = "produce_equivalence_message"; 2039 return $rh_ans unless $rh_ans->{prev_equals_current}; 2040 # 2041 # If the match is exact don't give an error since there may be multiple 2042 # entry blanks and the student is trying to get one of the other ones 2043 # right. We should only give this message when the student is actually 2044 # working on this answer. 2045 # 2046 return $rh_ans if $rh_ans->{prev_ans} eq $rh_ans->{original_student_ans}; 2047 $rh_ans->{ans_message} = "This answer is equivalent to the one you just submitted or previewed."; 2048 $rh_ans; 2049 } 2050 ); 2051 2052 return $cmp; 2053 } 2054 2055 # 2056 # The original version, for backward compatibility 2057 # (can be removed when the Parser-based version is more fully tested.) 2058 # 2059 sub ORIGINAL_FUNCTION_CMP { 2060 my %func_params = @_; 2061 2062 my $correctEqn = $func_params{'correctEqn'}; 2063 my $var = $func_params{'var'}; 2064 my $ra_limits = $func_params{'limits'}; 2065 my $tol = $func_params{'tolerance'}; 2066 my $tolType = $func_params{'tolType'}; 2067 my $numPoints = $func_params{'numPoints'}; 2068 my $mode = $func_params{'mode'}; 2069 my $maxConstantOfIntegration = $func_params{'maxConstantOfIntegration'}; 2070 my $zeroLevel = $func_params{'zeroLevel'}; 2071 my $zeroLevelTol = $func_params{'zeroLevelTol'}; 2072 my $ra_test_points = $func_params{'test_points'}; 2073 2074 # Check that everything is defined: 2075 $func_params{debug} = 0 unless defined $func_params{debug}; 2076 $mode = 'std' unless defined $mode; 2077 my @VARS = get_var_array($var); 2078 my @limits = get_limits_array($ra_limits); 2079 my @PARAMS = (); 2080 @PARAMS = @{$func_params{'params'}} if defined $func_params{'params'}; 2081 2082 my @evaluation_points; 2083 if(defined $ra_test_points) { 2084 # see if this is the standard format 2085 if(ref $ra_test_points->[0] eq 'ARRAY') { 2086 $numPoints = scalar @{$ra_test_points->[0]}; 2087 # now a little sanity check 2088 my $j; 2089 for $j (@{$ra_test_points}) { 2090 warn "Test points do not give the same number of values for each variable" 2091 unless(scalar(@{$j}) == $numPoints); 2092 } 2093 warn "Test points do not match the number of variables" 2094 unless scalar @{$ra_test_points} == scalar @VARS; 2095 } else { # we are got the one-variable format 2096 $ra_test_points = [$ra_test_points]; 2097 $numPoints = scalar $ra_test_points->[0]; 2098 } 2099 # The input format for test points is the transpose of what is used 2100 # internally below, so take care of that now. 2101 my ($j1, $j2); 2102 for ($j1 = 0; $j1 < scalar @{$ra_test_points}; $j1++) { 2103 for ($j2 = 0; $j2 < scalar @{$ra_test_points->[$j1]}; $j2++) { 2104 $evaluation_points[$j2][$j1] = $ra_test_points->[$j1][$j2]; 2105 } 2106 } 2107 } # end of handling of user supplied evaluation points 2108 2109 if ($mode eq 'antider') { 2110 # doctor the equation to allow addition of a constant 2111 my $CONSTANT_PARAM = 'Q'; # unfortunately parameters must be single letters. 2112 # There is the possibility of conflict here. 2113 # 'Q' seemed less dangerous than 'C'. 2114 $correctEqn = "( $correctEqn ) + $CONSTANT_PARAM"; 2115 push @PARAMS, $CONSTANT_PARAM; 2116 } 2117 my $dim_of_param_space = @PARAMS; # dimension of equivalence space 2118 2119 if($tolType eq 'relative') { 2120 $tol = $functRelPercentTolDefault unless defined $tol; 2121 $tol *= .01; 2122 } else { 2123 $tol = $functAbsTolDefault unless defined $tol; 2124 } 2125 2126 #loop ensures that number of limits matches number of variables 2127 for(my $i = 0; $i < scalar @VARS; $i++) { 2128 $limits[$i][0] = $functLLimitDefault unless defined $limits[$i][0]; 2129 $limits[$i][1] = $functULimitDefault unless defined $limits[$i][1]; 2130 } 2131 $numPoints = $functNumOfPoints unless defined $numPoints; 2132 $maxConstantOfIntegration = $functMaxConstantOfIntegration unless defined $maxConstantOfIntegration; 2133 $zeroLevel = $functZeroLevelDefault unless defined $zeroLevel; 2134 $zeroLevelTol = $functZeroLevelTolDefault unless defined $zeroLevelTol; 2135 2136 $func_params{'var'} = $var; 2137 $func_params{'limits'} = \@limits; 2138 $func_params{'tolerance'} = $tol; 2139 $func_params{'tolType'} = $tolType; 2140 $func_params{'numPoints'} = $numPoints; 2141 $func_params{'mode'} = $mode; 2142 $func_params{'maxConstantOfIntegration'} = $maxConstantOfIntegration; 2143 $func_params{'zeroLevel'} = $zeroLevel; 2144 $func_params{'zeroLevelTol'} = $zeroLevelTol; 2145 2146 ######################################################## 2147 # End of cleanup of calling parameters 2148 ######################################################## 2149 2150 my $i; # for use with loops 2151 my $PGanswerMessage = ""; 2152 my $originalCorrEqn = $correctEqn; 2153 2154 ###################################################################### 2155 # prepare the correct answer and check its syntax 2156 ###################################################################### 2157 2158 my $rh_correct_ans = new AnswerHash; 2159 $rh_correct_ans->input($correctEqn); 2160 $rh_correct_ans = check_syntax($rh_correct_ans); 2161 warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag}; 2162 $rh_correct_ans->clear_error(); 2163 $rh_correct_ans = function_from_string2($rh_correct_ans, 2164 ra_vars => [ @VARS, @PARAMS ], 2165 stdout => 'rf_correct_ans', 2166 debug => $func_params{debug} 2167 ); 2168 my $correct_eqn_sub = $rh_correct_ans->{rf_correct_ans}; 2169 warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag}; 2170 2171 ###################################################################### 2172 # define the points at which the functions are to be evaluated 2173 ###################################################################### 2174 2175 if(not defined $ra_test_points) { 2176 #create the evaluation points 2177 my $random_for_answers = new PGrandom($main::PG_original_problemSeed); 2178 my $NUMBER_OF_STEPS_IN_RANDOM = 1000; # determines the granularity of the random_for_answers number generator 2179 for(my $count = 0; $count < @PARAMS+1+$numPoints; $count++) { 2180 my (@vars,$iteration_limit); 2181 for(my $i = 0; $i < @VARS; $i++) { 2182 my $iteration_limit = 10; 2183 while (0 < --$iteration_limit) { # make sure that the endpoints of the interval are not included 2184 $vars[$i] = $random_for_answers->random($limits[$i][0], $limits[$i][1], abs($limits[$i][1] - $limits[$i][0])/$NUMBER_OF_STEPS_IN_RANDOM); 2185 last if $vars[$i]!=$limits[$i][0] and $vars[$i]!=$limits[$i][1]; 2186 } 2187 warn "Unable to properly choose evaluation points for this function in the interval ( $limits[$i][0] , $limits[$i][1] )" 2188 if $iteration_limit == 0; 2189 } 2190 2191 push @evaluation_points, \@vars; 2192 } 2193 } 2194 my $evaluation_points = Matrix->new_from_array_ref(\@evaluation_points); 2195 2196 #my $COEFFS = determine_param_coeffs($correct_eqn_sub,$evaluation_points[0],$numOfParameters); 2197 #warn "coeff", join(" | ", @{$COEFFS}); 2198 2199 #construct the answer evaluator 2200 my $answer_evaluator = new AnswerEvaluator; 2201 $answer_evaluator->{debug} = $func_params{debug}; 2202 $answer_evaluator->ans_hash( 2203 correct_ans => $originalCorrEqn, 2204 rf_correct_ans => $rh_correct_ans->{rf_correct_ans}, 2205 evaluation_points => \@evaluation_points, 2206 ra_param_vars => \@PARAMS, 2207 ra_vars => \@VARS, 2208 type => 'function', 2209 score => 0, 2210 ); 2211 2212 ######################################################### 2213 # Prepare the previous answer for evaluation, discard errors 2214 ######################################################### 2215 2216 $answer_evaluator->install_pre_filter( 2217 sub { 2218 my $rh_ans = shift; 2219 $rh_ans->{_filter_name} = "fetch_previous_answer"; 2220 my $prev_ans_label = "previous_".$rh_ans->{ans_label}; 2221 $rh_ans->{prev_ans} = (defined $inputs_ref->{$prev_ans_label} and $inputs_ref->{$prev_ans_label} =~/\S/) 2222 ? $inputs_ref->{$prev_ans_label} 2223 : undef; 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 $rh_ans->{prev_ans}; 2232 check_syntax($rh_ans, 2233 stdin => 'prev_ans', 2234 stdout => 'prev_ans', 2235 error_msg_flag => 0 2236 ); 2237 $rh_ans->{_filter_name} = "check_syntax_of_previous_answer"; 2238 $rh_ans; 2239 } 2240 ); 2241 2242 $answer_evaluator->install_pre_filter( 2243 sub { 2244 my $rh_ans = shift; 2245 return $rh_ans unless defined $rh_ans->{prev_ans}; 2246 function_from_string2($rh_ans, 2247 stdin => 'prev_ans', 2248 stdout => 'rf_prev_ans', 2249 ra_vars => \@VARS, 2250 debug => $func_params{debug} 2251 ); 2252 $rh_ans->{_filter_name} = "compile_previous_answer"; 2253 $rh_ans; 2254 } 2255 ); 2256 2257 ######################################################### 2258 # Prepare the current answer for evaluation 2259 ######################################################### 2260 2261 $answer_evaluator->install_pre_filter(\&check_syntax); 2262 $answer_evaluator->install_pre_filter(\&function_from_string2, 2263 ra_vars => \@VARS, 2264 debug => $func_params{debug} 2265 ); # @VARS has been guaranteed to be an array, $var might be a single string. 2266 2267 ######################################################### 2268 # Compare the previous and current answer. Discard errors 2269 ######################################################### 2270 2271 $answer_evaluator->install_evaluator( 2272 sub { 2273 my $rh_ans = shift; 2274 return $rh_ans unless defined $rh_ans->{rf_prev_ans}; 2275 calculate_difference_vector($rh_ans, 2276 %func_params, 2277 stdin1 => 'rf_student_ans', 2278 stdin2 => 'rf_prev_ans', 2279 stdout => 'ra_diff_with_prev_ans', 2280 error_msg_flag => 0, 2281 ); 2282 $rh_ans->{_filter_name} = "calculate_difference_vector_of_previous_answer"; 2283 $rh_ans; 2284 } 2285 ); 2286 2287 $answer_evaluator->install_evaluator( 2288 sub { 2289 my $rh_ans = shift; 2290 return $rh_ans unless defined $rh_ans->{ra_diff_with_prev_ans}; 2291 ## 2292 ## DPVC -- only give the message if the answer is specified differently 2293 ## 2294 return $rh_ans if $rh_ans->{prev_ans} eq $rh_ans->{student_ans}; 2295 ## 2296 ## /DPVC 2297 ## 2298 is_zero_array($rh_ans, 2299 stdin => 'ra_diff_with_prev_ans', 2300 stdout => 'ans_equals_prev_ans' 2301 ); 2302 } 2303 ); 2304 2305 ######################################################### 2306 # Calculate values for approximation parameters and 2307 # compare the current answer with the correct answer. Keep errors this time. 2308 ######################################################### 2309 2310 $answer_evaluator->install_pre_filter(\&best_approx_parameters, %func_params, param_vars => \@PARAMS); 2311 $answer_evaluator->install_evaluator(\&calculate_difference_vector, %func_params); 2312 $answer_evaluator->install_evaluator(\&is_zero_array, tolerance => $tol ); 2313 2314 $answer_evaluator->install_post_filter( 2315 sub { 2316 my $rh_ans = shift; 2317 $rh_ans->clear_error('SYNTAX'); 2318 $rh_ans; 2319 } 2320 ); 2321 2322 $answer_evaluator->install_post_filter( 2323 sub { 2324 my $rh_ans = shift; 2325 if ($rh_ans->catch_error('EVAL')) { 2326 $rh_ans->{ans_message} = $rh_ans->{error_message}; 2327 $rh_ans->clear_error('EVAL'); 2328 } 2329 $rh_ans; 2330 } 2331 ); 2332 2333 $answer_evaluator->install_post_filter( 2334 sub { 2335 my $rh_ans = shift; 2336 if ( defined($rh_ans->{'ans_equals_prev_ans'}) and $rh_ans->{'ans_equals_prev_ans'}) { 2337 ## $rh_ans->{ans_message} = "This answer is the same as the one you just submitted or previewed."; 2338 $rh_ans->{ans_message} = "This answer is equivalent to the one you just submitted or previewed."; ## DPVC 2339 } 2340 $rh_ans; 2341 } 2342 ); 2343 2344 $answer_evaluator; 2345 } 2346 2347 2348 ## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION 2349 ## 2350 ## IN: a hash containing the following items (error-checking to be added later?): 2351 ## correctAnswer -- the correct answer 2352 ## tolerance -- the allowable margin of error 2353 ## tolType -- 'relative' or 'absolute' 2354 ## format -- the display format of the answer 2355 ## mode -- one of 'std', 'strict', 'arith', or 'frac'; 2356 ## determines allowable formats for the input 2357 ## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies 2358 ## zeroLevelTol -- absolute tolerance to allow when answer is close to zero 2359 2360 2361 ########################################################################## 2362 ########################################################################## 2363 ## String answer evaluators 2364 2365 =head2 String Answer Evaluators 2366 2367 String answer evaluators compare a student string to the correct string. 2368 Different filters can be applied to allow various degrees of variation. 2369 Both the student and correct answers are subject to the same filters, to 2370 ensure that there are no unexpected matches or rejections. 2371 2372 String Filters 2373 2374 remove_whitespace -- Removes all whitespace from the string. 2375 It applies the following substitution 2376 to the string: 2377 $filteredAnswer =~ s/\s+//g; 2378 2379 compress_whitespace -- Removes leading and trailing whitespace, and 2380 replaces all other blocks of whitespace by a 2381 single space. Applies the following substitutions: 2382 $filteredAnswer =~ s/^\s*//; 2383 $filteredAnswer =~ s/\s*$//; 2384 $filteredAnswer =~ s/\s+/ /g; 2385 2386 trim_whitespace -- Removes leading and trailing whitespace. 2387 Applies the following substitutions: 2388 $filteredAnswer =~ s/^\s*//; 2389 $filteredAnswer =~ s/\s*$//; 2390 2391 ignore_case -- Ignores the case of the string. More accurately, 2392 it converts the string to uppercase (by convention). 2393 Applies the following function: 2394 $filteredAnswer = uc $filteredAnswer; 2395 2396 ignore_order -- Ignores the order of the letters in the string. 2397 This is used for problems of the form "Choose all 2398 that apply." Specifically, it removes all 2399 whitespace and lexically sorts the letters in 2400 ascending alphabetical order. Applies the following 2401 functions: 2402 $filteredAnswer = join( "", lex_sort( 2403 split( /\s*/, $filteredAnswer ) ) ); 2404 2405 =cut 2406 2407 ################################ 2408 ## STRING ANSWER FILTERS 2409 2410 ## IN: --the string to be filtered 2411 ## --a list of the filters to use 2412 ## 2413 ## OUT: --the modified string 2414 ## 2415 ## Use this subroutine instead of the 2416 ## individual filters below it 2417 2418 sub str_filters { 2419 my $stringToFilter = shift @_; 2420 # filters now take an answer hash, so encapsulate the string 2421 # in the answer hash. 2422 my $rh_ans = new AnswerHash; 2423 $rh_ans->{student_ans} = $stringToFilter; 2424 $rh_ans->{correct_ans}=''; 2425 my @filters_to_use = @_; 2426 my %known_filters = ( 2427 'remove_whitespace' => \&remove_whitespace, 2428 'compress_whitespace' => \&compress_whitespace, 2429 'trim_whitespace' => \&trim_whitespace, 2430 'ignore_case' => \&ignore_case, 2431 'ignore_order' => \&ignore_order, 2432 ); 2433 2434 #test for unknown filters 2435 foreach my $filter ( @filters_to_use ) { 2436 #check that filter is known 2437 die "Unknown string filter $filter (try checking the parameters to str_cmp() )" 2438 unless exists $known_filters{$filter}; 2439 $rh_ans = $known_filters{$filter}($rh_ans); # apply filter. 2440 } 2441 # foreach $filter (@filters_to_use) { 2442 # die "Unknown string filter $filter (try checking the parameters to str_cmp() )" 2443 # unless exists $known_filters{$filter}; 2444 # } 2445 # 2446 # if( grep( /remove_whitespace/i, @filters_to_use ) ) { 2447 # $rh_ans = remove_whitespace( $rh_ans ); 2448 # } 2449 # if( grep( /compress_whitespace/i, @filters_to_use ) ) { 2450 # $rh_ans = compress_whitespace( $rh_ans ); 2451 # } 2452 # if( grep( /trim_whitespace/i, @filters_to_use ) ) { 2453 # $rh_ans = trim_whitespace( $rh_ans ); 2454 # } 2455 # if( grep( /ignore_case/i, @filters_to_use ) ) { 2456 # $rh_ans = ignore_case( $rh_ans ); 2457 # } 2458 # if( grep( /ignore_order/i, @filters_to_use ) ) { 2459 # $rh_ans = ignore_order( $rh_ans ); 2460 # } 2461 2462 return $rh_ans->{student_ans}; 2463 } 2464 sub remove_whitespace { 2465 my $rh_ans = shift; 2466 die "expected an answer hash" unless ref($rh_ans)=~/HASH/i; 2467 $rh_ans->{_filter_name} = 'remove_whitespace'; 2468 $rh_ans->{student_ans} =~ s/\s+//g; # remove all whitespace 2469 $rh_ans->{correct_ans} =~ s/\s+//g; # remove all whitespace 2470 return $rh_ans; 2471 } 2472 2473 sub compress_whitespace { 2474 my $rh_ans = shift; 2475 die "expected an answer hash" unless ref($rh_ans)=~/HASH/i; 2476 $rh_ans->{_filter_name} = 'compress_whitespace'; 2477 $rh_ans->{student_ans} =~ s/^\s*//; # remove initial whitespace 2478 $rh_ans->{student_ans} =~ s/\s*$//; # remove trailing whitespace 2479 $rh_ans->{student_ans} =~ s/\s+/ /g; # replace spaces by single space 2480 $rh_ans->{correct_ans} =~ s/^\s*//; # remove initial whitespace 2481 $rh_ans->{correct_ans} =~ s/\s*$//; # remove trailing whitespace 2482 $rh_ans->{correct_ans} =~ s/\s+/ /g; # replace spaces by single space 2483 2484 return $rh_ans; 2485 } 2486 2487 sub trim_whitespace { 2488 my $rh_ans = shift; 2489 die "expected an answer hash" unless ref($rh_ans)=~/HASH/i; 2490 $rh_ans->{_filter_name} = 'trim_whitespace'; 2491 $rh_ans->{student_ans} =~ s/^\s*//; # remove initial whitespace 2492 $rh_ans->{student_ans} =~ s/\s*$//; # remove trailing whitespace 2493 $rh_ans->{correct_ans} =~ s/^\s*//; # remove initial whitespace 2494 $rh_ans->{correct_ans} =~ s/\s*$//; # remove trailing whitespace 2495 2496 return $rh_ans; 2497 } 2498 2499 sub ignore_case { 2500 my $rh_ans = shift; 2501 die "expected an answer hash" unless ref($rh_ans)=~/HASH/i; 2502 $rh_ans->{_filter_name} = 'ignore_case'; 2503 $rh_ans->{student_ans} =~ tr/a-z/A-Z/; 2504 $rh_ans->{correct_ans} =~ tr/a-z/A-Z/; 2505 return $rh_ans; 2506 } 2507 2508 sub ignore_order { 2509 my $rh_ans = shift; 2510 die "expected an answer hash" unless ref($rh_ans)=~/HASH/i; 2511 $rh_ans->{_filter_name} = 'ignore_order'; 2512 $rh_ans->{student_ans} = join( "", lex_sort( split( /\s*/, $rh_ans->{student_ans} ) ) ); 2513 $rh_ans->{correct_ans} = join( "", lex_sort( split( /\s*/, $rh_ans->{correct_ans} ) ) ); 2514 2515 return $rh_ans; 2516 } 2517 # sub remove_whitespace { 2518 # my $filteredAnswer = shift; 2519 # 2520 # $filteredAnswer =~ s/\s+//g; # remove all whitespace 2521 # 2522 # return $filteredAnswer; 2523 # } 2524 # 2525 # sub compress_whitespace { 2526 # my $filteredAnswer = shift; 2527 # 2528 # $filteredAnswer =~ s/^\s*//; # remove initial whitespace 2529 # $filteredAnswer =~ s/\s*$//; # remove trailing whitespace 2530 # $filteredAnswer =~ s/\s+/ /g; # replace spaces by single space 2531 # 2532 # return $filteredAnswer; 2533 # } 2534 # 2535 # sub trim_whitespace { 2536 # my $filteredAnswer = shift; 2537 # 2538 # $filteredAnswer =~ s/^\s*//; # remove initial whitespace 2539 # $filteredAnswer =~ s/\s*$//; # remove trailing whitespace 2540 # 2541 # return $filteredAnswer; 2542 # } 2543 # 2544 # sub ignore_case { 2545 # my $filteredAnswer = shift; 2546 # #warn "filtered answer is ", $filteredAnswer; 2547 # #$filteredAnswer = uc $filteredAnswer; # this didn't work on webwork xmlrpc, but does elsewhere ???? 2548 # $filteredAnswer =~ tr/a-z/A-Z/; 2549 # 2550 # return $filteredAnswer; 2551 # } 2552 # 2553 # sub ignore_order { 2554 # my $filteredAnswer = shift; 2555 # 2556 # $filteredAnswer = join( "", lex_sort( split( /\s*/, $filteredAnswer ) ) ); 2557 # 2558 # return $filteredAnswer; 2559 # } 2560 ################################ 2561 ## END STRING ANSWER FILTERS 2562 2563 2564 =head3 str_cmp() 2565 2566 Compares a string or a list of strings, using a named hash of options to set 2567 parameters. This can make for more readable code than using the "mode"_str_cmp() 2568 style, but some people find one or the other easier to remember. 2569 2570 ANS( str_cmp( answer or answer_array_ref, options_hash ) ); 2571 2572 1. the correct answer or a reference to an array of answers 2573 2. either a list of filters, or: 2574 a hash consisting of 2575 filters - a reference to an array of filters 2576 2577 Returns an answer evaluator, or (if given a reference to an array of answers), 2578 a list of answer evaluators 2579 2580 FILTERS: 2581 2582 remove_whitespace -- removes all whitespace 2583 compress_whitespace -- removes whitespace from the beginning and end of the string, 2584 and treats one or more whitespace characters in a row as a 2585 single space (true by default) 2586 trim_whitespace -- removes whitespace from the beginning and end of the string 2587 ignore_case -- ignores the case of the letters (true by default) 2588 ignore_order -- ignores the order in which letters are entered 2589 2590 EXAMPLES: 2591 2592 str_cmp( "Hello" ) -- matches "Hello", " hello" (same as std_str_cmp() ) 2593 str_cmp( ["Hello", "Goodbye"] ) -- same as std_str_cmp_list() 2594 str_cmp( " hello ", trim_whitespace ) -- matches "hello", " hello " 2595 str_cmp( "ABC", filters => 'ignore_order' ) -- matches "ACB", "A B C", but not "abc" 2596 str_cmp( "D E F", remove_whitespace, ignore_case ) -- matches "def" and "d e f" but not "fed" 2597 2598 2599 =cut 2600 2601 sub str_cmp { 2602 my $correctAnswer = shift @_; 2603 $correctAnswer = '' unless defined($correctAnswer); 2604 my @options = @_; 2605 my %options = (); 2606 # backward compatibility 2607 if (grep /filters|debug|filter/, @options) { # see whether we have hash keys in the input. 2608 %options = @options; 2609 } elsif (@options) { # all options are names of filters. 2610 $options{filters} = [@options]; 2611 } 2612 my $ra_filters; 2613 assign_option_aliases( \%options, 2614 'filter' => 'filters', 2615 ); 2616 set_default_options( \%options, 2617 'filters' => [qw(trim_whitespace compress_whitespace ignore_case)], 2618 'debug' => 0, 2619 'type' => 'str_cmp', 2620 ); 2621 $options{filters} = (ref($options{filters}))?$options{filters}:[$options{filters}]; 2622 # make sure this is a reference to an array. 2623 # error-checking for filters occurs in the filters() subroutine 2624 # if( not defined( $options[0] ) ) { # used with no filters as alias for std_str_cmp() 2625 # @options = ( 'compress_whitespace', 'ignore_case' ); 2626 # } 2627 # 2628 # if( $options[0] eq 'filters' ) { # using filters => [f1, f2, ...] notation 2629 # $ra_filters = $options[1]; 2630 # } 2631 # else { # using a list of filters 2632 # $ra_filters = \@options; 2633 # } 2634 2635 # thread over lists 2636 my @ans_list = (); 2637 2638 if ( ref($correctAnswer) eq 'ARRAY' ) { 2639 @ans_list = @{$correctAnswer}; 2640 } 2641 else { 2642 push( @ans_list, $correctAnswer ); 2643 } 2644 2645 # final_answer; 2646 my @output_list = (); 2647 2648 foreach my $ans (@ans_list) { 2649 push(@output_list, STR_CMP( 2650 'correct_ans' => $ans, 2651 'filters' => $options{filters}, 2652 'type' => $options{type}, 2653 'debug' => $options{debug}, 2654 ) 2655 ); 2656 } 2657 2658 return (wantarray) ? @output_list : $output_list[0] ; 2659 } 2660 2661 =head3 "mode"_str_cmp functions 2662 2663 The functions of the the form "mode"_str_cmp() use different functions to 2664 specify which filters to apply. They take no options except the correct 2665 string. There are also versions which accept a list of strings. 2666 2667 std_str_cmp( $correctString ) 2668 std_str_cmp_list( @correctStringList ) 2669 Filters: compress_whitespace, ignore_case 2670 2671 std_cs_str_cmp( $correctString ) 2672 std_cs_str_cmp_list( @correctStringList ) 2673 Filters: compress_whitespace 2674 2675 strict_str_cmp( $correctString ) 2676 strict_str_cmp_list( @correctStringList ) 2677 Filters: trim_whitespace 2678 2679 unordered_str_cmp( $correctString ) 2680 unordered_str_cmp_list( @correctStringList ) 2681 Filters: ignore_order, ignore_case 2682 2683 unordered_cs_str_cmp( $correctString ) 2684 unordered_cs_str_cmp_list( @correctStringList ) 2685 Filters: ignore_order 2686 2687 ordered_str_cmp( $correctString ) 2688 ordered_str_cmp_list( @correctStringList ) 2689 Filters: remove_whitespace, ignore_case 2690 2691 ordered_cs_str_cmp( $correctString ) 2692 ordered_cs_str_cmp_list( @correctStringList ) 2693 Filters: remove_whitespace 2694 2695 Examples 2696 2697 ANS( std_str_cmp( "W. Mozart" ) ) -- Accepts "W. Mozart", "W. MOZarT", 2698 and so forth. Case insensitive. All internal spaces treated 2699 as single spaces. 2700 ANS( std_cs_str_cmp( "Mozart" ) ) -- Rejects "mozart". Same as 2701 std_str_cmp() but case sensitive. 2702 ANS( strict_str_cmp( "W. Mozart" ) ) -- Accepts only the exact string. 2703 ANS( unordered_str_cmp( "ABC" ) ) -- Accepts "a c B", "CBA" and so forth. 2704 Unordered, case insensitive, spaces ignored. 2705 ANS( unordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc". Same as 2706 unordered_str_cmp() but case sensitive. 2707 ANS( ordered_str_cmp( "ABC" ) ) -- Accepts "a b C", "A B C" and so forth. 2708 Ordered, case insensitive, spaces ignored. 2709 ANS( ordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc", accepts "A BC" and 2710 so forth. Same as ordered_str_cmp() but case sensitive. 2711 2712 =cut 2713 2714 sub std_str_cmp { # compare strings 2715 my $correctAnswer = shift @_; 2716 my @filters = ( 'compress_whitespace', 'ignore_case' ); 2717 my $type = 'std_str_cmp'; 2718 STR_CMP('correct_ans' => $correctAnswer, 2719 'filters' => \@filters, 2720 'type' => $type 2721 ); 2722 } 2723 2724 sub std_str_cmp_list { # alias for std_str_cmp 2725 my @answerList = @_; 2726 my @output; 2727 while (@answerList) { 2728 push( @output, std_str_cmp(shift @answerList) ); 2729 } 2730 @output; 2731 } 2732 2733 sub std_cs_str_cmp { # compare strings case sensitive 2734 my $correctAnswer = shift @_; 2735 my @filters = ( 'compress_whitespace' ); 2736 my $type = 'std_cs_str_cmp'; 2737 STR_CMP( 'correct_ans' => $correctAnswer, 2738 'filters' => \@filters, 2739 'type' => $type 2740 ); 2741 } 2742 2743 sub std_cs_str_cmp_list { # alias for std_cs_str_cmp 2744 my @answerList = @_; 2745 my @output; 2746 while (@answerList) { 2747 push( @output, std_cs_str_cmp(shift @answerList) ); 2748 } 2749 @output; 2750 } 2751 2752 sub strict_str_cmp { # strict string compare 2753 my $correctAnswer = shift @_; 2754 my @filters = ( 'trim_whitespace' ); 2755 my $type = 'strict_str_cmp'; 2756 STR_CMP( 'correct_ans' => $correctAnswer, 2757 'filters' => \@filters, 2758 'type' => $type 2759 ); 2760 } 2761 2762 sub strict_str_cmp_list { # alias for strict_str_cmp 2763 my @answerList = @_; 2764 my @output; 2765 while (@answerList) { 2766 push( @output, strict_str_cmp(shift @answerList) ); 2767 } 2768 @output; 2769 } 2770 2771 sub unordered_str_cmp { # unordered, case insensitive, spaces ignored 2772 my $correctAnswer = shift @_; 2773 my @filters = ( 'ignore_order', 'ignore_case' ); 2774 my $type = 'unordered_str_cmp'; 2775 STR_CMP( 'correct_ans' => $correctAnswer, 2776 'filters' => \@filters, 2777 'type' => $type 2778 ); 2779 } 2780 2781 sub unordered_str_cmp_list { # alias for unordered_str_cmp 2782 my @answerList = @_; 2783 my @output; 2784 while (@answerList) { 2785 push( @output, unordered_str_cmp(shift @answerList) ); 2786 } 2787 @output; 2788 } 2789 2790 sub unordered_cs_str_cmp { # unordered, case sensitive, spaces ignored 2791 my $correctAnswer = shift @_; 2792 my @filters = ( 'ignore_order' ); 2793 my $type = 'unordered_cs_str_cmp'; 2794 STR_CMP( 'correct_ans' => $correctAnswer, 2795 'filters' => \@filters, 2796 'type' => $type 2797 ); 2798 } 2799 2800 sub unordered_cs_str_cmp_list { # alias for unordered_cs_str_cmp 2801 my @answerList = @_; 2802 my @output; 2803 while (@answerList) { 2804 push( @output, unordered_cs_str_cmp(shift @answerList) ); 2805 } 2806 @output; 2807 } 2808 2809 sub ordered_str_cmp { # ordered, case insensitive, spaces ignored 2810 my $correctAnswer = shift @_; 2811 my @filters = ( 'remove_whitespace', 'ignore_case' ); 2812 my $type = 'ordered_str_cmp'; 2813 STR_CMP( 'correct_ans' => $correctAnswer, 2814 'filters' => \@filters, 2815 'type' => $type 2816 ); 2817 } 2818 2819 sub ordered_str_cmp_list { # alias for ordered_str_cmp 2820 my @answerList = @_; 2821 my @output; 2822 while (@answerList) { 2823 push( @output, ordered_str_cmp(shift @answerList) ); 2824 } 2825 @output; 2826 } 2827 2828 sub ordered_cs_str_cmp { # ordered, case sensitive, spaces ignored 2829 my $correctAnswer = shift @_; 2830 my @filters = ( 'remove_whitespace' ); 2831 my $type = 'ordered_cs_str_cmp'; 2832 STR_CMP( 'correct_ans' => $correctAnswer, 2833 'filters' => \@filters, 2834 'type' => $type 2835 ); 2836 } 2837 2838 sub ordered_cs_str_cmp_list { # alias for ordered_cs_str_cmp 2839 my @answerList = @_; 2840 my @output; 2841 while (@answerList) { 2842 push( @output, ordered_cs_str_cmp(shift @answerList) ); 2843 } 2844 @output; 2845 } 2846 2847 2848 ## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION 2849 ## 2850 ## IN: a hashtable with the following entries (error-checking to be added later?): 2851 ## correctAnswer -- the correct answer, before filtering 2852 ## filters -- reference to an array containing the filters to be applied 2853 ## type -- a string containing the type of answer evaluator in use 2854 ## OUT: a reference to an answer evaluator subroutine 2855 sub STR_CMP { 2856 my %str_params = @_; 2857 #my $correctAnswer = str_filters( $str_params{'correct_ans'}, @{$str_params{'filters'}} ); 2858 my $answer_evaluator = new AnswerEvaluator; 2859 $answer_evaluator->{debug} = $str_params{debug}; 2860 $answer_evaluator->ans_hash( 2861 correct_ans => "$str_params{correct_ans}", 2862 type => $str_params{type}||'str_cmp', 2863 score => 0, 2864 2865 ); 2866 my %known_filters = ( 2867 'remove_whitespace' => \&remove_whitespace, 2868 'compress_whitespace' => \&compress_whitespace, 2869 'trim_whitespace' => \&trim_whitespace, 2870 'ignore_case' => \&ignore_case, 2871 'ignore_order' => \&ignore_order, 2872 ); 2873 2874 foreach my $filter ( @{$str_params{filters}} ) { 2875 #check that filter is known 2876 die "Unknown string filter |$filter|. Known filters are ". 2877 join(" ", keys %known_filters) . 2878 "(try checking the parameters to str_cmp() )" 2879 unless exists $known_filters{$filter}; 2880 # install related pre_filter 2881 $answer_evaluator->install_pre_filter( $known_filters{$filter} ); 2882 } 2883 $answer_evaluator->install_evaluator(sub { 2884 my $rh_ans = shift; 2885 $rh_ans->{_filter_name} = "Evaluator: Compare string answers with eq"; 2886 $rh_ans->{score} = ($rh_ans->{student_ans} eq $rh_ans->{correct_ans})?1:0 ; 2887 $rh_ans; 2888 }); 2889 $answer_evaluator->install_post_filter(sub { 2890 my $rh_hash = shift; 2891 $rh_hash->{_filter_name} = "clean up preview strings"; 2892 $rh_hash->{'preview_text_string'} = $rh_hash->{student_ans}; 2893 $rh_hash->{'preview_latex_string'} = "\\text{ ".$rh_hash->{student_ans}." }"; 2894 $rh_hash; 2895 }); 2896 return $answer_evaluator; 2897 } 2898 2899 # sub STR_CMP_old { 2900 # my %str_params = @_; 2901 # $str_params{'correct_ans'} = str_filters( $str_params{'correct_ans'}, @{$str_params{'filters'}} ); 2902 # my $answer_evaluator = sub { 2903 # my $in = shift @_; 2904 # $in = '' unless defined $in; 2905 # my $original_student_ans = $in; 2906 # $in = str_filters( $in, @{$str_params{'filters'}} ); 2907 # my $correctQ = ( $in eq $str_params{'correct_ans'} ) ? 1: 0; 2908 # my $ans_hash = new AnswerHash( 'score' => $correctQ, 2909 # 'correct_ans' => $str_params{'correctAnswer'}, 2910 # 'student_ans' => $in, 2911 # 'ans_message' => '', 2912 # 'type' => $str_params{'type'}, 2913 # 'preview_text_string' => $in, 2914 # 'preview_latex_string' => $in, 2915 # 'original_student_ans' => $original_student_ans 2916 # ); 2917 # return $ans_hash; 2918 # }; 2919 # return $answer_evaluator; 2920 # } 2921 2922 ########################################################################## 2923 ########################################################################## 2924 ## Miscellaneous answer evaluators 2925 2926 =head2 Miscellaneous Answer Evaluators (Checkboxes and Radio Buttons) 2927 2928 These evaluators do not fit any of the other categories. 2929 2930 checkbox_cmp( $correctAnswer ) 2931 2932 $correctAnswer -- a string containing the names of the correct boxes, 2933 e.g. "ACD". Note that this means that individual 2934 checkbox names can only be one character. Internally, 2935 this is largely the same as unordered_cs_str_cmp(). 2936 2937 radio_cmp( $correctAnswer ) 2938 2939 $correctAnswer -- a string containing the name of the correct radio 2940 button, e.g. "Choice1". This is case sensitive and 2941 whitespace sensitive, so the correct answer must match 2942 the name of the radio button exactly. 2943 2944 =cut 2945 2946 # added 6/14/2000 by David Etlinger 2947 # because of the conversion of the answer 2948 # string to an array, I thought it better not 2949 # to force STR_CMP() to work with this 2950 2951 #added 2/26/2003 by Mike Gage 2952 # handled the case where multiple answers are passed as an array reference 2953 # rather than as a \0 delimited string. 2954 sub checkbox_cmp { 2955 my $correctAnswer = shift @_; 2956 my %options = @_; 2957 assign_option_aliases( \%options, 2958 ); 2959 set_default_options( \%options, 2960 'debug' => 0, 2961 'type' => 'checkbox_cmp', 2962 ); 2963 my $answer_evaluator = new AnswerEvaluator( 2964 correct_ans => $correctAnswer, 2965 type => $options{type}, 2966 ); 2967 # pass along debug requests 2968 $answer_evaluator->{debug} = $options{debug}; 2969 2970 # join student answer array into a single string if necessary 2971 $answer_evaluator->install_pre_filter(sub { 2972 my $rh_ans = shift; 2973 $rh_ans->{_filter_name} = 'convert student_ans to string'; 2974 $rh_ans->{student_ans} = join("", @{$rh_ans->{student_ans}}) 2975 if ref($rh_ans->{student_ans}) =~/ARRAY/i; 2976 $rh_ans; 2977 }); 2978 # ignore order of check boxes 2979 $answer_evaluator->install_pre_filter(\&ignore_order); 2980 # compare as strings 2981 $answer_evaluator->install_evaluator(sub { 2982 my $rh_ans = shift; 2983 $rh_ans->{_filter_name} = 'compare strings generated by checked boxes'; 2984 $rh_ans->{score} = ($rh_ans->{student_ans} eq $rh_ans->{correct_ans}) ? 1 : 0; 2985 $rh_ans; 2986 }); 2987 # fix up preview displays 2988 $answer_evaluator->install_post_filter( sub { 2989 my $rh_ans = shift; 2990 $rh_ans->{_filter_name} = 'adjust preview strings'; 2991 $rh_ans->{type} = $options{type}; 2992 $rh_ans->{preview_text_string} = '\\text{'.$rh_ans->{student_ans}.'}', 2993 $rh_ans->{preview_latex_string} = '\\text{'.$rh_ans->{student_ans}.'}', 2994 $rh_ans; 2995 2996 2997 }); 2998 2999 # my $answer_evaluator = sub { 3000 # my $in = shift @_; 3001 # $in = '' unless defined $in; #in case no boxes checked 3002 # # multiple answers could come in two forms 3003 # # either a \0 delimited string or 3004 # # an array reference. We handle both. 3005 # if (ref($in) eq 'ARRAY') { 3006 # $in = join("",@{$in}); # convert array to single no-delimiter string 3007 # } else { 3008 # my @temp = split( "\0", $in ); #convert "\0"-delimited string to array... 3009 # $in = join( "", @temp ); #and then to a single no-delimiter string 3010 # } 3011 # my $original_student_ans = $in; #well, almost original 3012 # $in = str_filters( $in, 'ignore_order' ); 3013 # 3014 # my $correctQ = ($in eq $correctAnswer) ? 1: 0; 3015 # 3016 # my $ans_hash = new AnswerHash( 3017 # 'score' => $correctQ, 3018 # 'correct_ans' => "$correctAnswer", 3019 # 'student_ans' => $in, 3020 # 'ans_message' => "", 3021 # 'type' => "checkbox_cmp", 3022 # 'preview_text_string' => $in, 3023 # 'preview_latex_string' => $in, 3024 # 'original_student_ans' => $original_student_ans 3025 # ); 3026 # return $ans_hash; 3027 # 3028 # }; 3029 return $answer_evaluator; 3030 } 3031 # sub checkbox_cmp { 3032 # my $correctAnswer = shift @_; 3033 # $correctAnswer = str_filters( $correctAnswer, 'ignore_order' ); 3034 # 3035 # my $answer_evaluator = sub { 3036 # my $in = shift @_; 3037 # $in = '' unless defined $in; #in case no boxes checked 3038 # # multiple answers could come in two forms 3039 # # either a \0 delimited string or 3040 # # an array reference. We handle both. 3041 # if (ref($in) eq 'ARRAY') { 3042 # $in = join("",@{$in}); # convert array to single no-delimiter string 3043 # } else { 3044 # my @temp = split( "\0", $in ); #convert "\0"-delimited string to array... 3045 # $in = join( "", @temp ); #and then to a single no-delimiter string 3046 # } 3047 # my $original_student_ans = $in; #well, almost original 3048 # $in = str_filters( $in, 'ignore_order' ); 3049 # 3050 # my $correctQ = ($in eq $correctAnswer) ? 1: 0; 3051 # 3052 # my $ans_hash = new AnswerHash( 3053 # 'score' => $correctQ, 3054 # 'correct_ans' => "$correctAnswer", 3055 # 'student_ans' => $in, 3056 # 'ans_message' => "", 3057 # 'type' => "checkbox_cmp", 3058 # 'preview_text_string' => $in, 3059 # 'preview_latex_string' => $in, 3060 # 'original_student_ans' => $original_student_ans 3061 # ); 3062 # return $ans_hash; 3063 # 3064 # }; 3065 # return $answer_evaluator; 3066 # } 3067 3068 #added 6/28/2000 by David Etlinger 3069 #exactly the same as strict_str_cmp, 3070 #but more intuitive to the user 3071 3072 # check that answer is really a string and not an array 3073 # also use ordinary string compare 3074 sub radio_cmp { 3075 #strict_str_cmp( @_ ); 3076 my $response = shift; # there should be only one item. 3077 warn "Multiple choices -- this should not happen with radio buttons. Have 3078 you used checkboxes perhaps?" if ref($response); #triggered if an ARRAY is passed 3079 str_cmp($response); 3080 } 3081 3082 ########################################################################## 3083 ########################################################################## 3084 ## Text and e-mail routines 3085 3086 sub store_ans_at { 3087 my $answerStringRef = shift; 3088 my %options = @_; 3089 my $ans_eval= ''; 3090 if ( ref($answerStringRef) eq 'SCALAR' ) { 3091 $ans_eval= sub { 3092 my $text = shift; 3093 $text = '' unless defined($text); 3094 $$answerStringRef = $$answerStringRef . $text; 3095 my $ans_hash = new AnswerHash( 3096 'score' => 1, 3097 'correct_ans' => '', 3098 'student_ans' => $text, 3099 'ans_message' => '', 3100 'type' => 'store_ans_at', 3101 'original_student_ans' => $text, 3102 'preview_text_string' => '' 3103 ); 3104 3105 return $ans_hash; 3106 }; 3107 } 3108 else { 3109 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"; 3110 } 3111 3112 return $ans_eval; 3113 } 3114 3115 #### subroutines used in producing a questionnaire 3116 #### these are at least good models for other answers of this type 3117 3118 # my $QUESTIONNAIRE_ANSWERS=''; # stores the answers until it is time to send them 3119 # this must be initialized before the answer evaluators are run 3120 # but that happens long after all of the text in the problem is 3121 # evaluated. 3122 # this is a utility script for cleaning up the answer output for display in 3123 #the answers. 3124 3125 sub DUMMY_ANSWER { 3126 my $num = shift; 3127 qq{<INPUT TYPE="HIDDEN" NAME="answer$num" VALUE="">} 3128 } 3129 3130 sub escapeHTML { 3131 my $string = shift; 3132 $string =~ s/\n/$BR/ge; 3133 $string; 3134 } 3135 3136 # these next three subroutines show how to modify the "store_ans_at()" answer 3137 # evaluator to add extra information before storing the info 3138 # They provide a good model for how to tweak answer evaluators in special cases. 3139 3140 sub anstext { 3141 my $num = shift; 3142 my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS); 3143 my $psvnNumber = PG_restricted_eval(q!$main::psvnNumber!); 3144 my $probNum = PG_restricted_eval(q!$main::probNum!); 3145 my $courseName = PG_restricted_eval(q!$main::courseName!); 3146 my $setNumber = PG_restricted_eval(q!$main::setNumber!); 3147 3148 my $ans_eval = sub { 3149 my $text = shift; 3150 $text = '' unless defined($text); 3151 my $new_text = "\n${setNumber}_${courseName}_$psvnNumber-Problem-$probNum-Question-$num:\n $text "; # modify entered text 3152 my $out = &$ans_eval_template($new_text); # standard evaluator 3153 #warn "$QUESTIONNAIRE_ANSWERS"; 3154 $out->{student_ans} = escapeHTML($text); # restore original entered text 3155 $out->{correct_ans} = "Question $num answered"; 3156 $out->{original_student_ans} = escapeHTML($text); 3157 $out; 3158 }; 3159 $ans_eval; 3160 } 3161 3162 3163 sub ansradio { 3164 my $num = shift; 3165 my $psvnNumber = PG_restricted_eval(q!$main::psvnNumber!); 3166 my $probNum = PG_restricted_eval(q!$main::probNum!); 3167 3168 my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS); 3169 my $ans_eval = sub { 3170 my $text = shift; 3171 $text = '' unless defined($text); 3172 my $new_text = "\n$psvnNumber-Problem-$probNum-RADIO-$num:\n $text "; # modify entered text 3173 my $out = $ans_eval_template->($new_text); # standard evaluator 3174 $out->{student_ans} =escapeHTML($text); # restore original entered text 3175 $out->{original_student_ans} = escapeHTML($text); 3176 $out; 3177 }; 3178 3179 $ans_eval; 3180 } 3181 3182 sub anstext_non_anonymous { 3183 ## this emails identifying information 3184 my $num = shift; 3185 my $psvnNumber = PG_restricted_eval(q!$main::psvnNumber!); 3186 my $probNum = PG_restricted_eval(q!$main::probNum!); 3187 my $studentLogin = PG_restricted_eval(q!$main::studentLogin!); 3188 my $studentID = PG_restricted_eval(q!$main::studentID!); 3189 my $studentName = PG_restricted_eval(q!$main::studentName!); 3190 3191 3192 my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS); 3193 my $ans_eval = sub { 3194 my $text = shift; 3195 $text = '' unless defined($text); 3196 my $new_text = "\n$psvnNumber-Problem-$probNum-Question-$num:\n$studentLogin $main::studentID $studentName\n$text "; # modify entered text 3197 my $out = &$ans_eval_template($new_text); # standard evaluator 3198 #warn "$QUESTIONNAIRE_ANSWERS"; 3199 $out->{student_ans} = escapeHTML($text); # restore original entered text 3200 $out->{correct_ans} = "Question $num answered"; 3201 $out->{original_student_ans} = escapeHTML($text); 3202 $out; 3203 }; 3204 $ans_eval; 3205 } 3206 3207 3208 # This is another example of how to modify an answer evaluator to obtain 3209 # the desired behavior in a special case. Here the object is to have 3210 # have the last answer trigger the send_mail_to subroutine which mails 3211 # all of the answers to the designated address. 3212 # (This address must be listed in PG_environment{'ALLOW_MAIL_TO'} or an error occurs.) 3213 3214 # Fix me?? why is the body hard wired to the string QUESTIONNAIRE_ANSWERS? 3215 3216 sub mail_answers_to { #accepts the last answer and mails off the result 3217 my $user_address = shift; 3218 my $ans_eval = sub { 3219 3220 # then mail out all of the answers, including this last one. 3221 3222 send_mail_to( $user_address, 3223 'subject' => "$main::courseName WeBWorK questionnaire", 3224 'body' => $QUESTIONNAIRE_ANSWERS, 3225 'ALLOW_MAIL_TO' => $rh_envir->{ALLOW_MAIL_TO} 3226 ); 3227 3228 my $ans_hash = new AnswerHash( 'score' => 1, 3229 'correct_ans' => '', 3230 'student_ans' => 'Answer recorded', 3231 'ans_message' => '', 3232 'type' => 'send_mail_to', 3233 ); 3234 3235 return $ans_hash; 3236 }; 3237 3238 return $ans_eval; 3239 } 3240 3241 sub save_answer_to_file { #accepts the last answer and mails off the result 3242 my $fileID = shift; 3243 my $ans_eval = new AnswerEvaluator; 3244 $ans_eval->install_evaluator( 3245 sub { 3246 my $rh_ans = shift; 3247 3248 unless ( defined( $rh_ans->{student_ans} ) ) { 3249 $rh_ans->throw_error("save_answers_to_file","{student_ans} field not defined"); 3250 return $rh_ans; 3251 } 3252 3253 my $error; 3254 my $string = ''; 3255 $string = qq![[<$main::studentLogin> $main::studentName /!. time() . qq!/]]\n!. 3256 $rh_ans->{student_ans}. qq!\n\n============================\n\n!; 3257 3258 if ($error = AnswerIO::saveAnswerToFile('preflight',$string) ) { 3259 $rh_ans->throw_error("save_answers_to_file","Error: $error"); 3260 } else { 3261 $rh_ans->{'student_ans'} = 'Answer saved'; 3262 $rh_ans->{'score'} = 1; 3263 } 3264 $rh_ans; 3265 } 3266 ); 3267 3268 return $ans_eval; 3269 } 3270 3271 sub mail_answers_to2 { #accepts the last answer and mails off the result 3272 my $user_address = shift; 3273 my $subject = shift; 3274 my $ra_allow_mail_to = shift; 3275 $subject = "$main::courseName WeBWorK questionnaire" unless defined $subject; 3276 send_mail_to($user_address, 3277 'subject' => $subject, 3278 'body' => $QUESTIONNAIRE_ANSWERS, 3279 'ALLOW_MAIL_TO' => $rh_envir->{ALLOW_MAIL_TO}, 3280 ); 3281 } 3282 3283 ########################################################################## 3284 ########################################################################## 3285 3286 3287 ########################################################################### 3288 ### THE FOLLOWING ARE LOCAL SUBROUTINES THAT ARE MEANT TO BE CALLED ONLY FROM THIS SCRIPT. 3289 3290 ## Internal routine that converts variables into the standard array format 3291 ## 3292 ## IN: one of the following: 3293 ## an undefined value (i.e., no variable was specified) 3294 ## a reference to an array of variable names -- [var1, var2] 3295 ## a number (the number of variables desired) -- 3 3296 ## one or more variable names -- (var1, var2) 3297 ## OUT: an array of variable names 3298 3299 sub get_var_array { 3300 my $in = shift @_; 3301 my @out; 3302 3303 if( not defined($in) ) { #if nothing defined, build default array and return 3304 @out = ( $functVarDefault ); 3305 return @out; 3306 } 3307 elsif( ref( $in ) eq 'ARRAY' ) { #if given an array ref, dereference and return 3308 return @{$in}; 3309 } 3310 elsif( $in =~ /^\d+/ ) { #if given a number, set up the array and return 3311 if( $in == 1 ) { 3312 $out[0] = 'x'; 3313 } 3314 elsif( $in == 2 ) { 3315 $out[0] = 'x'; 3316 $out[1] = 'y'; 3317 } 3318 elsif( $in == 3 ) { 3319 $out[0] = 'x'; 3320 $out[1] = 'y'; 3321 $out[2] = 'z'; 3322 } 3323 else { #default to the x_1, x_2, ... convention 3324 my ($i, $tag); 3325 for($i = 0; $i < $in; $i++) {$out[$i] = "${functVarDefault}_".($i+1)} 3326 } 3327 return @out; 3328 } 3329 else { #if given one or more names, return as an array 3330 unshift( @_, $in ); 3331 return @_; 3332 } 3333 } 3334 3335 ## Internal routine that converts limits into the standard array of arrays format 3336 ## Some of the cases are probably unneccessary, but better safe than sorry 3337 ## 3338 ## IN: one of the following: 3339 ## an undefined value (i.e., no limits were specified) 3340 ## a reference to an array of arrays of limits -- [[llim,ulim], [llim,ulim]] 3341 ## a reference to an array of limits -- [llim, ulim] 3342 ## an array of array references -- ([llim,ulim], [llim,ulim]) 3343 ## an array of limits -- (llim,ulim) 3344 ## OUT: an array of array references -- ([llim,ulim], [llim,ulim]) or ([llim,ulim]) 3345 3346 sub get_limits_array { 3347 my $in = shift @_; 3348 my @out; 3349 3350 if( not defined($in) ) { #if nothing defined, build default array and return 3351 @out = ( [$functLLimitDefault, $functULimitDefault] ); 3352 return @out; 3353 } 3354 elsif( ref($in) eq 'ARRAY' ) { #$in is either ref to array, or ref to array of refs 3355 my @deref = @{$in}; 3356 3357 if( ref( $in->[0] ) eq 'ARRAY' ) { #$in is a ref to an array of array refs 3358 return @deref; 3359 } 3360 else { #$in was just a ref to an array of numbers 3361 @out = ( $in ); 3362 return @out; 3363 } 3364 } 3365 else { #$in was an array of references or numbers 3366 unshift( @_, $in ); 3367 3368 if( ref($_[0]) eq 'ARRAY' ) { #$in was an array of references, so just return it 3369 return @_; 3370 } 3371 else { #$in was an array of numbers 3372 @out = ( \@_ ); 3373 return @out; 3374 } 3375 } 3376 } 3377 3378 #sub check_option_list { 3379 # my $size = scalar(@_); 3380 # if( ( $size % 2 ) != 0 ) { 3381 # warn "ERROR in answer evaluator generator:\n" . 3382 # "Usage: <CODE>str_cmp([\$ans1, \$ans2],%options)</CODE> 3383 # or <CODE> num_cmp([\$num1, \$num2], %options)</CODE><BR> 3384 # A list of inputs must be inclosed in square brackets <CODE>[\$ans1, \$ans2]</CODE>"; 3385 # } 3386 #} 3387 3388 # simple subroutine to display an error message when 3389 # function compares are called with invalid parameters 3390 sub function_invalid_params { 3391 my $correctEqn = shift @_; 3392 my $error_response = sub { 3393 my $PGanswerMessage = "Tell your professor that there is an error with the parameters " . 3394 "to the function answer evaluator"; 3395 return ( 0, $correctEqn, "", $PGanswerMessage ); 3396 }; 3397 return $error_response; 3398 } 3399 3400 sub clean_up_error_msg { 3401 my $msg = $_[0]; 3402 $msg =~ s/^\[[^\]]*\][^:]*://; 3403 $msg =~ s/Unquoted string//g; 3404 $msg =~ s/may\s+clash.*/does not make sense here/; 3405 $msg =~ s/\sat.*line [\d]*//g; 3406 $msg = 'Error: '. $msg; 3407 3408 return $msg; 3409 } 3410 3411 #formats the student and correct answer as specified 3412 #format must be of a form suitable for sprintf (e.g. '%0.5g'), 3413 #with the exception that a '#' at the end of the string 3414 #will cause trailing zeros in the decimal part to be removed 3415 sub prfmt { 3416 my($number,$format) = @_; # attention, the order of format and number are reversed 3417 my $out; 3418 if ($format) { 3419 warn "Incorrect format used: $format. <BR> Format should look something like %4.5g<BR>" 3420 unless $format =~ /^\s*%\d*\.?\d*\w#?\s*$/; 3421 3422 if( $format =~ s/#\s*$// ) { # remove trailing zeros in the decimal 3423 $out = sprintf( $format, $number ); 3424 $out =~ s/(\.\d*?)0+$/$1/; 3425 $out =~ s/\.$//; # in case all decimal digits were zero, remove the decimal 3426 $out =~ s/e/E/g; # only use capital E's for exponents. Little e is for 2.71828... 3427 } elsif (is_a_number($number) ){ 3428 $out = sprintf( $format, $number ); 3429 $out =~ s/e/E/g; # only use capital E's for exponents. Little e is for 2.71828... 3430 } else { # number is probably a string representing an arithmetic expression 3431 $out = $number; 3432 } 3433 3434 } else { 3435 if (is_a_number($number)) {# only use capital E's for exponents. Little e is for 2.71828... 3436 $out = $number; 3437 $out =~ s/e/E/g; 3438 } else { # number is probably a string representing an arithmetic expression 3439 $out = $number; 3440 } 3441 } 3442 return $out; 3443 } 3444 ######################################################################### 3445 # Filters for answer evaluators 3446 ######################################################################### 3447 3448 =head2 Filters 3449 3450 =pod 3451 3452 A filter is a short subroutine with the following structure. It accepts an 3453 AnswerHash, followed by a hash of options. It returns an AnswerHash 3454 3455 $ans_hash = filter($ans_hash, %options); 3456 3457 See the AnswerHash.pm file for a list of entries which can be expected to be found 3458 in an AnswerHash, such as 'student_ans', 'score' and so forth. Other entries 3459 may be present for specialized answer evaluators. 3460 3461 The hope is that a well designed set of filters can easily be combined to form 3462 a new answer_evaluator and that this method will produce answer evaluators which are 3463 are more robust than the method of copying existing answer evaluators and modifying them. 3464 3465 Here is an outline of how a filter is constructed: 3466 3467 sub filter{ 3468 my $rh_ans = shift; 3469 my %options = @_; 3470 assign_option_aliases(\%options, 3471 'alias1' => 'option5' 3472 'alias2' => 'option7' 3473 ); 3474 set_default_options(\%options, 3475 '_filter_name' => 'filter', 3476 'option5' => .0001, 3477 'option7' => 'ascii', 3478 'allow_unknown_options => 0, 3479 } 3480 .... body code of filter ....... 3481 if ($error) { 3482 $rh_ans->throw_error("FILTER_ERROR", "Something went wrong"); 3483 # see AnswerHash.pm for details on using the throw_error method. 3484 3485 $rh_ans; #reference to an AnswerHash object is returned. 3486 } 3487 3488 =cut 3489 3490 =head4 compare_numbers 3491 3492 3493 =cut 3494 3495 3496 sub compare_numbers { 3497 my ($rh_ans, %options) = @_; 3498 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($rh_ans->{student_ans}); 3499 if ($PG_eval_errors) { 3500 $rh_ans->throw_error('EVAL','There is a syntax error in your answer'); 3501 $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors); 3502 # return $rh_ans; 3503 } else { 3504 $rh_ans->{student_ans} = prfmt($inVal,$options{format}); 3505 } 3506 3507 my $permitted_error; 3508 3509 if ($rh_ans->{tolType} eq 'absolute') { 3510 $permitted_error = $rh_ans->{tolerance}; 3511 } 3512 elsif ( abs($rh_ans->{correct_ans}) <= $options{zeroLevel}) { 3513 $permitted_error = $options{zeroLevelTol}; ## want $tol to be non zero 3514 } 3515 else { 3516 $permitted_error = abs($rh_ans->{tolerance}*$rh_ans->{correct_ans}); 3517 } 3518 3519 my $is_a_number = is_a_number($inVal); 3520 $rh_ans->{score} = 1 if ( ($is_a_number) and 3521 (abs( $inVal - $rh_ans->{correct_ans} ) <= $permitted_error) ); 3522 if (not $is_a_number) { 3523 $rh_ans->{error_message} = "$rh_ans->{error_message}". 'Your answer does not evaluate to a number '; 3524 } 3525 3526 $rh_ans; 3527 } 3528 3529 =head4 std_num_filter 3530 3531 std_num_filter($rh_ans, %options) 3532 returns $rh_ans 3533 3534 Replaces some constants using math_constants, then evaluates a perl expression. 3535 3536 3537 =cut 3538 3539 sub std_num_filter { 3540 my $rh_ans = shift; 3541 my %options = @_; 3542 my $in = $rh_ans->input(); 3543 $in = math_constants($in); 3544 $rh_ans->{type} = 'std_number'; 3545 my ($inVal,$PG_eval_errors,$PG_full_error_report); 3546 if ($in =~ /\S/) { 3547 ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($in); 3548 } else { 3549 $PG_eval_errors = ''; 3550 } 3551 3552 if ($PG_eval_errors) { ##error message from eval or above 3553 $rh_ans->{ans_message} = 'There is a syntax error in your answer'; 3554 $rh_ans->{student_ans} = 3555 clean_up_error_msg($PG_eval_errors); 3556 } else { 3557 $rh_ans->{student_ans} = $inVal; 3558 } 3559 $rh_ans; 3560 } 3561 3562 =head std_num_array_filter 3563 3564 std_num_array_filter($rh_ans, %options) 3565 returns $rh_ans 3566 3567 Assumes the {student_ans} field is a numerical array, and applies BOTH check_syntax and std_num_filter 3568 to each element of the array. Does it's best to generate sensible error messages for syntax errors. 3569 A typical error message displayed in {studnet_ans} might be ( 56, error message, -4). 3570 3571 =cut 3572 3573 sub std_num_array_filter { 3574 my $rh_ans= shift; 3575 my %options = @_; 3576 set_default_options( \%options, 3577 '_filter_name' => 'std_num_array_filter', 3578 ); 3579 my @in = @{$rh_ans->{student_ans}}; 3580 my $temp_hash = new AnswerHash; 3581 my @out=(); 3582 my $PGanswerMessage = ''; 3583 foreach my $item (@in) { # evaluate each number in the vector 3584 $temp_hash->input($item); 3585 $temp_hash = check_syntax($temp_hash); 3586 if (defined($temp_hash->{error_flag}) and $temp_hash->{error_flag} eq 'SYNTAX') { 3587 $PGanswerMessage .= $temp_hash->{ans_message}; 3588 $temp_hash->{ans_message} = undef; 3589 } else { 3590 #continue processing 3591 $temp_hash = std_num_filter($temp_hash); 3592 if (defined($temp_hash->{ans_message}) and $temp_hash->{ans_message} ) { 3593 $PGanswerMessage .= $temp_hash->{ans_message}; 3594 $temp_hash->{ans_message} = undef; 3595 } 3596 } 3597 push(@out, $temp_hash->input()); 3598 3599 } 3600 if ($PGanswerMessage) { 3601 $rh_ans->input( "( " . join(", ", @out ) . " )" ); 3602 $rh_ans->throw_error('SYNTAX', 'There is a syntax error in your answer.'); 3603 } else { 3604 $rh_ans->input( [@out] ); 3605 } 3606 $rh_ans; 3607 } 3608 3609 =head4 function_from_string2 3610 3611 3612 3613 =cut 3614 3615 sub function_from_string2 { 3616 my $rh_ans = shift; 3617 my %options = @_; 3618 assign_option_aliases(\%options, 3619 'vars' => 'ra_vars', 3620 'var' => 'ra_vars', 3621 'store_in' => 'stdout', 3622 ); 3623 set_default_options( \%options, 3624 'stdin' => 'student_ans', 3625 'stdout' => 'rf_student_ans', 3626 'ra_vars' => [qw( x y )], 3627 'debug' => 0, 3628 '_filter_name' => 'function_from_string2', 3629 ); 3630 # initialize 3631 $rh_ans->{_filter_name} = $options{_filter_name}; 3632 3633 my $eqn = $rh_ans->{ $options{stdin} }; 3634 my @VARS = @{ $options{ 'ra_vars'} }; 3635 #warn "VARS = ", join("<>", @VARS) if defined($options{debug}) and $options{debug} ==1; 3636 my $originalEqn = $eqn; 3637 $eqn = &math_constants($eqn); 3638 for( my $i = 0; $i < @VARS; $i++ ) { 3639 # This next line is a hack required for 5.6.0 -- it doesn't appear to be needed in 5.6.1 3640 my ($temp,$er1,$er2) = PG_restricted_eval('"'. $VARS[$i] . '"'); 3641 #$eqn =~ s/\b$VARS[$i]\b/\$VARS[$i]/g; 3642 $eqn =~ s/\b$temp\b/\$VARS[$i]/g; 3643 3644 } 3645 #warn "equation evaluated = $eqn",$rh_ans->pretty_print(), "<br>\noptions<br>\n", 3646 # pretty_print(\%options) 3647 # if defined($options{debug}) and $options{debug} ==1; 3648 my ($function_sub,$PG_eval_errors, $PG_full_errors) = PG_answer_eval( q! 3649 sub { 3650 my @VARS = @_; 3651 my $input_str = ''; 3652 for( my $i=0; $i<@VARS; $i++ ) { 3653 $input_str .= "\$VARS[$i] = $VARS[$i]; "; 3654 } 3655 my $PGanswerMessage; 3656 $input_str .= '! . $eqn . q!'; # need the single quotes to keep the contents of $eqn from being 3657 # evaluated when it is assigned to $input_str; 3658 my ($out, $PG_eval_errors, $PG_full_errors) = PG_answer_eval($input_str); #Finally evaluated 3659 3660 if ( defined($PG_eval_errors) and $PG_eval_errors =~ /\S/ ) { 3661 $PGanswerMessage = clean_up_error_msg($PG_eval_errors); 3662 # This message seemed too verbose, but it does give extra information, we'll see if it is needed. 3663 # "<br> There was an error in evaluating your function <br> 3664 # !. $originalEqn . q! <br> 3665 # at ( " . join(', ', @VARS) . " ) <br> 3666 # $PG_eval_errors 3667 # "; # this message appears in the answer section which is not process by Latex2HTML so it must 3668 # # be in HTML. That is why $BR is NOT used. 3669 3670 } 3671 (wantarray) ? ($out, $PGanswerMessage): $out; # PGanswerMessage may be undefined. 3672 }; 3673 !); 3674 3675 if (defined($PG_eval_errors) and $PG_eval_errors =~/\S/ ) { 3676 $PG_eval_errors = clean_up_error_msg($PG_eval_errors); 3677 3678 my $PGanswerMessage = "There was an error in converting the expression 3679 $BR $originalEqn $BR into a function. 3680 $BR $PG_eval_errors."; 3681 $rh_ans->{rf_student_ans} = $function_sub; 3682 $rh_ans->{ans_message} = $PGanswerMessage; 3683 $rh_ans->{error_message} = $PGanswerMessage; 3684 $rh_ans->{error_flag} = 1; 3685 # we couldn't compile the equation, we'll return an error message. 3686 } else { 3687 # if (defined($options{stdout} )) { 3688 # $rh_ans ->{$options{stdout}} = $function_sub; 3689 # } else { 3690 # $rh_ans->{rf_student_ans} = $function_sub; 3691 # } 3692 $rh_ans ->{$options{stdout}} = $function_sub; 3693 } 3694 3695 $rh_ans; 3696 } 3697 3698 =head4 is_zero_array 3699 3700 3701 =cut 3702 3703 3704 sub is_zero_array { 3705 my $rh_ans = shift; 3706 my %options = @_; 3707 set_default_options( \%options, 3708 '_filter_name' => 'is_zero_array', 3709 'tolerance' => 0.000001, 3710 'stdin' => 'ra_differences', 3711 'stdout' => 'score', 3712 ); 3713 #intialize 3714 $rh_ans->{_filter_name} = $options{_filter_name}; 3715 3716 my $array = $rh_ans -> {$options{stdin}}; # default ra_differences 3717 my $num = @$array; 3718 my $i; 3719 my $max = 0; my $mm; 3720 for ($i=0; $i< $num; $i++) { 3721 $mm = $array->[$i] ; 3722 if (not is_a_number($mm) ) { 3723 $max = $mm; # break out if one of the elements is not a number 3724 last; 3725 } 3726 $max = abs($mm) if abs($mm) > $max; 3727 } 3728 if (not is_a_number($max)) { 3729 $rh_ans->{score} = 0; 3730 my $error = "WeBWorK was unable evaluate your function. Please check that your 3731 expression doesn't take roots of negative numbers, or divide by zero."; 3732 $rh_ans->throw_error('EVAL',$error); 3733 } else { 3734 $rh_ans->{$options{stdout}} = ($max < $options{tolerance} ) ? 1: 0; # set 'score' to 1 if the array is close to 0; 3735 } 3736 $rh_ans; 3737 } 3738 3739 =head4 best_approx_parameters 3740 3741 best_approx_parameters($rh_ans,%options); #requires the following fields in $rh_ans 3742 {rf_student_ans} # reference to the test answer 3743 {rf_correct_ans} # reference to the comparison answer 3744 {evaluation_points}, # an array of row vectors indicating the points 3745 # to evaluate when comparing the functions 3746 3747 %options # debug => 1 gives more error answers 3748 # param_vars => [''] additional parameters used to adapt to function 3749 ) 3750 3751 3752 The parameters for the comparison function which best approximates the test_function are stored 3753 in the field {ra_parameters}. 3754 3755 3756 The last $dim_of_parms_space variables are assumed to be parameters, and it is also 3757 assumed that the function \&comparison_fun 3758 depends linearly on these variables. This function finds the values for these parameters which minimizes the 3759 Euclidean distance (L2 distance) between the test function and the comparison function and the test points specified 3760 by the array reference \@rows_of_test_points. This is assumed to be an array of arrays, with the inner arrays 3761 determining a test point. 3762 3763 The comparison function should have $dim_of_params_space more input variables than the test function. 3764 3765 3766 3767 3768 3769 =cut 3770 3771 # Used internally: 3772 # 3773 # &$determine_param_coeff( $rf_comparison_function # a reference to the correct answer function 3774 # $ra_variables # an array of the active input variables to the functions 3775 # $dim_of_params_space # indicates the number of parameters upon which the 3776 # # the comparison function depends linearly. These are assumed to 3777 # # be the last group of inputs to the comparison function. 3778 # 3779 # %options # $options{debug} gives more error messages 3780 # 3781 # # A typical function might look like 3782 # # f(x,y,z,a,b) = x^2+a*cos(xz) + b*sin(x) with a parameter 3783 # # space of dimension 2 and a variable space of dimension 3. 3784 # ) 3785 # # returns a list of coefficients 3786 3787 sub best_approx_parameters { 3788 my $rh_ans = shift; 3789 my %options = @_; 3790 set_default_options(\%options, 3791 '_filter_name' => 'best_approx_paramters', 3792 'allow_unknown_options' => 1, 3793 ); 3794 my $errors = undef; 3795 # This subroutine for the determining the coefficents of the parameters at a given point 3796 # is pretty specialized, so it is included here as a sub-subroutine. 3797 my $determine_param_coeffs = sub { 3798 my ($rf_fun, $ra_variables, $dim_of_params_space, %options) =@_; 3799 my @zero_params=(); 3800 for(my $i=1;$i<=$dim_of_params_space;$i++){push(@zero_params,0); } 3801 my @vars = @$ra_variables; 3802 my @coeff = (); 3803 my @inputs = (@vars,@zero_params); 3804 my ($f0, $f1, $err); 3805 ($f0, $err) = &{$rf_fun}(@inputs); 3806 if (defined($err) ) { 3807 $errors .= "$err "; 3808 } else { 3809 for (my $i=@vars;$i<@inputs;$i++) { 3810 $inputs[$i]=1; # set one parameter to 1; 3811 my($f1,$err) = &$rf_fun(@inputs); 3812 if (defined($err) ) { 3813 $errors .= " $err "; 3814 } else { 3815 push(@coeff, $f1-$f0); 3816 } 3817 $inputs[$i]=0; # set it back 3818 } 3819 } 3820 (\@coeff, $errors); 3821 }; 3822 my $rf_fun = $rh_ans->{rf_student_ans}; 3823 my $rf_correct_fun = $rh_ans->{rf_correct_ans}; 3824 my $ra_vars_matrix = $rh_ans->{evaluation_points}; 3825 my $dim_of_param_space = @{$options{param_vars}}; 3826 # Short cut. Bail if there are no param_vars 3827 unless ($dim_of_param_space >0) { 3828 $rh_ans ->{ra_parameters} = []; 3829 return $rh_ans; 3830 } 3831 # inputs are row arrays in this case. 3832 my @zero_params=(); 3833 3834 for(my $i=1;$i<=$dim_of_param_space;$i++){push(@zero_params,0); } 3835 my @rows_of_vars = @$ra_vars_matrix; 3836 warn "input rows ", pretty_print(\@rows_of_vars) if defined($options{debug}) and $options{debug}; 3837 my $rows = @rows_of_vars; 3838 my $matrix =new Matrix($rows,$dim_of_param_space); 3839 my $rhs_vec = new Matrix($rows, 1); 3840 my $row_num = 1; 3841 my ($ra_coeff,$val2, $val1, $err1,$err2,@inputs,@vars); 3842 my $number_of_data_points = $dim_of_param_space +2; 3843 while (@rows_of_vars and $row_num <= $number_of_data_points) { 3844 # get one set of data points from the test function; 3845 @vars = @{ shift(@rows_of_vars) }; 3846 ($val2, $err1) = &{$rf_fun}(@vars); 3847 $errors .= " $err1 " if defined($err1); 3848 @inputs = (@vars,@zero_params); 3849 ($val1, $err2) = &{$rf_correct_fun}(@inputs); 3850 $errors .= " $err2 " if defined($err2); 3851 3852 unless (defined($err1) or defined($err2) ) { 3853 $rhs_vec->assign($row_num,1, $val2-$val1 ); 3854 3855 # warn "rhs data val1=$val1, val2=$val2, val2 - val1 = ", $val2 - $val1 if $options{debug}; 3856 # warn "vars ", join(" | ", @vars) if $options{debug}; 3857 3858 ($ra_coeff, $err1) = &{$determine_param_coeffs}($rf_correct_fun,\@vars,$dim_of_param_space,%options); 3859 if (defined($err1) ) { 3860 $errors .= " $err1 "; 3861 } else { 3862 my @coeff = @$ra_coeff; 3863 my $col_num=1; 3864 while(@coeff) { 3865 $matrix->assign($row_num,$col_num, shift(@coeff) ); 3866 $col_num++; 3867 } 3868 } 3869 } 3870 $row_num++; 3871 last if $errors; # break if there are any errors. 3872 # This cuts down on the size of error messages. 3873 # However it impossible to check for equivalence at 95% of points 3874 # which might be useful for functions that are not defined at some points. 3875 } 3876 warn "<br> best_approx_parameters: matrix1 <br> ", " $matrix " if $options{debug}; 3877 warn "<br> best_approx_parameters: vector <br> ", " $rhs_vec " if $options{debug}; 3878 3879 # we have Matrix * parameter = data_vec + perpendicular vector 3880 # where the matrix has column vectors defining the span of the parameter space 3881 # multiply both sides by Matrix_transpose and solve for the parameters 3882 # This is exactly what the method proj_coeff method does. 3883 my @array; 3884 if (defined($errors) ) { 3885 @array = (); # new Matrix($dim_of_param_space,1); 3886 } else { 3887 @array = $matrix->proj_coeff($rhs_vec)->list(); 3888 } 3889 # check size (hack) 3890 my $max = 0; 3891 foreach my $val (@array ) { 3892 $max = abs($val) if $max < abs($val); 3893 if (not is_a_number($val) ) { 3894 $max = "NaN: $val"; 3895 last; 3896 } 3897 } 3898 if ($max =~/NaN/) { 3899 $errors .= "WeBWorK was unable evaluate your function. Please check that your 3900 expression doesn't take roots of negative numbers, or divide by zero."; 3901 } elsif ($max > $options{maxConstantOfIntegration} ) { 3902 $errors .= "At least one of the adapting parameters 3903 (perhaps the constant of integration) is too large: $max, 3904 ( the maximum allowed is $options{maxConstantOfIntegration} )"; 3905 } 3906 3907 $rh_ans->{ra_parameters} = \@array; 3908 $rh_ans->throw_error('EVAL', $errors) if defined($errors); 3909 $rh_ans; 3910 } 3911 3912 =head4 calculate_difference_vector 3913 3914 calculate_difference_vector( $ans_hash, %options); 3915 3916 {rf_student_ans}, # a reference to the test function 3917 {rf_correct_ans}, # a reference to the correct answer function 3918 {evaluation_points}, # an array of row vectors indicating the points 3919 # to evaluate when comparing the functions 3920 {ra_parameters} # these are the (optional) additional inputs to 3921 # the comparison function which adapt it properly 3922 # to the problem at hand. 3923 3924 %options # mode => 'rel' specifies that each element in the 3925 # difference matrix is divided by the correct answer. 3926 # unless the correct answer is nearly 0. 3927 ) 3928 3929 =cut 3930 3931 sub calculate_difference_vector { 3932 my $rh_ans = shift; 3933 my %options = @_; 3934 assign_option_aliases( \%options, 3935 ); 3936 set_default_options( \%options, 3937 allow_unknown_options => 1, 3938 stdin1 => 'rf_student_ans', 3939 stdin2 => 'rf_correct_ans', 3940 stdout => 'ra_differences', 3941 debug => 0, 3942 tolType => 'absolute', 3943 error_msg_flag => 1, 3944 ); 3945 # initialize 3946 $rh_ans->{_filter_name} = 'calculate_difference_vector'; 3947 my $rf_fun = $rh_ans -> {$options{stdin1}}; # rf_student_ans by default 3948 my $rf_correct_fun = $rh_ans -> {$options{stdin2}}; # rf_correct_ans by default 3949 my $ra_parameters = $rh_ans -> {ra_parameters}; 3950 my @evaluation_points = @{$rh_ans->{evaluation_points} }; 3951 my @parameters = (); 3952 @parameters = @$ra_parameters if defined($ra_parameters) and ref($ra_parameters) eq 'ARRAY'; 3953 my $errors = undef; 3954 my @zero_params = (); 3955 for (my $i=1;$i<=@{$ra_parameters};$i++) { 3956 push(@zero_params,0); 3957 } 3958 my @differences = (); 3959 my @student_values; 3960 my @adjusted_student_values; 3961 my @instructorVals; 3962 my ($diff,$instructorVal); 3963 # calculate the vector of differences between the test function and the comparison function. 3964 while (@evaluation_points) { 3965 my ($err1, $err2,$err3); 3966 my @vars = @{ shift(@evaluation_points) }; 3967 my @inputs = (@vars, @parameters); 3968 my ($inVal, $correctVal); 3969 ($inVal, $err1) = &{$rf_fun}(@vars); 3970 $errors .= " $err1 " if defined($err1); 3971 $errors .= " Error detected evaluating student input at (".join(' , ',@vars) ." ) " if defined($options{debug}) and $options{debug}==1 and defined($err1); 3972 ($correctVal, $err2) =&{$rf_correct_fun}(@inputs); 3973 $errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err2 " if defined($err2); 3974 $errors .= " Error detected evaluating correct adapted answer at (".join(' , ',@inputs) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err2); 3975 ($instructorVal,$err3)= &$rf_correct_fun(@vars, @zero_params); 3976 $errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err3 " if defined($err3); 3977 $errors .= " Error detected evaluating instructor answer at (".join(' , ',@vars, @zero_params) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err3); 3978 unless (defined($err1) or defined($err2) or defined($err3) ) { 3979 $diff = ( $inVal - ($correctVal -$instructorVal ) ) - $instructorVal; #prevents entering too high a number? 3980 #warn "taking the difference of ", $inVal, " and ", $correctVal, " is ", $diff; 3981 if ( $options{tolType} eq 'relative' ) { #relative tolerance 3982 #warn "diff = $diff"; 3983 #$diff = ( $inVal - ($correctVal-$instructorVal ) )/abs($instructorVal) -1 if abs($instructorVal) > $options{zeroLevel}; 3984 $diff = ( $inVal - ($correctVal-$instructorVal ) )/$instructorVal -1 if abs($instructorVal) > $options{zeroLevel}; 3985 #$diff = ( $inVal - ($correctVal-$instructorVal- $instructorVal ) )/abs($instructorVal) if abs($instructorVal) > $options{zeroLevel}; 3986 #warn "diff = $diff, ", abs( &$rf_correct_fun(@inputs) ) , "-- $correctVal"; 3987 } 3988 } 3989 last if $errors; # break if there are any errors. 3990 # This cuts down on the size of error messages. 3991 # However it impossible to check for equivalence at 95% of points 3992 # which might be useful for functions that are not defined at some points. 3993 push(@student_values,$inVal); 3994 push(@adjusted_student_values,( $inVal - ($correctVal -$instructorVal) ) ); 3995 push(@differences, $diff); 3996 push(@instructorVals,$instructorVal); 3997 } 3998 if (( not defined($errors) ) or $errors eq '' or $options{error_msg_flag} ) { 3999 $rh_ans ->{$options{stdout}} = \@differences; 4000 $rh_ans ->{ra_student_values} = \@student_values; 4001 $rh_ans ->{ra_adjusted_student_values} = \@adjusted_student_values; 4002 $rh_ans->{ra_instructor_values}=\@instructorVals; 4003 $rh_ans->throw_error('EVAL', $errors) if defined($errors); 4004 } else { 4005 4006 } # no output if error_msg_flag is set to 0. 4007 4008 $rh_ans; 4009 } 4010 4011 =head4 fix_answer_for_display 4012 4013 =cut 4014 4015 sub fix_answers_for_display { 4016 my ($rh_ans, %options) = @_; 4017 if ( $rh_ans->{answerIsString} ==1) { 4018 $rh_ans = evaluatesToNumber ($rh_ans, %options); 4019 } 4020 if (defined ($rh_ans->{student_units})) { 4021 $rh_ans->{student_ans} = $rh_ans->{student_ans}. ' '. $rh_ans->{student_units}; 4022 4023 } 4024 if ( $rh_ans->catch_error('UNITS') ) { # create preview latex string for expressions even if the units are incorrect 4025 my $rh_temp = new AnswerHash; 4026 $rh_temp->{student_ans} = $rh_ans->{student_ans}; 4027 $rh_temp = check_syntax($rh_temp); 4028 $rh_ans->{preview_latex_string} = $rh_temp->{preview_latex_string}; 4029 } 4030 $rh_ans->{correct_ans} = $rh_ans->{original_correct_ans}; 4031 4032 $rh_ans; 4033 } 4034 4035 =head4 evaluatesToNumber 4036 4037 =cut 4038 4039 sub evaluatesToNumber { 4040 my ($rh_ans, %options) = @_; 4041 if (is_a_numeric_expression($rh_ans->{student_ans})) { 4042 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($rh_ans->{student_ans}); 4043 if ($PG_eval_errors) { # this if statement should never be run 4044 # change nothing 4045 } else { 4046 # change this 4047 $rh_ans->{student_ans} = prfmt($inVal,$options{format}); 4048 } 4049 } 4050 $rh_ans; 4051 } 4052 4053 =head4 is_numeric_expression 4054 4055 =cut 4056 4057 sub is_a_numeric_expression { 4058 my $testString = shift; 4059 my $is_a_numeric_expression = 0; 4060 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($testString); 4061 if ($PG_eval_errors) { 4062 $is_a_numeric_expression = 0; 4063 } else { 4064 $is_a_numeric_expression = 1; 4065 } 4066 $is_a_numeric_expression; 4067 } 4068 4069 =head4 is_a_number 4070 4071 =cut 4072 4073 sub is_a_number { 4074 my ($num,%options) = @_; 4075 my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ; 4076 my ($rh_ans); 4077 if ($process_ans_hash) { 4078 $rh_ans = $num; 4079 $num = $rh_ans->{student_ans}; 4080 } 4081 4082 my $is_a_number = 0; 4083 return $is_a_number unless defined($num); 4084 $num =~ s/^\s*//; ## remove initial spaces 4085 $num =~ s/\s*$//; ## remove trailing spaces 4086 4087 ## the following is copied from the online perl manual 4088 if ($num =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/){ 4089 $is_a_number = 1; 4090 } 4091 4092 if ($process_ans_hash) { 4093 if ($is_a_number == 1 ) { 4094 $rh_ans->{student_ans}=$num; 4095 return $rh_ans; 4096 } else { 4097 $rh_ans->{student_ans} = "Incorrect number format: You must enter a number, e.g. -6, 5.3, or 6.12E-3"; 4098 $rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3'); 4099 return $rh_ans; 4100 } 4101 } else { 4102 return $is_a_number; 4103 } 4104 } 4105 4106 =head4 is_a_fraction 4107 4108 =cut 4109 4110 sub is_a_fraction { 4111 my ($num,%options) = @_; 4112 my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ; 4113 my ($rh_ans); 4114 if ($process_ans_hash) { 4115 $rh_ans = $num; 4116 $num = $rh_ans->{student_ans}; 4117 } 4118 4119 my $is_a_fraction = 0; 4120 return $is_a_fraction unless defined($num); 4121 $num =~ s/^\s*//; ## remove initial spaces 4122 $num =~ s/\s*$//; ## remove trailing spaces 4123 4124 if ($num =~ /^\s*\-?\s*[\/\d\.Ee\s]*$/) { 4125 $is_a_fraction = 1; 4126 } 4127 4128 if ($process_ans_hash) { 4129 if ($is_a_fraction == 1 ) { 4130 $rh_ans->{student_ans}=$num; 4131 return $rh_ans; 4132 } else { 4133 $rh_ans->{student_ans} = "Not a number of fraction: You must enter a number or fraction, e.g. -6 or 7/13"; 4134 $rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3'); 4135 return $rh_ans; 4136 } 4137 4138 } else { 4139 return $is_a_fraction; 4140 } 4141 } 4142 4143 =head4 phase_pi 4144 I often discovered that the answers I was getting, when using the arctan function would be off by phases of 4145 pi, which for the tangent function, were equivalent values. This method allows for this. 4146 =cut 4147 4148 sub phase_pi { 4149 my ($num,%options) = @_; 4150 my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ; 4151 my ($rh_ans); 4152 if ($process_ans_hash) { 4153 $rh_ans = $num; 4154 $num = $rh_ans->{correct_ans}; 4155 } 4156 while( ($rh_ans->{correct_ans}) > 3.14159265358979/2 ){ 4157 $rh_ans->{correct_ans} -= 3.14159265358979; 4158 } 4159 while( ($rh_ans->{correct_ans}) <= -3.14159265358979/2 ){ 4160 $rh_ans->{correct_ans} += 3.14159265358979; 4161 } 4162 $rh_ans; 4163 } 4164 4165 =head4 is_an_arithemetic_expression 4166 4167 =cut 4168 4169 sub is_an_arithmetic_expression { 4170 my ($num,%options) = @_; 4171 my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ; 4172 my ($rh_ans); 4173 if ($process_ans_hash) { 4174 $rh_ans = $num; 4175 $num = $rh_ans->{student_ans}; 4176 } 4177 4178 my $is_an_arithmetic_expression = 0; 4179 return $is_an_arithmetic_expression unless defined($num); 4180 $num =~ s/^\s*//; ## remove initial spaces 4181 $num =~ s/\s*$//; ## remove trailing spaces 4182 4183 if ($num =~ /^[+\-*\/\^\(\)\[\]\{\}\s\d\.Ee]*$/) { 4184 $is_an_arithmetic_expression = 1; 4185 } 4186 4187 if ($process_ans_hash) { 4188 if ($is_an_arithmetic_expression == 1 ) { 4189 $rh_ans->{student_ans}=$num; 4190 return $rh_ans; 4191 } else { 4192 4193 $rh_ans->{student_ans} = "Not an arithmetic expression: You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2"; 4194 $rh_ans->throw_error('NUMBER', 'You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2'); 4195 return $rh_ans; 4196 } 4197 4198 } else { 4199 return $is_an_arithmetic_expression; 4200 } 4201 } 4202 4203 # 4204 4205 =head4 math_constants 4206 4207 replaces pi, e, and ^ with their Perl equivalents 4208 if useBaseTenLog is non-zero, convert log to logten 4209 4210 =cut 4211 4212 sub math_constants { 4213 my($in,%options) = @_; 4214 my $rh_ans; 4215 my $process_ans_hash = ( ref( $in ) eq 'AnswerHash' ) ? 1 : 0 ; 4216 if ($process_ans_hash) { 4217 $rh_ans = $in; 4218 $in = $rh_ans->{student_ans}; 4219 } 4220 # The code fragment above allows this filter to be used when the input is simply a string 4221 # as well as when the input is an AnswerHash, and options. 4222 $in =~s/\bpi\b/(4*atan2(1,1))/ge; 4223 $in =~s/\be\b/(exp(1))/ge; 4224 $in =~s/\^/**/g; 4225 if($useBaseTenLog) { 4226 $in =~ s/\blog\b/logten/g; 4227 } 4228 4229 if ($process_ans_hash) { 4230 $rh_ans->{student_ans}=$in; 4231 return $rh_ans; 4232 } else { 4233 return $in; 4234 } 4235 } 4236 4237 4238 4239 =head4 is_array 4240 4241 is_array($rh_ans) 4242 returns: $rh_ans. Throws error "NOTARRAY" if this is not an array 4243 4244 =cut 4245 4246 sub is_array { 4247 my $rh_ans = shift; 4248 # return if the result is an array 4249 return($rh_ans) if ref($rh_ans->{student_ans}) eq 'ARRAY' ; 4250 $rh_ans->throw_error("NOTARRAY","The answer is not an array"); 4251 $rh_ans; 4252 } 4253 4254 =head4 check_syntax 4255 4256 check_syntax( $rh_ans, %options) 4257 returns an answer hash. 4258 4259 latex2html preview code are installed in the answer hash. 4260 The input has been transformed, changing 7pi to 7*pi or 7x to 7*x. 4261 Syntax error messages may be generated and stored in student_ans 4262 Additional syntax error messages are stored in {ans_message} and duplicated in {error_message} 4263 4264 4265 =cut 4266 4267 sub check_syntax { 4268 my $rh_ans = shift; 4269 my %options = @_; 4270 assign_option_aliases(\%options, 4271 ); 4272 set_default_options( \%options, 4273 'stdin' => 'student_ans', 4274 'stdout' => 'student_ans', 4275 'ra_vars' => [qw( x y )], 4276 'debug' => 0, 4277 '_filter_name' => 'check_syntax', 4278 error_msg_flag => 1, 4279 ); 4280 #initialize 4281 $rh_ans->{_filter_name} = $options{_filter_name}; 4282 unless ( defined( $rh_ans->{$options{stdin}} ) ) { 4283 warn "Check_syntax requires an equation in the field '$options{stdin}' or input"; 4284 $rh_ans->throw_error("1","'$options{stdin}' field not defined"); 4285 return $rh_ans; 4286 } 4287 my $in = $rh_ans->{$options{stdin}}; 4288 my $parser = new AlgParserWithImplicitExpand; 4289 my $ret = $parser -> parse($in); #for use with loops 4290 4291 if ( ref($ret) ) { ## parsed successfully 4292 # $parser -> tostring(); # FIXME? was this needed for some reason????? 4293 $parser -> normalize(); 4294 $rh_ans -> {$options{stdout}} = $parser -> tostring(); 4295 $rh_ans -> {preview_text_string} = $in; 4296 $rh_ans -> {preview_latex_string} = $parser -> tolatex(); 4297 4298 } elsif ($options{error_msg_flag} ) { ## error in parsing 4299 4300 $rh_ans->{$options{stdout}} = 'syntax error:'. $parser->{htmlerror}, 4301 $rh_ans->{'ans_message'} = $parser -> {error_msg}, 4302 $rh_ans->{'preview_text_string'} = '', 4303 $rh_ans->{'preview_latex_string'} = '', 4304 $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'. $parser->{htmlerror} . "$BR" .$parser -> {error_msg}); 4305 } # no output is produced if there is an error and the error_msg_flag is set to zero 4306 $rh_ans; 4307 4308 } 4309 4310 =head4 check_strings 4311 4312 check_strings ($rh_ans, %options) 4313 returns $rh_ans 4314 4315 =cut 4316 4317 sub check_strings { 4318 my ($rh_ans, %options) = @_; 4319 4320 # if the student's answer is a number, simply return the answer hash (unchanged). 4321 4322 # we allow constructions like -INF to be treated as a string. Thus we ignore an initial 4323 # - in deciding whether the student's answer is a number or string 4324 4325 my $temp_ans = $rh_ans->{student_ans}; 4326 $temp_ans =~ s/^\s*\-//; # remove an initial - 4327 4328 if ( $temp_ans =~ m/[\d+\-*\/^(){}\[\]]|^\s*e\s*$|^\s*pi\s*$/) { 4329 # if ( $rh_ans->{answerIsString} == 1) { 4330 # #$rh_ans->throw_error('STRING','Incorrect Answer'); # student's answer is a number 4331 # } 4332 return $rh_ans; 4333 } 4334 # the student's answer is recognized as a string 4335 my $ans = $rh_ans->{student_ans}; 4336 4337 # OVERVIEW of reminder of function: 4338 # if answer is correct, return correct. (adjust score to 1) 4339 # if answer is incorect: 4340 # 1) determine if the answer is sensible. if it is, return incorrect. 4341 # 2) if the answer is not sensible (and incorrect), then return an error message indicating so. 4342 # no matter what: throw a 'STRING' error to skip numerical evaluations. (error flag skips remainder of pre_filters and evaluators) 4343 # last: 'STRING' post_filter will clear the error (avoiding pink screen.) 4344 4345 my $sensibleAnswer = 0; 4346 $ans = str_filters( $ans, 'compress_whitespace' ); # remove trailing, leading, and double spaces. 4347 my ($ans_eval) = str_cmp($rh_ans->{correct_ans}); 4348 my $temp_ans_hash = $ans_eval->evaluate($ans); 4349 $rh_ans->{test} = $temp_ans_hash; 4350 4351 if ($temp_ans_hash->{score} ==1 ) { # students answer matches the correct answer. 4352 $rh_ans->{score} = 1; 4353 $sensibleAnswer = 1; 4354 } else { # students answer does not match the correct answer. 4355 my $legalString = ''; # find out if string makes sense 4356 my @legalStrings = @{$options{strings}}; 4357 foreach $legalString (@legalStrings) { 4358 if ( uc($ans) eq uc($legalString) ) { 4359 $sensibleAnswer = 1; 4360 last; 4361 } 4362 } 4363 $sensibleAnswer = 1 unless $ans =~ /\S/; ## empty answers are sensible 4364 $rh_ans->throw_error('EVAL', "Your answer is not a recognized answer") unless ($sensibleAnswer); 4365 # $temp_ans_hash -> setKeys( 'ans_message' => 'Your answer is not a recognized answer' ) unless ($sensibleAnswer); 4366 # $temp_ans_hash -> setKeys( 'student_ans' => uc($ans) ); 4367 } 4368 4369 $rh_ans->{student_ans} = $ans; 4370 4371 if ($sensibleAnswer) { 4372 $rh_ans->throw_error('STRING', "The student's answer $rh_ans->{student_ans} is interpreted as a string."); 4373 } 4374 4375 $rh_ans->{'preview_text_string'} = $ans, 4376 $rh_ans->{'preview_latex_string'} = $ans, 4377 4378 # warn ("\$rh_ans->{answerIsString} = $rh_ans->{answerIsString}"); 4379 $rh_ans; 4380 } 4381 4382 =head4 check_units 4383 4384 check_strings ($rh_ans, %options) 4385 returns $rh_ans 4386 4387 4388 =cut 4389 4390 sub check_units { 4391 my ($rh_ans, %options) = @_; 4392 my %correct_units = %{$rh_ans-> {rh_correct_units}}; 4393 my $ans = $rh_ans->{student_ans}; 4394 # $ans = '' unless defined ($ans); 4395 $ans = str_filters ($ans, 'trim_whitespace'); 4396 my $original_student_ans = $ans; 4397 $rh_ans->{original_student_ans} = $original_student_ans; 4398 4399 # it surprises me that the match below works since the first .* is greedy. 4400 my ($num_answer, $units) = $ans =~ /^(.*)\s+([^\s]*)$/; 4401 4402 unless ( defined($num_answer) && $units ) { 4403 # there is an error reading the input 4404 if ( $ans =~ /\S/ ) { # the answer is not blank 4405 $rh_ans -> setKeys( 'ans_message' => "The answer \"$ans\" could not be interpreted " . 4406 "as a number or an arithmetic expression followed by a unit specification. " . 4407 "Your answer must contain units." ); 4408 $rh_ans->throw_error('UNITS', "The answer \"$ans\" could not be interpreted " . 4409 "as a number or an arithmetic expression followed by a unit specification. " . 4410 "Your answer must contain units." ); 4411 } 4412 return $rh_ans; 4413 } 4414 4415 # we have been able to parse the answer into a numerical part and a unit part 4416 4417 # $num_answer = $1; #$1 and $2 from the regular expression above 4418 # $units = $2; 4419 4420 my %units = Units::evaluate_units($units); 4421 if ( defined( $units{'ERROR'} ) ) { 4422 # handle error condition 4423 $units{'ERROR'} = clean_up_error_msg($units{'ERROR'}); 4424 $rh_ans -> setKeys( 'ans_message' => "$units{'ERROR'}" ); 4425 $rh_ans -> throw_error('UNITS', "$units{'ERROR'}"); 4426 return $rh_ans; 4427 } 4428 4429 my $units_match = 1; 4430 my $fund_unit; 4431 foreach $fund_unit (keys %correct_units) { 4432 next if $fund_unit eq 'factor'; 4433 $units_match = 0 unless $correct_units{$fund_unit} == $units{$fund_unit}; 4434 } 4435 4436 if ( $units_match ) { 4437 # units are ok. Evaluate the numerical part of the answer 4438 $rh_ans->{'tolerance'} = $rh_ans->{'tolerance'}* $correct_units{'factor'}/$units{'factor'} if 4439 $rh_ans->{'tolType'} eq 'absolute'; # the tolerance is in the units specified by the instructor. 4440 $rh_ans->{correct_ans} = prfmt($rh_ans->{correct_ans}*$correct_units{'factor'}/$units{'factor'}); 4441 $rh_ans->{student_units} = $units; 4442 $rh_ans->{student_ans} = $num_answer; 4443 4444 } else { 4445 $rh_ans -> setKeys( ans_message => 'There is an error in the units for this answer.' ); 4446 $rh_ans -> throw_error ( 'UNITS', 'There is an error in the units for this answer.' ); 4447 } 4448 4449 return $rh_ans; 4450 } 4451 4452 4453 4454 =head2 Filter utilities 4455 4456 These two subroutines can be used in filters to set default options. They 4457 help make filters perform in uniform, predictable ways, and also make it 4458 easy to recognize from the code which options a given filter expects. 4459 4460 4461 =head4 assign_option_aliases 4462 4463 Use this to assign aliases for the standard options. It must come before set_default_options 4464 within the subroutine. 4465 4466 assign_option_aliases(\%options, 4467 'alias1' => 'option5' 4468 'alias2' => 'option7' 4469 ); 4470 4471 4472 If the subroutine is called with an option " alias1 => 23 " it will behave as if it had been 4473 called with the option " option5 => 23 " 4474 4475 =cut 4476 4477 4478 4479 sub assign_option_aliases { 4480 my $rh_options = shift; 4481 warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH'; 4482 my @option_aliases = @_; 4483 while (@option_aliases) { 4484 my $alias = shift @option_aliases; 4485 my $option_key = shift @option_aliases; 4486 4487 if (defined($rh_options->{$alias} )) { # if the alias appears in the option list 4488 if (not defined($rh_options->{$option_key}) ) { # and the option itself is not defined, 4489 $rh_options->{$option_key} = $rh_options->{$alias}; # insert the value defined by the alias into the option value 4490 # the FIRST alias for a given option takes precedence 4491 # (after the option itself) 4492 } else { 4493 warn "option $option_key is already defined as", $rh_options->{$option_key}, "<br>\n", 4494 "The attempt to override this option with the alias $alias with value ", $rh_options->{$alias}, 4495 " was ignored."; 4496 } 4497 } 4498 delete($rh_options->{$alias}); # remove the alias from the initial list 4499 } 4500 4501 } 4502 4503 =head4 set_default_options 4504 4505 set_default_options(\%options, 4506 '_filter_name' => 'filter', 4507 'option5' => .0001, 4508 'option7' => 'ascii', 4509 'allow_unknown_options => 0, 4510 } 4511 4512 Note that the first entry is a reference to the options with which the filter was called. 4513 4514 The option5 is set to .0001 unless the option is explicitly set when the subroutine is called. 4515 4516 The B<'_filter_name'> option should always be set, although there is no error if it is missing. 4517 It is used mainly for debugging answer evaluators and allows 4518 you to keep track of which filter is currently processing the answer. 4519 4520 If B<'allow_unknown_options'> is set to 0 then if the filter is called with options which do NOT appear in the 4521 set_default_options list an error will be signaled and a warning message will be printed out. This provides 4522 error checking against misspelling an option and is generally what is desired for most filters. 4523 4524 Occasionally one wants to write a filter which accepts a long list of options, not all of which are known in advance, 4525 but only uses a subset of the options 4526 provided. In this case, setting 'allow_unkown_options' to 1 prevents the error from being signaled. 4527 4528 =cut 4529 4530 sub set_default_options { 4531 my $rh_options = shift; 4532 warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH'; 4533 my %default_options = @_; 4534 unless ( defined($default_options{allow_unknown_options}) and $default_options{allow_unknown_options} == 1 ) { 4535 foreach my $key1 (keys %$rh_options) { 4536 warn "This option |$key1| is not recognized in this subroutine<br> ", pretty_print($rh_options) unless exists($default_options{$key1}); 4537 } 4538 } 4539 foreach my $key (keys %default_options) { 4540 if ( not defined($rh_options->{$key} ) and defined( $default_options{$key} ) ) { 4541 $rh_options->{$key} = $default_options{$key}; #this allows tol => undef to allow the tol option, but doesn't define 4542 # this key unless tol is explicitly defined. 4543 } 4544 } 4545 } 4546 4547 =head2 Problem Grader Subroutines 4548 4549 =cut 4550 4551 ## Problem Grader Subroutines 4552 4553 ##################################### 4554 # This is a model for plug-in problem graders 4555 ##################################### 4556 sub install_problem_grader { 4557 my $rf_problem_grader = shift; 4558 my $rh_flags = PG_restricted_eval(q!\\%main::PG_FLAGS!); 4559 $rh_flags->{PROBLEM_GRADER_TO_USE} = $rf_problem_grader; 4560 } 4561 4562 =head4 std_problem_grader 4563 4564 This is an all-or-nothing grader. A student must get all parts of the problem write 4565 before receiving credit. You should make sure to use this grader on multiple choice 4566 and true-false questions, otherwise students will be able to deduce how many 4567 answers are correct by the grade reported by webwork. 4568 4569 4570 install_problem_grader(~~&std_problem_grader); 4571 4572 =cut 4573 4574 sub std_problem_grader { 4575 my $rh_evaluated_answers = shift; 4576 my $rh_problem_state = shift; 4577 my %form_options = @_; 4578 my %evaluated_answers = %{$rh_evaluated_answers}; 4579 # The hash $rh_evaluated_answers typically contains: 4580 # 'answer1' => 34, 'answer2'=> 'Mozart', etc. 4581 4582 # By default the old problem state is simply passed back out again. 4583 my %problem_state = %$rh_problem_state; 4584 4585 # %form_options might include 4586 # The user login name 4587 # The permission level of the user 4588 # The studentLogin name for this psvn. 4589 # Whether the form is asking for a refresh or is submitting a new answer. 4590 4591 # initial setup of the answer 4592 my %problem_result = ( score => 0, 4593 errors => '', 4594 type => 'std_problem_grader', 4595 msg => '', 4596 ); 4597 # Checks 4598 4599 my $ansCount = keys %evaluated_answers; # get the number of answers 4600 4601 unless ($ansCount > 0 ) { 4602 4603 $problem_result{msg} = "This problem did not ask any questions."; 4604 return(\%problem_result,\%problem_state); 4605 } 4606 4607 if ($ansCount > 1 ) { 4608 $problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ; 4609 } 4610 4611 unless ($form_options{answers_submitted} == 1) { 4612 return(\%problem_result,\%problem_state); 4613 } 4614 4615 my $allAnswersCorrectQ=1; 4616 foreach my $ans_name (keys %evaluated_answers) { 4617 # I'm not sure if this check is really useful. 4618 if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) { 4619 $allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} ); 4620 } 4621 else { 4622 die "Error at file ",__FILE__,"line ", __LINE__,": Answer |$ans_name| is not a hash reference\n". 4623 $evaluated_answers{$ans_name} . 4624 "This probably means that the answer evaluator for this answer\n" . 4625 "is not working correctly."; 4626 $problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}"; 4627 } 4628 } 4629 # report the results 4630 $problem_result{score} = $allAnswersCorrectQ; 4631 4632 # I don't like to put in this bit of code. 4633 # It makes it hard to construct error free problem graders 4634 # I would prefer to know that the problem score was numeric. 4635 unless (defined($problem_state{recorded_score}) and $problem_state{recorded_score} =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/ ) { 4636 $problem_state{recorded_score} = 0; # This gets rid of non-numeric scores 4637 } 4638 # 4639 if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) { 4640 $problem_state{recorded_score} = 1; 4641 } 4642 else { 4643 $problem_state{recorded_score} = 0; 4644 } 4645 4646 $problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1; 4647 $problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0; 4648 4649 $problem_state{state_summary_msg} = ''; # an HTML formatted message printed at the bottom of the problem page 4650 4651 (\%problem_result, \%problem_state); 4652 } 4653 4654 =head4 std_problem_grader2 4655 4656 This is an all-or-nothing grader. A student must get all parts of the problem write 4657 before receiving credit. You should make sure to use this grader on multiple choice 4658 and true-false questions, otherwise students will be able to deduce how many 4659 answers are correct by the grade reported by webwork. 4660 4661 4662 install_problem_grader(~~&std_problem_grader2); 4663 4664 The only difference between the two versions 4665 is at the end of the subroutine, where std_problem_grader2 4666 records the attempt only if there have been no syntax errors, 4667 whereas std_problem_grader records it regardless. 4668 4669 =cut 4670 4671 4672 4673 sub std_problem_grader2 { 4674 my $rh_evaluated_answers = shift; 4675 my $rh_problem_state = shift; 4676 my %form_options = @_; 4677 my %evaluated_answers = %{$rh_evaluated_answers}; 4678 # The hash $rh_evaluated_answers typically contains: 4679 # 'answer1' => 34, 'answer2'=> 'Mozart', etc. 4680 4681 # By default the old problem state is simply passed back out again. 4682 my %problem_state = %$rh_problem_state; 4683 4684 # %form_options might include 4685 # The user login name 4686 # The permission level of the user 4687 # The studentLogin name for this psvn. 4688 # Whether the form is asking for a refresh or is submitting a new answer. 4689 4690 # initial setup of the answer 4691 my %problem_result = ( score => 0, 4692 errors => '', 4693 type => 'std_problem_grader', 4694 msg => '', 4695 ); 4696 4697 # syntax errors are not counted. 4698 my $record_problem_attempt = 1; 4699 # Checks 4700 4701 my $ansCount = keys %evaluated_answers; # get the number of answers 4702 unless ($ansCount > 0 ) { 4703 $problem_result{msg} = "This problem did not ask any questions."; 4704 return(\%problem_result,\%problem_state); 4705 } 4706 4707 if ($ansCount > 1 ) { 4708 $problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ; 4709 } 4710 4711 unless ($form_options{answers_submitted} == 1) { 4712 return(\%problem_result,\%problem_state); 4713 } 4714 4715 my $allAnswersCorrectQ=1; 4716 foreach my $ans_name (keys %evaluated_answers) { 4717 # I'm not sure if this check is really useful. 4718 if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) { 4719 $allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} ); 4720 } 4721 else { 4722 die "Error at file ",__FILE__,"line ", __LINE__,": Answer |$ans_name| is not a hash reference\n". 4723 $evaluated_answers{$ans_name} . 4724 "This probably means that the answer evaluator for this answer\n" . 4725 "is not working correctly."; 4726 $problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}"; 4727 } 4728 } 4729 # report the results 4730 $problem_result{score} = $allAnswersCorrectQ; 4731 4732 # I don't like to put in this bit of code. 4733 # It makes it hard to construct error free problem graders 4734 # I would prefer to know that the problem score was numeric. 4735 unless ($problem_state{recorded_score} =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/ ) { 4736 $problem_state{recorded_score} = 0; # This gets rid of non-numeric scores 4737 } 4738 # 4739 if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) { 4740 $problem_state{recorded_score} = 1; 4741 } 4742 else { 4743 $problem_state{recorded_score} = 0; 4744 } 4745 # record attempt only if there have been no syntax errors. 4746 4747 if ($record_problem_attempt == 1) { 4748 $problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1; 4749 $problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0; 4750 $problem_state{state_summary_msg} = ''; # an HTML formatted message printed at the bottom of the problem page 4751 4752 } 4753 else { 4754 $problem_result{show_partial_correct_answers} = 0 ; # prevent partial correct answers from being shown for syntax errors. 4755 } 4756 (\%problem_result, \%problem_state); 4757 } 4758 4759 =head4 avg_problem_grader 4760 4761 This grader gives a grade depending on how many questions from the problem are correct. (The highest 4762 grade is the one that is kept. One can never lower the recorded grade on a problem by repeating it.) 4763 Many professors (and almost all students :-) ) prefer this grader. 4764 4765 4766 install_problem_grader(~~&avg_problem_grader); 4767 4768 =cut 4769 4770 4771 sub avg_problem_grader { 4772 my $rh_evaluated_answers = shift; 4773 my $rh_problem_state = shift; 4774 my %form_options = @_; 4775 my %evaluated_answers = %{$rh_evaluated_answers}; 4776 # The hash $rh_evaluated_answers typically contains: 4777 # 'answer1' => 34, 'answer2'=> 'Mozart', etc. 4778 4779 # By default the old problem state is simply passed back out again. 4780 my %problem_state = %$rh_problem_state; 4781 4782 4783 # %form_options might include 4784 # The user login name 4785 # The permission level of the user 4786 # The studentLogin name for this psvn. 4787 # Whether the form is asking for a refresh or is submitting a new answer. 4788 4789 # initial setup of the answer 4790 my $total=0; 4791 my %problem_result = ( score => 0, 4792 errors => '', 4793 type => 'avg_problem_grader', 4794 msg => '', 4795 ); 4796 my $count = keys %evaluated_answers; 4797 $problem_result{msg} = 'You can earn partial credit on this problem.' if $count >1; 4798 # Return unless answers have been submitted 4799 unless ($form_options{answers_submitted} == 1) { 4800 return(\%problem_result,\%problem_state); 4801 } 4802 4803 # Answers have been submitted -- process them. 4804 foreach my $ans_name (keys %evaluated_answers) { 4805 # I'm not sure if this check is really useful. 4806 if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) { 4807 $total += $evaluated_answers{$ans_name}->{score}; 4808 } 4809 else { 4810 die "Error: Answer |$ans_name| is not a hash reference\n". 4811 $evaluated_answers{$ans_name} . 4812 "This probably means that the answer evaluator for this answer\n" . 4813 "is not working correctly."; 4814 $problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}"; 4815 } 4816 } 4817 # Calculate score rounded to three places to avoid roundoff problems 4818 $problem_result{score} = $total/$count if $count; 4819 # increase recorded score if the current score is greater. 4820 $problem_state{recorded_score} = $problem_result{score} if $problem_result{score} > $problem_state{recorded_score}; 4821 4822 4823 $problem_state{num_of_correct_ans}++ if $total == $count; 4824 $problem_state{num_of_incorrect_ans}++ if $total < $count ; 4825 4826 $problem_state{state_summary_msg} = ''; # an HTML formatted message printed at the bottom of the problem page 4827 4828 warn "Error in grading this problem the total $total is larger than $count" if $total > $count; 4829 (\%problem_result, \%problem_state); 4830 } 4831 4832 =head2 Utility subroutines 4833 4834 =head4 4835 4836 warn pretty_print( $rh_hash_input) 4837 4838 This can be very useful for printing out messages about objects while debugging 4839 4840 =cut 4841 4842 sub pretty_print { 4843 my $r_input = shift; 4844 my $out = ''; 4845 if ( not ref($r_input) ) { 4846 $out = $r_input; # not a reference 4847 } elsif ("$r_input" =~/hash/i) { # this will pick up objects whose '$self' is hash and so works better than ref($r_iput). 4848 local($^W) = 0; 4849 $out .= "$r_input " ."<TABLE border = \"2\" cellpadding = \"3\" BGCOLOR = \"#FFFFFF\">"; 4850 foreach my $key (lex_sort( keys %$r_input )) { 4851 $out .= "<tr><TD> $key</TD><TD>=></td><td> ".pretty_print($r_input->{$key}) . "</td></tr>"; 4852 } 4853 $out .="</table>"; 4854 } elsif (ref($r_input) eq 'ARRAY' ) { 4855 my @array = @$r_input; 4856 $out .= "( " ; 4857 while (@array) { 4858 $out .= pretty_print(shift @array) . " , "; 4859 } 4860 $out .= " )"; 4861 } elsif (ref($r_input) eq 'CODE') { 4862 $out = "$r_input"; 4863 } else { 4864 $out = $r_input; 4865 } 4866 $out; 4867 } 4868 4869 1;
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