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Added a new subroutine for constructing filters
1 #!/usr/local/bin/webwork-perl 2 3 # This file is PGanswermacros.pl 4 # This includes the subroutines for the ANS macros, that 5 # is, macros allowing a more flexible answer checking 6 #################################################################### 7 # Copyright @ 1995-2000 University of Rochester 8 # All Rights Reserved 9 #################################################################### 10 #$Id$ 11 12 =head1 NAME 13 14 PGanswermacros.pl -- located in the courseScripts directory 15 16 =head1 SYNPOSIS 17 18 Number Answer Evaluators: 19 num_cmp() -- uses an input hash to determine parameters 20 21 std_num_cmp(), std_num_cmp_list(), std_num_cmp_abs, std_num_cmp_abs_list() 22 frac_num_cmp(), frac_num_cmp_list(), frac_num_cmp_abs, frac_num_cmp_abs_list() 23 arith_num_cmp(), arith_num_cmp_list(), arith_num_cmp_abs, arith_num_cmp_abs_list() 24 strict_num_cmp(), strict_num_cmp_list(), strict_num_cmp_abs, strict_num_cmp_abs_list() 25 numerical_compare_with_units() -- requires units as part of the answer 26 std_num_str_cmp() -- also accepts a set of strings as possible answers 27 28 Function Answer Evaluators: 29 fun_cmp() -- uses an input hash to determine parameters 30 31 function_cmp(), function_cmp_abs() 32 function_cmp_up_to_constant(), function_cmp_up_to_constant_abs() 33 multivar_function_cmp() 34 35 String Answer Evaluators: 36 str_cmp() -- uses an input hash to determine parameters 37 38 std_str_cmp(), std_str_cmp_list(), std_cs_str_cmp(), std_cs_str_cmp_list() 39 strict_str_cmp(), strict_str_cmp_list() 40 ordered_str_cmp(), ordered_str_cmp_list(), ordered_cs_str_cmp(), ordered_cs_str_cmp_list() 41 unordered_str_cmp(), unordered_str_cmp_list(), unordered_cs_str_cmp(), unordered_cs_str_cmp_list() 42 43 Miscellaneous Answer Evaluators: 44 checkbox_cmp() 45 radio_cmp() 46 47 =cut 48 49 =head1 DESCRIPTION 50 51 This file adds subroutines which create "answer evaluators" for checking 52 answers. Each answer evaluator accepts a single input from a student answer, 53 checks it and creates an output hash %ans_hash with seven or eight entries 54 (the preview_latex_string is optional). The output hash is now being created 55 with the AnswerHash package "class", which is located at the end of this file. 56 This class is currently just a wrapper for the hash, but this might change in 57 the future as new capabilities are added. 58 59 score => $correctQ, 60 correct_ans => $originalCorrEqn, 61 student_ans => $modified_student_ans 62 original_student_ans => $original_student_answer, 63 ans_message => $PGanswerMessage, 64 type => 'typeString', 65 preview_text_string => $preview_text_string, 66 preview_latex_string => $preview_latex_string 67 68 69 $ans_hash{score} -- a number between 0 and 1 indicating 70 whether the answer is correct. Fractions 71 allow the implementation of partial 72 credit for incorrect answers. 73 $ans_hash{correct_ans} -- The correct answer, as supplied by the 74 instructor and then formatted. This can 75 be viewed by the student after the answer date. 76 $ans_hash{student_ans} -- This is the student answer, after reformatting; 77 for example the answer might be forced 78 to capital letters for comparison with 79 the instructors answer. For a numerical 80 answer, it gives the evaluated answer. 81 This is displayed in the section reporting 82 the results of checking the student answers. 83 $ans_hash{original_student_ans} -- This is the original student answer. This is displayed 84 on the preview page and may be used for sticky answers. 85 $ans_hash{ans_message} -- Any error message, or hint provided by the answer evaluator. 86 This is also displayed in the section reporting 87 the results of checking the student answers. 88 $ans_hash{type} -- A string indicating the type of answer evaluator. This 89 helps in preprocessing the student answer for errors. 90 Some examples: 91 'number_with_units' 92 'function' 93 'frac_number' 94 'arith_number' 95 $ans_hash{preview_text_string} -- This typically shows how the student answer was parsed. It is 96 displayed on the preview page. For a student answer of 2sin(3x) 97 this would be 2*sin(3*x). For string answers it is typically the 98 same as $ans_hash{student_ans}. 99 $ans_hash{preview_latex_string} -- THIS IS OPTIONAL. This is latex version of the student answer 100 which is used to show a typeset view on the answer on the preview 101 page. For a student answer of 2/3, this would be \frac{2}{3}. 102 103 Technical note: the routines in this file are not actually answer evaluators. Instead, they create 104 answer evaluators. An answer evaluator is an anonymous subroutine, referenced by a named scalar. The 105 routines in this file build the subroutine and return a reference to it. Later, when the student 106 actually enters an answer, the problem processor feeds that answer to the referenced subroutine, which 107 evaluates it and returns a score (usually 0 or 1). For most users, this distinction is unimportant, but 108 if you plan on writing your own answer evaluators, you should understand this point. 109 110 =cut 111 112 BEGIN { 113 be_strict(); # an alias for use strict. This means that all global variable must contain main:: as a prefix. 114 } 115 116 117 my ($BR , # convenient localizations. 118 $PAR , 119 $numRelPercentTolDefault , 120 $numZeroLevelDefault , 121 $numZeroLevelTolDefault , 122 $numAbsTolDefault , 123 $numFormatDefault , 124 $functRelPercentTolDefault , 125 $functZeroLevelDefault , 126 $functZeroLevelTolDefault , 127 $functAbsTolDefault , 128 $functNumOfPoints , 129 $functVarDefault , 130 $functLLimitDefault , 131 $functULimitDefault , 132 $functMaxConstantOfIntegration , 133 $CA 134 ); 135 136 137 138 139 sub _PGanswermacros_init { 140 141 $BR = $main::BR; # convenient localizations. 142 $PAR = $main::PAR; 143 144 # import defaults 145 # these are now imported from the %envir variable 146 $numRelPercentTolDefault = $main::numRelPercentTolDefault; 147 $numZeroLevelDefault = $main::numZeroLevelDefault; 148 $numZeroLevelTolDefault = $main::numZeroLevelTolDefault; 149 $numAbsTolDefault = $main::numAbsTolDefault; 150 $numFormatDefault = $main::numFormatDefault; 151 $functRelPercentTolDefault = $main::functRelPercentTolDefault; 152 $functZeroLevelDefault = $main::functZeroLevelDefault; 153 $functZeroLevelTolDefault = $main::functZeroLevelTolDefault; 154 $functAbsTolDefault = $main::functAbsTolDefault; 155 $functNumOfPoints = $main::functNumOfPoints; 156 $functVarDefault = $main::functVarDefault; 157 $functLLimitDefault = $main::functLLimitDefault; 158 $functULimitDefault = $main::functULimitDefault; 159 $functMaxConstantOfIntegration = $main::functMaxConstantOfIntegration; 160 161 162 163 } 164 165 ########################################################################## 166 ########################################################################## 167 ## Number answer evaluators 168 169 =head2 Number Answer Evaluators 170 171 Number answer evaluators take in a numerical answer, compare it to the correct answer, 172 and return a score. In addition, they can choose to accept or reject an answer based on 173 its format, closeness to the correct answer, and other criteria. There are two types 174 of numerical answer evaluators: num_cmp(), which takes a hash of named options as parameters, 175 and the "mode"_num_cmp() variety, which use different functions to access different sets of 176 options. In addition, there is the special case of std_num_str_cmp(), which can evaluate 177 both numbers and strings. 178 179 Numerical Comparison Options 180 181 correctAnswer -- This is the correct answer that the student answer will 182 be compared to. However, this does not mean that the 183 student answer must match this exactly. How close the 184 student answer must be is determined by the other 185 options, especially tolerance and format. 186 187 tolerance -- These options determine how close the student answer 188 must be to the correct answer to qualify. There are two 189 types of tolerance: relative and absolute. Relative 190 tolerances are given in percentages. A relative 191 tolerance of 1 indicates that the student answer must 192 be within 1% of the correct answer to qualify as correct. 193 In other words, a student answer is correct when 194 abs(studentAnswer - correctAnswer) <= abs(.01*relpercentTol*correctAnswer) 195 Using absolute tolerance, the student answer must be a 196 fixed distance from the correct answer to qualify. 197 For example, an absolute tolerance of 5 means that any 198 number which is +-5 of the correct answer qualifies as correct. 199 Final (rarely used) tolerance options are zeroLevel 200 and zeroLevelTol, used in conjunction with relative 201 tolerance. if correctAnswer has absolute value less than 202 or equal to zeroLevel, then the student answer must be, 203 in absolute terms, within zeroLevelTol of correctAnswer, i.e., 204 abs(studentAnswer - correctAnswer) <= zeroLevelTol. 205 In other words, if the correct answer is very near zero, 206 an absolute tolerance will be used. One must do this to 207 handle floating point answers very near zero, because of 208 the inaccuracy of floating point arithmetic. However, the 209 default values are almost always adequate. 210 211 mode -- This determines the allowable methods for entering an 212 answer. Answers which do not meet this requirement will 213 be graded as incorrect, regardless of their numerical 214 value. The recognized modes are: 215 'std' (default) -- allows any expression which evaluates 216 to a number, including those using 217 elementary functions like sin() and 218 exp(), as well as the operations of 219 arithmetic (+, -, *, /, ^) 220 'strict' -- only decimal numbers are allowed 221 'frac' -- whole numbers and fractions are allowed 222 'arith' -- arithmetic expressions are allowed, but 223 no functions 224 Note that all modes allow the use of "pi" and "e" as 225 constants, and also the use of "E" to represent scientific 226 notation. 227 228 format -- The format to use when displaying the correct and 229 submitted answers. This has no effect on how answers are 230 evaluated; it is only for cosmetic purposes. The 231 formatting syntax is the same as Perl uses for the sprintf() 232 function. Format strings are of the form '%m.nx' or '%m.nx#', 233 where m and n are described below, and x is a formatter. 234 Esentially, m is the minimum length of the field 235 (make this negative to left-justify). Note that the decimal 236 point counts as a character when determining the field width. 237 If m begins with a zero, the number will be padded with zeros 238 instead of spaces to fit the field. 239 The precision specifier (n) works differently, depending 240 on which formatter you are using. For d, i, o, u, x and X 241 formatters (non-floating point formatters), n is the minimum 242 number of digits to display. For e and f, it is the number of 243 digits that appear after the decimal point (extra digits will 244 be rounded; insufficient digits will be padded with spaces--see 245 '#' below). For g, it is the number of significant digits to 246 display. 247 The full list of formatters can be found in the manpage 248 for printf(3), or by typing "perldoc -f sprintf" at a 249 terminal prompt. The following is a brief summary of the 250 most frequent formatters: 251 d -- decimal number 252 ld -- long decimal number 253 u -- unsigned decimal number 254 lu -- long unsigned decimal number 255 x -- hexadecimal number 256 o -- octal number 257 e -- floating point number in scientific notation 258 f -- floating point number 259 g -- either e or f, whichever takes less space 260 Technically, g will use e if the exponent is less than -4 or 261 greater than or equal to the precision. Trailing zeros are 262 removed in this mode. 263 If the format string ends in '#', trailing zeros will be 264 removed in the decimal part. Note that this is not a standard 265 syntax; it is handled internally by WeBWorK and not by Perl 266 (although this should not be a concern to end users). 267 The default format is '%0.5f#', which displays as a floating 268 point number with 5 digits of precision and no trailing zeros. 269 Other useful format strings might be '%0.2f' for displaying 270 dollar amounts, or '%010d' to display an integer with leading 271 zeros. Setting format to an empty string ( '' ) means no 272 formatting will be used; this will show 'arbitrary' precision 273 floating points. 274 275 Default Values (As of 7/24/2000) (Option -- Variable Name -- Value) 276 277 Format -- $numFormatDefault -- "%0.5f#" 278 Relative Tolerance -- $numRelPercentTolDefault -- .1 279 Absolute Tolerance -- $numAbsTolDefault -- .001 280 Zero Level -- $numZeroLevelDefault -- 1E-14 281 Zero Level Tolerance -- $numZeroLevelTolDefault -- 1E-12 282 283 =cut 284 285 286 =head3 num_cmp() 287 288 Compares a number or a list of numbers, using a named hash of options to set 289 parameters. This can make for more readable code than using the "mode"_num_cmp() 290 style, but some people find one or the other easier to remember. 291 292 ANS( num_cmp( answer or answer_array_ref, options_hash ) ); 293 294 1. the correct answer, or a reference to an array of correct answers 295 2. a hash with the following keys (all optional): 296 mode -- 'std' (default) (allows any expression evaluating to 297 a number) 298 'strict' (only numbers are allowed) 299 'frac' (fractions are allowed) 300 'arith' (arithmetic expressions allowed) 301 format -- '%0.5f#' (default); defines formatting for the 302 correct answer 303 tol -- an absolute tolerance, or 304 relTol -- a relative tolerance 305 units -- the units to use for the answer(s) 306 strings -- a reference to an array of strings which are valid 307 answers (works like std_num_str_cmp() ) 308 zeroLevel -- if the correct answer is this close to zero, 309 then zeroLevelTol applies 310 zeroLevelTol -- absolute tolerance to allow when answer is close 311 to zero 312 313 debug -- if set to 1, provides verbose listing of 314 hash entries throughout fliters. 315 316 Returns an answer evaluator, or (if given a reference to an array of 317 answers), a list of answer evaluators. Note that a reference to an array of 318 answers results is just a shortcut for writing a separate <code>num_cmp()</code> for each 319 answer. 320 321 EXAMPLES: 322 323 num_cmp( 5 ) -- correct answer is 5, using defaults 324 for all options 325 num_cmp( [5,6,7] ) -- correct answers are 5, 6, and 7, 326 using defaults for all options 327 num_cmp( 5, mode => 'strict' ) -- correct answer is 5, mode is strict 328 num_cmp( [5,6], relTol => 5 ) -- correct answers are 5 and 6, 329 both with 5% relative tolerance 330 num_cmp( 6, strings => ["Inf", "Minf", "NaN"] ) 331 -- correct answer is 6, "Inf", "Minf", 332 and "NaN" recognized as valid, but 333 incorrect answers. 334 num_cmp( "-INF", strings => ["INF", "-INF"] ) 335 -- correct answer is "-INF", "INF" and 336 numerical expressions recognized as valid, 337 but incorrect answers. 338 339 340 =cut 341 342 sub num_cmp { 343 my $correctAnswer = shift @_; 344 $CA = $correctAnswer; 345 my @opt = @_; 346 my %out_options; 347 348 ######################################################################### 349 # Retain this first check for backword compatibility. Allows input of the form 350 # num_cmp($ans, 1, '%0.5f') but warns against it 351 ######################################################################### 352 my %known_options = ( 353 'mode' => 'std', 354 'format' => $numFormatDefault, 355 'tol' => $numAbsTolDefault, 356 'relTol' => $numRelPercentTolDefault, 357 'units' => undef, 358 'strings' => undef, 359 'zeroLevel' => $numZeroLevelDefault, 360 'zeroLevelTol' => $numZeroLevelTolDefault, 361 'tolType' => 'relative', 362 'tolerance' => 1, 363 'reltol' => undef, #alternate spelling 364 'unit' => undef, #alternate spelling 365 'debug' => 0 366 ); 367 368 my @output_list; 369 my( $relPercentTol, $format, $zeroLevel, $zeroLevelTol) = @opt; 370 371 unless( ref($correctAnswer) eq 'ARRAY' || scalar( @opt ) == 0 || 372 ( defined($opt[0]) and exists $known_options{$opt[0]} ) ) { 373 # unless the first parameter is a list of arrays 374 # or the second parameter is a known option or 375 # no options were used, 376 # use the old num_cmp which does not use options, but has inputs 377 # $relPercentTol,$format,$zeroLevel,$zeroLevelTol 378 warn "This method of using num_cmp() is deprecated. Please rewrite this" . 379 " problem using the options style of parameter passing (or" . 380 " check that your first option is spelled correctly)."; 381 382 %out_options = ( 'relTol' => $relPercentTol, 383 'format' => $format, 384 'zeroLevel' => $zeroLevel, 385 'zeroLevelTol' => $zeroLevelTol, 386 'mode' => 'std' 387 ); 388 } 389 390 ######################################################################### 391 # Now handle the options assuming they are entered in the form 392 # num_cmp($ans, relTol=>1, format=>'%0.5f') 393 ######################################################################### 394 %out_options = @opt; 395 assign_option_aliases( \%out_options, 396 'reltol' => 'relTol', 397 'unit' => 'units', 398 'abstol' => 'tol', 399 ); 400 401 set_default_options( \%out_options, 402 'tolType' => (defined($out_options{'tol'}) ) ? 'absolute' : 'relative', # the existence of "tol" means that we use absolute tolerance mode 403 'tolerance' => (defined($out_options{'tolType'}) && $out_options{'tolType'} eq 'absolute' ) ? $numAbsTolDefault : $numRelPercentTolDefault, # relative tolerance is the default 404 'mode' => 'std', 405 'format' => $numFormatDefault, 406 'tol' => undef, 407 'relTol' => undef, 408 'units' => undef, 409 'strings' => undef, 410 'zeroLevel' => $numZeroLevelDefault, 411 'zeroLevelTol' => $numZeroLevelTolDefault, 412 'debug' => 0, 413 ); 414 415 # can't use both units and strings 416 if( defined( $out_options{'units'} ) && defined( $out_options{'strings'} ) ) { 417 warn "Can't use both 'units' and 'strings' in the same problem " . 418 "(check your parameters to num_cmp() )"; 419 } 420 421 # absolute tolType and relTol are incompatible. So are relative tolType and tol 422 if( defined( $out_options{'relTol'} ) && $out_options{'tolType'} eq 'absolute' ) { 423 warn "The 'tolType' 'absolute' is not compatible with 'relTol' " . 424 "(check your parameters to num_cmp() )"; 425 } 426 if( defined( $out_options{'tol'} ) && $out_options{'tolType'} eq 'relative' ) { 427 warn "The 'tolType' 'relative' is not compatible with 'tol' " . 428 "(check your parameters to num_cmp() )"; 429 } 430 431 432 # Handle legacy options 433 if ($out_options{tolType} eq 'absolute') { 434 $out_options{'tolerance'}=$out_options{'tol'} if defined($out_options{'tol'}); 435 delete($out_options{'relTol'}) if exists( $out_options{'relTol'} ); 436 } else { 437 $out_options{'tolerance'}=$out_options{'relTol'} if defined($out_options{'relTol'}); 438 # delete($out_options{'tol'}) if exists( $out_options{'tol'} ); 439 } 440 # end legacy options 441 442 # thread over lists 443 my @ans_list = (); 444 445 if ( ref($correctAnswer) eq 'ARRAY' ) { 446 @ans_list = @{$correctAnswer}; 447 } 448 else { push( @ans_list, $correctAnswer ); 449 } 450 451 # produce answer evaluators 452 foreach my $ans (@ans_list) { 453 if( defined( $out_options{'units'} ) ) { 454 $ans = "$ans $out_options{'units'}"; 455 456 push( @output_list, NUM_CMP( 'correctAnswer' => $ans, 457 'tolerance' => $out_options{'tolerance'}, 458 'tolType' => $out_options{'tolType'}, 459 'format' => $out_options{'format'}, 460 'mode' => $out_options{'mode'}, 461 'zeroLevel' => $out_options{'zeroLevel'}, 462 'zeroLevelTol' => $out_options{'zeroLevelTol'}, 463 'debug' => $out_options{'debug'}, 464 'units' => $out_options{'units'}, 465 ) 466 ); 467 } elsif( defined( $out_options{'strings'} ) ) { 468 469 470 push( @output_list, NUM_CMP( 'correctAnswer' => $ans, 471 'tolerance' => $out_options{tolerance}, 472 'tolType' => $out_options{tolType}, 473 'format' => $out_options{'format'}, 474 'mode' => $out_options{'mode'}, 475 'zeroLevel' => $out_options{'zeroLevel'}, 476 'zeroLevelTol' => $out_options{'zeroLevelTol'}, 477 'debug' => $out_options{'debug'}, 478 'strings' => $out_options{'strings'}, 479 ) 480 ); 481 } else { 482 push(@output_list, 483 NUM_CMP( 'correctAnswer' => $ans, 484 'tolerance' => $out_options{tolerance}, 485 'tolType' => $out_options{tolType}, 486 'format' => $out_options{'format'}, 487 'mode' => $out_options{'mode'}, 488 'zeroLevel' => $out_options{'zeroLevel'}, 489 'zeroLevelTol' => $out_options{'zeroLevelTol'}, 490 'debug' => $out_options{'debug'}, 491 ), 492 ); 493 } 494 } 495 496 return (wantarray) ? @output_list : $output_list[0]; 497 } 498 499 #legacy code for compatability purposes 500 sub num_rel_cmp { # compare numbers 501 std_num_cmp( @_ ); 502 } 503 504 505 =head3 "mode"_num_cmp() functions 506 507 There are 16 functions total, 4 for each mode (std, frac, strict, arith). Each mode has 508 one "normal" function, one which accepts a list of answers, one which uses absolute 509 rather than relative tolerance, and one which uses absolute tolerance and accepts a list. 510 The "std" family is documented below; all others work precisely the same. 511 512 std_num_cmp($correctAnswer) OR 513 std_num_cmp($correctAnswer, $relPercentTol) OR 514 std_num_cmp($correctAnswer, $relPercentTol, $format) OR 515 std_num_cmp($correctAnswer, $relPercentTol, $format, $zeroLevel) OR 516 std_num_cmp($correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol) 517 518 $correctAnswer -- the correct answer 519 $relPercentTol -- the tolerance, as a percentage (optional) 520 $format -- the format of the displayed answer (optional) 521 $zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies (optional) 522 $zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero (optional) 523 524 std_num_cmp() uses standard mode (arithmetic operations and elementary 525 functions allowed) and relative tolerance. Options are specified by 526 one or more parameters. Note that if you wish to set an option which 527 is later in the parameter list, you must set all previous options. 528 529 std_num_cmp_abs($correctAnswer) OR 530 std_num_cmp_abs($correctAnswer, $absTol) OR 531 std_num_cmp_abs($correctAnswer, $absTol, $format) 532 533 $correctAnswer -- the correct answer 534 $absTol -- an absolute tolerance (optional) 535 $format -- the format of the displayed answer (optional) 536 537 std_num_cmp_abs() uses standard mode and absolute tolerance. Options 538 are set as with std_num_cmp(). Note that $zeroLevel and $zeroLevelTol 539 do not apply with absolute tolerance. 540 541 std_num_cmp_list($relPercentTol, $format, @answerList) 542 543 $relPercentTol -- the tolerance, as a percentage 544 $format -- the format of the displayed answer(s) 545 @answerList -- a list of one or more correct answers 546 547 std_num_cmp_list() uses standard mode and relative tolerance. There 548 is no way to set $zeroLevel or $zeroLevelTol. Note that no 549 parameters are optional. All answers in the list will be 550 evaluated with the same set of parameters. 551 552 std_num_cmp_abs_list($absTol, $format, @answerList) 553 554 $absTol -- an absolute tolerance 555 $format -- the format of the displayed answer(s) 556 @answerList -- a list of one or more correct answers 557 558 std_num_cmp_abs_list() uses standard mode and absolute tolerance. 559 Note that no parameters are optional. All answers in the list will be 560 evaluated with the same set of parameters. 561 562 arith_num_cmp(), arith_num_cmp_list(), arith_num_cmp_abs(), arith_num_cmp_abs_list() 563 strict_num_cmp(), strict_num_cmp_list(), strict_num_cmp_abs(), strict_num_cmp_abs_list() 564 frac_num_cmp(), frac_num_cmp_list(), frac_num_cmp_abs(), frac_num_cmp_abs_list() 565 566 Examples: 567 568 ANS( strict_num_cmp( 3.14159 ) ) -- The student answer must be a number 569 in decimal or scientific notation which is within .1 percent of 3.14159. 570 This assumes $numRelPercentTolDefault has been set to .1. 571 ANS( strict_num_cmp( $answer, .01 ) ) -- The student answer must be a 572 number within .01 percent of $answer (e.g. 3.14159 if $answer is 3.14159 573 or $answer is "pi" or $answer is 4*atan(1)). 574 ANS( frac_num_cmp( $answer) ) or ANS( frac_num_cmp( $answer,.01 )) -- 575 The student answer can be a number or fraction, e.g. 2/3. 576 ANS( arith_num_cmp( $answer) ) or ANS( arith_num_cmp( $answer,.01 )) -- 577 The student answer can be an arithmetic expression, e.g. (2+3)/7-2^.5 . 578 ANS( std_num_cmp( $answer) ) or ANS( std_num_cmp( $answer,.01 )) -- 579 The student answer can contain elementary functions, e.g. sin(.3+pi/2) 580 581 =cut 582 583 sub std_num_cmp { # compare numbers allowing use of elementary functions 584 my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_; 585 586 my %options = ( 'relTol' => $relPercentTol, 587 'format' => $format, 588 'zeroLevel' => $zeroLevel, 589 'zeroLevelTol' => $zeroLevelTol 590 ); 591 592 set_default_options( \%options, 593 'tolType' => 'relative', 594 'tolerance' => $numRelPercentTolDefault, 595 'mode' => 'std', 596 'format' => $numFormatDefault, 597 'relTol' => $numRelPercentTolDefault, 598 'zeroLevel' => $numZeroLevelDefault, 599 'zeroLevelTol' => $numZeroLevelTolDefault, 600 'debug' => 0, 601 ); 602 603 num_cmp([$correctAnswer], %options); 604 } 605 606 ## Similar to std_num_cmp but accepts a list of numbers in the form 607 ## std_num_cmp_list(relpercentTol,format,ans1,ans2,ans3,...) 608 ## format is of the form "%10.3g" or "", i.e., a format suitable for sprintf(). Use "" for default 609 ## You must enter a format and tolerance 610 611 sub std_num_cmp_list { 612 my ( $relPercentTol, $format, @answerList) = @_; 613 614 my %options = ( 'relTol' => $relPercentTol, 615 'format' => $format, 616 ); 617 618 set_default_options( \%options, 619 'tolType' => 'relative', 620 'tolerance' => $numRelPercentTolDefault, 621 'mode' => 'std', 622 'format' => $numFormatDefault, 623 'relTol' => $numRelPercentTolDefault, 624 'zeroLevel' => $numZeroLevelDefault, 625 'zeroLevelTol' => $numZeroLevelTolDefault, 626 'debug' => 0, 627 ); 628 629 num_cmp(\@answerList, %options); 630 631 } 632 633 sub std_num_cmp_abs { # compare numbers allowing use of elementary functions with absolute tolerance 634 my ( $correctAnswer, $absTol, $format) = @_; 635 my %options = ( 'tolerance' => $absTol, 636 'format' => $format 637 ); 638 639 set_default_options (\%options, 640 'tolType' => 'absolute', 641 'tolerance' => $absTol, 642 'mode' => 'std', 643 'format' => $numFormatDefault, 644 'zeroLevel' => 0, 645 'zeroLevelTol' => 0, 646 'debug' => 0, 647 ); 648 649 num_cmp([$correctAnswer], %options); 650 } 651 652 ## See std_num_cmp_list for usage 653 654 sub std_num_cmp_abs_list { 655 my ( $absTol, $format, @answerList ) = @_; 656 657 my %options = ( 'tolerance' => $absTol, 658 'format' => $format, 659 ); 660 661 set_default_options( \%options, 662 'tolType' => 'absolute', 663 'tolerance' => $absTol, 664 'mode' => 'std', 665 'format' => $numFormatDefault, 666 'zeroLevel' => 0, 667 'zeroLevelTol' => 0, 668 'debug' => 0, 669 ); 670 671 num_cmp(\@answerList, %options); 672 } 673 674 sub frac_num_cmp { # only allow fractions and numbers as submitted answer 675 676 my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_; 677 678 my %options = ( 'relTol' => $relPercentTol, 679 'format' => $format, 680 'zeroLevel' => $zeroLevel, 681 'zeroLevelTol' => $zeroLevelTol 682 ); 683 684 set_default_options( \%options, 685 'tolType' => 'relative', 686 'tolerance' => $relPercentTol, 687 'mode' => 'frac', 688 'format' => $numFormatDefault, 689 'zeroLevel' => $numZeroLevelDefault, 690 'zeroLevelTol' => $numZeroLevelTolDefault, 691 'relTol' => $numRelPercentTolDefault, 692 'debug' => 0, 693 ); 694 695 num_cmp([$correctAnswer], %options); 696 } 697 698 ## See std_num_cmp_list for usage 699 sub frac_num_cmp_list { 700 my ( $relPercentTol, $format, @answerList ) = @_; 701 702 my %options = ( 'relTol' => $relPercentTol, 703 'format' => $format 704 ); 705 706 set_default_options( \%options, 707 'tolType' => 'relative', 708 'tolerance' => $relPercentTol, 709 'mode' => 'frac', 710 'format' => $numFormatDefault, 711 'zeroLevel' => $numZeroLevelDefault, 712 'zeroLevelTol' => $numZeroLevelTolDefault, 713 'relTol' => $numRelPercentTolDefault, 714 'debug' => 0, 715 ); 716 717 num_cmp(\@answerList, %options); 718 } 719 720 sub frac_num_cmp_abs { # only allow fraction expressions as submitted answer with absolute tolerance 721 my ( $correctAnswer, $absTol, $format ) = @_; 722 723 my %options = ( 'tolerance' => $absTol, 724 'format' => $format 725 ); 726 727 set_default_options (\%options, 728 'tolType' => 'absolute', 729 'tolerance' => $absTol, 730 'mode' => 'frac', 731 'format' => $numFormatDefault, 732 'zeroLevel' => 0, 733 'zeroLevelTol' => 0, 734 'debug' => 0, 735 ); 736 737 num_cmp([$correctAnswer], %options); 738 } 739 740 ## See std_num_cmp_list for usage 741 742 sub frac_num_cmp_abs_list { 743 my ( $absTol, $format, @answerList ) = @_; 744 745 my %options = ( 'tolerance' => $absTol, 746 'format' => $format 747 ); 748 749 set_default_options (\%options, 750 'tolType' => 'absolute', 751 'tolerance' => $absTol, 752 'mode' => 'frac', 753 'format' => $numFormatDefault, 754 'zeroLevel' => 0, 755 'zeroLevelTol' => 0, 756 'debug' => 0, 757 ); 758 759 num_cmp(\@answerList, %options); 760 } 761 762 763 sub arith_num_cmp { # only allow arithmetic expressions as submitted answer 764 765 my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_; 766 767 my %options = ( 'relTol' => $relPercentTol, 768 'format' => $format, 769 'zeroLevel' => $zeroLevel, 770 'zeroLevelTol' => $zeroLevelTol 771 ); 772 773 set_default_options( \%options, 774 'tolType' => 'relative', 775 'tolerance' => $relPercentTol, 776 'mode' => 'arith', 777 'format' => $numFormatDefault, 778 'zeroLevel' => $numZeroLevelDefault, 779 'zeroLevelTol' => $numZeroLevelTolDefault, 780 'relTol' => $numRelPercentTolDefault, 781 'debug' => 0, 782 ); 783 784 num_cmp([$correctAnswer], %options); 785 } 786 787 ## See std_num_cmp_list for usage 788 sub arith_num_cmp_list { 789 my ( $relPercentTol, $format, @answerList ) = @_; 790 791 my %options = ( 'relTol' => $relPercentTol, 792 'format' => $format, 793 ); 794 795 set_default_options( \%options, 796 'tolType' => 'relative', 797 'tolerance' => $relPercentTol, 798 'mode' => 'arith', 799 'format' => $numFormatDefault, 800 'zeroLevel' => $numZeroLevelDefault, 801 'zeroLevelTol' => $numZeroLevelTolDefault, 802 'relTol' => $numRelPercentTolDefault, 803 'debug' => 0, 804 ); 805 806 num_cmp(\@answerList, %options); 807 } 808 809 sub arith_num_cmp_abs { # only allow arithmetic expressions as submitted answer with absolute tolerance 810 my ( $correctAnswer, $absTol, $format ) = @_; 811 812 my %options = ( 'tolerance' => $absTol, 813 'format' => $format 814 ); 815 816 set_default_options (\%options, 817 'tolType' => 'absolute', 818 'tolerance' => $absTol, 819 'mode' => 'arith', 820 'format' => $numFormatDefault, 821 'zeroLevel' => 0, 822 'zeroLevelTol' => 0, 823 'debug' => 0, 824 ); 825 826 num_cmp([$correctAnswer], %options); 827 } 828 829 ## See std_num_cmp_list for usage 830 sub arith_num_cmp_abs_list { 831 my ( $absTol, $format, @answerList ) = @_; 832 833 my %options = ( 'tolerance' => $absTol, 834 'format' => $format 835 ); 836 837 set_default_options (\%options, 838 'tolType' => 'absolute', 839 'tolerance' => $absTol, 840 'mode' => 'arith', 841 'format' => $numFormatDefault, 842 'zeroLevel' => 0, 843 'zeroLevelTol' => 0, 844 'debug' => 0, 845 ); 846 847 num_cmp(\@answerList, %options); 848 } 849 850 sub strict_num_cmp { # only allow numbers as submitted answer 851 my ( $correctAnswer, $relPercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_; 852 853 my %options = ( 'relTol' => $relPercentTol, 854 'format' => $format, 855 'zeroLevel' => $zeroLevel, 856 'zeroLevelTol' => $zeroLevelTol 857 ); 858 859 set_default_options( \%options, 860 'tolType' => 'relative', 861 'tolerance' => $relPercentTol, 862 'mode' => 'strict', 863 'format' => $numFormatDefault, 864 'zeroLevel' => $numZeroLevelDefault, 865 'zeroLevelTol' => $numZeroLevelTolDefault, 866 'relTol' => $numRelPercentTolDefault, 867 'debug' => 0, 868 ); 869 num_cmp([$correctAnswer], %options); 870 871 } 872 873 ## See std_num_cmp_list for usage 874 sub strict_num_cmp_list { # compare numbers 875 my ( $relPercentTol, $format, @answerList ) = @_; 876 877 my %options = ( 'relTol' => $relPercentTol, 878 'format' => $format, 879 ); 880 881 set_default_options( \%options, 882 'tolType' => 'relative', 883 'tolerance' => $relPercentTol, 884 'mode' => 'strict', 885 'format' => $numFormatDefault, 886 'zeroLevel' => $numZeroLevelDefault, 887 'zeroLevelTol' => $numZeroLevelTolDefault, 888 'relTol' => $numRelPercentTolDefault, 889 'debug' => 0, 890 ); 891 892 num_cmp(\@answerList, %options); 893 } 894 895 896 sub strict_num_cmp_abs { # only allow numbers as submitted answer with absolute tolerance 897 my ( $correctAnswer, $absTol, $format ) = @_; 898 899 my %options = ( 'tolerance' => $absTol, 900 'format' => $format 901 ); 902 903 set_default_options (\%options, 904 'tolType' => 'absolute', 905 'tolerance' => $absTol, 906 'mode' => 'strict', 907 'format' => $numFormatDefault, 908 'zeroLevel' => 0, 909 'zeroLevelTol' => 0, 910 'debug' => 0, 911 ); 912 num_cmp([$correctAnswer], %options); 913 914 } 915 916 ## See std_num_cmp_list for usage 917 sub strict_num_cmp_abs_list { # compare numbers 918 my ( $absTol, $format, @answerList ) = @_; 919 920 my %options = ( 'tolerance' => $absTol, 921 'format' => $format 922 ); 923 924 set_default_options (\%options, 925 'tolType' => 'absolute', 926 'tolerance' => $absTol, 927 'mode' => 'strict', 928 'format' => $numFormatDefault, 929 'zeroLevel' => 0, 930 'zeroLevelTol' => 0, 931 'debug' => 0, 932 ); 933 934 num_cmp(\@answerList, %options); 935 } 936 937 ## sub numerical_compare_with_units 938 ## Compares a number with units 939 ## Deprecated; use num_cmp() 940 ## 941 ## IN: a string which includes the numerical answer and the units 942 ## a hash with the following keys (all optional): 943 ## mode -- 'std', 'frac', 'arith', or 'strict' 944 ## format -- the format to use when displaying the answer 945 ## tol -- an absolute tolerance, or 946 ## relTol -- a relative tolerance 947 ## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies 948 ## zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero 949 950 # This mode is depricated. send input through num_cmp -- it can handle units. 951 952 sub numerical_compare_with_units { 953 my $correct_answer = shift; # the answer is a string which includes both the numerical answer and the units. 954 my %options = @_; # all of the other inputs are (key value) pairs 955 956 # Prepare the correct answer 957 $correct_answer = str_filters( $correct_answer, 'trim_whitespace' ); 958 959 # it surprises me that the match below works since the first .* is greedy. 960 my ($correct_num_answer, $correct_units) = $correct_answer =~ /^(.*)\s+([^\s]*)$/; 961 $options{units} = $correct_units; 962 963 num_cmp($correct_num_answer, %options); 964 } 965 966 967 =head3 std_num_str_cmp() 968 969 NOTE: This function is maintained for compatibility. num_cmp() with the 970 'strings' parameter is slightly preferred. 971 972 std_num_str_cmp() is used when the correct answer could be either a number or a 973 string. For example, if you wanted the student to evaluate a function at number 974 of points, but write "Inf" or "Minf" if the function is unbounded. This routine 975 will provide error messages that do not give a hint as to whether the correct 976 answer is a string or a number. For numerical comparisons, std_num_cmp() is 977 used internally; for string comparisons, std_str_cmp() is used. String answers 978 must consist entirely of letters except that an initial minus sign is allowed. 979 E.g. "inf" and "-inf" are valid strings where as "too-big" is not. 980 981 std_num_str_cmp( $correctAnswer ) OR 982 std_num_str_cmp( $correctAnswer, $ra_legalStrings ) OR 983 std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol ) OR 984 std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format ) OR 985 std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format, $zeroLevel ) OR 986 std_num_str_cmp( $correctAnswer, $ra_legalStrings, $relPercentTol, $format, 987 $zeroLevel, $zeroLevelTol ) 988 989 $correctAnswer -- the correct answer 990 $ra_legalStrings -- a reference to an array of legal strings, e.g. ["str1", "str2"] 991 $relPercentTol -- the error tolerance as a percentage 992 $format -- the display format 993 $zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies 994 $zeroLevelTol -- absolute tolerance to allow when correct answer is close to zero 995 996 Examples: 997 ANS( std_num_str_cmp( $ans, ["Inf", "Minf", "NaN"] ) ); 998 ANS( std_num_str_cmp( $ans, ["INF", "-INF"] ) ); 999 1000 =cut 1001 1002 sub std_num_str_cmp { 1003 my ( $correctAnswer, $ra_legalStrings, $relpercentTol, $format, $zeroLevel, $zeroLevelTol ) = @_; 1004 # warn ('This method is depreciated. Use num_cmp instead.'); 1005 return num_cmp ($correctAnswer, strings=>$ra_legalStrings, relTol=>$relpercentTol, format=>$format, 1006 zeroLevel=>$zeroLevel, zeroLevelTol=>$zeroLevelTol); 1007 } 1008 1009 sub NUM_CMP { # low level numeric compare 1010 my %num_params = @_; 1011 1012 my @keys = qw ( correctAnswer tolerance tolType format mode zeroLevel zeroLevelTol debug ); 1013 foreach my $key (@keys) { 1014 warn "$key must be defined in options when calling NUM_CMP" unless defined ($num_params{$key}); 1015 } 1016 1017 my $correctAnswer = $num_params{'correctAnswer'}; 1018 my $format = $num_params{'format'}; 1019 my $mode = $num_params{'mode'}; 1020 1021 if( $num_params{tolType} eq 'relative' ) { 1022 $num_params{'tolerance'} = .01*$num_params{'tolerance'}; 1023 } 1024 1025 my $formattedCorrectAnswer; 1026 my $correct_units; 1027 my $correct_num_answer; 1028 my %correct_units; 1029 my $corrAnswerIsString = 0; 1030 1031 1032 if (defined($num_params{units}) && $num_params{units}) { 1033 $correctAnswer = str_filters( $correctAnswer, 'trim_whitespace' ); 1034 # units are in form stuff space units where units contains no spaces. 1035 1036 ($correct_num_answer, $correct_units) = $correctAnswer =~ /^(.*)\s+([^\s]*)$/; 1037 %correct_units = Units::evaluate_units($correct_units); 1038 if ( defined( $correct_units{'ERROR'} ) ) { 1039 warn ("ERROR: The answer \"$correctAnswer\" in the problem definition cannot be parsed:\n" . 1040 "$correct_units{'ERROR'}\n"); 1041 } 1042 # $formattedCorrectAnswer = spf($correct_num_answer,$num_params{'format'}) . " $correct_units"; 1043 $formattedCorrectAnswer = prfmt($correct_num_answer,$num_params{'format'}) . " $correct_units"; 1044 1045 } elsif (defined($num_params{strings}) && $num_params{strings}) { 1046 my $legalString = ''; 1047 my @legalStrings = @{$num_params{strings}}; 1048 $correct_num_answer = $correctAnswer; 1049 $formattedCorrectAnswer = $correctAnswer; 1050 foreach $legalString (@legalStrings) { 1051 if ( uc($correctAnswer) eq uc($legalString) ) { 1052 $corrAnswerIsString = 1; 1053 1054 last; 1055 } 1056 } ## at this point $corrAnswerIsString = 0 iff correct answer is numeric 1057 } else { 1058 $correct_num_answer = $correctAnswer; 1059 $formattedCorrectAnswer = prfmt( $correctAnswer, $num_params{'format'} ); 1060 } 1061 1062 $correct_num_answer = math_constants($correct_num_answer); 1063 1064 my $PGanswerMessage = ''; 1065 1066 my ($inVal,$correctVal,$PG_eval_errors,$PG_full_error_report); 1067 1068 if (defined($correct_num_answer) && $correct_num_answer =~ /\S/ && $corrAnswerIsString == 0 ) { 1069 ($correctVal, $PG_eval_errors,$PG_full_error_report) = PG_answer_eval($correct_num_answer); 1070 } else { # case of a string answer 1071 $PG_eval_errors = ' '; 1072 $correctVal = $correctAnswer; 1073 } 1074 1075 if ( ($PG_eval_errors && $corrAnswerIsString == 0) or ((not is_a_number($correctVal)) && $corrAnswerIsString == 0)) { 1076 ##error message from eval or above 1077 warn "Error in 'correct' answer: $PG_eval_errors<br> 1078 The answer $correctAnswer evaluates to $correctVal, 1079 which cannot be interpreted as a number. "; 1080 1081 } 1082 ######################################################################### 1083 1084 #construct the answer evaluator 1085 my $answer_evaluator = new AnswerEvaluator; 1086 $answer_evaluator->{debug} = $num_params{debug}; 1087 $answer_evaluator->ans_hash( 1088 correct_ans => $correctVal, 1089 type => "${mode}_number", 1090 tolerance => $num_params{tolerance}, 1091 tolType => $num_params{tolType}, 1092 units => $correct_units, 1093 original_correct_ans => $formattedCorrectAnswer, 1094 rh_correct_units => \%correct_units, 1095 answerIsString => $corrAnswerIsString, 1096 ); 1097 my ($in, $formattedSubmittedAnswer); 1098 $answer_evaluator->install_pre_filter(sub {my $rh_ans = shift; 1099 $rh_ans->{original_student_ans} = $rh_ans->{student_ans}; $rh_ans;} 1100 ); 1101 if (defined($num_params{units}) && $num_params{units}) { 1102 $answer_evaluator->install_pre_filter(\&check_units); 1103 } 1104 if (defined($num_params{strings}) && $num_params{strings}) { 1105 $answer_evaluator->install_pre_filter(\&check_strings, %num_params); 1106 } 1107 1108 $answer_evaluator->install_pre_filter(\&check_syntax); 1109 1110 $answer_evaluator->install_pre_filter(\&math_constants); 1111 1112 if ($mode eq 'std') { 1113 # do nothing 1114 } elsif ($mode eq 'strict') { 1115 $answer_evaluator->install_pre_filter(\&is_a_number); 1116 } elsif ($mode eq 'arith') { 1117 $answer_evaluator->install_pre_filter(\&is_an_arithmetic_expression); 1118 } elsif ($mode eq 'frac') { 1119 $answer_evaluator->install_pre_filter(\&is_a_fraction); 1120 1121 } elsif ($mode eq 'phase_pi') { 1122 $answer_evaluator->install_pre_filter(\&phase_pi); 1123 1124 } else { 1125 $PGanswerMessage = 'Tell your professor that there is an error in his or her answer mechanism. No mode was specified.'; 1126 $formattedSubmittedAnswer = $in; 1127 } 1128 1129 if ($corrAnswerIsString == 0 ){ # avoiding running compare_numbers when correct answer is a string. 1130 $answer_evaluator->install_evaluator(\&compare_numbers, %num_params); 1131 } 1132 1133 1134 ############################################################################### 1135 # We'll leave these next lines out for now, so that the evaluated versions of the student's and professor's 1136 # can be displayed in the answer message. This may still cause a few anomolies when strings are used 1137 # 1138 ############################################################################### 1139 1140 $answer_evaluator->install_post_filter(\&fix_answers_for_display); 1141 1142 $answer_evaluator->install_post_filter(sub {my $rh_ans = shift; 1143 return $rh_ans unless $rh_ans->catch_error('EVAL'); 1144 $rh_ans->{student_ans} = $rh_ans->{original_student_ans}. ' '. $rh_ans->{error_message}; 1145 $rh_ans->clear_error('EVAL'); } ); 1146 $answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('SYNTAX'); } ); 1147 $answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('UNITS'); } ); 1148 $answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('NUMBER'); } ); 1149 $answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('STRING'); } ); 1150 $answer_evaluator; 1151 } 1152 1153 1154 1155 ########################################################################## 1156 ########################################################################## 1157 ## Function answer evaluators 1158 1159 =head2 Function Answer Evaluators 1160 1161 Function answer evaluators take in a function, compare it numerically to a 1162 correct function, and return a score. They can require an exactly equivalent 1163 function, or one that is equal up to a constant. They can accept or reject an 1164 answer based on specified tolerances for numerical deviation. 1165 1166 Function Comparison Options 1167 1168 correctEqn -- The correct equation, specified as a string. It may include 1169 all basic arithmetic operations, as well as elementary 1170 functions. Variable usage is described below. 1171 1172 Variables -- The independent variable(s). When comparing the correct 1173 equation to the student equation, each variable will be 1174 replaced by a certain number of numerical values. If 1175 the student equation agrees numerically with the correct 1176 equation, they are considered equal. Note that all 1177 comparison is numeric; it is possible (although highly 1178 unlikely and never a practical concern) for two unequal 1179 functions to yield the same numerical results. 1180 1181 Limits -- The limits of evaluation for the independent variables. 1182 Each variable is evaluated only in the half-open interval 1183 [lower_limit, upper_limit). This is useful if the function 1184 has a singularity or is not defined in a certain range. 1185 For example, the function "sqrt(-1-x)" could be evaluated 1186 in [-2,-1). 1187 1188 Tolerance -- Tolerance in function comparisons works exactly as in 1189 numerical comparisons; see the numerical comparison 1190 documentation for a complete description. Note that the 1191 tolerance does applies to the function as a whole, not 1192 each point individually. 1193 1194 Number of -- Specifies how many points to evaluate each variable at. This 1195 Points is typically 3, but can be set higher if it is felt that 1196 there is a strong possibility of "false positives." 1197 1198 Maximum -- Sets the maximum size of the constant of integration. For 1199 Constant of technical reasons concerning floating point arithmetic, if 1200 Integration the additive constant, i.e., the constant of integration, is 1201 greater (in absolute value) than maxConstantOfIntegration 1202 AND is greater than maxConstantOfIntegration times the 1203 correct value, WeBWorK will give an error message saying 1204 that it can not handle such a large constant of integration. 1205 This is to prevent e.g. cos(x) + 1E20 or even 1E20 as being 1206 accepted as a correct antiderivatives of sin(x) since 1207 floating point arithmetic cannot tell the difference 1208 between cos(x) + 1E20, 1E20, and -cos(x) + 1E20. 1209 1210 Technical note: if you examine the code for the function routines, you will see 1211 that most subroutines are simply doing some basic error-checking and then 1212 passing the parameters on to the low-level FUNCTION_CMP(). Because this routine 1213 is set up to handle multivariable functions, with single-variable functions as 1214 a special case, it is possible to pass multivariable parameters to single- 1215 variable functions. This usage is strongly discouraged as unnecessarily 1216 confusing. Avoid it. 1217 1218 Default Values (As of 7/24/2000) (Option -- Variable Name -- Value) 1219 1220 Variable -- $functVarDefault -- 'x' 1221 Relative Tolerance -- $functRelPercentTolDefault -- .1 1222 Absolute Tolerance -- $functAbsTolDefault -- .001 1223 Lower Limit -- $functLLimitDefault -- .0000001 1224 Upper Limit -- $functULimitDefault -- 1 1225 Number of Points -- $functNumOfPoints -- 3 1226 Zero Level -- $functZeroLevelDefault -- 1E-14 1227 Zero Level Tolerance -- $functZeroLevelTolDefault -- 1E-12 1228 Maximum Constant -- $functMaxConstantOfIntegration -- 1E8 1229 of Integration 1230 1231 =cut 1232 1233 1234 1235 =head3 fun_cmp() 1236 1237 Compares a function or a list of functions, using a named hash of options to set 1238 parameters. This can make for more readable code than using the function_cmp() 1239 style, but some people find one or the other easier to remember. 1240 1241 ANS( fun_cmp( answer or answer_array_ref, options_hash ) ); 1242 1243 1. a string containing the correct function, or a reference to an 1244 array of correct functions 1245 2. a hash containing the following items (all optional): 1246 var -- either the number of variables or a reference to an 1247 array of variable names (see below) 1248 limits -- reference to an array of arrays of limits (see below), or: 1249 mode -- 'std' (default) (function must match exactly), or: 1250 'antider' (function must match up to a constant) 1251 relTol -- (default) a relative tolerance (as a percentage), or: 1252 tol -- an absolute tolerance for error 1253 numPoints -- the number of points to evaluate the function at 1254 maxConstantOfIntegration -- maximum size of the constant of integration 1255 zeroLevel -- if the correct answer is this close to zero, then 1256 zeroLevelTol applies 1257 zeroLevelTol -- absolute tolerance to allow when answer is close to zero 1258 params an array of "free" parameters which can be used to adapt 1259 the correct answer to the submitted answer. (e.g. ['c'] for 1260 a constant of integration in the answer x^3/3 + c. 1261 debug -- when set to 1 this provides extra information while checking the 1262 the answer. 1263 1264 Returns an answer evaluator, or (if given a reference to an array 1265 of answers), a list of answer evaluators 1266 1267 ANSWER: 1268 1269 The answer must be in the form of a string. The answer can contain 1270 functions, pi, e, and arithmetic operations. However, the correct answer 1271 string follows a slightly stricter syntax than student answers; specifically, 1272 there is no implicit multiplication. So the correct answer must be "3*x" rather 1273 than "3 x". Students can still enter "3 x". 1274 1275 VARIABLES: 1276 1277 The var parameter can contain either a number or a reference to an array of 1278 variable names. If it contains a number, the variables are named automatically 1279 as follows: 1 variable -- x 1280 2 variables -- x, y 1281 3 variables -- x, y, z 1282 4 or more -- x_1, x_2, x_3, etc. 1283 If the var parameter contains a reference to an array of variable names, then 1284 the number of variables is determined by the number of items in the array. A 1285 reference to an array is created with brackets, e.g. "var => ['r', 's', 't']". 1286 If only one variable is being used, you can write either "var => ['t']" for 1287 consistency or "var => 't'" as a shortcut. The default is one variable, x. 1288 1289 LIMITS: 1290 1291 Limits are specified with the limits parameter. You may NOT use llimit/ulimit. 1292 If you specify limits for one variable, you must specify them for all variables. 1293 The limit parameter must be a reference to an array of arrays of the form 1294 [lower_limit. upper_limit], each array corresponding to the lower and upper 1295 endpoints of the (half-open) domain of one variable. For example, 1296 "vars => 2, limits => [[0,2], [-3,8]]" would cause x to be evaluated in [0,2) and 1297 y to be evaluated in [-3,8). If only one variable is being used, you can write 1298 either "limits => [[0,3]]" for consistency or "limits => [0,3]" as a shortcut. 1299 1300 EXAMPLES: 1301 1302 fun_cmp( "3*x" ) -- standard compare, variable is x 1303 fun_cmp( ["3*x", "4*x+3", "3*x**2"] ) -- standard compare, defaults used for all three functions 1304 fun_cmp( "3*t", var => 't' ) -- standard compare, variable is t 1305 fun_cmp( "5*x*y*z", var => 3 ) -- x, y and z are the variables 1306 fun_cmp( "5*x", mode => 'antider' ) -- student answer must match up to constant (i.e., 5x+C) 1307 fun_cmp( ["3*x*y", "4*x*y"], limits => [[0,2], [5,7]] ) -- x evaluated in [0,2) 1308 y evaluated in [5,7) 1309 1310 =cut 1311 1312 sub fun_cmp { 1313 my $correctAnswer = shift @_; 1314 my %opt = @_; 1315 1316 assign_option_aliases( \%opt, 1317 'vars' => 'var', # set the standard option 'var' to the one specified as vars 1318 'domain' => 'limits', # set the standard option 'limits' to the one specified as domain 1319 'reltol' => 'relTol', 1320 'param' => 'params', 1321 ); 1322 1323 set_default_options( \%opt, 1324 'var' => $functVarDefault, 1325 'params' => [], 1326 'limits' => [[$functLLimitDefault, $functULimitDefault]], 1327 'mode' => 'std', 1328 'tolType' => (defined($opt{tol}) ) ? 'absolute' : 'relative', 1329 'tol' => .01, # default mode should be relative, to obtain this tol must not be defined 1330 'relTol' => $functRelPercentTolDefault, 1331 'numPoints' => $functNumOfPoints, 1332 'maxConstantOfIntegration' => $functMaxConstantOfIntegration, 1333 'zeroLevel' => $functZeroLevelDefault, 1334 'zeroLevelTol' => $functZeroLevelTolDefault, 1335 'debug' => 0, 1336 ); 1337 1338 # allow var => 'x' as an abbreviation for var => ['x'] 1339 my %out_options = %opt; 1340 unless ( ref($out_options{var}) eq 'ARRAY' ) { 1341 $out_options{var} = [$out_options{var}]; 1342 } 1343 # allow params => 'c' as an abbreviation for params => ['c'] 1344 unless ( ref($out_options{params}) eq 'ARRAY' ) { 1345 $out_options{params} = [$out_options{params}]; 1346 } 1347 my ($tolType, $tol); 1348 if ($out_options{tolType} eq 'absolute') { 1349 $tolType = 'absolute'; 1350 $tol = $out_options{'tol'}; 1351 delete($out_options{'relTol'}) if exists( $out_options{'relTol'} ); 1352 } else { 1353 $tolType = 'relative'; 1354 $tol = $out_options{'relTol'}; 1355 delete($out_options{'tol'}) if exists( $out_options{'tol'} ); 1356 } 1357 1358 my @output_list = (); 1359 # thread over lists 1360 my @ans_list = (); 1361 1362 if ( ref($correctAnswer) eq 'ARRAY' ) { 1363 @ans_list = @{$correctAnswer}; 1364 } 1365 else { 1366 push( @ans_list, $correctAnswer ); 1367 } 1368 1369 # produce answer evaluators 1370 foreach my $ans (@ans_list) { 1371 push(@output_list, 1372 FUNCTION_CMP( 1373 'correctEqn' => $ans, 1374 'var' => $out_options{'var'}, 1375 'limits' => $out_options{'limits'}, 1376 'tolerance' => $tol, 1377 'tolType' => $tolType, 1378 'numPoints' => $out_options{'numPoints'}, 1379 'mode' => $out_options{'mode'}, 1380 'maxConstantOfIntegration' => $out_options{'maxConstantOfIntegration'}, 1381 'zeroLevel' => $out_options{'zeroLevel'}, 1382 'zeroLevelTol' => $out_options{'zeroLevelTol'}, 1383 'params' => $out_options{'params'}, 1384 'debug' => $out_options{'debug'}, 1385 ), 1386 ); 1387 } 1388 1389 return (wantarray) ? @output_list : $output_list[0]; 1390 } 1391 1392 =head3 Single-variable Function Comparisons 1393 1394 There are four single-variable function answer evaluators: "normal," absolute 1395 tolerance, antiderivative, and antiderivative with absolute tolerance. All 1396 parameters (other than the correct equation) are optional. 1397 1398 function_cmp( $correctEqn ) OR 1399 function_cmp( $correctEqn, $var ) OR 1400 function_cmp( $correctEqn, $var, $llimit, $ulimit ) OR 1401 function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol ) OR 1402 function_cmp( $correctEqn, $var, $llimit, $ulimit, 1403 $relPercentTol, $numPoints ) OR 1404 function_cmp( $correctEqn, $var, $llimit, $ulimit, 1405 $relPercentTol, $numPoints, $zeroLevel ) OR 1406 function_cmp( $correctEqn, $var, $llimit, $ulimit, $relPercentTol, $numPoints, 1407 $zeroLevel,$zeroLevelTol ) 1408 1409 $correctEqn -- the correct equation, as a string 1410 $var -- the string representing the variable (optional) 1411 $llimit -- the lower limit of the interval to evaluate the 1412 variable in (optional) 1413 $ulimit -- the upper limit of the interval to evaluate the 1414 variable in (optional) 1415 $relPercentTol -- the error tolerance as a percentage (optional) 1416 $numPoints -- the number of points at which to evaluate the 1417 variable (optional) 1418 $zeroLevel -- if the correct answer is this close to zero, then 1419 zeroLevelTol applies (optional) 1420 $zeroLevelTol -- absolute tolerance to allow when answer is close to zero 1421 1422 function_cmp() uses standard comparison and relative tolerance. It takes a 1423 string representing a single-variable function and compares the student 1424 answer to that function numerically. 1425 1426 function_cmp_up_to_constant( $correctEqn ) OR 1427 function_cmp_up_to_constant( $correctEqn, $var ) OR 1428 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit ) OR 1429 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1430 $relpercentTol ) OR 1431 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1432 $relpercentTol, $numOfPoints ) OR 1433 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1434 $relpercentTol, $numOfPoints, 1435 $maxConstantOfIntegration ) OR 1436 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1437 $relpercentTol, $numOfPoints, 1438 $maxConstantOfIntegration, $zeroLevel) OR 1439 function_cmp_up_to_constant( $correctEqn, $var, $llimit, $ulimit, 1440 $relpercentTol, $numOfPoints, 1441 $maxConstantOfIntegration, 1442 $zeroLevel, $zeroLevelTol ) 1443 1444 $maxConstantOfIntegration -- the maximum size of the constant of 1445 integration 1446 1447 function_cmp_up_to_constant() uses antiderivative compare and relative 1448 tolerance. All options work exactly like function_cmp(), except of course 1449 $maxConstantOfIntegration. It will accept as correct any function which 1450 differs from $correctEqn by at most a constant; that is, if 1451 $studentEqn = $correctEqn + C 1452 the answer is correct. 1453 1454 function_cmp_abs( $correctFunction ) OR 1455 function_cmp_abs( $correctFunction, $var ) OR 1456 function_cmp_abs( $correctFunction, $var, $llimit, $ulimit ) OR 1457 function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol ) OR 1458 function_cmp_abs( $correctFunction, $var, $llimit, $ulimit, $absTol, 1459 $numOfPoints ) 1460 1461 $absTol -- the tolerance as an absolute value 1462 1463 function_cmp_abs() uses standard compare and absolute tolerance. All 1464 other options work exactly as for function_cmp(). 1465 1466 function_cmp_up_to_constant_abs( $correctFunction ) OR 1467 function_cmp_up_to_constant_abs( $correctFunction, $var ) OR 1468 function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit ) OR 1469 function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit, 1470 $absTol ) OR 1471 function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit, 1472 $absTol, $numOfPoints ) OR 1473 function_cmp_up_to_constant_abs( $correctFunction, $var, $llimit, $ulimit, 1474 $absTol, $numOfPoints, 1475 $maxConstantOfIntegration ) 1476 1477 function_cmp_up_to_constant_abs() uses antiderivative compare 1478 and absolute tolerance. All other options work exactly as with 1479 function_cmp_up_to_constant(). 1480 1481 Examples: 1482 1483 ANS( function_cmp( "cos(x)" ) ) -- Accepts cos(x), sin(x+pi/2), 1484 sin(x)^2 + cos(x) + cos(x)^2 -1, etc. This assumes 1485 $functVarDefault has been set to "x". 1486 ANS( function_cmp( $answer, "t" ) ) -- Assuming $answer is "cos(t)", 1487 accepts cos(t), etc. 1488 ANS( function_cmp_up_to_constant( "cos(x)" ) ) -- Accepts any 1489 antiderivative of sin(x), e.g. cos(x) + 5. 1490 ANS( function_cmp_up_to_constant( "cos(z)", "z" ) ) -- Accepts any 1491 antiderivative of sin(z), e.g. sin(z+pi/2) + 5. 1492 1493 =cut 1494 1495 sub adaptive_function_cmp { 1496 my $correctEqn = shift; 1497 my %options = @_; 1498 set_default_options( \%options, 1499 'vars' => [qw( x y )], 1500 'params' => [], 1501 'limits' => [ [0,1], [0,1]], 1502 'reltol' => $main::functRelPercentTolDefault, 1503 'numPoints' => $main::functNumOfPoints, 1504 'zeroLevel' => $main::functZeroLevelDefault, 1505 'zeroLevelTol' => $main::functZeroLevelTolDefault, 1506 'debug' => 0, 1507 ); 1508 1509 my $var_ref = $options{'vars'}; 1510 my $ra_params = $options{ 'params'}; 1511 my $limit_ref = $options{'limits'}; 1512 my $relPercentTol= $options{'reltol'}; 1513 my $numPoints = $options{'numPoints'}; 1514 my $zeroLevel = $options{'zeroLevel'}; 1515 my $zeroLevelTol = $options{'zeroLevelTol'}; 1516 1517 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1518 'var' => $var_ref, 1519 'limits' => $limit_ref, 1520 'tolerance' => $relPercentTol, 1521 'tolType' => 'relative', 1522 'numPoints' => $numPoints, 1523 'mode' => 'std', 1524 'maxConstantOfIntegration' => 10**100, 1525 'zeroLevel' => $zeroLevel, 1526 'zeroLevelTol' => $zeroLevelTol, 1527 'scale_norm' => 1, 1528 'params' => $ra_params, 1529 'debug' => $options{debug} , 1530 ); 1531 } 1532 1533 sub function_cmp { 1534 my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_; 1535 1536 if ( (scalar(@_) == 3) or (scalar(@_) > 8) or (scalar(@_) == 0) ) { 1537 function_invalid_params( $correctEqn ); 1538 } 1539 else { 1540 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1541 'var' => $var, 1542 'limits' => [$llimit, $ulimit], 1543 'tolerance' => $relPercentTol, 1544 'tolType' => 'relative', 1545 'numPoints' => $numPoints, 1546 'mode' => 'std', 1547 'maxConstantOfIntegration' => 0, 1548 'zeroLevel' => $zeroLevel, 1549 'zeroLevelTol' => $zeroLevelTol 1550 ); 1551 } 1552 } 1553 1554 sub function_cmp_up_to_constant { ## for antiderivative problems 1555 my ($correctEqn,$var,$llimit,$ulimit,$relPercentTol,$numPoints,$maxConstantOfIntegration,$zeroLevel,$zeroLevelTol) = @_; 1556 1557 if ( (scalar(@_) == 3) or (scalar(@_) > 9) or (scalar(@_) == 0) ) { 1558 function_invalid_params( $correctEqn ); 1559 } 1560 else { 1561 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1562 'var' => $var, 1563 'limits' => [$llimit, $ulimit], 1564 'tolerance' => $relPercentTol, 1565 'tolType' => 'relative', 1566 'numPoints' => $numPoints, 1567 'mode' => 'antider', 1568 'maxConstantOfIntegration' => $maxConstantOfIntegration, 1569 'zeroLevel' => $zeroLevel, 1570 'zeroLevelTol' => $zeroLevelTol 1571 ); 1572 } 1573 } 1574 1575 sub function_cmp_abs { ## similar to function_cmp but uses absolute tolerance 1576 my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints) = @_; 1577 1578 if ( (scalar(@_) == 3) or (scalar(@_) > 6) or (scalar(@_) == 0) ) { 1579 function_invalid_params( $correctEqn ); 1580 } 1581 else { 1582 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1583 'var' => $var, 1584 'limits' => [$llimit, $ulimit], 1585 'tolerance' => $absTol, 1586 'tolType' => 'absolute', 1587 'numPoints' => $numPoints, 1588 'mode' => 'std', 1589 'maxConstantOfIntegration' => 0, 1590 'zeroLevel' => 0, 1591 'zeroLevelTol' => 0 1592 ); 1593 } 1594 } 1595 1596 1597 sub function_cmp_up_to_constant_abs { ## for antiderivative problems 1598 ## similar to function_cmp_up_to_constant 1599 ## but uses absolute tolerance 1600 my ($correctEqn,$var,$llimit,$ulimit,$absTol,$numPoints,$maxConstantOfIntegration) = @_; 1601 1602 if ( (scalar(@_) == 3) or (scalar(@_) > 7) or (scalar(@_) == 0) ) { 1603 function_invalid_params( $correctEqn ); 1604 } 1605 1606 else { 1607 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1608 'var' => $var, 1609 'limits' => [$llimit, $ulimit], 1610 'tolerance' => $absTol, 1611 'tolType' => 'absolute', 1612 'numPoints' => $numPoints, 1613 'mode' => 'antider', 1614 'maxConstantOfIntegration' => $maxConstantOfIntegration, 1615 'zeroLevel' => 0, 1616 'zeroLevelTol' => 0 1617 ); 1618 } 1619 } 1620 1621 ## The following answer evaluator for comparing multivarable functions was 1622 ## contributed by Professor William K. Ziemer 1623 ## (Note: most of the multivariable functionality provided by Professor Ziemer 1624 ## has now been integrated into fun_cmp and FUNCTION_CMP) 1625 ############################ 1626 # W.K. Ziemer, Sep. 1999 1627 # Math Dept. CSULB 1628 # email: wziemer@csulb.edu 1629 ############################ 1630 1631 =head3 multivar_function_cmp 1632 1633 NOTE: this function is maintained for compatibility. fun_cmp() is 1634 slightly preferred. 1635 1636 usage: 1637 1638 multivar_function_cmp( $answer, $var_reference, options) 1639 $answer -- string, represents function of several variables 1640 $var_reference -- number (of variables), or list reference (e.g. ["var1","var2"] ) 1641 options: 1642 $limit_reference -- reference to list of lists (e.g. [[1,2],[3,4]]) 1643 $relPercentTol -- relative percent tolerance in answer 1644 $numPoints -- number of points to sample in for each variable 1645 $zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies 1646 $zeroLevelTol -- absolute tolerance to allow when answer is close to zero 1647 1648 =cut 1649 1650 sub multivar_function_cmp { 1651 my ($correctEqn,$var_ref,$limit_ref,$relPercentTol,$numPoints,$zeroLevel,$zeroLevelTol) = @_; 1652 1653 if ( (scalar(@_) > 7) or (scalar(@_) < 2) ) { 1654 function_invalid_params( $correctEqn ); 1655 } 1656 1657 FUNCTION_CMP( 'correctEqn' => $correctEqn, 1658 'var' => $var_ref, 1659 'limits' => $limit_ref, 1660 'tolerance' => $relPercentTol, 1661 'tolType' => 'relative', 1662 'numPoints' => $numPoints, 1663 'mode' => 'std', 1664 'maxConstantOfIntegration' => 0, 1665 'zeroLevel' => $zeroLevel, 1666 'zeroLevelTol' => $zeroLevelTol 1667 ); 1668 } 1669 1670 ## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION 1671 ## NOTE: PG_answer_eval is used instead of PG_restricted_eval in order to insure that the answer 1672 ## evaluated within the context of the package the problem was originally defined in. 1673 ## Includes multivariable modifications contributed by Professor William K. Ziemer 1674 ## 1675 ## IN: a hash consisting of the following keys (error checking to be added later?) 1676 ## correctEqn -- the correct equation as a string 1677 ## var -- the variable name as a string, 1678 ## or a reference to an array of variables 1679 ## limits -- reference to an array of arrays of type [lower,upper] 1680 ## tolerance -- the allowable margin of error 1681 ## tolType -- 'relative' or 'absolute' 1682 ## numPoints -- the number of points to evaluate the function at 1683 ## mode -- 'std' or 'antider' 1684 ## maxConstantOfIntegration -- maximum size of the constant of integration 1685 ## zeroLevel -- if the correct answer is this close to zero, 1686 ## then zeroLevelTol applies 1687 ## zeroLevelTol -- absolute tolerance to allow when answer is close to zero 1688 1689 1690 sub FUNCTION_CMP { 1691 my %func_params = @_; 1692 1693 my $correctEqn = $func_params{'correctEqn'}; 1694 my $var = $func_params{'var'}; 1695 my $ra_limits = $func_params{'limits'}; 1696 my $tol = $func_params{'tolerance'}; 1697 my $tolType = $func_params{'tolType'}; 1698 my $numPoints = $func_params{'numPoints'}; 1699 my $mode = $func_params{'mode'}; 1700 my $maxConstantOfIntegration = $func_params{'maxConstantOfIntegration'}; 1701 my $zeroLevel = $func_params{'zeroLevel'}; 1702 my $zeroLevelTol = $func_params{'zeroLevelTol'}; 1703 1704 1705 # Check that everything is defined: 1706 $func_params{debug} = 0 unless defined($func_params{debug}); 1707 $mode = 'std' unless defined($mode); 1708 my @VARS = get_var_array( $var ); 1709 my @limits = get_limits_array( $ra_limits ); 1710 my @PARAMS = (); 1711 @PARAMS = @{$func_params{'params'}} if defined($func_params{'params'}); 1712 1713 if ($mode eq 'antider' ) { 1714 # doctor the equation to allow addition of a constant 1715 my $CONSTANT_PARAM = 'Q'; # unfortunately parameters must be single letters. 1716 # There is the possibility of conflict here. 1717 # 'Q' seemed less dangerous than 'C'. 1718 $correctEqn = "( $correctEqn ) + $CONSTANT_PARAM"; 1719 push(@PARAMS, $CONSTANT_PARAM); 1720 } 1721 my $dim_of_param_space = @PARAMS; # dimension of equivalence space 1722 1723 if( $tolType eq 'relative' ) { 1724 $tol = $functRelPercentTolDefault unless defined $tol; 1725 $tol *= .01; 1726 } 1727 else { 1728 $tol = $functAbsTolDefault unless defined $tol; 1729 } 1730 1731 #loop ensures that number of limits matches number of variables 1732 for( my $i = 0; $i < scalar(@VARS); $i++ ) { 1733 $limits[$i][0] = $functLLimitDefault unless defined $limits[$i][0]; 1734 $limits[$i][1] = $functULimitDefault unless defined $limits[$i][1]; 1735 } 1736 $numPoints = $functNumOfPoints unless defined $numPoints; 1737 $maxConstantOfIntegration = $functMaxConstantOfIntegration unless defined $maxConstantOfIntegration; 1738 $zeroLevel = $functZeroLevelDefault unless defined $zeroLevel; 1739 $zeroLevelTol = $functZeroLevelTolDefault unless defined $zeroLevelTol; 1740 1741 $func_params{'var'} = $var; 1742 $func_params{'limits'} = \@limits; 1743 $func_params{'tolerance'} = $tol; 1744 $func_params{'tolType'} = $tolType; 1745 $func_params{'numPoints'} = $numPoints; 1746 $func_params{'mode'} = $mode; 1747 $func_params{'maxConstantOfIntegration'} = $maxConstantOfIntegration; 1748 $func_params{'zeroLevel'} = $zeroLevel; 1749 $func_params{'zeroLevelTol'} = $zeroLevelTol; 1750 1751 ######################################################## 1752 # End of cleanup of calling parameters 1753 ######################################################## 1754 my $i; #for use with loops 1755 my $PGanswerMessage = ""; 1756 my $originalCorrEqn = $correctEqn; 1757 1758 #prepare the correct answer and check it's syntax 1759 my $rh_correct_ans = new AnswerHash; 1760 $rh_correct_ans->input($correctEqn); 1761 $rh_correct_ans = check_syntax($rh_correct_ans); 1762 warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag}; 1763 $rh_correct_ans->clear_error(); 1764 $rh_correct_ans = function_from_string2($rh_correct_ans, ra_vars => [ @VARS, @PARAMS ], 1765 store_in =>'rf_correct_ans', 1766 debug => $func_params{debug}); 1767 my $correct_eqn_sub = $rh_correct_ans->{rf_correct_ans}; 1768 warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag}; 1769 1770 #create the evaluation points 1771 my $random_for_answers = new PGrandom($main::PG_original_problemSeed); 1772 my $NUMBER_OF_STEPS_IN_RANDOM = 1000; # determines the granularity of the random_for_answers number generator 1773 my (@evaluation_points); 1774 for( my $count = 0; $count < @PARAMS+1+$numPoints; $count++ ) { 1775 my (@vars,$iteration_limit); 1776 for( my $i = 0; $i < @VARS; $i++ ) { 1777 my $iteration_limit = 10; 1778 while ( 0 < --$iteration_limit ) { # make sure that the endpoints of the interval are not included 1779 $vars[$i] = $random_for_answers->random($limits[$i][0], $limits[$i][1], abs($limits[$i][1] - $limits[$i][0])/$NUMBER_OF_STEPS_IN_RANDOM ); 1780 last if $vars[$i]!=$limits[$i][0] and $vars[$i]!=$limits[$i][1]; 1781 } 1782 warn "Unable to properly choose evaluation points for this function in the interval ( $limits[$i][0] , $limits[$i][1] )" 1783 if $iteration_limit == 0; 1784 }; 1785 1786 push(@evaluation_points,\@vars); 1787 } 1788 my $evaluation_points = Matrix->new_from_array_ref(\@evaluation_points); 1789 1790 #my $COEFFS = determine_param_coeffs($correct_eqn_sub,$evaluation_points[0],$numOfParameters); 1791 #warn "coeff", join(" | ", @{$COEFFS}); 1792 1793 #construct the answer evaluator 1794 my $answer_evaluator = new AnswerEvaluator; 1795 $answer_evaluator->{debug} = $func_params{debug}; 1796 $answer_evaluator->ans_hash( correct_ans => $originalCorrEqn, 1797 rf_correct_ans => $rh_correct_ans->{rf_correct_ans}, 1798 evaluation_points => \@evaluation_points, 1799 ra_param_vars => \@PARAMS, 1800 ra_vars => \@VARS, 1801 type => 'function', 1802 ); 1803 1804 $answer_evaluator->install_pre_filter(\&check_syntax); 1805 $answer_evaluator->install_pre_filter(\&function_from_string2, ra_vars => \@VARS,debug=>$func_params{debug},); # @VARS has been guaranteed to be an array, $var might be a single string. 1806 $answer_evaluator->install_pre_filter(\&best_approx_parameters, %func_params, param_vars => \@PARAMS); 1807 $answer_evaluator->install_evaluator(\&calculate_difference_vector, %func_params); 1808 $answer_evaluator->install_evaluator(\&is_zero_array, tolerance => $tol ); 1809 $answer_evaluator->install_post_filter(sub {my $rh_ans = shift; $rh_ans->clear_error('SYNTAX'); $rh_ans;} ); 1810 $answer_evaluator->install_post_filter( 1811 sub {my $rh_ans = shift; 1812 if ($rh_ans->catch_error('EVAL') ) { 1813 $rh_ans->{ans_message} = $rh_ans->{error_message}; 1814 $rh_ans->clear_error('EVAL'); 1815 } 1816 $rh_ans; 1817 } 1818 ); 1819 $answer_evaluator; 1820 } 1821 1822 1823 ## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION 1824 ## 1825 ## IN: a hash containing the following items (error-checking to be added later?): 1826 ## correctAnswer -- the correct answer 1827 ## tolerance -- the allowable margin of error 1828 ## tolType -- 'relative' or 'absolute' 1829 ## format -- the display format of the answer 1830 ## mode -- one of 'std', 'strict', 'arith', or 'frac'; 1831 ## determines allowable formats for the input 1832 ## zeroLevel -- if the correct answer is this close to zero, then zeroLevelTol applies 1833 ## zeroLevelTol -- absolute tolerance to allow when answer is close to zero 1834 1835 1836 ########################################################################## 1837 ########################################################################## 1838 ## String answer evaluators 1839 1840 =head2 String Answer Evaluators 1841 1842 String answer evaluators compare a student string to the correct string. 1843 Different filters can be applied to allow various degrees of variation. 1844 Both the student and correct answers are subject to the same filters, to 1845 ensure that there are no unexpected matches or rejections. 1846 1847 String Filters 1848 1849 remove_whitespace -- Removes all whitespace from the string. 1850 It applies the following substitution 1851 to the string: 1852 $filteredAnswer =~ s/\s+//g; 1853 1854 compress_whitespace -- Removes leading and trailing whitespace, and 1855 replaces all other blocks of whitespace by a 1856 single space. Applies the following substitutions: 1857 $filteredAnswer =~ s/^\s*//; 1858 $filteredAnswer =~ s/\s*$//; 1859 $filteredAnswer =~ s/\s+/ /g; 1860 1861 trim_whitespace -- Removes leading and trailing whitespace. 1862 Applies the following substitutions: 1863 $filteredAnswer =~ s/^\s*//; 1864 $filteredAnswer =~ s/\s*$//; 1865 1866 ignore_case -- Ignores the case of the string. More accurately, 1867 it converts the string to uppercase (by convention). 1868 Applies the following function: 1869 $filteredAnswer = uc $filteredAnswer; 1870 1871 ignore_order -- Ignores the order of the letters in the string. 1872 This is used for problems of the form "Choose all 1873 that apply." Specifically, it removes all 1874 whitespace and lexically sorts the letters in 1875 ascending alphabetical order. Applies the following 1876 functions: 1877 $filteredAnswer = join( "", lex_sort( 1878 split( /\s*/, $filteredAnswer ) ) ); 1879 1880 =cut 1881 1882 ################################ 1883 ## STRING ANSWER FILTERS 1884 1885 ## IN: --the string to be filtered 1886 ## --a list of the filters to use 1887 ## 1888 ## OUT: --the modified string 1889 ## 1890 ## Use this subroutine instead of the 1891 ## individual filters below it 1892 1893 sub str_filters { 1894 my $stringToFilter = shift @_; 1895 my @filters_to_use = @_; 1896 my %known_filters = ( 'remove_whitespace' => undef, 1897 'compress_whitespace' => undef, 1898 'trim_whitespace' => undef, 1899 'ignore_case' => undef, 1900 'ignore_order' => undef 1901 ); 1902 1903 #test for unknown filters 1904 my $filter; 1905 foreach $filter (@filters_to_use) { 1906 die "Unknown string filter $filter (try checking the parameters to str_cmp() )" 1907 unless exists $known_filters{$filter}; 1908 } 1909 1910 if( grep( /remove_whitespace/i, @filters_to_use ) ) { 1911 $stringToFilter = remove_whitespace( $stringToFilter ); 1912 } 1913 if( grep( /compress_whitespace/i, @filters_to_use ) ) { 1914 $stringToFilter = compress_whitespace( $stringToFilter ); 1915 } 1916 if( grep( /trim_whitespace/i, @filters_to_use ) ) { 1917 $stringToFilter = trim_whitespace( $stringToFilter ); 1918 } 1919 if( grep( /ignore_case/i, @filters_to_use ) ) { 1920 $stringToFilter = ignore_case( $stringToFilter ); 1921 } 1922 if( grep( /ignore_order/i, @filters_to_use ) ) { 1923 $stringToFilter = ignore_order( $stringToFilter ); 1924 } 1925 1926 return $stringToFilter; 1927 } 1928 1929 sub remove_whitespace { 1930 my $filteredAnswer = shift; 1931 1932 $filteredAnswer =~ s/\s+//g; # remove all whitespace 1933 1934 return $filteredAnswer; 1935 } 1936 1937 sub compress_whitespace { 1938 my $filteredAnswer = shift; 1939 1940 $filteredAnswer =~ s/^\s*//; # remove initial whitespace 1941 $filteredAnswer =~ s/\s*$//; # remove trailing whitespace 1942 $filteredAnswer =~ s/\s+/ /g; # replace spaces by single space 1943 1944 return $filteredAnswer; 1945 } 1946 1947 sub trim_whitespace { 1948 my $filteredAnswer = shift; 1949 1950 $filteredAnswer =~ s/^\s*//; # remove initial whitespace 1951 $filteredAnswer =~ s/\s*$//; # remove trailing whitespace 1952 1953 return $filteredAnswer; 1954 } 1955 1956 sub ignore_case { 1957 my $filteredAnswer = shift; 1958 1959 $filteredAnswer = uc $filteredAnswer; 1960 1961 return $filteredAnswer; 1962 } 1963 1964 sub ignore_order { 1965 my $filteredAnswer = shift; 1966 1967 $filteredAnswer = join( "", lex_sort( split( /\s*/, $filteredAnswer ) ) ); 1968 1969 return $filteredAnswer; 1970 } 1971 ################################ 1972 ## END STRING ANSWER FILTERS 1973 1974 1975 =head3 str_cmp() 1976 1977 Compares a string or a list of strings, using a named hash of options to set 1978 parameters. This can make for more readable code than using the "mode"_str_cmp() 1979 style, but some people find one or the other easier to remember. 1980 1981 ANS( str_cmp( answer or answer_array_ref, options_hash ) ); 1982 1983 1. the correct answer or a reference to an array of answers 1984 2. either a list of filters, or: 1985 a hash consisting of 1986 filters - a reference to an array of filters 1987 1988 Returns an answer evaluator, or (if given a reference to an array of answers), 1989 a list of answer evaluators 1990 1991 FILTERS: 1992 1993 remove_whitespace -- removes all whitespace 1994 compress_whitespace -- removes whitespace from the beginning and end of the string, 1995 and treats one or more whitespace characters in a row as a 1996 single space (true by default) 1997 trim_whitespace -- removes whitespace from the beginning and end of the string 1998 ignore_case -- ignores the case of the letters (true by default) 1999 ignore_order -- ignores the order in which letters are entered 2000 2001 EXAMPLES: 2002 2003 str_cmp( "Hello" ) -- matches "Hello", " hello" (same as std_str_cmp() ) 2004 str_cmp( ["Hello", "Goodbye"] ) -- same as std_str_cmp_list() 2005 str_cmp( " hello ", trim_whitespace ) -- matches "hello", " hello " 2006 str_cmp( "ABC", filters => 'ignore_order' ) -- matches "ACB", "A B C", but not "abc" 2007 str_cmp( "D E F", remove_whitespace, ignore_case ) -- matches "def" and "d e f" but not "fed" 2008 2009 2010 =cut 2011 2012 sub str_cmp { 2013 my $correctAnswer = shift @_; 2014 $correctAnswer = '' unless defined($correctAnswer); 2015 my @options = @_; 2016 my $ra_filters; 2017 2018 # error-checking for filters occurs in the filters() subroutine 2019 if( not defined( $options[0] ) ) { # used with no filters as alias for std_str_cmp() 2020 @options = ( 'compress_whitespace', 'ignore_case' ); 2021 } 2022 2023 if( $options[0] eq 'filters' ) { # using filters => [f1, f2, ...] notation 2024 $ra_filters = $options[1]; 2025 } 2026 else { # using a list of filters 2027 $ra_filters = \@options; 2028 } 2029 2030 # thread over lists 2031 my @ans_list = (); 2032 2033 if ( ref($correctAnswer) eq 'ARRAY' ) { 2034 @ans_list = @{$correctAnswer}; 2035 } 2036 else { 2037 push( @ans_list, $correctAnswer ); 2038 } 2039 2040 # final_answer; 2041 my @output_list = (); 2042 2043 foreach my $ans (@ans_list) { 2044 push(@output_list, STR_CMP( 'correctAnswer' => $ans, 2045 'filters' => $ra_filters, 2046 'type' => 'str_cmp' 2047 ) 2048 ); 2049 } 2050 2051 return (wantarray) ? @output_list : $output_list[0] ; 2052 } 2053 2054 =head3 "mode"_str_cmp functions 2055 2056 The functions of the the form "mode"_str_cmp() use different functions to 2057 specify which filters to apply. They take no options except the correct 2058 string. There are also versions which accept a list of strings. 2059 2060 std_str_cmp( $correctString ) 2061 std_str_cmp_list( @correctStringList ) 2062 Filters: compress_whitespace, ignore_case 2063 2064 std_cs_str_cmp( $correctString ) 2065 std_cs_str_cmp_list( @correctStringList ) 2066 Filters: compress_whitespace 2067 2068 strict_str_cmp( $correctString ) 2069 strict_str_cmp_list( @correctStringList ) 2070 Filters: trim_whitespace 2071 2072 unordered_str_cmp( $correctString ) 2073 unordered_str_cmp_list( @correctStringList ) 2074 Filters: ignore_order, ignore_case 2075 2076 unordered_cs_str_cmp( $correctString ) 2077 unordered_cs_str_cmp_list( @correctStringList ) 2078 Filters: ignore_order 2079 2080 ordered_str_cmp( $correctString ) 2081 ordered_str_cmp_list( @correctStringList ) 2082 Filters: remove_whitespace, ignore_case 2083 2084 ordered_cs_str_cmp( $correctString ) 2085 ordered_cs_str_cmp_list( @correctStringList ) 2086 Filters: remove_whitespace 2087 2088 Examples 2089 2090 ANS( std_str_cmp( "W. Mozart" ) ) -- Accepts "W. Mozart", "W. MOZarT", 2091 and so forth. Case insensitive. All internal spaces treated 2092 as single spaces. 2093 ANS( std_cs_str_cmp( "Mozart" ) ) -- Rejects "mozart". Same as 2094 std_str_cmp() but case sensitive. 2095 ANS( strict_str_cmp( "W. Mozart" ) ) -- Accepts only the exact string. 2096 ANS( unordered_str_cmp( "ABC" ) ) -- Accepts "a c B", "CBA" and so forth. 2097 Unordered, case insensitive, spaces ignored. 2098 ANS( unordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc". Same as 2099 unordered_str_cmp() but case sensitive. 2100 ANS( ordered_str_cmp( "ABC" ) ) -- Accepts "a b C", "A B C" and so forth. 2101 Ordered, case insensitive, spaces ignored. 2102 ANS( ordered_cs_str_cmp( "ABC" ) ) -- Rejects "abc", accepts "A BC" and 2103 so forth. Same as ordered_str_cmp() but case sensitive. 2104 2105 =cut 2106 2107 sub std_str_cmp { # compare strings 2108 my $correctAnswer = shift @_; 2109 my @filters = ( 'compress_whitespace', 'ignore_case' ); 2110 my $type = 'std_str_cmp'; 2111 STR_CMP( 'correctAnswer' => $correctAnswer, 2112 'filters' => \@filters, 2113 'type' => $type 2114 ); 2115 } 2116 2117 sub std_str_cmp_list { # alias for std_str_cmp 2118 my @answerList = @_; 2119 my @output; 2120 while (@answerList) { 2121 push( @output, std_str_cmp(shift @answerList) ); 2122 } 2123 @output; 2124 } 2125 2126 sub std_cs_str_cmp { # compare strings case sensitive 2127 my $correctAnswer = shift @_; 2128 my @filters = ( 'compress_whitespace' ); 2129 my $type = 'std_cs_str_cmp'; 2130 STR_CMP( 'correctAnswer' => $correctAnswer, 2131 'filters' => \@filters, 2132 'type' => $type 2133 ); 2134 } 2135 2136 sub std_cs_str_cmp_list { # alias for std_cs_str_cmp 2137 my @answerList = @_; 2138 my @output; 2139 while (@answerList) { 2140 push( @output, std_cs_str_cmp(shift @answerList) ); 2141 } 2142 @output; 2143 } 2144 2145 sub strict_str_cmp { # strict string compare 2146 my $correctAnswer = shift @_; 2147 my @filters = ( 'trim_whitespace' ); 2148 my $type = 'strict_str_cmp'; 2149 STR_CMP( 'correctAnswer' => $correctAnswer, 2150 'filters' => \@filters, 2151 'type' => $type 2152 ); 2153 } 2154 2155 sub strict_str_cmp_list { # alias for strict_str_cmp 2156 my @answerList = @_; 2157 my @output; 2158 while (@answerList) { 2159 push( @output, strict_str_cmp(shift @answerList) ); 2160 } 2161 @output; 2162 } 2163 2164 sub unordered_str_cmp { # unordered, case insensitive, spaces ignored 2165 my $correctAnswer = shift @_; 2166 my @filters = ( 'ignore_order', 'ignore_case' ); 2167 my $type = 'unordered_str_cmp'; 2168 STR_CMP( 'correctAnswer' => $correctAnswer, 2169 'filters' => \@filters, 2170 'type' => $type 2171 ); 2172 } 2173 2174 sub unordered_str_cmp_list { # alias for unordered_str_cmp 2175 my @answerList = @_; 2176 my @output; 2177 while (@answerList) { 2178 push( @output, unordered_str_cmp(shift @answerList) ); 2179 } 2180 @output; 2181 } 2182 2183 sub unordered_cs_str_cmp { # unordered, case sensitive, spaces ignored 2184 my $correctAnswer = shift @_; 2185 my @filters = ( 'ignore_order' ); 2186 my $type = 'unordered_cs_str_cmp'; 2187 STR_CMP( 'correctAnswer' => $correctAnswer, 2188 'filters' => \@filters, 2189 'type' => $type 2190 ); 2191 } 2192 2193 sub unordered_cs_str_cmp_list { # alias for unordered_cs_str_cmp 2194 my @answerList = @_; 2195 my @output; 2196 while (@answerList) { 2197 push( @output, unordered_cs_str_cmp(shift @answerList) ); 2198 } 2199 @output; 2200 } 2201 2202 sub ordered_str_cmp { # ordered, case insensitive, spaces ignored 2203 my $correctAnswer = shift @_; 2204 my @filters = ( 'remove_whitespace', 'ignore_case' ); 2205 my $type = 'ordered_str_cmp'; 2206 STR_CMP( 'correctAnswer' => $correctAnswer, 2207 'filters' => \@filters, 2208 'type' => $type 2209 ); 2210 } 2211 2212 sub ordered_str_cmp_list { # alias for ordered_str_cmp 2213 my @answerList = @_; 2214 my @output; 2215 while (@answerList) { 2216 push( @output, ordered_str_cmp(shift @answerList) ); 2217 } 2218 @output; 2219 } 2220 2221 sub ordered_cs_str_cmp { # ordered, case sensitive, spaces ignored 2222 my $correctAnswer = shift @_; 2223 my @filters = ( 'remove_whitespace' ); 2224 my $type = 'ordered_cs_str_cmp'; 2225 STR_CMP( 'correctAnswer' => $correctAnswer, 2226 'filters' => \@filters, 2227 'type' => $type 2228 ); 2229 } 2230 2231 sub ordered_cs_str_cmp_list { # alias for ordered_cs_str_cmp 2232 my @answerList = @_; 2233 my @output; 2234 while (@answerList) { 2235 push( @output, ordered_cs_str_cmp(shift @answerList) ); 2236 } 2237 @output; 2238 } 2239 2240 2241 ## LOW-LEVEL ROUTINE -- NOT NORMALLY FOR END USERS -- USE WITH CAUTION 2242 ## 2243 ## IN: a hashtable with the following entries (error-checking to be added later?): 2244 ## correctAnswer -- the correct answer, before filtering 2245 ## filters -- reference to an array containing the filters to be applied 2246 ## type -- a string containing the type of answer evaluator in use 2247 ## OUT: a reference to an answer evaluator subroutine 2248 2249 sub STR_CMP { 2250 my %str_params = @_; 2251 $str_params{'correctAnswer'} = str_filters( $str_params{'correctAnswer'}, @{$str_params{'filters'}} ); 2252 my $answer_evaluator = sub { 2253 my $in = shift @_; 2254 $in = '' unless defined $in; 2255 my $original_student_ans = $in; 2256 $in = str_filters( $in, @{$str_params{'filters'}} ); 2257 my $correctQ = ( $in eq $str_params{'correctAnswer'} ) ? 1: 0; 2258 my $ans_hash = new AnswerHash( 'score' => $correctQ, 2259 'correct_ans' => $str_params{'correctAnswer'}, 2260 'student_ans' => $in, 2261 'ans_message' => '', 2262 'type' => $str_params{'type'}, 2263 'preview_text_string' => $in, 2264 'preview_latex_string' => $in, 2265 'original_student_ans' => $original_student_ans 2266 ); 2267 return $ans_hash; 2268 }; 2269 return $answer_evaluator; 2270 } 2271 2272 ########################################################################## 2273 ########################################################################## 2274 ## Miscellaneous answer evaluators 2275 2276 =head2 Miscellaneous Answer Evaluators (Checkboxes and Radio Buttons) 2277 2278 These evaluators do not fit any of the other categories. 2279 2280 checkbox_cmp( $correctAnswer ) 2281 2282 $correctAnswer -- a string containing the names of the correct boxes, 2283 e.g. "ACD". Note that this means that individual 2284 checkbox names can only be one character. Internally, 2285 this is largely the same as unordered_cs_str_cmp(). 2286 2287 radio_cmp( $correctAnswer ) 2288 2289 $correctAnswer -- a string containing the name of the correct radio 2290 button, e.g. "Choice1". This is case sensitive and 2291 whitespace sensitive, so the correct answer must match 2292 the name of the radio button exactly. 2293 2294 =cut 2295 2296 # added 6/14/2000 by David Etlinger 2297 # because of the conversion of the answer 2298 # string to an array, I thought it better not 2299 # to force STR_CMP() to work with this 2300 2301 #added 2/26/2003 by Mike Gage 2302 # handled the case where multiple answers are passed as an array reference 2303 # rather than as a \0 delimited string. 2304 sub checkbox_cmp { 2305 my $correctAnswer = shift @_; 2306 $correctAnswer = str_filters( $correctAnswer, 'ignore_order' ); 2307 2308 my $answer_evaluator = sub { 2309 my $in = shift @_; 2310 $in = '' unless defined $in; #in case no boxes checked 2311 # multiple answers could come in two forms 2312 # either a \0 delimited string or 2313 # an array reference. We handle both. 2314 if (ref($in) eq 'ARRAY') { 2315 $in = join("",@{$in}); # convert array to single no-delimiter string 2316 } else { 2317 my @temp = split( "\0", $in ); #convert "\0"-delimited string to array... 2318 $in = join( "", @temp ); #and then to a single no-delimiter string 2319 } 2320 my $original_student_ans = $in; #well, almost original 2321 $in = str_filters( $in, 'ignore_order' ); 2322 2323 my $correctQ = ($in eq $correctAnswer) ? 1: 0; 2324 2325 my $ans_hash = new AnswerHash( 2326 'score' => $correctQ, 2327 'correct_ans' => "$correctAnswer", 2328 'student_ans' => $in, 2329 'ans_message' => "", 2330 'type' => "checkbox_cmp", 2331 'preview_text_string' => $in, 2332 'original_student_ans' => $original_student_ans 2333 ); 2334 return $ans_hash; 2335 2336 }; 2337 return $answer_evaluator; 2338 } 2339 2340 #added 6/28/2000 by David Etlinger 2341 #exactly the same as strict_str_cmp, 2342 #but more intuitive to the user 2343 sub radio_cmp { 2344 strict_str_cmp( @_ ); 2345 } 2346 2347 ########################################################################## 2348 ########################################################################## 2349 ## Text and e-mail routines 2350 2351 sub store_ans_at { 2352 my $answerStringRef = shift; 2353 my %options = @_; 2354 my $ans_eval= ''; 2355 if ( ref($answerStringRef) eq 'SCALAR' ) { 2356 $ans_eval= sub { 2357 my $text = shift; 2358 $text = '' unless defined($text); 2359 $$answerStringRef = $$answerStringRef . $text; 2360 my $ans_hash = new AnswerHash( 2361 'score' => 1, 2362 'correct_ans' => '', 2363 'student_ans' => $text, 2364 'ans_message' => '', 2365 'type' => 'store_ans_at', 2366 'original_student_ans' => $text, 2367 'preview_text_string' => '' 2368 ); 2369 2370 return $ans_hash; 2371 }; 2372 } 2373 else { 2374 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"; 2375 } 2376 2377 return $ans_eval; 2378 } 2379 2380 #### subroutines used in producing a questionnaire 2381 #### these are at least good models for other answers of this type 2382 2383 my $QUESTIONNAIRE_ANSWERS=''; # stores the answers until it is time to send them 2384 # this must be initialized before the answer evaluators are run 2385 # but that happens long after all of the text in the problem is 2386 # evaluated. 2387 # this is a utility script for cleaning up the answer output for display in 2388 #the answers. 2389 2390 sub DUMMY_ANSWER { 2391 my $num = shift; 2392 qq{<INPUT TYPE="HIDDEN" NAME="answer$num" VALUE="">} 2393 } 2394 2395 sub escapeHTML { 2396 my $string = shift; 2397 $string =~ s/\n/$BR/ge; 2398 $string; 2399 } 2400 2401 # these next three subroutines show how to modify the "store_ans_at()" answer 2402 # evaluator to add extra information before storing the info 2403 # They provide a good model for how to tweak answer evaluators in special cases. 2404 2405 sub anstext { 2406 my $num = shift; 2407 my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS); 2408 my $ans_eval = sub { 2409 my $text = shift; 2410 $text = '' unless defined($text); 2411 my $new_text = "\n$main::psvnNumber-Problem-$main::probNum-Question-$num:\n $text "; # modify entered text 2412 my $out = &$ans_eval_template($new_text); # standard evaluator 2413 #warn "$QUESTIONNAIRE_ANSWERS"; 2414 $out->{student_ans} = escapeHTML($text); # restore original entered text 2415 $out->{correct_ans} = "Question $num answered"; 2416 $out->{original_student_ans} = escapeHTML($text); 2417 $out; 2418 }; 2419 $ans_eval; 2420 } 2421 2422 sub ansradio { 2423 my $num = shift; 2424 my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS); 2425 my $ans_eval = sub { 2426 my $text = shift; 2427 $text = '' unless defined($text); 2428 my $new_text = "\n$main::psvnNumber-Problem-$main::probNum-RADIO-$num:\n $text "; # modify entered text 2429 my $out = $ans_eval_template->($new_text); # standard evaluator 2430 $out->{student_ans} =escapeHTML($text); # restore original entered text 2431 $out->{original_student_ans} = escapeHTML($text); 2432 $out; 2433 }; 2434 2435 $ans_eval; 2436 } 2437 2438 sub anstext_non_anonymous { 2439 ## this emails identifying information 2440 my $num = shift; 2441 my $ans_eval_template = store_ans_at(\$QUESTIONNAIRE_ANSWERS); 2442 my $ans_eval = sub { 2443 my $text = shift; 2444 $text = '' unless defined($text); 2445 my $new_text = "\n$main::psvnNumber-Problem-$main::probNum-Question-$num:\n$main::studentLogin $main::studentID $main::studentName\n$text "; # modify entered text 2446 my $out = &$ans_eval_template($new_text); # standard evaluator 2447 #warn "$QUESTIONNAIRE_ANSWERS"; 2448 $out->{student_ans} = escapeHTML($text); # restore original entered text 2449 $out->{correct_ans} = "Question $num answered"; 2450 $out->{original_student_ans} = escapeHTML($text); 2451 $out; 2452 }; 2453 $ans_eval; 2454 } 2455 2456 2457 # This is another example of how to modify an answer evaluator to obtain 2458 # the desired behavior in a special case. Here the object is to have 2459 # have the last answer trigger the send_mail_to subroutine which mails 2460 # all of the answers to the designated address. 2461 # (This address must be listed in PG_environment{'ALLOW_MAIL_TO'} or an error occurs.) 2462 2463 sub mail_answers_to { #accepts the last answer and mails off the result 2464 my $user_address = shift; 2465 my $ans_eval = sub { 2466 2467 # then mail out all of the answers, including this last one. 2468 2469 send_mail_to( $user_address, 2470 'subject' => "$main::courseName WeBWorK questionnaire", 2471 'body' => $QUESTIONNAIRE_ANSWERS, 2472 'ALLOW_MAIL_TO' => $main::ALLOW_MAIL_TO 2473 ); 2474 2475 my $ans_hash = new AnswerHash( 'score' => 1, 2476 'correct_ans' => '', 2477 'student_ans' => 'Answer recorded', 2478 'ans_message' => '', 2479 'type' => 'send_mail_to', 2480 ); 2481 2482 return $ans_hash; 2483 }; 2484 2485 return $ans_eval; 2486 } 2487 sub mail_answers_to2 { #accepts the last answer and mails off the result 2488 my $user_address = shift; 2489 my $subject = shift; 2490 $subject = "$main::courseName WeBWorK questionnaire" unless defined $subject; 2491 2492 send_mail_to($user_address, 2493 'subject' => $subject, 2494 'body' => $QUESTIONNAIRE_ANSWERS, 2495 'ALLOW_MAIL_TO' => $main::ALLOW_MAIL_TO 2496 ); 2497 } 2498 2499 ########################################################################## 2500 ########################################################################## 2501 2502 2503 ########################################################################### 2504 ### THE FOLLOWING ARE LOCAL SUBROUTINES THAT ARE MEANT TO BE CALLED ONLY FROM THIS SCRIPT. 2505 2506 ## Internal routine that converts variables into the standard array format 2507 ## 2508 ## IN: one of the following: 2509 ## an undefined value (i.e., no variable was specified) 2510 ## a reference to an array of variable names -- [var1, var2] 2511 ## a number (the number of variables desired) -- 3 2512 ## one or more variable names -- (var1, var2) 2513 ## OUT: an array of variable names 2514 2515 sub get_var_array { 2516 my $in = shift @_; 2517 my @out; 2518 2519 if( not defined($in) ) { #if nothing defined, build default array and return 2520 @out = ( $functVarDefault ); 2521 return @out; 2522 } 2523 elsif( ref( $in ) eq 'ARRAY' ) { #if given an array ref, dereference and return 2524 return @{$in}; 2525 } 2526 elsif( $in =~ /^\d+/ ) { #if given a number, set up the array and return 2527 if( $in == 1 ) { 2528 $out[0] = 'x'; 2529 } 2530 elsif( $in == 2 ) { 2531 $out[0] = 'x'; 2532 $out[1] = 'y'; 2533 } 2534 elsif( $in == 3 ) { 2535 $out[0] = 'x'; 2536 $out[1] = 'y'; 2537 $out[2] = 'z'; 2538 } 2539 else { #default to the x_1, x_2, ... convention 2540 my ($i, $tag); 2541 for( $i=0; $i < $in; $i++ ) { 2542 ## akp the above seems to be off by one 1/4/00 2543 $tag = $i + 1; ## akp 1/4/00 2544 $out[$i] = "${functVarDefault}_" . $tag; ## akp 1/4/00 2545 } 2546 } 2547 return @out; 2548 } 2549 else { #if given one or more names, return as an array 2550 unshift( @_, $in ); 2551 return @_; 2552 } 2553 } 2554 2555 ## Internal routine that converts limits into the standard array of arrays format 2556 ## Some of the cases are probably unneccessary, but better safe than sorry 2557 ## 2558 ## IN: one of the following: 2559 ## an undefined value (i.e., no limits were specified) 2560 ## a reference to an array of arrays of limits -- [[llim,ulim], [llim,ulim]] 2561 ## a reference to an array of limits -- [llim, ulim] 2562 ## an array of array references -- ([llim,ulim], [llim,ulim]) 2563 ## an array of limits -- (llim,ulim) 2564 ## OUT: an array of array references -- ([llim,ulim], [llim,ulim]) or ([llim,ulim]) 2565 2566 sub get_limits_array { 2567 my $in = shift @_; 2568 my @out; 2569 2570 if( not defined($in) ) { #if nothing defined, build default array and return 2571 @out = ( [$functLLimitDefault, $functULimitDefault] ); 2572 return @out; 2573 } 2574 elsif( ref($in) eq 'ARRAY' ) { #$in is either ref to array, or ref to array of refs 2575 my @deref = @{$in}; 2576 2577 if( ref( $in->[0] ) eq 'ARRAY' ) { #$in is a ref to an array of array refs 2578 return @deref; 2579 } 2580 else { #$in was just a ref to an array of numbers 2581 @out = ( $in ); 2582 return @out; 2583 } 2584 } 2585 else { #$in was an array of references or numbers 2586 unshift( @_, $in ); 2587 2588 if( ref($_[0]) eq 'ARRAY' ) { #$in was an array of references, so just return it 2589 return @_; 2590 } 2591 else { #$in was an array of numbers 2592 @out = ( \@_ ); 2593 return @out; 2594 } 2595 } 2596 } 2597 2598 #sub check_option_list { 2599 # my $size = scalar(@_); 2600 # if( ( $size % 2 ) != 0 ) { 2601 # warn "ERROR in answer evaluator generator:\n" . 2602 # "Usage: <CODE>str_cmp([\$ans1, \$ans2],%options)</CODE> 2603 # or <CODE> num_cmp([\$num1, \$num2], %options)</CODE><BR> 2604 # A list of inputs must be inclosed in square brackets <CODE>[\$ans1, \$ans2]</CODE>"; 2605 # } 2606 #} 2607 2608 # simple subroutine to display an error message when 2609 # function compares are called with invalid parameters 2610 sub function_invalid_params { 2611 my $correctEqn = shift @_; 2612 my $error_response = sub { 2613 my $PGanswerMessage = "Tell your professor that there is an error with the parameters " . 2614 "to the function answer evaluator"; 2615 return ( 0, $correctEqn, "", $PGanswerMessage ); 2616 }; 2617 return $error_response; 2618 } 2619 2620 sub clean_up_error_msg { 2621 my $msg = $_[0]; 2622 $msg =~ s/^\[[^\]]*\][^:]*://; 2623 $msg =~ s/Unquoted string//g; 2624 $msg =~ s/may\s+clash.*/does not make sense here/; 2625 $msg =~ s/\sat.*line [\d]*//g; 2626 $msg = 'error: '. $msg; 2627 2628 return $msg; 2629 } 2630 2631 #formats the student and correct answer as specified 2632 #format must be of a form suitable for sprintf (e.g. '%0.5g'), 2633 #with the exception that a '#' at the end of the string 2634 #will cause trailing zeros in the decimal part to be removed 2635 sub prfmt { 2636 my($number,$format) = @_; # attention, the order of format and number are reversed 2637 my $out; 2638 if ($format) { 2639 warn "Incorrect format used: $format. <BR> Format should look something like %4.5g<BR>" 2640 unless $format =~ /^\s*%\d*\.?\d*\w#?\s*$/; 2641 2642 if( $format =~ s/#\s*$// ) { # remove trailing zeros in the decimal 2643 $out = sprintf( $format, $number ); 2644 $out =~ s/(\.\d*?)0+$/$1/; 2645 $out =~ s/\.$//; # in case all decimal digits were zero, remove the decimal 2646 $out =~ s/e/E/g; # only use capital E's for exponents. Little e is for 2.71828... 2647 } elsif (is_a_number($number) ){ 2648 $out = sprintf( $format, $number ); 2649 $out =~ s/e/E/g; # only use capital E's for exponents. Little e is for 2.71828... 2650 } else { # number is probably a string representing an arithmetic expression 2651 $out = $number; 2652 } 2653 2654 } else { 2655 if (is_a_number($number)) {# only use capital E's for exponents. Little e is for 2.71828... 2656 $out = $number; 2657 $out =~ s/e/E/g; 2658 } else { # number is probably a string representing an arithmetic expression 2659 $out = $number; 2660 } 2661 } 2662 return $out; 2663 } 2664 ######################################################################### 2665 # Filters for answer evaluators 2666 ######################################################################### 2667 2668 =head2 Filters 2669 2670 =pod 2671 2672 A filter is a short subroutine with the following structure. It accepts an 2673 AnswerHash, followed by a hash of options. It returns an AnswerHash 2674 2675 $ans_hash = filter($ans_hash, %options); 2676 2677 See the AnswerHash.pm file for a list of entries which can be expected to be found 2678 in an AnswerHash, such as 'student_ans', 'score' and so forth. Other entries 2679 may be present for specialized answer evaluators. 2680 2681 The hope is that a well designed set of filters can easily be combined to form 2682 a new answer_evaluator and that this method will produce answer evaluators which are 2683 are more robust than the method of copying existing answer evaluators and modifying them. 2684 2685 Here is an outline of how a filter is constructed: 2686 2687 sub filter{ 2688 my $rh_ans = convert_to_AnswerHash(shift @_); 2689 my %options = @_; 2690 assign_option_aliases(\%options, 2691 'alias1' => 'option5' 2692 'alias2' => 'option7' 2693 ); 2694 set_default_options(\%options, 2695 '_filter_name' => 'filter', 2696 'option5' => .0001, 2697 'option7' => 'ascii', 2698 'allow_unknown_options => 0, 2699 } 2700 .... body code of filter ....... 2701 if ($error) { 2702 $rh_ans->throw_error("FILTER_ERROR", "Something went wrong"); 2703 # see AnswerHash.pm for details on using the throw_error method. 2704 2705 $rh_ans; #reference to an AnswerHash object is returned. 2706 } 2707 2708 =cut 2709 2710 =head4 compare_numbers 2711 2712 2713 =cut 2714 2715 2716 sub compare_numbers { 2717 my ($rh_ans, %options) = @_; 2718 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($rh_ans->{student_ans}); 2719 if ($PG_eval_errors) { 2720 $rh_ans->throw_error('EVAL','There is a syntax error in your answer'); 2721 $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors); 2722 # return $rh_ans; 2723 } else { 2724 $rh_ans->{student_ans} = prfmt($inVal,$options{format}); 2725 } 2726 2727 my $permitted_error; 2728 2729 if ($rh_ans->{tolType} eq 'absolute') { 2730 $permitted_error = $rh_ans->{tolerance}; 2731 } 2732 elsif ( abs($rh_ans->{correct_ans}) <= $options{zeroLevel}) { 2733 $permitted_error = $options{zeroLevelTol}; ## want $tol to be non zero 2734 } 2735 else { 2736 $permitted_error = abs($rh_ans->{tolerance}*$rh_ans->{correct_ans}); 2737 } 2738 2739 my $is_a_number = is_a_number($inVal); 2740 $rh_ans->{score} = 1 if ( ($is_a_number) and 2741 (abs( $inVal - $rh_ans->{correct_ans} ) <= $permitted_error) ); 2742 if (not $is_a_number) { 2743 $rh_ans->{error_message} = "$rh_ans->{error_message}". 'Your answer does not evaluate to a number '; 2744 } 2745 2746 $rh_ans; 2747 } 2748 2749 =head4 std_num_filter 2750 2751 std_num_filter($rh_ans, %options) 2752 returns $rh_ans 2753 2754 Replaces some constants using math_constants, then evaluates a perl expression. 2755 2756 2757 =cut 2758 2759 sub std_num_filter { 2760 my $rh_ans = shift; 2761 my %options = @_; 2762 my $in = $rh_ans->input(); 2763 $in = math_constants($in); 2764 $rh_ans->{type} = 'std_number'; 2765 my ($inVal,$PG_eval_errors,$PG_full_error_report); 2766 if ($in =~ /\S/) { 2767 ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($in); 2768 } else { 2769 $PG_eval_errors = ''; 2770 } 2771 2772 if ($PG_eval_errors) { ##error message from eval or above 2773 $rh_ans->{ans_message} = 'There is a syntax error in your answer'; 2774 $rh_ans->{student_ans} = clean_up_error_msg($PG_eval_errors); 2775 } else { 2776 $rh_ans->{student_ans} = $inVal; 2777 } 2778 $rh_ans; 2779 } 2780 2781 =head std_num_array_filter 2782 2783 std_num_array_filter($rh_ans, %options) 2784 returns $rh_ans 2785 2786 Assumes the {student_ans} field is a numerical array, and applies BOTH check_syntax and std_num_filter 2787 to each element of the array. Does it's best to generate sensible error messages for syntax errors. 2788 A typical error message displayed in {studnet_ans} might be ( 56, error message, -4). 2789 2790 =cut 2791 2792 sub std_num_array_filter { 2793 my $rh_ans= shift; 2794 my %options = @_; 2795 set_default_options( \%options, 2796 '_filter_name' => 'std_num_array_filter', 2797 ); 2798 my @in = @{$rh_ans->{student_ans}}; 2799 my $temp_hash = new AnswerHash; 2800 my @out=(); 2801 my $PGanswerMessage = ''; 2802 foreach my $item (@in) { # evaluate each number in the vector 2803 $temp_hash->input($item); 2804 $temp_hash = check_syntax($temp_hash); 2805 if (defined($temp_hash->{error_flag}) and $temp_hash->{error_flag} eq 'SYNTAX') { 2806 $PGanswerMessage .= $temp_hash->{ans_message}; 2807 $temp_hash->{ans_message} = undef; 2808 } else { 2809 #continue processing 2810 $temp_hash = std_num_filter($temp_hash); 2811 if (defined($temp_hash->{ans_message}) and $temp_hash->{ans_message} ) { 2812 $PGanswerMessage .= $temp_hash->{ans_message}; 2813 $temp_hash->{ans_message} = undef; 2814 } 2815 } 2816 push(@out, $temp_hash->input()); 2817 2818 } 2819 if ($PGanswerMessage) { 2820 $rh_ans->input( "( " . join(", ", @out ) . " )" ); 2821 $rh_ans->throw_error('SYNTAX', 'There is a syntax error in your answer.'); 2822 } else { 2823 $rh_ans->input( [@out] ); 2824 } 2825 $rh_ans; 2826 } 2827 2828 =head4 function_from_string2 2829 2830 2831 2832 =cut 2833 2834 sub function_from_string2 { 2835 my $rh_ans = convert_to_AnswerHash(shift); 2836 my %options = @_; 2837 my $eqn = $rh_ans->{student_ans}; 2838 assign_option_aliases(\%options, 2839 'vars' => 'ra_vars', 2840 'var' => 'ra_vars', 2841 ); 2842 set_default_options( \%options, 2843 'store_in' => 'rf_student_ans', 2844 'ra_vars' => [qw( x y )], 2845 'debug' => 0, 2846 '_filter_name' => 'function_from_string2', 2847 ); 2848 $rh_ans->{_filter_name} = $options{_filter_name}; 2849 my @VARS = @{ $options{ 'ra_vars'}}; 2850 #warn "VARS = ", join("<>", @VARS) if defined($options{debug}) and $options{debug} ==1; 2851 my $originalEqn = $eqn; 2852 $eqn = &math_constants($eqn); 2853 for( my $i = 0; $i < @VARS; $i++ ) { 2854 # This next line is a hack required for 5.6.0 -- it doesn't appear to be needed in 5.6.1 2855 my ($temp,$er1,$er2) = PG_restricted_eval('"'. $VARS[$i] . '"'); 2856 #$eqn =~ s/\b$VARS[$i]\b/\$VARS[$i]/g; 2857 $eqn =~ s/\b$temp\b/\$VARS[$i]/g; 2858 2859 } 2860 #warn "equation evaluated = $eqn",$rh_ans->pretty_print(), "<br>\noptions<br>\n", 2861 # pretty_print(\%options) 2862 # if defined($options{debug}) and $options{debug} ==1; 2863 my ($function_sub,$PG_eval_errors, $PG_full_errors) = PG_answer_eval( q! 2864 sub { 2865 my @VARS = @_; 2866 my $input_str = ''; 2867 for( my $i=0; $i<@VARS; $i++ ) { 2868 $input_str .= "\$VARS[$i] = $VARS[$i]; "; 2869 } 2870 my $PGanswerMessage; 2871 $input_str .= '! . $eqn . q!'; # need the single quotes to keep the contents of $eqn from being 2872 # evaluated when it is assigned to $input_str; 2873 my ($out, $PG_eval_errors, $PG_full_errors) = PG_answer_eval($input_str); #Finally evaluated 2874 2875 if ( defined($PG_eval_errors) and $PG_eval_errors =~ /\S/ ) { 2876 $PGanswerMessage = clean_up_error_msg($PG_eval_errors); 2877 # This message seemed too verbose, but it does give extra information, we'll see if it is needed. 2878 # "<br> There was an error in evaluating your function <br> 2879 # !. $originalEqn . q! <br> 2880 # at ( " . join(', ', @VARS) . " ) <br> 2881 # $PG_eval_errors 2882 # "; # this message appears in the answer section which is not process by Latex2HTML so it must 2883 # # be in HTML. That is why $BR is NOT used. 2884 2885 } 2886 (wantarray) ? ($out, $PGanswerMessage): $out; # PGanswerMessage may be undefined. 2887 }; 2888 !); 2889 2890 if (defined($PG_eval_errors) and $PG_eval_errors =~/\S/ ) { 2891 $PG_eval_errors = clean_up_error_msg($PG_eval_errors); 2892 2893 my $PGanswerMessage = "There was an error in converting the expression 2894 $main::BR $originalEqn $main::BR into a function. 2895 $main::BR $PG_eval_errors."; 2896 $rh_ans->{rf_student_ans} = $function_sub; 2897 $rh_ans->{ans_message} = $PGanswerMessage; 2898 $rh_ans->{error_message} = $PGanswerMessage; 2899 $rh_ans->{error_flag} = 1; 2900 # we couldn't compile the equation, we'll return an error message. 2901 } else { 2902 # if (defined($options{store_in} )) { 2903 # $rh_ans ->{$options{store_in}} = $function_sub; 2904 # } else { 2905 # $rh_ans->{rf_student_ans} = $function_sub; 2906 # } 2907 $rh_ans ->{$options{store_in}} = $function_sub; 2908 } 2909 2910 $rh_ans; 2911 } 2912 2913 =head4 is_zero_array 2914 2915 2916 =cut 2917 2918 2919 sub is_zero_array { 2920 my $rh_ans = convert_to_AnswerHash(shift); 2921 my %options = @_; 2922 set_default_options( \%options, 2923 '_filter_name' => 'is_zero_array', 2924 'tolerance' => 0.000001, 2925 ); 2926 my $array = $rh_ans -> {ra_differences}; 2927 my $num = @$array; 2928 my $i; 2929 my $max = 0; my $mm; 2930 for ($i=0; $i< $num; $i++) { 2931 $mm = $array->[$i] ; 2932 if (not is_a_number($mm) ) { 2933 $max = $mm; # break out if one of the elements is not a number 2934 last; 2935 } 2936 $max = abs($mm) if abs($mm) > $max; 2937 } 2938 if (not is_a_number($max)) { 2939 $rh_ans->{score} = 0; 2940 my $error = "WeBWorK was unable evaluate your function. Please check that your 2941 expression doesn't take roots of negative numbers, or divide by zero."; 2942 $rh_ans->throw_error('EVAL',$error); 2943 } else { 2944 $rh_ans->{score} = ($max < $options{tolerance} ) ? 1: 0; # 1 if the array is close to 0; 2945 } 2946 $rh_ans; 2947 } 2948 2949 =head4 best_approx_parameters 2950 2951 best_approx_parameters($rh_ans,%options); #requires the following fields in $rh_ans 2952 {rf_student_ans} # reference to the test answer 2953 {rf_correct_ans} # reference to the comparison answer 2954 {evaluation_points}, # an array of row vectors indicating the points 2955 # to evaluate when comparing the functions 2956 2957 %options # debug => 1 gives more error answers 2958 # param_vars => [''] additional parameters used to adapt to function 2959 ) 2960 2961 2962 The parameters for the comparison function which best approximates the test_function are stored 2963 in the field {ra_parameters}. 2964 2965 2966 The last $dim_of_parms_space variables are assumed to be parameters, and it is also 2967 assumed that the function \&comparison_fun 2968 depends linearly on these variables. This function finds the values for these parameters which minimizes the 2969 Euclidean distance (L2 distance) between the test function and the comparison function and the test points specified 2970 by the array reference \@rows_of_test_points. This is assumed to be an array of arrays, with the inner arrays 2971 determining a test point. 2972 2973 The comparison function should have $dim_of_params_space more input variables than the test function. 2974 2975 2976 2977 2978 2979 =cut 2980 2981 # Used internally: 2982 # 2983 # &$determine_param_coeff( $rf_comparison_function # a reference to the correct answer function 2984 # $ra_variables # an array of the active input variables to the functions 2985 # $dim_of_params_space # indicates the number of parameters upon which the 2986 # # the comparison function depends linearly. These are assumed to 2987 # # be the last group of inputs to the comparison function. 2988 # 2989 # %options # $options{debug} gives more error messages 2990 # 2991 # # A typical function might look like 2992 # # f(x,y,z,a,b) = x^2+a*cos(xz) + b*sin(x) with a parameter 2993 # # space of dimension 2 and a variable space of dimension 3. 2994 # ) 2995 # # returns a list of coefficients 2996 2997 sub best_approx_parameters { 2998 my $rh_ans = shift; 2999 my %options = @_; 3000 set_default_options(\%options, 3001 '_filter_name' => 'best_approx_paramters', 3002 'allow_unknown_options' => 1, 3003 ); 3004 my $errors = undef; 3005 # This subroutine for the determining the coefficents of the parameters at a given point 3006 # is pretty specialized, so it is included here as a sub-subroutine. 3007 my $determine_param_coeffs = sub { 3008 my ($rf_fun, $ra_variables, $dim_of_params_space, %options) =@_; 3009 my @zero_params=(); 3010 for(my $i=1;$i<=$dim_of_params_space;$i++){push(@zero_params,0); } 3011 my @vars = @$ra_variables; 3012 my @coeff = (); 3013 my @inputs = (@vars,@zero_params); 3014 my ($f0, $f1, $err); 3015 ($f0, $err) = &{$rf_fun}(@inputs); 3016 if (defined($err) ) { 3017 $errors .= "$err "; 3018 } else { 3019 for (my $i=@vars;$i<@inputs;$i++) { 3020 $inputs[$i]=1; # set one parameter to 1; 3021 my($f1,$err) = &$rf_fun(@inputs); 3022 if (defined($err) ) { 3023 $errors .= " $err "; 3024 } else { 3025 push(@coeff, $f1-$f0); 3026 } 3027 $inputs[$i]=0; # set it back 3028 } 3029 } 3030 (\@coeff, $errors); 3031 }; 3032 my $rf_fun = $rh_ans->{rf_student_ans}; 3033 my $rf_correct_fun = $rh_ans->{rf_correct_ans}; 3034 my $ra_vars_matrix = $rh_ans->{evaluation_points}; 3035 my $dim_of_param_space = @{$options{param_vars}}; 3036 # Short cut. Bail if there are no param_vars 3037 unless ($dim_of_param_space >0) { 3038 $rh_ans ->{ra_parameters} = []; 3039 return $rh_ans; 3040 } 3041 # inputs are row arrays in this case. 3042 my @zero_params=(); 3043 3044 for(my $i=1;$i<=$dim_of_param_space;$i++){push(@zero_params,0); } 3045 my @rows_of_vars = @$ra_vars_matrix; 3046 warn "input rows ", pretty_print(\@rows_of_vars) if defined($options{debug}) and $options{debug}; 3047 my $rows = @rows_of_vars; 3048 my $matrix =new Matrix($rows,$dim_of_param_space); 3049 my $rhs_vec = new Matrix($rows, 1); 3050 my $row_num = 1; 3051 my ($ra_coeff,$val2, $val1, $err1,$err2,@inputs,@vars); 3052 my $number_of_data_points = $dim_of_param_space +2; 3053 while (@rows_of_vars and $row_num <= $number_of_data_points) { 3054 # get one set of data points from the test function; 3055 @vars = @{ shift(@rows_of_vars) }; 3056 ($val2, $err1) = &{$rf_fun}(@vars); 3057 $errors .= " $err1 " if defined($err1); 3058 @inputs = (@vars,@zero_params); 3059 ($val1, $err2) = &{$rf_correct_fun}(@inputs); 3060 $errors .= " $err2 " if defined($err2); 3061 3062 unless (defined($err1) or defined($err2) ) { 3063 $rhs_vec->assign($row_num,1, $val2-$val1 ); 3064 3065 # warn "rhs data val1=$val1, val2=$val2, val2 - val1 = ", $val2 - $val1 if $options{debug}; 3066 # warn "vars ", join(" | ", @vars) if $options{debug}; 3067 3068 ($ra_coeff, $err1) = &{$determine_param_coeffs}($rf_correct_fun,\@vars,$dim_of_param_space,%options); 3069 if (defined($err1) ) { 3070 $errors .= " $err1 "; 3071 } else { 3072 my @coeff = @$ra_coeff; 3073 my $col_num=1; 3074 while(@coeff) { 3075 $matrix->assign($row_num,$col_num, shift(@coeff) ); 3076 $col_num++; 3077 } 3078 } 3079 } 3080 $row_num++; 3081 last if $errors; # break if there are any errors. 3082 # This cuts down on the size of error messages. 3083 # However it impossible to check for equivalence at 95% of points 3084 # which might be useful for functions that are not defined at some points. 3085 } 3086 warn "<br> best_approx_parameters: matrix1 <br> ", " $matrix " if $options{debug}; 3087 warn "<br> best_approx_parameters: vector <br> ", " $rhs_vec " if $options{debug}; 3088 3089 # we have Matrix * parameter = data_vec + perpendicular vector 3090 # where the matrix has column vectors defining the span of the parameter space 3091 # multiply both sides by Matrix_transpose and solve for the parameters 3092 # This is exactly what the method proj_coeff method does. 3093 my @array; 3094 if (defined($errors) ) { 3095 @array = (); # new Matrix($dim_of_param_space,1); 3096 } else { 3097 @array = $matrix->proj_coeff($rhs_vec)->list(); 3098 } 3099 # check size (hack) 3100 my $max = 0; 3101 foreach my $val (@array ) { 3102 $max = abs($val) if $max < abs($val); 3103 if (not is_a_number($val) ) { 3104 $max = "NaN: $val"; 3105 last; 3106 } 3107 } 3108 if ($max =~/NaN/) { 3109 $errors .= "WeBWorK was unable evaluate your function. Please check that your 3110 expression doesn't take roots of negative numbers, or divide by zero."; 3111 } elsif ($max > $options{maxConstantOfIntegration} ) { 3112 $errors .= "At least one of the adapting parameters 3113 (perhaps the constant of integration) is too large: $max, 3114 ( the maximum allowed is $options{maxConstantOfIntegration} )"; 3115 } 3116 3117 $rh_ans->{ra_parameters} = \@array; 3118 $rh_ans->throw_error('EVAL', $errors) if defined($errors); 3119 $rh_ans; 3120 } 3121 3122 =head4 calculate_difference_vector 3123 3124 calculate_difference_vector( $ans_hash, %options); 3125 3126 {rf_student_ans}, # a reference to the test function 3127 {rf_correct_ans}, # a reference to the correct answer function 3128 {evaluation_points}, # an array of row vectors indicating the points 3129 # to evaluate when comparing the functions 3130 {ra_parameters} # these are the (optional) additional inputs to 3131 # the comparison function which adapt it properly 3132 # to the problem at hand. 3133 3134 %options # mode => 'rel' specifies that each element in the 3135 # difference matrix is divided by the correct answer. 3136 # unless the correct answer is nearly 0. 3137 ) 3138 3139 =cut 3140 3141 sub calculate_difference_vector { 3142 my $rh_ans = shift; 3143 my %options = @_; 3144 # initialize 3145 my $rf_fun = $rh_ans -> {rf_student_ans}; 3146 my $rf_correct_fun = $rh_ans -> {rf_correct_ans}; 3147 my $ra_parameters = $rh_ans ->{ra_parameters}; 3148 my @evaluation_points = @{$rh_ans->{evaluation_points} }; 3149 my @parameters = (); 3150 @parameters = @$ra_parameters if defined($ra_parameters) and ref($ra_parameters) eq 'ARRAY'; 3151 my $errors = undef; 3152 my @zero_params=(); 3153 for(my $i=1;$i<=@{$ra_parameters};$i++){push(@zero_params,0); } 3154 my @differences = (); 3155 my @student_values; 3156 my @adjusted_student_values; 3157 my @instructorVals; 3158 my ($diff,$instructorVal); 3159 # calculate the vector of differences between the test function and the comparison function. 3160 while (@evaluation_points) { 3161 my ($err1, $err2,$err3); 3162 my @vars = @{ shift(@evaluation_points) }; 3163 my @inputs = (@vars, @parameters); 3164 my ($inVal, $correctVal); 3165 ($inVal, $err1) = &{$rf_fun}(@vars); 3166 $errors .= " $err1 " if defined($err1); 3167 $errors .= " Error detected evaluating student input at (".join(' , ',@vars) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err1); 3168 ($correctVal, $err2) =&{$rf_correct_fun}(@inputs); 3169 $errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err2 " if defined($err2); 3170 $errors .= " Error detected evaluating correct adapted answer at (".join(' , ',@inputs) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err2); 3171 ($instructorVal,$err3)= &$rf_correct_fun(@vars, @zero_params); 3172 $errors .= " There is an error in WeBWorK's answer to this problem, please alert your instructor.<br> $err3 " if defined($err3); 3173 $errors .= " Error detected evaluating instructor answer at (".join(' , ',@vars, @zero_params) ." ) " if defined($options{debug}) and $options{debug}=1 and defined($err3); 3174 unless (defined($err1) or defined($err2) or defined($err3) ) { 3175 $diff = ( $inVal - ($correctVal -$instructorVal ) ) - $instructorVal; #prevents entering too high a number? 3176 #warn "taking the difference of ", $inVal, " and ", $correctVal, " is ", $diff; 3177 if (defined($options{tolType}) and $options{tolType} eq 'relative' ) { #relative tolerance 3178 #warn "diff = $diff"; 3179 #$diff = ( $inVal - ($correctVal-$instructorVal ) )/abs($instructorVal) -1 if abs($instructorVal) > $options{zeroLevel}; 3180 $diff = ( $inVal - ($correctVal-$instructorVal ) )/$instructorVal -1 if abs($instructorVal) > $options{zeroLevel}; 3181 #$diff = ( $inVal - ($correctVal-$instructorVal- $instructorVal ) )/abs($instructorVal) if abs($instructorVal) > $options{zeroLevel}; 3182 #warn "diff = $diff, ", abs( &$rf_correct_fun(@inputs) ) , "-- $correctVal"; 3183 } 3184 } 3185 last if $errors; # break if there are any errors. 3186 # This cuts down on the size of error messages. 3187 # However it impossible to check for equivalence at 95% of points 3188 # which might be useful for functions that are not defined at some points. 3189 push(@student_values,$inVal); 3190 push(@adjusted_student_values,( $inVal - ($correctVal -$instructorVal) ) ); 3191 push(@differences, $diff); 3192 push(@instructorVals,$instructorVal); 3193 } 3194 $rh_ans ->{ra_differences} = \@differences; 3195 $rh_ans ->{ra_student_values} = \@student_values; 3196 $rh_ans ->{ra_adjusted_student_values} = \@adjusted_student_values; 3197 $rh_ans->{ra_instructor_values}=\@instructorVals; 3198 $rh_ans->throw_error('EVAL', $errors) if defined($errors); 3199 $rh_ans; 3200 } 3201 3202 =head4 fix_answer_for_display 3203 3204 =cut 3205 3206 sub fix_answers_for_display { 3207 my ($rh_ans, %options) = @_; 3208 if ( $rh_ans->{answerIsString} ==1) { 3209 $rh_ans = evaluatesToNumber ($rh_ans, %options); 3210 } 3211 if (defined ($rh_ans->{student_units})) { 3212 $rh_ans->{student_ans} = $rh_ans->{student_ans}. ' '. $rh_ans->{student_units}; 3213 } 3214 $rh_ans->{correct_ans} = $rh_ans->{original_correct_ans}; 3215 3216 $rh_ans; 3217 } 3218 3219 =head4 evaluatesToNumber 3220 3221 =cut 3222 3223 sub evaluatesToNumber { 3224 my ($rh_ans, %options) = @_; 3225 if (is_a_numeric_expression($rh_ans->{student_ans})) { 3226 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($rh_ans->{student_ans}); 3227 if ($PG_eval_errors) { # this if statement should never be run 3228 # change nothing 3229 } else { 3230 # change this 3231 $rh_ans->{student_ans} = prfmt($inVal,$options{format}); 3232 } 3233 } 3234 $rh_ans; 3235 } 3236 3237 =head4 is_numeric_expression 3238 3239 =cut 3240 3241 sub is_a_numeric_expression { 3242 my $testString = shift; 3243 my $is_a_numeric_expression = 0; 3244 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($testString); 3245 if ($PG_eval_errors) { 3246 $is_a_numeric_expression = 0; 3247 } else { 3248 $is_a_numeric_expression = 1; 3249 } 3250 $is_a_numeric_expression; 3251 } 3252 3253 =head4 is_a_number 3254 3255 =cut 3256 3257 sub is_a_number { 3258 my ($num,%options) = @_; 3259 my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ; 3260 my ($rh_ans); 3261 if ($process_ans_hash) { 3262 $rh_ans = $num; 3263 $num = $rh_ans->{student_ans}; 3264 } 3265 3266 my $is_a_number = 0; 3267 return $is_a_number unless defined($num); 3268 $num =~ s/^\s*//; ## remove initial spaces 3269 $num =~ s/\s*$//; ## remove trailing spaces 3270 3271 ## the following is copied from the online perl manual 3272 if ($num =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/){ 3273 $is_a_number = 1; 3274 } 3275 3276 if ($process_ans_hash) { 3277 if ($is_a_number == 1 ) { 3278 $rh_ans->{student_ans}=$num; 3279 return $rh_ans; 3280 } else { 3281 $rh_ans->{student_ans} = "Incorrect number format: You must enter a number, e.g. -6, 5.3, or 6.12E-3"; 3282 $rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3'); 3283 return $rh_ans; 3284 } 3285 } else { 3286 return $is_a_number; 3287 } 3288 } 3289 3290 =head4 is_a_fraction 3291 3292 =cut 3293 3294 sub is_a_fraction { 3295 my ($num,%options) = @_; 3296 my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ; 3297 my ($rh_ans); 3298 if ($process_ans_hash) { 3299 $rh_ans = $num; 3300 $num = $rh_ans->{student_ans}; 3301 } 3302 3303 my $is_a_fraction = 0; 3304 return $is_a_fraction unless defined($num); 3305 $num =~ s/^\s*//; ## remove initial spaces 3306 $num =~ s/\s*$//; ## remove trailing spaces 3307 3308 if ($num =~ /^\s*\-?\s*[\/\d\.Ee\s]*$/) { 3309 $is_a_fraction = 1; 3310 } 3311 3312 if ($process_ans_hash) { 3313 if ($is_a_fraction == 1 ) { 3314 $rh_ans->{student_ans}=$num; 3315 return $rh_ans; 3316 } else { 3317 $rh_ans->{student_ans} = "Not a number of fraction: You must enter a number or fraction, e.g. -6 or 7/13"; 3318 $rh_ans->throw_error('NUMBER', 'You must enter a number, e.g. -6, 5.3, or 6.12E-3'); 3319 return $rh_ans; 3320 } 3321 3322 } else { 3323 return $is_a_fraction; 3324 } 3325 } 3326 3327 =head4 phase_pi 3328 I often discovered that the answers I was getting, when using the arctan function would be off by phases of 3329 pi, which for the tangent function, were equivalent values. This method allows for this. 3330 =cut 3331 3332 sub phase_pi { 3333 my ($num,%options) = @_; 3334 my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ; 3335 my ($rh_ans); 3336 if ($process_ans_hash) { 3337 $rh_ans = $num; 3338 $num = $rh_ans->{correct_ans}; 3339 } 3340 while( ($rh_ans->{correct_ans}) > 3.14159265358979/2 ){ 3341 $rh_ans->{correct_ans} -= 3.14159265358979; 3342 } 3343 while( ($rh_ans->{correct_ans}) <= -3.14159265358979/2 ){ 3344 $rh_ans->{correct_ans} += 3.14159265358979; 3345 } 3346 $rh_ans; 3347 } 3348 3349 =head4 is_an_arithemetic_expression 3350 3351 =cut 3352 3353 sub is_an_arithmetic_expression { 3354 my ($num,%options) = @_; 3355 my $process_ans_hash = ( ref( $num ) eq 'AnswerHash' ) ? 1 : 0 ; 3356 my ($rh_ans); 3357 if ($process_ans_hash) { 3358 $rh_ans = $num; 3359 $num = $rh_ans->{student_ans}; 3360 } 3361 3362 my $is_an_arithmetic_expression = 0; 3363 return $is_an_arithmetic_expression unless defined($num); 3364 $num =~ s/^\s*//; ## remove initial spaces 3365 $num =~ s/\s*$//; ## remove trailing spaces 3366 3367 if ($num =~ /^[+\-*\/\^\(\)\[\]\{\}\s\d\.Ee]*$/) { 3368 $is_an_arithmetic_expression = 1; 3369 } 3370 3371 if ($process_ans_hash) { 3372 if ($is_an_arithmetic_expression == 1 ) { 3373 $rh_ans->{student_ans}=$num; 3374 return $rh_ans; 3375 } else { 3376 3377 $rh_ans->{student_ans} = "Not an arithmetic expression: You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2"; 3378 $rh_ans->throw_error('NUMBER', 'You must enter an arithmetic expression, e.g. -6 or (2.3*4+5/3)^2'); 3379 return $rh_ans; 3380 } 3381 3382 } else { 3383 return $is_an_arithmetic_expression; 3384 } 3385 } 3386 3387 # 3388 3389 =head4 math_constants 3390 3391 replaces pi, e, and ^ with their Perl equivalents 3392 if useBaseTenLog is non-zero, convert log to logten 3393 3394 =cut 3395 3396 sub math_constants { 3397 my($in,%options) = @_; 3398 my $rh_ans; 3399 my $process_ans_hash = ( ref( $in ) eq 'AnswerHash' ) ? 1 : 0 ; 3400 if ($process_ans_hash) { 3401 $rh_ans = $in; 3402 $in = $rh_ans->{student_ans}; 3403 } 3404 # The code fragment above allows this filter to be used when the input is simply a string 3405 # as well as when the input is an AnswerHash, and options. 3406 $in =~s/\bpi\b/(4*atan2(1,1))/ge; 3407 $in =~s/\be\b/(exp(1))/ge; 3408 $in =~s/\^/**/g; 3409 if($main::useBaseTenLog) { 3410 $in =~ s/\blog\b/logten/g; 3411 } 3412 3413 if ($process_ans_hash) { 3414 $rh_ans->{student_ans}=$in; 3415 return $rh_ans; 3416 } else { 3417 return $in; 3418 } 3419 } 3420 3421 3422 3423 =head4 is_array 3424 3425 is_array($rh_ans) 3426 returns: $rh_ans. Throws error "NOTARRAY" if this is not an array 3427 3428 =cut 3429 3430 sub is_array { 3431 my $rh_ans = shift; 3432 # return if the result is an array 3433 return($rh_ans) if ref($rh_ans->{student_ans}) eq 'ARRAY' ; 3434 $rh_ans->throw_error("NOTARRAY","The answer is not an array"); 3435 $rh_ans; 3436 } 3437 3438 =head4 check_syntax 3439 3440 check_syntax( $rh_ans, %options) 3441 returns an answer hash. 3442 3443 latex2html preview code are installed in the answer hash. 3444 The input has been transformed, changing 7pi to 7*pi or 7x to 7*x. 3445 Syntax error messages may be generated and stored in student_ans 3446 Additional syntax error messages are stored in {ans_message} and duplicated in {error_message} 3447 3448 3449 =cut 3450 3451 sub check_syntax { 3452 my $rh_ans = convert_to_AnswerHash(shift @_); 3453 my %options = @_; 3454 unless ( defined( $rh_ans->{student_ans} ) ) { 3455 warn "Check_syntax requires an equation in the field {student_ans} or input"; 3456 $rh_ans->throw_error("1","{student_ans} field not defined"); 3457 return $rh_ans; 3458 } 3459 my $in = $rh_ans->{student_ans}; 3460 my $parser = new AlgParserWithImplicitExpand; 3461 my $ret = $parser -> parse($in); #for use with loops 3462 3463 if ( ref($ret) ) { ## parsed successfully 3464 $parser -> tostring(); 3465 $parser -> normalize(); 3466 $rh_ans->input( $parser -> tostring() ); 3467 $rh_ans->{preview_text_string} = $in; 3468 $rh_ans->{preview_latex_string} = $parser -> tolatex(); 3469 3470 } else { ## error in parsing 3471 3472 $rh_ans->{'student_ans'} = 'syntax error:'. $parser->{htmlerror}, 3473 $rh_ans->{'ans_message'} = $parser -> {error_msg}, 3474 $rh_ans->{'preview_text_string'} = '', 3475 $rh_ans->{'preview_latex_string'} = '', 3476 $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'. $parser->{htmlerror} . "$BR" .$parser -> {error_msg}); 3477 } 3478 $rh_ans; 3479 3480 } 3481 3482 =head4 check_strings 3483 3484 check_strings ($rh_ans, %options) 3485 returns $rh_ans 3486 3487 =cut 3488 3489 sub check_strings { 3490 my $rh_ans = convert_to_AnswerHash(shift @_); 3491 my %options = @_; 3492 3493 # if the student's answer is a number, simply return the answer hash (unchanged). 3494 3495 # we allow constructions like -INF to be treated as a string. Thus we ignore an initial 3496 # - in deciding whether the student's answer is a number or string 3497 3498 my $temp_ans = $rh_ans->{student_ans}; 3499 $temp_ans =~ s/^\s*\-//; # remove an initial - 3500 3501 if ( $temp_ans =~ m/[\d+\-*\/^(){}\[\]]|^\s*e\s*$|^\s*pi\s*$/) { 3502 # if ( $rh_ans->{answerIsString} == 1) { 3503 # #$rh_ans->throw_error('STRING','Incorrect Answer'); # student's answer is a number 3504 # } 3505 return $rh_ans; 3506 } 3507 # the student's answer is recognized as a string 3508 my $ans = $rh_ans->{student_ans}; 3509 3510 # OVERVIEW of reminder of function: 3511 # if answer is correct, return correct. (adjust score to 1) 3512 # if answer is incorect: 3513 # 1) determine if the answer is sensible. if it is, return incorrect. 3514 # 2) if the answer is not sensible (and incorrect), then return an error message indicating so. 3515 # no matter what: throw a 'STRING' error to skip numerical evaluations. (error flag skips remainder of pre_filters and evaluators) 3516 # last: 'STRING' post_filter will clear the error (avoiding pink screen.) 3517 3518 my $sensibleAnswer = 0; 3519 $ans = str_filters( $ans, 'compress_whitespace' ); # remove trailing, leading, and double spaces. 3520 my ($ans_eval) = str_cmp($rh_ans->{correct_ans}); 3521 my $temp_ans_hash = &$ans_eval($ans); 3522 $rh_ans->{test} = $temp_ans_hash; 3523 if ($temp_ans_hash->{score} ==1 ) { # students answer matches the correct answer. 3524 $rh_ans->{score} = 1; 3525 $sensibleAnswer = 1; 3526 } else { # students answer does not match the correct answer. 3527 my $legalString = ''; # find out if string makes sense 3528 my @legalStrings = @{$options{strings}}; 3529 foreach $legalString (@legalStrings) { 3530 if ( uc($ans) eq uc($legalString) ) { 3531 $sensibleAnswer = 1; 3532 last; 3533 } 3534 } 3535 $sensibleAnswer = 1 unless $ans =~ /\S/; ## empty answers are sensible 3536 $rh_ans->throw_error('EVAL', "Your answer is not a recognized answer") unless ($sensibleAnswer); 3537 # $temp_ans_hash -> setKeys( 'ans_message' => 'Your answer is not a recognized answer' ) unless ($sensibleAnswer); 3538 # $temp_ans_hash -> setKeys( 'student_ans' => uc($ans) ); 3539 } 3540 $rh_ans->{student_ans} = $ans; 3541 if ($sensibleAnswer) { 3542 $rh_ans->throw_error('STRING', "The student's answer $rh_ans->{student_ans} is interpreted as a string."); 3543 } 3544 # warn ("\$rh_ans->{answerIsString} = $rh_ans->{answerIsString}"); 3545 $rh_ans; 3546 } 3547 3548 =head4 check_units 3549 3550 check_strings ($rh_ans, %options) 3551 returns $rh_ans 3552 3553 3554 =cut 3555 3556 sub check_units { 3557 my $rh_ans = convert_to_AnswerHash(shift @_); 3558 my %options = @_; 3559 my %correct_units = %{$rh_ans-> {rh_correct_units}}; 3560 my $ans = $rh_ans->{student_ans}; 3561 # $ans = '' unless defined ($ans); 3562 $ans = str_filters ($ans, 'trim_whitespace'); 3563 my $original_student_ans = $ans; 3564 $rh_ans->{original_student_ans} = $original_student_ans; 3565 3566 # it surprises me that the match below works since the first .* is greedy. 3567 my ($num_answer, $units) = $ans =~ /^(.*)\s+([^\s]*)$/; 3568 3569 unless ( defined($num_answer) && $units ) { 3570 # there is an error reading the input 3571 if ( $ans =~ /\S/ ) { # the answer is not blank 3572 $rh_ans -> setKeys( 'ans_message' => "The answer \"$ans\" could not be interpreted " . 3573 "as a number or an arithmetic expression followed by a unit specification. " . 3574 "Your answer must contain units." ); 3575 $rh_ans->throw_error('UNITS', "The answer \"$ans\" could not be interpreted " . 3576 "as a number or an arithmetic expression followed by a unit specification. " . 3577 "Your answer must contain units." ); 3578 } 3579 return $rh_ans; 3580 } 3581 3582 # we have been able to parse the answer into a numerical part and a unit part 3583 3584 # $num_answer = $1; #$1 and $2 from the regular expression above 3585 # $units = $2; 3586 3587 my %units = Units::evaluate_units($units); 3588 if ( defined( $units{'ERROR'} ) ) { 3589 # handle error condition 3590 $units{'ERROR'} = clean_up_error_msg($units{'ERROR'}); 3591 $rh_ans -> setKeys( 'ans_message' => "$units{'ERROR'}" ); 3592 $rh_ans -> throw_error('UNITS', "$units{'ERROR'}"); 3593 return $rh_ans; 3594 } 3595 3596 my $units_match = 1; 3597 my $fund_unit; 3598 foreach $fund_unit (keys %correct_units) { 3599 next if $fund_unit eq 'factor'; 3600 $units_match = 0 unless $correct_units{$fund_unit} == $units{$fund_unit}; 3601 } 3602 3603 if ( $units_match ) { 3604 # units are ok. Evaluate the numerical part of the answer 3605 $rh_ans->{'tolerance'} = $rh_ans->{'tolerance'}* $correct_units{'factor'}/$units{'factor'} if 3606 $rh_ans->{'tolType'} eq 'absolute'; # the tolerance is in the units specified by the instructor. 3607 $rh_ans->{correct_ans} = prfmt($rh_ans->{correct_ans}*$correct_units{'factor'}/$units{'factor'}); 3608 $rh_ans->{student_units} = $units; 3609 $rh_ans->{student_ans} = $num_answer; 3610 3611 } else { 3612 $rh_ans -> setKeys( ans_message => 'There is an error in the units for this answer.' ); 3613 $rh_ans -> throw_error ( 'UNITS', 'There is an error in the units for this answer.' ); 3614 } 3615 3616 return $rh_ans; 3617 } 3618 3619 3620 3621 =head2 Filter utilities 3622 3623 These three subroutines can be used in filters to set default options. They 3624 help make filters perform in uniform, predictable ways, and also make it 3625 easy to recognize from the code which options a given filter expects. 3626 3627 =head4 convert_to_AnswerHash 3628 3629 Useage: my $rh_ans = convert_to_AnswerHash(shift @_); 3630 3631 Use this as the first line of a filter. It allows the filter 3632 to accept a string, instead of an AnswerHash. An AnswerHash object 3633 is created and the string is entered as the student's answer. 3634 3635 3636 =cut 3637 3638 sub convert_to_AnswerHash { 3639 3640 my ($rh_ans) = @_; 3641 return $rh_ans if ref($rh_ans) =~/AnswerHash/; 3642 # if it's a string 3643 my $new_ans_hash = new AnswerHash; 3644 $new_ans_hash->{student_ans}=$rh_ans; 3645 $new_ans_hash->{original_student_ans}=$rh_ans; 3646 $new_ans_hash; 3647 } 3648 3649 3650 =head4 assign_option_aliases 3651 3652 Use this to assign aliases for the standard options. It must come before set_default_options 3653 within the subroutine. 3654 3655 assign_option_aliases(\%options, 3656 'alias1' => 'option5' 3657 'alias2' => 'option7' 3658 ); 3659 3660 3661 If the subroutine is called with an option " alias1 => 23 " it will behave as if it had been 3662 called with the option " option5 => 23 " 3663 3664 =cut 3665 3666 3667 3668 sub assign_option_aliases { 3669 my $rh_options = shift; 3670 warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH'; 3671 my @option_aliases = @_; 3672 while (@option_aliases) { 3673 my $alias = shift @option_aliases; 3674 my $option_key = shift @option_aliases; 3675 3676 if (defined($rh_options->{$alias} )) { # if the alias appears in the option list 3677 if (not defined($rh_options->{$option_key}) ) { # and the option itself is not defined, 3678 $rh_options->{$option_key} = $rh_options->{$alias}; # insert the value defined by the alias into the option value 3679 # the FIRST alias for a given option takes precedence 3680 # (after the option itself) 3681 } else { 3682 warn "option $option_key is already defined as", $rh_options->{$option_key}, "<br>\n", 3683 "The attempt to override this option with the alias $alias with value ", $rh_options->{$alias}, 3684 " was ignored."; 3685 } 3686 } 3687 delete($rh_options->{$alias}); # remove the alias from the initial list 3688 } 3689 3690 } 3691 3692 =head4 set_default_options 3693 3694 set_default_options(\%options, 3695 '_filter_name' => 'filter', 3696 'option5' => .0001, 3697 'option7' => 'ascii', 3698 'allow_unknown_options => 0, 3699 } 3700 3701 Note that the first entry is a reference to the options with which the filter was called. 3702 3703 The option5 is set to .0001 unless the option is explicitly set when the subroutine is called. 3704 3705 The B<'_filter_name'> option should always be set, although there is no error if it is missing. 3706 It is used mainly for debugging answer evaluators and allows 3707 you to keep track of which filter is currently processing the answer. 3708 3709 If B<'allow_unknown_options'> is set to 0 then if the filter is called with options which do NOT appear in the 3710 set_default_options list an error will be signaled and a warning message will be printed out. This provides 3711 error checking against misspelling an option and is generally what is desired for most filters. 3712 3713 Occasionally one wants to write a filter which accepts a long list of options, not all of which are known in advance, 3714 but only uses a subset of the options 3715 provided. In this case, setting 'allow_unkown_options' to 1 prevents the error from being signaled. 3716 3717 =cut 3718 3719 sub set_default_options { 3720 my $rh_options = shift; 3721 warn "The first entry to set_default_options must be a reference to the option hash" unless ref($rh_options) eq 'HASH'; 3722 my %default_options = @_; 3723 unless ( defined($default_options{allow_unknown_options}) and $default_options{allow_unknown_options} == 1 ) { 3724 foreach my $key1 (keys %$rh_options) { 3725 warn "This option |$key1| is not recognized in this subroutine<br> ", pretty_print($rh_options) unless exists($default_options{$key1}); 3726 } 3727 } 3728 foreach my $key (keys %default_options) { 3729 if ( not defined($rh_options->{$key} ) and defined( $default_options{$key} ) ) { 3730 $rh_options->{$key} = $default_options{$key}; #this allows tol => undef to allow the tol option, but doesn't define 3731 # this key unless tol is explicitly defined. 3732 } 3733 } 3734 } 3735 3736 =head2 Problem Grader Subroutines 3737 3738 =cut 3739 3740 ## Problem Grader Subroutines 3741 3742 ##################################### 3743 # This is a model for plug-in problem graders 3744 ##################################### 3745 sub install_problem_grader { 3746 my $rf_problem_grader = shift; 3747 $main::PG_FLAGS{PROBLEM_GRADER_TO_USE} = $rf_problem_grader; 3748 } 3749 3750 =head4 std_problem_grader 3751 3752 This is an all-or-nothing grader. A student must get all parts of the problem write 3753 before receiving credit. You should make sure to use this grader on multiple choice 3754 and true-false questions, otherwise students will be able to deduce how many 3755 answers are correct by the grade reported by webwork. 3756 3757 3758 install_problem_grader(~~&std_problem_grader); 3759 3760 =cut 3761 3762 sub std_problem_grader { 3763 my $rh_evaluated_answers = shift; 3764 my $rh_problem_state = shift; 3765 my %form_options = @_; 3766 my %evaluated_answers = %{$rh_evaluated_answers}; 3767 # The hash $rh_evaluated_answers typically contains: 3768 # 'answer1' => 34, 'answer2'=> 'Mozart', etc. 3769 3770 # By default the old problem state is simply passed back out again. 3771 my %problem_state = %$rh_problem_state; 3772 3773 # %form_options might include 3774 # The user login name 3775 # The permission level of the user 3776 # The studentLogin name for this psvn. 3777 # Whether the form is asking for a refresh or is submitting a new answer. 3778 3779 # initial setup of the answer 3780 my %problem_result = ( score => 0, 3781 errors => '', 3782 type => 'std_problem_grader', 3783 msg => '', 3784 ); 3785 # Checks 3786 3787 my $ansCount = keys %evaluated_answers; # get the number of answers 3788 3789 unless ($ansCount > 0 ) { 3790 3791 $problem_result{msg} = "This problem did not ask any questions."; 3792 return(\%problem_result,\%problem_state); 3793 } 3794 3795 if ($ansCount > 1 ) { 3796 $problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ; 3797 } 3798 3799 unless ($form_options{answers_submitted} == 1) { 3800 return(\%problem_result,\%problem_state); 3801 } 3802 3803 my $allAnswersCorrectQ=1; 3804 foreach my $ans_name (keys %evaluated_answers) { 3805 # I'm not sure if this check is really useful. 3806 if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) { 3807 $allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} ); 3808 } 3809 else { 3810 die "Error at file ",__FILE__,"line ", __LINE__,": Answer |$ans_name| is not a hash reference\n". 3811 $evaluated_answers{$ans_name} . 3812 "This probably means that the answer evaluator for this answer\n" . 3813 "is not working correctly."; 3814 $problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}"; 3815 } 3816 } 3817 # report the results 3818 $problem_result{score} = $allAnswersCorrectQ; 3819 3820 # I don't like to put in this bit of code. 3821 # It makes it hard to construct error free problem graders 3822 # I would prefer to know that the problem score was numeric. 3823 unless (defined($problem_state{recorded_score}) and $problem_state{recorded_score} =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/ ) { 3824 $problem_state{recorded_score} = 0; # This gets rid of non-numeric scores 3825 } 3826 # 3827 if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) { 3828 $problem_state{recorded_score} = 1; 3829 } 3830 else { 3831 $problem_state{recorded_score} = 0; 3832 } 3833 3834 $problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1; 3835 $problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0; 3836 (\%problem_result, \%problem_state); 3837 } 3838 3839 =head4 std_problem_grader2 3840 3841 This is an all-or-nothing grader. A student must get all parts of the problem write 3842 before receiving credit. You should make sure to use this grader on multiple choice 3843 and true-false questions, otherwise students will be able to deduce how many 3844 answers are correct by the grade reported by webwork. 3845 3846 3847 install_problem_grader(~~&std_problem_grader2); 3848 3849 The only difference between the two versions 3850 is at the end of the subroutine, where std_problem_grader2 3851 records the attempt only if there have been no syntax errors, 3852 whereas std_problem_grader records it regardless. 3853 3854 =cut 3855 3856 3857 3858 sub std_problem_grader2 { 3859 my $rh_evaluated_answers = shift; 3860 my $rh_problem_state = shift; 3861 my %form_options = @_; 3862 my %evaluated_answers = %{$rh_evaluated_answers}; 3863 # The hash $rh_evaluated_answers typically contains: 3864 # 'answer1' => 34, 'answer2'=> 'Mozart', etc. 3865 3866 # By default the old problem state is simply passed back out again. 3867 my %problem_state = %$rh_problem_state; 3868 3869 # %form_options might include 3870 # The user login name 3871 # The permission level of the user 3872 # The studentLogin name for this psvn. 3873 # Whether the form is asking for a refresh or is submitting a new answer. 3874 3875 # initial setup of the answer 3876 my %problem_result = ( score => 0, 3877 errors => '', 3878 type => 'std_problem_grader', 3879 msg => '', 3880 ); 3881 3882 # syntax errors are not counted. 3883 my $record_problem_attempt = 1; 3884 # Checks 3885 3886 my $ansCount = keys %evaluated_answers; # get the number of answers 3887 unless ($ansCount > 0 ) { 3888 $problem_result{msg} = "This problem did not ask any questions."; 3889 return(\%problem_result,\%problem_state); 3890 } 3891 3892 if ($ansCount > 1 ) { 3893 $problem_result{msg} = 'In order to get credit for this problem all answers must be correct.' ; 3894 } 3895 3896 unless ($form_options{answers_submitted} == 1) { 3897 return(\%problem_result,\%problem_state); 3898 } 3899 3900 my $allAnswersCorrectQ=1; 3901 foreach my $ans_name (keys %evaluated_answers) { 3902 # I'm not sure if this check is really useful. 3903 if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) { 3904 $allAnswersCorrectQ = 0 unless( 1 == $evaluated_answers{$ans_name}->{score} ); 3905 } 3906 else { 3907 die "Error at file ",__FILE__,"line ", __LINE__,": Answer |$ans_name| is not a hash reference\n". 3908 $evaluated_answers{$ans_name} . 3909 "This probably means that the answer evaluator for this answer\n" . 3910 "is not working correctly."; 3911 $problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}"; 3912 } 3913 } 3914 # report the results 3915 $problem_result{score} = $allAnswersCorrectQ; 3916 3917 # I don't like to put in this bit of code. 3918 # It makes it hard to construct error free problem graders 3919 # I would prefer to know that the problem score was numeric. 3920 unless ($problem_state{recorded_score} =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/ ) { 3921 $problem_state{recorded_score} = 0; # This gets rid of non-numeric scores 3922 } 3923 # 3924 if ($allAnswersCorrectQ == 1 or $problem_state{recorded_score} == 1) { 3925 $problem_state{recorded_score} = 1; 3926 } 3927 else { 3928 $problem_state{recorded_score} = 0; 3929 } 3930 # record attempt only if there have been no syntax errors. 3931 3932 if ($record_problem_attempt == 1) { 3933 $problem_state{num_of_correct_ans}++ if $allAnswersCorrectQ == 1; 3934 $problem_state{num_of_incorrect_ans}++ if $allAnswersCorrectQ == 0; 3935 } 3936 else { 3937 $problem_result{show_partial_correct_answers} = 0 ; # prevent partial correct answers from being shown for syntax errors. 3938 } 3939 (\%problem_result, \%problem_state); 3940 } 3941 3942 =head4 avg_problem_grader 3943 3944 This grader gives a grade depending on how many questions from the problem are correct. (The highest 3945 grade is the one that is kept. One can never lower the recorded grade on a problem by repeating it.) 3946 Many professors (and almost all students :-) ) prefer this grader. 3947 3948 3949 install_problem_grader(~~&avg_problem_grader); 3950 3951 =cut 3952 3953 3954 sub avg_problem_grader { 3955 my $rh_evaluated_answers = shift; 3956 my $rh_problem_state = shift; 3957 my %form_options = @_; 3958 my %evaluated_answers = %{$rh_evaluated_answers}; 3959 # The hash $rh_evaluated_answers typically contains: 3960 # 'answer1' => 34, 'answer2'=> 'Mozart', etc. 3961 3962 # By default the old problem state is simply passed back out again. 3963 my %problem_state = %$rh_problem_state; 3964 3965 3966 # %form_options might include 3967 # The user login name 3968 # The permission level of the user 3969 # The studentLogin name for this psvn. 3970 # Whether the form is asking for a refresh or is submitting a new answer. 3971 3972 # initial setup of the answer 3973 my $total=0; 3974 my %problem_result = ( score => 0, 3975 errors => '', 3976 type => 'avg_problem_grader', 3977 msg => '', 3978 ); 3979 my $count = keys %evaluated_answers; 3980 $problem_result{msg} = 'You can earn partial credit on this problem.' if $count >1; 3981 # Return unless answers have been submitted 3982 unless ($form_options{answers_submitted} == 1) { 3983 return(\%problem_result,\%problem_state); 3984 } 3985 3986 # Answers have been submitted -- process them. 3987 foreach my $ans_name (keys %evaluated_answers) { 3988 # I'm not sure if this check is really useful. 3989 if ( ( ref($evaluated_answers{$ans_name} ) eq 'HASH' ) or ( ref($evaluated_answers{$ans_name}) eq 'AnswerHash' ) ) { 3990 $total += $evaluated_answers{$ans_name}->{score}; 3991 } 3992 else { 3993 die "Error: Answer |$ans_name| is not a hash reference\n". 3994 $evaluated_answers{$ans_name} . 3995 "This probably means that the answer evaluator for this answer\n" . 3996 "is not working correctly."; 3997 $problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}"; 3998 } 3999 } 4000 # Calculate score rounded to three places to avoid roundoff problems 4001 $problem_result{score} = $total/$count if $count; 4002 # increase recorded score if the current score is greater. 4003 $problem_state{recorded_score} = $problem_result{score} if $problem_result{score} > $problem_state{recorded_score}; 4004 4005 4006 $problem_state{num_of_correct_ans}++ if $total == $count; 4007 $problem_state{num_of_incorrect_ans}++ if $total < $count ; 4008 warn "Error in grading this problem the total $total is larger than $count" if $total > $count; 4009 (\%problem_result, \%problem_state); 4010 } 4011 4012 =head2 Utility subroutines 4013 4014 =head4 4015 4016 warn pretty_print( $rh_hash_input) 4017 4018 This can be very useful for printing out messages about objects while debugging 4019 4020 =cut 4021 4022 sub pretty_print { 4023 my $r_input = shift; 4024 my $out = ''; 4025 if ( not ref($r_input) ) { 4026 $out = $r_input; # not a reference 4027 } elsif ("$r_input" =~/hash/i) { # this will pick up objects whose '$self' is hash and so works better than ref($r_iput). 4028 local($^W) = 0; 4029 $out .= "$r_input " ."<TABLE border = \"2\" cellpadding = \"3\" BGCOLOR = \"#FFFFFF\">"; 4030 foreach my $key (lex_sort( keys %$r_input )) { 4031 $out .= "<tr><TD> $key</TD><TD>=></td><td> ".pretty_print($r_input->{$key}) . "</td></tr>"; 4032 } 4033 $out .="</table>"; 4034 } elsif (ref($r_input) eq 'ARRAY' ) { 4035 my @array = @$r_input; 4036 $out .= "( " ; 4037 while (@array) { 4038 $out .= pretty_print(shift @array) . " , "; 4039 } 4040 $out .= " )"; 4041 } elsif (ref($r_input) eq 'CODE') { 4042 $out = "$r_input"; 4043 } else { 4044 $out = $r_input; 4045 } 4046 $out; 4047 } 4048 4049 1;
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