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Changed the naming of arrays from ArRaY[0,0,0] to ArRaY__0:0:0:__ This involved changes in PG.pl and PGmorematrixmacros (ans_array_filter) Made other cosmetic fixes to code. Added names to many filters to help with debugging. It seems to work for now.
1 BEGIN{ 2 be_strict(); 3 } 4 5 sub _PGmorematrixmacros_init{} 6 7 sub random_inv_matrix { ## Builds and returns a random invertible \$row by \$col matrix. 8 9 warn "Usage: \$new_matrix = random_inv_matrix(\$rows,\$cols)" 10 if (@_ != 2); 11 my $A = new Matrix($_[0],$_[1]); 12 my $A_lr = new Matrix($_[0],$_[1]); 13 my $det = 0; 14 my $safety=0; 15 while ($det == 0 and $safety < 6) { 16 foreach my $i (1..$_[0]) { 17 foreach my $j (1..$_[1]) { 18 $A->assign($i,$j,random(-9,9,1) ); 19 } 20 } 21 $A_lr = $A->decompose_LR(); 22 $det = $A_lr->det_LR(); 23 } 24 return $A; 25 } 26 27 =head4 random_diag_matrix 28 29 This method returns a random nxn diagonal matrix. 30 31 =cut 32 33 sub random_diag_matrix{ ## Builds and returns a random diagonal \$n by \$n matrix 34 35 warn "Usage: \$new_matrix = random_diag_matrix(\$n)" if (@_ != 1); 36 37 my $D = new Matrix($_[0],$_[0]); 38 my $norm = 0; 39 while( $norm == 0 ){ 40 foreach my $i (1..$_[0]){ 41 foreach my $j (1..$_[0]){ 42 if( $i != $j ){ 43 $D->assign($i,$j,0); 44 }else{ 45 $D->assign($i,$j,random(-9,9,1)); 46 } 47 } 48 } 49 $norm = abs($D); 50 } 51 return $D; 52 } 53 54 sub swap_rows{ 55 56 warn "Usage: \$new_matrix = swap_rows(\$matrix,\$row1,\$row2);" 57 if (@_ != 3); 58 my $matrix = $_[0]; 59 my ($i,$j) = ($_[1],$_[2]); 60 warn "Error: Rows to be swapped must exist!" 61 if ($i>@$matrix or $j >@$matrix); 62 warn "Warning: Swapping the same row is pointless" 63 if ($i==$j); 64 my $cols = @{$matrix->[0]}; 65 my $B = new Matrix(@$matrix,$cols); 66 foreach my $k (1..$cols){ 67 $B->assign($i,$k,element $matrix($j,$k)); 68 $B->assign($j,$k,element $matrix($i,$k)); 69 } 70 return $B; 71 } 72 73 sub row_mult{ 74 75 warn "Usage: \$new_matrix = row_mult(\$matrix,\$scalar,\$row);" 76 if (@_ != 3); 77 my $matrix = $_[0]; 78 my ($scalar,$row) = ($_[1],$_[2]); 79 warn "Undefined row multiplication" 80 if ($row > @$matrix); 81 my $B = new Matrix(@$matrix,@{$matrix->[0]}); 82 foreach my $j (1..@{$matrix->[0]}) { 83 $B->assign($row,$j,$scalar*element $matrix($row,$j)); 84 } 85 return $B; 86 } 87 88 sub linear_combo{ 89 90 warn "Usage: \$new_matrix = linear_combo(\$matrix,\$scalar,\$row1,\$row2);" 91 if (@_ != 4); 92 my $matrix = $_[0]; 93 my ($scalar,$row1,$row2) = ($_[1],$_[2],$_[3]); 94 warn "Undefined row in multiplication" 95 if ($row1>@$matrix or $row2>@$matrix); 96 warn "Warning: Using the same row" 97 if ($row1==$row2); 98 my $B = new Matrix(@$matrix,@{$matrix->[0]}); 99 foreach my $j (1..@$matrix) { 100 my ($t1,$t2) = (element $matrix($row1,$j),element $matrix($row2,$j)); 101 $B->assign($row2,$j,$scalar*$t1+$t2); 102 } 103 return $B; 104 } 105 106 =head3 basis_cmp() 107 108 Compares a list of vectors by finding the change of coordinate matrix 109 from the Prof's vectors to the students, and then taking the determinant of 110 that to determine the existence of the change of coordinate matrix going the 111 other way. 112 113 ANS( basis_cmp( vectors_as_array_ref_in_array_ref, options_hash ) ); 114 115 1. a reference to an array of correct vectors 116 2. a hash with the following keys (all optional): 117 mode -- 'basis' (default) (only a basis allowed) 118 'orthogonal' (only an orthogonal basis is allowed) 119 'unit' (only unit vectors in the basis allowed) 120 'orthonormal' (only orthogonal unit vectors in basis allowed) 121 zeroLevelTol -- absolute tolerance to allow when answer is close 122 to zero 123 124 debug -- if set to 1, provides verbose listing of 125 hash entries throughout fliters. 126 127 help -- 'none' (default) (is quiet on all errors) 128 'dim' (Tells student if wrong number of vectors are entered) 129 'length' (Tells student if there is a vector of the wrong length) 130 'orthogonal' (Tells student if their vectors are not orthogonal) 131 (This is only in orthogonal mode) 132 'unit' (Tells student if there is a vector not of unit length) 133 (This is only in unit mode) 134 'orthonormal' (Gives errors from orthogonal and orthonormal) 135 (This is only in orthonormal mode) 136 'verbose' (Gives all the above answer messages) 137 138 Returns an answer evaluator. 139 140 EXAMPLES: 141 142 basis_cmp([[1,0,0],[0,1,0],[0,0,1]]) 143 -- correct answer is any basis for R^3. 144 basis_cmp([1,0,2,0],[0,1,0,0], 'mode'=>orthonormal ) 145 -- correct answer is any orthonormal basis 146 for this space such as: 147 [1/sqrt(3),0,2/sqrt(3),0],[0,1,0,0] 148 149 =cut 150 151 152 sub basis_cmp { 153 my $correctAnswer = shift; 154 my %opt = @_; 155 156 set_default_options( \%opt, 157 'zeroLevelTol' => $main::functZeroLevelTolDefault, 158 'debug' => 0, 159 'mode' => 'basis', 160 'help' => 'none', 161 ); 162 163 # produce answer evaluator 164 BASIS_CMP( 165 'correct_ans' => $correctAnswer, 166 'zeroLevelTol' => $opt{'zeroLevelTol'}, 167 'debug' => $opt{'debug'}, 168 'mode' => $opt{'mode'}, 169 'help' => $opt{'help'}, 170 ); 171 } 172 173 =head BASIS_CMP 174 175 Made to keep the same format as num_cmp and fun_cmp. 176 177 =cut 178 179 sub BASIS_CMP { 180 my %mat_params = @_; 181 my $zeroLevelTol = $mat_params{'zeroLevelTol'}; 182 183 # Check that everything is defined: 184 $mat_params{debug} = 0 unless defined($mat_params{debug}); 185 $zeroLevelTol = $main::functZeroLevelTolDefault unless defined $zeroLevelTol; 186 $mat_params{'zeroLevelTol'} = $zeroLevelTol; 187 188 ## This is where the correct answer should be checked someday. 189 my $matrix = Matrix->new_from_col_vecs($mat_params{'correct_ans'}); 190 191 #construct the answer evaluator 192 my $answer_evaluator = new AnswerEvaluator; 193 194 $answer_evaluator->{debug} = $mat_params{debug}; 195 $answer_evaluator->ans_hash( 196 correct_ans => display_correct_vecs($mat_params{correct_ans}), 197 rm_correct_ans => $matrix, 198 zeroLevelTol => $mat_params{zeroLevelTol}, 199 debug => $mat_params{debug}, 200 mode => $mat_params{mode}, 201 help => $mat_params{help}, 202 ); 203 204 $answer_evaluator->install_pre_filter( 205 sub {my $rh_ans = shift; 206 $rh_ans->{_filter_name} = 'remove_white_space'; 207 $rh_ans->{student_ans} =~ s/\s+//g; # remove all whitespace 208 $rh_ans; 209 } 210 ); 211 $answer_evaluator->install_pre_filter( 212 sub{my $rh_ans = shift; 213 my @options = @_; 214 $rh_ans->{_filter_name} = 'mung_student_answer'; 215 if( $rh_ans->{ans_label} =~ /ArRaY/ ){ 216 $rh_ans = ans_array_filter($rh_ans,@options); 217 my @student_array = @{$rh_ans->{ra_student_ans}}; 218 my @array = (); 219 for( my $i = 0; $i < scalar(@student_array) ; $i ++ ) 220 { 221 push( @array, Matrix->new_from_array_ref($student_array[$i])); 222 } 223 $rh_ans->{ra_student_ans} = \@array; 224 $rh_ans; 225 }else{ 226 $rh_ans->{student_ans} = math_constants($rh_ans->{student_ans}); 227 vec_list_string($rh_ans, '_filter_name' => 'vec_list_string', @options); 228 } 229 } 230 );#ra_student_ans is now the students answer as an array of vectors 231 # anonymous subroutine to check dimension and length of the student vectors 232 # if either is wrong, the answer is wrong. 233 $answer_evaluator->install_pre_filter( 234 sub{ 235 my $rh_ans = shift; 236 $rh_ans->{_filter_name} = 'check_vector_size'; 237 my $length = $rh_ans->{rm_correct_ans}->[1]; 238 my $dim = $rh_ans->{rm_correct_ans}->[2]; 239 if( $dim != scalar(@{$rh_ans->{ra_student_ans}})) 240 { 241 242 $rh_ans->{score} = 0; 243 if( $rh_ans->{help} =~ /dim|verbose/ ) 244 { 245 $rh_ans->throw_error('EVAL','You have entered the wrong number of vectors.'); 246 }else{ 247 $rh_ans->throw_error('EVAL'); 248 } 249 } 250 for( my $i = 0; $i < scalar( @{$rh_ans->{ra_student_ans} }) ; $i++ ) 251 { 252 if( $length != $rh_ans->{ra_student_ans}->[$i]->[1]) 253 { 254 $rh_ans->{score} = 0; 255 if( $rh_ans->{help} =~ /length|verbose/ ) 256 { 257 $rh_ans->throw_error('EVAL','You have entered vector(s) of the wrong length.'); 258 }else{ 259 $rh_ans->throw_error('EVAL'); 260 } 261 } 262 } 263 $rh_ans; 264 } 265 ); 266 # Install prefilter for various modes 267 if( $mat_params{mode} ne 'basis' ) 268 { 269 if( $mat_params{mode} =~ /orthogonal|orthonormal/ ) 270 { 271 $answer_evaluator->install_pre_filter(\&are_orthogonal_vecs); 272 } 273 274 if( $mat_params{mode} =~ /unit|orthonormal/ ) 275 { 276 $answer_evaluator->install_pre_filter(\&are_unit_vecs); 277 278 } 279 } 280 $answer_evaluator->install_evaluator(\&compare_basis, %mat_params); 281 $answer_evaluator->install_post_filter( 282 sub {my $rh_ans = shift; 283 if ($rh_ans->catch_error('SYNTAX') ) { 284 $rh_ans->{ans_message} = $rh_ans->{error_message}; 285 $rh_ans->clear_error('SYNTAX'); 286 } 287 if ($rh_ans->catch_error('EVAL') ) { 288 $rh_ans->{ans_message} = $rh_ans->{error_message}; 289 $rh_ans->clear_error('EVAL'); 290 } 291 $rh_ans; 292 } 293 ); 294 $answer_evaluator; 295 } 296 297 =head4 compare_basis 298 299 compare_basis( $ans_hash, %options); 300 301 {ra_student_ans}, # a reference to the array of students answer vectors 302 {rm_correct_ans}, # a reference to the correct answer matrix 303 %options 304 ) 305 306 =cut 307 308 sub compare_basis { 309 my ($rh_ans, %options) = @_; 310 my @ch_coord; 311 my @vecs = @{$rh_ans->{ra_student_ans}}; 312 313 # A lot of the follosing code was taken from Matrix::proj_coeff 314 # calling this method recursively would be a waste of time since 315 # the prof's matrix never changes and solve_LR is an expensive 316 # operation. This way it is only done once. 317 my $matrix = $rh_ans->{rm_correct_ans}; 318 my ($dim,$x_vector, $base_matrix); 319 my $errors = undef; 320 my $lin_space_tr= ~ $matrix; 321 $matrix = $lin_space_tr * $matrix; 322 my $matrix_lr = $matrix->decompose_LR(); 323 324 #finds the coefficient vectors for each of the students vectors 325 for( my $i = 0; $i < scalar(@{$rh_ans->{ra_student_ans}}) ; $i++ ) 326 { 327 328 $vecs[$i] = $lin_space_tr*$vecs[$i]; 329 ($dim,$x_vector, $base_matrix) = $matrix_lr->solve_LR($vecs[$i]); 330 push( @ch_coord, $x_vector ); 331 $errors = "A unique adapted answer could not be determined. Possibly the parameters have coefficient zero.<br> dim = $dim base_matrix is $base_matrix\n" if $dim; # only print if the dim is not zero. 332 } 333 334 if( defined($errors)) 335 { 336 $rh_ans->throw_error('EVAL', $errors) ; 337 }else{ 338 my $ch_coord_mat = Matrix->new_from_col_vecs(\@ch_coord);#creates change of coordinate matrix 339 #existence of this matrix implies that 340 #the all of the students answers are a 341 #linear combo of the prof's 342 $ch_coord_mat = $ch_coord_mat->decompose_LR(); 343 344 if( abs($ch_coord_mat->det_LR()) > $options{zeroLevelTol} )# if the det of the change of coordinate matrix is 345 # non-zero, this implies the existence of an inverse 346 # which implies all of the prof's vectors are a linear 347 # combo of the students vectors, showing containment 348 # both ways. 349 { 350 # I think sometimes if the students space has the same dimension as the profs space it 351 # will get projected into the profs space even if it isn't a basis for that space. 352 # this just checks that the prof's matrix times the change of coordinate matrix is actually 353 #the students matrix 354 if( abs(Matrix->new_from_col_vecs(\@{$rh_ans->{ra_student_ans}}) - ($rh_ans->{rm_correct_ans})*(Matrix->new_from_col_vecs(\@ch_coord))) < $options{zeroLevelTol} ) 355 { 356 $rh_ans->{score} = 1; 357 }else{ 358 $rh_ans->{score} = 0; 359 } 360 } 361 else{ 362 $rh_ans->{score}=0; 363 } 364 } 365 $rh_ans; 366 367 } 368 369 370 =head 2 vec_list_string 371 372 This is a check_syntax type method (in fact I borrowed some of that method's code) for vector input. 373 The student needs to enter vectors like: [1,0,0],[1,2,3],[0,9/sqrt(10),1/sqrt(10)] 374 Each entry can contain functions and operations and the usual math constants (pi and e). 375 The vectors, however can not be added or multiplied or scalar multiplied by the student. 376 Most errors are handled well. Any error in an entry is caught by the PG_answer_eval like it is in num_cmp or fun_cmp. 377 Right now the method basically ignores every thing outside the vectors. Also, an unmatched open parenthesis is caught, 378 but a unmatched close parenthesis ends the vector, and since everything outside is ignored, no error is sent (other than the 379 later when the length of the vectors is checked. 380 In the end, the method returns an array of Matrix objects. 381 382 383 =cut 384 385 sub vec_list_string{ 386 my $rh_ans = shift; 387 my %options = @_; 388 my $i; 389 my $entry = ""; 390 my $char; 391 my @paren_stack; 392 my $length = length($rh_ans->{student_ans}); 393 my @temp; 394 my $j = 0; 395 my @answers; 396 my $paren; 397 my $display_ans; 398 399 for( $i = 0; $i < $length ; $i++ ) 400 { 401 $char = substr($rh_ans->{student_ans},$i,1); 402 403 if( $char =~ /\(|\[|\{/ ){ 404 push( @paren_stack, $char ) 405 } 406 407 if( !( $char =~ /\(|\[|\{/ && scalar(@paren_stack) == 1 ) ) 408 { 409 if( $char !~ /,|\)|\]|\}/ ){ 410 $entry .= $char; 411 }else{ 412 if( $char =~ /,/ || ( $char =~ /\)|\]|\}/ && scalar(@paren_stack) == 1 ) ) 413 { 414 if( length($entry) == 0 ){ 415 if( $char !~ /,/ ){ 416 $rh_ans->throw_error('EVAL','There is a syntax error in your answer'); 417 }else{ 418 $rh_ans->{preview_text_string} .= ","; 419 $rh_ans->{preview_latex_string} .= ","; 420 $display_ans .= ","; 421 } 422 }else{ 423 424 # This parser code was origianally taken from PGanswermacros::check_syntax 425 # but parts of it needed to be slighty modified for this context 426 my $parser = new AlgParserWithImplicitExpand; 427 my $ret = $parser -> parse($entry); #for use with loops 428 429 if ( ref($ret) ) { ## parsed successfully 430 $parser -> tostring(); 431 $parser -> normalize(); 432 $entry = $parser -> tostring(); 433 $rh_ans->{preview_text_string} .= $entry.","; 434 $rh_ans->{preview_latex_string} .= $parser -> tolatex().","; 435 436 } else { ## error in parsing 437 438 $rh_ans->{'student_ans'} = 'syntax error:'.$display_ans. $parser->{htmlerror}, 439 $rh_ans->{'ans_message'} = $display_ans.$parser -> {error_msg}, 440 $rh_ans->{'preview_text_string'} = '', 441 $rh_ans->{'preview_latex_string'} = '', 442 $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'.$display_ans.$parser->{htmlerror} . "$main::BR" .$parser -> {error_msg}.".$main::BR"); 443 } 444 445 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($entry); 446 447 if ($PG_eval_errors) { 448 $rh_ans->throw_error('EVAL','There is a syntax error in your answer.') ; 449 $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors); 450 last; 451 } else { 452 $entry = prfmt($inVal,$options{format}); 453 $display_ans .= $entry.","; 454 push(@temp , $entry); 455 } 456 457 if( $char =~ /\)|\]|\}/ && scalar(@paren_stack) == 1) 458 { 459 pop @paren_stack; 460 chop($rh_ans->{preview_text_string}); 461 chop($rh_ans->{preview_latex_string}); 462 chop($display_ans); 463 $rh_ans->{preview_text_string} .= "]"; 464 $rh_ans->{preview_latex_string} .= "]"; 465 $display_ans .= "]"; 466 if( scalar(@temp) > 0 ) 467 { 468 push( @answers,Matrix->new_from_col_vecs([\@temp])); 469 while(scalar(@temp) > 0 ){ 470 pop @temp; 471 } 472 }else{ 473 $rh_ans->throw_error('EVAL','There is a syntax error in your answer.'); 474 } 475 } 476 } 477 $entry = ""; 478 }else{ 479 $paren = pop @paren_stack; 480 if( scalar(@paren_stack) > 0 ){ 481 #this uses ASCII to check if the parens match up 482 # in ASCII ord ( = 40 , ord ) = 41 , ord [ = 91 , 483 # ord ] = 93 , ord { = 123 , ord } = 125 484 if( (ord($char) - ord($paren) <= 2) ){ 485 $entry = $entry . $char; 486 }else{ 487 $rh_ans->throw_error('EVAL','There is a syntax error in your answer'); 488 } 489 } 490 } 491 } 492 }else{ 493 $rh_ans->{preview_text_string} .= "["; 494 $rh_ans->{preview_latex_string} .= "["; 495 $display_ans .= "["; 496 } 497 } 498 $rh_ans->{ra_student_ans} = \@answers; 499 $rh_ans->{student_ans} = $display_ans unless $rh_ans->{error_flag}; 500 $rh_ans; 501 } 502 503 =head5 504 This filter was created to get, format, and evaluate each entry of the ans_array and ans_array_extension 505 answer entry methods. Running this filter is necessary to get all the entries out of the answer 506 hash. Each entry is evaluated and the resulting number is put in the display for student answer 507 as a string. For evaluation purposes an array of arrays of arrays is created called ra_student_ans 508 and placed in the hash. The entries are [array_number][row_number][column_number]. The latex strings 509 for each entry are taken from the parser and put, as a matrix, into the previewer. The preview text 510 string is also created, but this display method becomes confusing when large matrices are used. 511 =cut 512 513 514 sub ans_array_filter{ 515 my $rh_ans = shift; 516 my %options = @_; 517 # assign_option_aliases( \%opt, 518 # ); 519 set_default_options(\%options, 520 '_filter_name' => 'ans_array_filter', 521 ); 522 # $rh_ans->{ans_label} =~ /ArRaY(\d+)\[\d+,\d+,\d+\]/; # CHANGE made to accomodate HTML 4.01 standards for name attribute 523 $rh_ans->{ans_label} =~ /ArRaY(\d+)\_\_\d+:\d+:\d+\_\_/; 524 my $ans_num = $1; 525 my @keys = grep /ArRaY$ans_num/, keys(%{$main::inputs_ref}); 526 my $key; 527 my @array = (); 528 my ($i,$j,$k) = (0,0,0); 529 530 #the keys aren't in order, so their info has to be put into the array before doing anything with it 531 foreach $key (@keys){ 532 # $key =~ /ArRaY\d+\[(\d+),(\d+),(\d+)\]/; 533 # ($i,$j,$k) = ($1,$2,$3); 534 # $array[$i][$j][$k] = ${$main::inputs_ref}{'ArRaY'.$ans_num.'['.$i.','.$j.','.$k.']'}; 535 $key =~ /ArRaY\d+\_\_(\d+):(\d+):(\d+)\_\_/; 536 ($i,$j,$k) = ($1,$2,$3); 537 $array[$i][$j][$k] = ${$main::inputs_ref}{'ArRaY'.$ans_num.'__'.$i.':'.$j.':'.$k.'__'}; 538 539 } 540 $rh_ans->{debug_student_answer }= \@array; 541 my $display_ans = ""; 542 543 for( $i=0; $i < scalar(@array) ; $i ++ ) 544 { 545 $display_ans .= " ["; 546 $rh_ans->{preview_text_string} .= ' ['; 547 $rh_ans->{preview_latex_string} .= '\begin{pmatrix} '; 548 for( $j = 0; $j < scalar( @{$array[$i]} ) ; $j++ ) 549 { 550 $display_ans .= " ["; 551 $rh_ans->{preview_text_string} .= ' ['; 552 for( $k = 0; $k < scalar( @{$array[$i][$j]} ) ; $k ++ ){ 553 my $entry = $array[$i][$j][$k]; 554 $entry = math_constants($entry); 555 # This parser code was origianally taken from PGanswermacros::check_syntax 556 # but parts of it needed to be slighty modified for this context 557 my $parser = new AlgParserWithImplicitExpand; 558 my $ret = $parser -> parse($entry); #for use with loops 559 560 if ( ref($ret) ) { ## parsed successfully 561 $parser -> tostring(); 562 $parser -> normalize(); 563 $entry = $parser -> tostring(); 564 $rh_ans->{preview_text_string} .= $entry.","; 565 $rh_ans->{preview_latex_string} .= $parser -> tolatex() . '& '; 566 567 } else { ## error in parsing 568 $rh_ans->{'student_ans'} = 'syntax error:'.$display_ans. $parser->{htmlerror}, 569 $rh_ans->{'ans_message'} = $display_ans.$parser -> {error_msg}, 570 $rh_ans->{'preview_text_string'} = '', 571 $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'.$display_ans.$parser->{htmlerror} . "$main::BR" .$parser -> {error_msg}.".$main::BR"); 572 } 573 574 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($entry); 575 if ($PG_eval_errors) { 576 $rh_ans->throw_error('EVAL','There is a syntax error in your answer.') ; 577 $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors); 578 last; 579 } else { 580 $entry = prfmt($inVal,$options{format}); 581 $display_ans .= $entry.","; 582 $array[$i][$j][$k] = $entry; 583 } 584 } 585 chop($rh_ans->{preview_text_string}); 586 chop($display_ans); 587 $rh_ans->{preview_text_string} .= '] ,'; 588 $rh_ans->{preview_latex_string} .= '\\\\'; 589 $display_ans .= '] ,'; 590 591 } 592 chop($rh_ans->{preview_text_string}); 593 chop($display_ans); 594 $rh_ans->{preview_text_string} .= '] ,'; 595 $rh_ans->{preview_latex_string} .= '\end{pmatrix}'.' , '; 596 $display_ans .= '] ,'; 597 } 598 chop($rh_ans->{preview_text_string}); 599 chop($rh_ans->{preview_latex_string}); 600 chop($rh_ans->{preview_latex_string}); 601 chop($rh_ans->{preview_latex_string}); 602 chop($display_ans); 603 604 my @temp = (); 605 for( $i = 0 ; $i < scalar( @array ); $i++ ){ 606 push @temp , display_matrix($array[$i], 'left'=>'.', 'right'=>'.'); 607 push @temp , "," unless $i == scalar(@array) - 1; 608 } 609 $rh_ans->{student_ans} = mbox(\@temp); 610 $rh_ans->{ra_student_ans} = \@array; 611 612 $rh_ans; 613 614 } 615 616 617 sub are_orthogonal_vecs{ 618 my ($vec_ref , %opts) = @_; 619 $vec_ref->{_filter_name} = 'are_orthogonal_vecs'; 620 my @vecs = (); 621 if( ref($vec_ref) eq 'AnswerHash' ) 622 { 623 @vecs = @{$vec_ref->{ra_student_ans}}; 624 }else{ 625 @vecs = @{$vec_ref}; 626 } 627 my ($i,$j) = (0,0); 628 629 my $num = scalar(@vecs); 630 my $length = $vecs[0]->[1]; 631 632 for( ; $i < $num ; $i ++ ) 633 { 634 for( $j = $i+1; $j < $num ; $j++ ) 635 { 636 if( $vecs[$i]->scalar_product($vecs[$j]) > $main::functZeroLevelTolDefault ) 637 { 638 if( ref( $vec_ref ) eq 'AnswerHash' ){ 639 $vec_ref->{score} = 0; 640 if( $vec_ref->{help} =~ /orthogonal|orthonormal|verbose/ ) 641 { 642 $vec_ref->throw_error('EVAL','You have entered vectors which are not orthogonal. '); 643 }else{ 644 $vec_ref->throw_error('EVAL'); 645 } 646 return $vec_ref; 647 }else{ 648 return 0; 649 } 650 } 651 } 652 } 653 if( ref( $vec_ref ) eq 'AnswerHash' ){ 654 $vec_ref->{score} = 1; 655 $vec_ref; 656 }else{ 657 1; 658 } 659 } 660 661 sub is_diagonal{ 662 my $matrix = shift; 663 my %options = @_; 664 my $process_ans_hash = ( ref( $matrix ) eq 'AnswerHash' ) ? 1 : 0 ; 665 my ($rh_ans); 666 if ($process_ans_hash) { 667 $rh_ans = $matrix; 668 $matrix = $rh_ans->{ra_student_ans}; 669 } 670 671 return 0 unless defined($matrix); 672 673 if( ref($matrix) eq 'ARRAY' ){ 674 my @matrix = @{$matrix}; 675 @matrix = @{$matrix[0]} if ref($matrix[0][0]) eq 'ARRAY'; 676 if( ref($matrix[0]) ne 'ARRAY' or scalar( @matrix ) != scalar( @{$matrix[0]} ) ){ 677 warn "It is impossible for a non-square matrix to be diagonal, if you are a student, please tell your professor that there is a problem."; 678 } 679 680 for( my $i = 0; $i < scalar( @matrix ) ; $i++ ){ 681 for( my $j = 0; $j < scalar( @{$matrix[0]} ); $j++ ){ 682 if( $matrix[$i][$j] != 0 and $i != $j ) 683 { 684 if ($process_ans_hash){ 685 $rh_ans->throw_error('EVAL'); 686 return $rh_ans; 687 } else { 688 return 0; 689 } 690 } 691 } 692 } 693 if ($process_ans_hash){ 694 return $rh_ans; 695 } else { 696 return 1; 697 } 698 }elsif( ref($matrix) eq 'Matrix' ){ 699 if( $matrix->[1] != $matrix->[2] ){ 700 warn "It is impossible for a non-square matrix to be diagonal, if you are a student, please tell your professor that there is a problem."; 701 if ($process_ans_hash){ 702 $rh_ans->throw_error('EVAL'); 703 return $rh_ans; 704 } else { 705 return 0; 706 } 707 } 708 for( my $i = 0; $i < $matrix->[1] ; $i++ ){ 709 for( my $j = 0; $j < $matrix->[2] ; $j++ ){ 710 if( $matrix->[0][$i][$j] != 0 and $i != $j ){ 711 if ($process_ans_hash){ 712 $rh_ans->throw_error('EVAL'); 713 return $rh_ans; 714 } else { 715 return 0; 716 } 717 } 718 } 719 } 720 if ($process_ans_hash){ 721 return $rh_ans; 722 } else { 723 return 1; 724 } 725 }else{ 726 warn "There is a problem with the problem, please alert your professor."; 727 if ($process_ans_hash){ 728 $rh_ans->throw_error('EVAL'); 729 return $rh_ans; 730 } else { 731 return 0; 732 } 733 } 734 735 } 736 737 738 sub are_unit_vecs{ 739 my ( $vec_ref,%opts ) = @_; 740 $vec_ref->{_filter_name} = 'are_unit_vecs'; 741 my @vecs = (); 742 if( ref($vec_ref) eq 'AnswerHash' ) 743 { 744 @vecs = @{$vec_ref->{ra_student_ans}}; 745 }else{ 746 @vecs = @{$vec_ref}; 747 } 748 749 my $i = 0; 750 my $num = scalar(@vecs); 751 my $length = $vecs[0]->[1]; 752 753 for( ; $i < $num ; $i ++ ) 754 { 755 if( abs(sqrt($vecs[$i]->scalar_product($vecs[$i]))- 1) > $main::functZeroLevelTolDefault ) 756 { 757 if( ref( $vec_ref ) eq 'AnswerHash' ){ 758 $vec_ref->{score} = 0; 759 if( $vec_ref->{help} =~ /unit|orthonormal|verbose/ ) 760 { 761 $vec_ref->throw_error('EVAL','You have entered vector(s) which are not of unit length.'); 762 }else{ 763 $vec_ref->throw_error('EVAL'); 764 } 765 return $vec_ref; 766 }else{ 767 return 0; 768 } 769 770 } 771 } 772 773 if( ref( $vec_ref ) eq 'AnswerHash' ){ 774 $vec_ref->{score} = 1; 775 $vec_ref; 776 }else{ 777 1; 778 } 779 } 780 781 sub display_correct_vecs{ 782 my ( $ra_vecs,%opts ) = @_; 783 my @ra_vecs = @{$ra_vecs}; 784 my @temp = (); 785 786 for( my $i = 0 ; $i < scalar(@ra_vecs) ; $i++ ){ 787 push @temp, display_matrix(Matrix->new_from_col_vecs([$ra_vecs[$i]]),'left'=>'.','right'=>'.'); 788 push @temp, ","; 789 } 790 791 pop @temp; 792 793 mbox(\@temp); 794 795 } 796 797 sub vec_solution_cmp{ 798 my $correctAnswer = shift; 799 my %opt = @_; 800 801 set_default_options( \%opt, 802 'zeroLevelTol' => $main::functZeroLevelTolDefault, 803 'debug' => 0, 804 'mode' => 'basis', 805 'help' => 'none', 806 ); 807 808 $opt{debug} = 0 unless defined($opt{debug}); 809 810 ## This is where the correct answer should be checked someday. 811 my $matrix = Matrix->new_from_col_vecs($correctAnswer); 812 813 814 #construct the answer evaluator 815 my $answer_evaluator = new AnswerEvaluator; 816 817 $answer_evaluator->{debug} = $opt{debug}; 818 $answer_evaluator->ans_hash( correct_ans => display_correct_vecs($correctAnswer), 819 old_correct_ans => $correctAnswer, 820 rm_correct_ans => $matrix, 821 zeroLevelTol => $opt{zeroLevelTol}, 822 debug => $opt{debug}, 823 mode => $opt{mode}, 824 help => $opt{help}, 825 ); 826 827 $answer_evaluator->install_pre_filter(\&ans_array_filter); 828 $answer_evaluator->install_pre_filter(sub{ 829 my ($rh_ans,@options) = @_; 830 my @student_array = @{$rh_ans->{ra_student_ans}}; 831 my @array = (); 832 for( my $i = 0; $i < scalar(@student_array) ; $i ++ ) 833 { 834 push( @array, Matrix->new_from_array_ref($student_array[$i])); 835 } 836 $rh_ans->{ra_student_ans} = \@array; 837 $rh_ans; 838 });#ra_student_ans is now the students answer as an array of vectors 839 # anonymous subroutine to check dimension and length of the student vectors 840 # if either is wrong, the answer is wrong. 841 $answer_evaluator->install_pre_filter(sub{ 842 my $rh_ans = shift; 843 my $length = $rh_ans->{rm_correct_ans}->[1]; 844 my $dim = $rh_ans->{rm_correct_ans}->[2]; 845 if( $dim != scalar(@{$rh_ans->{ra_student_ans}})) 846 { 847 848 $rh_ans->{score} = 0; 849 if( $rh_ans->{help} =~ /dim|verbose/ ) 850 { 851 $rh_ans->throw_error('EVAL','You have entered the wrong number of vectors.'); 852 }else{ 853 $rh_ans->throw_error('EVAL'); 854 } 855 } 856 for( my $i = 0; $i < scalar( @{$rh_ans->{ra_student_ans} }) ; $i++ ) 857 { 858 if( $length != $rh_ans->{ra_student_ans}->[$i]->[1]) 859 { 860 $rh_ans->{score} = 0; 861 if( $rh_ans->{help} =~ /length|verbose/ ) 862 { 863 $rh_ans->throw_error('EVAL','You have entered vector(s) of the wrong length.'); 864 }else{ 865 $rh_ans->throw_error('EVAL'); 866 } 867 } 868 } 869 $rh_ans; 870 }); 871 # Install prefilter for various modes 872 if( $opt{mode} ne 'basis' ) 873 { 874 if( $opt{mode} =~ /orthogonal|orthonormal/ ) 875 { 876 $answer_evaluator->install_pre_filter(\&are_orthogonal_vecs); 877 } 878 879 if( $opt{mode} =~ /unit|orthonormal/ ) 880 { 881 $answer_evaluator->install_pre_filter(\&are_unit_vecs); 882 883 } 884 } 885 886 $answer_evaluator->install_evaluator(\&compare_vec_solution, %opt); 887 888 $answer_evaluator->install_post_filter( 889 sub {my $rh_ans = shift; 890 if ($rh_ans->catch_error('SYNTAX') ) { 891 $rh_ans->{ans_message} = $rh_ans->{error_message}; 892 $rh_ans->clear_error('SYNTAX'); 893 } 894 if ($rh_ans->catch_error('EVAL') ) { 895 $rh_ans->{ans_message} = $rh_ans->{error_message}; 896 $rh_ans->clear_error('EVAL'); 897 } 898 $rh_ans; 899 } 900 ); 901 $answer_evaluator; 902 903 } 904 905 906 sub compare_vec_solution { 907 my ( $rh_ans, %options ) = @_ ; 908 my @space = @{$rh_ans->{ra_student_ans}}; 909 my $solution = shift @space; 910 911 # A lot of the follosing code was taken from Matrix::proj_coeff 912 # calling this method recursively would be a waste of time since 913 # the prof's matrix never changes and solve_LR is an expensive 914 # operation. This way it is only done once. 915 my $matrix = $rh_ans->{rm_correct_ans}; 916 my ($dim,$x_vector, $base_matrix); 917 my $errors = undef; 918 my $lin_space_tr= ~ $matrix; 919 $matrix = $lin_space_tr * $matrix; 920 my $matrix_lr = $matrix->decompose_LR(); 921 922 #this section determines whether or not the first vector, a solution to 923 #the system, is a linear combination of the prof's vectors in which there 924 #is a nonzero coefficient on the first term, the prof's solution to the system 925 $solution = $lin_space_tr*$solution; 926 ($dim,$x_vector, $base_matrix) = $matrix_lr->solve_LR($solution); 927 if( $dim ){ 928 $rh_ans->throw_error('EVAL', "A unique adapted answer could not be determined. Possibly the parameters have coefficient zero.<br> dim = $dim base_matrix is $base_matrix\n" ); # only print if the dim is not zero. 929 $rh_ans->{score} = 0; 930 $rh_ans; 931 }elsif( abs($x_vector->[0][0][0]) <= $options{zeroLevelTol} ) 932 { 933 $rh_ans->{score} = 0; 934 $rh_ans; 935 }else{ 936 $rh_ans->{score} = 1; 937 my @correct_space = @{$rh_ans->{old_correct_ans}}; 938 shift @correct_space; 939 $rh_ans->{rm_correct_ans} = Matrix->new_from_col_vecs(\@correct_space); 940 $rh_ans->{ra_student_ans} = \@space; 941 return compare_basis( $rh_ans, %options ); 942 } 943 } 944 945 1;
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