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Fixed conceptual error in compare_vec_solution. This should fix bug #670. In my opinion the entire concept of vec_solution_cmp should be reconsidered. In solving an underdetermined linear equation of the form Ax-b=0 it seems to me that the solutions answer in the form: x= a +bt+cu+ds where a,b,c,d are vectors should simply be evaluated to see if it satisfies Ax-b=0 for 5 or six values of a,b,c,d -- checking the solution should use a vector valued version of fun_cmp. As it is, the student's coefficients for a,b,c,d are compared with the instructors to see if they span the same space. This is quite a bit more complicated -- and indeed the method came up with the wrong answer. I believe I have the method corrected, but I would suggest that this answer evaluator be replaced with one which operates more directly and is therefore easier to maintain. Am I missing something in this analysis? Has someone else created answer evaluators for this type of problem? -- Mike
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( $ans_hash, 300 %options 301 ra_student_ans # a reference to the array of students answer vectors 302 rm_correct_ans, # a reference to the correct answer matrix 303 %options 304 ) 305 306 307 =cut 308 309 310 311 sub compare_basis { 312 my ($rh_ans, %options) = @_; 313 $rh_ans->{_filter_name} = "compare_basis"; 314 my @ch_coord; 315 my @vecs = @{$rh_ans->{ra_student_ans}}; 316 317 # A lot of the following code was taken from Matrix::proj_coeff 318 # calling this method recursively would be a waste of time since 319 # the prof's matrix never changes and solve_LR is an expensive 320 # operation. This way it is only done once. 321 my $matrix = $rh_ans->{rm_correct_ans}; 322 my ($dim,$x_vector, $base_matrix); 323 my $errors = undef; 324 my $lin_space_tr= ~ $matrix; #transpose of the matrix 325 $matrix = $lin_space_tr * $matrix; #(~A * A) 326 my $matrix_lr = $matrix->decompose_LR(); 327 328 #finds the coefficient vectors for each of the students vectors 329 for( my $i = 0; $i < scalar(@{$rh_ans->{ra_student_ans}}) ; $i++ ) { 330 331 $vecs[$i] = $lin_space_tr*$vecs[$i]; 332 ($dim,$x_vector, $base_matrix) = $matrix_lr->solve_LR($vecs[$i]); 333 push( @ch_coord, $x_vector ); 334 $errors = "A unique adapted answer could not be determined. 335 Possibly the parameters have coefficient zero.<br> dim = $dim base_matrix 336 is $base_matrix\n" if $dim; # only print if the dim is not zero. 337 } 338 339 if( defined($errors)) { 340 $rh_ans->throw_error('EVAL', $errors) ; 341 } else { 342 my $ch_coord_mat = Matrix->new_from_col_vecs(\@ch_coord); 343 #creates change of coordinate matrix 344 #existence of this matrix implies that 345 #the all of the students answers are a 346 #linear combo of the prof's 347 $ch_coord_mat = $ch_coord_mat->decompose_LR(); 348 349 if( abs($ch_coord_mat->det_LR()) > $options{zeroLevelTol} ) { 350 # if the det of the change of coordinate matrix is 351 # non-zero, this implies the existence of an inverse 352 # which implies all of the prof's vectors are a linear 353 # combo of the students vectors, showing containment 354 # both ways. 355 356 # I think sometimes if the students space has the same dimension as the profs space it 357 # will get projected into the profs space even if it isn't a basis for that space. 358 # this just checks that the prof's matrix times the change of coordinate matrix is actually 359 #the students matrix 360 if( abs(Matrix->new_from_col_vecs(\@{$rh_ans->{ra_student_ans}}) - 361 ($rh_ans->{rm_correct_ans})*(Matrix->new_from_col_vecs(\@ch_coord))) 362 < $options{zeroLevelTol} ) { 363 $rh_ans->{score} = 1; 364 } else { 365 $rh_ans->{score} = 0; 366 } 367 } else { 368 $rh_ans->{score}=0; 369 } 370 } 371 $rh_ans; 372 373 } 374 375 376 =head 2 vec_list_string 377 378 This is a check_syntax type method (in fact I borrowed some of that method's code) for vector input. 379 The student needs to enter vectors like: [1,0,0],[1,2,3],[0,9/sqrt(10),1/sqrt(10)] 380 Each entry can contain functions and operations and the usual math constants (pi and e). 381 The vectors, however can not be added or multiplied or scalar multiplied by the student. 382 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. 383 Right now the method basically ignores every thing outside the vectors. Also, an unmatched open parenthesis is caught, 384 but a unmatched close parenthesis ends the vector, and since everything outside is ignored, no error is sent (other than the 385 later when the length of the vectors is checked. 386 In the end, the method returns an array of Matrix objects. 387 388 389 =cut 390 391 sub vec_list_string{ 392 my $rh_ans = shift; 393 my %options = @_; 394 my $i; 395 my $entry = ""; 396 my $char; 397 my @paren_stack; 398 my $length = length($rh_ans->{student_ans}); 399 my @temp; 400 my $j = 0; 401 my @answers; 402 my $paren; 403 my $display_ans; 404 405 for( $i = 0; $i < $length ; $i++ ) { 406 $char = substr($rh_ans->{student_ans},$i,1); 407 408 if( $char =~ /\(|\[|\{/ ){ 409 push( @paren_stack, $char ) 410 } 411 412 if( !( $char =~ /\(|\[|\{/ && scalar(@paren_stack) == 1 ) ) { 413 if( $char !~ /,|\)|\]|\}/ ){ 414 $entry .= $char; 415 } else { 416 if( $char =~ /,/ || ( $char =~ /\)|\]|\}/ && scalar(@paren_stack) == 1 ) ) { 417 if( length($entry) == 0 ){ 418 if( $char !~ /,/ ){ 419 $rh_ans->throw_error('EVAL','There is a syntax error in your answer'); 420 } else { 421 $rh_ans->{preview_text_string} .= ","; 422 $rh_ans->{preview_latex_string} .= ","; 423 $display_ans .= ","; 424 } 425 } else { 426 427 # This parser code was origianally taken from PGanswermacros::check_syntax 428 # but parts of it needed to be slighty modified for this context 429 my $parser = new AlgParserWithImplicitExpand; 430 my $ret = $parser -> parse($entry); #for use with loops 431 432 if ( ref($ret) ) { ## parsed successfully 433 $parser -> tostring(); 434 $parser -> normalize(); 435 $entry = $parser -> tostring(); 436 $rh_ans->{preview_text_string} .= $entry.","; 437 $rh_ans->{preview_latex_string} .= $parser -> tolatex().","; 438 439 } else { ## error in parsing 440 441 $rh_ans->{'student_ans'} = 'syntax error:'.$display_ans. $parser->{htmlerror}, 442 $rh_ans->{'ans_message'} = $display_ans.$parser -> {error_msg}, 443 $rh_ans->{'preview_text_string'} = '', 444 $rh_ans->{'preview_latex_string'} = '', 445 $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'.$display_ans.$parser->{htmlerror} . "$main::BR" .$parser -> {error_msg}.".$main::BR"); 446 } 447 448 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($entry); 449 450 if ($PG_eval_errors) { 451 $rh_ans->throw_error('EVAL','There is a syntax error in your answer.') ; 452 $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors); 453 last; 454 } else { 455 $entry = prfmt($inVal,$options{format}); 456 $display_ans .= $entry.","; 457 push(@temp , $entry); 458 } 459 460 if( $char =~ /\)|\]|\}/ && scalar(@paren_stack) == 1) { 461 pop @paren_stack; 462 chop($rh_ans->{preview_text_string}); 463 chop($rh_ans->{preview_latex_string}); 464 chop($display_ans); 465 $rh_ans->{preview_text_string} .= "]"; 466 $rh_ans->{preview_latex_string} .= "]"; 467 $display_ans .= "]"; 468 if( scalar(@temp) > 0 ) { 469 push( @answers,Matrix->new_from_col_vecs([\@temp])); 470 while(scalar(@temp) > 0 ){ 471 pop @temp; 472 } 473 } else { 474 $rh_ans->throw_error('EVAL','There is a syntax error in your answer.'); 475 } 476 } 477 } 478 $entry = ""; 479 } else { 480 $paren = pop @paren_stack; 481 if( scalar(@paren_stack) > 0 ){ 482 #this uses ASCII to check if the parens match up 483 # in ASCII ord ( = 40 , ord ) = 41 , ord [ = 91 , 484 # ord ] = 93 , ord { = 123 , ord } = 125 485 if( (ord($char) - ord($paren) <= 2) ){ 486 $entry = $entry . $char; 487 }else{ 488 $rh_ans->throw_error('EVAL','There is a syntax error in your answer'); 489 } 490 } 491 } 492 } 493 } else { 494 $rh_ans->{preview_text_string} .= "["; 495 $rh_ans->{preview_latex_string} .= "["; 496 $display_ans .= "["; 497 } 498 } 499 $rh_ans->{ra_student_ans} = \@answers; 500 $rh_ans->{student_ans} = $display_ans unless $rh_ans->{error_flag}; 501 $rh_ans; 502 } 503 504 =head5 505 506 This filter was created to get, format, and evaluate each entry of the ans_array and ans_array_extension 507 answer entry methods. Running this filter is necessary to get all the entries out of the answer 508 hash. Each entry is evaluated and the resulting number is put in the display for student answer 509 as a string. For evaluation purposes an array of arrays of arrays is created called ra_student_ans 510 and placed in the hash. The entries are [array_number][row_number][column_number]. The latex strings 511 for each entry are taken from the parser and put, as a matrix, into the previewer. The preview text 512 string is also created, but this display method becomes confusing when large matrices are used. 513 514 =cut 515 516 517 sub ans_array_filter{ 518 my $rh_ans = shift; 519 my %options = @_; 520 # assign_option_aliases( \%opt, 521 # ); 522 set_default_options(\%options, 523 _filter_name => 'ans_array_filter', 524 ); 525 # $rh_ans->{ans_label} =~ /ArRaY(\d+)\[\d+,\d+,\d+\]/; # CHANGE made to accomodate HTML 4.01 standards for name attribute 526 $rh_ans->{ans_label} =~ /ArRaY(\d+)\_\_\d+:\d+:\d+\_\_/; 527 my $ans_num = $1; 528 my @keys = grep /ArRaY$ans_num/, keys(%{$main::inputs_ref}); 529 my $key; 530 my @array = (); 531 my ($i,$j,$k) = (0,0,0); 532 533 #the keys aren't in order, so their info has to be put into the array before doing anything with it 534 foreach $key (@keys){ 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 $key =~ /ArRaY\d+\_\_(\d+):(\d+):(\d+)\_\_/; 539 ($i,$j,$k) = ($1,$2,$3); 540 $array[$i][$j][$k] = ${$main::inputs_ref}{'ArRaY'.$ans_num.'__'.$i.':'.$j.':'.$k.'__'}; 541 542 } 543 #$rh_ans->{debug_student_answer }= \@array; 544 my $display_ans = ""; 545 546 for( $i=0; $i < scalar(@array) ; $i ++ ) { 547 $display_ans .= " ["; 548 $rh_ans->{preview_text_string} .= ' ['; 549 $rh_ans->{preview_latex_string} .= '\begin{pmatrix} '; 550 for( $j = 0; $j < scalar( @{$array[$i]} ) ; $j++ ) { 551 $display_ans .= " ["; 552 $rh_ans->{preview_text_string} .= ' ['; 553 for( $k = 0; $k < scalar( @{$array[$i][$j]} ) ; $k ++ ){ 554 my $entry = $array[$i][$j][$k]; 555 $entry = math_constants($entry); 556 # This parser code was origianally taken from PGanswermacros::check_syntax 557 # but parts of it needed to be slighty modified for this context 558 my $parser = new AlgParserWithImplicitExpand; 559 my $ret = $parser -> parse($entry); #for use with loops 560 561 if ( ref($ret) ) { ## parsed successfully 562 $parser -> tostring(); 563 $parser -> normalize(); 564 $entry = $parser -> tostring(); 565 $rh_ans->{preview_text_string} .= $entry.","; 566 $rh_ans->{preview_latex_string} .= $parser -> tolatex() . '& '; 567 568 } else { ## error in parsing 569 $rh_ans->{'student_ans'} = 'syntax error:'.$display_ans. $parser->{htmlerror}, 570 $rh_ans->{'ans_message'} = $display_ans.$parser -> {error_msg}, 571 $rh_ans->{'preview_text_string'} = '', 572 $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'.$display_ans.$parser->{htmlerror} . "$main::BR" .$parser -> {error_msg}.".$main::BR"); 573 } 574 575 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($entry); 576 if ($PG_eval_errors) { 577 $rh_ans->throw_error('EVAL','There is a syntax error in your answer.') ; 578 $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors); 579 last; 580 } else { 581 $entry = prfmt($inVal,$options{format}); 582 $display_ans .= $entry.","; 583 $array[$i][$j][$k] = $entry; 584 } 585 } 586 chop($rh_ans->{preview_text_string}); 587 chop($display_ans); 588 $rh_ans->{preview_text_string} .= '] ,'; 589 $rh_ans->{preview_latex_string} .= '\\\\'; 590 $display_ans .= '] ,'; 591 592 } 593 chop($rh_ans->{preview_text_string}); 594 chop($display_ans); 595 $rh_ans->{preview_text_string} .= '] ,'; 596 $rh_ans->{preview_latex_string} .= '\end{pmatrix}'.' , '; 597 $display_ans .= '] ,'; 598 } 599 chop($rh_ans->{preview_text_string}); 600 chop($rh_ans->{preview_latex_string}); 601 chop($rh_ans->{preview_latex_string}); 602 chop($rh_ans->{preview_latex_string}); 603 chop($display_ans); 604 605 my @temp = (); 606 for( $i = 0 ; $i < scalar( @array ); $i++ ){ 607 push @temp , display_matrix($array[$i], 'left'=>'.', 'right'=>'.'); 608 push @temp , "," unless $i == scalar(@array) - 1; 609 } 610 $rh_ans->{student_ans} = mbox(\@temp); 611 $rh_ans->{ra_student_ans} = \@array; 612 613 $rh_ans; 614 615 } 616 617 618 sub are_orthogonal_vecs{ 619 my ($vec_ref , %opts) = @_; 620 $vec_ref->{_filter_name} = 'are_orthogonal_vecs'; 621 my @vecs = (); 622 if( ref($vec_ref) eq 'AnswerHash' ) 623 { 624 @vecs = @{$vec_ref->{ra_student_ans}}; 625 }else{ 626 @vecs = @{$vec_ref}; 627 } 628 629 my $num = scalar(@vecs); 630 my $length = $vecs[0]->[1]; 631 632 for( my $i=0; $i < $num ; $i ++ ) { 633 for( my $j = $i+1; $j < $num ; $j++ ) { 634 if( $vecs[$i]->scalar_product($vecs[$j]) > $main::functZeroLevelTolDefault ) { 635 if( ref( $vec_ref ) eq 'AnswerHash' ){ 636 $vec_ref->{score} = 0; 637 if( $vec_ref->{help} =~ /orthogonal|orthonormal|verbose/ ) 638 { 639 $vec_ref->throw_error('EVAL','You have entered vectors which are not orthogonal. '); 640 }else{ 641 $vec_ref->throw_error('EVAL'); 642 } 643 return $vec_ref; 644 } else { 645 return 0; 646 } 647 } 648 } 649 } 650 if( ref( $vec_ref ) eq 'AnswerHash' ){ 651 $vec_ref->{score} = 1; 652 $vec_ref; 653 } else { 654 1; 655 } 656 } 657 658 sub is_diagonal{ 659 my $matrix = shift; 660 my %options = @_; 661 my $process_ans_hash = ( ref( $matrix ) eq 'AnswerHash' ) ? 1 : 0 ; 662 my ($rh_ans); 663 if ($process_ans_hash) { 664 $rh_ans = $matrix; 665 $matrix = $rh_ans->{ra_student_ans}; 666 } 667 668 return 0 unless defined($matrix); 669 670 if( ref($matrix) eq 'ARRAY' ) { 671 my @matrix = @{$matrix}; 672 @matrix = @{$matrix[0]} if ref($matrix[0][0]) eq 'ARRAY'; 673 if( ref($matrix[0]) ne 'ARRAY' or scalar( @matrix ) != scalar( @{$matrix[0]} ) ){ 674 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."; 675 } 676 677 for( my $i = 0; $i < scalar( @matrix ) ; $i++ ) { 678 for( my $j = 0; $j < scalar( @{$matrix[0]} ); $j++ ){ 679 if( $matrix[$i][$j] != 0 and $i != $j ) 680 { 681 if ($process_ans_hash){ 682 $rh_ans->throw_error('EVAL'); 683 return $rh_ans; 684 } else { 685 return 0; 686 } 687 } 688 } 689 } 690 if ($process_ans_hash){ 691 return $rh_ans; 692 } else { 693 return 1; 694 } 695 } elsif ( ref($matrix) eq 'Matrix' ) { 696 if( $matrix->[1] != $matrix->[2] ) { 697 warn "It is impossible for a non-square matrix to be diagonal, if you are a student, please tell your professor that there is a problem."; 698 if ($process_ans_hash){ 699 $rh_ans->throw_error('EVAL'); 700 return $rh_ans; 701 } else { 702 return 0; 703 } 704 } 705 for( my $i = 0; $i < $matrix->[1] ; $i++ ) { 706 for( my $j = 0; $j < $matrix->[2] ; $j++ ) { 707 if( $matrix->[0][$i][$j] != 0 and $i != $j ){ 708 if ($process_ans_hash){ 709 $rh_ans->throw_error('EVAL'); 710 return $rh_ans; 711 } else { 712 return 0; 713 } 714 } 715 } 716 } 717 if ($process_ans_hash) { 718 return $rh_ans; 719 } else { 720 return 1; 721 } 722 } else { 723 warn "There is a problem with the problem, please alert your professor."; 724 if ($process_ans_hash){ 725 $rh_ans->throw_error('EVAL'); 726 return $rh_ans; 727 } else { 728 return 0; 729 } 730 } 731 732 } 733 734 735 sub are_unit_vecs{ 736 my ( $vec_ref,%opts ) = @_; 737 $vec_ref->{_filter_name} = 'are_unit_vecs'; 738 my @vecs = (); 739 if( ref($vec_ref) eq 'AnswerHash' ) 740 { 741 @vecs = @{$vec_ref->{ra_student_ans}}; 742 }else{ 743 @vecs = @{$vec_ref}; 744 } 745 746 my $i = 0; 747 my $num = scalar(@vecs); 748 my $length = $vecs[0]->[1]; 749 750 for( ; $i < $num ; $i ++ ) { 751 if( abs(sqrt($vecs[$i]->scalar_product($vecs[$i]))- 1) > $main::functZeroLevelTolDefault ) 752 { 753 if( ref( $vec_ref ) eq 'AnswerHash' ){ 754 $vec_ref->{score} = 0; 755 if( $vec_ref->{help} =~ /unit|orthonormal|verbose/ ) 756 { 757 $vec_ref->throw_error('EVAL','You have entered vector(s) which are not of unit length.'); 758 }else{ 759 $vec_ref->throw_error('EVAL'); 760 } 761 return $vec_ref; 762 }else{ 763 return 0; 764 } 765 766 } 767 } 768 769 if( ref( $vec_ref ) eq 'AnswerHash' ){ 770 $vec_ref->{score} = 1; 771 $vec_ref; 772 }else{ 773 1; 774 } 775 } 776 777 sub display_correct_vecs{ 778 my ( $ra_vecs,%opts ) = @_; 779 my @ra_vecs = @{$ra_vecs}; 780 my @temp = (); 781 782 for( my $i = 0 ; $i < scalar(@ra_vecs) ; $i++ ) { 783 push @temp, display_matrix(Matrix->new_from_col_vecs([$ra_vecs[$i]]),'left'=>'.','right'=>'.'); 784 push @temp, ","; 785 } 786 787 pop @temp; 788 789 mbox(\@temp); 790 791 } 792 793 sub vec_solution_cmp{ 794 my $correctAnswer = shift; 795 my %opt = @_; 796 797 set_default_options( \%opt, 798 'zeroLevelTol' => $main::functZeroLevelTolDefault, 799 'debug' => 0, 800 'mode' => 'basis', 801 'help' => 'none', 802 ); 803 804 805 ## This is where the correct answer should be checked someday. 806 my $matrix = Matrix->new_from_col_vecs($correctAnswer); 807 808 809 #construct the answer evaluator 810 my $answer_evaluator = new AnswerEvaluator; 811 812 $answer_evaluator->{debug} = $opt{debug}; 813 $answer_evaluator->ans_hash( 814 correct_ans => display_correct_vecs($correctAnswer), 815 old_correct_ans => $correctAnswer, 816 rm_correct_ans => $matrix, 817 zeroLevelTol => $opt{zeroLevelTol}, 818 debug => $opt{debug}, 819 mode => $opt{mode}, 820 help => $opt{help}, 821 ); 822 823 $answer_evaluator->install_pre_filter(\&ans_array_filter); 824 $answer_evaluator->install_pre_filter( 825 sub{ 826 my ($rh_ans,@options) = @_; 827 $rh_ans->{_filter_name} = "create student answer as an array of vectors"; 828 my @student_array = @{$rh_ans->{ra_student_ans}}; 829 my @array = (); 830 for( my $i = 0; $i < scalar(@student_array) ; $i ++ ) { 831 push( @array, Matrix->new_from_array_ref($student_array[$i])); 832 } 833 $rh_ans->{ra_student_ans} = \@array; 834 $rh_ans; 835 } 836 ); 837 #ra_student_ans is now the students answer as an array of vectors 838 # anonymous subroutine to check dimension and length of the student vectors 839 # if either is wrong, the answer is wrong. 840 $answer_evaluator->install_pre_filter( 841 sub{ 842 my $rh_ans = shift; 843 $rh_ans->{_filter_name} = "check_dimension_and_length"; 844 my $length = $rh_ans->{rm_correct_ans}->[1]; 845 my $dim = $rh_ans->{rm_correct_ans}->[2]; 846 if( $dim != scalar(@{$rh_ans->{ra_student_ans}})) 847 { 848 849 $rh_ans->{score} = 0; 850 if( $rh_ans->{help} =~ /dim|verbose/ ) 851 { 852 $rh_ans->throw_error('EVAL','You have entered the wrong number of vectors.'); 853 }else{ 854 $rh_ans->throw_error('EVAL'); 855 } 856 } 857 for( my $i = 0; $i < scalar( @{$rh_ans->{ra_student_ans} }) ; $i++ ) { 858 if( $length != $rh_ans->{ra_student_ans}->[$i]->[1]) { 859 $rh_ans->{score} = 0; 860 if( $rh_ans->{help} =~ /length|verbose/ ) { 861 $rh_ans->throw_error('EVAL','You have entered vector(s) of the wrong length.'); 862 }else{ 863 $rh_ans->throw_error('EVAL'); 864 } 865 } 866 } 867 $rh_ans; 868 } 869 ); 870 # Install prefilter for various modes 871 if( $opt{mode} ne 'basis' ) { 872 if( $opt{mode} =~ /orthogonal|orthonormal/ ) { 873 $answer_evaluator->install_pre_filter(\&are_orthogonal_vecs); 874 } 875 876 if( $opt{mode} =~ /unit|orthonormal/ ) { 877 $answer_evaluator->install_pre_filter(\&are_unit_vecs); 878 879 } 880 } 881 882 $answer_evaluator->install_evaluator(\&compare_vec_solution, %opt); 883 884 $answer_evaluator->install_post_filter( 885 sub {my $rh_ans = shift; 886 if ($rh_ans->catch_error('SYNTAX') ) { 887 $rh_ans->{ans_message} = $rh_ans->{error_message}; 888 $rh_ans->clear_error('SYNTAX'); 889 } 890 if ($rh_ans->catch_error('EVAL') ) { 891 $rh_ans->{ans_message} = $rh_ans->{error_message}; 892 $rh_ans->clear_error('EVAL'); 893 } 894 $rh_ans; 895 } 896 ); 897 $answer_evaluator; 898 899 } 900 901 902 sub compare_vec_solution { 903 my ( $rh_ans, %options ) = @_ ; 904 $rh_ans->{_filter_name} = "compare_vec_solution"; 905 my @space = @{$rh_ans->{ra_student_ans}}; 906 my $solution = shift @space; 907 908 # A lot of the following code was taken from Matrix::proj_coeff 909 # calling this method recursively would be a waste of time since 910 # the prof's matrix never changes and solve_LR is an expensive 911 # operation. This way it is only done once. 912 my $matrix = $rh_ans->{rm_correct_ans}; 913 my ($dim,$x_vector, $base_matrix); 914 my $errors = undef; 915 my $lin_space_tr= ~ $matrix; 916 $matrix = $lin_space_tr * $matrix; 917 my $matrix_lr = $matrix->decompose_LR(); 918 919 #this section determines whether or not the first vector, a solution to 920 #the system, is a linear combination of the prof's vectors in which there 921 #is a nonzero coefficient on the first term, the prof's solution to the system 922 $solution = $lin_space_tr*$solution; 923 ($dim,$x_vector, $base_matrix) = $matrix_lr->solve_LR($solution); 924 #$rh_ans->{debug_compare_vec_solution} = $x_vector->element(1,1); 925 if( $dim ){ 926 $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. 927 $rh_ans->{score} = 0; 928 $rh_ans; 929 } elsif( abs($x_vector->element(1,1) -1) >= $options{zeroLevelTol} ) { 930 # changes by MEG 6/24/05 931 # the student answer needs to be a linear combination of the instructors vectors 932 # and the coefficient of the first vector needs to be 1 (it is NOT enough that it be non-zero). 933 # if this is not the case, then the answer is wrong. 934 # replaced $x_vector->[0][0][0] by $x_vector->element(1,1) since this doesn't depend on the internal structure of the matrix object. 935 936 $rh_ans->{score} = 0; 937 $rh_ans; 938 } else { 939 $rh_ans->{score} = 1; 940 my @correct_space = @{$rh_ans->{old_correct_ans}}; 941 shift @correct_space; 942 $rh_ans->{rm_correct_ans} = Matrix->new_from_col_vecs(\@correct_space); 943 $rh_ans->{ra_student_ans} = \@space; 944 return compare_basis( $rh_ans, %options ); 945 } 946 } 947 948 1;
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