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| 1 : | gage | 4997 | |
| 2 : | gage | 1064 | BEGIN{ |
| 3 : | gage | 3314 | be_strict(); |
| 4 : | gage | 1064 | } |
| 5 : | gage | 6817 | # set the prefix used for arrays. |
| 6 : | our $ArRaY = $main::PG->{ARRAY_PREFIX}; | ||
| 7 : | gage | 1064 | |
| 8 : | sub _PGmorematrixmacros_init{} | ||
| 9 : | |||
| 10 : | sub random_inv_matrix { ## Builds and returns a random invertible \$row by \$col matrix. | ||
| 11 : | |||
| 12 : | warn "Usage: \$new_matrix = random_inv_matrix(\$rows,\$cols)" | ||
| 13 : | if (@_ != 2); | ||
| 14 : | my $A = new Matrix($_[0],$_[1]); | ||
| 15 : | my $A_lr = new Matrix($_[0],$_[1]); | ||
| 16 : | my $det = 0; | ||
| 17 : | my $safety=0; | ||
| 18 : | while ($det == 0 and $safety < 6) { | ||
| 19 : | foreach my $i (1..$_[0]) { | ||
| 20 : | foreach my $j (1..$_[1]) { | ||
| 21 : | $A->assign($i,$j,random(-9,9,1) ); | ||
| 22 : | } | ||
| 23 : | } | ||
| 24 : | $A_lr = $A->decompose_LR(); | ||
| 25 : | $det = $A_lr->det_LR(); | ||
| 26 : | } | ||
| 27 : | return $A; | ||
| 28 : | } | ||
| 29 : | |||
| 30 : | lr003k | 1327 | =head4 random_diag_matrix |
| 31 : | |||
| 32 : | This method returns a random nxn diagonal matrix. | ||
| 33 : | |||
| 34 : | =cut | ||
| 35 : | |||
| 36 : | sub random_diag_matrix{ ## Builds and returns a random diagonal \$n by \$n matrix | ||
| 37 : | gage | 3314 | |
| 38 : | warn "Usage: \$new_matrix = random_diag_matrix(\$n)" if (@_ != 1); | ||
| 39 : | |||
| 40 : | my $D = new Matrix($_[0],$_[0]); | ||
| 41 : | my $norm = 0; | ||
| 42 : | while( $norm == 0 ){ | ||
| 43 : | foreach my $i (1..$_[0]){ | ||
| 44 : | foreach my $j (1..$_[0]){ | ||
| 45 : | if( $i != $j ){ | ||
| 46 : | $D->assign($i,$j,0); | ||
| 47 : | }else{ | ||
| 48 : | $D->assign($i,$j,random(-9,9,1)); | ||
| 49 : | } | ||
| 50 : | } | ||
| 51 : | } | ||
| 52 : | $norm = abs($D); | ||
| 53 : | } | ||
| 54 : | return $D; | ||
| 55 : | lr003k | 1327 | } |
| 56 : | |||
| 57 : | gage | 1064 | sub swap_rows{ |
| 58 : | |||
| 59 : | warn "Usage: \$new_matrix = swap_rows(\$matrix,\$row1,\$row2);" | ||
| 60 : | if (@_ != 3); | ||
| 61 : | my $matrix = $_[0]; | ||
| 62 : | my ($i,$j) = ($_[1],$_[2]); | ||
| 63 : | warn "Error: Rows to be swapped must exist!" | ||
| 64 : | if ($i>@$matrix or $j >@$matrix); | ||
| 65 : | warn "Warning: Swapping the same row is pointless" | ||
| 66 : | if ($i==$j); | ||
| 67 : | my $cols = @{$matrix->[0]}; | ||
| 68 : | my $B = new Matrix(@$matrix,$cols); | ||
| 69 : | foreach my $k (1..$cols){ | ||
| 70 : | $B->assign($i,$k,element $matrix($j,$k)); | ||
| 71 : | $B->assign($j,$k,element $matrix($i,$k)); | ||
| 72 : | } | ||
| 73 : | return $B; | ||
| 74 : | } | ||
| 75 : | |||
| 76 : | sub row_mult{ | ||
| 77 : | |||
| 78 : | warn "Usage: \$new_matrix = row_mult(\$matrix,\$scalar,\$row);" | ||
| 79 : | if (@_ != 3); | ||
| 80 : | my $matrix = $_[0]; | ||
| 81 : | my ($scalar,$row) = ($_[1],$_[2]); | ||
| 82 : | warn "Undefined row multiplication" | ||
| 83 : | if ($row > @$matrix); | ||
| 84 : | my $B = new Matrix(@$matrix,@{$matrix->[0]}); | ||
| 85 : | foreach my $j (1..@{$matrix->[0]}) { | ||
| 86 : | $B->assign($row,$j,$scalar*element $matrix($row,$j)); | ||
| 87 : | } | ||
| 88 : | return $B; | ||
| 89 : | } | ||
| 90 : | |||
| 91 : | sub linear_combo{ | ||
| 92 : | |||
| 93 : | warn "Usage: \$new_matrix = linear_combo(\$matrix,\$scalar,\$row1,\$row2);" | ||
| 94 : | if (@_ != 4); | ||
| 95 : | my $matrix = $_[0]; | ||
| 96 : | my ($scalar,$row1,$row2) = ($_[1],$_[2],$_[3]); | ||
| 97 : | warn "Undefined row in multiplication" | ||
| 98 : | if ($row1>@$matrix or $row2>@$matrix); | ||
| 99 : | warn "Warning: Using the same row" | ||
| 100 : | if ($row1==$row2); | ||
| 101 : | my $B = new Matrix(@$matrix,@{$matrix->[0]}); | ||
| 102 : | foreach my $j (1..@$matrix) { | ||
| 103 : | my ($t1,$t2) = (element $matrix($row1,$j),element $matrix($row2,$j)); | ||
| 104 : | $B->assign($row2,$j,$scalar*$t1+$t2); | ||
| 105 : | } | ||
| 106 : | return $B; | ||
| 107 : | } | ||
| 108 : | |||
| 109 : | gage | 1071 | =head3 basis_cmp() |
| 110 : | gage | 1064 | |
| 111 : | gage | 1071 | Compares a list of vectors by finding the change of coordinate matrix |
| 112 : | from the Prof's vectors to the students, and then taking the determinant of | ||
| 113 : | that to determine the existence of the change of coordinate matrix going the | ||
| 114 : | other way. | ||
| 115 : | |||
| 116 : | ANS( basis_cmp( vectors_as_array_ref_in_array_ref, options_hash ) ); | ||
| 117 : | |||
| 118 : | gage | 3314 | 1. a reference to an array of correct vectors |
| 119 : | 2. a hash with the following keys (all optional): | ||
| 120 : | mode -- 'basis' (default) (only a basis allowed) | ||
| 121 : | 'orthogonal' (only an orthogonal basis is allowed) | ||
| 122 : | 'unit' (only unit vectors in the basis allowed) | ||
| 123 : | 'orthonormal' (only orthogonal unit vectors in basis allowed) | ||
| 124 : | zeroLevelTol -- absolute tolerance to allow when answer is close | ||
| 125 : | to zero | ||
| 126 : | gage | 1071 | |
| 127 : | gage | 3314 | debug -- if set to 1, provides verbose listing of |
| 128 : | hash entries throughout fliters. | ||
| 129 : | gage | 1071 | |
| 130 : | gage | 3314 | help -- 'none' (default) (is quiet on all errors) |
| 131 : | 'dim' (Tells student if wrong number of vectors are entered) | ||
| 132 : | 'length' (Tells student if there is a vector of the wrong length) | ||
| 133 : | 'orthogonal' (Tells student if their vectors are not orthogonal) | ||
| 134 : | (This is only in orthogonal mode) | ||
| 135 : | 'unit' (Tells student if there is a vector not of unit length) | ||
| 136 : | (This is only in unit mode) | ||
| 137 : | 'orthonormal' (Gives errors from orthogonal and orthonormal) | ||
| 138 : | (This is only in orthonormal mode) | ||
| 139 : | 'verbose' (Gives all the above answer messages) | ||
| 140 : | gage | 1071 | |
| 141 : | gage | 3314 | Returns an answer evaluator. |
| 142 : | gage | 1071 | |
| 143 : | EXAMPLES: | ||
| 144 : | |||
| 145 : | gage | 3314 | basis_cmp([[1,0,0],[0,1,0],[0,0,1]]) |
| 146 : | -- correct answer is any basis for R^3. | ||
| 147 : | basis_cmp([1,0,2,0],[0,1,0,0], 'mode'=>orthonormal ) | ||
| 148 : | -- correct answer is any orthonormal basis | ||
| 149 : | for this space such as: | ||
| 150 : | [1/sqrt(3),0,2/sqrt(3),0],[0,1,0,0] | ||
| 151 : | gage | 1071 | |
| 152 : | =cut | ||
| 153 : | |||
| 154 : | |||
| 155 : | sub basis_cmp { | ||
| 156 : | gage | 3314 | my $correctAnswer = shift; |
| 157 : | my %opt = @_; | ||
| 158 : | gage | 1071 | |
| 159 : | gage | 3314 | set_default_options( \%opt, |
| 160 : | 'zeroLevelTol' => $main::functZeroLevelTolDefault, | ||
| 161 : | 'debug' => 0, | ||
| 162 : | 'mode' => 'basis', | ||
| 163 : | 'help' => 'none', | ||
| 164 : | ); | ||
| 165 : | |||
| 166 : | # produce answer evaluator | ||
| 167 : | BASIS_CMP( | ||
| 168 : | 'correct_ans' => $correctAnswer, | ||
| 169 : | 'zeroLevelTol' => $opt{'zeroLevelTol'}, | ||
| 170 : | 'debug' => $opt{'debug'}, | ||
| 171 : | 'mode' => $opt{'mode'}, | ||
| 172 : | 'help' => $opt{'help'}, | ||
| 173 : | ); | ||
| 174 : | gage | 1071 | } |
| 175 : | |||
| 176 : | gage | 4969 | =head1 BASIS_CMP |
| 177 : | gage | 1071 | |
| 178 : | Made to keep the same format as num_cmp and fun_cmp. | ||
| 179 : | |||
| 180 : | =cut | ||
| 181 : | |||
| 182 : | sub BASIS_CMP { | ||
| 183 : | gage | 3314 | my %mat_params = @_; |
| 184 : | my $zeroLevelTol = $mat_params{'zeroLevelTol'}; | ||
| 185 : | |||
| 186 : | # Check that everything is defined: | ||
| 187 : | $mat_params{debug} = 0 unless defined($mat_params{debug}); | ||
| 188 : | $zeroLevelTol = $main::functZeroLevelTolDefault unless defined $zeroLevelTol; | ||
| 189 : | $mat_params{'zeroLevelTol'} = $zeroLevelTol; | ||
| 190 : | gage | 1071 | |
| 191 : | ## This is where the correct answer should be checked someday. | ||
| 192 : | gage | 3314 | my $matrix = Matrix->new_from_col_vecs($mat_params{'correct_ans'}); |
| 193 : | gage | 1071 | |
| 194 : | #construct the answer evaluator | ||
| 195 : | gage | 3314 | my $answer_evaluator = new AnswerEvaluator; |
| 196 : | gage | 1071 | |
| 197 : | gage | 1896 | $answer_evaluator->{debug} = $mat_params{debug}; |
| 198 : | gage | 3314 | $answer_evaluator->ans_hash( |
| 199 : | correct_ans => display_correct_vecs($mat_params{correct_ans}), | ||
| 200 : | rm_correct_ans => $matrix, | ||
| 201 : | zeroLevelTol => $mat_params{zeroLevelTol}, | ||
| 202 : | debug => $mat_params{debug}, | ||
| 203 : | mode => $mat_params{mode}, | ||
| 204 : | help => $mat_params{help}, | ||
| 205 : | gage | 1896 | ); |
| 206 : | gage | 1071 | |
| 207 : | gage | 3314 | $answer_evaluator->install_pre_filter( |
| 208 : | sub {my $rh_ans = shift; | ||
| 209 : | $rh_ans->{_filter_name} = 'remove_white_space'; | ||
| 210 : | $rh_ans->{student_ans} =~ s/\s+//g; # remove all whitespace | ||
| 211 : | $rh_ans; | ||
| 212 : | } | ||
| 213 : | ); | ||
| 214 : | $answer_evaluator->install_pre_filter( | ||
| 215 : | sub{my $rh_ans = shift; | ||
| 216 : | my @options = @_; | ||
| 217 : | $rh_ans->{_filter_name} = 'mung_student_answer'; | ||
| 218 : | gage | 6817 | if( $rh_ans->{ans_label} =~ /$ArRaY/ ){ |
| 219 : | gage | 3314 | $rh_ans = ans_array_filter($rh_ans,@options); |
| 220 : | my @student_array = @{$rh_ans->{ra_student_ans}}; | ||
| 221 : | my @array = (); | ||
| 222 : | for( my $i = 0; $i < scalar(@student_array) ; $i ++ ) | ||
| 223 : | { | ||
| 224 : | push( @array, Matrix->new_from_array_ref($student_array[$i])); | ||
| 225 : | } | ||
| 226 : | $rh_ans->{ra_student_ans} = \@array; | ||
| 227 : | $rh_ans; | ||
| 228 : | }else{ | ||
| 229 : | $rh_ans->{student_ans} = math_constants($rh_ans->{student_ans}); | ||
| 230 : | vec_list_string($rh_ans, '_filter_name' => 'vec_list_string', @options); | ||
| 231 : | } | ||
| 232 : | } | ||
| 233 : | );#ra_student_ans is now the students answer as an array of vectors | ||
| 234 : | # anonymous subroutine to check dimension and length of the student vectors | ||
| 235 : | # if either is wrong, the answer is wrong. | ||
| 236 : | $answer_evaluator->install_pre_filter( | ||
| 237 : | sub{ | ||
| 238 : | my $rh_ans = shift; | ||
| 239 : | $rh_ans->{_filter_name} = 'check_vector_size'; | ||
| 240 : | my $length = $rh_ans->{rm_correct_ans}->[1]; | ||
| 241 : | my $dim = $rh_ans->{rm_correct_ans}->[2]; | ||
| 242 : | if( $dim != scalar(@{$rh_ans->{ra_student_ans}})) | ||
| 243 : | { | ||
| 244 : | |||
| 245 : | $rh_ans->{score} = 0; | ||
| 246 : | if( $rh_ans->{help} =~ /dim|verbose/ ) | ||
| 247 : | { | ||
| 248 : | $rh_ans->throw_error('EVAL','You have entered the wrong number of vectors.'); | ||
| 249 : | }else{ | ||
| 250 : | $rh_ans->throw_error('EVAL'); | ||
| 251 : | } | ||
| 252 : | } | ||
| 253 : | for( my $i = 0; $i < scalar( @{$rh_ans->{ra_student_ans} }) ; $i++ ) | ||
| 254 : | { | ||
| 255 : | if( $length != $rh_ans->{ra_student_ans}->[$i]->[1]) | ||
| 256 : | { | ||
| 257 : | $rh_ans->{score} = 0; | ||
| 258 : | if( $rh_ans->{help} =~ /length|verbose/ ) | ||
| 259 : | { | ||
| 260 : | $rh_ans->throw_error('EVAL','You have entered vector(s) of the wrong length.'); | ||
| 261 : | }else{ | ||
| 262 : | $rh_ans->throw_error('EVAL'); | ||
| 263 : | } | ||
| 264 : | } | ||
| 265 : | } | ||
| 266 : | $rh_ans; | ||
| 267 : | } | ||
| 268 : | ); | ||
| 269 : | # Install prefilter for various modes | ||
| 270 : | if( $mat_params{mode} ne 'basis' ) | ||
| 271 : | { | ||
| 272 : | if( $mat_params{mode} =~ /orthogonal|orthonormal/ ) | ||
| 273 : | { | ||
| 274 : | $answer_evaluator->install_pre_filter(\&are_orthogonal_vecs); | ||
| 275 : | } | ||
| 276 : | |||
| 277 : | if( $mat_params{mode} =~ /unit|orthonormal/ ) | ||
| 278 : | { | ||
| 279 : | $answer_evaluator->install_pre_filter(\&are_unit_vecs); | ||
| 280 : | |||
| 281 : | } | ||
| 282 : | } | ||
| 283 : | $answer_evaluator->install_evaluator(\&compare_basis, %mat_params); | ||
| 284 : | $answer_evaluator->install_post_filter( | ||
| 285 : | sub {my $rh_ans = shift; | ||
| 286 : | if ($rh_ans->catch_error('SYNTAX') ) { | ||
| 287 : | $rh_ans->{ans_message} = $rh_ans->{error_message}; | ||
| 288 : | $rh_ans->clear_error('SYNTAX'); | ||
| 289 : | } | ||
| 290 : | if ($rh_ans->catch_error('EVAL') ) { | ||
| 291 : | $rh_ans->{ans_message} = $rh_ans->{error_message}; | ||
| 292 : | $rh_ans->clear_error('EVAL'); | ||
| 293 : | } | ||
| 294 : | $rh_ans; | ||
| 295 : | } | ||
| 296 : | ); | ||
| 297 : | $answer_evaluator; | ||
| 298 : | gage | 1071 | } |
| 299 : | |||
| 300 : | =head4 compare_basis | ||
| 301 : | |||
| 302 : | gage | 3314 | compare_basis( $ans_hash, |
| 303 : | %options | ||
| 304 : | ra_student_ans # a reference to the array of students answer vectors | ||
| 305 : | rm_correct_ans, # a reference to the correct answer matrix | ||
| 306 : | %options | ||
| 307 : | ) | ||
| 308 : | gage | 1071 | |
| 309 : | |||
| 310 : | =cut | ||
| 311 : | |||
| 312 : | gage | 3314 | |
| 313 : | |||
| 314 : | gage | 1071 | sub compare_basis { |
| 315 : | gage | 3314 | my ($rh_ans, %options) = @_; |
| 316 : | $rh_ans->{_filter_name} = "compare_basis"; | ||
| 317 : | my @ch_coord; | ||
| 318 : | my @vecs = @{$rh_ans->{ra_student_ans}}; | ||
| 319 : | |||
| 320 : | # A lot of the following code was taken from Matrix::proj_coeff | ||
| 321 : | # calling this method recursively would be a waste of time since | ||
| 322 : | # the prof's matrix never changes and solve_LR is an expensive | ||
| 323 : | # operation. This way it is only done once. | ||
| 324 : | my $matrix = $rh_ans->{rm_correct_ans}; | ||
| 325 : | my ($dim,$x_vector, $base_matrix); | ||
| 326 : | my $errors = undef; | ||
| 327 : | my $lin_space_tr= ~ $matrix; #transpose of the matrix | ||
| 328 : | $matrix = $lin_space_tr * $matrix; #(~A * A) | ||
| 329 : | my $matrix_lr = $matrix->decompose_LR(); | ||
| 330 : | |||
| 331 : | #finds the coefficient vectors for each of the students vectors | ||
| 332 : | for( my $i = 0; $i < scalar(@{$rh_ans->{ra_student_ans}}) ; $i++ ) { | ||
| 333 : | |||
| 334 : | $vecs[$i] = $lin_space_tr*$vecs[$i]; | ||
| 335 : | ($dim,$x_vector, $base_matrix) = $matrix_lr->solve_LR($vecs[$i]); | ||
| 336 : | push( @ch_coord, $x_vector ); | ||
| 337 : | $errors = "A unique adapted answer could not be determined. | ||
| 338 : | Possibly the parameters have coefficient zero.<br> dim = $dim base_matrix | ||
| 339 : | is $base_matrix\n" if $dim; # only print if the dim is not zero. | ||
| 340 : | } | ||
| 341 : | |||
| 342 : | if( defined($errors)) { | ||
| 343 : | $rh_ans->throw_error('EVAL', $errors) ; | ||
| 344 : | } else { | ||
| 345 : | my $ch_coord_mat = Matrix->new_from_col_vecs(\@ch_coord); | ||
| 346 : | #creates change of coordinate matrix | ||
| 347 : | #existence of this matrix implies that | ||
| 348 : | #the all of the students answers are a | ||
| 349 : | #linear combo of the prof's | ||
| 350 : | $ch_coord_mat = $ch_coord_mat->decompose_LR(); | ||
| 351 : | |||
| 352 : | if( abs($ch_coord_mat->det_LR()) > $options{zeroLevelTol} ) { | ||
| 353 : | # if the det of the change of coordinate matrix is | ||
| 354 : | # non-zero, this implies the existence of an inverse | ||
| 355 : | # which implies all of the prof's vectors are a linear | ||
| 356 : | # combo of the students vectors, showing containment | ||
| 357 : | # both ways. | ||
| 358 : | |||
| 359 : | # I think sometimes if the students space has the same dimension as the profs space it | ||
| 360 : | # will get projected into the profs space even if it isn't a basis for that space. | ||
| 361 : | # this just checks that the prof's matrix times the change of coordinate matrix is actually | ||
| 362 : | #the students matrix | ||
| 363 : | if( abs(Matrix->new_from_col_vecs(\@{$rh_ans->{ra_student_ans}}) - | ||
| 364 : | ($rh_ans->{rm_correct_ans})*(Matrix->new_from_col_vecs(\@ch_coord))) | ||
| 365 : | < $options{zeroLevelTol} ) { | ||
| 366 : | $rh_ans->{score} = 1; | ||
| 367 : | } else { | ||
| 368 : | $rh_ans->{score} = 0; | ||
| 369 : | } | ||
| 370 : | } else { | ||
| 371 : | $rh_ans->{score}=0; | ||
| 372 : | } | ||
| 373 : | } | ||
| 374 : | $rh_ans; | ||
| 375 : | |||
| 376 : | gage | 1071 | } |
| 377 : | |||
| 378 : | |||
| 379 : | gage | 4969 | =head2 vec_list_string |
| 380 : | gage | 1071 | |
| 381 : | This is a check_syntax type method (in fact I borrowed some of that method's code) for vector input. | ||
| 382 : | The student needs to enter vectors like: [1,0,0],[1,2,3],[0,9/sqrt(10),1/sqrt(10)] | ||
| 383 : | Each entry can contain functions and operations and the usual math constants (pi and e). | ||
| 384 : | The vectors, however can not be added or multiplied or scalar multiplied by the student. | ||
| 385 : | 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. | ||
| 386 : | Right now the method basically ignores every thing outside the vectors. Also, an unmatched open parenthesis is caught, | ||
| 387 : | but a unmatched close parenthesis ends the vector, and since everything outside is ignored, no error is sent (other than the | ||
| 388 : | later when the length of the vectors is checked. | ||
| 389 : | gage | 4997 | In the end, the method returns an array of Matrix objects. |
| 390 : | gage | 1071 | |
| 391 : | =cut | ||
| 392 : | |||
| 393 : | sub vec_list_string{ | ||
| 394 : | gage | 3314 | my $rh_ans = shift; |
| 395 : | my %options = @_; | ||
| 396 : | my $i; | ||
| 397 : | my $entry = ""; | ||
| 398 : | my $char; | ||
| 399 : | my @paren_stack; | ||
| 400 : | my $length = length($rh_ans->{student_ans}); | ||
| 401 : | my @temp; | ||
| 402 : | my $j = 0; | ||
| 403 : | my @answers; | ||
| 404 : | my $paren; | ||
| 405 : | my $display_ans; | ||
| 406 : | |||
| 407 : | for( $i = 0; $i < $length ; $i++ ) { | ||
| 408 : | $char = substr($rh_ans->{student_ans},$i,1); | ||
| 409 : | |||
| 410 : | if( $char =~ /\(|\[|\{/ ){ | ||
| 411 : | push( @paren_stack, $char ) | ||
| 412 : | } | ||
| 413 : | |||
| 414 : | if( !( $char =~ /\(|\[|\{/ && scalar(@paren_stack) == 1 ) ) { | ||
| 415 : | if( $char !~ /,|\)|\]|\}/ ){ | ||
| 416 : | $entry .= $char; | ||
| 417 : | } else { | ||
| 418 : | if( $char =~ /,/ || ( $char =~ /\)|\]|\}/ && scalar(@paren_stack) == 1 ) ) { | ||
| 419 : | if( length($entry) == 0 ){ | ||
| 420 : | if( $char !~ /,/ ){ | ||
| 421 : | $rh_ans->throw_error('EVAL','There is a syntax error in your answer'); | ||
| 422 : | } else { | ||
| 423 : | $rh_ans->{preview_text_string} .= ","; | ||
| 424 : | $rh_ans->{preview_latex_string} .= ","; | ||
| 425 : | $display_ans .= ","; | ||
| 426 : | } | ||
| 427 : | } else { | ||
| 428 : | |||
| 429 : | # This parser code was origianally taken from PGanswermacros::check_syntax | ||
| 430 : | # but parts of it needed to be slighty modified for this context | ||
| 431 : | my $parser = new AlgParserWithImplicitExpand; | ||
| 432 : | my $ret = $parser -> parse($entry); #for use with loops | ||
| 433 : | gage | 1071 | |
| 434 : | gage | 3314 | if ( ref($ret) ) { ## parsed successfully |
| 435 : | $parser -> tostring(); | ||
| 436 : | $parser -> normalize(); | ||
| 437 : | $entry = $parser -> tostring(); | ||
| 438 : | $rh_ans->{preview_text_string} .= $entry.","; | ||
| 439 : | $rh_ans->{preview_latex_string} .= $parser -> tolatex().","; | ||
| 440 : | gage | 1071 | |
| 441 : | gage | 3314 | } else { ## error in parsing |
| 442 : | gage | 1071 | |
| 443 : | gage | 3314 | $rh_ans->{'student_ans'} = 'syntax error:'.$display_ans. $parser->{htmlerror}, |
| 444 : | $rh_ans->{'ans_message'} = $display_ans.$parser -> {error_msg}, | ||
| 445 : | $rh_ans->{'preview_text_string'} = '', | ||
| 446 : | $rh_ans->{'preview_latex_string'} = '', | ||
| 447 : | $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'.$display_ans.$parser->{htmlerror} . "$main::BR" .$parser -> {error_msg}.".$main::BR"); | ||
| 448 : | } | ||
| 449 : | |||
| 450 : | my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($entry); | ||
| 451 : | |||
| 452 : | if ($PG_eval_errors) { | ||
| 453 : | $rh_ans->throw_error('EVAL','There is a syntax error in your answer.') ; | ||
| 454 : | $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors); | ||
| 455 : | last; | ||
| 456 : | } else { | ||
| 457 : | $entry = prfmt($inVal,$options{format}); | ||
| 458 : | $display_ans .= $entry.","; | ||
| 459 : | push(@temp , $entry); | ||
| 460 : | } | ||
| 461 : | |||
| 462 : | if( $char =~ /\)|\]|\}/ && scalar(@paren_stack) == 1) { | ||
| 463 : | pop @paren_stack; | ||
| 464 : | chop($rh_ans->{preview_text_string}); | ||
| 465 : | chop($rh_ans->{preview_latex_string}); | ||
| 466 : | chop($display_ans); | ||
| 467 : | $rh_ans->{preview_text_string} .= "]"; | ||
| 468 : | $rh_ans->{preview_latex_string} .= "]"; | ||
| 469 : | $display_ans .= "]"; | ||
| 470 : | if( scalar(@temp) > 0 ) { | ||
| 471 : | push( @answers,Matrix->new_from_col_vecs([\@temp])); | ||
| 472 : | while(scalar(@temp) > 0 ){ | ||
| 473 : | pop @temp; | ||
| 474 : | } | ||
| 475 : | } else { | ||
| 476 : | $rh_ans->throw_error('EVAL','There is a syntax error in your answer.'); | ||
| 477 : | } | ||
| 478 : | } | ||
| 479 : | } | ||
| 480 : | $entry = ""; | ||
| 481 : | } else { | ||
| 482 : | $paren = pop @paren_stack; | ||
| 483 : | if( scalar(@paren_stack) > 0 ){ | ||
| 484 : | #this uses ASCII to check if the parens match up | ||
| 485 : | # in ASCII ord ( = 40 , ord ) = 41 , ord [ = 91 , | ||
| 486 : | # ord ] = 93 , ord { = 123 , ord } = 125 | ||
| 487 : | if( (ord($char) - ord($paren) <= 2) ){ | ||
| 488 : | $entry = $entry . $char; | ||
| 489 : | }else{ | ||
| 490 : | $rh_ans->throw_error('EVAL','There is a syntax error in your answer'); | ||
| 491 : | } | ||
| 492 : | } | ||
| 493 : | } | ||
| 494 : | } | ||
| 495 : | } else { | ||
| 496 : | $rh_ans->{preview_text_string} .= "["; | ||
| 497 : | $rh_ans->{preview_latex_string} .= "["; | ||
| 498 : | $display_ans .= "["; | ||
| 499 : | } | ||
| 500 : | } | ||
| 501 : | $rh_ans->{ra_student_ans} = \@answers; | ||
| 502 : | $rh_ans->{student_ans} = $display_ans unless $rh_ans->{error_flag}; | ||
| 503 : | $rh_ans; | ||
| 504 : | gage | 1071 | } |
| 505 : | |||
| 506 : | gage | 4969 | =head5 ans_array_filter |
| 507 : | gage | 3314 | |
| 508 : | This filter was created to get, format, and evaluate each entry of the ans_array and ans_array_extension | ||
| 509 : | answer entry methods. Running this filter is necessary to get all the entries out of the answer | ||
| 510 : | hash. Each entry is evaluated and the resulting number is put in the display for student answer | ||
| 511 : | as a string. For evaluation purposes an array of arrays of arrays is created called ra_student_ans | ||
| 512 : | and placed in the hash. The entries are [array_number][row_number][column_number]. The latex strings | ||
| 513 : | for each entry are taken from the parser and put, as a matrix, into the previewer. The preview text | ||
| 514 : | string is also created, but this display method becomes confusing when large matrices are used. | ||
| 515 : | |||
| 516 : | lr003k | 1294 | =cut |
| 517 : | |||
| 518 : | |||
| 519 : | lr003k | 1123 | sub ans_array_filter{ |
| 520 : | gage | 3314 | my $rh_ans = shift; |
| 521 : | my %options = @_; | ||
| 522 : | # assign_option_aliases( \%opt, | ||
| 523 : | gage | 1896 | # ); |
| 524 : | gage | 3314 | set_default_options(\%options, |
| 525 : | _filter_name => 'ans_array_filter', | ||
| 526 : | ); | ||
| 527 : | gage | 6817 | # $rh_ans->{ans_label} =~ /$ArRaY(\d+)\[\d+,\d+,\d+\]/; # CHANGE made to accomodate HTML 4.01 standards for name attribute |
| 528 : | $rh_ans->{ans_label} =~ /$ArRaY(\d+)\_\_\d+\-\d+\-\d+\_\_/; | ||
| 529 : | gage | 3314 | my $ans_num = $1; |
| 530 : | gage | 6817 | my @keys = grep /$ArRaY$ans_num/, keys(%{$main::inputs_ref}); |
| 531 : | gage | 3314 | my $key; |
| 532 : | my @array = (); | ||
| 533 : | my ($i,$j,$k) = (0,0,0); | ||
| 534 : | |||
| 535 : | #the keys aren't in order, so their info has to be put into the array before doing anything with it | ||
| 536 : | foreach $key (@keys){ | ||
| 537 : | # $key =~ /ArRaY\d+\[(\d+),(\d+),(\d+)\]/; | ||
| 538 : | # ($i,$j,$k) = ($1,$2,$3); | ||
| 539 : | # $array[$i][$j][$k] = ${$main::inputs_ref}{'ArRaY'.$ans_num.'['.$i.','.$j.','.$k.']'}; | ||
| 540 : | gage | 6817 | $key =~ /$ArRaY\d+\_\_(\d+)\-(\d+)\-(\d+)\_\_/; |
| 541 : | gage | 3314 | ($i,$j,$k) = ($1,$2,$3); |
| 542 : | gage | 6817 | $array[$i][$j][$k] = ${$main::inputs_ref}{"$ArRaY".$ans_num.'__'.$i.'-'.$j.'-'.$k.'__'}; |
| 543 : | gage | 1896 | |
| 544 : | gage | 3314 | } |
| 545 : | #$rh_ans->{debug_student_answer }= \@array; | ||
| 546 : | my $display_ans = ""; | ||
| 547 : | |||
| 548 : | for( $i=0; $i < scalar(@array) ; $i ++ ) { | ||
| 549 : | $display_ans .= " ["; | ||
| 550 : | $rh_ans->{preview_text_string} .= ' ['; | ||
| 551 : | $rh_ans->{preview_latex_string} .= '\begin{pmatrix} '; | ||
| 552 : | for( $j = 0; $j < scalar( @{$array[$i]} ) ; $j++ ) { | ||
| 553 : | $display_ans .= " ["; | ||
| 554 : | $rh_ans->{preview_text_string} .= ' ['; | ||
| 555 : | for( $k = 0; $k < scalar( @{$array[$i][$j]} ) ; $k ++ ){ | ||
| 556 : | my $entry = $array[$i][$j][$k]; | ||
| 557 : | $entry = math_constants($entry); | ||
| 558 : | # This parser code was origianally taken from PGanswermacros::check_syntax | ||
| 559 : | # but parts of it needed to be slighty modified for this context | ||
| 560 : | my $parser = new AlgParserWithImplicitExpand; | ||
| 561 : | my $ret = $parser -> parse($entry); #for use with loops | ||
| 562 : | lr003k | 1123 | |
| 563 : | gage | 3314 | if ( ref($ret) ) { ## parsed successfully |
| 564 : | $parser -> tostring(); | ||
| 565 : | $parser -> normalize(); | ||
| 566 : | $entry = $parser -> tostring(); | ||
| 567 : | $rh_ans->{preview_text_string} .= $entry.","; | ||
| 568 : | $rh_ans->{preview_latex_string} .= $parser -> tolatex() . '& '; | ||
| 569 : | |||
| 570 : | } else { ## error in parsing | ||
| 571 : | $rh_ans->{'student_ans'} = 'syntax error:'.$display_ans. $parser->{htmlerror}, | ||
| 572 : | $rh_ans->{'ans_message'} = $display_ans.$parser -> {error_msg}, | ||
| 573 : | $rh_ans->{'preview_text_string'} = '', | ||
| 574 : | $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'.$display_ans.$parser->{htmlerror} . "$main::BR" .$parser -> {error_msg}.".$main::BR"); | ||
| 575 : | } | ||
| 576 : | |||
| 577 : | my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($entry); | ||
| 578 : | if ($PG_eval_errors) { | ||
| 579 : | $rh_ans->throw_error('EVAL','There is a syntax error in your answer.') ; | ||
| 580 : | $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors); | ||
| 581 : | last; | ||
| 582 : | } else { | ||
| 583 : | $entry = prfmt($inVal,$options{format}); | ||
| 584 : | $display_ans .= $entry.","; | ||
| 585 : | $array[$i][$j][$k] = $entry; | ||
| 586 : | } | ||
| 587 : | } | ||
| 588 : | chop($rh_ans->{preview_text_string}); | ||
| 589 : | chop($display_ans); | ||
| 590 : | $rh_ans->{preview_text_string} .= '] ,'; | ||
| 591 : | $rh_ans->{preview_latex_string} .= '\\\\'; | ||
| 592 : | $display_ans .= '] ,'; | ||
| 593 : | |||
| 594 : | } | ||
| 595 : | chop($rh_ans->{preview_text_string}); | ||
| 596 : | chop($display_ans); | ||
| 597 : | lr003k | 1123 | $rh_ans->{preview_text_string} .= '] ,'; |
| 598 : | lr003k | 1278 | $rh_ans->{preview_latex_string} .= '\end{pmatrix}'.' , '; |
| 599 : | gage | 3314 | $display_ans .= '] ,'; |
| 600 : | } | ||
| 601 : | chop($rh_ans->{preview_text_string}); | ||
| 602 : | chop($rh_ans->{preview_latex_string}); | ||
| 603 : | chop($rh_ans->{preview_latex_string}); | ||
| 604 : | chop($rh_ans->{preview_latex_string}); | ||
| 605 : | chop($display_ans); | ||
| 606 : | lr003k | 1278 | |
| 607 : | gage | 3314 | my @temp = (); |
| 608 : | for( $i = 0 ; $i < scalar( @array ); $i++ ){ | ||
| 609 : | push @temp , display_matrix($array[$i], 'left'=>'.', 'right'=>'.'); | ||
| 610 : | push @temp , "," unless $i == scalar(@array) - 1; | ||
| 611 : | } | ||
| 612 : | $rh_ans->{student_ans} = mbox(\@temp); | ||
| 613 : | $rh_ans->{ra_student_ans} = \@array; | ||
| 614 : | |||
| 615 : | $rh_ans; | ||
| 616 : | lr003k | 1123 | |
| 617 : | } | ||
| 618 : | |||
| 619 : | lr003k | 1265 | |
| 620 : | sub are_orthogonal_vecs{ | ||
| 621 : | gage | 3314 | my ($vec_ref , %opts) = @_; |
| 622 : | $vec_ref->{_filter_name} = 'are_orthogonal_vecs'; | ||
| 623 : | my @vecs = (); | ||
| 624 : | if( ref($vec_ref) eq 'AnswerHash' ) | ||
| 625 : | { | ||
| 626 : | @vecs = @{$vec_ref->{ra_student_ans}}; | ||
| 627 : | }else{ | ||
| 628 : | @vecs = @{$vec_ref}; | ||
| 629 : | } | ||
| 630 : | |||
| 631 : | my $num = scalar(@vecs); | ||
| 632 : | my $length = $vecs[0]->[1]; | ||
| 633 : | |||
| 634 : | for( my $i=0; $i < $num ; $i ++ ) { | ||
| 635 : | for( my $j = $i+1; $j < $num ; $j++ ) { | ||
| 636 : | if( $vecs[$i]->scalar_product($vecs[$j]) > $main::functZeroLevelTolDefault ) { | ||
| 637 : | if( ref( $vec_ref ) eq 'AnswerHash' ){ | ||
| 638 : | $vec_ref->{score} = 0; | ||
| 639 : | if( $vec_ref->{help} =~ /orthogonal|orthonormal|verbose/ ) | ||
| 640 : | { | ||
| 641 : | $vec_ref->throw_error('EVAL','You have entered vectors which are not orthogonal. '); | ||
| 642 : | }else{ | ||
| 643 : | $vec_ref->throw_error('EVAL'); | ||
| 644 : | } | ||
| 645 : | return $vec_ref; | ||
| 646 : | } else { | ||
| 647 : | return 0; | ||
| 648 : | } | ||
| 649 : | } | ||
| 650 : | } | ||
| 651 : | } | ||
| 652 : | if( ref( $vec_ref ) eq 'AnswerHash' ){ | ||
| 653 : | $vec_ref->{score} = 1; | ||
| 654 : | $vec_ref; | ||
| 655 : | } else { | ||
| 656 : | 1; | ||
| 657 : | } | ||
| 658 : | lr003k | 1265 | } |
| 659 : | |||
| 660 : | lr003k | 1327 | sub is_diagonal{ |
| 661 : | gage | 3314 | my $matrix = shift; |
| 662 : | my %options = @_; | ||
| 663 : | my $process_ans_hash = ( ref( $matrix ) eq 'AnswerHash' ) ? 1 : 0 ; | ||
| 664 : | my ($rh_ans); | ||
| 665 : | if ($process_ans_hash) { | ||
| 666 : | $rh_ans = $matrix; | ||
| 667 : | $matrix = $rh_ans->{ra_student_ans}; | ||
| 668 : | } | ||
| 669 : | lr003k | 1327 | |
| 670 : | gage | 3314 | return 0 unless defined($matrix); |
| 671 : | lr003k | 1327 | |
| 672 : | gage | 3314 | if( ref($matrix) eq 'ARRAY' ) { |
| 673 : | my @matrix = @{$matrix}; | ||
| 674 : | @matrix = @{$matrix[0]} if ref($matrix[0][0]) eq 'ARRAY'; | ||
| 675 : | if( ref($matrix[0]) ne 'ARRAY' or scalar( @matrix ) != scalar( @{$matrix[0]} ) ){ | ||
| 676 : | 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."; | ||
| 677 : | } | ||
| 678 : | |||
| 679 : | for( my $i = 0; $i < scalar( @matrix ) ; $i++ ) { | ||
| 680 : | for( my $j = 0; $j < scalar( @{$matrix[0]} ); $j++ ){ | ||
| 681 : | if( $matrix[$i][$j] != 0 and $i != $j ) | ||
| 682 : | { | ||
| 683 : | if ($process_ans_hash){ | ||
| 684 : | $rh_ans->throw_error('EVAL'); | ||
| 685 : | return $rh_ans; | ||
| 686 : | } else { | ||
| 687 : | return 0; | ||
| 688 : | } | ||
| 689 : | } | ||
| 690 : | } | ||
| 691 : | } | ||
| 692 : | if ($process_ans_hash){ | ||
| 693 : | return $rh_ans; | ||
| 694 : | } else { | ||
| 695 : | return 1; | ||
| 696 : | } | ||
| 697 : | } elsif ( ref($matrix) eq 'Matrix' ) { | ||
| 698 : | if( $matrix->[1] != $matrix->[2] ) { | ||
| 699 : | warn "It is impossible for a non-square matrix to be diagonal, if you are a student, please tell your professor that there is a problem."; | ||
| 700 : | if ($process_ans_hash){ | ||
| 701 : | $rh_ans->throw_error('EVAL'); | ||
| 702 : | return $rh_ans; | ||
| 703 : | } else { | ||
| 704 : | return 0; | ||
| 705 : | } | ||
| 706 : | } | ||
| 707 : | for( my $i = 0; $i < $matrix->[1] ; $i++ ) { | ||
| 708 : | for( my $j = 0; $j < $matrix->[2] ; $j++ ) { | ||
| 709 : | if( $matrix->[0][$i][$j] != 0 and $i != $j ){ | ||
| 710 : | if ($process_ans_hash){ | ||
| 711 : | $rh_ans->throw_error('EVAL'); | ||
| 712 : | return $rh_ans; | ||
| 713 : | } else { | ||
| 714 : | return 0; | ||
| 715 : | } | ||
| 716 : | } | ||
| 717 : | } | ||
| 718 : | } | ||
| 719 : | if ($process_ans_hash) { | ||
| 720 : | return $rh_ans; | ||
| 721 : | } else { | ||
| 722 : | return 1; | ||
| 723 : | } | ||
| 724 : | } else { | ||
| 725 : | warn "There is a problem with the problem, please alert your professor."; | ||
| 726 : | if ($process_ans_hash){ | ||
| 727 : | $rh_ans->throw_error('EVAL'); | ||
| 728 : | return $rh_ans; | ||
| 729 : | } else { | ||
| 730 : | return 0; | ||
| 731 : | } | ||
| 732 : | } | ||
| 733 : | lr003k | 1327 | |
| 734 : | } | ||
| 735 : | |||
| 736 : | |||
| 737 : | lr003k | 1265 | sub are_unit_vecs{ |
| 738 : | gage | 3314 | my ( $vec_ref,%opts ) = @_; |
| 739 : | $vec_ref->{_filter_name} = 'are_unit_vecs'; | ||
| 740 : | my @vecs = (); | ||
| 741 : | if( ref($vec_ref) eq 'AnswerHash' ) | ||
| 742 : | { | ||
| 743 : | @vecs = @{$vec_ref->{ra_student_ans}}; | ||
| 744 : | }else{ | ||
| 745 : | @vecs = @{$vec_ref}; | ||
| 746 : | } | ||
| 747 : | |||
| 748 : | my $i = 0; | ||
| 749 : | my $num = scalar(@vecs); | ||
| 750 : | my $length = $vecs[0]->[1]; | ||
| 751 : | |||
| 752 : | for( ; $i < $num ; $i ++ ) { | ||
| 753 : | if( abs(sqrt($vecs[$i]->scalar_product($vecs[$i]))- 1) > $main::functZeroLevelTolDefault ) | ||
| 754 : | { | ||
| 755 : | if( ref( $vec_ref ) eq 'AnswerHash' ){ | ||
| 756 : | $vec_ref->{score} = 0; | ||
| 757 : | if( $vec_ref->{help} =~ /unit|orthonormal|verbose/ ) | ||
| 758 : | { | ||
| 759 : | $vec_ref->throw_error('EVAL','You have entered vector(s) which are not of unit length.'); | ||
| 760 : | }else{ | ||
| 761 : | $vec_ref->throw_error('EVAL'); | ||
| 762 : | } | ||
| 763 : | return $vec_ref; | ||
| 764 : | }else{ | ||
| 765 : | return 0; | ||
| 766 : | } | ||
| 767 : | |||
| 768 : | } | ||
| 769 : | } | ||
| 770 : | |||
| 771 : | if( ref( $vec_ref ) eq 'AnswerHash' ){ | ||
| 772 : | $vec_ref->{score} = 1; | ||
| 773 : | $vec_ref; | ||
| 774 : | }else{ | ||
| 775 : | 1; | ||
| 776 : | } | ||
| 777 : | lr003k | 1265 | } |
| 778 : | |||
| 779 : | lr003k | 1274 | sub display_correct_vecs{ |
| 780 : | gage | 3314 | my ( $ra_vecs,%opts ) = @_; |
| 781 : | my @ra_vecs = @{$ra_vecs}; | ||
| 782 : | my @temp = (); | ||
| 783 : | |||
| 784 : | for( my $i = 0 ; $i < scalar(@ra_vecs) ; $i++ ) { | ||
| 785 : | push @temp, display_matrix(Matrix->new_from_col_vecs([$ra_vecs[$i]]),'left'=>'.','right'=>'.'); | ||
| 786 : | push @temp, ","; | ||
| 787 : | } | ||
| 788 : | |||
| 789 : | pop @temp; | ||
| 790 : | |||
| 791 : | mbox(\@temp); | ||
| 792 : | lr003k | 1274 | |
| 793 : | } | ||
| 794 : | |||
| 795 : | lr003k | 1294 | sub vec_solution_cmp{ |
| 796 : | gage | 3314 | my $correctAnswer = shift; |
| 797 : | my %opt = @_; | ||
| 798 : | lr003k | 1294 | |
| 799 : | gage | 3314 | set_default_options( \%opt, |
| 800 : | 'zeroLevelTol' => $main::functZeroLevelTolDefault, | ||
| 801 : | 'debug' => 0, | ||
| 802 : | 'mode' => 'basis', | ||
| 803 : | 'help' => 'none', | ||
| 804 : | ); | ||
| 805 : | |||
| 806 : | |||
| 807 : | lr003k | 1294 | ## This is where the correct answer should be checked someday. |
| 808 : | gage | 3314 | my $matrix = Matrix->new_from_col_vecs($correctAnswer); |
| 809 : | |||
| 810 : | |||
| 811 : | lr003k | 1294 | #construct the answer evaluator |
| 812 : | gage | 3314 | my $answer_evaluator = new AnswerEvaluator; |
| 813 : | lr003k | 1294 | |
| 814 : | gage | 3314 | $answer_evaluator->{debug} = $opt{debug}; |
| 815 : | $answer_evaluator->ans_hash( | ||
| 816 : | correct_ans => display_correct_vecs($correctAnswer), | ||
| 817 : | old_correct_ans => $correctAnswer, | ||
| 818 : | rm_correct_ans => $matrix, | ||
| 819 : | zeroLevelTol => $opt{zeroLevelTol}, | ||
| 820 : | debug => $opt{debug}, | ||
| 821 : | mode => $opt{mode}, | ||
| 822 : | help => $opt{help}, | ||
| 823 : | ); | ||
| 824 : | lr003k | 1294 | |
| 825 : | gage | 3314 | $answer_evaluator->install_pre_filter(\&ans_array_filter); |
| 826 : | $answer_evaluator->install_pre_filter( | ||
| 827 : | sub{ | ||
| 828 : | my ($rh_ans,@options) = @_; | ||
| 829 : | $rh_ans->{_filter_name} = "create student answer as an array of vectors"; | ||
| 830 : | my @student_array = @{$rh_ans->{ra_student_ans}}; | ||
| 831 : | my @array = (); | ||
| 832 : | for( my $i = 0; $i < scalar(@student_array) ; $i ++ ) { | ||
| 833 : | push( @array, Matrix->new_from_array_ref($student_array[$i])); | ||
| 834 : | } | ||
| 835 : | $rh_ans->{ra_student_ans} = \@array; | ||
| 836 : | $rh_ans; | ||
| 837 : | } | ||
| 838 : | ); | ||
| 839 : | #ra_student_ans is now the students answer as an array of vectors | ||
| 840 : | # anonymous subroutine to check dimension and length of the student vectors | ||
| 841 : | # if either is wrong, the answer is wrong. | ||
| 842 : | $answer_evaluator->install_pre_filter( | ||
| 843 : | sub{ | ||
| 844 : | my $rh_ans = shift; | ||
| 845 : | $rh_ans->{_filter_name} = "check_dimension_and_length"; | ||
| 846 : | my $length = $rh_ans->{rm_correct_ans}->[1]; | ||
| 847 : | my $dim = $rh_ans->{rm_correct_ans}->[2]; | ||
| 848 : | if( $dim != scalar(@{$rh_ans->{ra_student_ans}})) | ||
| 849 : | lr003k | 1294 | { |
| 850 : | gage | 3314 | |
| 851 : | lr003k | 1294 | $rh_ans->{score} = 0; |
| 852 : | gage | 3314 | if( $rh_ans->{help} =~ /dim|verbose/ ) |
| 853 : | lr003k | 1294 | { |
| 854 : | gage | 3314 | $rh_ans->throw_error('EVAL','You have entered the wrong number of vectors.'); |
| 855 : | lr003k | 1294 | }else{ |
| 856 : | $rh_ans->throw_error('EVAL'); | ||
| 857 : | } | ||
| 858 : | } | ||
| 859 : | gage | 3314 | for( my $i = 0; $i < scalar( @{$rh_ans->{ra_student_ans} }) ; $i++ ) { |
| 860 : | if( $length != $rh_ans->{ra_student_ans}->[$i]->[1]) { | ||
| 861 : | $rh_ans->{score} = 0; | ||
| 862 : | if( $rh_ans->{help} =~ /length|verbose/ ) { | ||
| 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 : | lr003k | 1294 | } |
| 868 : | gage | 3314 | } |
| 869 : | $rh_ans; | ||
| 870 : | } | ||
| 871 : | ); | ||
| 872 : | # Install prefilter for various modes | ||
| 873 : | if( $opt{mode} ne 'basis' ) { | ||
| 874 : | if( $opt{mode} =~ /orthogonal|orthonormal/ ) { | ||
| 875 : | $answer_evaluator->install_pre_filter(\&are_orthogonal_vecs); | ||
| 876 : | } | ||
| 877 : | |||
| 878 : | if( $opt{mode} =~ /unit|orthonormal/ ) { | ||
| 879 : | $answer_evaluator->install_pre_filter(\&are_unit_vecs); | ||
| 880 : | |||
| 881 : | } | ||
| 882 : | } | ||
| 883 : | |||
| 884 : | $answer_evaluator->install_evaluator(\&compare_vec_solution, %opt); | ||
| 885 : | |||
| 886 : | $answer_evaluator->install_post_filter( | ||
| 887 : | sub {my $rh_ans = shift; | ||
| 888 : | if ($rh_ans->catch_error('SYNTAX') ) { | ||
| 889 : | $rh_ans->{ans_message} = $rh_ans->{error_message}; | ||
| 890 : | $rh_ans->clear_error('SYNTAX'); | ||
| 891 : | } | ||
| 892 : | if ($rh_ans->catch_error('EVAL') ) { | ||
| 893 : | $rh_ans->{ans_message} = $rh_ans->{error_message}; | ||
| 894 : | $rh_ans->clear_error('EVAL'); | ||
| 895 : | } | ||
| 896 : | $rh_ans; | ||
| 897 : | } | ||
| 898 : | ); | ||
| 899 : | $answer_evaluator; | ||
| 900 : | |||
| 901 : | lr003k | 1294 | } |
| 902 : | |||
| 903 : | gage | 3314 | |
| 904 : | lr003k | 1294 | sub compare_vec_solution { |
| 905 : | gage | 3314 | my ( $rh_ans, %options ) = @_ ; |
| 906 : | $rh_ans->{_filter_name} = "compare_vec_solution"; | ||
| 907 : | my @space = @{$rh_ans->{ra_student_ans}}; | ||
| 908 : | my $solution = shift @space; | ||
| 909 : | |||
| 910 : | # A lot of the following code was taken from Matrix::proj_coeff | ||
| 911 : | # calling this method recursively would be a waste of time since | ||
| 912 : | # the prof's matrix never changes and solve_LR is an expensive | ||
| 913 : | # operation. This way it is only done once. | ||
| 914 : | my $matrix = $rh_ans->{rm_correct_ans}; | ||
| 915 : | my ($dim,$x_vector, $base_matrix); | ||
| 916 : | my $errors = undef; | ||
| 917 : | my $lin_space_tr= ~ $matrix; | ||
| 918 : | $matrix = $lin_space_tr * $matrix; | ||
| 919 : | my $matrix_lr = $matrix->decompose_LR(); | ||
| 920 : | |||
| 921 : | #this section determines whether or not the first vector, a solution to | ||
| 922 : | #the system, is a linear combination of the prof's vectors in which there | ||
| 923 : | #is a nonzero coefficient on the first term, the prof's solution to the system | ||
| 924 : | $solution = $lin_space_tr*$solution; | ||
| 925 : | ($dim,$x_vector, $base_matrix) = $matrix_lr->solve_LR($solution); | ||
| 926 : | #$rh_ans->{debug_compare_vec_solution} = $x_vector->element(1,1); | ||
| 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->element(1,1) -1) >= $options{zeroLevelTol} ) { | ||
| 932 : | # changes by MEG 6/24/05 | ||
| 933 : | # the student answer needs to be a linear combination of the instructors vectors | ||
| 934 : | # and the coefficient of the first vector needs to be 1 (it is NOT enough that it be non-zero). | ||
| 935 : | # if this is not the case, then the answer is wrong. | ||
| 936 : | # 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. | ||
| 937 : | |||
| 938 : | $rh_ans->{score} = 0; | ||
| 939 : | $rh_ans; | ||
| 940 : | } else { | ||
| 941 : | $rh_ans->{score} = 1; | ||
| 942 : | my @correct_space = @{$rh_ans->{old_correct_ans}}; | ||
| 943 : | shift @correct_space; | ||
| 944 : | $rh_ans->{rm_correct_ans} = Matrix->new_from_col_vecs(\@correct_space); | ||
| 945 : | $rh_ans->{ra_student_ans} = \@space; | ||
| 946 : | return compare_basis( $rh_ans, %options ); | ||
| 947 : | } | ||
| 948 : | lr003k | 1294 | } |
| 949 : | lr003k | 1327 | |
| 950 : | sh002i | 1534 | 1; |
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