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76 $B->assign($row2,$j,$scalar*$t1+$t2); 76 $B->assign($row2,$j,$scalar*$t1+$t2);
77 } 77 }
78 return $B; 78 return $B;
79} 79}
80 80
81=head3 basis_cmp()
82
83Compares a list of vectors by finding the change of coordinate matrix
84from the Prof's vectors to the students, and then taking the determinant of
85that to determine the existence of the change of coordinate matrix going the
86other way.
87
88ANS( basis_cmp( vectors_as_array_ref_in_array_ref, options_hash ) );
89
90 1. a reference to an array of correct vectors
91 2. a hash with the following keys (all optional):
92 mode -- 'basis' (default) (only a basis allowed)
93 'orthogonal' (only an orthogonal basis is allowed)
94 'unit' (only unit vectors in the basis allowed)
95 'orthonormal' (only orthogonal unit vectors in basis allowed)
96 zeroLevelTol -- absolute tolerance to allow when answer is close
97 to zero
98
99 debug -- if set to 1, provides verbose listing of
100 hash entries throughout fliters.
101
102 help -- 'none' (default) (is quiet on all errors)
103 'dim' (Tells student if wrong number of vectors are entered)
104 'length' (Tells student if there is a vector of the wrong length)
105 'orthogonal' (Tells student if their vectors are not orthogonal)
106 (This is only in orthogonal mode)
107 'unit' (Tells student if there is a vector not of unit length)
108 (This is only in unit mode)
109 'orthonormal' (Gives errors from orthogonal and orthonormal)
110 (This is only in orthonormal mode)
111 'verbose' (Gives all the above answer messages)
112
113 Returns an answer evaluator.
114
115EXAMPLES:
116
117 basis_cmp([[1,0,0],[0,1,0],[0,0,1]])
118 -- correct answer is any basis for R^3.
119 basis_cmp([1,0,2,0],[0,1,0,0], 'mode'=>orthonormal )
120 -- correct answer is any orthonormal basis
121 for this space such as:
122 [1/sqrt(3),0,2/sqrt(3),0],[0,1,0,0]
123
124=cut
125
126
127sub basis_cmp {
128 my $correctAnswer = shift;
129 my %opt = @_;
130
131 set_default_options( \%opt,
132 'zeroLevelTol' => $main::functZeroLevelTolDefault,
133 'debug' => 0,
134 'mode' => 'basis',
135 'help' => 'none',
136 );
137
138 # produce answer evaluator
139 BASIS_CMP(
140 'correct_ans' => $correctAnswer,
141 'zeroLevelTol' => $opt{'zeroLevelTol'},
142 'debug' => $opt{'debug'},
143 'mode' => $opt{'mode'},
144 'help' => $opt{'help'},
145 );
146}
147
148=head BASIS_CMP
149
150Made to keep the same format as num_cmp and fun_cmp.
151
152=cut
153
154sub BASIS_CMP {
155 my %mat_params = @_;
156 my $zeroLevelTol = $mat_params{'zeroLevelTol'};
157
158 # Check that everything is defined:
159 $mat_params{debug} = 0 unless defined($mat_params{debug});
160 $zeroLevelTol = $main::functZeroLevelTolDefault unless defined $zeroLevelTol;
161 $mat_params{'zeroLevelTol'} = $zeroLevelTol;
162
163## This is where the correct answer should be checked someday.
164 my $matrix = Matrix->new_from_col_vecs($mat_params{'correct_ans'});
165
166#construct the answer evaluator
167 my $answer_evaluator = new AnswerEvaluator;
168
169 $answer_evaluator->{debug} = $mat_params{debug};
170
171 $answer_evaluator->ans_hash( correct_ans => pretty_print($mat_params{correct_ans}),
172 rm_correct_ans => $matrix,
173 zeroLevelTol => $mat_params{zeroLevelTol},
174 debug => $mat_params{debug},
175 mode => $mat_params{mode},
176 help => $mat_params{help},
177 );
178
179 $answer_evaluator->install_pre_filter(sub {my $rh_ans = shift;
180 $rh_ans->{student_ans} =~ s/\s+//g; # remove all whitespace
181 $rh_ans;
182 });
183
184 $answer_evaluator->install_pre_filter(\&math_constants);
185 $answer_evaluator->install_pre_filter(\&vec_list_string);#ra_student_ans is now the students answer as an array of vectors
186 # anonymous subroutine to check dimension and length of the student vectors
187 # if either is wrong, the answer is wrong.
188 $answer_evaluator->install_pre_filter(sub{
189 my $rh_ans = shift;
190 my $length = $rh_ans->{rm_correct_ans}->[1];
191 my $dim = $rh_ans->{rm_correct_ans}->[2];
192 if( $dim != scalar(@{$rh_ans->{ra_student_ans}}))
193 {
194
195 $rh_ans->{score} = 0;
196 if( $rh_ans->{help} =~ /dim|verbose/ )
197 {
198 $rh_ans->throw_error('EVAL','You have entered the wrong number of vectors.');
199 }else{
200 $rh_ans->throw_error('EVAL');
201 }
202 }
203 for( my $i = 0; $i < scalar( @{$rh_ans->{ra_student_ans} }) ; $i++ )
204 {
205 if( $length != $rh_ans->{ra_student_ans}->[$i]->[1])
206 {
207 $rh_ans->{score} = 0;
208 if( $rh_ans->{help} =~ /length|verbose/ )
209 {
210 $rh_ans->throw_error('EVAL','You have entered vector(s) of the wrong length.');
211 }else{
212 $rh_ans->throw_error('EVAL');
213 }
214 }
215 }
216 $rh_ans;
217 });
218 # Install prefilter for various modes
219 if( $mat_params{mode} ne 'basis' )
220 {
221 if( $mat_params{mode} =~ /orthogonal|orthonormal/ )
222 {
223 $answer_evaluator->install_pre_filter(sub{
224 my $rh_ans = shift;
225 my @vecs = @{$rh_ans->{ra_student_ans}};
226 my ($i,$j) = (0,0);
227 my $num = scalar(@vecs);
228 my $length = $vecs[0]->[1];
229
230 for( ; $i < $num ; $i ++ )
231 {
232 for( $j = $i+1; $j < $num ; $j++ )
233 {
234 my $sum = 0;
235 my $k = 0;
236
237 for( ; $k < $length; $k++ ) {
238 $sum += $vecs[$i]->[0][$k][0]*$vecs[$j]->[0][$k][0];
239 }
240
241 if( $sum > $mat_params{zeroLevelTol} )
242 {
243 $rh_ans->{score} = 0;
244 if( $rh_ans->{help} =~ /orthogonal|orthonormal|verbose/ )
245 {
246 $rh_ans->throw_error('EVAL','You have entered vectors which are not orthogonal. ');
247 }else{
248 $rh_ans->throw_error('EVAL');
249 }
250 }
251 }
252 }
253
254
255 $rh_ans;
256 });
257 }
258
259 if( $mat_params{mode} =~ /unit|orthonormal/ )
260 {
261 $answer_evaluator->install_pre_filter(sub{
262 my $rh_ans = shift;
263 my @vecs = @{$rh_ans->{ra_student_ans}};
264 my $i = 0;
265 my $num = scalar(@vecs);
266 my $length = $vecs[0]->[1];
267
268 for( ; $i < $num ; $i ++ )
269 {
270 my $sum = 0;
271 my $k = 0;
272
273 for( ; $k < $length; $k++ ) {
274 $sum += $vecs[$i]->[0][$k][0]*$vecs[$i]->[0][$k][0];
275 }
276 if( abs(sqrt($sum) - 1) > $mat_params{zeroLevelTol} )
277 {
278 $rh_ans->{score} = 0;
279
280 if( $rh_ans->{help} =~ /unit|orthonormal|verbose/ )
281 {
282 $rh_ans->throw_error('EVAL','You have entered vector(s) which are not of unit length.');
283 }else{
284 $rh_ans->throw_error('EVAL');
285 }
286 }
287 }
288
289
290 $rh_ans;
291 });
292
293 }
294 }
295 $answer_evaluator->install_evaluator(\&compare_basis, %mat_params);
296 $answer_evaluator->install_post_filter(
297 sub {my $rh_ans = shift;
298 if ($rh_ans->catch_error('SYNTAX') ) {
299 $rh_ans->{ans_message} = $rh_ans->{error_message};
300 $rh_ans->clear_error('SYNTAX');
301 }
302 if ($rh_ans->catch_error('EVAL') ) {
303 $rh_ans->{ans_message} = $rh_ans->{error_message};
304 $rh_ans->clear_error('EVAL');
305 }
306 $rh_ans;
307 }
308 );
309 $answer_evaluator;
310}
311
312=head4 compare_basis
313
314 compare_basis( $ans_hash, %options);
315
316 {ra_student_ans}, # a reference to the array of students answer vectors
317 {rm_correct_ans}, # a reference to the correct answer matrix
318 %options
319 )
320
321=cut
322
323sub compare_basis {
324 my ($rh_ans, %options) = @_;
325 my @ch_coord;
326 my @vecs = @{$rh_ans->{ra_student_ans}};
327
328 # A lot of the follosing code was taken from Matrix::proj_coeff
329 # calling this method recursively would be a waste of time since
330 # the prof's matrix never changes and solve_LR is an expensive
331 # operation. This way it is only done once.
332 my $matrix = $rh_ans->{rm_correct_ans};
333 my ($dim,$x_vector, $base_matrix);
334 my $errors = undef;
335 my $lin_space_tr= ~ $matrix;
336 $matrix = $lin_space_tr * $matrix;
337 my $matrix_lr = $matrix->decompose_LR();
338
339 #finds the coefficient vectors for each of the students vectors
340 for( my $i = 0; $i < scalar(@{$rh_ans->{ra_student_ans}}) ; $i++ )
341 {
342
343 $vecs[$i] = $lin_space_tr*$vecs[$i];
344 ($dim,$x_vector, $base_matrix) = $matrix_lr->solve_LR($vecs[$i]);
345 push( @ch_coord, $x_vector );
346 $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 $dim; # only print if the dim is not zero.
347 }
348
349 if( defined($errors))
350 {
351 $rh_ans->throw_error('EVAL', $errors) ;
352 }else{
353 my $ch_coord_mat = Matrix->new_from_col_vecs(\@ch_coord);#creates change of coordinate matrix
354 #existence of this matrix implies that
355 #the all of the students answers are a
356 #linear combo of the prof's
357 $ch_coord_mat = $ch_coord_mat->decompose_LR();
358
359 if( $ch_coord_mat->det_LR() > $options{zeroLevelTol} )# if the det of the change of coordinate matrix is
360 # non-zero, this implies the existence of an inverse
361 # which implies all of the prof's vectors are a linear
362 # combo of the students vectors, showing containment
363 # both ways.
364 {
365 # I think sometimes if the students space has the same dimension as the profs space it
366 # will get projected into the profs space even if it isn't a basis for that space.
367 # this just checks that the prof's matrix times the change of coordinate matrix is actually
368 #the students matrix
369 if( abs(Matrix->new_from_col_vecs(\@{$rh_ans->{ra_student_ans}}) - ($rh_ans->{rm_correct_ans})*(Matrix->new_from_col_vecs(\@ch_coord))) < $options{zeroLevelTol} )
370 {
371 $rh_ans->{score} = 1;
372 }else{
373 $rh_ans->{score} = 0;
374 }
375 }
376 else{
377 $rh_ans->{score}=0;
378 }
379 }
380 $rh_ans;
381
382}
383
384
385=head 2 vec_list_string
386
387This is a check_syntax type method (in fact I borrowed some of that method's code) for vector input.
388The student needs to enter vectors like: [1,0,0],[1,2,3],[0,9/sqrt(10),1/sqrt(10)]
389Each entry can contain functions and operations and the usual math constants (pi and e).
390The vectors, however can not be added or multiplied or scalar multiplied by the student.
391Most 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.
392Right now the method basically ignores every thing outside the vectors. Also, an unmatched open parenthesis is caught,
393but a unmatched close parenthesis ends the vector, and since everything outside is ignored, no error is sent (other than the
394later when the length of the vectors is checked.
395In the end, the method returns an array of Matrix objects.
396
397
398=cut
399
400sub vec_list_string{
401 my $rh_ans = shift;
402 my %options = @_;
403 my $i;
404 my $entry = "";
405 my $char;
406 my @paren_stack;
407 my $length = length($rh_ans->{student_ans});
408 my @temp;
409 my $j = 0;
410 my @answers;
411 my $paren;
412 my $display_ans;
413
414 for( $i = 0; $i < $length ; $i++ )
415 {
416 $char = substr($rh_ans->{student_ans},$i,1);
417
418 if( $char =~ /\(|\[|\{/ ){
419 push( @paren_stack, $char )
420 }
421
422 if( !( $char =~ /\(|\[|\{/ && scalar(@paren_stack) == 1 ) )
423 {
424 if( $char !~ /,|\)|\]|\}/ ){
425 $entry .= $char;
426 }else{
427 if( $char =~ /,/ || ( $char =~ /\)|\]|\}/ && scalar(@paren_stack) == 1 ) )
428 {
429 if( length($entry) == 0 ){
430 if( $char !~ /,/ ){
431 $rh_ans->throw_error('EVAL','There is a syntax error in your answer');
432 }else{
433 $rh_ans->{preview_text_string} .= ",";
434 $rh_ans->{preview_latex_string} .= ",";
435 $display_ans .= ",";
436 }
437 }else{
438
439 # This parser code was origianally taken from PGanswermacros::check_syntax
440 # but parts of it needed to be slighty modified for this context
441 my $parser = new AlgParserWithImplicitExpand;
442 my $ret = $parser -> parse($entry); #for use with loops
443
444 if ( ref($ret) ) { ## parsed successfully
445 $parser -> tostring();
446 $parser -> normalize();
447 $entry = $parser -> tostring();
448 $rh_ans->{preview_text_string} .= $entry.",";
449 $rh_ans->{preview_latex_string} .= $parser -> tolatex().",";
450
451 } else { ## error in parsing
452
453 $rh_ans->{'student_ans'} = 'syntax error:'.$display_ans. $parser->{htmlerror},
454 $rh_ans->{'ans_message'} = $display_ans.$parser -> {error_msg},
455 $rh_ans->{'preview_text_string'} = '',
456 $rh_ans->{'preview_latex_string'} = '',
457 $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'.$display_ans.$parser->{htmlerror} . "$main::BR" .$parser -> {error_msg}.".$main::BR");
458 }
459
460 my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($entry);
461
462 if ($PG_eval_errors) {
463 $rh_ans->throw_error('EVAL','There is a syntax error in your answer.') ;
464 $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors);
465 last;
466 } else {
467 $entry = prfmt($inVal,$options{format});
468 $display_ans .= $entry.",";
469 push(@temp , $entry);
470 }
471
472 if( $char =~ /\)|\]|\}/ && scalar(@paren_stack) == 1)
473 {
474 pop @paren_stack;
475 chop($rh_ans->{preview_text_string});
476 chop($rh_ans->{preview_latex_string});
477 chop($display_ans);
478 $rh_ans->{preview_text_string} .= "]";
479 $rh_ans->{preview_latex_string} .= "]";
480 $display_ans .= "]";
481 if( scalar(@temp) > 0 )
482 {
483 push( @answers,Matrix->new_from_col_vecs([\@temp]));
484 while(scalar(@temp) > 0 ){
485 pop @temp;
486 }
487 }else{
488 $rh_ans->throw_error('EVAL','There is a syntax error in your answer.');
489 }
490 }
491 }
492 $entry = "";
493 }else{
494 $paren = pop @paren_stack;
495 if( scalar(@paren_stack) > 0 ){
496 #this uses ASCII to check if the parens match up
497 # in ASCII ord ( = 40 , ord ) = 41 , ord [ = 91 ,
498 # ord ] = 93 , ord { = 123 , ord } = 125
499 if( (ord($char) - ord($paren) <= 2) ){
500 $entry = $entry . $char;
501 }else{
502 $rh_ans->throw_error('EVAL','There is a syntax error in your answer');
503 }
504 }
505 }
506 }
507 }else{
508 $rh_ans->{preview_text_string} .= "[";
509 $rh_ans->{preview_latex_string} .= "[";
510 $display_ans .= "[";
511 }
512 }
513 $rh_ans->{ra_student_ans} = \@answers;
514 $rh_ans->{student_ans} = $display_ans unless $rh_ans->{error_flag};
515 $rh_ans;
516}
81 517
821; 5181;
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