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[WWcvs] pg: Fixed conceptual error in compare_vec_solution.
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From: Mike G. v. a. <we...@ma...> - 2005-06-24 19:13:10
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Log Message:
-----------
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
Tags:
----
rel-2-1-patches
Modified Files:
--------------
pg/macros:
PGmorematrixmacros.pl
Revision Data
-------------
Index: PGmorematrixmacros.pl
===================================================================
RCS file: /webwork/cvs/system/pg/macros/PGmorematrixmacros.pl,v
retrieving revision 1.17
retrieving revision 1.17.8.1
diff -Lmacros/PGmorematrixmacros.pl -Lmacros/PGmorematrixmacros.pl -u -r1.17 -r1.17.8.1
--- macros/PGmorematrixmacros.pl
+++ macros/PGmorematrixmacros.pl
@@ -1,5 +1,5 @@
BEGIN{
- be_strict();
+ be_strict();
}
sub _PGmorematrixmacros_init{}
@@ -31,24 +31,24 @@
=cut
sub random_diag_matrix{ ## Builds and returns a random diagonal \$n by \$n matrix
-
- warn "Usage: \$new_matrix = random_diag_matrix(\$n)" if (@_ != 1);
-
- my $D = new Matrix($_[0],$_[0]);
- my $norm = 0;
- while( $norm == 0 ){
- foreach my $i (1..$_[0]){
- foreach my $j (1..$_[0]){
- if( $i != $j ){
- $D->assign($i,$j,0);
- }else{
- $D->assign($i,$j,random(-9,9,1));
- }
- }
- }
- $norm = abs($D);
- }
- return $D;
+
+ warn "Usage: \$new_matrix = random_diag_matrix(\$n)" if (@_ != 1);
+
+ my $D = new Matrix($_[0],$_[0]);
+ my $norm = 0;
+ while( $norm == 0 ){
+ foreach my $i (1..$_[0]){
+ foreach my $j (1..$_[0]){
+ if( $i != $j ){
+ $D->assign($i,$j,0);
+ }else{
+ $D->assign($i,$j,random(-9,9,1));
+ }
+ }
+ }
+ $norm = abs($D);
+ }
+ return $D;
}
sub swap_rows{
@@ -112,62 +112,62 @@
ANS( basis_cmp( vectors_as_array_ref_in_array_ref, options_hash ) );
- 1. a reference to an array of correct vectors
- 2. a hash with the following keys (all optional):
- mode -- 'basis' (default) (only a basis allowed)
- 'orthogonal' (only an orthogonal basis is allowed)
- 'unit' (only unit vectors in the basis allowed)
- 'orthonormal' (only orthogonal unit vectors in basis allowed)
- zeroLevelTol -- absolute tolerance to allow when answer is close
- to zero
-
- debug -- if set to 1, provides verbose listing of
- hash entries throughout fliters.
-
- help -- 'none' (default) (is quiet on all errors)
- 'dim' (Tells student if wrong number of vectors are entered)
- 'length' (Tells student if there is a vector of the wrong length)
- 'orthogonal' (Tells student if their vectors are not orthogonal)
- (This is only in orthogonal mode)
- 'unit' (Tells student if there is a vector not of unit length)
- (This is only in unit mode)
- 'orthonormal' (Gives errors from orthogonal and orthonormal)
- (This is only in orthonormal mode)
- 'verbose' (Gives all the above answer messages)
+ 1. a reference to an array of correct vectors
+ 2. a hash with the following keys (all optional):
+ mode -- 'basis' (default) (only a basis allowed)
+ 'orthogonal' (only an orthogonal basis is allowed)
+ 'unit' (only unit vectors in the basis allowed)
+ 'orthonormal' (only orthogonal unit vectors in basis allowed)
+ zeroLevelTol -- absolute tolerance to allow when answer is close
+ to zero
+
+ debug -- if set to 1, provides verbose listing of
+ hash entries throughout fliters.
+
+ help -- 'none' (default) (is quiet on all errors)
+ 'dim' (Tells student if wrong number of vectors are entered)
+ 'length' (Tells student if there is a vector of the wrong length)
+ 'orthogonal' (Tells student if their vectors are not orthogonal)
+ (This is only in orthogonal mode)
+ 'unit' (Tells student if there is a vector not of unit length)
+ (This is only in unit mode)
+ 'orthonormal' (Gives errors from orthogonal and orthonormal)
+ (This is only in orthonormal mode)
+ 'verbose' (Gives all the above answer messages)
- Returns an answer evaluator.
+ Returns an answer evaluator.
EXAMPLES:
- basis_cmp([[1,0,0],[0,1,0],[0,0,1]])
- -- correct answer is any basis for R^3.
- basis_cmp([1,0,2,0],[0,1,0,0], 'mode'=>orthonormal )
- -- correct answer is any orthonormal basis
- for this space such as:
- [1/sqrt(3),0,2/sqrt(3),0],[0,1,0,0]
+ basis_cmp([[1,0,0],[0,1,0],[0,0,1]])
+ -- correct answer is any basis for R^3.
+ basis_cmp([1,0,2,0],[0,1,0,0], 'mode'=>orthonormal )
+ -- correct answer is any orthonormal basis
+ for this space such as:
+ [1/sqrt(3),0,2/sqrt(3),0],[0,1,0,0]
=cut
sub basis_cmp {
- my $correctAnswer = shift;
- my %opt = @_;
+ my $correctAnswer = shift;
+ my %opt = @_;
- set_default_options( \%opt,
- 'zeroLevelTol' => $main::functZeroLevelTolDefault,
- 'debug' => 0,
- 'mode' => 'basis',
- 'help' => 'none',
- );
-
- # produce answer evaluator
- BASIS_CMP(
- 'correct_ans' => $correctAnswer,
- 'zeroLevelTol' => $opt{'zeroLevelTol'},
- 'debug' => $opt{'debug'},
- 'mode' => $opt{'mode'},
- 'help' => $opt{'help'},
- );
+ set_default_options( \%opt,
+ 'zeroLevelTol' => $main::functZeroLevelTolDefault,
+ 'debug' => 0,
+ 'mode' => 'basis',
+ 'help' => 'none',
+ );
+
+ # produce answer evaluator
+ BASIS_CMP(
+ 'correct_ans' => $correctAnswer,
+ 'zeroLevelTol' => $opt{'zeroLevelTol'},
+ 'debug' => $opt{'debug'},
+ 'mode' => $opt{'mode'},
+ 'help' => $opt{'help'},
+ );
}
=head BASIS_CMP
@@ -177,193 +177,199 @@
=cut
sub BASIS_CMP {
- my %mat_params = @_;
- my $zeroLevelTol = $mat_params{'zeroLevelTol'};
-
- # Check that everything is defined:
- $mat_params{debug} = 0 unless defined($mat_params{debug});
- $zeroLevelTol = $main::functZeroLevelTolDefault unless defined $zeroLevelTol;
- $mat_params{'zeroLevelTol'} = $zeroLevelTol;
+ my %mat_params = @_;
+ my $zeroLevelTol = $mat_params{'zeroLevelTol'};
+
+ # Check that everything is defined:
+ $mat_params{debug} = 0 unless defined($mat_params{debug});
+ $zeroLevelTol = $main::functZeroLevelTolDefault unless defined $zeroLevelTol;
+ $mat_params{'zeroLevelTol'} = $zeroLevelTol;
## This is where the correct answer should be checked someday.
- my $matrix = Matrix->new_from_col_vecs($mat_params{'correct_ans'});
+ my $matrix = Matrix->new_from_col_vecs($mat_params{'correct_ans'});
#construct the answer evaluator
- my $answer_evaluator = new AnswerEvaluator;
+ my $answer_evaluator = new AnswerEvaluator;
$answer_evaluator->{debug} = $mat_params{debug};
- $answer_evaluator->ans_hash(
- correct_ans => display_correct_vecs($mat_params{correct_ans}),
- rm_correct_ans => $matrix,
- zeroLevelTol => $mat_params{zeroLevelTol},
- debug => $mat_params{debug},
- mode => $mat_params{mode},
- help => $mat_params{help},
+ $answer_evaluator->ans_hash(
+ correct_ans => display_correct_vecs($mat_params{correct_ans}),
+ rm_correct_ans => $matrix,
+ zeroLevelTol => $mat_params{zeroLevelTol},
+ debug => $mat_params{debug},
+ mode => $mat_params{mode},
+ help => $mat_params{help},
);
- $answer_evaluator->install_pre_filter(
- sub {my $rh_ans = shift;
- $rh_ans->{_filter_name} = 'remove_white_space';
- $rh_ans->{student_ans} =~ s/\s+//g; # remove all whitespace
- $rh_ans;
- }
- );
- $answer_evaluator->install_pre_filter(
- sub{my $rh_ans = shift;
- my @options = @_;
- $rh_ans->{_filter_name} = 'mung_student_answer';
- if( $rh_ans->{ans_label} =~ /ArRaY/ ){
- $rh_ans = ans_array_filter($rh_ans,@options);
- my @student_array = @{$rh_ans->{ra_student_ans}};
- my @array = ();
- for( my $i = 0; $i < scalar(@student_array) ; $i ++ )
- {
- push( @array, Matrix->new_from_array_ref($student_array[$i]));
- }
- $rh_ans->{ra_student_ans} = \@array;
- $rh_ans;
- }else{
- $rh_ans->{student_ans} = math_constants($rh_ans->{student_ans});
- vec_list_string($rh_ans, '_filter_name' => 'vec_list_string', @options);
- }
- }
- );#ra_student_ans is now the students answer as an array of vectors
- # anonymous subroutine to check dimension and length of the student vectors
- # if either is wrong, the answer is wrong.
- $answer_evaluator->install_pre_filter(
- sub{
- my $rh_ans = shift;
- $rh_ans->{_filter_name} = 'check_vector_size';
- my $length = $rh_ans->{rm_correct_ans}->[1];
- my $dim = $rh_ans->{rm_correct_ans}->[2];
- if( $dim != scalar(@{$rh_ans->{ra_student_ans}}))
- {
-
- $rh_ans->{score} = 0;
- if( $rh_ans->{help} =~ /dim|verbose/ )
- {
- $rh_ans->throw_error('EVAL','You have entered the wrong number of vectors.');
- }else{
- $rh_ans->throw_error('EVAL');
- }
- }
- for( my $i = 0; $i < scalar( @{$rh_ans->{ra_student_ans} }) ; $i++ )
- {
- if( $length != $rh_ans->{ra_student_ans}->[$i]->[1])
- {
- $rh_ans->{score} = 0;
- if( $rh_ans->{help} =~ /length|verbose/ )
- {
- $rh_ans->throw_error('EVAL','You have entered vector(s) of the wrong length.');
- }else{
- $rh_ans->throw_error('EVAL');
- }
- }
- }
- $rh_ans;
- }
- );
- # Install prefilter for various modes
- if( $mat_params{mode} ne 'basis' )
- {
- if( $mat_params{mode} =~ /orthogonal|orthonormal/ )
- {
- $answer_evaluator->install_pre_filter(\&are_orthogonal_vecs);
- }
-
- if( $mat_params{mode} =~ /unit|orthonormal/ )
- {
- $answer_evaluator->install_pre_filter(\&are_unit_vecs);
-
- }
- }
- $answer_evaluator->install_evaluator(\&compare_basis, %mat_params);
- $answer_evaluator->install_post_filter(
- sub {my $rh_ans = shift;
- if ($rh_ans->catch_error('SYNTAX') ) {
- $rh_ans->{ans_message} = $rh_ans->{error_message};
- $rh_ans->clear_error('SYNTAX');
- }
- if ($rh_ans->catch_error('EVAL') ) {
- $rh_ans->{ans_message} = $rh_ans->{error_message};
- $rh_ans->clear_error('EVAL');
- }
- $rh_ans;
- }
- );
- $answer_evaluator;
+ $answer_evaluator->install_pre_filter(
+ sub {my $rh_ans = shift;
+ $rh_ans->{_filter_name} = 'remove_white_space';
+ $rh_ans->{student_ans} =~ s/\s+//g; # remove all whitespace
+ $rh_ans;
+ }
+ );
+ $answer_evaluator->install_pre_filter(
+ sub{my $rh_ans = shift;
+ my @options = @_;
+ $rh_ans->{_filter_name} = 'mung_student_answer';
+ if( $rh_ans->{ans_label} =~ /ArRaY/ ){
+ $rh_ans = ans_array_filter($rh_ans,@options);
+ my @student_array = @{$rh_ans->{ra_student_ans}};
+ my @array = ();
+ for( my $i = 0; $i < scalar(@student_array) ; $i ++ )
+ {
+ push( @array, Matrix->new_from_array_ref($student_array[$i]));
+ }
+ $rh_ans->{ra_student_ans} = \@array;
+ $rh_ans;
+ }else{
+ $rh_ans->{student_ans} = math_constants($rh_ans->{student_ans});
+ vec_list_string($rh_ans, '_filter_name' => 'vec_list_string', @options);
+ }
+ }
+ );#ra_student_ans is now the students answer as an array of vectors
+ # anonymous subroutine to check dimension and length of the student vectors
+ # if either is wrong, the answer is wrong.
+ $answer_evaluator->install_pre_filter(
+ sub{
+ my $rh_ans = shift;
+ $rh_ans->{_filter_name} = 'check_vector_size';
+ my $length = $rh_ans->{rm_correct_ans}->[1];
+ my $dim = $rh_ans->{rm_correct_ans}->[2];
+ if( $dim != scalar(@{$rh_ans->{ra_student_ans}}))
+ {
+
+ $rh_ans->{score} = 0;
+ if( $rh_ans->{help} =~ /dim|verbose/ )
+ {
+ $rh_ans->throw_error('EVAL','You have entered the wrong number of vectors.');
+ }else{
+ $rh_ans->throw_error('EVAL');
+ }
+ }
+ for( my $i = 0; $i < scalar( @{$rh_ans->{ra_student_ans} }) ; $i++ )
+ {
+ if( $length != $rh_ans->{ra_student_ans}->[$i]->[1])
+ {
+ $rh_ans->{score} = 0;
+ if( $rh_ans->{help} =~ /length|verbose/ )
+ {
+ $rh_ans->throw_error('EVAL','You have entered vector(s) of the wrong length.');
+ }else{
+ $rh_ans->throw_error('EVAL');
+ }
+ }
+ }
+ $rh_ans;
+ }
+ );
+ # Install prefilter for various modes
+ if( $mat_params{mode} ne 'basis' )
+ {
+ if( $mat_params{mode} =~ /orthogonal|orthonormal/ )
+ {
+ $answer_evaluator->install_pre_filter(\&are_orthogonal_vecs);
+ }
+
+ if( $mat_params{mode} =~ /unit|orthonormal/ )
+ {
+ $answer_evaluator->install_pre_filter(\&are_unit_vecs);
+
+ }
+ }
+ $answer_evaluator->install_evaluator(\&compare_basis, %mat_params);
+ $answer_evaluator->install_post_filter(
+ sub {my $rh_ans = shift;
+ if ($rh_ans->catch_error('SYNTAX') ) {
+ $rh_ans->{ans_message} = $rh_ans->{error_message};
+ $rh_ans->clear_error('SYNTAX');
+ }
+ if ($rh_ans->catch_error('EVAL') ) {
+ $rh_ans->{ans_message} = $rh_ans->{error_message};
+ $rh_ans->clear_error('EVAL');
+ }
+ $rh_ans;
+ }
+ );
+ $answer_evaluator;
}
=head4 compare_basis
- compare_basis( $ans_hash, %options);
+ compare_basis( $ans_hash,
+ %options
+ ra_student_ans # a reference to the array of students answer vectors
+ rm_correct_ans, # a reference to the correct answer matrix
+ %options
+ )
- {ra_student_ans}, # a reference to the array of students answer vectors
- {rm_correct_ans}, # a reference to the correct answer matrix
- %options
- )
=cut
+
+
sub compare_basis {
- my ($rh_ans, %options) = @_;
- my @ch_coord;
- my @vecs = @{$rh_ans->{ra_student_ans}};
-
- # A lot of the follosing code was taken from Matrix::proj_coeff
- # calling this method recursively would be a waste of time since
- # the prof's matrix never changes and solve_LR is an expensive
- # operation. This way it is only done once.
- my $matrix = $rh_ans->{rm_correct_ans};
- my ($dim,$x_vector, $base_matrix);
- my $errors = undef;
- my $lin_space_tr= ~ $matrix;
- $matrix = $lin_space_tr * $matrix;
- my $matrix_lr = $matrix->decompose_LR();
-
- #finds the coefficient vectors for each of the students vectors
- for( my $i = 0; $i < scalar(@{$rh_ans->{ra_student_ans}}) ; $i++ )
- {
-
- $vecs[$i] = $lin_space_tr*$vecs[$i];
- ($dim,$x_vector, $base_matrix) = $matrix_lr->solve_LR($vecs[$i]);
- push( @ch_coord, $x_vector );
- $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 $dim; # only print if the dim is not zero.
- }
-
- if( defined($errors))
- {
- $rh_ans->throw_error('EVAL', $errors) ;
- }else{
- my $ch_coord_mat = Matrix->new_from_col_vecs(\@ch_coord);#creates change of coordinate matrix
- #existence of this matrix implies that
- #the all of the students answers are a
- #linear combo of the prof's
- $ch_coord_mat = $ch_coord_mat->decompose_LR();
-
- if( abs($ch_coord_mat->det_LR()) > $options{zeroLevelTol} )# if the det of the change of coordinate matrix is
- # non-zero, this implies the existence of an inverse
- # which implies all of the prof's vectors are a linear
- # combo of the students vectors, showing containment
- # both ways.
- {
- # I think sometimes if the students space has the same dimension as the profs space it
- # will get projected into the profs space even if it isn't a basis for that space.
- # this just checks that the prof's matrix times the change of coordinate matrix is actually
- #the students matrix
- if( abs(Matrix->new_from_col_vecs(\@{$rh_ans->{ra_student_ans}}) - ($rh_ans->{rm_correct_ans})*(Matrix->new_from_col_vecs(\@ch_coord))) < $options{zeroLevelTol} )
- {
- $rh_ans->{score} = 1;
- }else{
- $rh_ans->{score} = 0;
- }
- }
- else{
- $rh_ans->{score}=0;
- }
- }
- $rh_ans;
-
+ my ($rh_ans, %options) = @_;
+ $rh_ans->{_filter_name} = "compare_basis";
+ my @ch_coord;
+ my @vecs = @{$rh_ans->{ra_student_ans}};
+
+ # A lot of the following code was taken from Matrix::proj_coeff
+ # calling this method recursively would be a waste of time since
+ # the prof's matrix never changes and solve_LR is an expensive
+ # operation. This way it is only done once.
+ my $matrix = $rh_ans->{rm_correct_ans};
+ my ($dim,$x_vector, $base_matrix);
+ my $errors = undef;
+ my $lin_space_tr= ~ $matrix; #transpose of the matrix
+ $matrix = $lin_space_tr * $matrix; #(~A * A)
+ my $matrix_lr = $matrix->decompose_LR();
+
+ #finds the coefficient vectors for each of the students vectors
+ for( my $i = 0; $i < scalar(@{$rh_ans->{ra_student_ans}}) ; $i++ ) {
+
+ $vecs[$i] = $lin_space_tr*$vecs[$i];
+ ($dim,$x_vector, $base_matrix) = $matrix_lr->solve_LR($vecs[$i]);
+ push( @ch_coord, $x_vector );
+ $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 $dim; # only print if the dim is not zero.
+ }
+
+ if( defined($errors)) {
+ $rh_ans->throw_error('EVAL', $errors) ;
+ } else {
+ my $ch_coord_mat = Matrix->new_from_col_vecs(\@ch_coord);
+ #creates change of coordinate matrix
+ #existence of this matrix implies that
+ #the all of the students answers are a
+ #linear combo of the prof's
+ $ch_coord_mat = $ch_coord_mat->decompose_LR();
+
+ if( abs($ch_coord_mat->det_LR()) > $options{zeroLevelTol} ) {
+ # if the det of the change of coordinate matrix is
+ # non-zero, this implies the existence of an inverse
+ # which implies all of the prof's vectors are a linear
+ # combo of the students vectors, showing containment
+ # both ways.
+
+ # I think sometimes if the students space has the same dimension as the profs space it
+ # will get projected into the profs space even if it isn't a basis for that space.
+ # this just checks that the prof's matrix times the change of coordinate matrix is actually
+ #the students matrix
+ if( abs(Matrix->new_from_col_vecs(\@{$rh_ans->{ra_student_ans}}) -
+ ($rh_ans->{rm_correct_ans})*(Matrix->new_from_col_vecs(\@ch_coord)))
+ < $options{zeroLevelTol} ) {
+ $rh_ans->{score} = 1;
+ } else {
+ $rh_ans->{score} = 0;
+ }
+ } else {
+ $rh_ans->{score}=0;
+ }
+ }
+ $rh_ans;
+
}
@@ -378,568 +384,565 @@
but a unmatched close parenthesis ends the vector, and since everything outside is ignored, no error is sent (other than the
later when the length of the vectors is checked.
In the end, the method returns an array of Matrix objects.
-
+
=cut
sub vec_list_string{
- my $rh_ans = shift;
- my %options = @_;
- my $i;
- my $entry = "";
- my $char;
- my @paren_stack;
- my $length = length($rh_ans->{student_ans});
- my @temp;
- my $j = 0;
- my @answers;
- my $paren;
- my $display_ans;
-
- for( $i = 0; $i < $length ; $i++ )
- {
- $char = substr($rh_ans->{student_ans},$i,1);
-
- if( $char =~ /\(|\[|\{/ ){
- push( @paren_stack, $char )
- }
-
- if( !( $char =~ /\(|\[|\{/ && scalar(@paren_stack) == 1 ) )
- {
- if( $char !~ /,|\)|\]|\}/ ){
- $entry .= $char;
- }else{
- if( $char =~ /,/ || ( $char =~ /\)|\]|\}/ && scalar(@paren_stack) == 1 ) )
- {
- if( length($entry) == 0 ){
- if( $char !~ /,/ ){
- $rh_ans->throw_error('EVAL','There is a syntax error in your answer');
- }else{
- $rh_ans->{preview_text_string} .= ",";
- $rh_ans->{preview_latex_string} .= ",";
- $display_ans .= ",";
- }
- }else{
-
- # This parser code was origianally taken from PGanswermacros::check_syntax
- # but parts of it needed to be slighty modified for this context
- my $parser = new AlgParserWithImplicitExpand;
- my $ret = $parser -> parse($entry); #for use with loops
-
- if ( ref($ret) ) { ## parsed successfully
- $parser -> tostring();
- $parser -> normalize();
- $entry = $parser -> tostring();
- $rh_ans->{preview_text_string} .= $entry.",";
- $rh_ans->{preview_latex_string} .= $parser -> tolatex().",";
-
- } else { ## error in parsing
-
- $rh_ans->{'student_ans'} = 'syntax error:'.$display_ans. $parser->{htmlerror},
- $rh_ans->{'ans_message'} = $display_ans.$parser -> {error_msg},
- $rh_ans->{'preview_text_string'} = '',
- $rh_ans->{'preview_latex_string'} = '',
- $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'.$display_ans.$parser->{htmlerror} . "$main::BR" .$parser -> {error_msg}.".$main::BR");
- }
-
- my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($entry);
-
- if ($PG_eval_errors) {
- $rh_ans->throw_error('EVAL','There is a syntax error in your answer.') ;
- $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors);
- last;
- } else {
- $entry = prfmt($inVal,$options{format});
- $display_ans .= $entry.",";
- push(@temp , $entry);
- }
-
- if( $char =~ /\)|\]|\}/ && scalar(@paren_stack) == 1)
- {
- pop @paren_stack;
- chop($rh_ans->{preview_text_string});
- chop($rh_ans->{preview_latex_string});
- chop($display_ans);
- $rh_ans->{preview_text_string} .= "]";
- $rh_ans->{preview_latex_string} .= "]";
- $display_ans .= "]";
- if( scalar(@temp) > 0 )
- {
- push( @answers,Matrix->new_from_col_vecs([\@temp]));
- while(scalar(@temp) > 0 ){
- pop @temp;
- }
- }else{
- $rh_ans->throw_error('EVAL','There is a syntax error in your answer.');
- }
- }
- }
- $entry = "";
- }else{
- $paren = pop @paren_stack;
- if( scalar(@paren_stack) > 0 ){
- #this uses ASCII to check if the parens match up
- # in ASCII ord ( = 40 , ord ) = 41 , ord [ = 91 ,
- # ord ] = 93 , ord { = 123 , ord } = 125
- if( (ord($char) - ord($paren) <= 2) ){
- $entry = $entry . $char;
- }else{
- $rh_ans->throw_error('EVAL','There is a syntax error in your answer');
- }
- }
- }
- }
- }else{
- $rh_ans->{preview_text_string} .= "[";
- $rh_ans->{preview_latex_string} .= "[";
- $display_ans .= "[";
- }
- }
- $rh_ans->{ra_student_ans} = \@answers;
- $rh_ans->{student_ans} = $display_ans unless $rh_ans->{error_flag};
- $rh_ans;
+ my $rh_ans = shift;
+ my %options = @_;
+ my $i;
+ my $entry = "";
+ my $char;
+ my @paren_stack;
+ my $length = length($rh_ans->{student_ans});
+ my @temp;
+ my $j = 0;
+ my @answers;
+ my $paren;
+ my $display_ans;
+
+ for( $i = 0; $i < $length ; $i++ ) {
+ $char = substr($rh_ans->{student_ans},$i,1);
+
+ if( $char =~ /\(|\[|\{/ ){
+ push( @paren_stack, $char )
+ }
+
+ if( !( $char =~ /\(|\[|\{/ && scalar(@paren_stack) == 1 ) ) {
+ if( $char !~ /,|\)|\]|\}/ ){
+ $entry .= $char;
+ } else {
+ if( $char =~ /,/ || ( $char =~ /\)|\]|\}/ && scalar(@paren_stack) == 1 ) ) {
+ if( length($entry) == 0 ){
+ if( $char !~ /,/ ){
+ $rh_ans->throw_error('EVAL','There is a syntax error in your answer');
+ } else {
+ $rh_ans->{preview_text_string} .= ",";
+ $rh_ans->{preview_latex_string} .= ",";
+ $display_ans .= ",";
+ }
+ } else {
+
+ # This parser code was origianally taken from PGanswermacros::check_syntax
+ # but parts of it needed to be slighty modified for this context
+ my $parser = new AlgParserWithImplicitExpand;
+ my $ret = $parser -> parse($entry); #for use with loops
+
+ if ( ref($ret) ) { ## parsed successfully
+ $parser -> tostring();
+ $parser -> normalize();
+ $entry = $parser -> tostring();
+ $rh_ans->{preview_text_string} .= $entry.",";
+ $rh_ans->{preview_latex_string} .= $parser -> tolatex().",";
+
+ } else { ## error in parsing
+
+ $rh_ans->{'student_ans'} = 'syntax error:'.$display_ans. $parser->{htmlerror},
+ $rh_ans->{'ans_message'} = $display_ans.$parser -> {error_msg},
+ $rh_ans->{'preview_text_string'} = '',
+ $rh_ans->{'preview_latex_string'} = '',
+ $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'.$display_ans.$parser->{htmlerror} . "$main::BR" .$parser -> {error_msg}.".$main::BR");
+ }
+
+ my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($entry);
+
+ if ($PG_eval_errors) {
+ $rh_ans->throw_error('EVAL','There is a syntax error in your answer.') ;
+ $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors);
+ last;
+ } else {
+ $entry = prfmt($inVal,$options{format});
+ $display_ans .= $entry.",";
+ push(@temp , $entry);
+ }
+
+ if( $char =~ /\)|\]|\}/ && scalar(@paren_stack) == 1) {
+ pop @paren_stack;
+ chop($rh_ans->{preview_text_string});
+ chop($rh_ans->{preview_latex_string});
+ chop($display_ans);
+ $rh_ans->{preview_text_string} .= "]";
+ $rh_ans->{preview_latex_string} .= "]";
+ $display_ans .= "]";
+ if( scalar(@temp) > 0 ) {
+ push( @answers,Matrix->new_from_col_vecs([\@temp]));
+ while(scalar(@temp) > 0 ){
+ pop @temp;
+ }
+ } else {
+ $rh_ans->throw_error('EVAL','There is a syntax error in your answer.');
+ }
+ }
+ }
+ $entry = "";
+ } else {
+ $paren = pop @paren_stack;
+ if( scalar(@paren_stack) > 0 ){
+ #this uses ASCII to check if the parens match up
+ # in ASCII ord ( = 40 , ord ) = 41 , ord [ = 91 ,
+ # ord ] = 93 , ord { = 123 , ord } = 125
+ if( (ord($char) - ord($paren) <= 2) ){
+ $entry = $entry . $char;
+ }else{
+ $rh_ans->throw_error('EVAL','There is a syntax error in your answer');
+ }
+ }
+ }
+ }
+ } else {
+ $rh_ans->{preview_text_string} .= "[";
+ $rh_ans->{preview_latex_string} .= "[";
+ $display_ans .= "[";
+ }
+ }
+ $rh_ans->{ra_student_ans} = \@answers;
+ $rh_ans->{student_ans} = $display_ans unless $rh_ans->{error_flag};
+ $rh_ans;
}
=head5
- This filter was created to get, format, and evaluate each entry of the ans_array and ans_array_extension
- answer entry methods. Running this filter is necessary to get all the entries out of the answer
- hash. Each entry is evaluated and the resulting number is put in the display for student answer
- as a string. For evaluation purposes an array of arrays of arrays is created called ra_student_ans
- and placed in the hash. The entries are [array_number][row_number][column_number]. The latex strings
- for each entry are taken from the parser and put, as a matrix, into the previewer. The preview text
- string is also created, but this display method becomes confusing when large matrices are used.
+
+ This filter was created to get, format, and evaluate each entry of the ans_array and ans_array_extension
+ answer entry methods. Running this filter is necessary to get all the entries out of the answer
+ hash. Each entry is evaluated and the resulting number is put in the display for student answer
+ as a string. For evaluation purposes an array of arrays of arrays is created called ra_student_ans
+ and placed in the hash. The entries are [array_number][row_number][column_number]. The latex strings
+ for each entry are taken from the parser and put, as a matrix, into the previewer. The preview text
+ string is also created, but this display method becomes confusing when large matrices are used.
+
=cut
sub ans_array_filter{
- my $rh_ans = shift;
- my %options = @_;
-# assign_option_aliases( \%opt,
+ my $rh_ans = shift;
+ my %options = @_;
+# assign_option_aliases( \%opt,
# );
- set_default_options(\%options,
- '_filter_name' => 'ans_array_filter',
- );
-# $rh_ans->{ans_label} =~ /ArRaY(\d+)\[\d+,\d+,\d+\]/; # CHANGE made to accomodate HTML 4.01 standards for name attribute
- $rh_ans->{ans_label} =~ /ArRaY(\d+)\_\_\d+:\d+:\d+\_\_/;
- my $ans_num = $1;
- my @keys = grep /ArRaY$ans_num/, keys(%{$main::inputs_ref});
- my $key;
- my @array = ();
- my ($i,$j,$k) = (0,0,0);
-
- #the keys aren't in order, so their info has to be put into the array before doing anything with it
- foreach $key (@keys){
-# $key =~ /ArRaY\d+\[(\d+),(\d+),(\d+)\]/;
-# ($i,$j,$k) = ($1,$2,$3);
-# $array[$i][$j][$k] = ${$main::inputs_ref}{'ArRaY'.$ans_num.'['.$i.','.$j.','.$k.']'};
- $key =~ /ArRaY\d+\_\_(\d+):(\d+):(\d+)\_\_/;
- ($i,$j,$k) = ($1,$2,$3);
- $array[$i][$j][$k] = ${$main::inputs_ref}{'ArRaY'.$ans_num.'__'.$i.':'.$j.':'.$k.'__'};
-
- }
- $rh_ans->{debug_student_answer }= \@array;
- my $display_ans = "";
-
- for( $i=0; $i < scalar(@array) ; $i ++ )
- {
- $display_ans .= " [";
- $rh_ans->{preview_text_string} .= ' [';
- $rh_ans->{preview_latex_string} .= '\begin{pmatrix} ';
- for( $j = 0; $j < scalar( @{$array[$i]} ) ; $j++ )
- {
- $display_ans .= " [";
- $rh_ans->{preview_text_string} .= ' [';
- for( $k = 0; $k < scalar( @{$array[$i][$j]} ) ; $k ++ ){
- my $entry = $array[$i][$j][$k];
- $entry = math_constants($entry);
- # This parser code was origianally taken from PGanswermacros::check_syntax
- # but parts of it needed to be slighty modified for this context
- my $parser = new AlgParserWithImplicitExpand;
- my $ret = $parser -> parse($entry); #for use with loops
-
- if ( ref($ret) ) { ## parsed successfully
- $parser -> tostring();
- $parser -> normalize();
- $entry = $parser -> tostring();
- $rh_ans->{preview_text_string} .= $entry.",";
- $rh_ans->{preview_latex_string} .= $parser -> tolatex() . '& ';
-
- } else { ## error in parsing
- $rh_ans->{'student_ans'} = 'syntax error:'.$display_ans. $parser->{htmlerror},
- $rh_ans->{'ans_message'} = $display_ans.$parser -> {error_msg},
- $rh_ans->{'preview_text_string'} = '',
- $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'.$display_ans.$parser->{htmlerror} . "$main::BR" .$parser -> {error_msg}.".$main::BR");
- }
-
- my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($entry);
- if ($PG_eval_errors) {
- $rh_ans->throw_error('EVAL','There is a syntax error in your answer.') ;
- $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors);
- last;
- } else {
- $entry = prfmt($inVal,$options{format});
- $display_ans .= $entry.",";
- $array[$i][$j][$k] = $entry;
- }
- }
- chop($rh_ans->{preview_text_string});
- chop($display_ans);
- $rh_ans->{preview_text_string} .= '] ,';
- $rh_ans->{preview_latex_string} .= '\\\\';
- $display_ans .= '] ,';
-
- }
- chop($rh_ans->{preview_text_string});
- chop($display_ans);
+ set_default_options(\%options,
+ _filter_name => 'ans_array_filter',
+ );
+# $rh_ans->{ans_label} =~ /ArRaY(\d+)\[\d+,\d+,\d+\]/; # CHANGE made to accomodate HTML 4.01 standards for name attribute
+ $rh_ans->{ans_label} =~ /ArRaY(\d+)\_\_\d+:\d+:\d+\_\_/;
+ my $ans_num = $1;
+ my @keys = grep /ArRaY$ans_num/, keys(%{$main::inputs_ref});
+ my $key;
+ my @array = ();
+ my ($i,$j,$k) = (0,0,0);
+
+ #the keys aren't in order, so their info has to be put into the array before doing anything with it
+ foreach $key (@keys){
+# $key =~ /ArRaY\d+\[(\d+),(\d+),(\d+)\]/;
+# ($i,$j,$k) = ($1,$2,$3);
+# $array[$i][$j][$k] = ${$main::inputs_ref}{'ArRaY'.$ans_num.'['.$i.','.$j.','.$k.']'};
+ $key =~ /ArRaY\d+\_\_(\d+):(\d+):(\d+)\_\_/;
+ ($i,$j,$k) = ($1,$2,$3);
+ $array[$i][$j][$k] = ${$main::inputs_ref}{'ArRaY'.$ans_num.'__'.$i.':'.$j.':'.$k.'__'};
+
+ }
+ #$rh_ans->{debug_student_answer }= \@array;
+ my $display_ans = "";
+
+ for( $i=0; $i < scalar(@array) ; $i ++ ) {
+ $display_ans .= " [";
+ $rh_ans->{preview_text_string} .= ' [';
+ $rh_ans->{preview_latex_string} .= '\begin{pmatrix} ';
+ for( $j = 0; $j < scalar( @{$array[$i]} ) ; $j++ ) {
+ $display_ans .= " [";
+ $rh_ans->{preview_text_string} .= ' [';
+ for( $k = 0; $k < scalar( @{$array[$i][$j]} ) ; $k ++ ){
+ my $entry = $array[$i][$j][$k];
+ $entry = math_constants($entry);
+ # This parser code was origianally taken from PGanswermacros::check_syntax
+ # but parts of it needed to be slighty modified for this context
+ my $parser = new AlgParserWithImplicitExpand;
+ my $ret = $parser -> parse($entry); #for use with loops
+
+ if ( ref($ret) ) { ## parsed successfully
+ $parser -> tostring();
+ $parser -> normalize();
+ $entry = $parser -> tostring();
+ $rh_ans->{preview_text_string} .= $entry.",";
+ $rh_ans->{preview_latex_string} .= $parser -> tolatex() . '& ';
+
+ } else { ## error in parsing
+ $rh_ans->{'student_ans'} = 'syntax error:'.$display_ans. $parser->{htmlerror},
+ $rh_ans->{'ans_message'} = $display_ans.$parser -> {error_msg},
+ $rh_ans->{'preview_text_string'} = '',
+ $rh_ans->throw_error('SYNTAX', 'syntax error in answer:'.$display_ans.$parser->{htmlerror} . "$main::BR" .$parser -> {error_msg}.".$main::BR");
+ }
+
+ my ($inVal,$PG_eval_errors,$PG_full_error_report) = PG_answer_eval($entry);
+ if ($PG_eval_errors) {
+ $rh_ans->throw_error('EVAL','There is a syntax error in your answer.') ;
+ $rh_ans->{ans_message} = clean_up_error_msg($PG_eval_errors);
+ last;
+ } else {
+ $entry = prfmt($inVal,$options{format});
+ $display_ans .= $entry.",";
+ $array[$i][$j][$k] = $entry;
+ }
+ }
+ chop($rh_ans->{preview_text_string});
+ chop($display_ans);
+ $rh_ans->{preview_text_string} .= '] ,';
+ $rh_ans->{preview_latex_string} .= '\\\\';
+ $display_ans .= '] ,';
+
+ }
+ chop($rh_ans->{preview_text_string});
+ chop($display_ans);
$rh_ans->{preview_text_string} .= '] ,';
$rh_ans->{preview_latex_string} .= '\end{pmatrix}'.' , ';
- $display_ans .= '] ,';
- }
- chop($rh_ans->{preview_text_string});
- chop($rh_ans->{preview_latex_string});
- chop($rh_ans->{preview_latex_string});
- chop($rh_ans->{preview_latex_string});
- chop($display_ans);
-
- my @temp = ();
- for( $i = 0 ; $i < scalar( @array ); $i++ ){
- push @temp , display_matrix($array[$i], 'left'=>'.', 'right'=>'.');
- push @temp , "," unless $i == scalar(@array) - 1;
- }
- $rh_ans->{student_ans} = mbox(\@temp);
- $rh_ans->{ra_student_ans} = \@array;
-
- $rh_ans;
+ $display_ans .= '] ,';
+ }
+ chop($rh_ans->{preview_text_string});
+ chop($rh_ans->{preview_latex_string});
+ chop($rh_ans->{preview_latex_string});
+ chop($rh_ans->{preview_latex_string});
+ chop($display_ans);
+
+ my @temp = ();
+ for( $i = 0 ; $i < scalar( @array ); $i++ ){
+ push @temp , display_matrix($array[$i], 'left'=>'.', 'right'=>'.');
+ push @temp , "," unless $i == scalar(@array) - 1;
+ }
+ $rh_ans->{student_ans} = mbox(\@temp);
+ $rh_ans->{ra_student_ans} = \@array;
+
+ $rh_ans;
}
sub are_orthogonal_vecs{
- my ($vec_ref , %opts) = @_;
- $vec_ref->{_filter_name} = 'are_orthogonal_vecs';
- my @vecs = ();
- if( ref($vec_ref) eq 'AnswerHash' )
- {
- @vecs = @{$vec_ref->{ra_student_ans}};
- }else{
- @vecs = @{$vec_ref};
- }
- my ($i,$j) = (0,0);
-
- my $num = scalar(@vecs);
- my $length = $vecs[0]->[1];
-
- for( ; $i < $num ; $i ++ )
- {
- for( $j = $i+1; $j < $num ; $j++ )
- {
- if( $vecs[$i]->scalar_product($vecs[$j]) > $main::functZeroLevelTolDefault )
- {
- if( ref( $vec_ref ) eq 'AnswerHash' ){
- $vec_ref->{score} = 0;
- if( $vec_ref->{help} =~ /orthogonal|orthonormal|verbose/ )
- {
- $vec_ref->throw_error('EVAL','You have entered vectors which are not orthogonal. ');
- }else{
- $vec_ref->throw_error('EVAL');
- }
- return $vec_ref;
- }else{
- return 0;
- }
- }
- }
- }
- if( ref( $vec_ref ) eq 'AnswerHash' ){
- $vec_ref->{score} = 1;
- $vec_ref;
- }else{
- 1;
- }
+ my ($vec_ref , %opts) = @_;
+ $vec_ref->{_filter_name} = 'are_orthogonal_vecs';
+ my @vecs = ();
+ if( ref($vec_ref) eq 'AnswerHash' )
+ {
+ @vecs = @{$vec_ref->{ra_student_ans}};
+ }else{
+ @vecs = @{$vec_ref};
+ }
+
+ my $num = scalar(@vecs);
+ my $length = $vecs[0]->[1];
+
+ for( my $i=0; $i < $num ; $i ++ ) {
+ for( my $j = $i+1; $j < $num ; $j++ ) {
+ if( $vecs[$i]->scalar_product($vecs[$j]) > $main::functZeroLevelTolDefault ) {
+ if( ref( $vec_ref ) eq 'AnswerHash' ){
+ $vec_ref->{score} = 0;
+ if( $vec_ref->{help} =~ /orthogonal|orthonormal|verbose/ )
+ {
+ $vec_ref->throw_error('EVAL','You have entered vectors which are not orthogonal. ');
+ }else{
+ $vec_ref->throw_error('EVAL');
+ }
+ return $vec_ref;
+ } else {
+ return 0;
+ }
+ }
+ }
+ }
+ if( ref( $vec_ref ) eq 'AnswerHash' ){
+ $vec_ref->{score} = 1;
+ $vec_ref;
+ } else {
+ 1;
+ }
}
sub is_diagonal{
- my $matrix = shift;
- my %options = @_;
- my $process_ans_hash = ( ref( $matrix ) eq 'AnswerHash' ) ? 1 : 0 ;
- my ($rh_ans);
- if ($process_ans_hash) {
- $rh_ans = $matrix;
- $matrix = $rh_ans->{ra_student_ans};
- }
-
- return 0 unless defined($matrix);
-
- if( ref($matrix) eq 'ARRAY' ){
- my @matrix = @{$matrix};
- @matrix = @{$matrix[0]} if ref($matrix[0][0]) eq 'ARRAY';
- if( ref($matrix[0]) ne 'ARRAY' or scalar( @matrix ) != scalar( @{$matrix[0]} ) ){
- 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.";
- }
-
- for( my $i = 0; $i < scalar( @matrix ) ; $i++ ){
- for( my $j = 0; $j < scalar( @{$matrix[0]} ); $j++ ){
- if( $matrix[$i][$j] != 0 and $i != $j )
- {
- if ($process_ans_hash){
- $rh_ans->throw_error('EVAL');
- return $rh_ans;
- } else {
- return 0;
- }
- }
- }
- }
- if ($process_ans_hash){
- return $rh_ans;
- } else {
- return 1;
- }
- }elsif( ref($matrix) eq 'Matrix' ){
- if( $matrix->[1] != $matrix->[2] ){
- warn "It is impossible for a non-square matrix to be diagonal, if you are a student, please tell your professor that there is a problem.";
- if ($process_ans_hash){
- $rh_ans->throw_error('EVAL');
- return $rh_ans;
- } else {
- return 0;
- }
- }
- for( my $i = 0; $i < $matrix->[1] ; $i++ ){
- for( my $j = 0; $j < $matrix->[2] ; $j++ ){
- if( $matrix->[0][$i][$j] != 0 and $i != $j ){
- if ($process_ans_hash){
- $rh_ans->throw_error('EVAL');
- return $rh_ans;
- } else {
- return 0;
- }
- }
- }
- }
- if ($process_ans_hash){
- return $rh_ans;
- } else {
- return 1;
- }
- }else{
- warn "There is a problem with the problem, please alert your professor.";
- if ($process_ans_hash){
- $rh_ans->throw_error('EVAL');
- return $rh_ans;
- } else {
- return 0;
- }
- }
+ my $matrix = shift;
+ my %options = @_;
+ my $process_ans_hash = ( ref( $matrix ) eq 'AnswerHash' ) ? 1 : 0 ;
+ my ($rh_ans);
+ if ($process_ans_hash) {
+ $rh_ans = $matrix;
+ $matrix = $rh_ans->{ra_student_ans};
+ }
+
+ return 0 unless defined($matrix);
+
+ if( ref($matrix) eq 'ARRAY' ) {
+ my @matrix = @{$matrix};
+ @matrix = @{$matrix[0]} if ref($matrix[0][0]) eq 'ARRAY';
+ if( ref($matrix[0]) ne 'ARRAY' or scalar( @matrix ) != scalar( @{$matrix[0]} ) ){
+ 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.";
+ }
+
+ for( my $i = 0; $i < scalar( @matrix ) ; $i++ ) {
+ for( my $j = 0; $j < scalar( @{$matrix[0]} ); $j++ ){
+ if( $matrix[$i][$j] != 0 and $i != $j )
+ {
+ if ($process_ans_hash){
+ $rh_ans->throw_error('EVAL');
+ return $rh_ans;
+ } else {
+ return 0;
+ }
+ }
+ }
+ }
+ if ($process_ans_hash){
+ return $rh_ans;
+ } else {
+ return 1;
+ }
+ } elsif ( ref($matrix) eq 'Matrix' ) {
+ if( $matrix->[1] != $matrix->[2] ) {
+ warn "It is impossible for a non-square matrix to be diagonal, if you are a student, please tell your professor that there is a problem.";
+ if ($process_ans_hash){
+ $rh_ans->throw_error('EVAL');
+ return $rh_ans;
+ } else {
+ return 0;
+ }
+ }
+ for( my $i = 0; $i < $matrix->[1] ; $i++ ) {
+ for( my $j = 0; $j < $matrix->[2] ; $j++ ) {
+ if( $matrix->[0][$i][$j] != 0 and $i != $j ){
+ if ($process_ans_hash){
+ $rh_ans->throw_error('EVAL');
+ return $rh_ans;
+ } else {
+ return 0;
+ }
+ }
+ }
+ }
+ if ($process_ans_hash) {
+ return $rh_ans;
+ } else {
+ return 1;
+ }
+ } else {
+ warn "There is a problem with the problem, please alert your professor.";
+ if ($process_ans_hash){
+ $rh_ans->throw_error('EVAL');
+ return $rh_ans;
+ } else {
+ return 0;
+ }
+ }
}
sub are_unit_vecs{
- my ( $vec_ref,%opts ) = @_;
- $vec_ref->{_filter_name} = 'are_unit_vecs';
- my @vecs = ();
- if( ref($vec_ref) eq 'AnswerHash' )
- {
- @vecs = @{$vec_ref->{ra_student_ans}};
- }else{
- @vecs = @{$vec_ref};
- }
-
- my $i = 0;
- my $num = scalar(@vecs);
- my $length = $vecs[0]->[1];
-
- for( ; $i < $num ; $i ++ )
- {
- if( abs(sqrt($vecs[$i]->scalar_product($vecs[$i]))- 1) > $main::functZeroLevelTolDefault )
- {
- if( ref( $vec_ref ) eq 'AnswerHash' ){
- $vec_ref->{score} = 0;
- if( $vec_ref->{help} =~ /unit|orthonormal|verbose/ )
- {
- $vec_ref->throw_error('EVAL','You have entered vector(s) which are not of unit length.');
- }else{
- $vec_ref->throw_error('EVAL');
- }
- return $vec_ref;
- }else{
- return 0;
- }
-
- }
- }
-
- if( ref( $vec_ref ) eq 'AnswerHash' ){
- $vec_ref->{score} = 1;
- $vec_ref;
- }else{
- 1;
- }
+ my ( $vec_ref,%opts ) = @_;
+ $vec_ref->{_filter_name} = 'are_unit_vecs';
+ my @vecs = ();
+ if( ref($vec_ref) eq 'AnswerHash' )
+ {
+ @vecs = @{$vec_ref->{ra_student_ans}};
+ }else{
+ @vecs = @{$vec_ref};
+ }
+
+ my $i = 0;
+ my $num = scalar(@vecs);
+ my $length = $vecs[0]->[1];
+
+ for( ; $i < $num ; $i ++ ) {
+ if( abs(sqrt($vecs[$i]->scalar_product($vecs[$i]))- 1) > $main::functZeroLevelTolDefault )
+ {
+ if( ref( $vec_ref ) eq 'AnswerHash' ){
+ $vec_ref->{score} = 0;
+ if( $vec_ref->{help} =~ /unit|orthonormal|verbose/ )
+ {
+ $vec_ref->throw_error('EVAL','You have entered vector(s) which are not of unit length.');
+ }else{
+ $vec_ref->throw_error('EVAL');
+ }
+ return $vec_ref;
+ }else{
+ return 0;
+ }
+
+ }
+ }
+
+ if( ref( $vec_ref ) eq 'AnswerHash' ){
+ $vec_ref->{score} = 1;
+ $vec_ref;
+ }else{
+ 1;
+ }
}
sub display_correct_vecs{
- my ( $ra_vecs,%opts ) = @_;
- my @ra_vecs = @{$ra_vecs};
- my @temp = ();
-
- for( my $i = 0 ; $i < scalar(@ra_vecs) ; $i++ ){
- push @temp, display_matrix(Matrix->new_from_col_vecs([$ra_vecs[$i]]),'left'=>'.','right'=>'.');
- push @temp, ",";
- }
-
- pop @temp;
-
- mbox(\@temp);
+ my ( $ra_vecs,%opts ) = @_;
+ my @ra_vecs = @{$ra_vecs};
+ my @temp = ();
+
+ for( my $i = 0 ; $i < scalar(@ra_vecs) ; $i++ ) {
+ push @temp, display_matrix(Matrix->new_from_col_vecs([$ra_vecs[$i]]),'left'=>'.','right'=>'.');
+ push @temp, ",";
+ }
+
+ pop @temp;
+
+ mbox(\@temp);
}
sub vec_solution_cmp{
- my $correctAnswer = shift;
- my %opt = @_;
+ my $correctAnswer = shift;
+ my %opt = @_;
- set_default_options( \%opt,
- 'zeroLevelTol' => $main::functZeroLevelTolDefault,
- 'debug' => 0,
- 'mode' => 'basis',
- 'help' => 'none',
- );
-
- $opt{debug} = 0 unless defined($opt{debug});
-
+ set_default_options( \%opt,
+ 'zeroLevelTol' => $main::functZeroLevelTolDefault,
+ 'debug' => 0,
+ 'mode' => 'basis',
+ 'help' => 'none',
+ );
+
+
## This is where the correct answer should be checked someday.
- my $matrix = Matrix->new_from_col_vecs($correctAnswer);
-
-
+ my $matrix = Matrix->new_from_col_vecs($correctAnswer);
+
+
#construct the answer evaluator
- my $answer_evaluator = new AnswerEvaluator;
+ my $answer_evaluator = new AnswerEvaluator;
- $answer_evaluator->{debug} = $opt{debug};
- $answer_evaluator->ans_hash( correct_ans => display_correct_vecs($correctAnswer),
- old_correct_ans => $correctAnswer,
- rm_correct_ans => $matrix,
- zeroLevelTol => $opt{zeroLevelTol},
- debug => $opt{debug},
- mode => $opt{mode},
- help => $opt{help},
- );
-
- $answer_evaluator->install_pre_filter(\&ans_array_filter);
- $answer_evaluator->install_pre_filter(sub{
- my ($rh_ans,@options) = @_;
- my @student_array = @{$rh_ans->{ra_student_ans}};
- my @array = ();
- for( my $i = 0; $i < scalar(@student_array) ; $i ++ )
- {
- push( @array, Matrix->new_from_array_ref($student_array[$i]));
- }
- $rh_ans->{ra_student_ans} = \@array;
- $rh_ans;
- });#ra_student_ans is now the students answer as an array of vectors
- # anonymous subroutine to check dimension and length of the student vectors
- # if either is wrong, the answer is wrong.
- $answer_evaluator->install_pre_filter(sub{
- my $rh_ans = shift;
- my $length = $rh_ans->{rm_correct_ans}->[1];
- my $dim = $rh_ans->{rm_correct_ans}->[2];
- if( $dim != scalar(@{$rh_ans->{ra_student_ans}}))
- {
-
- $rh_ans->{score} = 0;
- if( $rh_ans->{help} =~ /dim|verbose/ )
- {
- $rh_ans->throw_error('EVAL','You have entered the wrong number of vectors.');
- }else{
- $rh_ans->throw_error('EVAL');
- }
- }
- for( my $i = 0; $i < scalar( @{$rh_ans->{ra_student_ans} }) ; $i++ )
- {
- if( $length != $rh_ans->{ra_student_ans}->[$i]->[1])
+ $answer_evaluator->{debug} = $opt{debug};
+ $answer_evaluator->ans_hash(
+ correct_ans => display_correct_vecs($correctAnswer),
+ old_correct_ans => $correctAnswer,
+ rm_correct_ans => $matrix,
+ zeroLevelTol => $opt{zeroLevelTol},
+ debug => $opt{debug},
+ mode => $opt{mode},
+ help => $opt{help},
+ );
+
+ $answer_evaluator->install_pre_filter(\&ans_array_filter);
+ $answer_evaluator->install_pre_filter(
+ sub{
+ my ($rh_ans,@options) = @_;
+ $rh_ans->{_filter_name} = "create student answer as an array of vectors";
+ my @student_array = @{$rh_ans->{ra_student_ans}};
+ my @array = ();
+ for( my $i = 0; $i < scalar(@student_array) ; $i ++ ) {
+ push( @array, Matrix->new_from_array_ref($student_array[$i]));
+ }
+ $rh_ans->{ra_student_ans} = \@array;
+ $rh_ans;
+ }
+ );
+ #ra_student_ans is now the students answer as an array of vectors
+ # anonymous subroutine to check dimension and length of the student vectors
+ # if either is wrong, the answer is wrong.
+ $answer_evaluator->install_pre_filter(
+ sub{
+ my $rh_ans = shift;
+ $rh_ans->{_filter_name} = "check_dimension_and_length";
+ my $length = $rh_ans->{rm_correct_ans}->[1];
+ my $dim = $rh_ans->{rm_correct_ans}->[2];
+ if( $dim != scalar(@{$rh_ans->{ra_student_ans}}))
{
+
$rh_ans->{score} = 0;
- if( $rh_ans->{help} =~ /length|verbose/ )
+ if( $rh_ans->{help} =~ /dim|verbose/ )
{
- $rh_ans->throw_error('EVAL','You have entered vector(s) of the wrong length.');
+ $rh_ans->throw_error('EVAL','You have entered the wrong number of vectors.');
}else{
$rh_ans->throw_error('EVAL');
}
}
- }
- $rh_ans;
- });
- # Install prefilter for various modes
- if( $opt{mode} ne 'basis' )
- {
- if( $opt{mode} =~ /orthogonal|orthonormal/ )
- {
- $answer_evaluator->install_pre_filter(\&are_orthogonal_vecs);
- }
-
- if( $opt{mode} =~ /unit|orthonormal/ )
- {
- $answer_evaluator->install_pre_filter(\&are_unit_vecs);
-
- }
- }
-
- $answer_evaluator->install_evaluator(\&compare_vec_solution, %opt);
-
- $answer_evaluator->install_post_filter(
- sub {my $rh_ans = shift;
- if ($rh_ans->catch_error('SYNTAX') ) {
- $rh_ans->{ans_message} = $rh_ans->{error_message};
- $rh_ans->clear_error('SYNTAX');
- }
- if ($rh_ans->catch_error('EVAL') ) {
- $rh_ans->{ans_message} = $rh_ans->{error_message};
- $rh_ans->clear_error('EVAL');
+ for( my $i = 0; $i < scalar( @{$rh_ans->{ra_student_ans} }) ; $i++ ) {
+ if( $length != $rh_ans->{ra_student_ans}->[$i]->[1]) {
+ $rh_ans->{score} = 0;
+ if( $rh_ans->{help} =~ /length|verbose/ ) {
+ $rh_ans->throw_error('EVAL','You have entered vector(s) of the wrong length.');
+ }else{
+ $rh_ans->throw_error('EVAL');
+ }
}
- $rh_ans;
- }
- );
- $answer_evaluator;
-
+ }
+ $rh_ans;
+ }
+ );
+ # Install prefilter for various modes
+ if( $opt{mode} ne 'basis' ) {
+ if( $opt{mode} =~ /orthogonal|orthonormal/ ) {
+ $answer_evaluator->install_pre_filter(\&are_orthogonal_vecs);
+ }
+
+ if( $opt{mode} =~ /unit|orthonormal/ ) {
+ $answer_evaluator->install_pre_filter(\&are_unit_vecs);
+
+ }
+ }
+
+ $answer_evaluator->install_evaluator(\&compare_vec_solution, %opt);
+
+ $answer_evaluator->install_post_filter(
+ sub {my $rh_ans = shift;
+ if ($rh_ans->catch_error('SYNTAX') ) {
+ $rh_ans->{ans_message} = $rh_ans->{error_message};
+ $rh_ans->clear_error('SYNTAX');
+ }
+ if ($rh_ans->catch_error('EVAL') ) {
+ $rh_ans->{ans_message} = $rh_ans->{error_message};
+ $rh_ans->clear_error('EVAL');
+ }
+ $rh_ans;
+ }
+ );
+ $answer_evaluator;
+
}
-
+
sub compare_vec_solution {
- my ( $rh_ans, %options ) = @_ ;
- my @space = @{$rh_ans->{ra_student_ans}};
- my $solution = shift @space;
-
- # A lot of the follosing code was taken from Matrix::proj_coeff
- # calling this method recursively would be a waste of time since
- # the prof's matrix never changes and solve_LR is an expensive
- # operation. This way it is only done once.
- my $matrix = $rh_ans->{rm_correct_ans};
- my ($dim,$x_vector, $base_matrix);
- my $errors = undef;
- my $lin_space_tr= ~ $matrix;
- $matrix = $lin_space_tr * $matrix;
- my $matrix_lr = $matrix->decompose_LR();
-
- #this section determines whether or not the first vector, a solution to
- #the system, is a linear combination of the prof's vectors in which there
- #is a nonzero coefficient on the first term, the prof's solution to the system
- $solution = $lin_space_tr*$solution;
- ($dim,$x_vector, $base_matrix) = $matrix_lr->solve_LR($solution);
- if( $dim ){
- $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.
- $rh_ans->{score} = 0;
- $rh_ans;
- }elsif( abs($x_vector->[0][0][0]) <= $options{zeroLevelTol} )
- {
- $rh_ans->{score} = 0;
- $rh_ans;
- }else{
- $rh_ans->{score} = 1;
- my @correct_space = @{$rh_ans->{old_correct_ans}};
- shift @correct_space;
- $rh_ans->{rm_correct_ans} = Matrix->new_from_col_vecs(\@correct_space);
- $rh_ans->{ra_student_ans} = \@space;
- return compare_basis( $rh_ans, %options );
- }
+ my ( $rh_ans, %options ) = @_ ;
+ $rh_ans->{_filter_name} = "compare_vec_solution";
+ my @space = @{$rh_ans->{ra_student_ans}};
+ my $solution = shift @space;
+
+ # A lot of the following code was taken from Matrix::proj_coeff
+ # calling this method recursively would be a waste of time since
+ # the prof's matrix never changes and solve_LR is an expensive
+ # operation. This way it is only done once.
+ my $matrix = $rh_ans->{rm_correct_ans};
+ my ($dim,$x_vector, $base_matrix);
+ my $errors = undef;
+ my $lin_space_tr= ~ $matrix;
+ $matrix = $lin_space_tr * $matrix;
+ my $matrix_lr = $matrix->decompose_LR();
+
+ #this section determines whether or not the first vector, a solution to
+ #the system, is a linear combination of the prof's vectors in which there
+ #is a nonzero coefficient on the first term, the prof's solution to the system
+ $solution = $lin_space_tr*$solution;
+ ($dim,$x_vector, $base_matrix) = $matrix_lr->solve_LR($solution);
+ #$rh_ans->{debug_compare_vec_solution} = $x_vector->element(1,1);
+ if( $dim ){
+ $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.
+ $rh_ans->{score} = 0;
+ $rh_ans;
+ } elsif( abs($x_vector->element(1,1) -1) >= $options{zeroLevelTol} ) {
+ # changes by MEG 6/24/05
+ # the student answer needs to be a linear combination of the instructors vectors
+ # and the coefficient of the first vector needs to be 1 (it is NOT enough that it be non-zero).
+ # if this is not the case, then the answer is wrong.
+ # 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.
+
+ $rh_ans->{score} = 0;
+ $rh_ans;
+ } else {
+ $rh_ans->{score} = 1;
+ my @correct_space = @{$rh_ans->{old_correct_ans}};
+ shift @correct_space;
+ $rh_ans->{rm_correct_ans} = Matrix->new_...
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