# The LearningOnline Network with CAPA # used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run() # # $Id: default_homework.lcpm,v 1.171 2016/12/06 20:51:11 damieng Exp $ # # Copyright Michigan State University Board of Trustees # # This file is part of the LearningOnline Network with CAPA (LON-CAPA). # # LON-CAPA is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 2 of the License, or # (at your option) any later version. # # LON-CAPA is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with LON-CAPA; if not, write to the Free Software # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA # # /home/httpd/html/adm/gpl.txt # # http://www.lon-capa.org/ # # #init some globals $hidden::RANDOMINIT=0; $pi=atan2(1,1)*4; $rad2deg=180.0/$pi; $deg2rad=$pi/180.0; $"=' '; use strict; { my $n = 0; my $total = 0; my $num_left = 0; my @order; my $type; sub init_permutation { my ($size,$requested_type) = @_; @order = (0..$size-1); $n = $size; $type = $requested_type; if ($type eq 'ordered') { $total = $num_left = 1; } elsif ($type eq 'unordered') { $total = $num_left = &factorial($size); } else { die("Unkown type: $type"); } } sub get_next_permutation { if ($num_left == $total) { $num_left--; return \@order; } # Find largest index j with a[j] < a[j+1] my $j = scalar(@order) - 2; while ($order[$j] > $order[$j+1]) { $j--; } # Find index k such that a[k] is smallest integer # greater than a[j] to the right of a[j] my $k = scalar(@order) - 1; while ($order[$j] > $order[$k]) { $k--; } # Interchange a[j] and a[k] @order[($k,$j)] = @order[($j,$k)]; # Put tail end of permutation after jth position in increasing order my $r = scalar(@order) - 1; my $s = $j + 1; while ($r > $s) { @order[($s,$r)]=@order[($r,$s)]; $r--; $s++; } $num_left--; return(\@order); } sub get_permutations_left { return $num_left; } } sub check_commas { my ($response)=@_; #print("$response "); my @numbers=split(',',$response); #print(" numbers ".join('-',@numbers)." "); if (scalar(@numbers) > 1) { #print(" numbers[0] ".$numbers[0]." "); if (length($numbers[0]) > 3 || length($numbers[0]) == 0) { return -1; } shift(@numbers); #print(" numbers ".scalar(@numbers)." "); while (scalar(@numbers) > 1) { #print(" numbers ".join('-',@numbers)." "); if (length($numbers[0]) != 3) { return -2; } shift(@numbers); } my ($number)=split('\.',$numbers[0]); #print(" number ".$number." "); #print(" numbers[0] ".$numbers[0]." "); if (length($number) != 3) { return -3; } } else { my ($number)=split('\.',$numbers[0]); if (length($number) > 3) { return -4; } } return 1; } sub caparesponse_check { my ($answer,$response)=@_; #not properly used yet: calc #not to be used: $ans_fmt my $type=$LONCAPA::CAPAresponse_args{'type'}; my $tol=$LONCAPA::CAPAresponse_args{'tol'}; my $sig=$LONCAPA::CAPAresponse_args{'sig'}; my $ans_fmt=$LONCAPA::CAPAresponse_args{'format'}; my $unit=$LONCAPA::CAPAresponse_args{'unit'}; my $calc=$LONCAPA::CAPAresponse_args{'calc'}; my $samples=$LONCAPA::CAPAresponse_args{'samples'}; my $tol_type=''; # gets it's value from whether tol has a % or not done my $sig_lbound=''; #done my $sig_ubound=''; #done #type's definitons come from capaParser.h #remove leading and trailing whitespace if (!defined($response)) { $response=''; } if ($response=~ /^\s|\s$/) { $response=~ s:^\s+|\s+$::g; } if ($type eq 'cs' || $type eq 'ci') { #for string answers make sure all places spaces occur, there is #really only 1 space, in both the answer and the response $answer=~s/ +/ /g; $response=~s/ +/ /g; } elsif ($type eq 'mc') { $answer=~s/[\s,]//g; $response=~s/[\s,]//g; } if ($type eq 'float' && $unit=~/\$/) { if ($response!~/^\$|\$$/) { return ('NO_UNIT', undef); } $response=~s/\$//g; } if ($type eq 'float' && $unit=~/\,/ && (&check_commas($response)<0)) { return "COMMA_FAIL:"; } $ans_fmt=~s/\W//g; $unit=~s/[\$,]//g; if ($type eq 'float') { $response=~s/,//g; } if (length($response) > 500) { return ('TOO_LONG',undef); } if ($type eq '' ) { if ( $answer eq ($answer *1.0)) { $type = 2; } else { $type = 3; } } else { if ($type eq 'cs') { $type = 4; } elsif ($type eq 'ci') { $type = 3 } elsif ($type eq 'mc') { $type = 5; } elsif ($type eq 'fml') { $type = 8; } elsif ($type eq 'math') { $type = 9; } elsif ($type eq 'subj') { $type = 7; } elsif ($type eq 'float') { $type = 2; } elsif ($type eq 'int') { $type = 1; } else { return ('ERROR', "Unknown type of answer: $type") } } my $points; my $id_list; #formula type setup the sample points if ($type eq '8') { ($id_list,$points)=split(/@/,$samples); } if ($tol eq '') { $tol=0.0; $tol_type=1; #TOL_ABSOLUTE } else { if ($tol =~ /%$/) { chop $tol; $tol_type=2; #TOL_PERCENTAGE } else { $tol_type=1; #TOL_ABSOLUTE } } ($sig_ubound,$sig_lbound)=&LONCAPA_INTERNAL_get_sigrange($sig); my $reterror=""; my $result; if (($type eq '9') || ($type eq '8')) { if ($response=~/\=/) { return ('BAD_FORMULA','Please submit just an expression, not an equation.'); } elsif ($response =~ /\,/ and $response !~ /^\s*\{.*\}\s*$/) { return ('BAD_FORMULA'); } } if ($type eq '9') { $result = &maxima_check(&maxima_cas_formula_fix($response),&maxima_cas_formula_fix($answer),\$reterror); } else { if ($type eq '8') { # fml type $response = &capa_formula_fix($response); $answer = &capa_formula_fix($answer); } $result = &caparesponse_capa_check_answer($response,$answer,$type, $tol_type,$tol, $sig_lbound,$sig_ubound, $ans_fmt,$unit,$calc,$id_list, $points,$external::randomseed, \$reterror); } if ($result == '1') { $result='EXACT_ANS'; } elsif ($result == '2') { $result='APPROX_ANS'; } elsif ($result == '3') { $result='SIG_FAIL'; } elsif ($result == '4') { $result='UNIT_FAIL'; } elsif ($result == '5') { $result='NO_UNIT'; } elsif ($result == '6') { $result='UNIT_OK'; } elsif ($result == '7') { $result='INCORRECT'; } elsif ($result == '8') { $result='UNIT_NOTNEEDED'; } elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; } elsif ($result =='10') { $result='SUB_RECORDED'; } elsif ($result =='11') { $result='BAD_FORMULA'; } elsif ($result =='12' && !$response) { $result='MISSING_ANSWER'; } elsif ($result =='12') { $result='WANTED_NUMERIC'; } elsif ($result =='13') { $result='UNIT_INVALID_INSTRUCTOR'; } elsif ($result =='141') { $result='UNIT_INVALID_STUDENT'; } elsif ($result =='142') { $result='UNIT_INVALID_STUDENT'; } elsif ($result =='143') { $result='UNIT_INVALID_STUDENT'; } elsif ($result =='15') { $result='UNIT_IRRECONCIBLE'; } else {$result = "ERROR: Unknown Result:$result:$@:";} return ($result,$reterror); } sub caparesponse_check_list { my $responses=$LONCAPA::CAPAresponse_args{'response'}; &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args)); my $type = $LONCAPA::CAPAresponse_args{'type'}; my $answerunit=$LONCAPA::CAPAresponse_args{'unit'}; &LONCAPA_INTERNAL_DEBUG("Got type :$type: answer unit :$answerunit:\n"); my $preprocess=$LONCAPA::CAPAresponse_args{'preprocess'}; $preprocess=~s/^\&//; my $num_input_lines = scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}}); if ($type ne '' ) { if (scalar(@$responses) < $num_input_lines) { return 'MISSING_ANSWER'; } if (scalar(@$responses) > $num_input_lines) { return 'EXTRA_ANSWER'; } } foreach my $which (0..($num_input_lines-1)) { my $answer_size = scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]}); if ($type ne '' && $answer_size > 1) { $responses->[$which]=[split(/,/,$responses->[$which])]; } else { $responses->[$which]=[$responses->[$which]]; } } foreach my $which (0..($num_input_lines-1)) { my $answer_size = scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]}); my $response_size = scalar(@{$responses->[$which]}); if ($answer_size > $response_size) { return 'MISSING_ANSWER'; } if ($answer_size < $response_size) { return 'EXTRA_ANSWER'; } } my $unit; my ($allowalgebra)=($LONCAPA::CAPAresponse_args{'allowalgebra'}=~/^(yes|1|on)$/i); if ($type eq 'float' || $type eq '') { #for numerical problems split off the unit my $part1; my $part2; if ($allowalgebra) { ($part1,$part2)=($responses->[0][-1]=~ /^(.*[^\s])\s+([^\s]+)$/); } else { ($part1,$part2)=($responses->[0][-1]=~ /^([\d\.\,\s\$]*(?:(?:[xX\*]10[\^\*]*|[eE]*)[\+\-]*\d*)*(?:^|\S)\d+)([\$\s\w\^\*\/\(\)\+\-]*[^\d\.\s\,][\$\s\w\^\*\/\(\)\+\-]*)$/); } if (defined($part1) && defined($part2)) { $responses->[0][-1]=$part1; $unit=&capa_formula_fix($part2); my $customunits=$LONCAPA::CAPAresponse_args{'customunits'}; if ($customunits =~ /\S/) { foreach my $replacement (split(/\s*\,\s*/,$customunits)) { my ($which,$what)=split(/\s*\=\s*/,$replacement); if ((defined($which)) && (defined($what))) { $what=&capa_formula_fix($what); $unit=~s/$which/\($what\)/g; } } } } } $unit=~s/\s//; my $error; foreach my $response (@$responses) { foreach my $element (@$response) { # See if we have preprocessor if ($preprocess=~/\S/) { if (defined(&$preprocess)) { no strict 'refs'; $element=&$preprocess($element,$unit); use strict 'refs'; } } if (($type eq 'float') || (($type eq '') && ($unit ne ''))) { $element =~ s/\s//g; } my $appendunit=$unit; # Deal with percentages # unit is unit entered by student, answerunit is unit by author # Deprecated: divide answer by 100 if student entered percent, # but author did not. Too much confusion # if (($unit=~/\%/) && ($answerunit ne '%')) { # $element=$element/100; # $appendunit=~s/\%//; # } # Author entered percent, student did not if (($unit!~/\%/) && ($answerunit=~/\%/)) { $element=$element*100; $appendunit='%'.$appendunit; } # Zero does not need a dimension if (($element =~ /^[0\.]+$/) && ($unit!~/\w/) && ($answerunit=~/\w/)) { $appendunit=$answerunit; } # Do the math for the student if allowed if ($allowalgebra) { $element=&cas('maxima',$element); } if ($appendunit ne '') { $element .= " $appendunit"; } &LONCAPA_INTERNAL_DEBUG("Made response element :$element:"); } } foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) { if (!defined($thisanswer)) { return ('ERROR','answer was undefined'); } } my $allow_control_char = 0; my $control_chars_removed = 0; my $ansstring; if ($type eq 'cs' || $type eq 'ci') { if (ref($LONCAPA::CAPAresponse_answer->{'answers'}) eq 'ARRAY') { foreach my $strans (@{$LONCAPA::CAPAresponse_answer->{'answers'}}) { if (ref($strans) eq 'ARRAY') { $ansstring = join("\0",@{$strans}); foreach my $item (@{$strans}) { if ($item =~ /[\000-\037]/) { $allow_control_char = 1; } } } } } } # &LONCAPA_INTERNAL_DEBUG(&LONCAPA_INTERNAL_Dumper($responses)); my %memoized; if ($LONCAPA::CAPAresponse_answer->{'type'} eq 'ordered') { for (my $i=0; $i{'answers'}[$i]; my $response = $responses->[$i]; my $key = "$answer\0$response"; my (@awards,@msgs); for (my $j=0; $j[$j] =~ /[\000-\037]/) { $response->[$j] =~ s/[\000-\037]//g; $control_chars_removed = 1; } } } # See if we have preprocessor for string responses if (($preprocess=~/\S/) && ($type eq 'cs' || $type eq 'ci')) { if (defined(&$preprocess)) { no strict 'refs'; $response->[$j]=&$preprocess($response->[$j]); use strict 'refs'; } } my ($award,$msg) = &caparesponse_check($answer->[$j], $response->[$j]); if ($type eq 'cs' || $type eq 'ci') { $error = &verify_stringresponse($type,$award,$response->[$j], $answer->[$j]); } push(@awards,$award); push(@msgs, $msg); } my ($award,$msg) = &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs); $memoized{$key} = [$award,$msg]; } } else { #FIXME broken with unorder responses where one is a # and the other is a (need to delay parse til # inside the loop?) foreach my $response (@$responses) { my $response_size = scalar(@{$response}); foreach my $answer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) { my $key = "$answer\0$response"; my $answer_size = scalar(@{$answer}); my ($award,$msg); if ($answer_size > $response_size) { $award = 'MISSING_ANSWER'; } elsif ($answer_size < $response_size) { $award = 'EXTRA_ANSWER'; } else { my (@awards,@msgs); for (my $j=0; $j[$j] =~ /[\000-\037]/) { $response->[$j] =~ s/[\000-\037]//g; $control_chars_removed = 1; } } } # See if we have preprocessor if (($preprocess=~/\S/) && ($type eq 'cs' || $type eq 'ci')) { if (defined(&$preprocess)) { no strict 'refs'; $response->[$j]=&$preprocess($response->[$j]); use strict 'refs'; } } my ($award,$msg) = &caparesponse_check($answer->[$j], $response->[$j]); if ($type eq 'cs' || $type eq 'ci') { $error = &verify_stringresponse($type,$award,$response->[$j], $answer->[$j]); } push(@awards,$award); push(@msgs, $msg); } ($award,$msg) = &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs); } $memoized{$key} = [$award,$msg]; } } } my ($final_award,$final_msg); &init_permutation(scalar(@$responses), $LONCAPA::CAPAresponse_answer->{'type'}); # possible FIXMEs # - significant time is spent calling non-safe space routine # from safe space # - early outs could be possible with classifying awards is to stratas # and stopping as so as hitting the top strata # - some early outs also might be possible with check ing the # memoized hash of results (is correct even possible? etc.) my (@final_awards,@final_msg); while( &get_permutations_left() ) { my $order = &get_next_permutation(); my (@awards, @msgs, $i); foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) { my $key = "$thisanswer\0".$responses->[$order->[$i]]; push(@awards,$memoized{$key}[0]); push(@msgs,$memoized{$key}[1]); $i++; } &LONCAPA_INTERNAL_DEBUG(" all awards ".join(':',@awards)); my ($possible_award,$possible_msg) = &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs); &LONCAPA_INTERNAL_DEBUG(" pos awards ".$possible_award); push(@final_awards,$possible_award); push(@final_msg,$possible_msg); } &LONCAPA_INTERNAL_DEBUG(" all final_awards ".join(':',@final_awards)); my ($final_award,$final_msg) = &LONCAPA_INTERNAL_FINALIZEAWARDS(\@final_awards,\@final_msg,undef,1); return ($final_award,$final_msg,$error,$control_chars_removed,$ansstring); } sub verify_stringresponse { my ($type,$award,$resp,$ans) = @_; return if ($award eq 'EXACT_ANS'); my $error; if ($resp =~ /^\s|\s$/) { $resp =~ s{^\s+|\s+$}{}g; } if ($ans =~ /^\s|\s$/) { $ans =~ s{^\s+|\s+$}{}g; } if ($type eq 'ci') { $resp = lc($resp); $ans = lc($ans); } if ($resp eq $ans) { if ($award eq 'INCORRECT') { $error = 'MISGRADED'; } } return $error; } sub cas { my ($system,$input,$library)=@_; my $output; my $dump; if ($system eq 'maxima') { $output=&maxima_eval($input,$library); } elsif ($system eq 'R') { ($output,$dump)=&r_eval($input,$library,0); } else { $output='Error: unrecognized CAS'; } return $output; } sub cas_hashref { my ($system,$input,$library)=@_; if ($system eq 'maxima') { return 'Error: unsupported CAS'; } elsif ($system eq 'R') { return &r_eval($input,$library,1); } else { return 'Error: unrecognized CAS'; } } # # cas_hashref_entry takes a list of indices and gets the entry in a hash generated by Rreturn. # Call: cas_hashref_entry(Rvalue, index1, index2, ...) where Rvalue is a hash returned by Rreturn. # Rentry will return the first scalar value it encounters (ignoring excess indices). # If an invalid key is given, it returns undef. # sub cas_hashref_entry { return &Rentry(@_); } # # cas_hashref_array takes a list of indices and gets a column array from a hash generated by Rreturn. # Call: cas_hashref_array(Rvalue, index1, index2, ...) where Rvalue is a hash returned by Rreturn. # If an invalid key is given, it returns undef. # sub cas_hashref_array { return &Rarray(@_); } sub tex { if ( $external::target eq "tex" ) { return $_[0]; } else { return $_[1]; } } sub var_in_tex { if ( $external::target eq "tex" ) { return $_[0]; } else { return ""; } } sub web { if ( $external::target eq "tex" ) { return $_[1]; } else { if ( $external::target eq "web" || $external::target eq "answer") { return $_[2]; } else { return $_[0]; } } } sub html { if ( $external::target eq "web" ) { return shift; } } sub hinton { return 0; } sub random { my ($start,$end,$step)=@_; if ( ! $hidden::RANDOMINIT ) { if ($external::randomseed == 0) { $external::randomseed=1; } if ($external::randomseed =~/,/) { my ($num1,$num2)=split(/,/,$external::randomseed); &random_set_seed(1,abs($num1)); } elsif ($external::randomseed =~/:/) { my ($num1,$num2)=split(/:/,$external::randomseed); &random_set_seed(abs($num1),abs($num2)); } else { &random_set_seed(1,int(abs($external::randomseed))); } &math_random_uniform(); $hidden::RANDOMINIT=1; } if (!defined($step)) { $step=1; } my $num=1+int(($end-$start)/$step); my $result=$start + int(&math_random_uniform() * $num)*$step; return $result; } sub random_normal { my ($item_cnt,$seed,$av,$std_dev) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_normal($item_cnt,$av,$std_dev); &random_set_seed(@oldseed); return @retArray; } sub random_beta { my ($item_cnt,$seed,$aa,$bb) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_beta($item_cnt,$aa,$bb); &random_set_seed(@oldseed); return @retArray; } sub random_gamma { my ($item_cnt,$seed,$a,$r) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_gamma($item_cnt,$a,$r); &random_set_seed(@oldseed); return @retArray; } sub random_exponential { my ($item_cnt,$seed,$av) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_exponential($item_cnt,$av); &random_set_seed(@oldseed); return @retArray; } sub random_poisson { my ($item_cnt,$seed,$mu) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_poisson($item_cnt,$mu); &random_set_seed(@oldseed); return @retArray; } sub random_chi { my ($item_cnt,$seed,$df) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_chi_square($item_cnt,$df); &random_set_seed(@oldseed); return @retArray; } sub random_noncentral_chi { my ($item_cnt,$seed,$df,$nonc) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc); &random_set_seed(@oldseed); return @retArray; } sub random_f { my ($item_cnt,$seed,$dfn,$dfd) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_f($item_cnt,$dfn,$dfd); &random_set_seed(@oldseed); return @retArray; } sub random_noncentral_f { my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc); &random_set_seed(@oldseed); return @retArray; } sub random_multivariate_normal { my ($item_cnt,$seed,$mean,$covar) = @_; my @oldseed=&random_get_seed(); &random_set_seed_from_phrase($seed); my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar); &random_set_seed(@oldseed); return @retArray; } sub random_multinomial { my ($item_cnt,$seed,@p) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); my @retArray=&math_random_multinomial($item_cnt,@p); &random_set_seed(@oldseed); return @retArray; } sub random_permutation { my ($seed,@inArray) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_permutation(@inArray); &random_set_seed(@oldseed); return @retArray; } sub random_uniform { my ($item_cnt,$seed,$low,$high) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_uniform($item_cnt,$low,$high); &random_set_seed(@oldseed); return @retArray; } sub random_uniform_integer { my ($item_cnt,$seed,$low,$high) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_uniform_integer($item_cnt,$low,$high); &random_set_seed(@oldseed); return @retArray; } sub random_binomial { my ($item_cnt,$seed,$nt,$p) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_binomial($item_cnt,$nt,$p); &random_set_seed(@oldseed); return @retArray; } sub random_negative_binomial { my ($item_cnt,$seed,$ne,$p) = @_; my @oldseed=&random_get_seed(); my @retArray; &random_set_seed_from_phrase($seed); @retArray=&math_random_negative_binomial($item_cnt,$ne,$p); &random_set_seed(@oldseed); return @retArray; } sub abs { CORE::abs(shift) } sub sin { CORE::sin(shift) } sub cos { CORE::cos(shift) } sub exp { CORE::exp(shift) } sub int { CORE::int(shift) } sub log { CORE::log(shift) } sub ln { CORE::log(shift) } sub atan2 { CORE::atan2($_[0],$_[1]) } sub sqrt { CORE::sqrt(shift) } sub tan { CORE::sin($_[0]) / CORE::cos($_[0]) } #sub atan { atan2($_[0], 1); } #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); } #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) ); } sub log10 { CORE::log($_[0])/CORE::log(10); } sub factorial { my $input = CORE::int(shift); return "Error - unable to take factorial of an negative number ($input)" if $input < 0; return "Error - factorial result is greater than system limit ($input)" if $input > 170; return 1 if $input == 0; my $result = 1; for (my $i=2; $i<=$input; $i++) { $result *= $i } return $result; } sub sgn { return -1 if $_[0] < 0; return 0 if $_[0] == 0; return 1 if $_[0] > 0; } sub min { my @sorted = sort { $a <=> $b || $a cmp $b } @_; return shift @sorted; } sub max { my @sorted = sort { $a <=> $b || $a cmp $b } @_; return pop @sorted; } sub roundto { my ($input,$n) = @_; return sprintf('%.'.$n.'f',$input); } sub to_string { my ($input,$n) = @_; return sprintf($input) if $n eq ""; $n = '.'.$n if $n !~ /^\./; return sprintf('%'.$n,$input) if $n ne ""; } sub sub_string { my ($str,$start,$len) = @_; return substr($str,$start-1,$len); } sub pow {return $_[0] ** $_[1]; } sub ceil {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); } sub floor {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); } #sub floor {return int($_[0]); } sub format { my ($value,$fmt)=@_; my ($dollarmode,$commamode,$alwaysperiod,$options); if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; } #if ($options =~ /\$/) { $dollamode=1; } #if ($options =~ /,/) { $commamode=1; } if ($options =~ /\./) { $alwaysperiod=1; } my $result; if ($fmt=~/s$/i) { $result=&format_significant_figures($value,$fmt); } else { $fmt=~s/e/E/g; $result=sprintf('%.'.$fmt,$value); if ($alwaysperiod && $fmt eq '0f') { $result .='.'; } $result=~s/(E[+-]*)0/$1/; } #if ($dollarmode) {$result=&dollarformat($result);} #if ($commamode) {$result=&commaformat($result);} return $result; } sub chemparse { my ($reaction) = @_; my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction); my $formula = ''; foreach my $token (@tokens) { if ($token eq '->' ) { $formula .= '\ensuremath{\rightarrow} '; next; } if ($token eq '<-' ) { $formula .= '\ensuremath{\leftarrow} '; next; } if ($token eq '<=>') { if ($external::target eq 'web' && &EXT('request.browser.unicode')) { $formula .= '⇌ '; } else { $formula .= &web('<=> ','\ensuremath{\rightleftharpoons} ', '<=> '); } next; } if ($token eq '.') { $formula =~ s/(\ \;| )$//; $formula .= '·'; next; } $token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/; $formula .= $1 if ($1 ne '1'); # stoichiometric coefficient my $molecule = $2; # subscripts $molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|$1|g; # superscripts $molecule =~ s|\^(\d*[+\-]*)|$1|g; # strip whitespace $molecule =~ s/\s*//g; # forced space $molecule =~ s/_/ /g; $molecule =~ s/-/−/g; $formula .= $molecule.' '; } # get rid of trailing space $formula =~ s/(\ \;| )$//; return &xmlparse($formula); } sub prettyprint { my ($value,$fmt,$target)=@_; my $result; if (!$target) { $target = $external::target; } if ($fmt =~ /chem/i) { return(&chemparse($value)); } my ($dollarmode,$commamode,$alwaysperiod,$options); if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; } if ($options =~ /\$/) { $dollarmode=1; } if ($options =~ /,/) { $commamode=1; } if ($options =~ /\./) { $alwaysperiod=1; } if ($fmt=~/s$/i) { $value=&format_significant_figures($value,$fmt); } elsif ($fmt) { $value=sprintf('%.'.$fmt,$value); } if ($alwaysperiod && $fmt eq '0f') { if ($target eq 'tex') { $value .='\\ensuremath{.}'; } else { $value .='.'; } } if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) { my $frac=$1; if ($dollarmode) { $frac=&dollarformat($frac); } if ($commamode) { $frac=&commaformat($frac); } my $exponent=$2; $exponent=~s/^\+0*//; $exponent=~s/^-0*/-/; $exponent=~s/^-0*/-/; if ($exponent eq '-') { undef($exponent); } if ($exponent) { if ($target eq 'web') { $result=$frac.'×10'.$exponent.''; } elsif ($target eq 'tex') { $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}'; } else { $result=$value; } } else { $result=$frac; } } else { $result=$value; if ($dollarmode) { $result=&dollarformat($result,$target); } elsif ($commamode) { $result=&commaformat($result,$target); } } return $result; } sub commaformat { my ($number,$target) = @_; if ($number =~ /\./) { while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) { $number = $1.$2.','.$3.$4; } } else { while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) { $number = $1.$2.','.$3.$4; } } return $number; } sub dollarformat { my ($number,$target) = @_; if (!$target) { $target = $external::target; } $number=&commaformat($number,$target); if ($target eq 'tex') { $number='\$'.$number; #' stupid emacs } else { $number='$'.$number; #' stupid emacs } return $number; } # format of form ns or nS where n is an integer sub format_significant_figures { my ($number,$format) = @_; return '0' if ($number == 0); # extract number of significant figures needed my ($sig) = ($format =~ /(\d+)s/i); # arbitrary choice - suggestions ?? or throw error message? $sig = 3 if ($sig eq ''); # save the minus sign my $sign = ($number < 0) ? '-' : ''; $number = abs($number); # needed to correct for a number greater than 1 (or my $power = ($number < 1) ? 0 : 1; # could round up. Take the integer part of log10. my $x10 = int(log($number)/log(10)); # find number with values left of decimal pt = # of sign figs. my $xsig = $number*10**($sig-$x10-$power); # get just digits left of decimal pt - also rounds off correctly my $xint = sprintf('%.0f',$xsig); # save any trailing zero's my ($zeros) = ($xint =~ /(0+)$/); # return number to original magnitude my $numSig = $xint*10**($x10-$sig+$power); if ($numSig =~ /^(\d+)\.(\d+)/) { # insert trailing zero's if have decimal point my @digarray = split('',$1.$2); my $sigcount; while (@digarray > 0) { my $item = shift(@digarray); if ($item) { $sigcount = 1 + @digarray; last; } } if (($sigcount) && ($sig >= $sigcount)) { $zeros = substr($zeros,0,($sig - $sigcount)); } $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/; } else { if ($numSig =~ /^(\d+)e([\+\-]\d+)$/i) { my $pre_exp = $1; my $exponent = $2; $numSig = $pre_exp.'.'.$zeros.'E'.$exponent; } elsif ($numSig =~ /0$/) { # add decimal pt for number ending with 0 and length == # of sig figs if (length($numSig) == $sig) { $numSig.='.'; } elsif (length($numSig) > $sig) { # exponential form for number ending with 0 and length > # of sig figs my $fmtsig = $sig-1; if ($fmtsig) { $numSig = sprintf('%.'.$fmtsig.'E',$numSig); } } elsif (length($numSig) < $sig) { $numSig.='.'.substr($zeros,0,($sig-length($numSig))); } } else { if (length($numSig) < $sig) { $numSig.='.'.substr($zeros,0,($sig-length($numSig))); } } } # return number with sign return $sign.$numSig; } sub map { my ($phrase,$dest,$source)=@_; my @oldseed=&random_get_seed(); my @seed = &random_seed_from_phrase($phrase); &random_set_seed(@seed); my $destct = scalar(@$dest); if (!$source) { my @output; my @idx = &math_random_permuted_index($destct); my $ctr = 0; while ($ctr < $destct) { $output[$ctr] = $$dest[$idx[$ctr]]; $ctr++; } &random_set_seed(@oldseed); return @output; } else { my $num = scalar(@$source); my @idx = &math_random_permuted_index($num); my $ctr = 0; my $tot = $num; $tot = $destct if $destct < $num; if (ref($$dest[0])) { while ($ctr < $tot) { ${$$dest[$ctr]} = $$source[$idx[$ctr]]; $ctr++; } } else { while ($ctr < $tot) { $$dest[$ctr] = $$source[$idx[$ctr]]; $ctr++; } } } &random_set_seed(@oldseed); return ''; } sub rmap { my ($phrase,$dest,$source)=@_; my @oldseed=&random_get_seed(); my @seed = &random_seed_from_phrase($phrase); &random_set_seed(@seed); my $destct = scalar(@$dest); if (!$source) { my @idx = &math_random_permuted_index($destct); my $ctr = 0; my @r_idx; while ($ctr < $destct) { $r_idx[$idx[$ctr]] = $ctr; $ctr++; } my @output; $ctr = 0; while ($ctr < $destct) { $output[$ctr] = $$dest[$r_idx[$ctr]]; $ctr++; } &random_set_seed(@oldseed); return @output; } else { my $num = scalar(@$source); my @idx = &math_random_permuted_index($num); my $ctr = 0; my $tot = $num; $tot = $destct if $destct < $num; my @r_idx; while ($ctr < $tot) { $r_idx[$idx[$ctr]] = $ctr; $ctr++; } $ctr = 0; if (ref($$dest[0])) { while ($ctr < $tot) { ${$$dest[$ctr]} = $$source[$r_idx[$ctr]]; $ctr++; } } else { while ($ctr < $tot) { $$dest[$ctr] = $$source[$r_idx[$ctr]]; $ctr++; } } } &random_set_seed(@oldseed); return ''; } sub capa_id { return } sub problem { return } sub name{ my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename'); $fullname = "" if $fullname eq ", "; $fullname =~ s/\%2d/-/g; return $fullname; } sub student_number { my $id = &EXT('environment.id'); $id = '' if $id eq ""; return $id; } sub class { my $course = &EXT('course.description'); $course = '' if $course eq ""; return $course; } sub classid { my $courseid = &EXT('request.course.id'); $courseid = '' if $courseid eq ""; return $courseid; } sub firstname { my $firstname = &EXT('environment.firstname'); $firstname = '' if $firstname eq ""; return $firstname; } sub middlename { my $middlename = &EXT('environment.middlename'); $middlename = '' if $middlename eq ""; return $middlename; } sub lastname { my $lastname = &EXT('environment.lastname'); $lastname = '' if $lastname eq ""; return $lastname; } sub sec { my $sec = &EXT('request.course.sec'); $sec = '' if $sec eq ""; return $sec; } sub submission { my ($partid,$responseid,$subnumber,$encode,$cleanupnum,$mapalias)=@_; my $sub=''; if ($subnumber) { $sub=$subnumber.':'; } my $output = &EXT('user.resource.'.$sub.'resource.'.$partid.'.'.$responseid.'.submission',$mapalias); if (ref($output) eq 'ARRAY') { my @items = @{$output}; if ($encode) { @items = map { &encode_response($_); } @items; } if (ref($cleanupnum) eq 'HASH') { @items = map { &cleanup_numerical_response($cleanupnum,$_); } @items; } return \@items; } else { if ($encode) { $output = &encode_response($output); } if (ref($cleanupnum) eq 'HASH') { $output = &cleanup_numerical_response($cleanupnum,$output); } return $output; } } sub encode_response { my ($value) = @_; $value =~ s/&/&/g; $value =~ s//>/g; $value =~ s/"/"/g; return $value; } sub cleanup_numerical_response { my ($cleanupnum,$value) = @_; if (ref($cleanupnum) eq 'HASH') { if ($cleanupnum->{exponent}) { if ($value =~ m{^(.*)[\*xX]\s*10\s*\^\s*(\+|\-)?\s*(\d+)(.*)$}) { my $pre_exp = $1; my $sign = $2; my $exponent = $3; my $post_exp = $4; if ($pre_exp !~ /\./) { $pre_exp .= '.'; } if ($sign eq '') { $sign = '+'; } $value = $pre_exp.'E'.$sign.$exponent.$post_exp; } } if ($cleanupnum->{comma}) { $value =~ s{(\d+),(\d+)}{$1$2}; } if ($cleanupnum->{letterforzero}) { $value =~ s/^\s*o(\.\d+)/0$1/i; } if ($cleanupnum->{spaces}) { $value =~ s{^\s+|\s+$}{}g; if ($value =~ m{^(.*)\.\s+(\d+)(.*)$}) { my $pre_pt = $1; my $decimal = $2; my $post_dec = $3; $value = $pre_pt.'.'.$decimal.$post_dec; } } if ($cleanupnum->{format} =~ /^\d+s$/i) { $value = &format_significant_figures($value,$cleanupnum->{format}); } } return $value; } sub currentpart { return $external::part; } sub eval_time { my ($timestamp)=@_; unless ($timestamp) { return ''; } return &locallocaltime($timestamp); } sub open_date { my ($partid)=@_; unless ($partid) { $partid=0; } return &eval_time(&EXT('resource.'.$partid.'.opendate')); } sub due_date { my ($partid)=@_; unless ($partid) { $partid=0; } return &eval_time(&EXT('resource.'.$partid.'.duedate')); } sub answer_date { my ($partid)=@_; unless ($partid) { $partid=0; } return &eval_time(&EXT('resource.'.$partid.'.answerdate')); } sub open_date_epoch { my ($partid)=@_; unless ($partid) { $partid=0; } return &EXT('resource.'.$partid.'.opendate'); } sub due_date_epoch { my ($partid)=@_; unless ($partid) { $partid=0; } return &EXT('resource.'.$partid.'.duedate'); } sub answer_date_epoch { my ($partid)=@_; unless ($partid) { $partid=0; } return &EXT('resource.'.$partid.'.answerdate'); } sub parameter_setting { my ($which,$partid)=@_; unless ($partid) { $partid=0; } return &EXT('resource.'.$partid.'.'.$which); } sub stored_data { my ($which,$partid)=@_; unless ($partid) { $partid=0; } return &EXT('user.resource.resource.'.$partid.'.'.$which); } sub wrong_bubbles { my ($correct,$lower,$upper,$step,@given)=@_; my @array=(); my %hash=(); foreach my $new (@given) { $hash{$new}=1; } my $num=int(¶meter_setting('numbubbles',¤tpart())); unless ($num) { $num=8; } if ($num>1) { for (my $i=0;$i<=500;$i++) { my $new=&random($lower,$upper,$step); if ($hash{$new}) { next; } if (abs($new-$correct)<$step) { next; } $hash{$new}=1; @array=keys(%hash); if ($#array+2>=$num) { last; } } } return @array; } sub array_moments { my @input=@_; my (@output,$N); $N=scalar (@input); $output[0]=$N; if ($N <= 1) { $output[1]=$input[0]; $output[1]="Input array not defined" if ($N == 0); $output[2]="variance undefined for N<=1"; $output[3]="skewness undefined for N<=1"; $output[4]="kurtosis undefined for N<=1"; return @output; } my $sum=0; foreach my $line (@input) { $sum+=$line; } $output[1] = $sum/$N; my ($x,$sdev,$var,$skew,$kurt) = 0; foreach my $line (@input) { $x=$line-$output[1]; $var+=$x**2; $skew+=$x**3; $kurt+=$x**4; } $output[2]=$var/($N-1); $sdev=CORE::sqrt($output[2]); if ($sdev == 0) { $output[3]="inf-variance=0"; $output[4]="inf-variance=0"; return @output; } $output[3]=$skew/($sdev**3*$N); $output[4]=$kurt/($sdev**4*$N)-3; return @output; } sub choose { my $num = $_[0]; return $_[$num]; } #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })}); #sub sum1 { # my ($start,$end,$sub)=@_; # my $sum=0; # for (my $i=$start;$i<=$end;$i++) { # $sum+=&$sub($i); # } # return $sum #} #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')'); #sub sum2 { # my ($varname,$start,$end,$line)=@_; # my $sum=0; # for (my $i=$start;$i<=$end;$i++) { # my $func=sub { # eval("\$".$varname."=$i"); # eval($line); # }; # $sum+=&$func($i); # } # return $sum #} # expiremental idea sub proper_path { my ($path)=@_; if ( $external::target eq "tex" ) { return '/home/httpd/html'.$path; } else { return $path; } } sub input_id { my ($part_id, $response_id, $textline_id) = @_; return 'HWVAL_'.$part_id.'_'.$response_id.'_'.$textline_id; }