loncom/homework/default_homework.lcpm - view

File: [LON-CAPA] / loncom / homework / default_homework.lcpm
Revision 1.152.2.2: download - view: text, annotated - select for diffs
Thu Oct 6 17:20:37 2011 UTC (12 years, 6 months ago) by raeburn
Branches: version_2_10_X
CVS tags: version_2_10_1, loncapaMITrelate_1
Diff to branchpoint 1.152: preferred, unified

- Backport 1.153, 1,154, 1.155, 1.156, 1.157, 1.158, 1.159, 1.161.

1: # The LearningOnline Network with CAPA 2: # used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run() 3: # 4: # $Id: default_homework.lcpm,v 1.152.2.2 2011/10/06 17:20:37 raeburn Exp $ 5: # 6: # Copyright Michigan State University Board of Trustees 7: # 8: # This file is part of the LearningOnline Network with CAPA (LON-CAPA). 9: # 10: # LON-CAPA is free software; you can redistribute it and/or modify 11: # it under the terms of the GNU General Public License as published by 12: # the Free Software Foundation; either version 2 of the License, or 13: # (at your option) any later version. 14: # 15: # LON-CAPA is distributed in the hope that it will be useful, 16: # but WITHOUT ANY WARRANTY; without even the implied warranty of 17: # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18: # GNU General Public License for more details. 19: # 20: # You should have received a copy of the GNU General Public License 21: # along with LON-CAPA; if not, write to the Free Software 22: # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 23: # 24: # /home/httpd/html/adm/gpl.txt 25: # 26: # http://www.lon-capa.org/ 27: # 28: # 29: 30: #init some globals 31: $hidden::RANDOMINIT=0; 32: $pi=atan2(1,1)*4; 33: $rad2deg=180.0/$pi; 34: $deg2rad=$pi/180.0; 35: $"=' '; 36: use strict; 37: { 38: my $n = 0; 39: my $total = 0; 40: my $num_left = 0; 41: my @order; 42: my $type; 43: 44: sub init_permutation { 45: my ($size,$requested_type) = @_; 46: @order = (0..$size-1); 47: $n = $size; 48: $type = $requested_type; 49: if ($type eq 'ordered') { 50: $total = $num_left = 1; 51: } elsif ($type eq 'unordered') { 52: $total = $num_left = &factorial($size); 53: } else { 54: die("Unkown type: $type"); 55: } 56: } 57: 58: sub get_next_permutation { 59: if ($num_left == $total) { 60: $num_left--; 61: return \@order; 62: } 63: 64: # Find largest index j with a[j] < a[j+1] 65: 66: my $j = scalar(@order) - 2; 67: while ($order[$j] > $order[$j+1]) { 68: $j--; 69: } 70: 71: # Find index k such that a[k] is smallest integer 72: # greater than a[j] to the right of a[j] 73: 74: my $k = scalar(@order) - 1; 75: while ($order[$j] > $order[$k]) { 76: $k--; 77: } 78: 79: # Interchange a[j] and a[k] 80: 81: @order[($k,$j)] = @order[($j,$k)]; 82: 83: # Put tail end of permutation after jth position in increasing order 84: 85: my $r = scalar(@order) - 1; 86: my $s = $j + 1; 87: 88: while ($r > $s) { 89: @order[($s,$r)]=@order[($r,$s)]; 90: $r--; 91: $s++; 92: } 93: 94: $num_left--; 95: return(\@order); 96: } 97: 98: sub get_permutations_left { 99: return $num_left; 100: } 101: } 102: 103: sub check_commas { 104: my ($response)=@_; 105: #print("$response "); 106: my @numbers=split(',',$response); 107: #print(" numbers ".join('-',@numbers)." "); 108: if (scalar(@numbers) > 1) { 109: #print(" numbers[0] ".$numbers[0]." "); 110: if (length($numbers[0]) > 3 || length($numbers[0]) == 0) { return -1; } 111: shift(@numbers); 112: #print(" numbers ".scalar(@numbers)." "); 113: while (scalar(@numbers) > 1) { 114: #print(" numbers ".join('-',@numbers)." "); 115: if (length($numbers[0]) != 3) { return -2; } 116: shift(@numbers); 117: } 118: my ($number)=split('\.',$numbers[0]); 119: #print(" number ".$number." "); 120: #print(" numbers[0] ".$numbers[0]." "); 121: if (length($number) != 3) { return -3; } 122: } else { 123: my ($number)=split('\.',$numbers[0]); 124: if (length($number) > 3) { return -4; } 125: } 126: return 1; 127: } 128: 129: 130: sub caparesponse_check { 131: my ($answer,$response)=@_; 132: #not properly used yet: calc 133: #not to be used: $ans_fmt 134: my $type=$LONCAPA::CAPAresponse_args{'type'}; 135: my $tol=$LONCAPA::CAPAresponse_args{'tol'}; 136: my $sig=$LONCAPA::CAPAresponse_args{'sig'}; 137: my $ans_fmt=$LONCAPA::CAPAresponse_args{'format'}; 138: my $unit=$LONCAPA::CAPAresponse_args{'unit'}; 139: my $calc=$LONCAPA::CAPAresponse_args{'calc'}; 140: my $samples=$LONCAPA::CAPAresponse_args{'samples'}; 141: 142: my $tol_type=''; # gets it's value from whether tol has a % or not done 143: my $sig_lbound=''; #done 144: my $sig_ubound=''; #done 145: 146: #type's definitons come from capaParser.h 147: 148: #remove leading and trailing whitespace 149: if (!defined($response)) { 150: $response=''; 151: } 152: if ($response=~ /^\s|\s$/) { 153: $response=~ s:^\s+|\s+$::g; 154: } 155: 156: if ($type eq 'cs' || $type eq 'ci') { 157: #for string answers make sure all places spaces occur, there is 158: #really only 1 space, in both the answer and the response 159: $answer=~s/ +/ /g; 160: $response=~s/ +/ /g; 161: } elsif ($type eq 'mc') { 162: $answer=~s/[\s,]//g; 163: $response=~s/[\s,]//g; 164: } 165: if ($type eq 'float' && $unit=~/\$/) { 166: if ($response!~/^\$|\$$/) { return ('NO_UNIT', undef); } 167: $response=~s/\$//g; 168: } 169: if ($type eq 'float' && $unit=~/\,/ && (&check_commas($response)<0)) { 170: return "COMMA_FAIL:"; 171: } 172: $ans_fmt=~s/\W//g; 173: $unit=~s/[\$,]//g; 174: if ($type eq 'float') { $response=~s/,//g; } 175: 176: if (length($response) > 500) { return ('TOO_LONG',undef); } 177: 178: if ($type eq '' ) { 179: if ( $answer eq ($answer *1.0)) { $type = 2; 180: } else { $type = 3; } 181: } else { 182: if ($type eq 'cs') { $type = 4; } 183: elsif ($type eq 'ci') { $type = 3 } 184: elsif ($type eq 'mc') { $type = 5; } 185: elsif ($type eq 'fml') { $type = 8; } 186: elsif ($type eq 'math') { $type = 9; } 187: elsif ($type eq 'subj') { $type = 7; } 188: elsif ($type eq 'float') { $type = 2; } 189: elsif ($type eq 'int') { $type = 1; } 190: else { return ('ERROR', "Unknown type of answer: $type") } 191: } 192: 193: my $points; 194: my $id_list; 195: #formula type setup the sample points 196: if ($type eq '8') { 197: ($id_list,$points)=split(/@/,$samples); 198: } 199: if ($tol eq '') { 200: $tol=0.0; 201: $tol_type=1; #TOL_ABSOLUTE 202: } else { 203: if ($tol =~ /%$/) { 204: chop $tol; 205: $tol_type=2; #TOL_PERCENTAGE 206: } else { 207: $tol_type=1; #TOL_ABSOLUTE 208: } 209: } 210: 211: ($sig_ubound,$sig_lbound)=&LONCAPA_INTERNAL_get_sigrange($sig); 212: 213: my $reterror=""; 214: my $result; 215: if (($type eq '9') || ($type eq '8')) { 216: if ($response=~/\=/) { 217: return ('BAD_FORMULA','Please submit just an expression, not an equation.'); 218: } elsif ($response =~ /\,/ and $response !~ /^\s*\{.*\}\s*$/) { 219: return ('BAD_FORMULA'); 220: } 221: } 222: if ($type eq '9') { 223: $result = &maxima_check(&maxima_cas_formula_fix($response),&maxima_cas_formula_fix($answer),\$reterror); 224: } else { 225: if ($type eq '8') { # fml type 226: $response = &capa_formula_fix($response); 227: $answer = &capa_formula_fix($answer); 228: } 229: $result = &caparesponse_capa_check_answer($response,$answer,$type, 230: $tol_type,$tol, 231: $sig_lbound,$sig_ubound, 232: $ans_fmt,$unit,$calc,$id_list, 233: $points,$external::randomseed, 234: \$reterror); 235: } 236: if ($result == '1') { $result='EXACT_ANS'; } 237: elsif ($result == '2') { $result='APPROX_ANS'; } 238: elsif ($result == '3') { $result='SIG_FAIL'; } 239: elsif ($result == '4') { $result='UNIT_FAIL'; } 240: elsif ($result == '5') { $result='NO_UNIT'; } 241: elsif ($result == '6') { $result='UNIT_OK'; } 242: elsif ($result == '7') { $result='INCORRECT'; } 243: elsif ($result == '8') { $result='UNIT_NOTNEEDED'; } 244: elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; } 245: elsif ($result =='10') { $result='SUB_RECORDED'; } 246: elsif ($result =='11') { $result='BAD_FORMULA'; } 247: elsif ($result =='12' && !$response) { $result='MISSING_ANSWER'; } 248: elsif ($result =='12') { $result='WANTED_NUMERIC'; } 249: elsif ($result =='13') { $result='UNIT_INVALID_INSTRUCTOR'; } 250: elsif ($result =='141') { $result='UNIT_INVALID_STUDENT'; } 251: elsif ($result =='142') { $result='UNIT_INVALID_STUDENT'; } 252: elsif ($result =='143') { $result='UNIT_INVALID_STUDENT'; } 253: elsif ($result =='15') { $result='UNIT_IRRECONCIBLE'; } 254: else {$result = "ERROR: Unknown Result:$result:$@:";} 255: 256: # &LONCAPA_INTERNAL_DEBUG("RetError $reterror: Answer $answer: Response $response: type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|"); 257: # &LONCAPA_INTERNAL_DEBUG(" $answer $response $result "); 258: return ($result,$reterror); 259: } 260: 261: 262: sub caparesponse_check_list { 263: my $responses=$LONCAPA::CAPAresponse_args{'response'}; 264: &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args)); 265: my $type = $LONCAPA::CAPAresponse_args{'type'}; 266: my $answerunit=$LONCAPA::CAPAresponse_args{'unit'}; 267: &LONCAPA_INTERNAL_DEBUG("Got type :$type: answer unit :$answerunit:\n"); 268: 269: my $preprocess=$LONCAPA::CAPAresponse_args{'preprocess'}; 270: $preprocess=~s/^\&//; 271: 272: my $num_input_lines = 273: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}}); 274: 275: if ($type ne '' ) { 276: if (scalar(@$responses) < $num_input_lines) { 277: return 'MISSING_ANSWER'; 278: } 279: if (scalar(@$responses) > $num_input_lines) { 280: return 'EXTRA_ANSWER'; 281: } 282: 283: } 284: 285: foreach my $which (0..($num_input_lines-1)) { 286: my $answer_size = 287: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]}); 288: if ($type ne '' 289: && $answer_size > 1) { 290: $responses->[$which]=[split(/,/,$responses->[$which])]; 291: } else { 292: $responses->[$which]=[$responses->[$which]]; 293: } 294: } 295: foreach my $which (0..($num_input_lines-1)) { 296: my $answer_size = 297: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]}); 298: my $response_size = 299: scalar(@{$responses->[$which]}); 300: if ($answer_size > $response_size) { 301: return 'MISSING_ANSWER'; 302: } 303: if ($answer_size < $response_size) { 304: return 'EXTRA_ANSWER'; 305: } 306: } 307: 308: my $unit; 309: my ($allowalgebra)=($LONCAPA::CAPAresponse_args{'allowalgebra'}=~/^(yes|1|on)$/i); 310: if ($type eq 'float' || $type eq '') { 311: #for numerical problems split off the unit 312: my ($part1,$part2); 313: if ($allowalgebra) { 314: ($part1,$part2)=($responses->[0][-1]=~ /^(.*[^\s])\s+([^\s]+)$/); 315: } else { 316: ($part1,$part2)=($responses->[0][-1]=~ /^([\d\.\,\s\$]*(?:(?:[xX\*]10[\^\*]*|[eE]*)[\+\-]*\d*)*(?:^|\S)\d+)([\$\s\w\^\*\/\+\-]*[^\d\.\s\,][\$\s\w\^\*\/\+\-]*)$/); 317: } 318: if (defined($part1) && defined($part2)) { 319: $responses->[0][-1]=$part1; 320: $unit=&capa_formula_fix($part2); 321: my $customunits=$LONCAPA::CAPAresponse_args{'customunits'}; 322: if ($customunits =~ /\S/) { 323: foreach my $replacement (split(/\s*\,\s*/,$customunits)) { 324: my ($which,$what)=split(/\s*\=\s*/,$replacement); 325: if ((defined($which)) && (defined($what))) { 326: $what=&capa_formula_fix($what); 327: $unit=~s/$which/$$what$/g; 328: } 329: } 330: } 331: } 332: } 333: $unit=~s/\s//; 334: my $error; 335: foreach my $response (@$responses) { 336: foreach my $element (@$response) { 337: # See if we have preprocessor 338: if ($preprocess=~/\S/) { 339: if (defined(&$preprocess)) { 340: no strict 'refs'; 341: $element=&$preprocess($element,$unit); 342: use strict 'refs'; 343: } 344: } 345: if (($type eq 'float') || (($type eq '') && ($unit ne ''))) { 346: $element =~ s/\s//g; 347: } 348: my $appendunit=$unit; 349: # Deal with percentages 350: # unit is unit entered by student, answerunit is unit by author 351: # Deprecated: divide answer by 100 if student entered percent, 352: # but author did not. Too much confusion 353: # if (($unit=~/\%/) && ($answerunit ne '%')) { 354: # $element=$element/100; 355: # $appendunit=~s/\%//; 356: # } 357: # Author entered percent, student did not 358: if (($unit!~/\%/) && ($answerunit=~/\%/)) { 359: $element=$element*100; 360: $appendunit='%'.$appendunit; 361: } 362: # Zero does not need a dimension 363: if (($element =~ /^[0\.]+$/) && ($unit!~/\w/) && ($answerunit=~/\w/)) { 364: $appendunit=$answerunit; 365: } 366: # Do the math for the student if allowed 367: if ($allowalgebra) { 368: $element=&cas('maxima',$element); 369: } 370: if ($appendunit ne '') { 371: $element .= " $appendunit"; 372: } 373: &LONCAPA_INTERNAL_DEBUG("Made response element :$element:"); 374: } 375: } 376: 377: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) { 378: if (!defined($thisanswer)) { 379: return ('ERROR','answer was undefined'); 380: } 381: } 382: 383: my $allow_control_char = 0; 384: my $control_chars_removed = 0; 385: my $ansstring; 386: if ($type eq 'cs' || $type eq 'ci') { 387: if (ref($LONCAPA::CAPAresponse_answer->{'answers'}) eq 'ARRAY') { 388: foreach my $strans (@{$LONCAPA::CAPAresponse_answer->{'answers'}}) { 389: if (ref($strans) eq 'ARRAY') { 390: $ansstring = join("\0",@{$strans}); 391: foreach my $item (@{$strans}) { 392: if ($item =~ /[\000-\037]/) { 393: $allow_control_char = 1; 394: } 395: } 396: } 397: } 398: } 399: } 400: 401: # &LONCAPA_INTERNAL_DEBUG(&LONCAPA_INTERNAL_Dumper($responses)); 402: my %memoized; 403: if ($LONCAPA::CAPAresponse_answer->{'type'} eq 'ordered') { 404: for (my $i=0; $i<scalar(@$responses);$i++) { 405: my $answer = $LONCAPA::CAPAresponse_answer->{'answers'}[$i]; 406: my $response = $responses->[$i]; 407: my $key = "$answer\0$response"; 408: my (@awards,@msgs); 409: for (my $j=0; $j<scalar(@$response); $j++) { 410: if ($type eq 'cs' || $type eq 'ci') { 411: unless ($allow_control_char) { 412: if ($response->[$j] =~ /[\000-\037]/) { 413: $response->[$j] =~ s/[\000-\037]//g; 414: $control_chars_removed = 1; 415: } 416: } 417: } 418: # See if we have preprocessor for string responses 419: if (($preprocess=~/\S/) && ($type eq 'cs' || $type eq 'ci')) { 420: if (defined(&$preprocess)) { 421: no strict 'refs'; 422: $response->[$j]=&$preprocess($response->[$j]); 423: use strict 'refs'; 424: } 425: } 426: 427: my ($award,$msg) = &caparesponse_check($answer->[$j], 428: $response->[$j]); 429: if ($type eq 'cs' || $type eq 'ci') { 430: $error = &verify_stringresponse($type,$award,$response->[$j], 431: $answer->[$j]); 432: } 433: push(@awards,$award); 434: push(@msgs, $msg); 435: } 436: my ($award,$msg) = 437: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs); 438: $memoized{$key} = [$award,$msg]; 439: } 440: } else { 441: #FIXME broken with unorder responses where one is a <value> 442: # and the other is a <vector> (need to delay parse til 443: # inside the loop?) 444: foreach my $response (@$responses) { 445: my $response_size = scalar(@{$response}); 446: foreach my $answer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) { 447: my $key = "$answer\0$response"; 448: my $answer_size = scalar(@{$answer}); 449: my ($award,$msg); 450: if ($answer_size > $response_size) { 451: $award = 'MISSING_ANSWER'; 452: } elsif ($answer_size < $response_size) { 453: $award = 'EXTRA_ANSWER'; 454: } else { 455: my (@awards,@msgs); 456: for (my $j=0; $j<scalar(@$response); $j++) { 457: if ($type eq 'cs' || $type eq 'ci') { 458: unless ($allow_control_char) { 459: if ($response->[$j] =~ /[\000-\037]/) { 460: $response->[$j] =~ s/[\000-\037]//g; 461: $control_chars_removed = 1; 462: } 463: } 464: } 465: # See if we have preprocessor 466: if (($preprocess=~/\S/) && ($type eq 'cs' || $type eq 'ci')) { 467: if (defined(&$preprocess)) { 468: no strict 'refs'; 469: $response->[$j]=&$preprocess($response->[$j]); 470: use strict 'refs'; 471: } 472: } 473: 474: my ($award,$msg) = &caparesponse_check($answer->[$j], 475: $response->[$j]); 476: if ($type eq 'cs' || $type eq 'ci') { 477: $error = &verify_stringresponse($type,$award,$response->[$j], 478: $answer->[$j]); 479: } 480: push(@awards,$award); 481: push(@msgs, $msg); 482: } 483: ($award,$msg) = 484: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs); 485: } 486: $memoized{$key} = [$award,$msg]; 487: } 488: } 489: } 490: 491: my ($final_award,$final_msg); 492: &init_permutation(scalar(@$responses), 493: $LONCAPA::CAPAresponse_answer->{'type'}); 494: 495: # possible FIXMEs 496: # - significant time is spent calling non-safe space routine 497: # from safe space 498: # - early outs could be possible with classifying awards is to stratas 499: # and stopping as so as hitting the top strata 500: # - some early outs also might be possible with check ing the 501: # memoized hash of results (is correct even possible? etc.) 502: 503: my (@final_awards,@final_msg); 504: while( &get_permutations_left() ) { 505: my $order = &get_next_permutation(); 506: my (@awards, @msgs, $i); 507: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) { 508: my $key = "$thisanswer\0".$responses->[$order->[$i]]; 509: push(@awards,$memoized{$key}[0]); 510: push(@msgs,$memoized{$key}[1]); 511: $i++; 512: 513: } 514: &LONCAPA_INTERNAL_DEBUG(" all awards ".join(':',@awards)); 515: 516: my ($possible_award,$possible_msg) = 517: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs); 518: &LONCAPA_INTERNAL_DEBUG(" pos awards ".$possible_award); 519: push(@final_awards,$possible_award); 520: push(@final_msg,$possible_msg); 521: } 522: 523: &LONCAPA_INTERNAL_DEBUG(" all final_awards ".join(':',@final_awards)); 524: my ($final_award,$final_msg) = 525: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@final_awards,\@final_msg,undef,1); 526: return ($final_award,$final_msg,$error,$control_chars_removed,$ansstring); 527: } 528: 529: sub verify_stringresponse { 530: my ($type,$award,$resp,$ans) = @_; 531: return if ($award eq 'EXACT_ANS'); 532: my $error; 533: if ($resp =~ /^\s|\s$/) { 534: $resp =~ s{^\s+|\s+$}{}g; 535: } 536: if ($ans =~ /^\s|\s$/) { 537: $ans =~ s{^\s+|\s+$}{}g; 538: } 539: if ($type eq 'ci') { 540: $resp = lc($resp); 541: $ans = lc($ans); 542: } 543: if ($resp eq $ans) { 544: if ($award eq 'INCORRECT') { 545: $error = 'MISGRADED'; 546: } 547: } 548: return $error; 549: } 550: 551: sub cas { 552: my ($system,$input,$library)=@_; 553: my $output; 554: my $dump; 555: if ($system eq 'maxima') { 556: $output=&maxima_eval($input,$library); 557: } elsif ($system eq 'R') { 558: ($output,$dump)=&r_eval($input,$library,0); 559: } else { 560: $output='Error: unrecognized CAS'; 561: } 562: return $output; 563: } 564: 565: sub cas_hashref { 566: my ($system,$input,$library)=@_; 567: if ($system eq 'maxima') { 568: return 'Error: unsupported CAS'; 569: } elsif ($system eq 'R') { 570: return &r_eval($input,$library,1); 571: } else { 572: return 'Error: unrecognized CAS'; 573: } 574: } 575: 576: # 577: # cas_hashref_entry takes a list of indices and gets the entry in a hash generated by Rreturn. 578: # Call: cas_hashref_entry(Rvalue, index1, index2, ...) where Rvalue is a hash returned by Rreturn. 579: # Rentry will return the first scalar value it encounters (ignoring excess indices). 580: # If an invalid key is given, it returns undef. 581: # 582: sub cas_hashref_entry { 583: return &Rentry(@_); 584: } 585: 586: # 587: # cas_hashref_array takes a list of indices and gets a column array from a hash generated by Rreturn. 588: # Call: cas_hashref_array(Rvalue, index1, index2, ...) where Rvalue is a hash returned by Rreturn. 589: # If an invalid key is given, it returns undef. 590: # 591: sub cas_hashref_array { 592: return &Rarray(@_); 593: } 594: 595: sub tex { 596: if ( $external::target eq "tex" ) { 597: return $_[0]; 598: } else { 599: return $_[1]; 600: } 601: } 602: 603: sub var_in_tex { 604: if ( $external::target eq "tex" ) { 605: return $_[0]; 606: } else { 607: return ""; 608: } 609: } 610: 611: sub web { 612: if ( $external::target eq "tex" ) { 613: return $_[1]; 614: } else { 615: if ( $external::target eq "web" || $external::target eq "answer") { 616: return $_[2]; 617: } else { 618: return $_[0]; 619: } 620: } 621: } 622: 623: sub html { 624: if ( $external::target eq "web" ) { 625: return shift; 626: } 627: } 628: 629: sub hinton { 630: return 0; 631: } 632: 633: sub random { 634: my ($start,$end,$step)=@_; 635: if ( ! $hidden::RANDOMINIT ) { 636: if ($external::randomseed == 0) { $external::randomseed=1; } 637: if ($external::randomseed =~/,/) { 638: my ($num1,$num2)=split(/,/,$external::randomseed); 639: &random_set_seed(1,abs($num1)); 640: } elsif ($external::randomseed =~/:/) { 641: my ($num1,$num2)=split(/:/,$external::randomseed); 642: &random_set_seed(abs($num1),abs($num2)); 643: } else { 644: &random_set_seed(1,int(abs($external::randomseed))); 645: } 646: &math_random_uniform(); 647: $hidden::RANDOMINIT=1; 648: } 649: if (!defined($step)) { $step=1; } 650: my $num=1+int(($end-$start)/$step); 651: my $result=$start + int(&math_random_uniform() * $num)*$step; 652: return $result; 653: } 654: 655: sub random_normal { 656: my ($item_cnt,$seed,$av,$std_dev) = @_; 657: my @oldseed=&random_get_seed(); 658: my @retArray; 659: &random_set_seed_from_phrase($seed); 660: @retArray=&math_random_normal($item_cnt,$av,$std_dev); 661: &random_set_seed(@oldseed); 662: return @retArray; 663: } 664: 665: sub random_beta { 666: my ($item_cnt,$seed,$aa,$bb) = @_; 667: my @oldseed=&random_get_seed(); 668: my @retArray; 669: &random_set_seed_from_phrase($seed); 670: @retArray=&math_random_beta($item_cnt,$aa,$bb); 671: &random_set_seed(@oldseed); 672: return @retArray; 673: } 674: 675: sub random_gamma { 676: my ($item_cnt,$seed,$a,$r) = @_; 677: my @oldseed=&random_get_seed(); 678: my @retArray; 679: &random_set_seed_from_phrase($seed); 680: @retArray=&math_random_gamma($item_cnt,$a,$r); 681: &random_set_seed(@oldseed); 682: return @retArray; 683: } 684: 685: sub random_exponential { 686: my ($item_cnt,$seed,$av) = @_; 687: my @oldseed=&random_get_seed(); 688: my @retArray; 689: &random_set_seed_from_phrase($seed); 690: @retArray=&math_random_exponential($item_cnt,$av); 691: &random_set_seed(@oldseed); 692: return @retArray; 693: } 694: 695: sub random_poisson { 696: my ($item_cnt,$seed,$mu) = @_; 697: my @oldseed=&random_get_seed(); 698: my @retArray; 699: &random_set_seed_from_phrase($seed); 700: @retArray=&math_random_poisson($item_cnt,$mu); 701: &random_set_seed(@oldseed); 702: return @retArray; 703: } 704: 705: sub random_chi { 706: my ($item_cnt,$seed,$df) = @_; 707: my @oldseed=&random_get_seed(); 708: my @retArray; 709: &random_set_seed_from_phrase($seed); 710: @retArray=&math_random_chi_square($item_cnt,$df); 711: &random_set_seed(@oldseed); 712: return @retArray; 713: } 714: 715: sub random_noncentral_chi { 716: my ($item_cnt,$seed,$df,$nonc) = @_; 717: my @oldseed=&random_get_seed(); 718: my @retArray; 719: &random_set_seed_from_phrase($seed); 720: @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc); 721: &random_set_seed(@oldseed); 722: return @retArray; 723: } 724: 725: sub random_f { 726: my ($item_cnt,$seed,$dfn,$dfd) = @_; 727: my @oldseed=&random_get_seed(); 728: my @retArray; 729: &random_set_seed_from_phrase($seed); 730: @retArray=&math_random_f($item_cnt,$dfn,$dfd); 731: &random_set_seed(@oldseed); 732: return @retArray; 733: } 734: 735: sub random_noncentral_f { 736: my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_; 737: my @oldseed=&random_get_seed(); 738: my @retArray; 739: &random_set_seed_from_phrase($seed); 740: @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc); 741: &random_set_seed(@oldseed); 742: return @retArray; 743: } 744: 745: sub random_multivariate_normal { 746: my ($item_cnt,$seed,$mean,$covar) = @_; 747: my @oldseed=&random_get_seed(); 748: &random_set_seed_from_phrase($seed); 749: my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar); 750: &random_set_seed(@oldseed); 751: return @retArray; 752: } 753: 754: sub random_multinomial { 755: my ($item_cnt,$seed,@p) = @_; 756: my @oldseed=&random_get_seed(); 757: my @retArray; 758: &random_set_seed_from_phrase($seed); 759: my @retArray=&math_random_multinomial($item_cnt,@p); 760: &random_set_seed(@oldseed); 761: return @retArray; 762: } 763: 764: sub random_permutation { 765: my ($seed,@inArray) = @_; 766: my @oldseed=&random_get_seed(); 767: my @retArray; 768: &random_set_seed_from_phrase($seed); 769: @retArray=&math_random_permutation(@inArray); 770: &random_set_seed(@oldseed); 771: return @retArray; 772: } 773: 774: sub random_uniform { 775: my ($item_cnt,$seed,$low,$high) = @_; 776: my @oldseed=&random_get_seed(); 777: my @retArray; 778: &random_set_seed_from_phrase($seed); 779: @retArray=&math_random_uniform($item_cnt,$low,$high); 780: &random_set_seed(@oldseed); 781: return @retArray; 782: } 783: 784: sub random_uniform_integer { 785: my ($item_cnt,$seed,$low,$high) = @_; 786: my @oldseed=&random_get_seed(); 787: my @retArray; 788: &random_set_seed_from_phrase($seed); 789: @retArray=&math_random_uniform_integer($item_cnt,$low,$high); 790: &random_set_seed(@oldseed); 791: return @retArray; 792: } 793: 794: sub random_binomial { 795: my ($item_cnt,$seed,$nt,$p) = @_; 796: my @oldseed=&random_get_seed(); 797: my @retArray; 798: &random_set_seed_from_phrase($seed); 799: @retArray=&math_random_binomial($item_cnt,$nt,$p); 800: &random_set_seed(@oldseed); 801: return @retArray; 802: } 803: 804: sub random_negative_binomial { 805: my ($item_cnt,$seed,$ne,$p) = @_; 806: my @oldseed=&random_get_seed(); 807: my @retArray; 808: &random_set_seed_from_phrase($seed); 809: @retArray=&math_random_negative_binomial($item_cnt,$ne,$p); 810: &random_set_seed(@oldseed); 811: return @retArray; 812: } 813: 814: sub abs { CORE::abs(shift) } 815: sub sin { CORE::sin(shift) } 816: sub cos { CORE::cos(shift) } 817: sub exp { CORE::exp(shift) } 818: sub int { CORE::int(shift) } 819: sub log { CORE::log(shift) } 820: sub atan2 { CORE::atan2($_[0],$_[1]) } 821: sub sqrt { CORE::sqrt(shift) } 822: 823: sub tan { CORE::sin($_[0]) / CORE::cos($_[0]) } 824: #sub atan { atan2($_[0], 1); } 825: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); } 826: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) ); } 827: 828: sub log10 { CORE::log($_[0])/CORE::log(10); } 829: 830: sub factorial { 831: my $input = CORE::int(shift); 832: return "Error - unable to take factorial of an negative number ($input)" if $input < 0; 833: return "Error - factorial result is greater than system limit ($input)" if $input > 170; 834: return 1 if $input == 0; 835: my $result = 1; 836: for (my $i=2; $i<=$input; $i++) { $result *= $i } 837: return $result; 838: } 839: 840: sub sgn { 841: return -1 if $_[0] < 0; 842: return 0 if $_[0] == 0; 843: return 1 if $_[0] > 0; 844: } 845: 846: sub min { 847: my @sorted = sort { $a <=> $b || $a cmp $b } @_; 848: return shift @sorted; 849: } 850: 851: sub max { 852: my @sorted = sort { $a <=> $b || $a cmp $b } @_; 853: return pop @sorted; 854: } 855: 856: sub roundto { 857: my ($input,$n) = @_; 858: return sprintf('%.'.$n.'f',$input); 859: } 860: 861: sub to_string { 862: my ($input,$n) = @_; 863: return sprintf($input) if $n eq ""; 864: $n = '.'.$n if $n !~ /^\./; 865: return sprintf('%'.$n,$input) if $n ne ""; 866: } 867: 868: sub sub_string { 869: my ($str,$start,$len) = @_; 870: return substr($str,$start-1,$len); 871: } 872: 873: sub pow {return $_[0] ** $_[1]; } 874: sub ceil {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); } 875: sub floor {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); } 876: #sub floor {return int($_[0]); } 877: 878: sub format { 879: my ($value,$fmt)=@_; 880: my ($dollarmode,$commamode,$alwaysperiod,$options); 881: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; } 882: #if ($options =~ /\$/) { $dollamode=1; } 883: #if ($options =~ /,/) { $commamode=1; } 884: if ($options =~ /\./) { $alwaysperiod=1; } 885: my $result; 886: if ($fmt=~/s$/i) { 887: $result=&format_significant_figures($value,$fmt); 888: } else { 889: $fmt=~s/e/E/g; 890: $result=sprintf('%.'.$fmt,$value); 891: if ($alwaysperiod && $fmt eq '0f') { $result .='.'; } 892: $result=~s/(E[+-]*)0/$1/; 893: } 894: #if ($dollarmode) {$result=&dollarformat($result);} 895: #if ($commamode) {$result=&commaformat($result);} 896: return $result; 897: } 898: 899: sub chemparse { 900: my ($reaction) = @_; 901: my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction); 902: my $formula = ''; 903: foreach my $token (@tokens) { 904: if ($token eq '->' ) { 905: $formula .= '<m>\ensuremath{\rightarrow}</m> '; 906: next; 907: } 908: if ($token eq '<-' ) { 909: $formula .= '<m>\ensuremath{\leftarrow}</m> '; 910: next; 911: } 912: if ($token eq '<=>') { 913: if ($external::target eq 'web' && 914: &EXT('request.browser.unicode')) { 915: $formula .= '⇌ '; 916: } else { 917: $formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ', 918: '<=> '); 919: } 920: next; 921: } 922: if ($token eq '.') { 923: $formula =~ s/(\&nbsp\;| )$//; 924: $formula .= '·'; 925: next; 926: } 927: $token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/; 928: $formula .= $1 if ($1 ne '1'); # stoichiometric coefficient 929: 930: my $molecule = $2; 931: # subscripts 932: $molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|$1|g; 933: # superscripts 934: $molecule =~ s|\^(\d*[+\-]*)|$1|g; 935: # strip whitespace 936: $molecule =~ s/\s*//g; 937: # forced space 938: $molecule =~ s/_/ /g; 939: $molecule =~ s/-/−/g; 940: $formula .= $molecule.' '; 941: } 942: # get rid of trailing space 943: $formula =~ s/(\&nbsp\;| )$//; 944: return &xmlparse($formula); 945: } 946: 947: sub prettyprint { 948: my ($value,$fmt,$target)=@_; 949: my $result; 950: if (!$target) { $target = $external::target; } 951: if ($fmt =~ /chem/i) { return(&chemparse($value)); } 952: my ($dollarmode,$commamode,$alwaysperiod,$options); 953: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; } 954: if ($options =~ /\$/) { $dollarmode=1; } 955: if ($options =~ /,/) { $commamode=1; } 956: if ($options =~ /\./) { $alwaysperiod=1; } 957: if ($fmt=~/s$/i) { 958: $value=&format_significant_figures($value,$fmt); 959: } elsif ($fmt) { 960: $value=sprintf('%.'.$fmt,$value); 961: } 962: if ($alwaysperiod && $fmt eq '0f') { 963: if ($target eq 'tex') { 964: $value .='\\ensuremath{.}'; 965: } else { 966: $value .='.'; 967: } 968: } 969: if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) { 970: my $frac=$1; 971: if ($dollarmode) { $frac=&dollarformat($frac); } 972: if ($commamode) { $frac=&commaformat($frac); } 973: my $exponent=$2; 974: $exponent=~s/^\+0*//; 975: $exponent=~s/^-0*/-/; 976: $exponent=~s/^-0*/-/; 977: if ($exponent eq '-') { undef($exponent); } 978: if ($exponent) { 979: if ($target eq 'web') { 980: $result=$frac.'×10'.$exponent.''; 981: } elsif ($target eq 'tex') { 982: $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}'; 983: } else { 984: $result=$value; 985: } 986: } else { 987: $result=$frac; 988: } 989: } else { 990: $result=$value; 991: if ($dollarmode) { $result=&dollarformat($result,$target); } 992: elsif ($commamode) { $result=&commaformat($result,$target); } 993: } 994: return $result; 995: } 996: 997: sub commaformat { 998: my ($number,$target) = @_; 999: if ($number =~ /\./) { 1000: while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) { 1001: $number = $1.$2.','.$3.$4; 1002: } 1003: } else { 1004: while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) { 1005: $number = $1.$2.','.$3.$4; 1006: } 1007: } 1008: return $number; 1009: } 1010: 1011: sub dollarformat { 1012: my ($number,$target) = @_; 1013: if (!$target) { $target = $external::target; } 1014: $number=&commaformat($number,$target); 1015: if ($target eq 'tex') { 1016: $number='\$'.$number; #' stupid emacs 1017: } else { 1018: $number='$'.$number; #' stupid emacs 1019: } 1020: return $number; 1021: } 1022: 1023: # format of form ns or nS where n is an integer 1024: sub format_significant_figures { 1025: my ($number,$format) = @_; 1026: return '0' if ($number == 0); 1027: # extract number of significant figures needed 1028: my ($sig) = ($format =~ /(\d+)s/i); 1029: # arbitrary choice - suggestions ?? or throw error message? 1030: $sig = 3 if ($sig eq ''); 1031: # save the minus sign 1032: my $sign = ($number < 0) ? '-' : ''; 1033: $number = abs($number); 1034: # needed to correct for a number greater than 1 (or 1035: my $power = ($number < 1) ? 0 : 1; 1036: # could round up. Take the integer part of log10. 1037: my $x10 = int(log($number)/log(10)); 1038: # find number with values left of decimal pt = # of sign figs. 1039: my $xsig = $number*10**($sig-$x10-$power); 1040: # get just digits left of decimal pt - also rounds off correctly 1041: my $xint = sprintf('%.0f',$xsig); 1042: # save any trailing zero's 1043: my ($zeros) = ($xint =~ /(0+)$/); 1044: # return number to original magnitude 1045: my $numSig = $xint*10**($x10-$sig+$power); 1046: # insert trailing zero's if have decimal point 1047: $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/; 1048: # put a decimal pt for number ending with 0 and length = # of sig fig 1049: $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/); 1050: if (length($numSig) < $sig) { 1051: $numSig.='.'.substr($zeros,0,($sig-length($numSig))); 1052: } 1053: # return number with sign 1054: return $sign.$numSig; 1055: 1056: } 1057: 1058: sub map { 1059: my ($phrase,$dest,$source)=@_; 1060: my @oldseed=&random_get_seed(); 1061: my @seed = &random_seed_from_phrase($phrase); 1062: &random_set_seed(@seed); 1063: my $destct = scalar(@$dest); 1064: if (!$source) { 1065: my @output; 1066: my @idx = &math_random_permuted_index($destct); 1067: my $ctr = 0; 1068: while ($ctr < $destct) { 1069: $output[$ctr] = $$dest[$idx[$ctr]]; 1070: $ctr++; 1071: } 1072: &random_set_seed(@oldseed); 1073: return @output; 1074: } else { 1075: my $num = scalar(@$source); 1076: my @idx = &math_random_permuted_index($num); 1077: my $ctr = 0; 1078: my $tot = $num; 1079: $tot = $destct if $destct < $num; 1080: if (ref($$dest[0])) { 1081: while ($ctr < $tot) { 1082: ${$$dest[$ctr]} = $$source[$idx[$ctr]]; 1083: $ctr++; 1084: } 1085: } else { 1086: while ($ctr < $tot) { 1087: $$dest[$ctr] = $$source[$idx[$ctr]]; 1088: $ctr++; 1089: } 1090: } 1091: } 1092: &random_set_seed(@oldseed); 1093: return ''; 1094: } 1095: 1096: sub rmap { 1097: my ($phrase,$dest,$source)=@_; 1098: my @oldseed=&random_get_seed(); 1099: my @seed = &random_seed_from_phrase($phrase); 1100: &random_set_seed(@seed); 1101: my $destct = scalar(@$dest); 1102: if (!$source) { 1103: my @idx = &math_random_permuted_index($destct); 1104: my $ctr = 0; 1105: my @r_idx; 1106: while ($ctr < $destct) { 1107: $r_idx[$idx[$ctr]] = $ctr; 1108: $ctr++; 1109: } 1110: my @output; 1111: $ctr = 0; 1112: while ($ctr < $destct) { 1113: $output[$ctr] = $$dest[$r_idx[$ctr]]; 1114: $ctr++; 1115: } 1116: &random_set_seed(@oldseed); 1117: return @output; 1118: } else { 1119: my $num = scalar(@$source); 1120: my @idx = &math_random_permuted_index($num); 1121: my $ctr = 0; 1122: my $tot = $num; 1123: $tot = $destct if $destct < $num; 1124: my @r_idx; 1125: while ($ctr < $tot) { 1126: $r_idx[$idx[$ctr]] = $ctr; 1127: $ctr++; 1128: } 1129: $ctr = 0; 1130: if (ref($$dest[0])) { 1131: while ($ctr < $tot) { 1132: ${$$dest[$ctr]} = $$source[$r_idx[$ctr]]; 1133: $ctr++; 1134: } 1135: } else { 1136: while ($ctr < $tot) { 1137: $$dest[$ctr] = $$source[$r_idx[$ctr]]; 1138: $ctr++; 1139: } 1140: } 1141: } 1142: &random_set_seed(@oldseed); 1143: return ''; 1144: } 1145: 1146: sub capa_id { return } 1147: 1148: sub problem { return } 1149: 1150: sub name{ 1151: my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename'); 1152: $fullname = "" if $fullname eq ", "; 1153: $fullname =~ s/\%2d/-/g; 1154: return $fullname; 1155: } 1156: 1157: sub student_number { 1158: my $id = &EXT('environment.id'); 1159: $id = '' if $id eq ""; 1160: return $id; 1161: } 1162: 1163: sub class { 1164: my $course = &EXT('course.description'); 1165: $course = '' if $course eq ""; 1166: return $course; 1167: } 1168: 1169: sub classid { 1170: my $courseid = &EXT('request.course.id'); 1171: $courseid = '' if $courseid eq ""; 1172: return $courseid; 1173: } 1174: 1175: sub firstname { 1176: my $firstname = &EXT('environment.firstname'); 1177: $firstname = '' if $firstname eq ""; 1178: return $firstname; 1179: } 1180: 1181: sub middlename { 1182: my $middlename = &EXT('environment.middlename'); 1183: $middlename = '' if $middlename eq ""; 1184: return $middlename; 1185: } 1186: 1187: sub lastname { 1188: my $lastname = &EXT('environment.lastname'); 1189: $lastname = '' if $lastname eq ""; 1190: return $lastname; 1191: } 1192: 1193: sub sec { 1194: my $sec = &EXT('request.course.sec'); 1195: $sec = '' if $sec eq ""; 1196: return $sec; 1197: } 1198: 1199: sub submission { 1200: my ($partid,$responseid,$subnumber)=@_; 1201: my $sub=''; 1202: if ($subnumber) { $sub=$subnumber.':'; } 1203: return &EXT('user.resource.'.$sub.'resource.'.$partid.'.'.$responseid.'.submission'); 1204: } 1205: 1206: sub currentpart { 1207: return $external::part; 1208: } 1209: 1210: sub eval_time { 1211: my ($timestamp)=@_; 1212: unless ($timestamp) { return ''; } 1213: return &locallocaltime($timestamp); 1214: } 1215: 1216: sub open_date { 1217: my ($partid)=@_; 1218: unless ($partid) { $partid=0; } 1219: return &eval_time(&EXT('resource.'.$partid.'.opendate')); 1220: } 1221: 1222: sub due_date { 1223: my ($partid)=@_; 1224: unless ($partid) { $partid=0; } 1225: return &eval_time(&EXT('resource.'.$partid.'.duedate')); 1226: } 1227: 1228: sub answer_date { 1229: my ($partid)=@_; 1230: unless ($partid) { $partid=0; } 1231: return &eval_time(&EXT('resource.'.$partid.'.answerdate')); 1232: } 1233: 1234: sub open_date_epoch { 1235: my ($partid)=@_; 1236: unless ($partid) { $partid=0; } 1237: return &EXT('resource.'.$partid.'.opendate'); 1238: } 1239: 1240: sub due_date_epoch { 1241: my ($partid)=@_; 1242: unless ($partid) { $partid=0; } 1243: return &EXT('resource.'.$partid.'.duedate'); 1244: } 1245: 1246: sub answer_date_epoch { 1247: my ($partid)=@_; 1248: unless ($partid) { $partid=0; } 1249: return &EXT('resource.'.$partid.'.answerdate'); 1250: } 1251: 1252: sub parameter_setting { 1253: my ($which,$partid)=@_; 1254: unless ($partid) { $partid=0; } 1255: return &EXT('resource.'.$partid.'.'.$which); 1256: } 1257: 1258: sub stored_data { 1259: my ($which,$partid)=@_; 1260: unless ($partid) { $partid=0; } 1261: return &EXT('user.resource.resource.'.$partid.'.'.$which); 1262: } 1263: 1264: sub wrong_bubbles { 1265: my ($correct,$lower,$upper,$step,@given)=@_; 1266: my @array=(); 1267: my %hash=(); 1268: foreach my $new (@given) { 1269: $hash{$new}=1; 1270: } 1271: my $num=int(&parameter_setting('numbubbles',&currentpart())); 1272: unless ($num) { $num=8; } 1273: if ($num>1) { 1274: for (my $i=0;$i<=500;$i++) { 1275: my $new=&random($lower,$upper,$step); 1276: if ($hash{$new}) { next; } 1277: if (abs($new-$correct)<$step) { next; } 1278: $hash{$new}=1; 1279: @array=keys(%hash); 1280: if ($#array+2>=$num) { last; } 1281: } 1282: } 1283: return @array; 1284: } 1285: 1286: sub array_moments { 1287: my @input=@_; 1288: my (@output,$N); 1289: $N=scalar (@input); 1290: $output[0]=$N; 1291: if ($N <= 1) { 1292: $output[1]=$input[0]; 1293: $output[1]="Input array not defined" if ($N == 0); 1294: $output[2]="variance undefined for N<=1"; 1295: $output[3]="skewness undefined for N<=1"; 1296: $output[4]="kurtosis undefined for N<=1"; 1297: return @output; 1298: } 1299: my $sum=0; 1300: foreach my $line (@input) { 1301: $sum+=$line; 1302: } 1303: $output[1] = $sum/$N; 1304: my ($x,$sdev,$var,$skew,$kurt) = 0; 1305: foreach my $line (@input) { 1306: $x=$line-$output[1]; 1307: $var+=$x**2; 1308: $skew+=$x**3; 1309: $kurt+=$x**4; 1310: } 1311: $output[2]=$var/($N-1); 1312: $sdev=CORE::sqrt($output[2]); 1313: if ($sdev == 0) { 1314: $output[3]="inf-variance=0"; 1315: $output[4]="inf-variance=0"; 1316: return @output; 1317: } 1318: $output[3]=$skew/($sdev**3*$N); 1319: $output[4]=$kurt/($sdev**4*$N)-3; 1320: return @output; 1321: } 1322: 1323: sub choose { 1324: my $num = $_[0]; 1325: return $_[$num]; 1326: } 1327: 1328: #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })}); 1329: #sub sum1 { 1330: # my ($start,$end,$sub)=@_; 1331: # my $sum=0; 1332: # for (my $i=$start;$i<=$end;$i++) { 1333: # $sum+=&$sub($i); 1334: # } 1335: # return $sum 1336: #} 1337: 1338: #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')'); 1339: #sub sum2 { 1340: # my ($varname,$start,$end,$line)=@_; 1341: # my $sum=0; 1342: # for (my $i=$start;$i<=$end;$i++) { 1343: # my $func=sub { 1344: # eval("\$".$varname."=$i"); 1345: # eval($line); 1346: # }; 1347: # $sum+=&$func($i); 1348: # } 1349: # return $sum 1350: #} 1351: 1352: # expiremental idea 1353: sub proper_path { 1354: my ($path)=@_; 1355: if ( $external::target eq "tex" ) { 1356: return '/home/httpd/html'.$path; 1357: } else { 1358: return $path; 1359: } 1360: } 1361: