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Added jsMath support to these files. Basically, HTML_jsMath should do whatever HTML_dpng mode does. I simply included it HTML_jsMath every time HTML_dpng appeared.
1 ########### 2 #use Carp; 3 4 =head1 NAME 5 6 Matrix macros for the PG language 7 8 =head1 SYNPOSIS 9 10 11 12 =head1 DESCRIPTION 13 14 Almost all of the macros in the file are very rough at best. The most useful is display_matrix. 15 Many of the other macros work with vectors and matrices stored as anonymous arrays. 16 17 Frequently it may be 18 more useful to use the Matrix objects defined RealMatrix.pm and Matrix.pm and the constructs listed there. 19 20 21 =cut 22 23 BEGIN { 24 be_strict(); 25 } 26 27 sub _PGmatrixmacros_init { 28 } 29 30 # this subroutine zero_check is not very well designed below -- if it is used much it should receive 31 # more work -- particularly for checking relative tolerance. More work needs to be done if this is 32 # actually used. 33 34 sub zero_check{ 35 my $array = shift; 36 my %options = @_; 37 my $num = @$array; 38 my $i; 39 my $max = 0; my $mm; 40 for ($i=0; $i< $num; $i++) { 41 $mm = $array->[$i] ; 42 $max = abs($mm) if abs($mm) > $max; 43 } 44 my $tol = $options{tol}; 45 $tol = 0.01*$options{reltol}*$options{avg} if defined($options{reltol}) and defined $options{avg}; 46 $tol = .000001 unless defined($tol); 47 ($max <$tol) ? 1: 0; # 1 if the array is close to zero; 48 } 49 sub vec_dot{ 50 my $vec1 = shift; 51 my $vec2 = shift; 52 warn "vectors must have the same length" unless @$vec1 == @$vec2; # the vectors must have the same length. 53 my @vec1=@$vec1; 54 my @vec2=@$vec2; 55 my $sum = 0; 56 57 while(@vec1) { 58 $sum += shift(@vec1)*shift(@vec2); 59 } 60 $sum; 61 } 62 sub proj_vec { 63 my $vec = shift; 64 warn "First input must be a column matrix" unless ref($vec) eq 'Matrix' and ${$vec->dim()}[1] == 1; 65 my $matrix = shift; # the matrix represents a set of vectors spanning the linear space 66 # onto which we want to project the vector. 67 warn "Second input must be a matrix" unless ref($matrix) eq 'Matrix' and ${$matrix->dim()}[1] == ${$vec->dim()}[0]; 68 $matrix * transpose($matrix) * $vec; 69 } 70 71 sub vec_cmp{ #check to see that the submitted vector is a non-zero multiple of the correct vector 72 my $correct_vector = shift; 73 my %options = @_; 74 my $ans_eval = sub { 75 my $in = shift @_; 76 77 my $ans_hash = new AnswerHash; 78 my @in = split("\0",$in); 79 my @correct_vector=@$correct_vector; 80 $ans_hash->{student_ans} = "( " . join(", ", @in ) . " )"; 81 $ans_hash->{correct_ans} = "( " . join(", ", @correct_vector ) . " )"; 82 83 return($ans_hash) unless @$correct_vector == @in; # make sure the vectors are the same dimension 84 85 my $correct_length = vec_dot($correct_vector,$correct_vector); 86 my $in_length = vec_dot(\@in,\@in); 87 return($ans_hash) if $in_length == 0; 88 89 if (defined($correct_length) and $correct_length != 0) { 90 my $constant = vec_dot($correct_vector,\@in)/$correct_length; 91 my @difference = (); 92 for(my $i=0; $i < @correct_vector; $i++ ) { 93 $difference[$i]=$constant*$correct_vector[$i] - $in[$i]; 94 } 95 $ans_hash->{score} = zero_check(\@difference); 96 97 } else { 98 $ans_hash->{score} = 1 if vec_dot(\@in,\@in) == 0; 99 } 100 $ans_hash; 101 102 }; 103 104 $ans_eval; 105 } 106 107 ############ 108 109 =head4 display_matrix 110 111 Usage \{ display_matrix( [ [1, '\(\sin x\)'], [ans_rule(5), 6] ]) \} 112 \{ display_matrix($A, align=>'crvl') \} 113 \[ \{ display_matrix_mm($A) \} \] 114 \[ \{ display_matrix_mm([ [1, 3], [4, 6] ]) \} \] 115 116 display_matrix produces a matrix for display purposes. It checks whether 117 it is producing LaTeX output, or if it is displaying on a web page in one 118 of the various modes. The input can either be of type Matrix, or a 119 reference to an array. 120 121 Entries can be numbers, Fraction objects, bits of math mode, or answer 122 boxes. An entire row can be replaced by the string 'hline' to produce 123 a horizontal line in the matrix. 124 125 display_matrix_mm functions similarly, except that it should be inside 126 math mode. display_matrix_mm cannot contain answer boxes in its entries. 127 Entries to display_matrix_mm should assume that they are already in 128 math mode. 129 130 Both functions take an optional alignment string, similar to ones in 131 LaTeX tabulars and arrays. Here c for centered columns, l for left 132 flushed columns, and r for right flushed columns. 133 134 The alignment string can also specify vertical rules to be placed in the 135 matrix. Here s or | denote a solid line, d is a dashed line, and v 136 requests the default vertical line. This can be set on a system-wide 137 or course-wide basis via the variable $defaultDisplayMatrixStyle, and 138 it can default to solid, dashed, or no vertical line (n for none). 139 140 The matrix has left and right delimiters also specified by 141 $defaultDisplayMatrixStyle. They can be parentheses, square brackets, 142 braces, vertical bars, or none. The default can be overridden in 143 an individual problem with optional arguments such as left=>"|", or 144 right=>"]". 145 146 You can specify an optional argument of 'top_labels'=> ['a', 'b', 'c']. 147 These are placed above the columns of the matrix (as is typical for 148 linear programming tableau, for example). The entries will be typeset 149 in math mode. 150 151 Top labels require a bit of care. For image modes, they look better 152 with display_matrix_mm where it is all one big image, but they work with 153 display_matrix. With tth, you pretty much have to use display_matrix 154 since tth can't handle the TeX tricks used to get the column headers 155 up there if it gets the whole matrix at once. 156 157 158 =cut 159 160 161 sub display_matrix_mm{ # will display a matrix in tex format. 162 # the matrix can be either of type array or type 'Matrix' 163 return display_matrix(@_, 'force_tex'=>1); 164 } 165 166 sub display_matrix_math_mode { 167 return display_matrix_mm(@_); 168 } 169 170 sub display_matrix { 171 my $ra_matrix = shift; 172 my %opts = @_; 173 my $styleParams = defined($main::defaultDisplayMatrixStyle) ? 174 $main::defaultDisplayMatrixStyle : "(s)"; 175 176 set_default_options(\%opts, 177 '_filter_name' => 'display_matrix', 178 'force_tex' => 0, 179 'left' => substr($styleParams,0,1), 180 'right' => substr($styleParams,2,1), 181 'midrule' => substr($styleParams,1,1), 182 'top_labels' => 0, 183 'box'=>[-1,-1], # pair location of boxed element 184 'allow_unknown_options'=> 1, 185 'num_format' => "%.0f", 186 ); 187 188 my ($numRows, $numCols, @myRows); 189 190 if (ref($ra_matrix) eq 'Matrix' ) { 191 ($numRows, $numCols) = $ra_matrix->dim(); 192 for( my $i=0; $i<$numRows; $i++) { 193 $myRows[$i] = []; 194 for (my $j=0; $j<$numCols; $j++) { 195 my $entry = $ra_matrix->element($i+1,$j+1); 196 $entry = "#" unless defined($entry); 197 push @{ $myRows[$i] }, $entry; 198 } 199 } 200 } else { # matrix is input as [ [1,2,3],[4,5,6]] 201 $numCols = 0; 202 @myRows = @{$ra_matrix}; 203 $numRows = scalar(@myRows); # counts horizontal rules too 204 my $tmp; 205 for $tmp (@myRows) { 206 if($tmp ne 'hline') { 207 my @arow = @{$tmp}; 208 $numCols= scalar(@arow); #number of columns in table 209 last; 210 } 211 } 212 } 213 214 my $out; 215 my $j; 216 my $alignString=''; # alignment as a string for dvi/pdf 217 my $alignList; # alignment as a list 218 219 if(defined($opts{'align'})) { 220 $alignString= $opts{'align'}; 221 $alignString =~ s/v/$opts{'midrule'}/g; 222 $alignString =~ tr/s/|/; # Treat "s" as "|" 223 $alignString =~ tr/n//; # Remove "n" altogether 224 @$alignList = split //, $alignString; 225 } else { 226 for($j=0; $j<$numCols; $j++) { 227 $alignList->[$j] = "c"; 228 $alignString .= "c"; 229 } 230 } 231 # Before we start, we cannot let top_labels proceed if we 232 # are in tth mode and force_tex is true since tth can't handle 233 # the resulting code 234 if($opts{'force_tex'} and $main::displayMode eq 'HTML_tth') { 235 $opts{'top_labels'} = 0; 236 } 237 238 $out .= dm_begin_matrix($alignString, %opts); 239 # column labels for linear programming 240 $out .= dm_special_tops(%opts, 'alignList'=>$alignList) if ($opts{'top_labels'}); 241 $out .= dm_mat_left($numRows, %opts); 242 my $cnt = 1; # we count rows in in case an element is boxed 243 # vertical lines put in with first row 244 $j = shift @myRows; 245 $out .= dm_mat_row($j, $alignList, %opts, 'isfirst'=>$numRows, 246 'cnt' => $cnt); 247 $cnt++ unless ($j eq 'hline'); 248 $out .= dm_mat_right($numRows, %opts); 249 for $j (@myRows) { 250 $out .= dm_mat_row($j, $alignList, %opts, 'isfirst'=>0, 251 'cnt' => $cnt); 252 $cnt++ unless ($j eq 'hline'); 253 } 254 $out .= dm_end_matrix(%opts); 255 $out; 256 } 257 258 sub dm_begin_matrix { 259 my ($aligns)=shift; #alignments of columns in table 260 my %opts = @_; 261 my $out = ""; 262 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 263 # This should be doable by regexp, but it wasn't working for me 264 my ($j, @tmp); 265 @tmp = split //, $aligns; 266 $aligns=''; 267 for $j (@tmp) { 268 # I still can't get an @ expression sent to TeX, so plain 269 # vertical line 270 $aligns .= ($j eq "d") ? '|' : $j; 271 } 272 $out .= $opts{'force_tex'} ? '' : '\('; 273 if($opts{'top_labels'}) { 274 $out .= '\begingroup\setbox3=\hbox{\ensuremath{'; 275 } 276 $out .= '\displaystyle\left'.$opts{'left'}."\\begin{array}{$aligns} \n"; 277 } elsif ($main::displayMode eq 'Latex2HTML') { 278 $out .= "\n\\begin{rawhtml} <TABLE BORDER=0>\n\\end{rawhtml}"; 279 } elsif ($main::displayMode eq 'HTML' or $main::displayMode eq 'HTML_tth' 280 or $main::displayMode eq 'HTML_jsMath' 281 or $main::displayMode eq 'HTML_asciimath' 282 or $main::displayMode eq 'HTML_dpng' 283 or $main::displayMode eq 'HTML_img') { 284 $out .= qq!<TABLE BORDER="0" Cellspacing="8">\n!; 285 } 286 else { 287 $out = "Error: dm_begin_matrix: Unknown displayMode: $main::displayMode.\n"; 288 } 289 $out; 290 } 291 292 sub dm_special_tops { 293 my %opts = @_; 294 my @top_labels = @{$opts{'top_labels'}}; 295 my $out = ''; 296 my @alignList = @{$opts{'alignList'}}; 297 my ($j, $k); 298 my ($brh, $erh) = ("",""); # Start and end raw html 299 if($main::displayMode eq 'Latex2HTML') { 300 $brh = "\\begin{rawhtml}"; 301 $erh = "\\end{rawhtml}"; 302 } 303 304 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 305 for $j (@top_labels) { 306 $out .= '\smash{\raisebox{2.9ex}{\ensuremath{'. 307 $j . '}}} &'; 308 } 309 chop($out); # remove last & 310 $out .= '\cr\noalign{\vskip -2.5ex}'."\n"; # want skip jump up 2.5ex 311 } elsif ($main::displayMode eq 'HTML' or $main::displayMode eq 'HTML_tth' 312 or $main::displayMode eq 'HTML_jsMath' 313 or $main::displayMode eq 'HTML_asciimath' 314 or $main::displayMode eq 'HTML_dpng' 315 or $main::displayMode eq 'HTML_img' 316 or $main::displayMode eq 'Latex2HTML') { 317 $out .= "$brh<tr><td>$erh"; # Skip a column for the left brace 318 for $j (@top_labels) { 319 $k = shift @alignList; 320 while(defined($k) and ($k !~ /[lrc]/)) { 321 $out .= "$brh<td></td>$erh"; 322 $k = shift @alignList; 323 } 324 $out .= "$brh<td align=\"center\">$erh". ' \('.$j.'\)'."$brh</td>$erh"; 325 } 326 $out .= "<td></td>"; 327 } else { 328 $out = "Error: dm_begin_matrix: Unknown displayMode: $main::displayMode.\n"; 329 } 330 return $out; 331 } 332 333 sub dm_mat_left { 334 my $numrows = shift; 335 my %opts = @_; 336 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 337 return ""; # left delim is built into begin matrix 338 } 339 my $out=''; 340 my $j; 341 my ($brh, $erh) = ("",""); # Start and end raw html 342 if($main::displayMode eq 'Latex2HTML') { 343 $brh = "\\begin{rawhtml}"; 344 $erh = "\\end{rawhtml}"; 345 } 346 347 if($main::displayMode eq 'HTML_dpng' 348 or $main::displayMode eq 'HTML_jsMath' 349 or $main::displayMode eq 'HTML_asciimath' 350 or $main::displayMode eq 'HTML_img' 351 or $main::displayMode eq 'Latex2HTML') { 352 $out .= "$brh<tr valign=\"center\"><td nowrap=\"nowrap\" align=\"left\" rowspan=\"$numrows\">$erh"; 353 $out .= dm_image_delimeter($numrows, $opts{'left'}); 354 # $out .= "$brh<td><table border=0 cellspacing=5>\n$erh"; 355 return $out; 356 } 357 # Mode is now tth 358 359 $out .= "<tr valign=\"center\"><td nowrap=\"nowrap\" align=\"left\" rowspan=\"$numrows\">"; 360 $out .= dm_tth_delimeter($numrows, $opts{'left'}); 361 # $out .= "<td><table border=0 cellspacing=5>\n"; 362 return $out; 363 } 364 365 sub dm_mat_right { 366 my $numrows = shift; 367 my %opts = @_; 368 my $out=''; 369 my $j; 370 my ($brh, $erh) = ("",""); # Start and end raw html 371 if($main::displayMode eq 'Latex2HTML') { 372 $brh = "\\begin{rawhtml}"; 373 $erh = "\\end{rawhtml}"; 374 } 375 376 377 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 378 return ""; 379 } 380 381 if($main::displayMode eq 'HTML_dpng' 382 or $main::displayMode eq 'HTML_jsMath' 383 or $main::displayMode eq 'HTML_asciimath' 384 or $main::displayMode eq 'Latex2HTML' 385 or $main::displayMode eq 'HTML_img') { 386 $out .= "$brh<td nowrap=\"nowrap\" align=\"right\" rowspan=\"$numrows\">$erh"; 387 388 $out.= dm_image_delimeter($numrows, $opts{'right'}); 389 return $out; 390 } 391 392 # $out .= "</table>"; 393 $out .= '<td nowrap="nowrap" align="left" rowspan="'.$numrows.'2">'; 394 $out .= dm_tth_delimeter($numrows, $opts{'right'}); 395 $out .= '</td>'; 396 return $out; 397 } 398 399 sub dm_end_matrix { 400 my %opts = @_; 401 402 my $out = ""; 403 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 404 $out .= "\\end{array}\\right$opts{right}"; 405 if($opts{'top_labels'}) { 406 $out .= '}} \dimen3=\ht3 \advance\dimen3 by 3ex \ht3=\dimen3'."\n". 407 '\box3\endgroup'; 408 } 409 $out .= $opts{'force_tex'} ? '' : "\\) "; 410 } 411 elsif ($main::displayMode eq 'Latex2HTML') { 412 $out .= "\n\\begin{rawhtml} </TABLE >\n\\end{rawhtml}"; 413 } 414 elsif ($main::displayMode eq 'HTML' or $main::displayMode eq 'HTML_tth' 415 or $main::displayMode eq 'HTML_jsMath' 416 or $main::displayMode eq 'HTML_asciimath' 417 or $main::displayMode eq 'HTML_img' 418 or $main::displayMode eq 'HTML_dpng') { 419 $out .= "</TABLE>\n"; 420 } 421 else { 422 $out = "Error: PGmatrixmacros: dm_end_matrix: Unknown displayMode: $main::displayMode.\n"; 423 } 424 $out; 425 } 426 427 # Make an image of a big delimiter for a matrix 428 sub dm_image_delimeter { 429 my $numRows = shift; 430 my $char = shift; 431 my ($out, $j); 432 433 if($char eq ".") {return("");} 434 if($char eq "d") { # special treatment for dashed lines 435 $out='\(\vbox to '.($numRows*1.7).'\baselineskip '; 436 $out .='{\cleaders\hbox{\vbox{\hrule width0pt height3pt depth0pt'; 437 $out .='\hrule width0.3pt height6pt depth0pt'; 438 $out .='\hrule width0pt height3pt depth0pt}}\vfil}\)'; 439 return($out); 440 } 441 if($char eq "|") { 442 $out='\(\vbox to '.($numRows*1.4).'\baselineskip '; 443 $out .='{\cleaders\vrule width0.3pt'; 444 $out .='\vfil}\)'; 445 return($out); 446 } 447 if($char eq "{") {$char = '\lbrace';} 448 if($char eq "}") {$char = '\rbrace';} 449 $out .= '\(\setlength{\arraycolsep}{0in}\left.\begin{array}{c}'; 450 for($j=0;$j<=$numRows;$j++) { $out .= '\! \\\\'; } 451 $out .= '\end{array}\right'.$char.'\)'; 452 return($out); 453 } 454 455 # Basically uses a table of special characters and simple 456 # recipe to produce big delimeters a la tth mode 457 sub dm_tth_delimeter { 458 my $numRows = shift; 459 my $char = shift; 460 461 if($char eq ".") { return("");} 462 my ($top, $mid, $bot, $extra); 463 my ($j, $out); 464 465 if($char eq "(") { ($top, $mid, $bot, $extra) = ('æ','ç','è','ç');} 466 elsif($char eq ")") { ($top, $mid, $bot, $extra) = ('ö','÷','ø','÷');} 467 elsif($char eq "|") { ($top, $mid, $bot, $extra) = ('ê','ê','ê','ê');} 468 elsif($char eq "[") { ($top, $mid, $bot, $extra) = ('é','ê','ë','ê');} 469 elsif($char eq "]") { ($top, $mid, $bot, $extra) = ('ù','ú','û','ú');} 470 elsif($char eq "{") { ($top, $mid, $bot, $extra) = ('ì','ï','î','í');} 471 elsif($char eq "}") { ($top, $mid, $bot, $extra) = ('ü','ï','þ','ý');} 472 else { warn "Unknown delimiter in dm_tth_delimeter";} 473 474 # old version 475 # $out = '<td nowrap="nowrap" align="left"><font face="symbol">'; 476 $out = '<font face="symbol">'; 477 $out .= "$top<br />"; 478 for($j=1;$j<$numRows; $j++) { 479 $out .= "$mid<br />"; 480 } 481 $out .= "$extra<br />"; 482 for($j=1;$j<$numRows; $j++) { 483 $out .= "$mid<br />"; 484 } 485 $out .= "$bot</font></td>"; 486 return $out; 487 } 488 489 # Make a row for the matrix 490 sub dm_mat_row { 491 my $elements = shift; 492 my $tmp = shift; 493 my @align = @{$tmp} ; 494 my %opts = @_; 495 496 if($elements eq 'hline') { 497 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 498 return '\hline '; 499 } else { 500 # Making a hline in a table 501 return '<tr><td colspan="'.scalar(@align).'"><hr></td></tr>'; 502 } 503 } 504 505 my @elements = @{$elements}; 506 my $out = ""; 507 my ($brh, $erh) = ("",""); # Start and end raw html 508 my $element; 509 my $colcount=0; 510 if($main::displayMode eq 'Latex2HTML') { 511 $brh = "\\begin{rawhtml}"; 512 $erh = "\\end{rawhtml}"; 513 } 514 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 515 while (@elements) { 516 $colcount++; 517 $out .= '\fbox{' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 518 $element= shift(@elements); 519 if(ref($element) eq 'Fraction') { 520 $element= $element->print_inline(); 521 } 522 $out .= '\\mbox{'."$element".'}'; 523 $out .= '}' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 524 $out .= " &"; 525 } 526 chop($out); # remove last & 527 $out .= "\\cr \n"; 528 # carriage returns must be added manually for tex 529 } elsif ($main::displayMode eq 'HTML' or $main::displayMode eq 'HTML_tth' 530 or $main::displayMode eq 'HTML_jsMath' 531 or $main::displayMode eq 'HTML_asciimath' 532 or $main::displayMode eq 'HTML_dpng' 533 or $main::displayMode eq 'HTML_img' 534 or $main::displayMode eq 'Latex2HTML') { 535 if(not $opts{'isfirst'}) { $out .= "$brh\n<TR>\n$erh";} 536 while (@elements) { 537 my $myalign; 538 $myalign = shift @align; 539 if($myalign eq "|" or $myalign eq "d") { 540 if($opts{'isfirst'} && $main::displayMode ne 'HTML_tth') { 541 $out .= $brh.'<td rowspan="'.$opts{'isfirst'}.'">'.$erh; 542 $out .= dm_image_delimeter($opts{'isfirst'}-1, $myalign); 543 } elsif($main::displayMode eq 'HTML_tth') { 544 if($myalign eq "d") { # dashed line in tth mode 545 $out .= '<td> | </td>'; 546 } elsif($opts{'isfirst'}) { # solid line in tth mode 547 $out .= '<td rowspan="'.$opts{'isfirst'}.'"<table border="0"><tr>'; 548 $out .= dm_tth_delimeter($opts{'isfirst'}-1, "|"); 549 $out .= '</td></tr></table>'; 550 } 551 } 552 } else { 553 if($myalign eq "c") { $myalign = "center";} 554 if($myalign eq "l") { $myalign = "left";} 555 if($myalign eq "r") { $myalign = "right";} 556 $colcount++; 557 $out .= '\fbox{' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 558 $element= shift(@elements); 559 if (ref($element) eq 'Fraction') { 560 $element= $element->print_inline(); 561 #}elsif( $element =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/ and $element != sprintf($opts{'num_format'},$element) and $element - sprintf($opts{'num_format'},$element) < $main::functZeroLevelTolDefault){ 562 # $element = sprintf($opts{'num_format'},$element); 563 # $element = 0 if abs($element) < $main::functZeroLevelTolDefault; 564 } 565 $out .= "$brh<TD nowrap=\"nowrap\" align=\"$myalign\">$erh"; 566 $out .= '<table border="1"><tr><td>' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 567 $out .= $element; 568 $out .= '</td></tr></table>' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 569 $out .= "$brh</TD>$erh"; 570 } 571 } 572 if(not $opts{'isfirst'}) {$out .="$brh</TR>$erh\n";} 573 } 574 else { 575 $out = "Error: dm_mat_row: Unknown displayMode: $main::displayMode.\n"; 576 } 577 $out; 578 } 579 580 =head4 mbox 581 582 Usage \{ mbox(thing1, thing2, thing3) \} 583 \{ mbox([thing1, thing2, thing3], valign=>'top') \} 584 585 mbox takes a list of constructs, such as strings, or outputs of 586 display_matrix, and puts them together on a line. Without mbox, the 587 output of display_matrix would always start a new line. 588 589 The inputs can be just listed, or given as a reference to an array. 590 With the latter, optional arguments can be given. 591 592 Optional arguments are allowbreaks=>'yes' to allow line breaks in TeX 593 output; and valign which sets vertical alignment on web page output. 594 595 =cut 596 597 sub mbox { 598 my $inList = shift; 599 my %opts; 600 if(ref($inList) eq 'ARRAY') { 601 %opts = @_; 602 } else { 603 %opts = (); 604 $inList = [$inList, @_]; 605 } 606 607 set_default_options(\%opts, 608 '_filter_name' => 'mbox', 609 'valign' => 'middle', 610 'allowbreaks' => 'no', 611 'allow_unknown_options'=> 0); 612 if(! $opts{'allowbreaks'}) { $opts{'allowbreaks'}='no';} 613 my $out = ""; 614 my $j; 615 my ($brh, $erh) = ("",""); # Start and end raw html if needed 616 if($main::displayMode eq 'Latex2HTML') { 617 $brh = "\\begin{rawhtml}"; 618 $erh = "\\end{rawhtml}"; 619 } 620 my @hlist = @{$inList}; 621 if($main::displayMode eq 'TeX') { 622 if($opts{allowbreaks} ne 'no') {$out .= '\mbox{';} 623 for $j (@hlist) { $out .= $j;} 624 if($opts{allowbreaks} ne 'no') {$out .= '}';} 625 } else { 626 $out .= qq!$brh<table><tr valign="$opts{'valign'}">$erh!; 627 for $j (@hlist) { 628 $out .= qq!$brh<td align="center" nowrap="nowrap">$erh$j$brh</td>$erh!; 629 } 630 $out .= "$brh</table>$erh"; 631 } 632 return $out; 633 } 634 635 636 =head4 ra_flatten_matrix 637 638 Usage: ra_flatten_matrix($A) 639 640 where $A is a matrix object 641 The output is a reference to an array. The matrix is placed in the array by iterating 642 over columns on the inside 643 loop, then over the rows. (e.g right to left and then down, as one reads text) 644 645 646 =cut 647 648 649 sub ra_flatten_matrix{ 650 my $matrix = shift; 651 warn "The argument must be a matrix object" unless ref($matrix) =~ /Matrix/; 652 my @array = (); 653 my ($rows, $cols ) = $matrix->dim(); 654 foreach my $i (1..$rows) { 655 foreach my $j (1..$cols) { 656 push(@array, $matrix->element($i,$j) ); 657 } 658 } 659 \@array; 660 } 661 662 # This subroutine is probably obsolete and not generally useful. It was patterned after the APL 663 # constructs for multiplying matrices. It might come in handy for non-standard multiplication of 664 # of matrices (e.g. mod 2) for indice matrices. 665 sub apl_matrix_mult{ 666 my $ra_a= shift; 667 my $ra_b= shift; 668 my %options = @_; 669 my $rf_op_times= sub {$_[0] *$_[1]}; 670 my $rf_op_plus = sub {my $sum = 0; my @in = @_; while(@in){ $sum = $sum + shift(@in) } $sum; }; 671 $rf_op_times = $options{'times'} if defined($options{'times'}) and ref($options{'times'}) eq 'CODE'; 672 $rf_op_plus = $options{'plus'} if defined($options{'plus'}) and ref($options{'plus'}) eq 'CODE'; 673 my $rows = @$ra_a; 674 my $cols = @{$ra_b->[0]}; 675 my $k_size = @$ra_b; 676 my $out ; 677 my ($i, $j, $k); 678 for($i=0;$i<$rows;$i++) { 679 for($j=0;$j<$cols;$j++) { 680 my @r = (); 681 for($k=0;$k<$k_size;$k++) { 682 $r[$k] = &$rf_op_times($ra_a->[$i]->[$k] , $ra_b->[$k]->[$j]); 683 } 684 $out->[$i]->[$j] = &$rf_op_plus( @r ); 685 } 686 } 687 $out; 688 } 689 690 sub matrix_mult { 691 apl_matrix_mult($_[0], $_[1]); 692 } 693 694 sub make_matrix{ 695 my $function = shift; 696 my $rows = shift; 697 my $cols = shift; 698 my ($i, $j, $k); 699 my $ra_out; 700 for($i=0;$i<$rows;$i++) { 701 for($j=0;$j<$cols;$j++) { 702 $ra_out->[$i]->[$j] = &$function($i,$j); 703 } 704 } 705 $ra_out; 706 } 707 708 709 # sub format_answer{ 710 # my $ra_eigenvalues = shift; 711 # my $ra_eigenvectors = shift; 712 # my $functionName = shift; 713 # my @eigenvalues=@$ra_eigenvalues; 714 # my $size= @eigenvalues; 715 # my $ra_eigen = make_matrix( sub {my ($i,$j) = @_; ($i==$j) ? "e^{$eigenvalues[$j] t}": 0 }, $size,$size); 716 # my $out = qq! 717 # $functionName(t) =! . 718 # displayMatrix(apl_matrix_mult($ra_eigenvectors,$ra_eigen, 719 # 'times'=>sub{($_[0] and $_[1]) ? "$_[0]$_[1]" : ''}, 720 # 'plus'=>sub{ my $out = join("",@_); ($out) ?$out : '0' } 721 # ) ) ; 722 # $out; 723 # } 724 # sub format_vector_answer{ 725 # my $ra_eigenvalues = shift; 726 # my $ra_eigenvectors = shift; 727 # my $functionName = shift; 728 # my @eigenvalues=@$ra_eigenvalues; 729 # my $size= @eigenvalues; 730 # my $ra_eigen = make_matrix( sub {my ($i,$j) = @_; ($i==$j) ? "e^{$eigenvalues[$j] t}": 0 }, $size,$size); 731 # my $out = qq! 732 # $functionName(t) =! . 733 # displayMatrix($ra_eigenvectors)."e^{$eigenvalues[0] t}" ; 734 # $out; 735 # } 736 # sub format_question{ 737 # my $ra_matrix = shift; 738 # my $out = qq! y'(t) = ! . displayMatrix($B). q! y(t)! 739 # 740 # } 741 742 1;
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