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This commit was manufactured by cvs2svn to create branch 'rel-2-4-patches'.
1 2 ########### 3 #use Carp; 4 5 =head1 NAME 6 7 Matrix macros for the PG language 8 9 =head1 SYNPOSIS 10 11 12 13 =head1 DESCRIPTION 14 15 Almost all of the macros in the file are very rough at best. The most useful is display_matrix. 16 Many of the other macros work with vectors and matrices stored as anonymous arrays. 17 18 Frequently it may be 19 more useful to use the Matrix objects defined RealMatrix.pm and Matrix.pm and the constructs listed there. 20 21 22 =cut 23 24 BEGIN { 25 be_strict(); 26 } 27 28 sub _PGmatrixmacros_init { 29 } 30 31 # this subroutine zero_check is not very well designed below -- if it is used much it should receive 32 # more work -- particularly for checking relative tolerance. More work needs to be done if this is 33 # actually used. 34 35 sub zero_check{ 36 my $array = shift; 37 my %options = @_; 38 my $num = @$array; 39 my $i; 40 my $max = 0; my $mm; 41 for ($i=0; $i< $num; $i++) { 42 $mm = $array->[$i] ; 43 $max = abs($mm) if abs($mm) > $max; 44 } 45 my $tol = $options{tol}; 46 $tol = 0.01*$options{reltol}*$options{avg} if defined($options{reltol}) and defined $options{avg}; 47 $tol = .000001 unless defined($tol); 48 ($max <$tol) ? 1: 0; # 1 if the array is close to zero; 49 } 50 sub vec_dot{ 51 my $vec1 = shift; 52 my $vec2 = shift; 53 warn "vectors must have the same length" unless @$vec1 == @$vec2; # the vectors must have the same length. 54 my @vec1=@$vec1; 55 my @vec2=@$vec2; 56 my $sum = 0; 57 58 while(@vec1) { 59 $sum += shift(@vec1)*shift(@vec2); 60 } 61 $sum; 62 } 63 sub proj_vec { 64 my $vec = shift; 65 warn "First input must be a column matrix" unless ref($vec) eq 'Matrix' and ${$vec->dim()}[1] == 1; 66 my $matrix = shift; # the matrix represents a set of vectors spanning the linear space 67 # onto which we want to project the vector. 68 warn "Second input must be a matrix" unless ref($matrix) eq 'Matrix' and ${$matrix->dim()}[1] == ${$vec->dim()}[0]; 69 $matrix * transpose($matrix) * $vec; 70 } 71 72 sub vec_cmp{ #check to see that the submitted vector is a non-zero multiple of the correct vector 73 my $correct_vector = shift; 74 my %options = @_; 75 my $ans_eval = sub { 76 my $in = shift @_; 77 78 my $ans_hash = new AnswerHash; 79 my @in = split("\0",$in); 80 my @correct_vector=@$correct_vector; 81 $ans_hash->{student_ans} = "( " . join(", ", @in ) . " )"; 82 $ans_hash->{correct_ans} = "( " . join(", ", @correct_vector ) . " )"; 83 84 return($ans_hash) unless @$correct_vector == @in; # make sure the vectors are the same dimension 85 86 my $correct_length = vec_dot($correct_vector,$correct_vector); 87 my $in_length = vec_dot(\@in,\@in); 88 return($ans_hash) if $in_length == 0; 89 90 if (defined($correct_length) and $correct_length != 0) { 91 my $constant = vec_dot($correct_vector,\@in)/$correct_length; 92 my @difference = (); 93 for(my $i=0; $i < @correct_vector; $i++ ) { 94 $difference[$i]=$constant*$correct_vector[$i] - $in[$i]; 95 } 96 $ans_hash->{score} = zero_check(\@difference); 97 98 } else { 99 $ans_hash->{score} = 1 if vec_dot(\@in,\@in) == 0; 100 } 101 $ans_hash; 102 103 }; 104 105 $ans_eval; 106 } 107 108 ############ 109 110 =head4 display_matrix 111 112 Usage \{ display_matrix( [ [1, '\(\sin x\)'], [ans_rule(5), 6] ]) \} 113 \{ display_matrix($A, align=>'crvl') \} 114 \[ \{ display_matrix_mm($A) \} \] 115 \[ \{ display_matrix_mm([ [1, 3], [4, 6] ]) \} \] 116 117 display_matrix produces a matrix for display purposes. It checks whether 118 it is producing LaTeX output, or if it is displaying on a web page in one 119 of the various modes. The input can either be of type Matrix, or a 120 reference to an array. 121 122 Entries can be numbers, Fraction objects, bits of math mode, or answer 123 boxes. An entire row can be replaced by the string 'hline' to produce 124 a horizontal line in the matrix. 125 126 display_matrix_mm functions similarly, except that it should be inside 127 math mode. display_matrix_mm cannot contain answer boxes in its entries. 128 Entries to display_matrix_mm should assume that they are already in 129 math mode. 130 131 Both functions take an optional alignment string, similar to ones in 132 LaTeX tabulars and arrays. Here c for centered columns, l for left 133 flushed columns, and r for right flushed columns. 134 135 The alignment string can also specify vertical rules to be placed in the 136 matrix. Here s or | denote a solid line, d is a dashed line, and v 137 requests the default vertical line. This can be set on a system-wide 138 or course-wide basis via the variable $defaultDisplayMatrixStyle, and 139 it can default to solid, dashed, or no vertical line (n for none). 140 141 The matrix has left and right delimiters also specified by 142 $defaultDisplayMatrixStyle. They can be parentheses, square brackets, 143 braces, vertical bars, or none. The default can be overridden in 144 an individual problem with optional arguments such as left=>"|", or 145 right=>"]". 146 147 You can specify an optional argument of 'top_labels'=> ['a', 'b', 'c']. 148 These are placed above the columns of the matrix (as is typical for 149 linear programming tableau, for example). The entries will be typeset 150 in math mode. 151 152 Top labels require a bit of care. For image modes, they look better 153 with display_matrix_mm where it is all one big image, but they work with 154 display_matrix. With tth, you pretty much have to use display_matrix 155 since tth can't handle the TeX tricks used to get the column headers 156 up there if it gets the whole matrix at once. 157 158 159 =cut 160 161 162 sub display_matrix_mm{ # will display a matrix in tex format. 163 # the matrix can be either of type array or type 'Matrix' 164 return display_matrix(@_, 'force_tex'=>1); 165 } 166 167 sub display_matrix_math_mode { 168 return display_matrix_mm(@_); 169 } 170 171 sub display_matrix { 172 my $ra_matrix = shift; 173 my %opts = @_; 174 my $styleParams = defined($main::defaultDisplayMatrixStyle) ? 175 $main::defaultDisplayMatrixStyle : "(s)"; 176 177 set_default_options(\%opts, 178 '_filter_name' => 'display_matrix', 179 'force_tex' => 0, 180 'left' => substr($styleParams,0,1), 181 'right' => substr($styleParams,2,1), 182 'midrule' => substr($styleParams,1,1), 183 'top_labels' => 0, 184 'box'=>[-1,-1], # pair location of boxed element 185 'allow_unknown_options'=> 1, 186 'num_format' => "%.0f", 187 ); 188 189 my ($numRows, $numCols, @myRows); 190 191 if (ref($ra_matrix) eq 'Matrix' ) { 192 ($numRows, $numCols) = $ra_matrix->dim(); 193 for( my $i=0; $i<$numRows; $i++) { 194 $myRows[$i] = []; 195 for (my $j=0; $j<$numCols; $j++) { 196 my $entry = $ra_matrix->element($i+1,$j+1); 197 $entry = "#" unless defined($entry); 198 push @{ $myRows[$i] }, $entry; 199 } 200 } 201 } else { # matrix is input as [ [1,2,3],[4,5,6]] 202 $numCols = 0; 203 @myRows = @{$ra_matrix}; 204 $numRows = scalar(@myRows); # counts horizontal rules too 205 my $tmp; 206 for $tmp (@myRows) { 207 if($tmp ne 'hline') { 208 my @arow = @{$tmp}; 209 $numCols= scalar(@arow); #number of columns in table 210 last; 211 } 212 } 213 } 214 215 my $out; 216 my $j; 217 my $alignString=''; # alignment as a string for dvi/pdf 218 my $alignList; # alignment as a list 219 220 if(defined($opts{'align'})) { 221 $alignString= $opts{'align'}; 222 $alignString =~ s/v/$opts{'midrule'}/g; 223 $alignString =~ tr/s/|/; # Treat "s" as "|" 224 $alignString =~ tr/n//; # Remove "n" altogether 225 @$alignList = split //, $alignString; 226 } else { 227 for($j=0; $j<$numCols; $j++) { 228 $alignList->[$j] = "c"; 229 $alignString .= "c"; 230 } 231 } 232 # Before we start, we cannot let top_labels proceed if we 233 # are in tth mode and force_tex is true since tth can't handle 234 # the resulting code 235 if($opts{'force_tex'} and $main::displayMode eq 'HTML_tth') { 236 $opts{'top_labels'} = 0; 237 } 238 239 $out .= dm_begin_matrix($alignString, %opts); 240 # column labels for linear programming 241 $out .= dm_special_tops(%opts, 'alignList'=>$alignList) if ($opts{'top_labels'}); 242 $out .= dm_mat_left($numRows, %opts); 243 my $cnt = 1; # we count rows in in case an element is boxed 244 # vertical lines put in with first row 245 $j = shift @myRows; 246 $out .= dm_mat_row($j, $alignList, %opts, 'isfirst'=>$numRows, 247 'cnt' => $cnt); 248 $cnt++ unless ($j eq 'hline'); 249 $out .= dm_mat_right($numRows, %opts); 250 for $j (@myRows) { 251 $out .= dm_mat_row($j, $alignList, %opts, 'isfirst'=>0, 252 'cnt' => $cnt); 253 $cnt++ unless ($j eq 'hline'); 254 } 255 $out .= dm_end_matrix(%opts); 256 $out; 257 } 258 259 sub dm_begin_matrix { 260 my ($aligns)=shift; #alignments of columns in table 261 my %opts = @_; 262 my $out = ""; 263 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 264 # This should be doable by regexp, but it wasn't working for me 265 my ($j, @tmp); 266 @tmp = split //, $aligns; 267 $aligns=''; 268 for $j (@tmp) { 269 # I still can't get an @ expression sent to TeX, so plain 270 # vertical line 271 $aligns .= ($j eq "d") ? '|' : $j; 272 } 273 $out .= $opts{'force_tex'} ? '' : '\('; 274 if($opts{'top_labels'}) { 275 $out .= '\begingroup\setbox3=\hbox{\ensuremath{'; 276 } 277 $out .= '\displaystyle\left'.$opts{'left'}."\\begin{array}{$aligns} \n"; 278 } elsif ($main::displayMode eq 'Latex2HTML') { 279 $out .= "\n\\begin{rawhtml} <TABLE BORDER=0>\n\\end{rawhtml}"; 280 } elsif ($main::displayMode eq 'HTML' or $main::displayMode eq 'HTML_tth' 281 or $main::displayMode eq 'HTML_jsMath' 282 or $main::displayMode eq 'HTML_asciimath' 283 or $main::displayMode eq 'HTML_LaTeXMathML' 284 or $main::displayMode eq 'HTML_dpng' 285 or $main::displayMode eq 'HTML_img') { 286 $out .= qq!<TABLE BORDER="0" Cellspacing="8">\n!; 287 } 288 else { 289 $out = "Error: dm_begin_matrix: Unknown displayMode: $main::displayMode.\n"; 290 } 291 $out; 292 } 293 294 sub dm_special_tops { 295 my %opts = @_; 296 my @top_labels = @{$opts{'top_labels'}}; 297 my $out = ''; 298 my @alignList = @{$opts{'alignList'}}; 299 my ($j, $k); 300 my ($brh, $erh) = ("",""); # Start and end raw html 301 if($main::displayMode eq 'Latex2HTML') { 302 $brh = "\\begin{rawhtml}"; 303 $erh = "\\end{rawhtml}"; 304 } 305 306 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 307 for $j (@top_labels) { 308 $out .= '\smash{\raisebox{2.9ex}{\ensuremath{'. 309 $j . '}}} &'; 310 } 311 chop($out); # remove last & 312 $out .= '\cr\noalign{\vskip -2.5ex}'."\n"; # want skip jump up 2.5ex 313 } elsif ($main::displayMode eq 'HTML' or $main::displayMode eq 'HTML_tth' 314 or $main::displayMode eq 'HTML_jsMath' 315 or $main::displayMode eq 'HTML_asciimath' 316 or $main::displayMode eq 'HTML_LaTeXMathML' 317 or $main::displayMode eq 'HTML_dpng' 318 or $main::displayMode eq 'HTML_img' 319 or $main::displayMode eq 'Latex2HTML') { 320 $out .= "$brh<tr><td>$erh"; # Skip a column for the left brace 321 for $j (@top_labels) { 322 $k = shift @alignList; 323 while(defined($k) and ($k !~ /[lrc]/)) { 324 $out .= "$brh<td></td>$erh"; 325 $k = shift @alignList; 326 } 327 $out .= "$brh<td align=\"center\">$erh". ' \('.$j.'\)'."$brh</td>$erh"; 328 } 329 $out .= "<td></td>"; 330 } else { 331 $out = "Error: dm_begin_matrix: Unknown displayMode: $main::displayMode.\n"; 332 } 333 return $out; 334 } 335 336 sub dm_mat_left { 337 my $numrows = shift; 338 my %opts = @_; 339 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 340 return ""; # left delim is built into begin matrix 341 } 342 my $out=''; 343 my $j; 344 my ($brh, $erh) = ("",""); # Start and end raw html 345 if($main::displayMode eq 'Latex2HTML') { 346 $brh = "\\begin{rawhtml}"; 347 $erh = "\\end{rawhtml}"; 348 } 349 350 if($main::displayMode eq 'HTML_dpng' 351 or $main::displayMode eq 'HTML_jsMath' 352 or $main::displayMode eq 'HTML_asciimath' 353 or $main::displayMode eq 'HTML_LaTeXMathML' 354 or $main::displayMode eq 'HTML_img' 355 or $main::displayMode eq 'Latex2HTML') { 356 $out .= "$brh<tr valign=\"center\"><td nowrap=\"nowrap\" align=\"left\" rowspan=\"$numrows\">$erh"; 357 $out .= dm_image_delimeter($numrows, $opts{'left'}); 358 # $out .= "$brh<td><table border=0 cellspacing=5>\n$erh"; 359 return $out; 360 } 361 # Mode is now tth 362 363 $out .= "<tr valign=\"center\"><td nowrap=\"nowrap\" align=\"left\" rowspan=\"$numrows\">"; 364 $out .= dm_tth_delimeter($numrows, $opts{'left'}); 365 # $out .= "<td><table border=0 cellspacing=5>\n"; 366 return $out; 367 } 368 369 sub dm_mat_right { 370 my $numrows = shift; 371 my %opts = @_; 372 my $out=''; 373 my $j; 374 my ($brh, $erh) = ("",""); # Start and end raw html 375 if($main::displayMode eq 'Latex2HTML') { 376 $brh = "\\begin{rawhtml}"; 377 $erh = "\\end{rawhtml}"; 378 } 379 380 381 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 382 return ""; 383 } 384 385 if($main::displayMode eq 'HTML_dpng' 386 or $main::displayMode eq 'HTML_jsMath' 387 or $main::displayMode eq 'HTML_asciimath' 388 or $main::displayMode eq 'HTML_LaTeXMathML' 389 or $main::displayMode eq 'Latex2HTML' 390 or $main::displayMode eq 'HTML_img') { 391 $out .= "$brh<td nowrap=\"nowrap\" align=\"right\" rowspan=\"$numrows\">$erh"; 392 393 $out.= dm_image_delimeter($numrows, $opts{'right'}); 394 return $out; 395 } 396 397 # $out .= "</table>"; 398 $out .= '<td nowrap="nowrap" align="left" rowspan="'.$numrows.'2">'; 399 $out .= dm_tth_delimeter($numrows, $opts{'right'}); 400 $out .= '</td>'; 401 return $out; 402 } 403 404 sub dm_end_matrix { 405 my %opts = @_; 406 407 my $out = ""; 408 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 409 $out .= "\\end{array}\\right$opts{right}"; 410 if($opts{'top_labels'}) { 411 $out .= '}} \dimen3=\ht3 \advance\dimen3 by 3ex \ht3=\dimen3'."\n". 412 '\box3\endgroup'; 413 } 414 $out .= $opts{'force_tex'} ? '' : "\\) "; 415 } 416 elsif ($main::displayMode eq 'Latex2HTML') { 417 $out .= "\n\\begin{rawhtml} </TABLE >\n\\end{rawhtml}"; 418 } 419 elsif ($main::displayMode eq 'HTML' or $main::displayMode eq 'HTML_tth' 420 or $main::displayMode eq 'HTML_jsMath' 421 or $main::displayMode eq 'HTML_asciimath' 422 or $main::displayMode eq 'HTML_LaTeXMathML' 423 or $main::displayMode eq 'HTML_img' 424 or $main::displayMode eq 'HTML_dpng') { 425 $out .= "</TABLE>\n"; 426 } 427 else { 428 $out = "Error: PGmatrixmacros: dm_end_matrix: Unknown displayMode: $main::displayMode.\n"; 429 } 430 $out; 431 } 432 433 # Make an image of a big delimiter for a matrix 434 sub dm_image_delimeter { 435 my $numRows = shift; 436 my $char = shift; 437 my ($out, $j); 438 439 if($char eq ".") {return("");} 440 if($char eq "d") { # special treatment for dashed lines 441 $out='\(\vbox to '.($numRows*1.7).'\baselineskip '; 442 $out .='{\cleaders\hbox{\vbox{\hrule width0pt height3pt depth0pt'; 443 $out .='\hrule width0.3pt height6pt depth0pt'; 444 $out .='\hrule width0pt height3pt depth0pt}}\vfil}\)'; 445 return($out); 446 } 447 if($char eq "|") { 448 $out='\(\vbox to '.($numRows*1.4).'\baselineskip '; 449 $out .='{\cleaders\vrule width0.3pt'; 450 $out .='\vfil}\)'; 451 return($out); 452 } 453 if($char eq "{") {$char = '\lbrace';} 454 if($char eq "}") {$char = '\rbrace';} 455 $out .= '\(\setlength{\arraycolsep}{0in}\left.\begin{array}{c}'; 456 for($j=0;$j<=$numRows;$j++) { $out .= '\! \\\\'; } 457 $out .= '\end{array}\right'.$char.'\)'; 458 return($out); 459 } 460 461 # Basically uses a table of special characters and simple 462 # recipe to produce big delimeters a la tth mode 463 sub dm_tth_delimeter { 464 my $numRows = shift; 465 my $char = shift; 466 467 if($char eq ".") { return("");} 468 my ($top, $mid, $bot, $extra); 469 my ($j, $out); 470 471 if($char eq "(") { ($top, $mid, $bot, $extra) = ('æ','ç','è','ç');} 472 elsif($char eq ")") { ($top, $mid, $bot, $extra) = ('ö','÷','ø','÷');} 473 elsif($char eq "|") { ($top, $mid, $bot, $extra) = ('ê','ê','ê','ê');} 474 elsif($char eq "[") { ($top, $mid, $bot, $extra) = ('é','ê','ë','ê');} 475 elsif($char eq "]") { ($top, $mid, $bot, $extra) = ('ù','ú','û','ú');} 476 elsif($char eq "{") { ($top, $mid, $bot, $extra) = ('ì','ï','î','í');} 477 elsif($char eq "}") { ($top, $mid, $bot, $extra) = ('ü','ï','þ','ý');} 478 else { warn "Unknown delimiter in dm_tth_delimeter";} 479 480 # old version 481 # $out = '<td nowrap="nowrap" align="left"><font face="symbol">'; 482 $out = '<font face="symbol">'; 483 $out .= "$top<br />"; 484 for($j=1;$j<$numRows; $j++) { 485 $out .= "$mid<br />"; 486 } 487 $out .= "$extra<br />"; 488 for($j=1;$j<$numRows; $j++) { 489 $out .= "$mid<br />"; 490 } 491 $out .= "$bot</font></td>"; 492 return $out; 493 } 494 495 # Make a row for the matrix 496 sub dm_mat_row { 497 my $elements = shift; 498 my $tmp = shift; 499 my @align = @{$tmp} ; 500 my %opts = @_; 501 502 if($elements eq 'hline') { 503 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 504 return '\hline '; 505 } else { 506 # Making a hline in a table 507 return '<tr><td colspan="'.scalar(@align).'"><hr></td></tr>'; 508 } 509 } 510 511 my @elements = @{$elements}; 512 my $out = ""; 513 my ($brh, $erh) = ("",""); # Start and end raw html 514 my $element; 515 my $colcount=0; 516 if($main::displayMode eq 'Latex2HTML') { 517 $brh = "\\begin{rawhtml}"; 518 $erh = "\\end{rawhtml}"; 519 } 520 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 521 while (@elements) { 522 $colcount++; 523 $out .= '\fbox{' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 524 $element= shift(@elements); 525 if(ref($element) eq 'Fraction') { 526 $element= $element->print_inline(); 527 } 528 if($opts{'force_tex'}) { 529 $out .= "$element"; 530 } else { 531 $out .= '\\mbox{'."$element".'}'; 532 } 533 $out .= '}' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 534 $out .= " &"; 535 } 536 chop($out); # remove last & 537 $out .= "\\cr \n"; 538 # carriage returns must be added manually for tex 539 } elsif ($main::displayMode eq 'HTML' or $main::displayMode eq 'HTML_tth' 540 or $main::displayMode eq 'HTML_jsMath' 541 or $main::displayMode eq 'HTML_asciimath' 542 or $main::displayMode eq 'HTML_LaTeXMathML' 543 or $main::displayMode eq 'HTML_dpng' 544 or $main::displayMode eq 'HTML_img' 545 or $main::displayMode eq 'Latex2HTML') { 546 if(not $opts{'isfirst'}) { $out .= "$brh\n<TR>\n$erh";} 547 while (@elements) { 548 my $myalign; 549 $myalign = shift @align; 550 if($myalign eq "|" or $myalign eq "d") { 551 if($opts{'isfirst'} && $main::displayMode ne 'HTML_tth') { 552 $out .= $brh.'<td rowspan="'.$opts{'isfirst'}.'">'.$erh; 553 $out .= dm_image_delimeter($opts{'isfirst'}-1, $myalign); 554 } elsif($main::displayMode eq 'HTML_tth') { 555 if($myalign eq "d") { # dashed line in tth mode 556 $out .= '<td> | </td>'; 557 } elsif($opts{'isfirst'}) { # solid line in tth mode 558 $out .= '<td rowspan="'.$opts{'isfirst'}.'"<table border="0"><tr>'; 559 $out .= dm_tth_delimeter($opts{'isfirst'}-1, "|"); 560 $out .= '</td></tr></table>'; 561 } 562 } 563 } else { 564 if($myalign eq "c") { $myalign = "center";} 565 if($myalign eq "l") { $myalign = "left";} 566 if($myalign eq "r") { $myalign = "right";} 567 $colcount++; 568 $out .= '\fbox{' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 569 $element= shift(@elements); 570 if (ref($element) eq 'Fraction') { 571 $element= $element->print_inline(); 572 #}elsif( $element =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/ and $element != sprintf($opts{'num_format'},$element) and $element - sprintf($opts{'num_format'},$element) < $main::functZeroLevelTolDefault){ 573 # $element = sprintf($opts{'num_format'},$element); 574 # $element = 0 if abs($element) < $main::functZeroLevelTolDefault; 575 } 576 $out .= "$brh<TD nowrap=\"nowrap\" align=\"$myalign\">$erh"; 577 $out .= '<table border="1"><tr><td>' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 578 $out .= $element; 579 $out .= '</td></tr></table>' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 580 $out .= "$brh</TD>$erh"; 581 } 582 } 583 if(not $opts{'isfirst'}) {$out .="$brh</TR>$erh\n";} 584 } 585 else { 586 $out = "Error: dm_mat_row: Unknown displayMode: $main::displayMode.\n"; 587 } 588 $out; 589 } 590 591 =head4 mbox 592 593 Usage \{ mbox(thing1, thing2, thing3) \} 594 \{ mbox([thing1, thing2, thing3], valign=>'top') \} 595 596 mbox takes a list of constructs, such as strings, or outputs of 597 display_matrix, and puts them together on a line. Without mbox, the 598 output of display_matrix would always start a new line. 599 600 The inputs can be just listed, or given as a reference to an array. 601 With the latter, optional arguments can be given. 602 603 Optional arguments are allowbreaks=>'yes' to allow line breaks in TeX 604 output; and valign which sets vertical alignment on web page output. 605 606 =cut 607 608 sub mbox { 609 my $inList = shift; 610 my %opts; 611 if(ref($inList) eq 'ARRAY') { 612 %opts = @_; 613 } else { 614 %opts = (); 615 $inList = [$inList, @_]; 616 } 617 618 set_default_options(\%opts, 619 '_filter_name' => 'mbox', 620 'valign' => 'middle', 621 'allowbreaks' => 'no', 622 'allow_unknown_options'=> 0); 623 if(! $opts{'allowbreaks'}) { $opts{'allowbreaks'}='no';} 624 my $out = ""; 625 my $j; 626 my ($brh, $erh) = ("",""); # Start and end raw html if needed 627 if($main::displayMode eq 'Latex2HTML') { 628 $brh = "\\begin{rawhtml}"; 629 $erh = "\\end{rawhtml}"; 630 } 631 my @hlist = @{$inList}; 632 if($main::displayMode eq 'TeX') { 633 if($opts{allowbreaks} ne 'no') {$out .= '\mbox{';} 634 for $j (@hlist) { $out .= $j;} 635 if($opts{allowbreaks} ne 'no') {$out .= '}';} 636 } else { 637 $out .= qq!$brh<table><tr valign="$opts{'valign'}">$erh!; 638 for $j (@hlist) { 639 $out .= qq!$brh<td align="center" nowrap="nowrap">$erh$j$brh</td>$erh!; 640 } 641 $out .= "$brh</table>$erh"; 642 } 643 return $out; 644 } 645 646 647 =head4 ra_flatten_matrix 648 649 Usage: ra_flatten_matrix($A) 650 651 where $A is a matrix object 652 The output is a reference to an array. The matrix is placed in the array by iterating 653 over columns on the inside 654 loop, then over the rows. (e.g right to left and then down, as one reads text) 655 656 657 =cut 658 659 660 sub ra_flatten_matrix{ 661 my $matrix = shift; 662 warn "The argument must be a matrix object" unless ref($matrix) =~ /Matrix/; 663 my @array = (); 664 my ($rows, $cols ) = $matrix->dim(); 665 foreach my $i (1..$rows) { 666 foreach my $j (1..$cols) { 667 push(@array, $matrix->element($i,$j) ); 668 } 669 } 670 \@array; 671 } 672 673 # This subroutine is probably obsolete and not generally useful. It was patterned after the APL 674 # constructs for multiplying matrices. It might come in handy for non-standard multiplication of 675 # of matrices (e.g. mod 2) for indice matrices. 676 sub apl_matrix_mult{ 677 my $ra_a= shift; 678 my $ra_b= shift; 679 my %options = @_; 680 my $rf_op_times= sub {$_[0] *$_[1]}; 681 my $rf_op_plus = sub {my $sum = 0; my @in = @_; while(@in){ $sum = $sum + shift(@in) } $sum; }; 682 $rf_op_times = $options{'times'} if defined($options{'times'}) and ref($options{'times'}) eq 'CODE'; 683 $rf_op_plus = $options{'plus'} if defined($options{'plus'}) and ref($options{'plus'}) eq 'CODE'; 684 my $rows = @$ra_a; 685 my $cols = @{$ra_b->[0]}; 686 my $k_size = @$ra_b; 687 my $out ; 688 my ($i, $j, $k); 689 for($i=0;$i<$rows;$i++) { 690 for($j=0;$j<$cols;$j++) { 691 my @r = (); 692 for($k=0;$k<$k_size;$k++) { 693 $r[$k] = &$rf_op_times($ra_a->[$i]->[$k] , $ra_b->[$k]->[$j]); 694 } 695 $out->[$i]->[$j] = &$rf_op_plus( @r ); 696 } 697 } 698 $out; 699 } 700 701 sub matrix_mult { 702 apl_matrix_mult($_[0], $_[1]); 703 } 704 705 sub make_matrix{ 706 my $function = shift; 707 my $rows = shift; 708 my $cols = shift; 709 my ($i, $j, $k); 710 my $ra_out; 711 for($i=0;$i<$rows;$i++) { 712 for($j=0;$j<$cols;$j++) { 713 $ra_out->[$i]->[$j] = &$function($i,$j); 714 } 715 } 716 $ra_out; 717 } 718 719 720 # sub format_answer{ 721 # my $ra_eigenvalues = shift; 722 # my $ra_eigenvectors = shift; 723 # my $functionName = shift; 724 # my @eigenvalues=@$ra_eigenvalues; 725 # my $size= @eigenvalues; 726 # my $ra_eigen = make_matrix( sub {my ($i,$j) = @_; ($i==$j) ? "e^{$eigenvalues[$j] t}": 0 }, $size,$size); 727 # my $out = qq! 728 # $functionName(t) =! . 729 # displayMatrix(apl_matrix_mult($ra_eigenvectors,$ra_eigen, 730 # 'times'=>sub{($_[0] and $_[1]) ? "$_[0]$_[1]" : ''}, 731 # 'plus'=>sub{ my $out = join("",@_); ($out) ?$out : '0' } 732 # ) ) ; 733 # $out; 734 # } 735 # sub format_vector_answer{ 736 # my $ra_eigenvalues = shift; 737 # my $ra_eigenvectors = shift; 738 # my $functionName = shift; 739 # my @eigenvalues=@$ra_eigenvalues; 740 # my $size= @eigenvalues; 741 # my $ra_eigen = make_matrix( sub {my ($i,$j) = @_; ($i==$j) ? "e^{$eigenvalues[$j] t}": 0 }, $size,$size); 742 # my $out = qq! 743 # $functionName(t) =! . 744 # displayMatrix($ra_eigenvectors)."e^{$eigenvalues[0] t}" ; 745 # $out; 746 # } 747 # sub format_question{ 748 # my $ra_matrix = shift; 749 # my $out = qq! y'(t) = ! . displayMatrix($B). q! y(t)! 750 # 751 # } 752 753 1;
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