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Fixed a rounding problem.
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_dpng' 281 or $main::displayMode eq 'HTML_img') { 282 $out .= qq!<TABLE BORDER="0" Cellspacing="8">\n!; 283 } 284 else { 285 $out = "Error: dm_begin_matrix: Unknown displayMode: $main::displayMode.\n"; 286 } 287 $out; 288 } 289 290 sub dm_special_tops { 291 my %opts = @_; 292 my @top_labels = @{$opts{'top_labels'}}; 293 my $out = ''; 294 my @alignList = @{$opts{'alignList'}}; 295 my ($j, $k); 296 my ($brh, $erh) = ("",""); # Start and end raw html 297 if($main::displayMode eq 'Latex2HTML') { 298 $brh = "\\begin{rawhtml}"; 299 $erh = "\\end{rawhtml}"; 300 } 301 302 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 303 for $j (@top_labels) { 304 $out .= '\smash{\raisebox{2.9ex}{\ensuremath{'. 305 $j . '}}} &'; 306 } 307 chop($out); # remove last & 308 $out .= '\cr\noalign{\vskip -2.5ex}'."\n"; # want skip jump up 2.5ex 309 } elsif ($main::displayMode eq 'HTML' or $main::displayMode eq 'HTML_tth' 310 or $main::displayMode eq 'HTML_dpng' 311 or $main::displayMode eq 'HTML_img' 312 or $main::displayMode eq 'Latex2HTML') { 313 $out .= "$brh<tr><td>$erh"; # Skip a column for the left brace 314 for $j (@top_labels) { 315 $k = shift @alignList; 316 while(defined($k) and ($k !~ /[lrc]/)) { 317 $out .= "$brh<td></td>$erh"; 318 $k = shift @alignList; 319 } 320 $out .= "$brh<td align=\"center\">$erh". ' \('.$j.'\)'."$brh</td>$erh"; 321 } 322 $out .= "<td></td>"; 323 } else { 324 $out = "Error: dm_begin_matrix: Unknown displayMode: $main::displayMode.\n"; 325 } 326 return $out; 327 } 328 329 sub dm_mat_left { 330 my $numrows = shift; 331 my %opts = @_; 332 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 333 return ""; # left delim is built into begin matrix 334 } 335 my $out=''; 336 my $j; 337 my ($brh, $erh) = ("",""); # Start and end raw html 338 if($main::displayMode eq 'Latex2HTML') { 339 $brh = "\\begin{rawhtml}"; 340 $erh = "\\end{rawhtml}"; 341 } 342 343 if($main::displayMode eq 'HTML_dpng' 344 or $main::displayMode eq 'HTML_img' 345 or $main::displayMode eq 'Latex2HTML') { 346 $out .= "$brh<tr valign=\"center\"><td nowrap=\"nowrap\" align=\"left\" rowspan=\"$numrows\">$erh"; 347 $out .= dm_image_delimeter($numrows, $opts{'left'}); 348 # $out .= "$brh<td><table border=0 cellspacing=5>\n$erh"; 349 return $out; 350 } 351 # Mode is now tth 352 353 $out .= "<tr valign=\"center\"><td nowrap=\"nowrap\" align=\"left\" rowspan=\"$numrows\">"; 354 $out .= dm_tth_delimeter($numrows, $opts{'left'}); 355 # $out .= "<td><table border=0 cellspacing=5>\n"; 356 return $out; 357 } 358 359 sub dm_mat_right { 360 my $numrows = shift; 361 my %opts = @_; 362 my $out=''; 363 my $j; 364 my ($brh, $erh) = ("",""); # Start and end raw html 365 if($main::displayMode eq 'Latex2HTML') { 366 $brh = "\\begin{rawhtml}"; 367 $erh = "\\end{rawhtml}"; 368 } 369 370 371 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 372 return ""; 373 } 374 375 if($main::displayMode eq 'HTML_dpng' 376 or $main::displayMode eq 'Latex2HTML' 377 or $main::displayMode eq 'HTML_dpng') { 378 $out .= "$brh<td nowrap=\"nowrap\" align=\"right\" rowspan=\"$numrows\">$erh"; 379 380 $out.= dm_image_delimeter($numrows, $opts{'right'}); 381 return $out; 382 } 383 384 # $out .= "</table>"; 385 $out .= '<td nowrap="nowrap" align="left" rowspan="'.$numrows.'2">'; 386 $out .= dm_tth_delimeter($numrows, $opts{'right'}); 387 $out .= '</td>'; 388 return $out; 389 } 390 391 sub dm_end_matrix { 392 my %opts = @_; 393 394 my $out = ""; 395 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 396 $out .= "\\end{array}\\right$opts{right}"; 397 if($opts{'top_labels'}) { 398 $out .= '}} \dimen3=\ht3 \advance\dimen3 by 3ex \ht3=\dimen3'."\n". 399 '\box3\endgroup'; 400 } 401 $out .= $opts{'force_tex'} ? '' : "\\) "; 402 } 403 elsif ($main::displayMode eq 'Latex2HTML') { 404 $out .= "\n\\begin{rawhtml} </TABLE >\n\\end{rawhtml}"; 405 } 406 elsif ($main::displayMode eq 'HTML' or $main::displayMode eq 'HTML_tth' 407 or $main::displayMode eq 'HTML_img' 408 or $main::displayMode eq 'HTML_dpng') { 409 $out .= "</TABLE>\n"; 410 } 411 else { 412 $out = "Error: PGmatrixmacros: dm_end_matrix: Unknown displayMode: $main::displayMode.\n"; 413 } 414 $out; 415 } 416 417 # Make an image of a big delimiter for a matrix 418 sub dm_image_delimeter { 419 my $numRows = shift; 420 my $char = shift; 421 my ($out, $j); 422 423 if($char eq ".") {return("");} 424 if($char eq "d") { # special treatment for dashed lines 425 $out='\(\vbox to '.($numRows*1.7).'\baselineskip '; 426 $out .='{\cleaders\hbox{\vbox{\hrule width0pt height3pt depth0pt'; 427 $out .='\hrule width0.3pt height6pt depth0pt'; 428 $out .='\hrule width0pt height3pt depth0pt}}\vfil}\)'; 429 return($out); 430 } 431 if($char eq "|") { 432 $out='\(\vbox to '.($numRows*1.4).'\baselineskip '; 433 $out .='{\cleaders\vrule width0.3pt'; 434 $out .='\vfil}\)'; 435 return($out); 436 } 437 if($char eq "{") {$char = '\lbrace';} 438 if($char eq "}") {$char = '\rbrace';} 439 $out .= '\(\setlength{\arraycolsep}{0in}\left.\begin{array}{c}'; 440 for($j=0;$j<=$numRows;$j++) { $out .= '\! \\\\'; } 441 $out .= '\end{array}\right'.$char.'\)'; 442 return($out); 443 } 444 445 # Basically uses a table of special characters and simple 446 # recipe to produce big delimeters a la tth mode 447 sub dm_tth_delimeter { 448 my $numRows = shift; 449 my $char = shift; 450 451 if($char eq ".") { return("");} 452 my ($top, $mid, $bot, $extra); 453 my ($j, $out); 454 455 if($char eq "(") { ($top, $mid, $bot, $extra) = ('æ','ç','è','ç');} 456 elsif($char eq ")") { ($top, $mid, $bot, $extra) = ('ö','÷','ø','÷');} 457 elsif($char eq "|") { ($top, $mid, $bot, $extra) = ('ê','ê','ê','ê');} 458 elsif($char eq "[") { ($top, $mid, $bot, $extra) = ('é','ê','ë','ê');} 459 elsif($char eq "]") { ($top, $mid, $bot, $extra) = ('ù','ú','û','ú');} 460 elsif($char eq "{") { ($top, $mid, $bot, $extra) = ('ì','ï','î','í');} 461 elsif($char eq "}") { ($top, $mid, $bot, $extra) = ('ü','ï','þ','ý');} 462 else { warn "Unknown delimiter in dm_tth_delimeter";} 463 464 # old version 465 # $out = '<td nowrap="nowrap" align="left"><font face="symbol">'; 466 $out = '<font face="symbol">'; 467 $out .= "$top<br />"; 468 for($j=1;$j<$numRows; $j++) { 469 $out .= "$mid<br />"; 470 } 471 $out .= "$extra<br />"; 472 for($j=1;$j<$numRows; $j++) { 473 $out .= "$mid<br />"; 474 } 475 $out .= "$bot</font></td>"; 476 return $out; 477 } 478 479 # Make a row for the matrix 480 sub dm_mat_row { 481 my $elements = shift; 482 my $tmp = shift; 483 my @align = @{$tmp} ; 484 my %opts = @_; 485 486 if($elements eq 'hline') { 487 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 488 return '\hline '; 489 } else { 490 # Making a hline in a table 491 return '<tr><td colspan="'.scalar(@align).'"><hr></td></tr>'; 492 } 493 } 494 495 my @elements = @{$elements}; 496 my $out = ""; 497 my ($brh, $erh) = ("",""); # Start and end raw html 498 my $element; 499 my $colcount=0; 500 if($main::displayMode eq 'Latex2HTML') { 501 $brh = "\\begin{rawhtml}"; 502 $erh = "\\end{rawhtml}"; 503 } 504 if ($main::displayMode eq 'TeX' or $opts{'force_tex'}) { 505 while (@elements) { 506 $colcount++; 507 $out .= '\fbox{' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 508 $element= shift(@elements); 509 if(ref($element) eq 'Fraction') { 510 $element= $element->print_inline(); 511 } 512 $out .= "$element"; 513 $out .= '}' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 514 $out .= " &"; 515 } 516 chop($out); # remove last & 517 $out .= "\\cr \n"; 518 # carriage returns must be added manually for tex 519 } elsif ($main::displayMode eq 'HTML' or $main::displayMode eq 'HTML_tth' 520 or $main::displayMode eq 'HTML_dpng' 521 or $main::displayMode eq 'HTML_img' 522 or $main::displayMode eq 'Latex2HTML') { 523 if(not $opts{'isfirst'}) { $out .= "$brh\n<TR>\n$erh";} 524 while (@elements) { 525 my $myalign; 526 $myalign = shift @align; 527 if($myalign eq "|" or $myalign eq "d") { 528 if($opts{'isfirst'} && $main::displayMode ne 'HTML_tth') { 529 $out .= $brh.'<td rowspan="'.$opts{'isfirst'}.'">'.$erh; 530 $out .= dm_image_delimeter($opts{'isfirst'}-1, $myalign); 531 } elsif($main::displayMode eq 'HTML_tth') { 532 if($myalign eq "d") { # dashed line in tth mode 533 $out .= '<td> | </td>'; 534 } elsif($opts{'isfirst'}) { # solid line in tth mode 535 $out .= '<td rowspan="'.$opts{'isfirst'}.'"<table border="0"><tr>'; 536 $out .= dm_tth_delimeter($opts{'isfirst'}-1, "|"); 537 $out .= '</td></tr></table>'; 538 } 539 } 540 } else { 541 if($myalign eq "c") { $myalign = "center";} 542 if($myalign eq "l") { $myalign = "left";} 543 if($myalign eq "r") { $myalign = "right";} 544 $colcount++; 545 $out .= '\fbox{' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 546 $element= shift(@elements); 547 if (ref($element) eq 'Fraction') { 548 $element= $element->print_inline(); 549 }elsif( $element =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/ and $element != sprintf($opts{'num_format'},$element) and $element - sprintf($opts{'num_format'},$element) < $main::functZeroLevelTolDefault){ 550 $element = sprintf($opts{'num_format'},$element); 551 $element = 0 if abs($element) < $main::functZeroLevelTolDefault; 552 } 553 $out .= "$brh<TD nowrap=\"nowrap\" align=\"$myalign\">$erh"; 554 $out .= '<table border="1"><tr><td>' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 555 $out .= $element; 556 $out .= '</td></tr></table>' if ($colcount == $opts{'box'}->[1] and $opts{'cnt'} == $opts{'box'}->[0]); 557 $out .= "$brh</TD>$erh"; 558 } 559 } 560 if(not $opts{'isfirst'}) {$out .="$brh</TR>$erh\n";} 561 } 562 else { 563 $out = "Error: dm_mat_row: Unknown displayMode: $main::displayMode.\n"; 564 } 565 $out; 566 } 567 568 =head4 mbox 569 570 Usage \{ mbox(thing1, thing2, thing3) \} 571 \{ mbox([thing1, thing2, thing3], valign=>'top') \} 572 573 mbox takes a list of constructs, such as strings, or outputs of 574 display_matrix, and puts them together on a line. Without mbox, the 575 output of display_matrix would always start a new line. 576 577 The inputs can be just listed, or given as a reference to an array. 578 With the latter, optional arguments can be given. 579 580 Optional arguments are allowbreaks=>'yes' to allow line breaks in TeX 581 output; and valign which sets vertical alignment on web page output. 582 583 =cut 584 585 sub mbox { 586 my $inList = shift; 587 my %opts; 588 if(ref($inList) eq 'ARRAY') { 589 %opts = @_; 590 } else { 591 %opts = (); 592 $inList = [$inList, @_]; 593 } 594 595 set_default_options(\%opts, 596 '_filter_name' => 'mbox', 597 'valign' => 'middle', 598 'allowbreaks' => 'no', 599 'allow_unknown_options'=> 0); 600 if(! $opts{'allowbreaks'}) { $opts{'allowbreaks'}='no';} 601 my $out = ""; 602 my $j; 603 my ($brh, $erh) = ("",""); # Start and end raw html if needed 604 if($main::displayMode eq 'Latex2HTML') { 605 $brh = "\\begin{rawhtml}"; 606 $erh = "\\end{rawhtml}"; 607 } 608 my @hlist = @{$inList}; 609 if($main::displayMode eq 'TeX') { 610 if($opts{allowbreaks} ne 'no') {$out .= '\mbox{';} 611 for $j (@hlist) { $out .= $j;} 612 if($opts{allowbreaks} ne 'no') {$out .= '}';} 613 } else { 614 $out .= qq!$brh<table><tr valign="$opts{'valign'}">$erh!; 615 for $j (@hlist) { 616 $out .= qq!$brh<td align="center" nowrap="nowrap">$erh$j$brh</td>$erh!; 617 } 618 $out .= "$brh</table>$erh"; 619 } 620 return $out; 621 } 622 623 624 =head4 ra_flatten_matrix 625 626 Usage: ra_flatten_matrix($A) 627 628 where $A is a matrix object 629 The output is a reference to an array. The matrix is placed in the array by iterating 630 over columns on the inside 631 loop, then over the rows. (e.g right to left and then down, as one reads text) 632 633 634 =cut 635 636 637 sub ra_flatten_matrix{ 638 my $matrix = shift; 639 warn "The argument must be a matrix object" unless ref($matrix) =~ /Matrix/; 640 my @array = (); 641 my ($rows, $cols ) = $matrix->dim(); 642 foreach my $i (1..$rows) { 643 foreach my $j (1..$cols) { 644 push(@array, $matrix->element($i,$j) ); 645 } 646 } 647 \@array; 648 } 649 650 # This subroutine is probably obsolete and not generally useful. It was patterned after the APL 651 # constructs for multiplying matrices. It might come in handy for non-standard multiplication of 652 # of matrices (e.g. mod 2) for indice matrices. 653 sub apl_matrix_mult{ 654 my $ra_a= shift; 655 my $ra_b= shift; 656 my %options = @_; 657 my $rf_op_times= sub {$_[0] *$_[1]}; 658 my $rf_op_plus = sub {my $sum = 0; my @in = @_; while(@in){ $sum = $sum + shift(@in) } $sum; }; 659 $rf_op_times = $options{'times'} if defined($options{'times'}) and ref($options{'times'}) eq 'CODE'; 660 $rf_op_plus = $options{'plus'} if defined($options{'plus'}) and ref($options{'plus'}) eq 'CODE'; 661 my $rows = @$ra_a; 662 my $cols = @{$ra_b->[0]}; 663 my $k_size = @$ra_b; 664 my $out ; 665 my ($i, $j, $k); 666 for($i=0;$i<$rows;$i++) { 667 for($j=0;$j<$cols;$j++) { 668 my @r = (); 669 for($k=0;$k<$k_size;$k++) { 670 $r[$k] = &$rf_op_times($ra_a->[$i]->[$k] , $ra_b->[$k]->[$j]); 671 } 672 $out->[$i]->[$j] = &$rf_op_plus( @r ); 673 } 674 } 675 $out; 676 } 677 678 sub matrix_mult { 679 apl_matrix_mult($_[0], $_[1]); 680 } 681 682 sub make_matrix{ 683 my $function = shift; 684 my $rows = shift; 685 my $cols = shift; 686 my ($i, $j, $k); 687 my $ra_out; 688 for($i=0;$i<$rows;$i++) { 689 for($j=0;$j<$cols;$j++) { 690 $ra_out->[$i]->[$j] = &$function($i,$j); 691 } 692 } 693 $ra_out; 694 } 695 696 697 # sub format_answer{ 698 # my $ra_eigenvalues = shift; 699 # my $ra_eigenvectors = shift; 700 # my $functionName = shift; 701 # my @eigenvalues=@$ra_eigenvalues; 702 # my $size= @eigenvalues; 703 # my $ra_eigen = make_matrix( sub {my ($i,$j) = @_; ($i==$j) ? "e^{$eigenvalues[$j] t}": 0 }, $size,$size); 704 # my $out = qq! 705 # $functionName(t) =! . 706 # displayMatrix(apl_matrix_mult($ra_eigenvectors,$ra_eigen, 707 # 'times'=>sub{($_[0] and $_[1]) ? "$_[0]$_[1]" : ''}, 708 # 'plus'=>sub{ my $out = join("",@_); ($out) ?$out : '0' } 709 # ) ) ; 710 # $out; 711 # } 712 # sub format_vector_answer{ 713 # my $ra_eigenvalues = shift; 714 # my $ra_eigenvectors = shift; 715 # my $functionName = shift; 716 # my @eigenvalues=@$ra_eigenvalues; 717 # my $size= @eigenvalues; 718 # my $ra_eigen = make_matrix( sub {my ($i,$j) = @_; ($i==$j) ? "e^{$eigenvalues[$j] t}": 0 }, $size,$size); 719 # my $out = qq! 720 # $functionName(t) =! . 721 # displayMatrix($ra_eigenvectors)."e^{$eigenvalues[0] t}" ; 722 # $out; 723 # } 724 # sub format_question{ 725 # my $ra_matrix = shift; 726 # my $out = qq! y'(t) = ! . displayMatrix($B). q! y(t)! 727 # 728 # } 729 730 1;
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