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Fixed index problem with matrix multiplciation. (It was returning the transpose!)
1 ########################################################################### 2 # 3 # Implements the Matrix class. 4 # 5 # @@@ Still needs lots of work @@@ 6 # 7 package Value::Matrix; 8 my $pkg = 'Value::Matrix'; 9 10 use strict; 11 use vars qw(@ISA); 12 @ISA = qw(Value); 13 14 use overload 15 '+' => \&add, 16 '-' => \&sub, 17 '*' => \&mult, 18 '/' => \&div, 19 '**' => \&power, 20 '.' => \&Value::_dot, 21 'x' => \&Value::cross, 22 '<=>' => \&compare, 23 'cmp' => \&Value::cmp, 24 'neg' => sub {$_[0]->neg}, 25 'nomethod' => \&Value::nomethod, 26 '""' => \&stringify; 27 28 # 29 # Convert a value to a matrix. The value can be: 30 # a list of numbers or list of (nested) references to arrays of numbers 31 # a point, vector or matrix object 32 # 33 sub new { 34 my $self = shift; my $class = ref($self) || $self; 35 my $M = shift; 36 return bless {data => $M->data}, $class 37 if (Value::class($M) =~ m/Point|Vector|Matrix/ && scalar(@_) == 0); 38 $M = [$M,@_] if ((defined($M) && ref($M) ne 'ARRAY') || scalar(@_) > 0); 39 Value::Error("Matrices must have at least one entry") unless defined($M) && scalar(@{$M}) > 0; 40 return $self->numberMatrix(@{$M}) if Value::isNumber($M->[0]); 41 return $self->matrixMatrix(@{$M}); 42 } 43 44 # 45 # (Recusrively) make a matrix from a list of array refs 46 # and report errors about the entry types 47 # 48 sub matrixMatrix { 49 my $self = shift; my $class = ref($self) || $self; 50 my ($x,$m); my @M = (); my $isFormula = 0; 51 foreach $x (@_) { 52 if (Value::isFormula($x)) {push(@M,$x); $isFormula = 1} else { 53 $m = $pkg->new($x); push(@M,$m); 54 $isFormula = 1 if Value::isFormula($m); 55 } 56 } 57 my ($type,$len) = ($M[0]->entryType->{name},$M[0]->length); 58 foreach $x (@M) { 59 Value::Error("Matrix rows must all be the same type") 60 unless (defined($x->entryType) && $type eq $x->entryType->{name}); 61 Value::Error("Matrix rows must all be the same length") unless ($len eq $x->length); 62 } 63 return $self->formula([@M]) if $isFormula; 64 bless {data => [@M]}, $class; 65 } 66 67 # 68 # Form a 1 x n matrix from a list of numbers 69 # (could become a row of an m x n matrix) 70 # 71 sub numberMatrix { 72 my $self = shift; my $class = ref($self) || $self; 73 my @M = (); my $isFormula = 0; 74 foreach my $x (@_) { 75 Value::Error("Matrix row entries must be numbers") unless (Value::isNumber($x)); 76 $x = Value::Real->make($x) if !ref($x); 77 push(@M,$x); $isFormula = 1 if Value::isFormula($x); 78 } 79 return $self->formula([@M]) if $isFormula; 80 bless {data => [@M]}, $class; 81 } 82 83 # 84 # Recursively get the entries in the matrix and return 85 # an array of (references to arrays of ... ) numbers 86 # 87 sub value { 88 my $self = shift; 89 my $M = $self->data; 90 return @{$M} if Value::class($M->[0]) ne 'Matrix'; 91 my @M = (); 92 foreach my $x (@{$M}) {push(@M,[$x->value])} 93 return @M; 94 } 95 # 96 # The number of rows in the matrix (for n x m) 97 # or the number of entries in a 1 x n matrix 98 # 99 sub length {return scalar(@{shift->{data}})} 100 # 101 # Recursively get the dimensions of the matrix. 102 # Returns (n) for a 1 x n, or (n,m) for an n x m, etc. 103 # 104 sub dimensions { 105 my $self = shift; 106 my $r = $self->length; 107 my $v = $self->data; 108 return ($r,) if (Value::class($v->[0]) ne 'Matrix'); 109 return ($r,$v->[0]->dimensions); 110 } 111 # 112 # Return the proper type for the matrix 113 # 114 sub typeRef { 115 my $self = shift; 116 return Value::Type($self->class, $self->length, $Value::Type{number}) 117 if (Value::class($self->data->[0]) ne 'Matrix'); 118 return Value::Type($self->class, $self->length, $self->data->[0]->typeRef); 119 } 120 121 # 122 # True if the matrix is a square matrix 123 # 124 sub isSquare { 125 my $self = shift; 126 my @d = $self->dimensions; 127 return 0 if scalar(@d) > 2; 128 return 1 if scalar(@d) == 1 && $d[0] == 1; 129 return $d[0] == $d[1]; 130 } 131 132 # 133 # True if the matrix is 1-dimensional (i.e., is a matrix row) 134 # 135 sub isRow { 136 my $self = shift; 137 my @d = $self->dimensions; 138 return scalar(@d) == 1; 139 } 140 141 # 142 # See if the matrix is an Indenity matrix 143 # 144 sub isOne { 145 my $self = shift; 146 return 0 unless $self->isSquare; 147 my $i = 0; 148 foreach my $row (@{$self->{data}}) { 149 my $j = 0; 150 foreach my $k (@{$row->{data}}) { 151 return 0 unless $k eq (($i == $j)? "1": "0"); 152 $j++; 153 } 154 $i++; 155 } 156 return 1; 157 } 158 159 # 160 # See if the matrix is all zeros 161 # 162 sub isZero { 163 my $self = shift; 164 foreach my $x (@{$self->{data}}) {return 0 unless $x->isZero} 165 return 1; 166 } 167 168 # 169 # Make arbitrary data into a matrix, if possible 170 # 171 sub promote { 172 my $x = shift; 173 return $pkg->new($x,@_) if scalar(@_) > 0 || ref($x) eq 'ARRAY'; 174 return $x if ref($x) eq $pkg; 175 return $pkg->make(@{$x->data}) if Value::class($x) =~ m/Point|Vector/; 176 Value::Error("Can't convert ".Value::showClass($x)." to a Matrix"); 177 } 178 179 ############################################ 180 # 181 # Operations on matrices 182 # 183 184 sub add { 185 my ($l,$r,$flag) = @_; 186 if ($l->promotePrecedence($r)) {return $r->add($l,!$flag)} 187 ($l,$r) = (promote($l)->data,promote($r)->data); 188 Value::Error("Matrix addition with different dimensions") 189 unless scalar(@{$l}) == scalar(@{$r}); 190 my @s = (); 191 foreach my $i (0..scalar(@{$l})-1) {push(@s,$l->[$i] + $r->[$i])} 192 return $pkg->make(@s); 193 } 194 195 sub sub { 196 my ($l,$r,$flag) = @_; 197 if ($l->promotePrecedence($r)) {return $r->sub($l,!$flag)} 198 ($l,$r) = (promote($l)->data,promote($r)->data); 199 Value::Error("Matrix subtraction with different dimensions") 200 unless scalar(@{$l}) == scalar(@{$r}); 201 if ($flag) {my $tmp = $l; $l = $r; $r = $tmp}; 202 my @s = (); 203 foreach my $i (0..scalar(@{$l})-1) {push(@s,$l->[$i] - $r->[$i])} 204 return $pkg->make(@s); 205 } 206 207 sub mult { 208 my ($l,$r,$flag) = @_; 209 if ($l->promotePrecedence($r)) {return $r->mult($l,!$flag)} 210 # 211 # Constant multiplication 212 # 213 if (Value::matchNumber($r) || Value::isComplex($r)) { 214 my @coords = (); 215 foreach my $x (@{$l->data}) {push(@coords,$x*$r)} 216 return $pkg->make(@coords); 217 } 218 # 219 # Make points and vectors into columns if they are on the right 220 # 221 if (!$flag && Value::class($r) =~ m/Point|Vector/) 222 {$r = (promote($r))->transpose} else {$r = promote($r)} 223 # 224 if ($flag) {my $tmp = $l; $l = $r; $r = $tmp} 225 my @dl = $l->dimensions; my @dr = $r->dimensions; 226 if (scalar(@dl) == 1) {@dl = (1,@dl); $l = $pkg->make($l)} 227 if (scalar(@dr) == 1) {@dr = (@dr,1); $r = $pkg->make($r)->transpose} 228 Value::Error("Can only multiply 2-dimensional matrices") if scalar(@dl) > 2 || scalar(@dr) > 2; 229 Value::Error("Matices of dimensions $dl[0]x$dl[1] and $dr[0]x$dr[1] can't be multiplied") 230 unless ($dl[1] == $dr[0]); 231 # 232 # Do matrix multiplication 233 # 234 my @l = $l->value; my @r = $r->value; 235 my @M = (); 236 foreach my $i (0..$dl[0]-1) { 237 my @row = (); 238 foreach my $j (0..$dr[1]-1) { 239 my $s = 0; 240 foreach my $k (0..$dl[1]-1) {$s += $l[$i]->[$k] * $r[$k]->[$j]} 241 push(@row,$s); 242 } 243 push(@M,$pkg->make(@row)); 244 } 245 return $pkg->make(@M); 246 } 247 248 sub div { 249 my ($l,$r,$flag) = @_; 250 if ($l->promotePrecedence($r)) {return $r->div($l,!$flag)} 251 Value::Error("Can't divide by a Matrix") if $flag; 252 Value::Error("Matrices can only be divided by numbers") 253 unless (Value::matchNumber($r) || Value::isComplex($r)); 254 Value::Error("Division by zero") if $r == 0; 255 my @coords = (); 256 foreach my $x (@{$l->data}) {push(@coords,$x/$r)} 257 return $pkg->make(@coords); 258 } 259 260 sub power { 261 my ($l,$r,$flag) = @_; 262 if ($l->promotePrecedence($r)) {return $r->power($l,!$flag)} 263 Value::Error("Can't use Matrices in exponents") if $flag; 264 Value::Error("Only square matrices can be raised to a power") unless $l->isSquare; 265 return Value::Matrix::I($l->length) if $r == 0; 266 Value::Error("Matrix powers must be positive integers") unless $r =~ m/^[1-9]\d*$/; 267 my $M = $l; foreach my $i (2..$r) {$M = $M*$l} 268 return $M; 269 } 270 271 # 272 # Do lexicographic comparison 273 # 274 sub compare { 275 my ($l,$r,$flag) = @_; 276 if ($l->promotePrecedence($r)) {return $r->compare($l,!$flag)} 277 ($l,$r) = (promote($l)->data,promote($r)->data); 278 Value::Error("Matrix comparison with different dimensions") 279 unless scalar(@{$l}) == scalar(@{$r}); 280 if ($flag) {my $tmp = $l; $l = $r; $r = $tmp}; 281 my $cmp = 0; 282 foreach my $i (0..scalar(@{$l})-1) { 283 $cmp = $l->[$i] <=> $r->[$i]; 284 last if $cmp; 285 } 286 return $cmp; 287 } 288 289 sub neg { 290 my $p = promote(@_)->data; 291 my @coords = (); 292 foreach my $x (@{$p}) {push(@coords,-$x)} 293 return $pkg->make(@coords); 294 } 295 296 # 297 # Transpose an n x m matrix 298 # 299 sub transpose { 300 my $self = shift; 301 my @d = $self->dimensions; 302 if (scalar(@d) == 1) {@d = (1,@d); $self = $pkg->make($self)} 303 Value::Error("Can't transpose ".scalar(@d)."-dimensional matrices") unless scalar(@d) == 2; 304 my @M = (); my $M = $self->data; 305 foreach my $j (0..$d[1]-1) { 306 my @row = (); 307 foreach my $i (0..$d[0]-1) {push(@row,$M->[$i]->data->[$j])} 308 push(@M,$pkg->make(@row)); 309 } 310 return $pkg->make(@M); 311 } 312 313 # 314 # Get an identity matrix of the requested size 315 # 316 sub I { 317 my $d = shift; $d = shift if ref($d) eq $pkg; 318 my @M = (); my @Z = split('',0 x $d); 319 foreach my $i (0..$d-1) { 320 my @row = @Z; $row[$i] = 1; 321 push(@M,$pkg->make(@row)); 322 } 323 return $pkg->make(@M); 324 } 325 326 # 327 # Extract a given row from the matrix 328 # 329 sub row { 330 my $M = promote(shift); my $i = shift; 331 return if $i == 0; $i-- if $i > 0; 332 if ($M->isRow) {return if $i != 0; return $M} 333 return $M->data->[$i]; 334 } 335 336 # 337 # Extract a given element from the matrix 338 # 339 sub element { 340 my $M = promote(shift); 341 return $M->extract(@_); 342 } 343 344 # 345 # Extract a given column from the matrix 346 # 347 sub column { 348 my $M = promote(shift); my $j = shift; 349 return if $j == 0; $j-- if $j > 0; 350 my @d = $M->dimensions; my @col = (); 351 return if $j+1 > $d[1]; 352 return $M->data->[$j] if scalar(@d) == 1; 353 foreach my $row (@{$M->data}) {push(@col,$pkg->make($row->data->[$j]))} 354 return $pkg->make(@col); 355 } 356 357 # @@@ removeRow, removeColumn @@@ 358 # @@@ Det, inverse @@@ 359 360 ############################################ 361 # 362 # Generate the various output formats 363 # 364 365 sub stringify { 366 my $self = shift; 367 return $self->TeX(undef,$self->{open},$self->{close}) if $$Value::context->flag('StringifyAsTeX'); 368 return $self->string(undef,$self->{open},$self->{close}) 369 } 370 371 sub string { 372 my $self = shift; my $equation = shift; 373 my $def = ($equation->{context} || $$Value::context)->lists->get('Matrix'); 374 my $open = shift || $def->{open}; my $close = shift || $def->{close}; 375 my @coords = (); 376 foreach my $x (@{$self->data}) { 377 if (Value::isValue($x)) {push(@coords,$x->string($equation,$open,$close))} 378 else {push(@coords,$x)} 379 } 380 return $open.join(',',@coords).$close; 381 } 382 383 # 384 # Use \matrix to lay out matrices 385 # 386 sub TeX { 387 my $self = shift; my $equation = shift; 388 my $def = ($equation->{context} || $$Value::context)->lists->get('Matrix'); 389 my $open = shift || $def->{open}; my $close = shift || $def->{close}; 390 $open = '\{' if $open eq '{'; $close = '\}' if $close eq '}'; 391 my $TeX = ''; my @entries = (); my $d; 392 if ($self->isRow) { 393 foreach my $x (@{$self->data}) { 394 push(@entries,(Value::isValue($x))? $x->TeX($equation): $x); 395 } 396 $TeX .= join(' &',@entries) . "\n"; 397 $d = scalar(@entries); 398 } else { 399 foreach my $row (@{$self->data}) { 400 foreach my $x (@{$row->data}) { 401 push(@entries,(Value::isValue($x))? $x->TeX($equation): $x); 402 } 403 $TeX .= join(' &',@entries) . '\cr'."\n"; 404 $d = scalar(@entries); @entries = (); 405 } 406 } 407 return '\left'.$open.'\begin{array}{'.('c'x$d).'}'."\n".$TeX.'\end{array}\right'.$close; 408 } 409 410 ########################################################################### 411 412 1; 413
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