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lib/Math/Zap/Matrix.pm  view on Meta::CPAN

sub new3v($$$)
 {my ($a, $b, $c) = @_; 
  vectorCheck(@_) if debug; 
  my $m = round(bless(
   {11=>$a->x, 12=>$b->x, 13=>$c->x,
    21=>$a->y, 22=>$b->y, 23=>$c->y,
    31=>$a->z, 32=>$b->z, 33=>$c->z,
   }));
  singular($m, 1);
  $m;
 }


=head3 new3vnc

Create a matrix from three vectors without checking

=cut


sub new3vnc($$$)
 {my ($a, $b, $c) = vectorCheck(@_); 
  my $m = round(bless(
   {11=>$a->x, 12=>$b->x, 13=>$c->x,
    21=>$a->y, 22=>$b->y, 23=>$c->y,
    31=>$a->z, 32=>$b->z, 33=>$c->z,
   }));
  $m;
 }


=head2 Methods


=head3 check

Check its a matrix

=cut


sub check(@)
 {if (debug)
   {for my $m(@_)
     {confess "$m is not a matrix" unless ref($m) eq __PACKAGE__;
     }
    }
  return (@_)
 }


=head3 is

Test its a matrix

=cut


sub is(@)
 {for my $m(@_)
   {return 0 unless ref($m) eq __PACKAGE__;
   }
  'matrix';
 }


=head3 singular

Singular matrix?

=cut


sub singular($$)
 {my $m = shift;  # Matrix   
  my $a = 1e-2;   # Accuracy
  my $A = shift;  # Action 0: return indicator, 1: confess 

  my $n = abs
   ($m->{11}*$m->{22}*$m->{33}
   -$m->{11}*$m->{23}*$m->{32}
   -$m->{12}*$m->{21}*$m->{33}
   +$m->{12}*$m->{23}*$m->{31}
   +$m->{13}*$m->{21}*$m->{32}
   -$m->{13}*$m->{22}*$m->{31})
   < $a;
  confess "Singular matrix2" if $n and $A;
  $n;      
 }


=head3 accuracy

Get/Set accuracy for comparisons

=cut


my $accuracy = 1e-10;

sub accuracy
 {return $accuracy unless scalar(@_);
  $accuracy = shift();
 }


=head3 round

Round: round to nearest integer if within accuracy of that integer 

=cut


sub round($)
 {my ($a) = @_;
  check(@_) if debug; 
  my ($n, $N);
  for my $k(qw(11 12 13  21 22 23 31 32 33))
   {$n = $a->{$k};

lib/Math/Zap/Matrix.pm  view on Meta::CPAN

=cut


sub matrixMatrixMultiply($$)
 {my ($a, $b) = check(@_); # Matrices
  round bless
   {11=>$a->{11}*$b->{11}+$a->{12}*$b->{21}+$a->{13}*$b->{31}, 12=>$a->{11}*$b->{12}+$a->{12}*$b->{22}+$a->{13}*$b->{32}, 13=>$a->{11}*$b->{13}+$a->{12}*$b->{23}+$a->{13}*$b->{33},
    21=>$a->{21}*$b->{11}+$a->{22}*$b->{21}+$a->{23}*$b->{31}, 22=>$a->{21}*$b->{12}+$a->{22}*$b->{22}+$a->{23}*$b->{32}, 23=>$a->{21}*$b->{13}+$a->{22}*$b->{23}+$a->{23}*$b->{33},
    31=>$a->{31}*$b->{11}+$a->{32}*$b->{21}+$a->{33}*$b->{31}, 32=>$a->{31}*$b->{12}+$a->{32}*$b->{22}+$a->{33}*$b->{32}, 33=>$a->{31}*$b->{13}+$a->{32}*$b->{23}+$a->{33}*$b->{33},
   }; 
 }


=head3 matrixScalarDivide

Matrix=Matrix / non zero scalar

=cut


sub matrixScalarDivide($$)
 {my ($a) = check(@_[0..0]); # Matrices
  my ($b) = @_[1..1];        # Scalar
  confess "$b is not a scalar" if ref($b);   
  confess "$b is zero"         if $b == 0;   
  round bless
   {11=>$a->{11}/$b, 12=>$a->{12}/$b, 13=>$a->{13}/$b,
    21=>$a->{21}/$b, 22=>$a->{22}/$b, 23=>$a->{23}/$b,
    31=>$a->{31}/$b, 32=>$a->{32}/$b, 33=>$a->{33}/$b,
   }; 
 }


=head3 det

Determinant of matrix.

=cut


sub det($)
 {my ($a) = @_;       # Matrix
  check(@_) if debug; # Check

+$a->{11}*$a->{22}*$a->{33}
-$a->{11}*$a->{23}*$a->{32}
-$a->{12}*$a->{21}*$a->{33}
+$a->{12}*$a->{23}*$a->{31}
+$a->{13}*$a->{21}*$a->{32}
-$a->{13}*$a->{22}*$a->{31};
 }


=head3 d2

Determinant of 2*2 matrix

=cut


sub d2($$$$)
 {my ($a, $b, $c, $d) = @_;    
  $a*$d-$b*$c;
 }


=head3 inverse

Inverse of matrix

=cut


sub inverse($)
 {my ($a) = @_;       # Matrix
  check(@_) if debug; # Check
  return $a->{inverse} if defined($a->{inverse});

  my $d = det($a);
  return undef if $d == 0;

  my $i = round bless
   {11=>d2($a->{22}, $a->{32}, $a->{23}, $a->{33})/$d,
    21=>d2($a->{23}, $a->{33}, $a->{21}, $a->{31})/$d,
    31=>d2($a->{21}, $a->{31}, $a->{22}, $a->{32})/$d,

    12=>d2($a->{13}, $a->{33}, $a->{12}, $a->{32})/$d,
    22=>d2($a->{11}, $a->{31}, $a->{13}, $a->{33})/$d,
    32=>d2($a->{12}, $a->{32}, $a->{11}, $a->{31})/$d,

    13=>d2($a->{12}, $a->{22}, $a->{13}, $a->{23})/$d,
    23=>d2($a->{13}, $a->{23}, $a->{11}, $a->{21})/$d,
    33=>d2($a->{11}, $a->{21}, $a->{12}, $a->{22})/$d,
   };
  $a->{inverse} = $i;
  $i;
 }


=head3 identity

Identity matrix

=cut


sub identity()
 {bless
   {11=>1, 21=>0, 31=>0,                              
    12=>0, 22=>1, 32=>0,                              
    13=>0, 23=>0, 33=>1,
   }; 
 }


=head3 equals

Equals to within accuracy

=cut