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Merged
merged 3 commits into from
Apr 3, 2024
Merged

add elementary, permutation, and zero matrix constructors #1012

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7a5b2f9
add elementary, permutation, and zero matrix constructors
Alex-Jordan Feb 12, 2024
5388832
changes suggested in PR#1012
Alex-Jordan Feb 24, 2024
0abcab6
use matrix generator methods on a matrix
Alex-Jordan Feb 25, 2024
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122 changes: 118 additions & 4 deletions lib/Value/Matrix.pm
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Original file line number Diff line number Diff line change
Expand Up @@ -473,26 +473,140 @@ sub transpose {

#
# Get an identity matrix of the requested size
# Value::Matrix->I(n)
# $A->I # n is the number of rows of $A
#
sub I {
my $self = shift;
my $d = shift;
my $context = shift || $self->context;
$d = ($self->dimensions)[0] if !defined $d && ref($self) && $self->isSquare;
$d = ($self->dimensions)[0] if !defined $d && ref($self);
Value::Error("You must provide a dimension for the Identity matrix") unless defined $d;
Value::Error("Dimension must be a positive integer") unless $d =~ m/^[1-9]\d*$/;
my @M = ();
my @Z = split('', 0 x $d);
my $REAL = $context->Package('Real');

foreach my $i (0 .. $d - 1) {
my @row = @Z;
for my $i (0 .. $d - 1) {
push(@M, $self->make($context, map { $REAL->new(($_ == $i) ? 1 : 0) } 0 .. $d - 1));
}
return $self->make($context, @M);
}

#
# Get an elementary matrix of the requested size and type
# Value::Matrix->E(n,[i,j]) nxn, swap rows i and j
# Value::Matrix->E(n,[i,j],k) nxn, replace row i with row i added to k times row j
# Value::Matrix->E(n,[i],k) nxn, scale row i by k
# $A->E([i,j]) # n is the number of rows of $A
# $A->E([i,j],k) # n is the number of rows of $A
# $A->E([i],k) # n is the number of rows of $A
#
sub E {
my ($self, $d, $rows, $k, $context) = @_;
if (ref $d eq 'ARRAY') {
($rows, $k, $context) = ($d, $rows, $k);
$d = ($self->dimensions)[0] if ref($self);
}
$context = $self->context unless $context;
Value::Error("You must provide a dimension for an Elementary matrix") unless defined $d;
Value::Error("Dimension must be a positive integer") unless $d =~ m/^[1-9]\d*$/;
my @ij = @{$rows};
Value::Error("Either one or two rows must be specified for an Elementary matrix") unless (@ij == 1 || @ij == 2);
Value::Error(
"If only one row is specified for an Elementary matrix, then a number to scale by must also be specified")
if (@ij == 1 && !defined $k);
for (@ij) {
Value::Error("Row indices must be integers between 1 and $d")
unless ($_ =~ m/^[1-9]\d*$/ && $_ >= 1 && $_ <= $d);
}
@ij = map { $_ - 1 } (@ij);

my @M = ();
my $REAL = $context->Package('Real');

for my $i (0 .. $d - 1) {
my @row = (0) x $d;
$row[$i] = 1;
if (@ij == 1) {
$row[$i] = $k if ($i == $ij[0]);
} elsif (defined $k) {
$row[ $ij[1] ] = $k if ($i == $ij[0]);
} else {
($row[ $ij[0] ], $row[ $ij[1] ]) = ($row[ $ij[1] ], $row[ $ij[0] ]) if ($i == $ij[0] || $i == $ij[1]);
}
push(@M, $self->make($context, map { $REAL->new($_) } @row));
}
return $self->make($context, @M);
}

#
# Get a permutation matrix of the requested size
# E.g. P(3,[1,2,3]) corresponds to cycle (123) applied to rows of I_3i,
# and P(6,[1,4],[2,4,6]) corresponds to cycle product (14)(246) applied to rows of I_6
# Value::Matrix->P(n,(cycles))
# $A->P((cycles)) # n is the number of rows of $A
#
sub P {
my ($self, $d, @cycles) = @_;
if (ref $d eq 'ARRAY') {
unshift(@cycles, $d);
$d = ($self->dimensions)[0] if ref($self);
}
my $context = $self->context;
$d = ($self->dimensions)[0] if !defined $d && ref($self) && $self->isSquare;
Value::Error("You must provide a dimension for a Permutation matrix") unless defined $d;
Value::Error("Dimension must be a positive integer") unless $d =~ m/^[1-9]\d*$/;
for my $c (@cycles) {
Value::Error("Permutation cycles should be array references") unless (ref($c) eq 'ARRAY');
for (@$c) {
Value::Error("Permutation cycle indices must be integers between 1 and $d")
unless ($_ =~ m/^[1-9]\d*$/ && $_ >= 1 && $_ <= $d);
}
my %cycle_hash = map { $_ => '' } (@$c);
Value::Error("A permutation cycle should not repeat an index") unless (@$c == keys %cycle_hash);
}
my @M = ();
my $REAL = $context->Package('Real');

# Make an identity matrix
for my $i (0 .. $d - 1) {
push(@M, $self->make($context, map { $REAL->new(($_ == $i) ? 1 : 0) } 0 .. $d - 1));
}

# Then apply the permutation cycles to it
for my $c (@cycles) {
my $swap;
for my $i (0 .. $#$c, 0) {
($swap, $M[ $c->[$i] - 1 ]) = ($M[ $c->[$i] - 1 ], $swap);
}
}

return $self->make($context, @M);
}

#
# Get an all zero matrix of the requested size
# Value::Matrix->Zero(m,n)
# Value::Matrix->Zero(n)
# $A->Zero # n is the number of rows of $A
#
sub Zero {
my ($self, $m, $n, $context) = @_;
$context = $self->context unless $context;
$n = $m if !defined $n && defined $m;
$m = ($self->dimensions)[0] if !defined $m && ref($self);
$n = ($self->dimensions)[1] if !defined $n && ref($self);
Value::Error("You must provide dimensions for the Zero matrix") unless defined $m && defined $n;
Value::Error("Dimension must be a positive integer") unless $m =~ m/^[1-9]\d*$/ && $n =~ m/^[1-9]\d*$/;
my @M = ();
my $REAL = $context->Package('Real');

for my $i (0 .. $m - 1) {
push(@M, $self->make($context, map { $REAL->new(0) } 0 .. $n - 1));
}
return $self->make($context, @M);
}

#
# Extract a given row from the matrix
#
Expand Down