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Update subMatrix function to handle non 2D matrices.
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Also fix some documentation typos and clarifications.
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@pstaabp
pstaabp committed Aug 13, 2024
1 parent eea08bb commit 34fd8ed
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192 changes: 128 additions & 64 deletions lib/Value/Matrix.pm
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Original file line number Diff line number Diff line change
Expand Up @@ -6,7 +6,9 @@

=head1 Value::Matrix class
References:
This is the Math Object code for a Matrix.
=head2 References:
=over
Expand All @@ -18,11 +20,7 @@ References:
=back
For allowing Matrices in Fractions, see L<http://webwork.maa.org/moodle/mod/forum/discuss.php?d=2978>
Context()->parens->set("[" => {formMatrix => 1});
=head2 Files interacting with Matrices:
=head2 Matrix-Related libraries and macros:
=over
Expand All @@ -46,7 +44,7 @@ For allowing Matrices in Fractions, see L<http://webwork.maa.org/moodle/mod/foru
=item L<tableau.pl>
=item quickMatrixEntry.pl
=item L<quickMatrixEntry.pl>
=item L<LinearProgramming.pl>
Expand All @@ -55,12 +53,18 @@ For allowing Matrices in Fractions, see L<http://webwork.maa.org/moodle/mod/foru
=head2 Contexts
=over
=item C<Matrix> -- allows students to enter [[3,4],[3,6]]
-- formMatrix =>1 also allows this?
=item C<Complex-Matrix> -- allows complex entries
=item C<Matrix>
Allows students to enter C<[[3,4],[3,6]]>
=item C<Complex-Matrix>
Allows complex entries
=back
=head2 Creation of Matrices
Using the C<Matrix>, C<Vector> or C<ColumnVector> methods
Expand All @@ -69,16 +73,16 @@ Examples:
$M1 = Matrix([1,2],[3,4]);
$M2 = Matrix([5,6],[7,8]);
$v = Vector(9,10);
$w = ColumnVector(9,10); # differs in how it is printed
Commands added in Value::matrix
Conversion:
$matrix->value produces [[3,4,5],[1,3,4]] recursive array references of numbers (not MathObjects)
$matrix->wwMatrix produces CPAN MatrixReal1 matrix, used for computation subroutines
Information
$matrix->dimension: ARRAY
Access values
Expand All @@ -88,7 +92,8 @@ Access values
element : Real or Complex value
Update values
setElement.
setElement
See C<change_matrix_entry()> in MatrixReduce and L<http://webwork.maa.org/moodle/mod/forum/discuss.php?d=2970>
Expand Down Expand Up @@ -128,6 +133,20 @@ The commands below are Value::Matrix B<methods> unless otherwise noted.
solve_SSM
solve_RM
=head2 Fractions in Matrices
One can use fractions in Matrices by including C<Context("Fraction")>. For example
Context("Fraction");
$A = Matrix([
[Fraction(1,1), Fraction(1,2), Fraction(1,3)],
[Fraction(1,2), Fraction(1,3), Fraction(1,4)],
[Fraction(1,3), Fraction(1,4), Fraction(1,5)]]);
and operations will be done using rational arithmetic. Also helpful is the method
C<apply_fraction_to_matrix_entries> in the L<MatrixReduce.pl> macro. Some additional information can be
found in L<https://webwork.maa.org/moodle/mod/forum/discuss.php?d=2978>.
=head2 methods
=cut
Expand Down Expand Up @@ -548,20 +567,17 @@ sub mult {
}

# Make points and vectors into columns if they are on the right.

if (!$flag && Value::classMatch($r, 'Point', 'Vector')) { $r = ($self->promote($r))->transpose }
else { $r = $self->promote($r) }
$r = !$flag && Value::classMatch($r, 'Point', 'Vector') ? ($self->promote($r))->transpose : $self->promote($r);

if ($flag) { my $tmp = $l; $l = $r; $r = $tmp }
my @dl = $l->dimensions;
my @dr = $r->dimensions;
if (scalar(@dl) == 1) { @dl = (1, @dl); $l = $self->make($l) }
if (scalar(@dr) == 1) { @dr = (@dr, 1); $r = $self->make($r)->transpose }
Value::Error("Can only multiply 2-dimensional matrices") if scalar(@dl) > 2 || scalar(@dr) > 2;
Value::Error("Matrices of dimensions %dx%d and %dx%d can't be multiplied", @dl, @dr)
unless ($dl[1] == $dr[0]);
Value::Error("Matrices of dimensions %dx%d and %dx%d can't be multiplied", @dl, @dr) unless ($dl[1] == $dr[0]);

# Perform atrix multiplication.
# Perform matrix multiplication.

my @l = $l->value;
my @r = $r->value;
Expand Down Expand Up @@ -635,7 +651,7 @@ sub conj { shift->twiddle(@_) }
sub twiddle {
my $self = promote(@_);
my @coords = ();
foreach my $x (@{ $self->data }) { push(@coords, ($x->can("conj") ? $x->conj : $x)) }
for my $x (@{ $self->data }) { push(@coords, ($x->can("conj") ? $x->conj : $x)); }
return $self->make(@coords);
}

Expand All @@ -655,6 +671,7 @@ sub transpose {
my @d = $self->dimensions;
if (scalar(@d) == 1) { @d = (1, @d); $self = $self->make($self) }
Value::Error("Can't transpose %d-dimensional matrices", scalar(@d)) unless scalar(@d) == 2;

my @M = ();
my $M = $self->data;
for my $j (0 .. $d[1] - 1) {
Expand Down Expand Up @@ -683,8 +700,10 @@ sub I {
my $d = shift;
my $context = shift || $self->context;
$d = ($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 $REAL = $context->Package('Real');

Expand Down Expand Up @@ -772,14 +791,16 @@ sub E {
($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 $d =~ m/^[1-9]\d*$/;
$context = $self->context unless $context;
my @ij = @{$rows};

Value::Error("You must provide a dimension for an Elementary matrix") unless defined $d;
Value::Error("Dimension must be a positive integer") unless $d =~ m/^[1-9]\d*$/;
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);
Expand Down Expand Up @@ -845,6 +866,7 @@ sub P {
}
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) {
Expand Down Expand Up @@ -895,6 +917,7 @@ sub Zero {
$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 = ();
Expand Down Expand Up @@ -933,7 +956,7 @@ Extract a given column from the matrix.
Usage:
my $A1 = Matrix([ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 9, 10, 11, 12 ] ]);
$A1 = Matrix([ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 9, 10, 11, 12 ] ]);
$A1->column(2); # returns the column Matrix [[2],[6],[10]]
=cut
Expand Down Expand Up @@ -962,13 +985,13 @@ Extract an element from the given row/col.
Usage:
my $A = Matrix([ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 9, 10, 11, 12 ] ]);
$A = Matrix([ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 9, 10, 11, 12 ] ]);
$A->element(2,3); # returns 7
my $B = Matrix([ [ [ 1, 2 ], [ 3, 4 ] ], [ [ 5, 6 ], [ 7, 8 ] ] ]);
$B = Matrix([ [ [ 1, 2 ], [ 3, 4 ] ], [ [ 5, 6 ], [ 7, 8 ] ] ]);
$B->element(1,2,1); # returns 3;
my $row = Matrix([4,3,2,1]);
$row = Matrix([4,3,2,1]);
$row->element(2); # returns 3;
=cut

Expand All @@ -988,21 +1011,52 @@ Note: this mutates the matrix itself.
Usage:
my $A = Matrix([ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 9, 10, 11, 12 ] ]);
$A = Matrix([ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [ 9, 10, 11, 12 ] ]);
$A->setElement([2,3],-5);
=cut

sub setElement {
my ($self, $ind, $value) = @_;

Value::Error("The index $ind->[0] does not exist in the matrix") unless defined $self->{data}[ $ind->[0] - 1 ];

# Drill down into the matrix
my $el = $self->{data}[ $ind->[0] - 1 ];
for my $i (1 .. scalar(@$ind) - 1) { $el = $el->{data}[ $ind->[$i] - 1 ]; }
my $el = \($self->{data}[ $ind->[0] - 1 ]);
for my $i (1 .. scalar(@$ind) - 1) {
Value::Error("The index $ind->[$i] does not exist in the matrix") unless defined $$el->{data}[ $ind->[$i] - 1 ];
$el = \($$el->{data}[ $ind->[$i] - 1 ]);
}

# update the value of $el
$el = Value::makeValue($value);
$$el = Value::makeValue($value);
}

# The subroutine extractElements is used in the subMatrix routine. This called recursively to handle
# any dimension of a Matrix. initially $indices needs to be [] and $elements an arrayref of the
# elements to be extracted.
#
# Through subsequent passes through the subroutine, the indices in the $elements arguments are passed to the $indices.

sub extractElements {
my ($self, $indices, $elements) = @_;

# These need to be copies of the array arguments.
my @ind_copy = @$indices;
my @elements_copy = @$elements;

my $ind = shift @elements_copy;
push(@ind_copy, [ 1 .. scalar(@$ind) ]);

my @M;
for my $i (@$ind) {
push(@M,
ref $self->element($i) eq 'Value::Matrix'
? $self->element($i)->extractElements(\@ind_copy, \@elements_copy)
: $self->element($i));
}

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

=head3 C<subMatrix>
Expand All @@ -1022,37 +1076,51 @@ Usage:
$A->subMatrix(2,3); # returns Matrix([ [ 1, 2, 4 ], [ 9, 10, 12 ] ]);
$A->subMatrix([3,1,2],[1,4,2]); # returns Matrix([9,12,10],[1,4,2],[5,8,6]);
This subroutine can be used on non 2D matrices. For example,
$B = Matrix([2, 4, 6, 8]);
$B->subMatrix([1, 3]); # returns Matrix([2, 6]);
$B->subMatrix(2); # returns Matrix([2, 6, 8]);
And for 3D matrices:
$C = Matrix([ [ [ 1, 2, 3 ], [ 4, 5, 6 ] ], [ [ 7, 8, 9 ], [ 10, 11, 12 ] ] ]);
$C->subMatrix([1, 2], [1, 2], [1, 3]); # returns Matrix([ [ [ 1, 3 ], [ 4, 6 ] ], [ [ 7, 9 ], [ 10, 12 ] ] ]);
$C->subMatrix(1,2,3); # returns Matrix([ [ [ 7, 8 ] ] ]);
=cut

sub subMatrix {
my ($self, $r, $c) = @_;
my $context = $self->context;
my ($rows, $cols);
my ($nrow, $ncol) = $self->dimensions;

# check if the inputs are integers.
if (ref $r eq '' && ref $c eq '') {
Value::Error("The input $r is not a valid row.") unless $r >= 1 && $r <= $nrow && int($r) == $r;
Value::Error("The input $c is not a valid column.") unless $c >= 1 && $c <= $ncol && int($c) == $c;
$rows = [ grep { $_ != $r } (1 .. $nrow) ];
$cols = [ grep { $_ != $c } (1 .. $ncol) ];
} elsif (ref $r eq 'ARRAY' && ref $c eq 'ARRAY') {
$rows = $r;
$cols = $c;
for my $i (@$rows) {
Value::Error("The input $i is not a valid row.") unless int($i) == $i && $i >= 1 && $i <= $nrow;
}
for my $i (@$cols) {
Value::Error("The input $i is not a valid column.") unless int($i) == $i && $i >= 1 && $i <= $ncol;
my ($self, @ind) = @_;
my @dim = $self->dimensions;
my @indices; # Indices to keep for submatrix.

# check that the input is appropriate for the size of the matrix.
Value::Error("The indices must be array refs the same size as the dimension of the matrix.") unless $#dim == $#ind;

# check that inputs are either all integers or all array refs
my @index_types = keys %{ { map { ref $_, 1 } @ind } };

Value::Error('The inputs must both be integers or array refs.')
unless scalar(@index_types) == 1 && ($index_types[0] eq '' || $index_types[0] eq 'ARRAY');

for my $i (0 .. $#ind) {
if ($index_types[0] eq '') { # input is a scalar (integer)
Value::Error("The input $ind[$i] is not a valid index")
unless $ind[$i] >= 1 && $ind[$i] <= $dim[$i] && int($ind[$i]) == $ind[$i];
push(@indices, [ grep { $_ != $ind[$i] } (1 .. $dim[$i]) ]);

} elsif ($index_types[0] eq 'ARRAY') { # input are array refs
for my $j (@{ $ind[$i] }) {
Value::Error("The input $j is not a valid index") unless int($j) == $j && $j >= 1 && $j <= $dim[$i];
}
push(@indices, $ind[$i]);
}
} else {
Value::Error('The inputs must both be integers or array refs.');
}
my @M = ();
for my $r (@$rows) {
push(@M, $self->make($context, map { $self->element($r, $_) } @$cols));
}
return $self->make($context, @M);

return $self->extractElements([], \@indices);
}

=head3 C<removeRow>
Expand All @@ -1072,13 +1140,13 @@ sub removeRow {
my ($self, $row) = @_;
my $context = $self->context;
my @d = $self->dimensions;
Value::Error("The method removeRow is only valid for 2D matrices.") unless scalar(@d) eq 2;
Value::Error("The method removeRow is only valid for 2D matrices.") unless scalar(@d) == 2;
my ($nrow, $ncol) = @d;
Value::Error("The input $row is not a valid row.")
unless ref($row) eq '' && $row >= 1 && $row <= $nrow && int($row) == $row;

my @M = ();
for my $r (1 .. $nrow) { push(@M, $self->make($context, $r)) unless $r eq $row; }
for my $r (1 .. $nrow) { push(@M, $self->row($r)) unless $r eq $row; }
return $self->make($context, @M);
}

Expand Down Expand Up @@ -1113,9 +1181,6 @@ sub removeColumn {
return $self->make($context, @M);
}

# @@@ removeRow, removeColumn @@@
# @@@ Minor @@@

# Convert MathObject Matrix to old-style Matrix
sub wwMatrix {
my $self = (ref($_[0]) ? $_[0] : shift);
Expand Down Expand Up @@ -1373,4 +1438,3 @@ sub TeX {
}

1;

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