Math::Symbolic::Custom::DefaultTests - Default Math::Symbolic tree tests

Math-Symbolic documentation

Contained in the Math-Symbolic distribution.

Index

NAME
SYNOPSIS
DESCRIPTION
- EXPORT
SUBROUTINES
AUTHOR
SEE ALSO

Code Index:

package Math::Symbolic::Custom::DefaultTests
__END__
EOF

NAME

Math::Symbolic::Custom::DefaultTests - Default Math::Symbolic tree tests

SYNOPSIS

  use Math::Symbolic;

DESCRIPTION

This is a class of default tests for Math::Symbolic trees. Likewise, Math::Symbolic::Custom::DefaultMods defines default tree transformation routines. For details on how the custom method delegation model works, please have a look at the Math::Symbolic::Custom and Math::Symbolic::Custom::Base classes.

EXPORT

Please see the docs for Math::Symbolic::Custom::Base for details, but you should not try to use the standard Exporter semantics with this class.

SUBROUTINES

is_zero()

Returns true (1) of the tree is a constant and '0'. Returns false (0) otherwise.

is_one()

Returns true (1) of the tree is a constant and '1'. Returns false (0) otherwise.

is_zero_or_one()

Returns true ('1' for 1, '0E0' for 0) of the tree is a constant and '1' or '0'. Returns false (0) otherwise.

is_integer()

is_integer() returns a boolean.

It returns true (1) if the tree is a constant object representing an integer value. It does not compute the value of the tree. (eg. '5*10' is not considered an integer, but '50' is.)

It returns false (0) otherwise.

is_simple_constant()

is_simple_constant() returns a boolean.

It returns true if the tree consists of only constants and operators. As opposed to is_constant(), is_simple_constant() does not apply derivatives if necessary.

It returns false (0) otherwise.

is_constant()

is_constant() returns a boolean.

It returns true (1) if the tree consists of only constants and operators or if it becomes a tree of only constants and operators after application of derivatives.

It returns false (0) otherwise.

If you need not pay the price of applying derivatives, you should use the is_simple_constant() method instead.

is_identical()

is_identical() returns a boolean.

It compares the tree it is called on to its first argument. If the first argument is not a Math::Symbolic tree, it is sent through the parser.

is_identical() returns true (1) if the trees are completely identical. That includes operands of commutating operators having the same order, etc. This does not test of mathematical equivalence! (Which is much, much harder to test for. If you know how to, please let me know!)

It returns false (0) otherwise.

is_identical_base

is_identical_base() returns a boolean.

It compares the tree it is called on to its first argument. If the first argument is not a Math::Symbolic tree, it is sent through the parser.

is_identical_base() returns true (1) if the trees are identical or if they are exponentiations with the same base. The same gotchas that apply to is_identical apply here, too.

For example, 'x*y' and '(x*y)^e' result in a true return value because 'x*y' is equal to '(x*y)^1' and this has the same base as '(x*y)^e'.

It returns false (0) otherwise.

is_sum()

(beta)

is_constant() returns a boolean.

It returns true (1) if the tree contains no variables (because it can then be evaluated to a single constant which is a sum). It also returns true if it is a sum or difference of constants and variables. Furthermore, it is true for products of integers and constants because those products are really sums of variables. If none of the above cases match, it applies all derivatives and tries again.

It returns false (0) otherwise.

Please contact the author in case you encounter bugs in the specs or implementation. The heuristics aren't all that great.

test_num_equiv()

Takes another Math::Symbolic tree or a code ref as first argument. Tests the tree it is called on and the one passed in as first argument for equivalence by sampling random numbers for their parameters and evaluating them.

This is no guarantee that the functions are actually similar. The computation required for this test may be very high for large numbers of tests.

In case of a subroutine reference passed in, the values of the parameters of the Math::Symbolic tree are passed to the sub ref sorted by the parameter names.

Following the test-tree, there may be various options as key/value pairs:

  limits: A hash reference with parameter names as keys and code refs
          as arguments. A code ref for parameter 'x', will be executed
          for every number of 'x' that is generated. If the code
          returns false, the number is discarded and regenerated.
  tests:  The number of tests to carry out. Default: 20
  epsilon: The accuracy of the numeric comparison. Default: 1e-7
  retries: The number of attempts to make if a function evaluation
           throws an error.
  upper:   Upper limit of the random numbers. Default: 10
  lower:   Lower limit of the random numbers. Default: -10

AUTHOR

Please send feedback, bug reports, and support requests to the Math::Symbolic support mailing list: math-symbolic-support at lists dot sourceforge dot net. Please consider letting us know how you use Math::Symbolic. Thank you.

If you're interested in helping with the development or extending the module's functionality, please contact the developers' mailing list: math-symbolic-develop at lists dot sourceforge dot net.

List of contributors:

  Steffen M�ller, symbolic-module at steffen-mueller dot net
  Stray Toaster, mwk at users dot sourceforge dot net
  Oliver Ebenh�h

SEE ALSO

New versions of this module can be found on http://steffen-mueller.net or CPAN. The module development takes place on Sourceforge at http://sourceforge.net/projects/math-symbolic/

Math::Symbolic::Custom Math::Symbolic::Custom::DefaultDumpers Math::Symbolic::Custom::DefaultMods Math::Symbolic

Math-Symbolic documentation

Contained in the Math-Symbolic distribution.

package Math::Symbolic::Custom::DefaultTests;

use 5.006;
use strict;
use warnings;
use Data::Dumper; # for numerical equivalence test

no warnings 'recursion';

our $VERSION = '0.606';

use Math::Symbolic::Custom::Base;
BEGIN { *import = \&Math::Symbolic::Custom::Base::aggregate_import }

use Math::Symbolic::ExportConstants qw/:all/;

use Carp;

# Class Data: Special variable required by Math::Symbolic::Custom
# importing/exporting functionality.
# All subroutines that are to be exported to the Math::Symbolic::Custom
# namespace should be listed here.

our $Aggregate_Export = [
    qw/
      is_one
      is_zero
      is_zero_or_one
      is_sum
      is_constant
      is_simple_constant
      is_integer
      is_identical
      is_identical_base
      test_num_equiv
      /
];

sub is_zero {
    my $tree = shift;
    return 0 unless $tree->term_type() == T_CONSTANT;
    return 1 if $tree->{value} == 0;
    return 0;
}

sub is_one {
    my $tree = shift;
    return 0 unless $tree->term_type() == T_CONSTANT;
    return 1 if $tree->{value} == 1;
    return 0;
}

sub is_zero_or_one {
    my $tree = shift;
    return 0 unless $tree->term_type() == T_CONSTANT;
    return 1 if $tree->{value} == 1;
    return "0E0" if $tree->{value} == 0;
    return 0;
}

sub is_integer {
    my $tree = shift;
    return 0 unless $tree->term_type() == T_CONSTANT;
    my $value = $tree->value();
    return ( int($value) == $value );
}

sub is_simple_constant {
    my $tree = shift;

    my $return = 1;
    $tree->descend(
        in_place => 1,
        before   => sub {
            my $tree  = shift;
            my $ttype = $tree->term_type();
            if ( $ttype == T_CONSTANT ) {
                return undef;
            }
            elsif ( $ttype == T_VARIABLE ) {
                $return = 0;
                return undef;
            }
            elsif ( $ttype == T_OPERATOR ) {
                return ();
            }
            else {
                croak "is_simple_constant called on " . "invalid tree type.";
            }
        },
    );
    return $return;
}

sub is_constant {
    my $tree = shift;

    my $return = 1;
    $tree->descend(
        in_place => 1,
        before   => sub {
            my $tree  = shift;
            my $ttype = $tree->term_type();
            if ( $ttype == T_CONSTANT ) {
                return undef;
            }
            elsif ( $ttype == T_VARIABLE ) {
                $return = 0;
                return undef;
            }
            elsif ( $ttype == T_OPERATOR ) {
                my $tree = $tree->apply_derivatives();
                $ttype = $tree->term_type();
                return undef if $ttype == T_CONSTANT;
                ( $return = 0 ), return undef
                  if $ttype == T_VARIABLE;

                return { descend_into => [ @{ $tree->{operands} } ], };
            }
            else {
                croak "is_constant called on " . "invalid tree type.";
            }
        },
    );
    return $return;
}

sub is_identical {
    my $tree1 = shift;
    my $tree2 = shift;
    $tree2 = Math::Symbolic::parse_from_string($tree2)
      if not ref($tree2) =~ /^Math::Symbolic/;

    my $tt1 = $tree1->term_type();
    my $tt2 = $tree2->term_type();

    if ( $tt1 != $tt2 ) {
        return 0;
    }
    else {
        if ( $tt1 == T_VARIABLE ) {
            return 0 if $tree1->name() ne $tree2->name();
            my @sig1 = $tree1->signature();
            my @sig2 = $tree2->signature();
            return 0 if scalar(@sig1) != scalar(@sig2);
            for ( my $i = 0 ; $i < @sig1 ; $i++ ) {
                return 0 if $sig1[$i] ne $sig2[$i];
            }
            return 1;
        }
        elsif ( $tt1 == T_CONSTANT ) {
            my $sp1 = $tree1->special();
            my $sp2 = $tree2->special();
            if (    defined $sp1
                and defined $sp2
                and $sp1 eq $sp2
                and $sp1 ne ''
                and $sp1 =~ /\S/ )
            {
                return 1;
            }
            return 1 if $tree1->value() == $tree2->value();
            return 0;
        }
        elsif ( $tt1 == T_OPERATOR ) {
            my $t1 = $tree1->type();
            my $t2 = $tree2->type();
            return 0 if $t1 != $t2;
            return 0
              if @{ $tree1->{operands} } != @{ $tree2->{operands} };

            my $i = 0;
            foreach ( @{ $tree1->{operands} } ) {
                return 0
                  unless is_identical( $_, $tree2->{operands}[ $i++ ] );
            }
            return 1;
        }
        else {
            croak "is_identical() called on invalid term type.";
        }
        die "Sanity check in is_identical(). Should not be reached.";
    }
}

sub is_identical_base {
    my $o1 = shift;
    my $o2 = shift;
    $o2 = Math::Symbolic::parse_from_string($o2)
      if ref($o2) !~ /^Math::Symbolic/;

    my $tt1 = $o1->term_type();
    my $tt2 = $o2->term_type();

    my $so1 =
      ( $tt1 == T_OPERATOR and $o1->type() == B_EXP ) ? $o1->op1() : $o1;
    my $so2 =
      ( $tt2 == T_OPERATOR and $o2->type() == B_EXP ) ? $o2->op1() : $o2;

    return Math::Symbolic::Custom::is_identical( $so1, $so2 );
}

sub is_sum {
    my $tree = shift;

    my $return = 1;
    $tree->descend(
        in_place => 1,
        before   => sub {
            my $tree  = shift;
            my $ttype = $tree->term_type();

            if ( $ttype == T_CONSTANT or $ttype == T_VARIABLE ) {
                return undef;
            }
            elsif ( $ttype == T_OPERATOR ) {
                my $type = $tree->type();
                if (   $type == B_SUM
                    or $type == B_DIFFERENCE
                    or $type == U_MINUS )
                {
                    return ();
                }
                elsif ( $type == B_PRODUCT ) {
                    $return = $tree->{operands}[0]->is_integer()
                      || $tree->{operands}[1]->is_integer();
                    return undef;
                }
                elsif ($type == U_P_DERIVATIVE
                    or $type == U_T_DERIVATIVE )
                {
                    my $tree = $tree->apply_derivatives();
                    $tree = $tree->simplify();
                    my $ttype = $tree->term_type();
                    return undef
                      if ( $ttype == T_CONSTANT
                        or $ttype == T_VARIABLE );

                    if ( $ttype == T_OPERATOR ) {
                        my $type = $tree->type();
                        if (   $type == U_P_DERIVATIVE
                            || $type == U_T_DERIVATIVE )
                        {
                            $return = 0;
                            return undef;
                        }
                        else {
                            return { descend_into => [$tree] };
                        }
                    }
                    else {
                        die "apply_derivatives "
                          . "screwed the pooch in "
                          . "is_sum().";
                    }
                }
                elsif ( is_constant($tree) ) {
                    return undef;
                }
                else {
                    $return = 0;
                    return undef;
                }
            }
            else {
                croak "is_sum called on invalid tree type.";
            }
            die;
        },
    );
    return $return;
}

sub test_num_equiv {
    my ($t1, $t2) = (shift(), shift());
    if (ref($t1) !~ /^Math::Symbolic/) {
        croak("test_numeric_equivalence() must be called on Math::Symbolic tree");
    }
    if (ref($t2) !~ /^Math::Symbolic/ and ref($t2) ne 'CODE') {
        croak("first argument to test_numeric_equivalence() must be a Math::Symbolic tree or a code reference");
    }

    my $is_code = ref($t2) eq 'CODE' ? 1 : 0;

    my %args = @_;
    my $limits = $args{limits} || {};
    my $tests = $args{tests} || 20;
    my $eps = $args{epsilon} || 1e-7;
    my $retries = $args{retries} || 5;
    my $upper = $args{upper} || 10;
    my $lower = $args{lower} || -10;

    my @s1 = $t1->signature();
    my @s2 = $is_code ? () : $t2->signature();

    my %sig = map {($_=>undef)} @s1, @s2;

    my $mult = $upper-$lower;

    my $retry = 0;
    foreach (1..$tests) {
        croak("Could not evaluate test functions with numbers -10..10")
          if $retry > $retries-1;
        for (keys %sig) {
            my $num = rand()*$mult - $mult/2;
            redo if $limits->{$_} and not $limits->{$_}->($num);
            $sig{$_} = $num;
        }

        no warnings;
        my($y1, $y2);
        eval {$y1 = $t1->value(%sig);};
        if ($@) {
            warn "error during evaluation: $@";
            $retry++;
            $mult /= 2;
            redo;
        }
        if ($is_code) {
            eval {$y2 = $t2->(map {$sig{$_}} sort keys %sig)};
        }
        else {
            eval {$y2 = $t2->value(%sig);};
        }
        if ($@) {
            warn "error during evaluation: $@";
            $retry++;
            $mult /= 2;
            redo;
        }

        if (not defined $y1) {
            warn "Result of '$t1' not defined; ".Dumper(\%sig);
            next if not defined $y2;
            $retry++;
            redo;
        }
        elsif (not defined $y2) {
            warn "Result of '$t2' not defined; ".Dumper(\%sig);
            $retry++;
            redo;
        }


        warn("1: $y1, 2: $y2; ".Dumper(\%sig)), return 0 if $y1+$eps < $y2 or $y1-$eps > $y2;

        $mult = $upper-$lower;
        $retry = 0;
    }

    return 1;
}

1;
__END__