Fiddle with Eigen+FFT tests and add nonsymmetric eigenvalue example

[Math-GSL.git] / pod / Complex.pod

%perlcode %{

@EXPORT_OK = qw(
    gsl_complex_arg gsl_complex_abs gsl_complex_rect gsl_complex_polar doubleArray_getitem 
    gsl_complex_rect gsl_complex_polar gsl_complex_arg gsl_complex_abs gsl_complex_abs2 
    gsl_complex_logabs gsl_complex_add gsl_complex_sub gsl_complex_mul gsl_complex_div 
    gsl_complex_add_real gsl_complex_sub_real gsl_complex_mul_real gsl_complex_div_real 
    gsl_complex_add_imag gsl_complex_sub_imag gsl_complex_mul_imag gsl_complex_div_imag 
    gsl_complex_conjugate gsl_complex_inverse gsl_complex_negative gsl_complex_sqrt 
    gsl_complex_sqrt_real gsl_complex_pow gsl_complex_pow_real gsl_complex_exp 
    gsl_complex_log gsl_complex_log10 gsl_complex_log_b gsl_complex_sin 
    gsl_complex_cos gsl_complex_sec gsl_complex_csc gsl_complex_tan 
    gsl_complex_cot gsl_complex_arcsin gsl_complex_arcsin_real gsl_complex_arccos 
    gsl_complex_arccos_real gsl_complex_arcsec gsl_complex_arcsec_real gsl_complex_arccsc 
    gsl_complex_arccsc_real gsl_complex_arctan gsl_complex_arccot gsl_complex_sinh 
    gsl_complex_cosh gsl_complex_sech gsl_complex_csch gsl_complex_tanh 
    gsl_complex_coth gsl_complex_arcsinh gsl_complex_arccosh gsl_complex_arccosh_real 
    gsl_complex_arcsech gsl_complex_arccsch gsl_complex_arctanh gsl_complex_arctanh_real 
    gsl_complex_arccoth new_doubleArray delete_doubleArray doubleArray_setitem
    gsl_real gsl_imag gsl_parts
    gsl_complex_eq gsl_set_real gsl_set_imag gsl_set_complex
    $GSL_COMPLEX_ONE $GSL_COMPLEX_ZERO $GSL_COMPLEX_NEGONE
);
# macros to implement
# gsl_set_complex gsl_set_complex_packed
our ($GSL_COMPLEX_ONE, $GSL_COMPLEX_ZERO, $GSL_COMPLEX_NEGONE) = map { gsl_complex_rect($_, 0) } qw(1 0 -1); 


%EXPORT_TAGS = ( all => [ @EXPORT_OK ] );

### wrapper interface ###
sub new {
    my ($class, @values) = @_;
    my $this = {};
    $this->{_complex} = gsl_complex_rect($values[0], $values[1]);
    bless $this, $class;
}
sub real {
    my ($self) = @_;
    gsl_real($self->{_complex}->{dat});
}

sub imag {
    my ($self) = @_;
    gsl_imag($self->{_complex}->{dat});
}

sub parts {
    my ($self) = @_;
    gsl_parts($self->{_complex}->{dat});
}

sub raw  { (shift)->{_complex} }

### end wrapper interface ###

### some important macros that are in gsl_complex.h
sub gsl_complex_eq {
    my ($z,$w) = @_;
    gsl_real($z) == gsl_real($w) && gsl_imag($z) == gsl_imag($w) ? 1 : 0;
}

sub gsl_set_real {
    my ($z,$r) = @_;
    doubleArray_setitem($z->{dat}, 0, $r);
}

sub gsl_set_imag {
    my ($z,$i) = @_;
    doubleArray_setitem($z->{dat}, 1, $i);
}

sub gsl_real {
    my $z = shift;
    return doubleArray_getitem($z->{dat}, 0 );
}

sub gsl_imag {
    my $z = shift;
    return doubleArray_getitem($z->{dat}, 1 );
}

sub gsl_parts {
    my $z = shift;
    return (gsl_real($z), gsl_imag($z));
}

sub gsl_set_complex {
    my ($z, $r, $i) = @_;
    gsl_set_real($z, $r);
    gsl_set_imag($z, $i);
}

__END__

=head1 NAME

Math::GSL::Complex - Complex Numbers

=head1 SYNOPSIS

    use Math::GSL::Complex qw/:all/;
    my $complex = Math::GSL::Complex->new([3,2]); # creates a complex number 3+2*i
    my $real = $complex->real; # returns the real value of the complex number
    my $imag = $complex->imag; # returns the imaginary value of the complex number
    $complex->gsl_set_real(5); # changes the real value of the complex number to 5
    $complex->gsl_set_imag(4); # changes the imaginary value of the complex number to 4
    $complex->gsl_set_complex(7,6); # changes the real value of the complex number to 7 and the imaginary value to 6
    ($real, $imag) = $complex->parts; # returns the real and imaginary values of the complex number
    my $abs = gsl_complex_abs2($complex->raw); # the raw method gives access to the underlying gsl_complex structure, it is needed for the functions below.

=head1 DESCRIPTION

Here is a list of all the functions included in this module :

=over 1

=item C<gsl_complex_arg($z)> - return the argument of the complex number $z 

=item C<gsl_complex_abs($z)> - return |$z|, the magnitude of the complex number $z 

=item C<gsl_complex_rect($x,$y)> - create a complex number in cartesian form $x + $y*I

=item C<gsl_complex_polar($r,$theta)> - create a complex number in polar form $r*exp(I*$theta) 

=item C<gsl_complex_abs2($z)> - return |$z|^2, the squared magnitude of the complex number $z

=item C<gsl_complex_logabs($z)> - return log(|$z|), the natural logarithm of the magnitude of the complex number $z 

=item C<gsl_complex_add($c1, $c2)> - return a complex number which is the sum of the complex numbers $c1 and $c2 

=item C<gsl_complex_sub($c1, $c2)> - return a complex number which is the difference between $c1 and $c2 ($c1 - $c2) 

=item C<gsl_complex_mul($c1, $c2)> - return a complex number which is the product of the complex numbers $c1 and $c2

=item C<gsl_complex_div($c1, $c2)> - return a complex number which is the quotient of the complex numbers $c1 and $c2 ($c1 / $c2)

=item C<gsl_complex_add_real($c, $x)> - return the sum of the complex number $c and the real number $x 

=item C<gsl_complex_sub_real($c, $x)> - return the difference of the complex number $c and the real number $x 

=item C<gsl_complex_mul_real($c, $x)> - return the product of the complex number $c and the real number $x 

=item C<gsl_complex_div_real($c, $x)> - return the quotient of the complex number $c and the real number $x  

=item C<gsl_complex_add_imag($c, $y)> - return sum of the complex number $c and the imaginary number i*$x 

=item C<gsl_complex_sub_imag($c, $y)> - return the diffrence of the complex number $c and the imaginary number i*$x 

=item C<gsl_complex_mul_imag($c, $y)> - return the product of the complex number $c and the imaginary number i*$x  

=item C<gsl_complex_div_imag($c, $y)> - return the quotient of the complex number $c and the imaginary number i*$x 

=item C<gsl_complex_conjugate($c)> - return the conjugate of the of the complex number $c (x - i*y)  

=item C<gsl_complex_inverse($c)> - return the inverse, or reciprocal of the complex number $c (1/$c) 

=item C<gsl_complex_negative($c)> - return the negative of the complex number $c (-x -i*y) 

=item C<gsl_complex_sqrt($c)> - return the square root of the complex number $c 

=item C<gsl_complex_sqrt_real($x)> - return the complex square root of the real number $x, where $x may be negative

=item C<gsl_complex_pow($c1, $c2)> - return the complex number $c1 raised to the complex power $c2 

=item C<gsl_complex_pow_real($c, $x)> - return the complex number raised to the real power $x 

=item C<gsl_complex_exp($c)> - return the complex exponential of the complex number $c 

=item C<gsl_complex_log($c)> - return the complex natural logarithm (base e) of the complex number $c 

=item C<gsl_complex_log10($c)> - return the complex base-10 logarithm of the complex number $c

=item C<gsl_complex_log_b($c, $b)> - return the complex base-$b of the complex number $c 

=item C<gsl_complex_sin($c)> - return the complex sine of the complex number $c

=item C<gsl_complex_cos($c)> - return the complex cosine of the complex number $c 

=item C<gsl_complex_sec($c)> - return the complex secant of the complex number $c 

=item C<gsl_complex_csc($c)> - return the complex cosecant of the complex number $c 

=item C<gsl_complex_tan($c)> - return the complex tangent of the complex number $c 

=item C<gsl_complex_cot($c)> - return the complex cotangent of the complex number $c 

=item C<gsl_complex_arcsin($c)> - return the complex arcsine of the complex number $c 

=item C<gsl_complex_arcsin_real($x)> - return the complex arcsine of the real number $x 

=item C<gsl_complex_arccos($c)> - return the complex arccosine of the complex number $c 

=item C<gsl_complex_arccos_real($x)> - return the complex arccosine of the real number $x 

=item C<gsl_complex_arcsec($c)> - return the complex arcsecant of the complex number $c 

=item C<gsl_complex_arcsec_real($x)> - return the complex arcsecant of the real number $x

=item C<gsl_complex_arccsc($c)> - return the complex arccosecant of the complex number $c 

=item C<gsl_complex_arccsc_real($x)> - return the complex arccosecant of the real number $x

=item C<gsl_complex_arctan($c)> - return the complex arctangent of the complex number $c

=item C<gsl_complex_arccot($c)> - return the complex arccotangent of the complex number $c 

=item C<gsl_complex_sinh($c)> - return the complex hyperbolic sine of the complex number $c 

=item C<gsl_complex_cosh($c)> - return the complex hyperbolic cosine of the complex number $cy

=item C<gsl_complex_sech($c)> - return the complex hyperbolic secant of the complex number $c

=item C<gsl_complex_csch($c)> - return the complex hyperbolic cosecant of the complex number $c

=item C<gsl_complex_tanh($c)> - return the complex hyperbolic tangent of the complex number $c

=item C<gsl_complex_coth($c)> - return the complex hyperbolic cotangent of the complex number $c

=item C<gsl_complex_arcsinh($c)> - return the complex hyperbolic arcsine of the complex number $c

=item C<gsl_complex_arccosh($c)> - return the complex hyperbolic arccosine of the complex number $c

=item C<gsl_complex_arccosh_real($x)> - return the complex hyperbolic arccosine of the real number $x 

=item C<gsl_complex_arcsech($c)> - return the complex hyperbolic arcsecant of the complex number $c

=item C<gsl_complex_arccsch($c)> - return the complex hyperbolic arccosecant of the complex number $c

=item C<gsl_complex_arctanh($c)> - return the complex hyperbolic arctangent of the complex number $c

=item C<gsl_complex_arctanh_real($x)> - return the complex hyperbolic arctangent of the real number $x 

=item C<gsl_complex_arccoth($c)> - return the complex hyperbolic arccotangent of the complex number $c

=item C<gsl_real($z)> - return the real part of $z 

=item C<gsl_imag($z)> - return the imaginary part of $z 

=item C<gsl_parts($z)> - return a list of the real and imaginary parts of $z

=item C<gsl_set_real($z, $x)> - sets the real part of $z to $x

=item C<gsl_set_imag($z, $y)> - sets the imaginary part of $z to $y

=item C<gsl_set_complex($z, $x, $h)> - sets the real part of $z to $x and the imaginary part to $y

=back

You have to add the functions you want to use inside the qw /put_funtion_here / with spaces between each function. 
You can also write use Math::GSL::Complex qw/:all/ to use all avaible functions of the module.

For more informations on the functions, we refer you to the GSL offcial documentation: L<http://www.gnu.org/software/gsl/manual/html_node/>
Tip : search on google: site:http://www.gnu.org/software/gsl/manual/html_node/ name_of_the_function_you_want

=head1 EXAMPLES

This code defines $z as 6 + 4*I, takes the complex conjugate of that number, then prints it out.

=over 1

=item C<my $z = gsl_complex_rect(6,4);>

=item C<my $y = gsl_complex_conjugate($z);>

=item C<my ($real, $imag) = gsl_parts($y);>

=item C<print "z = $real + $imag*I\n";>

=back

This code defines $z as 5 + 3*I, multiplies it by 2 and then prints it out.

=over 1

=item C<my $x = gsl_complex_rect(5,3);>

=item C<my $z = gsl_complex_mul_real($x, 2);>

=item C<my $real = gsl_real($z);>

=item C<my $imag = gsl_imag($z);>

=item C<print "Re(\$z) = $real\n";>

=back

=head1 AUTHORS

Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>

=head1 COPYRIGHT AND LICENSE

Copyright (C) 2008 Jonathan Leto and Thierry Moisan

This program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.

=cut
%}