############# Class : cmplx ##############
package Math::Cephes::Complex;
use strict;
use warnings;
use vars qw(%OWNER %ITERATORS @ISA
@EXPORT_OK %EXPORT_TAGS $VERSION);
require Math::Cephes;
require Exporter;
*import = \&Exporter::import;
@ISA = qw( Math::Cephes );
#my @cmplx = qw(clog cexp csin ccos ctan ccot casin cmplx
# cacos catan cadd csub cmul cdiv cmov cneg cabs csqrt
# csinh ccosh ctanh cpow casinh cacosh catanh);
@EXPORT_OK = qw(cmplx);
#%EXPORT_TAGS = ('cmplx' => [qw(cmplx)]);
%OWNER = ();
%ITERATORS = ();
$VERSION = '0.5304';
*swig_r_get = *Math::Cephesc::cmplx_r_get;
*swig_r_set = *Math::Cephesc::cmplx_r_set;
*swig_i_get = *Math::Cephesc::cmplx_i_get;
*swig_i_set = *Math::Cephesc::cmplx_i_set;
sub new {
my $pkg = shift;
my $self = Math::Cephesc::new_cmplx(@_);
bless $self, $pkg if defined($self);
}
sub DESTROY {
return unless $_[0]->isa('HASH');
my $self = tied(%{$_[0]});
return unless defined $self;
delete $ITERATORS{$self};
if (exists $OWNER{$self}) {
Math::Cephesc::delete_cmplx($self);
delete $OWNER{$self};
}
}
sub DISOWN {
my $self = shift;
my $ptr = tied(%$self);
delete $OWNER{$ptr};
}
sub ACQUIRE {
my $self = shift;
my $ptr = tied(%$self);
$OWNER{$ptr} = 1;
}
sub r {
my ($self, $value) = @_;
return $self->{r} unless (defined $value);
$self->{r} = $value;
return $value;
}
sub i {
my ($self, $value) = @_;
return $self->{i} unless (defined $value);
$self->{i} = $value;
return $value;
}
sub cmplx {
return Math::Cephes::Complex->new(@_);
}
sub as_string {
my $z = shift;
my $string;
my $re = $z->{r};
my $im = $z->{i};
if ($im == 0) {
$string = "$re";
}
else {
$string = sprintf "%f %s %f %s", $re,
(int( $im / abs($im) ) == -1) ? '-' : '+' ,
($im < 0) ? abs($im) : $im, 'i';
}
return $string;
}
sub cadd {
my ($z1, $z2) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::cadd($z1, $z2, $z);
return $z;
}
sub csub {
my ($z1, $z2) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::csub($z2, $z1, $z);
return $z;
}
sub cmul {
my ($z1, $z2) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::cmul($z1, $z2, $z);
return $z;
}
sub cdiv {
my ($z1, $z2) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::cdiv($z2, $z1, $z);
return $z;
}
sub cpow {
my ($z1, $z2) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::cpow($z1, $z2, $z);
return $z;
}
sub clog {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::clog($z1, $z);
return $z;
}
sub cexp {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::cexp($z1, $z);
return $z;
}
sub csin {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::csin($z1, $z);
return $z;
}
sub ccos {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::ccos($z1, $z);
return $z;
}
sub ctan {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::ctan($z1, $z);
return $z;
}
sub ccot {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::ccot($z1, $z);
return $z;
}
sub casin {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::casin($z1, $z);
return $z;
}
sub cacos {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::cacos($z1, $z);
return $z;
}
sub catan {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::catan($z1, $z);
return $z;
}
sub cmov {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::cmov($z1, $z);
return $z;
}
sub cneg {
my ($z1) = @_;
Math::Cephes::cneg($z1);
return $z1;
}
sub csqrt {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::csqrt($z1, $z);
return $z;
}
sub cabs {
my ($z1) = @_;
my $abs = Math::Cephes::cabs($z1);
return $abs;
}
sub csinh {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::csinh($z1, $z);
return $z;
}
sub ccosh {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::ccosh($z1, $z);
return $z;
}
sub ctanh {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::ctanh($z1, $z);
return $z;
}
sub casinh {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::casinh($z1, $z);
return $z;
}
sub cacosh {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::cacosh($z1, $z);
return $z;
}
sub catanh {
my ($z1) = @_;
my $z = Math::Cephes::Complex->new();
Math::Cephes::catanh($z1, $z);
return $z;
}
1;
__END__
=head1 NAME
Math::Cephes::Complex - Perl interface to the cephes complex number routines
=head1 SYNOPSIS
use Math::Cephes::Complex qw(cmplx);
my $z1 = cmplx(2,3); # $z1 = 2 + 3 i
my $z2 = cmplx(3,4); # $z2 = 3 + 4 i
my $z3 = $z1->radd($z2); # $z3 = $z1 + $z2
=head1 DESCRIPTION
This module is a layer on top of the basic routines in the
cephes math library to handle complex numbers. A complex
number is created via any of the following syntaxes:
my $f = Math::Cephes::Complex->new(3, 2); # $f = 3 + 2 i
my $g = new Math::Cephes::Complex(5, 3); # $g = 5 + 3 i
my $h = cmplx(7, 5); # $h = 7 + 5 i
the last one being available by importing I<cmplx>. If no arguments
are specified, as in
my $h = cmplx();
then the defaults $z = 0 + 0 i are assumed. The real and imaginary
part of a complex number are represented respectively by
$f->{r}; $f->{i};
or, as methods,
$f->r; $f->i;
and can be set according to
$f->{r} = 4; $f->{i} = 9;
or, again, as methods,
$f->r(4); $f->i(9);
The complex number can be printed out as
print $f->as_string;
A summary of the usage is as follows.
=over 4
=item I<csin>: Complex circular sine
SYNOPSIS:
# void csin();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->csin;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
If
z = x + iy,
then
w = sin x cosh y + i cos x sinh y.
=item I<ccos>: Complex circular cosine
SYNOPSIS:
# void ccos();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->ccos;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
If
z = x + iy,
then
w = cos x cosh y - i sin x sinh y.
=item I<ctan>: Complex circular tangent
SYNOPSIS:
# void ctan();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->ctan;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
If
z = x + iy,
then
sin 2x + i sinh 2y
w = --------------------.
cos 2x + cosh 2y
On the real axis the denominator is zero at odd multiples
of PI/2. The denominator is evaluated by its Taylor
series near these points.
=item I<ccot>: Complex circular cotangent
SYNOPSIS:
# void ccot();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->ccot;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
If
z = x + iy,
then
sin 2x - i sinh 2y
w = --------------------.
cosh 2y - cos 2x
On the real axis, the denominator has zeros at even
multiples of PI/2. Near these points it is evaluated
by a Taylor series.
=item I<casin>: Complex circular arc sine
SYNOPSIS:
# void casin();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->casin;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
Inverse complex sine:
2
w = -i clog( iz + csqrt( 1 - z ) ).
=item I<cacos>: Complex circular arc cosine
SYNOPSIS:
# void cacos();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->cacos;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
w = arccos z = PI/2 - arcsin z.
=item I<catan>: Complex circular arc tangent
SYNOPSIS:
# void catan();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->catan;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
If
z = x + iy,
then
1 ( 2x )
Re w = - arctan(-----------) + k PI
2 ( 2 2)
(1 - x - y )
( 2 2)
1 (x + (y+1) )
Im w = - log(------------)
4 ( 2 2)
(x + (y-1) )
Where k is an arbitrary integer.
=item I<csinh>: Complex hyperbolic sine
SYNOPSIS:
# void csinh();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->csinh;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
csinh z = (cexp(z) - cexp(-z))/2
= sinh x * cos y + i cosh x * sin y .
=item I<casinh>: Complex inverse hyperbolic sine
SYNOPSIS:
# void casinh();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->casinh;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
casinh z = -i casin iz .
=item I<ccosh>: Complex hyperbolic cosine
SYNOPSIS:
# void ccosh();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->ccosh;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
ccosh(z) = cosh x cos y + i sinh x sin y .
=item I<cacosh>: Complex inverse hyperbolic cosine
SYNOPSIS:
# void cacosh();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->cacosh;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
acosh z = i acos z .
=item I<ctanh>: Complex hyperbolic tangent
SYNOPSIS:
# void ctanh();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->ctanh;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
tanh z = (sinh 2x + i sin 2y) / (cosh 2x + cos 2y) .
=item I<catanh>: Complex inverse hyperbolic tangent
SYNOPSIS:
# void catanh();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->catanh;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
Inverse tanh, equal to -i catan (iz);
=item I<cpow>: Complex power function
SYNOPSIS:
# void cpow();
# cmplx a, z, w;
$a = cmplx(5, 6); # $z = 5 + 6 i
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $a->cpow($z);
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
Raises complex A to the complex Zth power.
Definition is per AMS55 # 4.2.8,
analytically equivalent to cpow(a,z) = cexp(z clog(a)).
=item I<cmplx>: Complex number arithmetic
SYNOPSIS:
# typedef struct {
# double r; real part
# double i; imaginary part
# }cmplx;
# cmplx *a, *b, *c;
$a = cmplx(3, 5); # $a = 3 + 5 i
$b = cmplx(2, 3); # $b = 2 + 3 i
$c = $a->cadd( $b ); # c = a + b
$c = $a->csub( $b ); # c = a - b
$c = $a->cmul( $b ); # c = a * b
$c = $a->cdiv( $b ); # c = a / b
$c = $a->cneg; # c = -a
$c = $a->cmov; # c = a
print $c->{r}, ' ', $c->{i}; # prints real and imaginary parts of $c
print $c->as_string; # prints $c as Re($c) + i Im($c)
DESCRIPTION:
Addition:
c.r = b.r + a.r
c.i = b.i + a.i
Subtraction:
c.r = b.r - a.r
c.i = b.i - a.i
Multiplication:
c.r = b.r * a.r - b.i * a.i
c.i = b.r * a.i + b.i * a.r
Division:
d = a.r * a.r + a.i * a.i
c.r = (b.r * a.r + b.i * a.i)/d
c.i = (b.i * a.r - b.r * a.i)/d
=item I<cabs>: Complex absolute value
SYNOPSIS:
# double a, cabs();
# cmplx z;
$z = cmplx(2, 3); # $z = 2 + 3 i
$a = cabs( $z );
DESCRIPTION:
If z = x + iy
then
a = sqrt( x**2 + y**2 ).
Overflow and underflow are avoided by testing the magnitudes
of x and y before squaring. If either is outside half of
the floating point full scale range, both are rescaled.
=item I<csqrt>: Complex square root
SYNOPSIS:
# void csqrt();
# cmplx z, w;
$z = cmplx(2, 3); # $z = 2 + 3 i
$w = $z->csqrt;
print $w->{r}, ' ', $w->{i}; # prints real and imaginary parts of $w
print $w->as_string; # prints $w as Re($w) + i Im($w)
DESCRIPTION:
If z = x + iy, r = |z|, then
1/2
Im w = [ (r - x)/2 ] ,
Re w = y / 2 Im w.
Note that -w is also a square root of z. The root chosen
is always in the upper half plane.
Because of the potential for cancellation error in r - x,
the result is sharpened by doing a Heron iteration
(see sqrt.c) in complex arithmetic.
=back
=head1 BUGS
Please report any to Randy Kobes <randy@theoryx5.uwinnipeg.ca>
=head1 SEE ALSO
For the basic interface to the cephes complex number routines, see
L<Math::Cephes>. See also L<Math::Complex>
for a more extensive interface to complex number routines.
=head1 COPYRIGHT
The C code for the Cephes Math Library is
Copyright 1984, 1987, 1989, 2002 by Stephen L. Moshier,
and is available at http://www.netlib.org/cephes/.
Direct inquiries to 30 Frost Street, Cambridge, MA 02140.
The perl interface is copyright 2000, 2002 by Randy Kobes.
This library is free software; you can redistribute it and/or
modify it under the same terms as Perl itself.
=cut