.\" -*- mode: troff; coding: utf-8 -*-
.\" Automatically generated by Pod::Man 5.01 (Pod::Simple 3.43)
.\"
.\" Standard preamble:
.\" ========================================================================
.de Sp \" Vertical space (when we can't use .PP)
.if t .sp .5v
.if n .sp
..
.de Vb \" Begin verbatim text
.ft CW
.nf
.ne \\$1
..
.de Ve \" End verbatim text
.ft R
.fi
..
.\" \*(C` and \*(C' are quotes in nroff, nothing in troff, for use with C<>.
.ie n \{\
.    ds C` ""
.    ds C' ""
'br\}
.el\{\
.    ds C`
.    ds C'
'br\}
.\"
.\" Escape single quotes in literal strings from groff's Unicode transform.
.ie \n(.g .ds Aq \(aq
.el       .ds Aq '
.\"
.\" If the F register is >0, we'll generate index entries on stderr for
.\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index
.\" entries marked with X<> in POD.  Of course, you'll have to process the
.\" output yourself in some meaningful fashion.
.\"
.\" Avoid warning from groff about undefined register 'F'.
.de IX
..
.nr rF 0
.if \n(.g .if rF .nr rF 1
.if (\n(rF:(\n(.g==0)) \{\
.    if \nF \{\
.        de IX
.        tm Index:\\$1\t\\n%\t"\\$2"
..
.        if !\nF==2 \{\
.            nr % 0
.            nr F 2
.        \}
.    \}
.\}
.rr rF
.\" ========================================================================
.\"
.IX Title "Math::GSL::Complex 3pm"
.TH Math::GSL::Complex 3pm 2024-01-10 "perl v5.38.2" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SS \fBcopy()\fP
.IX Subsection "copy()"
Returns a copy of the Complex number, which resides at a different location in
memory.
.PP
.Vb 2
\&    my $z    = Math::GSL::Complex\->new([10,5]);
\&    my $copy = $z\->copy;
.Ve
.SH NAME
Math::GSL::Complex \- Complex Numbers
.SH SYNOPSIS
.IX Header "SYNOPSIS"
.Vb 8
\&    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 part
\&    my $imag = $complex\->imag;                    # returns the imaginary part
\&    $complex\->gsl_set_real(5);                    # changes the real part to 5
\&    $complex\->gsl_set_imag(4);                    # changes the imaginary part to 4
\&    $complex\->gsl_set_complex(7,6);               # changes it to 7 + 6*i
\&    ($real, $imag) = $complex\->parts;             # get both at once
.Ve
.SH DESCRIPTION
.IX Header "DESCRIPTION"
Here is a list of all the functions included in this module :
.ie n .IP gsl_complex_arg($z) 1
.el .IP \f(CWgsl_complex_arg($z)\fR 1
.IX Item "gsl_complex_arg($z)"
Return the argument of the complex number \f(CW$z\fR
.ie n .IP gsl_complex_abs($z) 1
.el .IP \f(CWgsl_complex_abs($z)\fR 1
.IX Item "gsl_complex_abs($z)"
Return |$z|, the magnitude of the complex number \f(CW$z\fR
.ie n .IP """gsl_complex_rect($x,$y)""" 1
.el .IP \f(CWgsl_complex_rect($x,$y)\fR 1
.IX Item "gsl_complex_rect($x,$y)"
Create a complex number in cartesian form \f(CW$x\fR + \f(CW$y\fR*i
.ie n .IP """gsl_complex_polar($r,$theta)""" 1
.el .IP \f(CWgsl_complex_polar($r,$theta)\fR 1
.IX Item "gsl_complex_polar($r,$theta)"
Create a complex number in polar form \f(CW$r\fR*exp(i*$theta)
.ie n .IP gsl_complex_abs2($z) 1
.el .IP \f(CWgsl_complex_abs2($z)\fR 1
.IX Item "gsl_complex_abs2($z)"
Return |$z|^2, the squared magnitude of the complex number \f(CW$z\fR
.ie n .IP gsl_complex_logabs($z) 1
.el .IP \f(CWgsl_complex_logabs($z)\fR 1
.IX Item "gsl_complex_logabs($z)"
Return log(|$z|), the natural logarithm of the magnitude of the complex number \f(CW$z\fR
.ie n .IP """gsl_complex_add($c1, $c2)""" 1
.el .IP "\f(CWgsl_complex_add($c1, $c2)\fR" 1
.IX Item "gsl_complex_add($c1, $c2)"
Return a complex number which is the sum of the complex numbers \f(CW$c1\fR and \f(CW$c2\fR
.ie n .IP """gsl_complex_sub($c1, $c2)""" 1
.el .IP "\f(CWgsl_complex_sub($c1, $c2)\fR" 1
.IX Item "gsl_complex_sub($c1, $c2)"
Return a complex number which is the difference between \f(CW$c1\fR and \f(CW$c2\fR ($c1 \- \f(CW$c2\fR)
.ie n .IP """gsl_complex_mul($c1, $c2)""" 1
.el .IP "\f(CWgsl_complex_mul($c1, $c2)\fR" 1
.IX Item "gsl_complex_mul($c1, $c2)"
Return a complex number which is the product of the complex numbers \f(CW$c1\fR and \f(CW$c2\fR
.ie n .IP """gsl_complex_div($c1, $c2)""" 1
.el .IP "\f(CWgsl_complex_div($c1, $c2)\fR" 1
.IX Item "gsl_complex_div($c1, $c2)"
Return a complex number which is the quotient of the complex numbers \f(CW$c1\fR and \f(CW$c2\fR ($c1 / \f(CW$c2\fR)
.ie n .IP """gsl_complex_add_real($c, $x)""" 1
.el .IP "\f(CWgsl_complex_add_real($c, $x)\fR" 1
.IX Item "gsl_complex_add_real($c, $x)"
Return the sum of the complex number \f(CW$c\fR and the real number \f(CW$x\fR
.ie n .IP """gsl_complex_sub_real($c, $x)""" 1
.el .IP "\f(CWgsl_complex_sub_real($c, $x)\fR" 1
.IX Item "gsl_complex_sub_real($c, $x)"
Return the difference of the complex number \f(CW$c\fR and the real number \f(CW$x\fR
.ie n .IP """gsl_complex_mul_real($c, $x)""" 1
.el .IP "\f(CWgsl_complex_mul_real($c, $x)\fR" 1
.IX Item "gsl_complex_mul_real($c, $x)"
Return the product of the complex number \f(CW$c\fR and the real number \f(CW$x\fR
.ie n .IP """gsl_complex_div_real($c, $x)""" 1
.el .IP "\f(CWgsl_complex_div_real($c, $x)\fR" 1
.IX Item "gsl_complex_div_real($c, $x)"
Return the quotient of the complex number \f(CW$c\fR and the real number \f(CW$x\fR
.ie n .IP """gsl_complex_add_imag($c, $y)""" 1
.el .IP "\f(CWgsl_complex_add_imag($c, $y)\fR" 1
.IX Item "gsl_complex_add_imag($c, $y)"
Return sum of the complex number \f(CW$c\fR and the imaginary number i*$x
.ie n .IP """gsl_complex_sub_imag($c, $y)""" 1
.el .IP "\f(CWgsl_complex_sub_imag($c, $y)\fR" 1
.IX Item "gsl_complex_sub_imag($c, $y)"
Return the diffrence of the complex number \f(CW$c\fR and the imaginary number i*$x
.ie n .IP """gsl_complex_mul_imag($c, $y)""" 1
.el .IP "\f(CWgsl_complex_mul_imag($c, $y)\fR" 1
.IX Item "gsl_complex_mul_imag($c, $y)"
Return the product of the complex number \f(CW$c\fR and the imaginary number i*$x
.ie n .IP """gsl_complex_div_imag($c, $y)""" 1
.el .IP "\f(CWgsl_complex_div_imag($c, $y)\fR" 1
.IX Item "gsl_complex_div_imag($c, $y)"
Return the quotient of the complex number \f(CW$c\fR and the imaginary number i*$x
.ie n .IP gsl_complex_conjugate($c) 1
.el .IP \f(CWgsl_complex_conjugate($c)\fR 1
.IX Item "gsl_complex_conjugate($c)"
Return the conjugate of the of the complex number \f(CW$c\fR (x \- i*y)
.ie n .IP gsl_complex_inverse($c) 1
.el .IP \f(CWgsl_complex_inverse($c)\fR 1
.IX Item "gsl_complex_inverse($c)"
Return the inverse, or reciprocal of the complex number \f(CW$c\fR (1/$c)
.ie n .IP gsl_complex_negative($c) 1
.el .IP \f(CWgsl_complex_negative($c)\fR 1
.IX Item "gsl_complex_negative($c)"
Return the negative of the complex number \f(CW$c\fR (\-x \-i*y)
.ie n .IP gsl_complex_sqrt($c) 1
.el .IP \f(CWgsl_complex_sqrt($c)\fR 1
.IX Item "gsl_complex_sqrt($c)"
Return the square root of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_sqrt_real($x) 1
.el .IP \f(CWgsl_complex_sqrt_real($x)\fR 1
.IX Item "gsl_complex_sqrt_real($x)"
Return the complex square root of the real number \f(CW$x\fR, where \f(CW$x\fR may be negative
.ie n .IP """gsl_complex_pow($c1, $c2)""" 1
.el .IP "\f(CWgsl_complex_pow($c1, $c2)\fR" 1
.IX Item "gsl_complex_pow($c1, $c2)"
Return the complex number \f(CW$c1\fR raised to the complex power \f(CW$c2\fR
.ie n .IP """gsl_complex_pow_real($c, $x)""" 1
.el .IP "\f(CWgsl_complex_pow_real($c, $x)\fR" 1
.IX Item "gsl_complex_pow_real($c, $x)"
Return the complex number raised to the real power \f(CW$x\fR
.ie n .IP gsl_complex_exp($c) 1
.el .IP \f(CWgsl_complex_exp($c)\fR 1
.IX Item "gsl_complex_exp($c)"
Return the complex exponential of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_log($c) 1
.el .IP \f(CWgsl_complex_log($c)\fR 1
.IX Item "gsl_complex_log($c)"
Return the complex natural logarithm (base e) of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_log10($c) 1
.el .IP \f(CWgsl_complex_log10($c)\fR 1
.IX Item "gsl_complex_log10($c)"
Return the complex base\-10 logarithm of the complex number \f(CW$c\fR
.ie n .IP """gsl_complex_log_b($c, $b)""" 1
.el .IP "\f(CWgsl_complex_log_b($c, $b)\fR" 1
.IX Item "gsl_complex_log_b($c, $b)"
Return the complex base\-$b of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_sin($c) 1
.el .IP \f(CWgsl_complex_sin($c)\fR 1
.IX Item "gsl_complex_sin($c)"
Return the complex sine of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_cos($c) 1
.el .IP \f(CWgsl_complex_cos($c)\fR 1
.IX Item "gsl_complex_cos($c)"
Return the complex cosine of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_sec($c) 1
.el .IP \f(CWgsl_complex_sec($c)\fR 1
.IX Item "gsl_complex_sec($c)"
Return the complex secant of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_csc($c) 1
.el .IP \f(CWgsl_complex_csc($c)\fR 1
.IX Item "gsl_complex_csc($c)"
Return the complex cosecant of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_tan($c) 1
.el .IP \f(CWgsl_complex_tan($c)\fR 1
.IX Item "gsl_complex_tan($c)"
Return the complex tangent of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_cot($c) 1
.el .IP \f(CWgsl_complex_cot($c)\fR 1
.IX Item "gsl_complex_cot($c)"
Return the complex cotangent of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_arcsin($c) 1
.el .IP \f(CWgsl_complex_arcsin($c)\fR 1
.IX Item "gsl_complex_arcsin($c)"
Return the complex arcsine of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_arcsin_real($x) 1
.el .IP \f(CWgsl_complex_arcsin_real($x)\fR 1
.IX Item "gsl_complex_arcsin_real($x)"
Return the complex arcsine of the real number \f(CW$x\fR
.ie n .IP gsl_complex_arccos($c) 1
.el .IP \f(CWgsl_complex_arccos($c)\fR 1
.IX Item "gsl_complex_arccos($c)"
Return the complex arccosine of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_arccos_real($x) 1
.el .IP \f(CWgsl_complex_arccos_real($x)\fR 1
.IX Item "gsl_complex_arccos_real($x)"
Return the complex arccosine of the real number \f(CW$x\fR
.ie n .IP gsl_complex_arcsec($c) 1
.el .IP \f(CWgsl_complex_arcsec($c)\fR 1
.IX Item "gsl_complex_arcsec($c)"
Return the complex arcsecant of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_arcsec_real($x) 1
.el .IP \f(CWgsl_complex_arcsec_real($x)\fR 1
.IX Item "gsl_complex_arcsec_real($x)"
Return the complex arcsecant of the real number \f(CW$x\fR
.ie n .IP gsl_complex_arccsc($c) 1
.el .IP \f(CWgsl_complex_arccsc($c)\fR 1
.IX Item "gsl_complex_arccsc($c)"
Return the complex arccosecant of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_arccsc_real($x) 1
.el .IP \f(CWgsl_complex_arccsc_real($x)\fR 1
.IX Item "gsl_complex_arccsc_real($x)"
Return the complex arccosecant of the real number \f(CW$x\fR
.ie n .IP gsl_complex_arctan($c) 1
.el .IP \f(CWgsl_complex_arctan($c)\fR 1
.IX Item "gsl_complex_arctan($c)"
Return the complex arctangent of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_arccot($c) 1
.el .IP \f(CWgsl_complex_arccot($c)\fR 1
.IX Item "gsl_complex_arccot($c)"
Return the complex arccotangent of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_sinh($c) 1
.el .IP \f(CWgsl_complex_sinh($c)\fR 1
.IX Item "gsl_complex_sinh($c)"
Return the complex hyperbolic sine of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_cosh($c) 1
.el .IP \f(CWgsl_complex_cosh($c)\fR 1
.IX Item "gsl_complex_cosh($c)"
Return the complex hyperbolic cosine of the complex number \f(CW$cy\fR
.ie n .IP gsl_complex_sech($c) 1
.el .IP \f(CWgsl_complex_sech($c)\fR 1
.IX Item "gsl_complex_sech($c)"
Return the complex hyperbolic secant of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_csch($c) 1
.el .IP \f(CWgsl_complex_csch($c)\fR 1
.IX Item "gsl_complex_csch($c)"
Return the complex hyperbolic cosecant of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_tanh($c) 1
.el .IP \f(CWgsl_complex_tanh($c)\fR 1
.IX Item "gsl_complex_tanh($c)"
Return the complex hyperbolic tangent of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_coth($c) 1
.el .IP \f(CWgsl_complex_coth($c)\fR 1
.IX Item "gsl_complex_coth($c)"
Return the complex hyperbolic cotangent of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_arcsinh($c) 1
.el .IP \f(CWgsl_complex_arcsinh($c)\fR 1
.IX Item "gsl_complex_arcsinh($c)"
Return the complex hyperbolic arcsine of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_arccosh($c) 1
.el .IP \f(CWgsl_complex_arccosh($c)\fR 1
.IX Item "gsl_complex_arccosh($c)"
Return the complex hyperbolic arccosine of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_arccosh_real($x) 1
.el .IP \f(CWgsl_complex_arccosh_real($x)\fR 1
.IX Item "gsl_complex_arccosh_real($x)"
Return the complex hyperbolic arccosine of the real number \f(CW$x\fR
.ie n .IP gsl_complex_arcsech($c) 1
.el .IP \f(CWgsl_complex_arcsech($c)\fR 1
.IX Item "gsl_complex_arcsech($c)"
Return the complex hyperbolic arcsecant of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_arccsch($c) 1
.el .IP \f(CWgsl_complex_arccsch($c)\fR 1
.IX Item "gsl_complex_arccsch($c)"
Return the complex hyperbolic arccosecant of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_arctanh($c) 1
.el .IP \f(CWgsl_complex_arctanh($c)\fR 1
.IX Item "gsl_complex_arctanh($c)"
Return the complex hyperbolic arctangent of the complex number \f(CW$c\fR
.ie n .IP gsl_complex_arctanh_real($x) 1
.el .IP \f(CWgsl_complex_arctanh_real($x)\fR 1
.IX Item "gsl_complex_arctanh_real($x)"
Return the complex hyperbolic arctangent of the real number \f(CW$x\fR
.ie n .IP gsl_complex_arccoth($c) 1
.el .IP \f(CWgsl_complex_arccoth($c)\fR 1
.IX Item "gsl_complex_arccoth($c)"
Return the complex hyperbolic arccotangent of the complex number \f(CW$c\fR
.ie n .IP gsl_real($z) 1
.el .IP \f(CWgsl_real($z)\fR 1
.IX Item "gsl_real($z)"
Return the real part of \f(CW$z\fR
.ie n .IP gsl_imag($z) 1
.el .IP \f(CWgsl_imag($z)\fR 1
.IX Item "gsl_imag($z)"
Return the imaginary part of \f(CW$z\fR
.ie n .IP gsl_parts($z) 1
.el .IP \f(CWgsl_parts($z)\fR 1
.IX Item "gsl_parts($z)"
Return a list of the real and imaginary parts of \f(CW$z\fR
.ie n .IP """gsl_set_real($z, $x)""" 1
.el .IP "\f(CWgsl_set_real($z, $x)\fR" 1
.IX Item "gsl_set_real($z, $x)"
Sets the real part of \f(CW$z\fR to \f(CW$x\fR
.ie n .IP """gsl_set_imag($z, $y)""" 1
.el .IP "\f(CWgsl_set_imag($z, $y)\fR" 1
.IX Item "gsl_set_imag($z, $y)"
Sets the imaginary part of \f(CW$z\fR to \f(CW$y\fR
.ie n .IP """gsl_set_complex($z, $x, $h)""" 1
.el .IP "\f(CWgsl_set_complex($z, $x, $h)\fR" 1
.IX Item "gsl_set_complex($z, $x, $h)"
Sets the real part of \f(CW$z\fR to \f(CW$x\fR and the imaginary part to \f(CW$y\fR
.SH EXAMPLES
.IX Header "EXAMPLES"
This code defines \f(CW$z\fR as 6 + 4*i, takes the complex conjugate of that number, then prints it out.
.Sp
.Vb 4
\&    my $z = gsl_complex_rect(6,4);
\&    my $y = gsl_complex_conjugate($z);
\&    my ($real, $imag) = gsl_parts($y);
\&    print "z = $real + $imag*i\en";
.Ve
.PP
This code defines \f(CW$z\fR as 5 + 3*i, multiplies it by 2 and then prints it out.
.Sp
.Vb 5
\&    my $x = gsl_complex_rect(5,3);
\&    my $z = gsl_complex_mul_real($x, 2);
\&    my $real = gsl_real($z);
\&    my $imag = gsl_imag($z);
\&    print "Re(\e$z) = $real\en";
.Ve
.SH AUTHORS
.IX Header "AUTHORS"
Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
.SH "COPYRIGHT AND LICENSE"
.IX Header "COPYRIGHT AND LICENSE"
Copyright (C) 2008\-2023 Jonathan "Duke" Leto and Thierry Moisan
.PP
This program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.