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.\" ========================================================================
.\"
.IX Title "Math::GSL::Complex 3pm"
.TH Math::GSL::Complex 3pm "2019-02-23" "perl v5.28.1" "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 \*(L"Duke\*(R" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
.SH "COPYRIGHT AND LICENSE"
.IX Header "COPYRIGHT AND LICENSE"
Copyright (C) 2008\-2014 Jonathan \*(L"Duke\*(R" 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.