Math::GSL::Complex - Complex Numbers

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

       Copyright (C) 2008-2024 Jonathan "Duke" Leto and Thierry Moisan

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

perl v5.40.0                                       2024-10-20                            Math::GSL::Complex(3pm)

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

       gsl_complex_arg($z)
        Return the argument of the complex number $z

       gsl_complex_abs($z)
        Return |$z|, the magnitude of the complex number $z

       "gsl_complex_rect($x,$y)"
        Create a complex number in cartesian form $x + $y*i

       "gsl_complex_polar($r,$theta)"
        Create a complex number in polar form $r*exp(i*$theta)

       gsl_complex_abs2($z)
        Return |$z|^2, the squared magnitude of the complex number $z

       gsl_complex_logabs($z)
        Return log(|$z|), the natural logarithm of the magnitude of the complex number $z

       "gsl_complex_add($c1, $c2)"
        Return a complex number which is the sum of the complex numbers $c1 and $c2

       "gsl_complex_sub($c1, $c2)"
        Return a complex number which is the difference between $c1 and $c2 ($c1 - $c2)

       "gsl_complex_mul($c1, $c2)"
        Return a complex number which is the product of the complex numbers $c1 and $c2

       "gsl_complex_div($c1, $c2)"
        Return a complex number which is the quotient of the complex numbers $c1 and $c2 ($c1 / $c2)

       "gsl_complex_add_real($c, $x)"
        Return the sum of the complex number $c and the real number $x

       "gsl_complex_sub_real($c, $x)"
        Return the difference of the complex number $c and the real number $x

       "gsl_complex_mul_real($c, $x)"
        Return the product of the complex number $c and the real number $x

       "gsl_complex_div_real($c, $x)"
        Return the quotient of the complex number $c and the real number $x

       "gsl_complex_add_imag($c, $y)"
        Return sum of the complex number $c and the imaginary number i*$x

       "gsl_complex_sub_imag($c, $y)"
        Return the diffrence of the complex number $c and the imaginary number i*$x

       "gsl_complex_mul_imag($c, $y)"
        Return the product of the complex number $c and the imaginary number i*$x

       "gsl_complex_div_imag($c, $y)"
        Return the quotient of the complex number $c and the imaginary number i*$x

       gsl_complex_conjugate($c)
        Return the conjugate of the of the complex number $c (x - i*y)

       gsl_complex_inverse($c)
        Return the inverse, or reciprocal of the complex number $c (1/$c)

       gsl_complex_negative($c)
        Return the negative of the complex number $c (-x -i*y)

       gsl_complex_sqrt($c)
        Return the square root of the complex number $c

       gsl_complex_sqrt_real($x)
        Return the complex square root of the real number $x, where $x may be negative

       "gsl_complex_pow($c1, $c2)"
        Return the complex number $c1 raised to the complex power $c2

       "gsl_complex_pow_real($c, $x)"
        Return the complex number raised to the real power $x

       gsl_complex_exp($c)
        Return the complex exponential of the complex number $c

       gsl_complex_log($c)
        Return the complex natural logarithm (base e) of the complex number $c

       gsl_complex_log10($c)
        Return the complex base-10 logarithm of the complex number $c

       "gsl_complex_log_b($c, $b)"
        Return the complex base-$b of the complex number $c

       gsl_complex_sin($c)
        Return the complex sine of the complex number $c

       gsl_complex_cos($c)
        Return the complex cosine of the complex number $c

       gsl_complex_sec($c)
        Return the complex secant of the complex number $c

       gsl_complex_csc($c)
        Return the complex cosecant of the complex number $c

       gsl_complex_tan($c)
        Return the complex tangent of the complex number $c

       gsl_complex_cot($c)
        Return the complex cotangent of the complex number $c

       gsl_complex_arcsin($c)
        Return the complex arcsine of the complex number $c

       gsl_complex_arcsin_real($x)
        Return the complex arcsine of the real number $x

       gsl_complex_arccos($c)
        Return the complex arccosine of the complex number $c

       gsl_complex_arccos_real($x)
        Return the complex arccosine of the real number $x

       gsl_complex_arcsec($c)
        Return the complex arcsecant of the complex number $c

       gsl_complex_arcsec_real($x)
        Return the complex arcsecant of the real number $x

       gsl_complex_arccsc($c)
        Return the complex arccosecant of the complex number $c

       gsl_complex_arccsc_real($x)
        Return the complex arccosecant of the real number $x

       gsl_complex_arctan($c)
        Return the complex arctangent of the complex number $c

       gsl_complex_arccot($c)
        Return the complex arccotangent of the complex number $c

       gsl_complex_sinh($c)
        Return the complex hyperbolic sine of the complex number $c

       gsl_complex_cosh($c)
        Return the complex hyperbolic cosine of the complex number $cy

       gsl_complex_sech($c)
        Return the complex hyperbolic secant of the complex number $c

       gsl_complex_csch($c)
        Return the complex hyperbolic cosecant of the complex number $c

       gsl_complex_tanh($c)
        Return the complex hyperbolic tangent of the complex number $c

       gsl_complex_coth($c)
        Return the complex hyperbolic cotangent of the complex number $c

       gsl_complex_arcsinh($c)
        Return the complex hyperbolic arcsine of the complex number $c

       gsl_complex_arccosh($c)
        Return the complex hyperbolic arccosine of the complex number $c

       gsl_complex_arccosh_real($x)
        Return the complex hyperbolic arccosine of the real number $x

       gsl_complex_arcsech($c)
        Return the complex hyperbolic arcsecant of the complex number $c

       gsl_complex_arccsch($c)
        Return the complex hyperbolic arccosecant of the complex number $c

       gsl_complex_arctanh($c)
        Return the complex hyperbolic arctangent of the complex number $c

       gsl_complex_arctanh_real($x)
        Return the complex hyperbolic arctangent of the real number $x

       gsl_complex_arccoth($c)
        Return the complex hyperbolic arccotangent of the complex number $c

       gsl_real($z)
        Return the real part of $z

       gsl_imag($z)
        Return the imaginary part of $z

       gsl_parts($z)
        Return a list of the real and imaginary parts of $z

       "gsl_set_real($z, $x)"
        Sets the real part of $z to $x

       "gsl_set_imag($z, $y)"
        Sets the imaginary part of $z to $y

       "gsl_set_complex($z, $x, $h)"
        Sets the real part of $z to $x and the imaginary part to $y

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

           my $z = gsl_complex_rect(6,4);
           my $y = gsl_complex_conjugate($z);
           my ($real, $imag) = gsl_parts($y);
           print "z = $real + $imag*i\n";

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

           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(\$z) = $real\n";

       Math::GSL::Complex - Complex Numbers

           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