--- name: "Math::GSL::Complex" section: "3pm" platform: "linux" package: "libmath-gsl-perl" version: "0.45-2+b1" release: "Debian 13 (Trixie)" platforms: ["linux"] url: "https://new.carta.tech/Math::GSL::Complex" --- # Math::GSL::Complex(3pm) Complex Numbers ### copy() Returns a copy of the Complex number, which resides at a different location in memory. ``` my $z = Math::GSL::Complex->new([10,5]); my $copy = $z->copy; ``` ## NAME Math::GSL::Complex - Complex Numbers ## 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 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) = $complex->parts; # get both at once ``` ## DESCRIPTION Here is a list of all the functions included in this module : - gsl\_complex\_arg($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` ## EXAMPLES 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"; ``` ## AUTHORS Jonathan "Duke" Leto \ and Thierry Moisan \ ## COPYRIGHT AND LICENSE 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.