Struct rgsl::types::complex::ComplexF32

#[repr(C)]
pub struct ComplexF32 {
    pub dat: [f32; 2],
}

Fields

dat: [f32; 2]

Implementations

impl ComplexF32

pub fn rect(x: f32, y: f32) -> ComplexF32

This function uses the rectangular Cartesian components (x,y) to return the complex number z = x + i y.

pub fn polar(r: f32, theta: f32) -> ComplexF32

This function returns the complex number z = r \exp(i \theta) = r (\cos(\theta) + i \sin(\theta)) from the polar representation (r,theta).

pub fn arg(&self) -> f32

This function returns the argument of the complex number z, \arg(z), where -\pi < \arg(z) <= \pi.

pub fn abs(&self) -> f32

This function returns the magnitude of the complex number z, |z|.

pub fn abs2(&self) -> f32

This function returns the squared magnitude of the complex number z, |z|^2.

pub fn logabs(&self) -> f32

This function returns the natural logarithm of the magnitude of the complex number z, \log|z|.

It allows an accurate evaluation of \log|z| when |z| is close to one. The direct evaluation of log(gsl_complex_abs(z)) would lead to a loss of precision in this case.

pub fn add(&self, other: &ComplexF32) -> ComplexF32

This function returns the sum of the complex numbers a and b, z=a+b.

pub fn sub(&self, other: &ComplexF32) -> ComplexF32

This function returns the difference of the complex numbers a and b, z=a-b.

pub fn mul(&self, other: &ComplexF32) -> ComplexF32

This function returns the product of the complex numbers a and b, z=ab.

pub fn div(&self, other: &ComplexF32) -> ComplexF32

This function returns the quotient of the complex numbers a and b, z=a/b.

pub fn add_real(&self, x: f32) -> ComplexF32

This function returns the sum of the complex number a and the real number x, z=a+x.

pub fn sub_real(&self, x: f32) -> ComplexF32

This function returns the difference of the complex number a and the real number x, z=a-x.

pub fn mul_real(&self, x: f32) -> ComplexF32

This function returns the product of the complex number a and the real number x, z=ax.

pub fn div_real(&self, x: f32) -> ComplexF32

This function returns the quotient of the complex number a and the real number x, z=a/x.

pub fn add_imag(&self, x: f32) -> ComplexF32

This function returns the sum of the complex number a and the imaginary number iy, z=a+iy.

pub fn sub_imag(&self, x: f32) -> ComplexF32

This function returns the difference of the complex number a and the imaginary number iy, z=a-iy.

pub fn mul_imag(&self, x: f32) -> ComplexF32

This function returns the product of the complex number a and the imaginary number iy, z=a*(iy).

pub fn div_imag(&self, x: f32) -> ComplexF32

This function returns the quotient of the complex number a and the imaginary number iy, z=a/(iy).

pub fn conjugate(&self) -> ComplexF32

This function returns the complex conjugate of the complex number z, z^* = x - i y.

pub fn inverse(&self) -> ComplexF32

This function returns the inverse, or reciprocal, of the complex number z, 1/z = (x - i y)/ (x^2 + y^2).

pub fn negative(&self) -> ComplexF32

This function returns the negative of the complex number z, -z = (-x) + i(-y).

pub fn sqrt(&self) -> ComplexF32

This function returns the square root of the complex number z, \sqrt z.

The branch cut is the negative real axis. The result always lies in the right half of the complex plane.

pub fn sqrt_real(x: f32) -> ComplexF32

This function returns the complex square root of the real number x, where x may be negative.

pub fn pow(&self, other: &ComplexF32) -> ComplexF32

The function returns the complex number z raised to the complex power a, z^a.

This is computed as \exp(\log(z)*a) using complex logarithms and complex exponentials.

pub fn pow_real(&self, x: f32) -> ComplexF32

This function returns the complex number z raised to the real power x, z^x.

pub fn exp(&self) -> ComplexF32

This function returns the complex exponential of the complex number z, \exp(z).

pub fn log(&self) -> ComplexF32

This function returns the complex natural logarithm (base e) of the complex number z, \log(z). The branch cut is the negative real axis.

pub fn log10(&self) -> ComplexF32

This function returns the complex base-10 logarithm of the complex number z, \log_10 (z).

pub fn log_b(&self, other: &ComplexF32) -> ComplexF32

This function returns the complex base-b logarithm of the complex number z, \log_b(z). This quantity is computed as the ratio \log(z)/\log(b).

pub fn sin(&self) -> ComplexF32

This function returns the complex sine of the complex number z, \sin(z) = (\exp(iz) - \exp(-iz))/(2i).

pub fn cos(&self) -> ComplexF32

This function returns the complex cosine of the complex number z, \cos(z) = (\exp(iz) + \exp(-iz))/2.

pub fn tan(&self) -> ComplexF32

This function returns the complex tangent of the complex number z, \tan(z) = \sin(z)/\cos(z).

pub fn sec(&self) -> ComplexF32

This function returns the complex secant of the complex number z, \sec(z) = 1/\cos(z).

pub fn csc(&self) -> ComplexF32

This function returns the complex cosecant of the complex number z, \csc(z) = 1/\sin(z).

pub fn cot(&self) -> ComplexF32

This function returns the complex cotangent of the complex number z, \cot(z) = 1/\tan(z).

pub fn arcsin(&self) -> ComplexF32

This function returns the complex arcsine of the complex number z, \arcsin(z). The branch cuts are on the real axis, less than -1 and greater than 1.

pub fn arcsin_real(z: f32) -> ComplexF32

This function returns the complex arcsine of the real number z, \arcsin(z).

• For z between -1 and 1, the function returns a real value in the range [-\pi/2,\pi/2].
• For z less than -1 the result has a real part of -\pi/2 and a positive imaginary part.
• For z greater than 1 the result has a real part of \pi/2 and a negative imaginary part.

pub fn arccos(&self) -> ComplexF32

This function returns the complex arccosine of the complex number z, \arccos(z). The branch cuts are on the real axis, less than -1 and greater than 1.

pub fn arccos_real(z: f32) -> ComplexF32

This function returns the complex arccosine of the real number z, \arccos(z).

• For z between -1 and 1, the function returns a real value in the range [0,\pi].
• For z less than -1 the result has a real part of \pi and a negative imaginary part.
• For z greater than 1 the result is purely imaginary and positive.

pub fn arctan(&self) -> ComplexF32

This function returns the complex arctangent of the complex number z, \arctan(z). The branch cuts are on the imaginary axis, below -i and above i.

pub fn arcsec(&self) -> ComplexF32

This function returns the complex arcsecant of the complex number z, \arcsec(z) = \arccos(1/z).

pub fn arcsec_real(z: f32) -> ComplexF32

This function returns the complex arcsecant of the real number z, \arcsec(z) = \arccos(1/z).

pub fn arccsc(&self) -> ComplexF32

This function returns the complex arccosecant of the complex number z, \arccsc(z) = \arcsin(1/z).

pub fn arccsc_real(z: f32) -> ComplexF32

This function returns the complex arccosecant of the real number z, \arccsc(z) = \arcsin(1/z).

pub fn arccot(&self) -> ComplexF32

This function returns the complex arccotangent of the complex number z, \arccot(z) = \arctan(1/z).

pub fn sinh(&self) -> ComplexF32

This function returns the complex hyperbolic sine of the complex number z, \sinh(z) = (\exp(z) - \exp(-z))/2.

pub fn cosh(&self) -> ComplexF32

This function returns the complex hyperbolic cosine of the complex number z, \cosh(z) = (\exp(z) + \exp(-z))/2.

pub fn tanh(&self) -> ComplexF32

This function returns the complex hyperbolic tangent of the complex number z, \tanh(z) = \sinh(z)/\cosh(z).

pub fn sech(&self) -> ComplexF32

This function returns the complex hyperbolic secant of the complex number z, \sech(z) = 1/\cosh(z).

pub fn csch(&self) -> ComplexF32

This function returns the complex hyperbolic cosecant of the complex number z, \csch(z) = 1/\sinh(z).

pub fn coth(&self) -> ComplexF32

This function returns the complex hyperbolic cotangent of the complex number z, \coth(z) = 1/\tanh(z).

pub fn arcsinh(&self) -> ComplexF32

This function returns the complex hyperbolic arcsine of the complex number z, \arcsinh(z). The branch cuts are on the imaginary axis, below -i and above i.

pub fn arccosh(&self) -> ComplexF32

This function returns the complex hyperbolic arccosine of the complex number z, \arccosh(z).

The branch cut is on the real axis, less than 1.

Note that in this case we use the negative square root in formula 4.6.21 of Abramowitz & Stegun giving \arccosh(z)=\log(z-\sqrt{z^2-1}).

pub fn arccosh_real(z: f32) -> ComplexF32

This function returns the complex hyperbolic arccosine of the real number z, \arccosh(z).

pub fn arctanh(&self) -> ComplexF32

This function returns the complex hyperbolic arctangent of the complex number z, arctanh(z).

The branch cuts are on the real axis, less than -1 and greater than 1.

pub fn arctanh_real(z: f32) -> ComplexF32

This function returns the complex hyperbolic arctangent of the real number z, \arctanh(z).

pub fn arcsech(&self) -> ComplexF32

This function returns the complex hyperbolic arcsecant of the complex number z, \arcsech(z) = \arccosh(1/z).

pub fn arccsch(&self) -> ComplexF32

This function returns the complex hyperbolic arccosecant of the complex number z, \arccsch(z) = \arcsin(1/z).

pub fn arccoth(&self) -> ComplexF32

This function returns the complex hyperbolic arccotangent of the complex number z, \arccoth(z) = \arctanh(1/z).

Trait Implementations

impl Clone for ComplexF32

fn clone(&self) -> ComplexF32

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for ComplexF32

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for ComplexF32

fn default() -> ComplexF32

Returns the “default value” for a type.

impl PartialEq<ComplexF32> for ComplexF32

fn eq(&self, other: &ComplexF32) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Copy for ComplexF32

impl StructuralPartialEq for ComplexF32