complex

nimony/lib/std/complex.nim

This module implements complex numbers and basic mathematical operations on them.

A complex number is a number of the form a + b*i, where a is the real part and b is the imaginary part (and i is the imaginary unit with the property i*i == -1).

Complex[T] is generic over the floating-point component type T. Following the modelling of std/math, each operation depends precisely on the concepts it needs: the arithmetic operators come from Arithmetic, and the transcendental functions add HasSqrt, HasExp, HasLn, HasSin, HasCos and HasArctan2. So Complex[float32] and Complex[float64] both work, and a user float type satisfying the relevant concepts works too.

```
type Complex = object
  re: T
  im: T
```
type Complex64 = Complex
A complex number with 64-bit float components.
type Complex32 = Complex
A complex number with 32-bit float components.
func complex(re: T; im: T): Complex[T]
Returns a complex number with real part re and imaginary part im.
func complex(re: T): Complex[T]
Returns a complex number with real part re and zero imaginary part.
func abs2(z: Complex[T]): T
Returns the squared absolute value of z, i.e. z.re^2 + z.im^2. Cheaper than abs because it avoids the square root.
func abs(z: Complex[T]): T
Returns the absolute value (modulus) of z.
func arg(z: Complex[T]): T
Returns the argument (phase angle, in radians) of z.
func conjugate(z: Complex[T]): Complex[T]
Returns the complex conjugate of z (z.im negated).
func ==(a: Complex[T]; b: Complex[T]): bool
Compares two complex numbers for equality.
func +(a: Complex[T]; b: Complex[T]): Complex[T]
func +(a: Complex[T]; b: T): Complex[T]
func +(a: T; b: Complex[T]): Complex[T]
func -(z: Complex[T]): Complex[T]
Unary minus.
func -(a: Complex[T]; b: Complex[T]): Complex[T]
func -(a: Complex[T]; b: T): Complex[T]
func -(a: T; b: Complex[T]): Complex[T]
func *(a: Complex[T]; b: Complex[T]): Complex[T]
func *(a: Complex[T]; b: T): Complex[T]
func *(a: T; b: Complex[T]): Complex[T]
func /(a: Complex[T]; b: Complex[T]): Complex[T]
func /(a: Complex[T]; b: T): Complex[T]
func inv(z: Complex[T]): Complex[T]
Returns the multiplicative inverse 1 / z.
func sqrt(z: Complex[T]): Complex[T]
Returns the principal square root of z.
func exp(z: Complex[T]): Complex[T]
Returns the exponential e^z.
func ln(z: Complex[T]): Complex[T]
Returns the principal natural logarithm of z.
func pow(z: Complex[T]; w: Complex[T]): Complex[T]
Returns z raised to the power w (principal value).
proc $(z: Complex[T]): string
Returns a textual representation of z as "(re, im)".