fastmath.complex — generateme/fastmath 3.0.0-alpha4

Complex numbers operations.

Complex numbers are represented using the [[Vec2]] type defined in the fastmath.vector namespace. A complex number $z = a + bi$ corresponds to the vector (Vec2. a b).

To create a complex number, use complex, [[vec2]], or convert from sequences/arrays using functions like fastmath.vector/seq->vec2.

The implementation correctly handles floating-point special values such as ##Inf, ##NaN, and distinguishes between +0.0 and -0.0 where necessary.

This namespace provides standard complex number operations like arithmetic (+, -, *, /), exponentiation (pow, exp, log), trigonometric functions (sin, cos, tan, etc.), and their inverses, as well as utility functions like abs, arg, conjugate, etc.

-I clj

z=0-i

abs clj

(abs z)

Calculates the magnitude (absolute value) of the complex number z.

acos clj

(acos z)

acos(z)

acosh clj

(acosh z)

acosh(z)

acot clj

(acot z)

acot(z)

acoth clj

(acoth z)

acoth(z)

acsc clj

(acsc z)

acsc(z)

acsch clj

(acsch z)

acsch(z)

add clj

(add z1 z2)

Sum of two complex numbers.

adds clj

(adds z v)

Add scalar to complex number.

arg clj

(arg z)

Argument (angle) of the complex number.

asec clj

(asec z)

asec(z)

asech clj

(asech z)

asech(z)

asin clj

(asin z)

asin(z)

asinh clj

(asinh z)

asinh(z)

atan clj

(atan z)

atan(z)

atanh clj

(atanh z)

atanh(z)

complex clj

(complex)

(complex a)

(complex a b)

Creates a complex number represented as a [[Vec2]]. Takes optional real and imaginary parts.

Examples:

(complex 1 2) ;; => #vec2 [1.0, 2.0] (complex 3) ;; => #vec2 [3.0, 0.0] (complex) ;; => #vec2 [0.0, 0.0]

conjugate clj

(conjugate z)

Complex conjugate.

cos clj

(cos z)

cos(z)

cosh clj

(cosh z)

cosh(z)

cot clj

(cot z)

csc(z)

coth clj

(coth z)

coth(z)

csc clj

(csc z)

csc(z)

csch clj

(csch z)

csch(z)

csgn clj

(csgn z)

(csgn re im)

Complex signum function.

Returns 0.0 for the zero. For any other vector, returns the sign of the real part.

delta-eq clj

(delta-eq q1 q2)

(delta-eq q1 q2 accuracy)

Compare complex numbers with given accuracy (10e-6 by default)

div clj

(div z1 z2)

Division of two complex numbers.

ensure-complex clj

(ensure-complex v)

Convert possible number to complex or return input.

exp clj

(exp z)

exp(z)

flip clj

(flip z)

Exchange imaginary and real parts

I clj

z=0+i

I- clj

z=0-i

im clj

(im z)

Imaginary part

imaginary? clj

(imaginary? z)

Is z is a pure imaginary number?

inf? clj

(inf? z)

Is infinite?

invalid? clj

(invalid? z)

Is NaN or Inf?

log clj

(log z)

log(z), principal value

logb clj

(logb z b)

log with base b

muladd clj

(muladd x y z)

(+ z (* x y))

mult clj

(mult z1 z2)

Multiplication of two complex numbers.

mult-I clj

(mult-I z)

Multiplication by 0+i.

mult-I- clj

(mult-I- z)

Multiplication by 0-i.

nan? clj

(nan? z)

Is NaN?

neg clj

(neg z)

Negation of the complex number, -z.

norm clj

(norm z)

Calculates the squared magnitude (norm) of the complex number z.

Also known as the squared modulus or squared Euclidean norm.

normalize clj

(normalize z)

Normalize complex number to make abs(z) = 1

ONE clj

z=1+0i

PI clj

z=pi+0i

pow clj

(pow z1 z2)

Complex power, z^z

re clj

(re z)

Real part

real? clj

(real? z)

Is z is a real number?

reciprocal clj

(reciprocal z)

Reciprocal, 1/z.

scale clj

(scale z v)

Multiplication by real number

sec clj

(sec z)

sec(z)

sech clj

(sech z)

sech(z)

sin clj

(sin z)

sin(z)

sinh clj

(sinh z)

sinh(z)

sq clj

(sq z)

Square of the complex number.

sqrt clj

(sqrt z)

Sqrt of the complex number, sqrt(z)

sqrt1z clj

(sqrt1z z)

sqrt(1-z^2)

sub clj

(sub z1 z2)

Difference of two complex numbers.

tan clj

(tan z)

tan(z)

tanh clj

(tanh z)

tanh(z)

TWO clj

z=2+0i

valid? clj

(valid? z)

Is valid complex (not NaN or Inf)?

ZERO clj

z=0+0i

zero? clj

(zero? z)

Is zero?