9.3. cmath

__complex__() __float__() Python

(branch cut)

9.3.1.

Python z z.real z.imag :

z == z.real + z.imag*1j

z r phi r z phi x z

cmath.phase(x)

x (x ) phase(x) math.atan2(x.imag, x.real) [-, ] () x.imag x.imag :

>>> phase(complex(-1.0, 0.0))
3.141592653589793
>>> phase(complex(-1.0, -0.0))
-3.141592653589793

x () abs() cmath

cmath.polar(x)

x x r x phi (r, phi) polar(x) (abs(x), phase(x))

cmath.rect(r, phi)

r, phi x r * (math.cos(phi) + math.sin(phi)*1j)

9.3.2.

cmath.exp(x)

e**x

cmath.log(x[, base])

base x base x 0 -

cmath.log10(x)

x 10 log()

cmath.sqrt(x)

x log()

9.3.3.

cmath.acos(x)

x (branch cut) : 1 -1 -

cmath.asin(x)

x acos()

cmath.atan(x)

x : 1j j -1j -j

cmath.cos(x)

x

cmath.sin(x)

x

cmath.tan(x)

x

9.3.4.

cmath.acosh(x)

x 1 -

cmath.asinh(x)

x : 1j j -1j -j

cmath.atanh(x)

x : 1 -1 -

cmath.cosh(x)

x

cmath.sinh(x)

x

cmath.tanh(x)

x

9.3.5.

cmath.isfinite(x)

x True False

3.2 .

cmath.isinf(x)

x True False

cmath.isnan(x)

x NaN True False

cmath.isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)

a b True False

2

rel_tol a b a b 5% rel_tol=0.05 1e-09 29 rel_tol 0

abs_tol 0abs_tol 0

abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)

IEEE 754 NaNinf-inf IEEE NaN inf -inf

3.5 .

PEP 485 A function for testing approximate equality

9.3.6.

cmath.pi

()

cmath.e

e ()

cmath.tau

3.6 .

cmath.inf

float('inf')

3.6 .

cmath.infj

complex(0.0, float('inf'))

3.6 .

cmath.nan

"not a number" (NaN) float('nan')

3.6 .

cmath.nanj

NaN complex(0.0, float('nan'))

3.6 .

math math.sqrt(-1) cmath ()

(branch cut) : () :

Kahan, W: Branch cuts for complex elementary functions; or, Much ado about nothingss sign bit. In Iserles, A., and Powell, M. (eds.), The state of the art in numerical analysis. Clarendon Press (1987) pp165211.