np.emath (complex-valued math)

np.emath.{sqrt, log, log2, log10, logn, power, arccos, arcsin, arctanh}

The numpy.emath (numpy.lib.scimath) namespace: math functions that return complex results where the real function is undefined, instead of NaN.

Returns

namespace object

Example

Object.keys(np.emath).length; // => 9

np.emath.sqrt(x) · np.emath.log(x) · np.emath.log2(x) · np.emath.log10(x)

Square root and logarithms. When any real element is negative the whole input is converted to complex first (complex64 for int8/uint8/int16/uint16/float32, otherwise complex128); otherwise the result is real with the ufunc's float dtype. Complex input stays complex.

Parameters

xArrayLike

An NDArray, nested JS array or scalar.

Returns

NDArray (real or complex)

Example

np.emath.sqrt([4, 9]);                  // => [2, 3]
np.real(np.emath.sqrt([-4, 4]));        // => [0, 2]
np.imag(np.emath.sqrt([-4, 4]));        // => [2, 0]
np.emath.sqrt([-4]).dtype.name;         // => "complex128"
np.emath.log10([100]);                  // => [2]
np.imag(np.emath.log(-1)).item();       // => 3.141592653589793

np.emath.sqrt(x: ArrayLike): NDArray
np.emath.log(x: ArrayLike): NDArray
np.emath.log2(x: ArrayLike): NDArray
np.emath.log10(x: ArrayLike): NDArray

np.emath.arcsin(x) · np.emath.arccos(x) · np.emath.arctanh(x)

Inverse sine, cosine and hyperbolic tangent; real input with any |x| > 1 is converted to complex first (same dtype rule as emath.sqrt).

Parameters

xArrayLike

An NDArray, nested JS array or scalar.

Returns

NDArray (real or complex)

Example

np.emath.arcsin([0]);                   // => [0]
np.emath.arccos([2]).dtype.name;        // => "complex128"
np.real(np.emath.arccos([2]));          // => [0]
np.imag(np.emath.arcsin([2])).item();   // => 1.3169578969248166

np.emath.arcsin(x: ArrayLike): NDArray
np.emath.arccos(x: ArrayLike): NDArray
np.emath.arctanh(x: ArrayLike): NDArray

np.emath.logn(n, x) · np.emath.power(x, p)

logn is the base-n logarithm log(x) / log(n). power is x ** p, complex when a real x is negative; a negative integer p is converted to float64 first, so power([2], -1) is 0.5.

Parameters

n / xArrayLike

An NDArray, nested JS array or scalar.

x / pArrayLike

An NDArray, nested JS array or scalar.

Returns

NDArray

Example

np.emath.logn(2, [4, 8]);               // => [2, 3]
np.emath.power([2, 4], -1);             // => [0.5, 0.25]
np.imag(np.emath.power([-4], 0.5));     // => [2]

np.emath.logn(n: ArrayLike, x: ArrayLike): NDArray
np.emath.power(x: ArrayLike, p: ArrayLike): NDArray