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dq.rand_complex

rand_complex(
    key: PRNGKeyArray, shape: int | tuple[int, ...], *, rmax: float = 1.0
) -> Array

Returns an array of uniformly distributed random complex numbers.

Each element of the returned array is sampled uniformly in the disk of radius \(\text{rmax}\).

Uniform sampling in the complex plane

Here are three common options to generate random complex numbers, dq.rand_complex() returns the last one:

_, (ax0, ax1, ax2) = dq.gridplot(3, sharexy=True)
ax0.set(xlim=(-1.1, 1.1), ylim=(-1.1, 1.1))

n = 10_000

# option 1: uniformly distributed real and imaginary part
x = np.random.rand(n) * 2 - 1 + 1j * (np.random.rand(n) * 2 - 1)
ax0.scatter(x.real, x.imag, s=1.0)

# option 2: uniformly distributed magnitude and phase
x = np.random.rand(n) * np.exp(1j * 2 * np.pi * np.random.rand(n))
ax1.scatter(x.real, x.imag, s=1.0)

# option 3: uniformly distributed in a disk (in dynamiqs)
key = jax.random.PRNGKey(42)
x = dq.rand_complex(key, n)
ax2.scatter(x.real, x.imag, s=1.0)

rand_complex

Parameters

  • key

    A PRNG key used as the random key.

  • shape (int or tuple of ints)

    Shape of the returned array.

  • rmax

    Maximum magnitude.

Returns

(array of shape (*shape)) Random complex number array.

Examples

>>> key = jax.random.PRNGKey(42)
>>> dq.rand_complex(key, (2, 3), rmax=5.0)
Array([[ 1.341+4.17j ,  3.978-0.979j, -2.592-0.946j],
       [-4.428+1.744j, -0.53 +1.668j,  2.582+0.65j ]], dtype=complex64)