Add numba support to perlin2d noise generator

[andrekv17]

Numba support decrease the computation time up to nearly 5 times. No much changes are required

import numpy as np
from numba import njit

@njit
def interpolant(t: np.ndarray):
    return t*t*t*(t*(t*6 - 15) + 10)

@njit
def generate_perlin_noise_2d(
        shape, res, tileable=(False, False), interpolant=interpolant
):
    """Generate a 2D numpy array of perlin noise.
    Args:
        shape: The shape of the generated array (tuple of two ints).
            This must be a multple of res.
        res: The number of periods of noise to generate along each
            axis (tuple of two ints). Note shape must be a multiple of
            res.
        tileable: If the noise should be tileable along each axis
            (tuple of two bools). Defaults to (False, False).
        interpolant: The interpolation function, defaults to
            t*t*t*(t*(t*6 - 15) + 10).
    Returns:
        A numpy array of shape shape with the generated noise.
    Raises:
        ValueError: If shape is not a multiple of res.
    """
    delta = (res[0] / shape[0], res[1] / shape[1])
    d = (shape[0] // res[0], shape[1] // res[1])
    xvals = np.arange(0,res[0], delta[0])
    yvals = np.arange(0,res[1], delta[1])
    grid = np.empty((2, len(xvals), len(yvals)))
    for j, y in enumerate(yvals):
        for i, x in enumerate(xvals):
            grid[0][i, j] = x
    yy = np.empty((len(xvals), len(yvals)))
    for i, x in enumerate(xvals):
        grid[1][i, :] = yvals
    grid = grid.transpose(1, 2, 0) % 1
    # Gradients
    angles = 2*np.pi*np.random.rand(res[0]+1, res[1]+1)
    gradients = np.dstack((np.cos(angles), np.sin(angles)))
    if tileable[0]:
        gradients[-1,:] = gradients[0,:]
    if tileable[1]:
        gradients[:,-1] = gradients[:,0]
    grad_matrix = np.empty((d[0] * gradients.shape[0], d[1] * gradients.shape[1], 2))
    for i in range(gradients.shape[0]):
        for j in range(gradients.shape[1]):
            grad_matrix[i * d[0] : (i+1) * d[0], j * d[1] : (j+1) * d[1]] = gradients[i, j]
    gradients = grad_matrix
        
    g00 = gradients[    :-d[0],    :-d[1]]
    g10 = gradients[d[0]:     ,    :-d[1]]
    g01 = gradients[    :-d[0],d[1]:     ]
    g11 = gradients[d[0]:     ,d[1]:     ]
    # Ramps
    n00 = np.sum(np.dstack((grid[:,:,0]  , grid[:,:,1]  )) * g00, 2)
    n10 = np.sum(np.dstack((grid[:,:,0]-1, grid[:,:,1]  )) * g10, 2)
    n01 = np.sum(np.dstack((grid[:,:,0]  , grid[:,:,1]-1)) * g01, 2)
    n11 = np.sum(np.dstack((grid[:,:,0]-1, grid[:,:,1]-1)) * g11, 2)
    # Interpolation
    t = interpolant(grid)
    n0 = n00*(1-t[:,:,0]) + t[:,:,0]*n10
    n1 = n01*(1-t[:,:,0]) + t[:,:,0]*n11
    t1 = (1-t[:,:,1])*n0
    t2 = t[:,:,1]*n1
    sum_t = t1 + t2
    mult_s2 = np.sqrt(2)*sum_t
    return mult_s2

@njit
def generate_fractal_noise_2d(
        shape, res, octaves=1, persistence=0.5,
        lacunarity=2, tileable=(False, False),
        interpolant=interpolant
):
    """Generate a 2D numpy array of fractal noise.
    Args:
        shape: The shape of the generated array (tuple of two ints).
            This must be a multiple of lacunarity**(octaves-1)*res.
        res: The number of periods of noise to generate along each
            axis (tuple of two ints). Note shape must be a multiple of
            (lacunarity**(octaves-1)*res).
        octaves: The number of octaves in the noise. Defaults to 1.
        persistence: The scaling factor between two octaves.
        lacunarity: The frequency factor between two octaves.
        tileable: If the noise should be tileable along each axis
            (tuple of two bools). Defaults to (False, False).
        interpolant: The, interpolation function, defaults to
            t*t*t*(t*(t*6 - 15) + 10).
    Returns:
        A numpy array of fractal noise and of shape shape generated by
        combining several octaves of perlin noise.
    Raises:
        ValueError: If shape is not a multiple of
            (lacunarity**(octaves-1)*res).
    """
    noise = np.zeros(shape)
    frequency = 1
    amplitude = 1
    for _ in range(octaves):
        noise += amplitude * generate_perlin_noise_2d(
            shape, (frequency*res[0], frequency*res[1]), tileable, interpolant
        )
        frequency *= lacunarity
        amplitude *= persistence
    return noise

Works for numba==0.53.1 and numpy==1.21.1

[davidsvy]

Here is the numba implementation for the 3d case:
link

[pvigier]

Thank you for sharing! What speedup do you get with numba?

[davidsvy]

The numba code runs roughly 3 times faster on google colab compared to numpy.
Everything is already vectorized, so:

1. Numba cannot do much.
2. A cuda implementation is suitable. One could consider pytorch, numba-cuda, taichi etc for more significant speedup.

[pvigier]

OK, that's already nice! I will add a link to this issue in the README.