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theano-simplex-matrix.py
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theano-simplex-matrix.py
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#!/usr/bin/python3
# -*- coding: utf-8 -*-
from __future__ import division, print_function, unicode_literals
import numpy as np
import theano.tensor as T
import theano
from time import time
from image_helpers import show
np_perm = [151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8, 99,
37, 240, 21, 10, 23, 190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11, 32,
57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71, 134, 139, 48, 27,
166, 77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244, 102,
143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169, 200, 196, 135, 130, 116,
188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, 226, 250, 124, 123, 5, 202, 38, 147, 118, 126,
255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42, 223, 183, 170, 213, 119, 248, 152,
2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172, 9, 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224,
232, 178, 185, 112, 104, 218, 246, 97, 228, 251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81,
51, 145, 235, 249, 14, 239, 107, 49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50,
45, 127, 4, 150, 254, 138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61,
156, 180]
np_perm = np.array(np_perm + np_perm, dtype=np.uint8)
np_grad3 = np.array([[1, 1, 0], [-1, 1, 0], [1, -1, 0], [-1, -1, 0],
[1, 0, 1], [-1, 0, 1], [1, 0, -1], [-1, 0, -1],
[0, 1, 1], [0, -1, 1], [0, 1, -1], [0, -1, -1]], dtype=np.float32)
vertices_options = np.array([
[1, 0, 0, 1, 1, 0],
[1, 0, 0, 1, 0, 1],
[0, 0, 1, 1, 0, 1],
[0, 0, 1, 0, 1, 1],
[0, 1, 0, 0, 1, 1],
[0, 1, 0, 1, 1, 0]
], dtype=np.uint8)
# Dimensions are: x0 >= y0, y0 >= z0, x0 >= z0
np_vertex_table = np.array([
[[vertices_options[3], vertices_options[3]],
[vertices_options[4], vertices_options[5]]],
[[vertices_options[2], vertices_options[1]],
[vertices_options[2], vertices_options[0]]]
], dtype=np.uint8)
def get_input_vectors(shape, phases, scaling, offset):
x = T.repeat(offset[0] + T.arange(shape[0]) / scaling, shape[1] * phases).reshape(
(shape[0], shape[1], phases)) * T.pow(2, T.arange(phases))
y = T.repeat(T.tile(offset[1] + T.arange(shape[1]) / scaling, shape[0]).reshape(
(shape[0], shape[1], 1)), phases, axis=2) * T.pow(2, T.arange(phases))
z = T.tile(offset[2] + 10 * T.arange(phases), shape[0] * shape[1]).reshape((shape[0], shape[1], phases, 1))
x = x.reshape((shape[0], shape[1], phases, 1))
y = y.reshape((shape[0], shape[1], phases, 1))
return T.concatenate([x, y, z], axis=3).reshape((shape[0] * shape[1] * phases, 3)).astype('float32')
def calculate_gradient_contribution(offsets, gis, gradient_map):
t = 0.5 - offsets[:, 0] ** 2 - offsets[:, 1] ** 2 - offsets[:, 2] ** 2
return T.gt(t, 0) * t ** 4 * T.batched_dot(gradient_map[gis], offsets)
def matrix_noise3d(input_vectors, perm, grad3, vertex_table):
skew_factors = (input_vectors[:, 0] + input_vectors[:, 1] + input_vectors[:, 2]) * 1.0 / 3.0
skewed_vectors = T.floor(input_vectors + skew_factors[:, np.newaxis])
unskew_factors = (skewed_vectors[:, 0] + skewed_vectors[:, 1] + skewed_vectors[:, 2]) * 1.0 / 6.0
offsets_0 = input_vectors - (skewed_vectors - unskew_factors[:, np.newaxis])
vertex_table_x_index = T.ge(offsets_0[:, 0], offsets_0[:, 1])
vertex_table_y_index = T.ge(offsets_0[:, 1], offsets_0[:, 2])
vertex_table_z_index = T.ge(offsets_0[:, 0], offsets_0[:, 2])
simplex_vertices = vertex_table[
vertex_table_x_index,
vertex_table_y_index,
vertex_table_z_index].reshape((input_vectors.shape[0], 2, 3))
offsets_1 = offsets_0 - simplex_vertices[:, 0] + 1.0 / 6.0
offsets_2 = offsets_0 - simplex_vertices[:, 1] + 1.0 / 3.0
offsets_3 = offsets_0 - 0.5
masked_skewed_vectors = T.bitwise_and(skewed_vectors.astype('int32'), 255)
gi0s = perm[masked_skewed_vectors[:, 0] + perm[
masked_skewed_vectors[:, 1] + perm[
masked_skewed_vectors[:, 2]].astype('int32')].astype('int32')] % 12
gi1s = perm[masked_skewed_vectors[:, 0] + simplex_vertices[:, 0, 0] + perm[
masked_skewed_vectors[:, 1] + simplex_vertices[:, 0, 1] + perm[
masked_skewed_vectors[:, 2] + simplex_vertices[:, 0, 2]].astype('int32')].astype('int32')] % 12
gi2s = perm[masked_skewed_vectors[:, 0] + simplex_vertices[:, 1, 0] + perm[
masked_skewed_vectors[:, 1] + simplex_vertices[:, 1, 1] + perm[
masked_skewed_vectors[:, 2] + simplex_vertices[:, 1, 2]].astype('int32')].astype('int32')] % 12
gi3s = perm[masked_skewed_vectors[:, 0] + 1 + perm[
masked_skewed_vectors[:, 1] + 1 + perm[
masked_skewed_vectors[:, 2] + 1].astype('int32')].astype('int32')] % 12
n0s = calculate_gradient_contribution(offsets_0, gi0s, grad3)
n1s = calculate_gradient_contribution(offsets_1, gi1s, grad3)
n2s = calculate_gradient_contribution(offsets_2, gi2s, grad3)
n3s = calculate_gradient_contribution(offsets_3, gi3s, grad3)
return 23.0 * (n0s + n1s + n2s + n3s)
def calculate_image(noise_values, phases, shape):
val = T.floor((T.sum(noise_values.reshape((shape[0], shape[1], phases)) / T.pow(
2.0, T.arange(phases)), axis=2) + 1) * 128).astype('uint8').reshape((shape[0], shape[1], 1))
return T.concatenate([val, val, val], axis=2)
if __name__ == "__main__":
shape = (512, 512)
phases = 5
scaling = 200.0
offset = np.array([0.0, 0.0, 1.7], dtype=np.float32)
theano.config.mode = 'FAST_RUN'
theano.config.floatX = 'float32'
theano.config.openmp = True
theano.config.openmp_elemwise_minsize = 2000
# theano.config.compute_test_value = 'warn'
perm = T.vector('perm', dtype='int32')
# perm.tag.test_value = np_perm
grad3 = T.matrix('grad3', dtype='float32')
# grad3.tag.test_value = np_grad3
vertex_table = T.tensor4('vertex_table', dtype='int32')
# vertex_table.tag.test_value = np_vertex_table
v_shape = T.vector('shape', dtype='int32')
# v_shape.tag.test_value = shape
v_phases = T.constant(phases, name='phases', dtype='int32')
# v_phases.tag.test_value = phases
v_scaling = T.constant(scaling, name='scaling', dtype='float32')
# v_scaling.tag.test_value = scaling
v_offset = T.vector(name='offset', dtype='float32')
# v_offset.tag.test_value = offset
vl = get_input_vectors(v_shape, v_phases, v_scaling, v_offset)
v_noise = matrix_noise3d(vl, perm, grad3, vertex_table)
v_image_data = calculate_image(v_noise, v_phases, v_shape)
simplex_noise = theano.function([v_shape, v_offset, perm, grad3, vertex_table], v_image_data)
print("Compiled")
num_steps_burn_in = 10
num_steps_benchmark = 20
for i in range(num_steps_burn_in):
image_data = simplex_noise(shape, offset, np_perm, np_grad3, np_vertex_table)
start_time = time()
for i in range(num_steps_benchmark):
image_data = simplex_noise(shape, offset, np_perm, np_grad3, np_vertex_table)
print("The calculation took %.4f seconds." % ((time() - start_time) / num_steps_benchmark))
show(image_data)