def zoom_numbaThread(data, chunkIndices, zoomArray):
"""
2-D zoom interpolation using purely python - fast if compiled with numba.
Both the array to zoom and the output array are required as arguments, the
zoom level is calculated from the size of the new array.
Parameters:
array (ndarray): The 2-D array to zoom
zoomArray (ndarray): The array to place the calculation
Returns:
interpArray (ndarray): A pointer to the calculated ``zoomArray''
"""
for i in range(chunkIndices[0], chunkIndices[1]):
x = i*numba.float32(data.shape[0]-1)/(zoomArray.shape[0]-0.99999999)
x1 = numba.int32(x)
for j in range(zoomArray.shape[1]):
y = j*numba.float32(data.shape[1]-1)/(zoomArray.shape[1]-0.99999999)
y1 = numba.int32(y)
xGrad1 = data[x1+1, y1] - data[x1, y1]
a1 = data[x1, y1] + xGrad1*(x-x1)
xGrad2 = data[x1+1, y1+1] - data[x1, y1+1]
a2 = data[x1, y1+1] + xGrad2*(x-x1)
yGrad = a2 - a1
zoomArray[i,j] = a1 + yGrad*(y-y1)
return zoomArray
def bilinear_interp_numba_inbounds(data, xCoords, yCoords, chunkIndices, interpArray):
"""
2-D interpolation using purely python - fast if compiled with numba
This version also accepts a parameter specifying how much of the array
to operate on. This is useful for multi-threading applications.
Parameters:
array (ndarray): The 2-D array to interpolate
xCoords (ndarray): A 1-D array of x-coordinates
yCoords (ndarray): A 2-D array of y-coordinates
chunkIndices (ndarray): A 2 element array, with (start Index, stop Index) to work on for the x-dimension.
interpArray (ndarray): The array to place the calculation
Returns:
interpArray (ndarray): A pointer to the calculated ``interpArray''
"""
jRange = range(yCoords.shape[0])
for i in range(chunkIndices[0], chunkIndices[1]):
x = xCoords[i]
x1 = numba.int32(x)
for j in jRange:
y = yCoords[j]
y1 = numba.int32(y)
xGrad1 = data[x1 + 1, y1] - data[x1, y1]
a1 = data[x1, y1] + xGrad1 * (x - x1)
xGrad2 = data[x1 + 1, y1 + 1] - data[x1, y1 + 1]
a2 = data[x1, y1 + 1] + xGrad2 * (x - x1)
yGrad = a2 - a1
interpArray[i, j] = a1 + yGrad * (y - y1)
return interpArray
def cu_mat_power(A, power, power_A):
y, x = cuda.grid(2)
m, n = power_A.shape
if x >= n or y >= m:
return
power_A[y, x] = math.pow(A[y, x], int32(power))
def geometric_propagation_numba(phase_screens, metapupil_coords, output_phase, thread_indices):
"""
2-D interpolation using purely python - fast if compiled with numba
This version also accepts a parameter specifying how much of the array
to operate on. This is useful for multi-threading applications.
Parameters:
array (ndarray): The 2-D array to interpolate
xCoords (ndarray): A 1-D array of x-coordinates
yCoords (ndarray): A 2-D array of y-coordinates
chunkIndices (ndarray): A 2 element array, with (start Index, stop Index) to work on for the x-dimension.
interpArray (ndarray): The array to place the calculation
Returns:
interpArray (ndarray): A pointer to the calculated ``interpArray''
"""
jRange = range(metapupil_coords.shape[0])
for layer in range(phase_screens.shape[0]):
if metapupil_coords[layer, 0, -1] == phase_screens.shape[1] - 1:
metapupil_coords[layer, 0, -1] -= 1e-6
if metapupil_coords[layer, 1, -1] == phase_screens.shape[2] - 1:
metapupil_coords[layer, 1, -1] -= 1e-6
for i in range(thread_indices[0], thread_indices[1]):
print(i)
x = metapupil_coords[layer, 0, i]
x1 = numba.int32(x)
for j in jRange:
y = metapupil_coords[layer, 1, j]
y1 = numba.int32(y)
print(layer, x, y)
xGrad1 = phase_screens[layer, x1 + 1, y1] - phase_screens[layer, x1, y1]
a1 = phase_screens[layer, x1, y1] + xGrad1 * (x - x1)
xGrad2 = phase_screens[layer, x1 + 1, y1 + 1] - phase_screens[layer, x1, y1 + 1]
a2 = phase_screens[layer, x1, y1 + 1] + xGrad2 * (x - x1)
yGrad = a2 - a1
output_phase[i, j] += a1 + yGrad * (y - y1)
return output_phase
def test_4(self):
sig = [
int32(int32, int32),
uint32(uint32, uint32),
float32(float32, float32),
float64(float64, float64),
]
func = self.funcs['func3']
A = np.arange(100, dtype=np.float64)
self._run_and_compare(func, sig, A, A)
A = A.astype(np.float32)
self._run_and_compare(func, sig, A, A)
A = A.astype(np.int32)
self._run_and_compare(func, sig, A, A)
A = A.astype(np.uint32)
self._run_and_compare(func, sig, A, A)
def _test_template_4(self, target):
sig = [int32(int32, int32),
uint32(uint32, uint32),
float32(float32, float32),
float64(float64, float64)]
basic_ufunc = vectorize(sig, target=target)(vector_add)
np_ufunc = np.add
def test(ty):
data = np.linspace(0., 100., 500).astype(ty)
result = basic_ufunc(data, data)
gold = np_ufunc(data, data)
np.testing.assert_allclose(gold, result)
test(np.double)
test(np.float32)
test(np.int32)
test(np.uint32)
def sentiment_feature(basic_train,basic_test):
@guvectorize([(int64[:] )], '(n),()->(n)')
def compute_scores(x):
if x['极性'] =='0' or x['极性'] =='3':
return 0
flag =(1 if x['极性']=='1' else -1)
return flag * int(x['强度'])
@vectorize([int32()])
def compute_sentiment_scores(line):
words = np.array(line.split(' '))
mask = sentiment['词语'].isin(words)
if mask.any() == False :
return 0
else:
return sum(sentiment[mask].apply(compute_scores,axis=1))
with open('sentiment_word.csv') as file:
result = [line.strip().split('\t') for line in file.readlines()]
for line in result:
if len(line)>10:
result.remove(line)
sentiment = pd.DataFrame(columns=result[0],data=result[1:])
sentiment['词语']=sentiment['词语'].map(lambda x:x.decode("utf-8"))
sentiment.columns = range(10)
sentiment.drop([7,8,9],axis=1,inplace=True)
sentiment.columns = ['词语','词性','词义数','词义序号','分类','强度','极性']
sentiment.drop(['词性','词义数','词义序号','分类'],axis=1,inplace=True)
train = basic_train[['clean&segment','pid']].copy()
test = basic_test[['clean&segment','pid']].copy()
train['sentiment'] = train['clean&segment'].map(compute_sentiment_scores)
test['sentiment'] = test['clean&segment'].map(compute_sentiment_scores)
train.drop('clean&segment',axis=1,inplace=True)
test.drop('clean&segment',axis=1,inplace=True)
train.set_index('pid',inplace=True)
test.set_index('pid',inplace=True)
return train,test
def template_vectorize(self, target):
# build basic native code ufunc
sig = [int32(int32, int32),
uint32(uint32, uint32),
float32(float32, float32),
float64(float64, float64)]
basic_ufunc = vectorize(sig, target=target)(vector_add)
# build python ufunc
np_ufunc = np.add
# test it out
def test(ty):
data = np.linspace(0., 100., 500).astype(ty)
result = basic_ufunc(data, data)
gold = np_ufunc(data, data)
self.assertTrue(np.allclose(gold, result))
test(np.double)
test(np.float32)
test(np.int32)
test(np.uint32)
return wij, B, proportions
@njit
def calc_mult(w, p):
n = w.shape[0]
wij=np.zeros((n,n), dtype=np.int32)
for i in range(n):
if w[i]!=0:
wij[i,:]=np.random.multinomial(w[i], p[i])
else:
wij[i,:]=np.zeros(n)
return wij
#from numba import vectorize, int64, float64
@vectorize([int32(int32, int32)])
def vec_randunif(l, h):
return np.random.uniform(l,h)
@njit
#@jit(locals={'new_observation': numba.types.int32[:]}, nopython=True)
def calc(observation, action, price, action_L, high, p, distance_ij, lost_sales_cost ):
epsilons = vec_randunif(action_L, high)
demand = action + epsilons
w = np.minimum(demand, observation)
wij = calc_mult(w, p)
num_lost_sales = demand - w
dwij=np.multiply(distance_ij, wij)
xc -= xc_floor
for i in range(yc_floor.shape[0]):
for j in range(yc_floor.shape[1]):
yf = min(Ly - 1, max(0, yc_floor[i, j]))
xf = min(Lx - 1, max(0, xc_floor[i, j]))
yf1 = min(Ly - 1, yf + 1)
xf1 = min(Lx - 1, xf + 1)
y = yc[i, j]
x = xc[i, j]
Y[i, j] = (np.float32(I[yf, xf]) * (1 - y) * (1 - x) +
np.float32(I[yf, xf1]) * (1 - y) * x +
np.float32(I[yf1, xf]) * y * (1 - x) +
np.float32(I[yf1, xf1]) * y * x)
@vectorize([int32(float32)], nopython=True)
def nfloor(y):
return math.floor(y) #np.int32(np.floor(y))
@njit([
'int16[:, :,:], float32[:,:,:], float32[:,:,:], float32[:,:], float32[:,:], float32[:,:,:]',
'float32[:, :,:], float32[:,:,:], float32[:,:,:], float32[:,:], float32[:,:], float32[:,:,:]'
],
parallel=True)
def shift_coordinates(data, yup, xup, mshy, mshx, Y):
""" shift data into yup and xup coordinates
Parameters
-------------
if thresholds is None:
thresholds = cfg.SZO.EVALUATION.THRESHOLDS
assert 5 == prediction.ndim
assert 5 == truth.ndim
assert prediction.shape == truth.shape
assert prediction.shape[2] == 1
thresholds = [rainfall_to_pixel(thresholds[i]) for i in range(len(thresholds))]
thresholds = sorted(thresholds)
ret = _get_hit_miss_counts_numba(prediction=prediction,
truth=truth,
mask=mask,
thresholds=thresholds)
return ret[:, :, :, 0], ret[:, :, :, 1], ret[:, :, :, 2], ret[:, :, :, 3]
@jit(int32(float32, float32, boolean, float32))
def _get_hit_miss_counts_numba(prediction, truth, mask, thresholds):
seqlen, batch_size, _, height, width = prediction.shape
threshold_num = len(thresholds)
ret = np.zeros(shape=(seqlen, batch_size, threshold_num, 4), dtype=np.int32)
for i in range(seqlen):
for j in range(batch_size):
for m in range(height):
for n in range(width):
if mask[i][j][0][m][n]:
for k in range(threshold_num):
bpred = prediction[i][j][0][m][n] >= thresholds[k]
btruth = truth[i][j][0][m][n] >= thresholds[k]
ind = (1 - btruth) * 2 + (1 - bpred)
ret[i][j][k][ind] += 1
def hist(val, vmin, vptp, vres):
return int32(((val - vmin) / vptp) * vres)
def decode(self):
width = self.ihdr_info['width']
height = self.ihdr_info['height']
bit_depth = self.ihdr_info['bit depth']
color_type = self.ihdr_info['color type']
pixel_width = self.__pixel_width
def ifilter0(m, N, buf, bpp):
'''Type 0: No filter'''
return
@numba.jit((int32, int32, int32[:, :], int32))
def ifilter1(m, N, buf, bpp):
'''Type 1: Inverse Sub filter'''
for k in range(bpp, N):
buf[m, k] += buf[m, k-bpp]
buf[m, k] &= 0xff
@numba.jit((int32, int32, int32[:, :], int32))
def ifilter2(m, N, buf, bpp):
'''Type 2: Inverse Up filter'''
buf[m, :] += buf[(m-1), :]
buf[m, :] &= 0xff
@numba.jit((int32, int32, int32[:, :], int32))
def ifilter3(m, N, buf, bpp):
'''Type 3: Inverse Average filter'''
for k in range(bpp):
buf[m, k] += buf[(m-1), k] // 2
buf[m, k] &= 0xff
for k in range(bpp, N):
buf[m, k] += (buf[m, (k-bpp)] + buf[(m-1), k]) // 2
buf[m, k] &= 0xff
@numba.jit(int32(int32, int32, int32))
def predictor(a, b, c):
'''Helper function for ifilter4.
a = left, b = above, c = upper left.'''
p = a + b -c
pa = abs(p - a)
pb = abs(p - b)
pc = abs(p - c)
if pa <= pb and pa <= pc:
return a
elif pb <= pc:
return b
else:
return c
@numba.jit((int32, int32, int32[:, :], int32))
def ifilter4(m, N, buf, bpp):
'''Type 4: Inverse Paeth filter'''
for k in range(bpp):
buf[m, k] += buf[(m-1), k]
buf[m, k] &= 0xff
for k in range(bpp, N):
buf[m, k] += predictor(buf[m, (k-bpp)], buf[(m-1), k], buf[(m-1), (k-bpp)])
buf[m, k] &= 0xff
def ifilter(byte_stream):
'''inverse filter
before: decompressed data stream
width: width of the image
height: height of the image
return value: data stream which has been inverse filtered'''
bwidth = int(math.ceil(width * bit_depth * pixel_width[color_type] / 8.0))
bpp = self.__bpp
filter_list = [ifilter0, ifilter1, ifilter2, ifilter3, ifilter4]
buf = np.empty((height+1, bwidth+1), dtype=np.int)
buf[0, :] = 0
buf[1:, :] = np.reshape(np.fromstring(byte_stream, dtype=np.ubyte), (height, bwidth+1))
for m in range(1, height+1):
filter_type = buf[m, 0]
if filter_type == 0: continue
filter_list[filter_type](m, bwidth, buf[:, 1:], bpp)
byte_mtx = np.empty((height, bwidth), dtype=np.ubyte)
byte_mtx[:, :] = buf[1:, 1:]
return byte_mtx
def split_byte(b, width):
mask = 2**width - 1
li = []
for k in range(8//width):
li.append(b & mask)
b >>= width
li.reverse()
return li
def bytes_to_pixels(mtx, bit_depth, img_width):
# if bit_depth < 8:
# for idx, line in enumerate(mtx):
# pixels = []
# for B in line:
# pixels.extend(split_byte(B, bit_depth))
# pixels = pixels[:img_width]
# mtx[idx] = pixels
# if bit_depth == 16:
# for idx, line in enumerate(mtx):
# pixels = []
# for k in range(img_width):
# pixels.append(line[2*k]*2**8 + line[2*k+1])
# mtx[idx] = pixels
if bit_depth == 8:
return mtx
if bit_depth == 16:
return mtx.view(np.ushort) # reinterpret_cast
else:
raise NotImplementedError
com_stream = StringIO()
with open(self.__filename, 'rb') as f:
for chunk in self.__chunks:
if chunk['type'] == 'IDAT':
f.seek(chunk['data pos'])
com_stream.write(f.read(chunk['len']))
byte_stream = zlib.decompress(com_stream.getvalue())
pix_mtx = ifilter(byte_stream)
pix_mtx = bytes_to_pixels(pix_mtx, bit_depth, width)
pixel_type = np.ubyte if bit_depth <=8 else np.ushort
pix_mtx = np.array(pix_mtx, dtype=pixel_type)
pix_mtx.shape = (height, width, pixel_width[color_type])
return pix_mtx
r = linspace(xmin, xmax, width)
i = linspace(ymin, ymax, height)
n = [[0] * width for _ in range(height)]
for x in range(width):
for y in range(height):
n[y][x] = mandel_numba(complex(r[x], i[y]), maxiter)
return n
##############################################################################
#Numba Vectorize
@vectorize([int32(complex64, int32)], target='parallel')
def mandel_numba_vect(c, maxiter):
nreal = 0
real = 0
imag = 0
for n in range(maxiter):
nreal = real * real - imag * imag + c.real
imag = 2 * real * imag + c.imag
real = nreal
if real * real + imag * imag > 4.0: #squared modulus
return n
return n
def mandel_set_numba_vect(xmin, xmax, ymin, ymax, width, height, maxiter):
r1 = np.linspace(xmin, xmax, width, dtype=np.float32)
Args:
x1 (array): First component of vector 1
y1 (array): Second component of vector 1
z1 (array): Third component of vector 1
x2 (array): First component of vector 2
y2 (array): Second component of vector 2
z2 (array): Third component of vector 2
Returns:
r2 (array): Element-wise squared distance (see definition)
.. math::
r2 = (x1 - x2)^{2} + (y1 - y2)^{2} + (z1 - z2)^{2}
'''
return (x1 - x2)**2 + (y1 - y2)**2 + (z1 - z2)**2
if global_config['pkg_numba']:
from numba import vectorize, float64, float32, int64, int32
vmag3 = vectorize([int32(int32, int32, int32),
int64(int64, int64, int64),
float32(float32, float32, float32),
float64(float64, float64, float64)])(vmag3)
vdist3 = vectorize([int32(int32, int32, int32, int32, int32, int32),
int64(int64, int64, int64, int64, int64, int64),
float32(float32, float32, float32, float32, float32, float32),
float64(float64, float64, float64, float64, float64, float64)])(vdist3)
from numba import njit
from numba import int32, float32, prange
from numba.core import types
from numba import typeof
from numba.typed import List, Dict
from numba.core.errors import TypingError
from numba.tests.support import (TestCase, MemoryLeakMixin, override_config,
forbid_codegen, skip_parfors_unsupported)
from numba.core.unsafe.refcount import get_refcount
from numba.experimental import jitclass
# global typed-list for testing purposes
global_typed_list = List.empty_list(int32)
for i in (1, 2, 3):
global_typed_list.append(int32(i))
def to_tl(l):
""" Convert cpython list to typed-list. """
tl = List.empty_list(int32)
for k in l:
tl.append(k)
return tl
class TestTypedList(MemoryLeakMixin, TestCase):
def test_basic(self):
l = List.empty_list(int32)
# len
self.assertEqual(len(l), 0)
import numpy as np
from numba import vectorize
from numba import cuda, int32, float32, float64
from numba.cuda.testing import skip_on_cudasim
from numba.cuda.testing import CUDATestCase
from numba.core import config
import unittest
sig = [
int32(int32, int32),
float32(float32, float32),
float64(float64, float64)
]
target = "cuda"
if config.ENABLE_CUDASIM:
target = "cpu"
test_dtypes = np.float32, np.int32
@skip_on_cudasim("ufunc API unsupported in the simulator")
class TestCUDAVectorize(CUDATestCase):
N = 1000001
def test_scalar(self):
@vectorize(sig, target=target)
def vector_add(a, b):
return a + b
eq_t[h] += 1.0 / nb_best_hand
# impossible : error
else:
return -1
# normalize eq_w_agg and eq_t_agg
for h in xrange(p):
eq_agg[h, 0] = eq_w[h] / n
eq_agg[h, 1] = eq_t[h] / n
return eq_agg
rank_fast = jit(
int32(int32[:], int32[:], uint32[:], int32[:], int32, int32, int32[:],
int32[:], int32[:]))(rank)
exhaustive_block_fast = jit(int32[:](int32[:, :], int32[:], int32[:],
uint32[:], int32[:], int32, int32,
int32[:], int32[:],
int32[:]))(exhaustive_block)
def exhaustive_eval(player_card, table_card):
"""compute all possible games given the player/table cards (as a numbers from 0 to 51) and return equity win/tie for each player"""
p = player_card.shape[0]
equity_arr = np.zeros([p, 2], dtype=np.float32)
print '\n---------------- Exhaustive eval start'
print 'player_card=\n{}'.format(player_card)
print 'table_card=\n{}'.format(table_card)
neighbours[6, 0] = i + 1
neighbours[7, 0] = i + 1
neighbours[0, 1] = j + 1
neighbours[1, 1] = j - 1
neighbours[2, 1] = j
neighbours[3, 1] = j
neighbours[4, 1] = j + 1
neighbours[5, 1] = j - 1
neighbours[6, 1] = j + 1
neighbours[7, 1] = j - 1
neighbours %= grid_length
@jit(int32(int8[:, :], int32[:, :]), nopython=True)
def count_neighbours(in_grid, neighbours):
"""Count the number of live neighbours of the site."""
count = np.int32(0)
for n_count in range(neighbours.shape[0]):
if in_grid[neighbours[n_count, 0], neighbours[n_count, 1]] == 1:
count += 1
return count
@jit((int32[:, :], int8[:, :], int8[:, :]), nopython=True)
def grid_sweep(neighbours, in_grid, out_grid):
"""Sweep the grid once with game of life rules."""
for i in range(in_grid.shape[0]):
for j in range(in_grid.shape[1]):
j += 1
t[j] = t0
# Update t0, y0, z0
t0, y0, z0 = t1, y1, z1
# end
# Update y if last y0 is greater than (or equal) threshold
if cmp2(h, abs(y0 - y[t[j]])):
j += 1
t[j] = t0
return j + 1
return findrfc2
@jit(int32(float64, float64), nopython=True)
def a_le_b(a, b):
return a <= b
@jit(int32(float64, float64), nopython=True)
def a_lt_b(a, b):
return a < b
_findrfc_le = _make_findrfc(a_le_b, a_lt_b)
_findrfc_lt = _make_findrfc(a_lt_b, a_le_b)
@jit(int64(int64[:], float64[:], float64), nopython=True)
def _findrfc(ind, y, h):
def cuda_ij_to_k(i, j):
return int32(j + i * (i - 1) / 2)
def argcast(a, b):
return argcast_inner(int32(a), b)
@jit(int64(int32, int32))
def EncodeMorton2D(x, y):
"""
Calculates the 2D morton code from the x, y dimensions
Args:
x (int): the x dimension
y (int): the y dimension
Returns:
int: 64 bit morton code in 2D
"""
return Expand2D(x) + (Expand2D(y) << 1)
@jit(int32(int64))
def Compact2D(m):
"""
Decodes the 64 bit morton code into a 32 bit number in the 2D space using
a divide and conquer approach for separating the bits.
1 bit is not used because the integers are not unsigned
Args:
n (int): a 64 bit morton code
Returns:
int: a dimension in 2D space
Raises:
Exception: ERROR: Morton code is always positive
"""
ret += d**2
return ret
@cuda.jit(nb_float(nb_float[:], nb_float[:], nb_float[:]), device=True)
def cu_pbc_dist(a, b, box):
ret = 0
for i in range(a.shape[0]):
d = a[i] - b[i]
d -= box[i] * floor(d / box[i] + 0.5)
ret += d**2
return sqrt(ret)
return cu_pbc_dist2, cu_pbc_dist_diameter, cu_pbc_dist
@cuda.jit(int32(int32[:], int32[:]), device=True)
def cu_ravel_index_f_pbc(i, dim): # ravel index in Fortran way.
ret = (i[0] + dim[0]) % dim[0]
tmp = dim[0]
for k in range(1, dim.shape[0]):
ret += ((i[k] + dim[k]) % dim[k]) * tmp
tmp *= dim[k]
return ret
@cuda.jit(void(int32, int32[:], int32[:]), device=True)
def cu_unravel_index_f(i, dim, ret): # unravel index in Fortran way.
for k in range(dim.shape[0]):
ret[k] = int(i % dim[k])
i = (i - ret[k]) / dim[k]
def foo():
l = listobject.new_list(types.unicode_type)
l.append(int32(0))
def make_test_list():
l = listobject.new_list(int32)
l.append(int32(1))
return l
xy + \\text{trunc}\\left(\\frac{\\left(\\left|x - y\\right| -
1\\right)^{2}}{4}\\right)
Args:
x (array): First value array
y (array): Second value array
Returns:
p (array): Pairing function result
Note:
This function has a vectorized version that is imported as
:func:`~exa.algorithms.indexing.unordered_pairing`; use that
function when working with array data.
.. _pairing function: http://www.mattdipasquale.com/blog/2014/03/09/unique-unordered-pairing-function/
'''
return np.int64(x * y + np.trunc((np.abs(x - y) - 1)**2 / 4))
if global_config['pkg_numba']:
from numba import jit, vectorize, int32, int64, float32, float64
arange1 = jit(nopython=True, cache=True)(arange1)
arange2 = jit(nopython=True, cache=True)(arange2)
indexes_sc1 = jit(nopython=True, cache=True)(indexes_sc1)
indexes_sc2 = jit(nopython=True, cache=True)(indexes_sc2)
unordered_pairing = vectorize([int32(int32, int32), int64(int64, int64),
float32(float32, float32), float64(float64, float64)],
nopython=True)(unordered_pairing)
def foo():
l = make_test_list()
l._make_immutable()
l.append(int32(1))
#! /usr/bin/python
# -*- coding: utf-8 -*-
# ising.py
# Version: 2018.11.16.01
# Requiered libraries
from __future__ import division
import time, random, math, time, sys, os
import matplotlib.pyplot as plt
from numba import jit, prange, njit, int32
import numpy as np
from numpy.random import random as nrand
@njit(int32(int32, int32, int32)) # Periodic Boundary Condition
def PBC(idx, lim, add):
return (idx + lim + add) % lim
# Monte Carlo Alg
def MC(temperature, spins,
MCc): # Temperature, Number of Spins, Number of cycles
MSpins = np.ones((spins, spins), np.int32) # Spins Matrix pointing up
# Initialize Statistics
E = 0.
Eavr = 0.
Evar = 0.
E2av = 0.
Mavr = 0.
""" Core math functions to compute escape times for the Mandelbrot set. """
from numba import float64, int32, jit
from numpy import empty
@jit(int32(float64, float64, int32))
def mandelbrot_escape(x, y, n):
"""Mandelbrot set escape time algorithm for a given c = x + i*y coordinate.
Returnautojit, the number of iterations necessary to escape abouve a fixed threshold
(4.0) by repeatedly applying the formula:
z_0 = 0
z_n = z_{n-1} ^ 2 + c
If the formula did not escape after `n` iterations, return -1 .
Parameters
----------
x, y -- float
Real and imaginary part of the complex number z.
n -- integer
Maximum number of iterations.
"""
z_x = 0
z_y = 0
for i in range(n):
old_z_x = z_x
from __future__ import print_function, absolute_import
import numpy as np
from numba import vectorize
from numba import cuda, int32, float32, float64
from numba import unittest_support as unittest
from numba.cuda.testing import skip_on_cudasim
from numba.cuda.testing import CUDATestCase
from numba import config
sig = [int32(int32, int32),
float32(float32, float32),
float64(float64, float64)]
target='cuda'
if config.ENABLE_CUDASIM:
target='cpu'
test_dtypes = np.float32, np.int32
@skip_on_cudasim('ufunc API unsupported in the simulator')
class TestCUDAVectorize(CUDATestCase):
N = 1000001
def test_scalar(self):
@vectorize(sig, target=target)
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Fri Oct 25 20:50:52 2019
@author: daniel
"""
from numba import jit, vectorize, guvectorize, float64, complex64, int32, float32, int64
import numpy as np
@jit(int32(complex64, int32))
def mandelbrot(c, maxiter):
nreal = 0
real = 0
imag = 0
for n in range(maxiter):
nreal = real * real - imag * imag + c.real
imag = 2 * real * imag + c.imag
real = nreal
if real * real + imag * imag > 4.0:
return n
return 0
@guvectorize([(complex64[:], int32[:], int32[:])],
'(n),()->(n)',
target='parallel')
def mandelbrot_numpy(c, maxit, output):
maxiter = maxit[0]
if current_interval == result_buffer_size:
return current_interval
# Add bounds to result buffer
result_buffer[current_interval, 0] = current_interval_start
result_buffer[current_interval, 1] = itv_end
current_interval += 1
if current_interval == result_buffer_size:
return current_interval
n_intervals = current_interval # No +1, as current_interval was incremented also when the last interval closed
return n_intervals
@numba.jit(numba.int32(numba.float64[:], numba.float64, numba.int64[:, :]),
nopython=True)
def find_intervals_above_threshold_no_splitting(w, threshold, result_buffer):
"""Fills result_buffer with l, r bounds of intervals in w > threshold.
Unlike find_intervals_above_threshold(), does not smooth and split hits,
which allows speed increase in ZLE simulation.
:param w: Waveform to do hitfinding in
:param threshold: Threshold for including an interval
:param result_buffer: numpy N*2 array of ints, will be filled by function.
if more than N intervals are found, none past the first N will be processed.
:returns : number of intervals processed
Boundary indices are inclusive, i.e. the right boundary is the last index which was > threshold
"""
result_buffer_size = len(result_buffer)
last_index_in_w = len(w) - 1
#!/usr/bin/env python
# coding: utf-8
import numpy as np
from numba import jit, guvectorize, complex128, int32
# burning ship set
@jit(int32(complex128, int32))
def burning_ship_iter(z, maxiter):
nreal = 0
real = 0
imag = 0
for n in range(maxiter):
real2 = real * real
imag2 = imag * imag
if real2 + imag2 > 4.0:
return n
imag = abs(2 * real * imag + z.imag)
real = abs(real2 - imag2 + z.real)
return 0
@guvectorize([(complex128[:], int32[:], int32[:])],
'(n),()->(n)',
target='parallel')
def burning_ship_numpy(z, maxit, output):
maxiter = maxit[0]
for i in range(z.shape[0]):
output[i] = burning_ship_iter(z[i], maxiter)
from numba import vectorize, int32, complex128
from __init__ import plot, field
IMAX = 0xFFFF
@vectorize([int32(complex128)], target="parallel")
def mandelbrot_vector(c):
z = 0
n = 0
while abs(z) <= 2 and n < IMAX:
z = z * z + c
n += 1
return n
def main():
f = field(1024)
m = mandelbrot_vector(f)
m[m == IMAX] = 0
plot(m, "numba_vectorize.png")
if __name__ == "__main__":
main()
def cu_delay_cfun(horizon,
cfpre,
cfpost,
n_cvar,
n_thread_per_block,
step_stride=0,
aff_node_stride=0):
"Construct CUDA device function for delayed coupling with given pre & post summation functions."
if horizon < 2 or (horizon & (horizon - 1)) != 0:
msg = "cu_delay_cfun argument `horizon` should be a positive power of 2, but received %d"
msg %= horizon
raise ValueError(msg)
# 0 except for testing
step_stride = int32(step_stride)
aff_node_stride = int32(aff_node_stride)
@cuda.jit(device=True)
def dcfun(aff, delays, weights, state, i_post, i_thread, step, cvars,
buf): #, delayed_step):
# shared mem temporary for summation, indexed by block-local thread index
aff_i = cuda.shared.array((n_cvar, n_thread_per_block), float32)
i_t = cuda.threadIdx.x
# 0 except for testing
step_ = step_stride * step
# update buffer with state
for i_cvar in range(cvars.shape[0]):
buf[i_post, _cu_mod_pow_2(step, horizon), i_cvar,
i_thread] = state[step_, i_post, cvars[i_cvar], i_thread]
# initialize sums to zero
for i_cvar in range(cvars.shape[0]):
aff_i[i_cvar, i_t] = float32(0.0)
#aff[step_, i_post * aff_node_stride, i_cvar, i_thread*0] = float32(0.0)
# query buffer, summing over cfpre applied to delayed efferent cvar values
for i_pre in range(weights.shape[0]):
weight = weights[i_post, i_pre]
if weight == 0.0:
continue
# delayed_step[i_post, i_pre] = _cu_mod_pow_2(step - delays[i_post, i_pre] + horizon, horizon)
delayed_step = _cu_mod_pow_2(
step - delays[i_post, i_pre] + horizon, horizon)
for i_cvar in range(cvars.shape[0]):
cval = buf[i_pre, delayed_step, i_cvar, i_thread]
#aff[step_, i_post * aff_node_stride, i_cvar, i_thread*0] += \
aff_i[i_cvar, i_t] += \
weight * cfpre(state[step_, i_post, cvars[i_cvar], i_thread], cval)
# apply cfpost
for i_cvar in range(cvars.shape[0]):
# i_t use and i_thread for tests...
aff[step_, i_post * aff_node_stride, i_cvar, i_t] = cfpost(
aff_i[i_cvar, i_t]
#aff[step_, i_post * aff_node_stride, i_cvar, i_thread*0]
)
return dcfun
#
# i = 0
#
# while True:
# mother = np.random.randint(0,len(fit))
# father = np.random.randint(0,len(fit))
# r_rec = recombine_arrays(population[:, mother], population[:, father])
# new_pop[:, i] = r_rec[:, 0]
# new_pop[:, i+1] = r_rec[:, 1]
# i += 2
# if i >= n:
# break
#
# return new_pop
@jit(int32(float32[:]),nopython=True)
def weighted_choice(weights):
i = 0
rnd = np.random.random() * np.sum(weights)
for i in range(len(weights)):
rnd -= weights[i]
if rnd < 0:
break
return i
@jit(float32[:,:](float32[:,:],float32[:]),nopython=True)
def recombine_population(population,fitness):
weights = fitness.max()-fitness
new_pop = np.zeros(population.shape,dtype=np.float32)
n = population.shape[1]
fit = np.arange(0,int(n/20))
from __future__ import print_function, absolute_import
import numpy as np
from numba import vectorize
from numba import cuda, int32, float32, float64
from timeit import default_timer as time
from numba import unittest_support as unittest
from numba.cuda.testing import skip_on_cudasim
from numba.cuda.testing import CUDATestCase
from numba import config
sig = [int32(int32, int32), float32(float32, float32), float64(float64, float64)]
target = "cuda"
if config.ENABLE_CUDASIM:
target = "cpu"
test_dtypes = np.float32, np.int32
@skip_on_cudasim("ufunc API unsupported in the simulator")
class TestCUDAVectorize(CUDATestCase):
def test_scalar(self):
@vectorize(sig, target=target)
def vector_add(a, b):
return a + b
a = 1.2
b = 2.3
c = vector_add(a, b)
import numpy as np
import numba
@numba.vectorize([numba.int32(numba.uint8)], nopython=True)
def hammard(n):
"""
fast uint8 Hammard Weight
:param n: np.uint8
:return: np.uint8
"""
# recursively divide in two, combinig sums by bit shifting and adding
n = (n & np.uint8(85)) + ((n >> 1) & np.uint8(85)) # 85=01010101b
n = (n & np.uint8(51)) + ((n >> 2) & np.uint8(51)) # 51=00110011b
n = (n & np.uint8(15)) + ((n >> 4) & np.uint8(15)) # 15=00001111b
return n
@numba.vectorize([numba.int32(numba.int32)], nopython=True)
def log2(n):
"""
fast integer floor log 2
:param n: input integer, must be positive
:return:
"""
result = 0
for i in range(1, 32):
if not n >> i:
result = i - 1
def complete_grid(self):
"""Array of (edge,vertex,vertex) triples defining a complete graph."""
if self._complete_grid is None:
self._complete_grid = make_complete_graph(self._num_vertices)
return self._complete_grid
@property
def vertices(self):
return self._vertices
def gc(self):
"""Garbage collect temporary cached data structures."""
self._complete_grid = None
@jit(numba.int32(numba.int32, numba.int32), nopython=True, cache=True)
def find_complete_edge(v1, v2):
"""Find the edge index k of an unsorted pair of vertices (v1, v2)."""
if v2 < v1:
v1, v2 = v2, v1
return v1 + v2 * (v2 - 1) // 2
def make_complete_graph(num_vertices):
"""Constructs a complete graph.
The pairing function is: k = v1 + v2 * (v2 - 1) // 2
Args:
num_vertices: Number of vertices.
def cast_as_numba_type_attribute():
value = 4.4
return numba.int32(value)
def argcast(a, b):
return argcast_inner(int32(a), b)
import math
import json
import base64
import numpy as np
from numba import njit, int32
# this is a 1-to-1 translation of our js bloom filters to python
@njit(int32(int32))
def popcnt(v):
v -= (v >> 1) & 0x55555555
v = (v & 0x33333333) + ((v >> 2) & 0x33333333)
return ((v + (v >> 4) & 0xf0f0f0f) * 0x1010101) >> 24
# a * 16777619 mod 2**32
@njit(int32(int32))
def fnv_multiply(a):
return a + (a << 1) + (a << 4) + (a << 7) + (a << 8) + (a << 24)
#// See https://web.archive.org/web/20131019013225/http://home.comcast.net/~bretm/hash/6.html
@njit(int32(int32))
def fnv_mix(a):
a += (a << 13)
a ^= (a >> 7)
a += (a << 3)
a ^= (a >> 17)
from numba import float32, int32, jit
import cProfile
from dis import dis
@jit(int32(int32, int32), nopython=True, nogil=True)
def add_two(a, b):
acc = 0
i = 0
while i < 1000:
acc += a + b
i += 1
return acc
def add_two_wrap(a, b):
return add_two(a, b)
def add_two2(a, b):
acc = 0
i = 0
while i < 1000:
acc += a + b
i += 1
return acc
def test():
num = 100
print add_two_wrap(num, num + 1)
# i = 0
#
# while True:
# mother = np.random.randint(0,len(fit))
# father = np.random.randint(0,len(fit))
# r_rec = recombine_arrays(population[:, mother], population[:, father])
# new_pop[:, i] = r_rec[:, 0]
# new_pop[:, i+1] = r_rec[:, 1]
# i += 2
# if i >= n:
# break
#
# return new_pop
@jit(int32(float32[:]), nopython=True)
def weighted_choice(weights):
i = 0
rnd = np.random.random() * np.sum(weights)
for i in range(len(weights)):
rnd -= weights[i]
if rnd < 0:
break
return i
@jit(float32[:, :](float32[:, :], float32[:]), nopython=True)
def recombine_population(population, fitness):
weights = fitness.max() - fitness
new_pop = np.zeros(population.shape, dtype=np.float32)
n = population.shape[1]
def cu_angle_force(npa, pos, params, box0, box1, box2, box0_half,
box1_half, box2_half, angle_size, angle_list, force,
virial_potential, one_three, one_sixth):
i = cuda.grid(1)
if i < npa:
pi = pos[i]
# result = cuda.local.array(5, dtype = nb.float32)
result0 = force[i][0]
result1 = force[i][1]
result2 = force[i][2]
result3 = virial_potential[i][0]
result4 = virial_potential[i][1]
for ai in range(nb.int32(0), angle_size[i]):
j = angle_list[i][ai][0]
k = angle_list[i][ai][1]
type = angle_list[i][ai][2]
order = angle_list[i][ai][3]
pj = pos[j]
pk = pos[k]
if order == 0:
pa = pi
pb = pj
pc = pk
if order == 1:
pa = pj
pb = pi
pc = pk
if order == 2:
pa = pj
pb = pk
pc = pi
d_ab0 = pa[0] - pb[0]
d_ab1 = pa[1] - pb[1]
d_ab2 = pa[2] - pb[2]
d_cb0 = pc[0] - pb[0]
d_cb1 = pc[1] - pb[1]
d_cb2 = pc[2] - pb[2]
if d_ab0 >= box0_half:
d_ab0 -= box0
elif d_ab0 < -box0_half:
d_ab0 += box0
if d_ab1 >= box1_half:
d_ab1 -= box1
elif d_ab1 < -box1_half:
d_ab1 += box1
if d_ab2 >= box2_half:
d_ab2 -= box2
elif d_ab2 < -box2_half:
d_ab2 += box2
if d_cb0 >= box0_half:
d_cb0 -= box0
elif d_cb0 < -box0_half:
d_cb0 += box0
if d_cb1 >= box1_half:
d_cb1 -= box1
elif d_cb1 < -box1_half:
d_cb1 += box1
if d_cb2 >= box2_half:
d_cb2 -= box2
elif d_cb2 < -box2_half:
d_cb2 += box2
rsq_ab = d_ab0 * d_ab0 + d_ab1 * d_ab1 + d_ab2 * d_ab2
r_ab = math.sqrt(rsq_ab)
rsq_cb = d_cb0 * d_cb0 + d_cb1 * d_cb1 + d_cb2 * d_cb2
r_cb = math.sqrt(rsq_cb)
cos_abc = d_ab0 * d_cb0 + d_ab1 * d_cb1 + d_ab2 * d_cb2
cos_abc /= r_ab * r_cb
if cos_abc > nb.float32(1.0):
cos_abc = nb.float32(1.0)
if cos_abc < -nb.float32(1.0):
cos_abc = -nb.float32(1.0)
sin_abc = math.sqrt(nb.float32(1.0) - cos_abc * cos_abc)
if sin_abc < minimum_value:
sin_abc = minimum_value
sin_abc = nb.float32(1.0) / sin_abc
pms = params[type]
fp = cuda.local.array(2, dtype=nb.float32)
cu_func(cos_abc, sin_abc, pms, fp)
a = -fp[0] * sin_abc
a11 = a * cos_abc / rsq_ab
a12 = -a / (r_ab * r_cb)
a22 = a * cos_abc / rsq_cb
fab0 = a11 * d_ab0 + a12 * d_cb0
fab1 = a11 * d_ab1 + a12 * d_cb1
fab2 = a11 * d_ab2 + a12 * d_cb2
fcb0 = a22 * d_cb0 + a12 * d_ab0
fcb1 = a22 * d_cb1 + a12 * d_ab1
fcb2 = a22 * d_cb2 + a12 * d_ab2
if order == 0:
result0 += fab0
result1 += fab1
result2 += fab2
if order == 1:
result0 -= fab0 + fcb0
result1 -= fab1 + fcb1
result2 -= fab2 + fcb2
if order == 2:
result0 += fcb0
result1 += fcb1
result2 += fcb2
vx = d_ab0 * fab0 + d_cb0 * fcb0
vy = d_ab1 * fab1 + d_cb1 * fcb1
vz = d_ab2 * fab2 + d_cb2 * fcb2
virial = one_sixth * (vx + vy + vz)
# if i==35 and ai == 0:
# print(i, ai, vy, a, cos_abc, rsq_cb)
potential = fp[1] * one_three
result3 += virial
result4 += potential
force[i][0] = result0
force[i][1] = result1
force[i][2] = result2
virial_potential[i][0] = result3
virial_potential[i][1] = result4
if np.isnan(ai):
f = True
break
return f
@ndreduce([int64(int32), int64(int64), int64(float32), int64(float64)])
def count(a):
non_missing = 0
for ai in a.flat:
if not np.isnan(ai):
non_missing += 1
return non_missing
@ndreduce([int32(int32), int64(int64), float32(float32), float64(float64)])
def nansum(a):
asum = 0
for ai in a.flat:
if not np.isnan(ai):
asum += ai
return asum
@ndreduce([float32(float32), float64(float64)])
def nanmean(a):
asum = 0.0
count = 0
for ai in a.flat:
if not np.isnan(ai):
asum += ai
def dowork(M_f_start, nfs_sq, d_src_ar, d_dst_ar, weight_ar, sigma_m, E2,
sigma_0, fovshift, nfs, W_cut, osd0p, osd1r):
# Work out i_src and i_dst based on the 2-D thread index
i_src, i_dst = cuda.grid(2)
if i_src < nfs_sq and i_dst < nfs_sq:
# Temporary shared memory for weights
tmp_w = cuda.shared.array(12288, dtype=float32)
myidx = (cuda.threadIdx.y * cuda.blockDim.x + cuda.threadIdx.x)
offsidx = shifted_idx3(myidx)
tmp_w[offsidx] = float32(0.0)
tmp_w[offsidx + 1] = float32(0.0)
tmp_w[offsidx + 2] = float32(0.0)
cuda.syncthreads()
# Compute the location of d_src_ar, this defines what sigma will
# be. As r (as opp. to phi) increases, the sigma should increase.
M_f = float32(nfs) / (E2 * math.log(((1 + d_src_ar[i_src, 1]) /
(2 * E2)) + 1))
# Set some of M_f to 1 to ensure the fan-out starts at around the
# edge of the foveal region.
if (1 + d_src_ar[i_src, 1]) < fovshift:
M_f = M_f_start
# Compute modified sigma and 3 times this value. _sigma is a
# function of r, aka d_src_ar[1]. M_f is the function of r.
_sigma = (sigma_m / M_f) - (sigma_m / M_f_start) + sigma_0
three_sigma = float32(3.0) * _sigma
# in-xy-plane distance (ignore d_src_ar[2]/dstdoc[2])
xd = (d_src_ar[i_src, 0] - d_dst_ar[i_dst, 0] + osd0p)
yd = (d_src_ar[i_src, 1] - d_dst_ar[i_dst, 1] + osd1r)
if abs(xd) < three_sigma and abs(yd) < three_sigma:
dist = math.sqrt(math.pow(xd, 2) + math.pow(yd, 2))
gauss = math.exp(-0.5 * math.pow(dist / _sigma, 2))
if gauss > W_cut:
# Write result into weight_ar
tmp_w[offsidx] = float32(gauss)
tmp_w[offsidx + 1] = float32(i_src)
tmp_w[offsidx + 2] = float32(i_dst)
# Sync threads, then access device memory with any results
cuda.syncthreads()
if cuda.threadIdx.x == 0 and cuda.threadIdx.y == 0:
tpb = cuda.blockDim.x * cuda.blockDim.y
# Write data from tmp_w to res_ar, but only in ONE thread from
# the threadblock. Should avoid racing.
for idx in range(
0, tpb): # 512 was hard coded here; changed it for tpb
offsidx2 = shifted_idx3(idx)
theweight = tmp_w[
offsidx2] # weight should be the first one, so no +1/+2
# Add to weight_ar
weight_idx = int32(tmp_w[offsidx2 + 2]) * nfs_sq + int32(
tmp_w[offsidx2 + 1])
weight_ar[weight_idx] = theweight
return # end dowork()
def foo():
li, lf = List(), List()
li.append(int32(1))
lf.append(float32(1.0))
return li._dtype, lf._dtype
def exprefixsum(masks, indices, init = 0, nelem = None):
"""
exclusive prefix sum
"""
nelem = masks.size if nelem is None else nelem
carry = init
for i in xrange(nelem):
indices[i] = carry
if masks[i] != 0:
carry += masks[i]
#indices[nelem] = carry
return carry
@numba.jit(int32(int32[:],int32[:],int32), nopython=False)
def exprefixsumNumba(in_ary, out_ary, init = 0):
"""
exclusive prefix sum
"""
nelem = in_ary.size
carry = init
for i in range(nelem):
out_ary[i] = carry
carry += in_ary[i]
return carry
#@numba.jit(int32(int32[:],int32), nopython=False)
@numba.njit
eq_t[h] += 1.0/nb_best_hand
# impossible : error
else:
return -1
# normalize eq_w_agg and eq_t_agg
for h in xrange(p):
eq_agg[h, 0] = eq_w[h]/n
eq_agg[h, 1] = eq_t[h]/n
return eq_agg
rank_fast = jit(int32(int32[:], int32[:], uint32[:], int32[:], int32, int32, int32[:], int32[:], int32[:]))(rank)
exhaustive_block_fast = jit(int32[:](int32[:, :], int32[:], int32[:], uint32[:], int32[:], int32, int32, int32[:], int32[:], int32[:]))(exhaustive_block)
def exhaustive_eval(player_card, table_card):
"""compute all possible games given the player/table cards (as a numbers from 0 to 51) and return equity win/tie for each player"""
p = player_card.shape[0]
equity_arr = np.zeros([p, 2], dtype=np.float32)
print '\n---------------- Exhaustive eval start'
print 'player_card=\n{}'.format(player_card)
print 'table_card=\n{}'.format(table_card)
print 'p={}'.format(p)
return np.array([x3d, y3d, z3d])
@numba.njit(
numba.typeof(
(0.0, 0.0))(numba.float32, numba.float32, numba.float32, numba.float32,
numba.float32, numba.float32, numba.float32))
def project_to_2d(x, y, z, cx, cy, fx, fy):
if z == 0:
z = 0.001
x2d = fx * x / z + cx
y2d = fy * y / z + cy
return x2d, y2d
@numba.njit(numba.int32(numba.float32, numba.float32, numba.float32))
def clip_round(value, minvalue, maxvalue):
return int(round((min(max((value, minvalue)), maxvalue))))
@numba.njit(numba.float32[:, :](numba.float32[:, :], numba.float32[:, :],
numba.float32[:, :], numba.float32[:, :],
numba.float32[:], numba.typeof((0, 0))))
def reproject(d_image, rgb_mat, d_mat, R, T, shape):
buffer = np.zeros(shape, np.float32)
h, w = d_image.shape
dfx = d_mat[0, 0]
dfy = d_mat[1, 1]
dcx = d_mat[0, 2]
dcy = d_mat[1, 2]
import math
@jit
def f(x,y):
# A somewhat trivial example
return x + y
'''
在此模式下，编译将推迟到第一个函数执行。Numba将在调用时推断参数类型，并根据
此信息生成优化代码。Numba还可以根据输入类型编译单独的特化。例如，f()使用整数或复数调用上面的函数将生成不同的代码路径：
'''
print(f(1, 2))
print(f(1j, 2))
from numba import jit, int32
@jit(int32(int32,int32))
def f(x, y):
return x + y
'''
int32(int32, int32)是函数的签名。在这种情况下，相应的特化将由@jit装饰器编译，并且不允许其他专门化。如果您希望对编译器
选择的类型进行细粒度控制（例如，使用单精度浮点数），这将非常有用。
如果省略返回类型，例如通过写而不是 ，Numba将尝试为您推断它。函数签名也可以是字符串，您可以将
其中的几个作为列表传递;
'''
print(f(1, 2))
print(f(2**31, 2**31 + 1))
# 调用和内联其他函数
@jit
return np.interp(xp, [x1, x2], [y1, y2])
def complex_grid(xlim, ylim, nx, ny):
'''
returns a nx x ny grid of complex numbers
bounded by xlim and ylim ranges.
'''
x = np.linspace(xlim[0], xlim[1], nx)
y = np.linspace(ylim[0], ylim[1], ny)
xx, yy = np.meshgrid(x, y)
return xx + 1j*yy
@jit(int32(complex128, complex128, int32, float64, int32), nopython=True, cache=True)
def iterate(z, C, n, zmax, niter):
'''
Return the number of iteration
needed for the absolute value
of z to become greater than zmax
'''
zmax2 = zmax**2
for k in range(niter):
z = pow(z, n) + C
if z.imag**2 + z.real**2 > zmax2:
break
return k