def sample_function(x, y, z):
return cupy.square(cupy.add(x, y))
def __radd__(self, other):
return cupy.add(other, self)
def g(x, y, z):
x += z
cupy.add(x, y, z)
return z
def g(x, y, z):
a = x
a += y
cupy.add(x, y, z)
def map_coordinates(input, coordinates, output=None, order=None,
mode='constant', cval=0.0, prefilter=True):
"""Map the input array to new coordinates by interpolation.
The array of coordinates is used to find, for each point in the output, the
corresponding coordinates in the input. The value of the input at those
coordinates is determined by spline interpolation of the requested order.
The shape of the output is derived from that of the coordinate array by
dropping the first axis. The values of the array along the first axis are
the coordinates in the input array at which the output value is found.
Args:
input (cupy.ndarray): The input array.
coordinates (array_like): The coordinates at which ``input`` is
evaluated.
output (cupy.ndarray or ~cupy.dtype): The array in which to place the
output, or the dtype of the returned array.
order (int): The order of the spline interpolation. If it is not given,
order 1 is used. It is different from :mod:`scipy.ndimage` and can
change in the future. Currently it supports only order 0 and 1.
mode (str): Points outside the boundaries of the input are filled
according to the given mode (``'constant'``, ``'nearest'``,
``'mirror'`` or ``'opencv'``). Default is ``'constant'``.
cval (scalar): Value used for points outside the boundaries of
the input if ``mode='constant'`` or ``mode='opencv'``. Default is
0.0
prefilter (bool): It is not used yet. It just exists for compatibility
with :mod:`scipy.ndimage`.
Returns:
cupy.ndarray:
The result of transforming the input. The shape of the output is
derived from that of ``coordinates`` by dropping the first axis.
.. seealso:: :func:`scipy.ndimage.map_coordinates`
"""
_check_parameter('map_coordinates', order, mode)
if mode == 'opencv' or mode == '_opencv_edge':
input = cupy.pad(input, [(1, 1)] * input.ndim, 'constant',
constant_values=cval)
coordinates = cupy.add(coordinates, 1)
mode = 'constant'
ret = _get_output(output, input, coordinates.shape[1:])
if mode == 'nearest':
for i in range(input.ndim):
coordinates[i] = coordinates[i].clip(0, input.shape[i] - 1)
elif mode == 'mirror':
for i in range(input.ndim):
length = input.shape[i] - 1
if length == 0:
coordinates[i] = 0
else:
coordinates[i] = cupy.remainder(coordinates[i], 2 * length)
coordinates[i] = 2 * cupy.minimum(
coordinates[i], length) - coordinates[i]
if input.dtype.kind in 'iu':
input = input.astype(cupy.float32)
if order == 0:
out = input[tuple(cupy.rint(coordinates).astype(cupy.int32))]
else:
coordinates_floor = cupy.floor(coordinates).astype(cupy.int32)
coordinates_ceil = coordinates_floor + 1
sides = []
for i in range(input.ndim):
# TODO(mizuno): Use array_equal after it is implemented
if cupy.all(coordinates[i] == coordinates_floor[i]):
sides.append([0])
else:
sides.append([0, 1])
out = cupy.zeros(coordinates.shape[1:], dtype=input.dtype)
if input.dtype in (cupy.float64, cupy.complex128):
weight = cupy.empty(coordinates.shape[1:], dtype=cupy.float64)
else:
weight = cupy.empty(coordinates.shape[1:], dtype=cupy.float32)
for side in itertools.product(*sides):
weight.fill(1)
ind = []
for i in range(input.ndim):
if side[i] == 0:
ind.append(coordinates_floor[i])
weight *= coordinates_ceil[i] - coordinates[i]
else:
ind.append(coordinates_ceil[i])
weight *= coordinates[i] - coordinates_floor[i]
out += input[ind] * weight
del weight
if mode == 'constant':
mask = cupy.zeros(coordinates.shape[1:], dtype=cupy.bool_)
for i in range(input.ndim):
mask += coordinates[i] < 0
mask += coordinates[i] > input.shape[i] - 1
out[mask] = cval
del mask
if ret.dtype.kind in 'iu':
out = cupy.rint(out)
ret[:] = out
return ret
def g(x, y, z):
a = x
a += y
cupy.add(x, y, z)
def sample_function(x, y, z):
return cupy.square(cupy.add(x, y))
def gradient_function(x, y, w):
return (1.0 / M) * (cp.add(
cp.add(cp.dot(cp.dot(x.T, x), w), -1 * cp.dot(x.T, y)), 0.001 * w))
def make_blobs(n_samples=100,
n_features=2,
centers=None,
cluster_std=1.0,
center_box=(-10.0, 10.0),
shuffle=True,
random_state=None,
return_centers=False,
order='F',
dtype='float32'):
"""Generate isotropic Gaussian blobs for clustering.
Parameters
----------
n_samples : int or array-like, optional (default=100)
If int, it is the total number of points equally divided among
clusters.
If array-like, each element of the sequence indicates
the number of samples per cluster.
n_features : int, optional (default=2)
The number of features for each sample.
centers : int or array of shape [n_centers, n_features], optional
(default=None)
The number of centers to generate, or the fixed center locations.
If n_samples is an int and centers is None, 3 centers are generated.
If n_samples is array-like, centers must be
either None or an array of length equal to the length of n_samples.
cluster_std : float or sequence of floats, optional (default=1.0)
The standard deviation of the clusters.
center_box : pair of floats (min, max), optional (default=(-10.0, 10.0))
The bounding box for each cluster center when centers are
generated at random.
shuffle : boolean, optional (default=True)
Shuffle the samples.
random_state : int, RandomState instance, default=None
Determines random number generation for dataset creation. Pass an int
for reproducible output across multiple function calls.
return_centers : bool, optional (default=False)
If True, then return the centers of each cluster
order: str, optional (default='F')
The order of the generated samples
dtype : str, optional (default='float32')
Dtype of the generated samples
Returns
-------
X : device array of shape [n_samples, n_features]
The generated samples.
y : device array of shape [n_samples]
The integer labels for cluster membership of each sample.
centers : device array, shape [n_centers, n_features]
The centers of each cluster. Only returned if
``return_centers=True``.
Examples
--------
>>> from sklearn.datasets import make_blobs
>>> X, y = make_blobs(n_samples=10, centers=3, n_features=2,
... random_state=0)
>>> print(X.shape)
(10, 2)
>>> y
array([0, 0, 1, 0, 2, 2, 2, 1, 1, 0])
>>> X, y = make_blobs(n_samples=[3, 3, 4], centers=None, n_features=2,
... random_state=0)
>>> print(X.shape)
(10, 2)
>>> y
array([0, 1, 2, 0, 2, 2, 2, 1, 1, 0])
See also
--------
make_classification: a more intricate variant
"""
generator = _create_rs_generator(random_state=random_state)
centers, n_centers = _get_centers(generator, centers, center_box,
n_samples, n_features, dtype)
# stds: if cluster_std is given as list, it must be consistent
# with the n_centers
if (hasattr(cluster_std, "__len__") and len(cluster_std) != n_centers):
raise ValueError("Length of `clusters_std` not consistent with "
"number of centers. Got centers = {} "
"and cluster_std = {}".format(centers, cluster_std))
if isinstance(cluster_std, numbers.Real):
cluster_std = cp.full(len(centers), cluster_std)
if isinstance(n_samples, Iterable):
n_samples_per_center = n_samples
else:
n_samples_per_center = [int(n_samples // n_centers)] * n_centers
for i in range(n_samples % n_centers):
n_samples_per_center[i] += 1
X = cp.zeros(n_samples * n_features, dtype=dtype)
X = X.reshape((n_samples, n_features), order=order)
y = cp.zeros(n_samples, dtype=dtype)
if shuffle:
proba_samples_per_center = np.array(n_samples_per_center) / np.sum(
n_samples_per_center)
np_seed = int(generator.randint(n_samples, size=1))
np.random.seed(np_seed)
shuffled_sample_indices = cp.array(
np.random.choice(n_centers,
n_samples,
replace=True,
p=proba_samples_per_center))
for i, (n, std) in enumerate(zip(n_samples_per_center, cluster_std)):
center_indices = cp.where(shuffled_sample_indices == i)
y[center_indices[0]] = i
X_k = generator.normal(scale=std,
size=(len(center_indices[0]), n_features),
dtype=dtype)
# NOTE: Adding the loc explicitly as cupy has a bug
# when calling generator.normal with an array for loc.
# cupy.random.normal, however, works with the same
# arguments
cp.add(X_k, centers[i], out=X_k)
X[center_indices[0], :] = X_k
else:
stop = 0
for i, (n, std) in enumerate(zip(n_samples_per_center, cluster_std)):
start, stop = stop, stop + n_samples_per_center[i]
y[start:stop] = i
X_k = generator.normal(scale=std,
size=(n, n_features),
dtype=dtype)
cp.add(X_k, centers[i], out=X_k)
X[start:stop, :] = X_k
if return_centers:
return X, y, centers
else:
return X, y
def least_square_regular(X, Y):
return cp.dot(
cp.dot(cp.linalg.inv(cp.add(cp.dot(X.T, X), lambd * cp.eye(M, k=0))),
X.T), Y)
def loss(x, y, w):
diff = cp.add(cp.dot(x, w), -1 * y)
loss = 1.0 / (2 * data_size) * cp.dot(diff.T, diff)
return loss[0, 0]
def srrf(
images: np.array,
mag: float = 5,
radius: float = 0.4,
sample_n: int = 12,
do_gw: bool = False,
do_iw: bool = True,
sofi_delay: int = 1,
sofi_order: int = 2,
avg_every_n: int = 1,
do_drift_correction: bool = False,
signal=None,
) -> cp.array:
# designating memory pool for async data loading (deprecated)
# ban memory pool for memory safety
cp.cuda.set_allocator(None)
cp.cuda.set_pinned_memory_allocator(None)
# clean memory pool
# cp.get_default_memory_pool().free_all_blocks()
# pinned_memory_pool.free_all_blocks()
# preparing
frame_n, h, w = shape = images.shape[:3]
batch_size = get_batch_size(frame_n, shape, mag)
if batch_size is 0:
raise ValueError("Image shape is too large to process!")
if batch_size * avg_every_n > frame_n:
if avg_every_n < frame_n:
batch_size = frame_n // avg_every_n * avg_every_n
else:
avg_every_n = frame_n
batch_size = frame_n
warnings.warn(
"avg_every_n is greater than total number of frames. All frames will be averaged."
)
else:
batch_size = batch_size * avg_every_n
result = cp.zeros((int(h * mag), int(w * mag)), dtype=cp.float64)
gradientX = cp.zeros((ceil(batch_size / avg_every_n), h, w),
dtype=cp.float32)
gradientY = cp.zeros((ceil(batch_size / avg_every_n), h, w),
dtype=cp.float32)
gradientX_zoomed = cp.zeros(
(ceil(batch_size / avg_every_n), int(h * mag), int(w * mag)),
dtype=cp.float32)
gradientY_zoomed = cp.zeros(
(ceil(batch_size / avg_every_n), int(h * mag), int(w * mag)),
dtype=cp.float32)
image_mat_zoomed = cp.empty(
(ceil(batch_size / avg_every_n), int(h * mag), int(w * mag)),
dtype=cp.float32)
radiality = cp.empty(
(ceil(batch_size / avg_every_n), int(h * mag), int(w * mag)),
dtype=cp.float32)
trac_mat = cp.empty((int(h * mag), int(w * mag)), dtype=cp.float64)
drift_correction = drift_correction_wrapper(
images) if do_drift_correction else None
catmullrom_zoom = catmullrom_zoom_wrapper(images, mag,
ceil(batch_size / avg_every_n))
calculate_radiality = calculate_radiality_wrapper(images, sample_n, mag,
radius, do_gw, do_iw)
# init CUDA streams
sm_n = 2 # number of stream managers used in graphic card.
streams = [cp.cuda.Stream(non_blocking=True) for _ in range(sm_n)]
mats = [
cp.empty(images[:batch_size].shape, images[:batch_size].dtype)
for _ in range(sm_n)
]
for i, image_mat in enumerate(split_image_sequence(images, batch_size)):
# send signal for gui progress bar
if signal is not None:
signal.emit(i * batch_size * 100 / frame_n)
# dispatch the task of copying image mat from CPU to GPU asynchronously
# select 2 streams
index_next = i % sm_n
index_current = (i - 1) % sm_n
# Use next stream to load image data in advance
if image_mat is not None:
np_mat = to_pinned_memory(image_mat)
mats[index_next].set(np_mat, stream=streams[index_next])
# skip the first time(the copy is not finished yet)
if i is 0:
continue
# Use the current stream to process the image mat on GPU
image_mat = mats[index_current]
with streams[index_current]:
print("dispatching %d/%d" % (i * batch_size, frame_n))
# average every n images to reduce the calculation. Optional
if avg_every_n != 1:
image_mat = avg_every_n_frames(image_mat, avg_every_n)
calculate_gradient(image_mat, gradientX, gradientY)
# 这里梯度也必须是原始图像的梯度插值得到。如果直接使用放大后的图像计算梯度，会受到插值算法的影响出现方格状图案
drift = drift_correction(
image_mat
) if do_drift_correction and image_mat.shape[0] > 1 else None
catmullrom_zoom(image_mat, image_mat_zoomed, drift)
catmullrom_zoom(gradientX, gradientX_zoomed, drift)
catmullrom_zoom(gradientY, gradientY_zoomed, drift)
# calculate srrf radiality in every frame
calculate_radiality(image_mat_zoomed, gradientX_zoomed,
gradientY_zoomed, radiality)
# do TRAC calculation (sofi)
calculate_trac(radiality, trac_mat, sofi_delay, sofi_order)
cp.add(result, trac_mat, out=result)
streams[index_current].synchronize()
# The next stream will be started only if the current stream is done
# This is to protect the data on the next stream, otherwise the data will be
# overwritten and the result will be wrong
stop_event = streams[index_current].record()
streams[index_next].wait_event(stop_event)
[stream.synchronize() for stream in streams]
return cp.asnumpy(result)
import numexpr as ne
import scipy as sp
import pyculib as pc
import cupy as cp
#init
N = 1000
A = np.ones((N, N), dtype=np.float32)
B = np.ones((N, N), dtype=np.float32)
C = np.ones((N, N), dtype=np.float32)
del A2, B2
A2 = cp.array(A)
B2 = cp.array(B)
C_list = []
C2 = cp.add(A2, B2)
C_list.append(C2)
#sigmoid
#注：使用exp(n)比e**n快
#numpy
def sigmoid0(a):
return 1. / (1. + np.exp(-1. * a))
#numexpr
def sigmoid3(a):
return ne.evaluate("1./(1.+exp(-1.*a))")
def logisticmap_calc(x, p, mu):
return cp.mod(cp.multiply(mu, cp.multiply(x, cp.add(x, 1))), p)
def func(x, y, z):
return cupy.add(x, y, out=z)
def map_coordinates(
input,
coordinates,
output=None,
order=3,
mode="constant",
cval=0.0,
prefilter=True,
*,
allow_float32=True,
):
"""Map the input array to new coordinates by interpolation.
The array of coordinates is used to find, for each point in the output, the
corresponding coordinates in the input. The value of the input at those
coordinates is determined by spline interpolation of the requested order.
The shape of the output is derived from that of the coordinate array by
dropping the first axis. The values of the array along the first axis are
the coordinates in the input array at which the output value is found.
Args:
input (cupy.ndarray): The input array.
coordinates (array_like): The coordinates at which ``input`` is
evaluated.
output (cupy.ndarray or ~cupy.dtype): The array in which to place the
output, or the dtype of the returned array.
order (int): The order of the spline interpolation. Must be between 0
and 5.
mode (str): Points outside the boundaries of the input are filled
according to the given mode (``'constant'``, ``'nearest'``,
``'mirror'`` or ``'opencv'``). Default is ``'constant'``.
cval (scalar): Value used for points outside the boundaries of
the input if ``mode='constant'`` or ``mode='opencv'``. Default is
0.0
prefilter (bool): It is not used yet. It just exists for compatibility
with :mod:`scipy.ndimage`.
Returns:
cupy.ndarray:
The result of transforming the input. The shape of the output is
derived from that of ``coordinates`` by dropping the first axis.
Notes
-----
This implementation handles boundary modes 'wrap' and 'reflect' correctly,
while SciPy does not (at least as of release 1.4.0). So, if comparing to
SciPy, some disagreement near the borders may occur unless
``mode == 'mirror'``.
For ``order > 1`` with ``prefilter == True``, the spline prefilter boundary
conditions are implemented correctly only for modes 'mirror', 'reflect'
and 'wrap'. For the other modes ('constant' and 'nearest'), there is some
innacuracy near the boundary of the array.
.. seealso:: :func:`scipy.ndimage.map_coordinates`
"""
_check_parameter("map_coordinates", order, mode)
if mode == "opencv" or mode == "_opencv_edge":
input = cupy.pad(input, [(1, 1)] * input.ndim,
"constant",
constant_values=cval)
coordinates = cupy.add(coordinates, 1)
mode = "constant"
ret = _get_output(output, input, coordinates.shape[1:])
integer_output = ret.dtype.kind in "iu"
if input.dtype.kind in "iu":
input = input.astype(cupy.float32)
if coordinates.dtype.kind in "iu":
if order > 1:
# order > 1 (spline) kernels require floating-point coordinates
if allow_float32:
coord_dtype = cupy.promote_types(coordinates.dtype,
cupy.float32)
else:
coord_dtype = cupy.promote_types(coordinates.dtype,
cupy.float64)
coordinates = coordinates.astype(coord_dtype)
elif coordinates.dtype.kind != "f":
raise ValueError("coordinates should have floating point dtype")
else:
if allow_float32:
coord_dtype = cupy.promote_types(coordinates.dtype, cupy.float32)
else:
coord_dtype = cupy.promote_types(coordinates.dtype, cupy.float64)
coordinates = coordinates.astype(coord_dtype, copy=False)
if prefilter and order > 1:
padded, npad = _prepad_for_spline_filter(input, mode, cval)
filtered = spline_filter(
padded,
order,
output=input.dtype,
mode=mode,
allow_float32=allow_float32,
)
else:
npad = 0
filtered = input
large_int = max(_misc._prod(input.shape), coordinates.shape[0]) > 1 << 31
kern = _get_map_kernel(
filtered.ndim,
large_int,
yshape=coordinates.shape,
mode=mode,
cval=cval,
order=order,
integer_output=integer_output,
nprepad=npad,
)
# kernel assumes C-contiguous arrays
if not filtered.flags.c_contiguous:
filtered = cupy.ascontiguousarray(filtered)
if not coordinates.flags.c_contiguous:
coordinates = cupy.ascontiguousarray(coordinates)
kern(filtered, coordinates, ret)
return ret
def func(x, y, z, u, v):
cupy.add(x, y, out=z)
cupy.subtract(z, x, out=u)
cupy.multiply(z, x, out=v)
return u
def _convert(image, dtype, force_copy=False, uniform=False):
"""
Convert an image to the requested data-type.
Warnings are issued in case of precision loss, or when negative values
are clipped during conversion to unsigned integer types (sign loss).
Floating point values are expected to be normalized and will be clipped
to the range [0.0, 1.0] or [-1.0, 1.0] when converting to unsigned or
signed integers respectively.
Numbers are not shifted to the negative side when converting from
unsigned to signed integer types. Negative values will be clipped when
converting to unsigned integers.
Parameters
----------
image : ndarray
Input image.
dtype : dtype
Target data-type.
force_copy : bool, optional
Force a copy of the data, irrespective of its current dtype.
uniform : bool, optional
Uniformly quantize the floating point range to the integer range.
By default (uniform=False) floating point values are scaled and
rounded to the nearest integers, which minimizes back and forth
conversion errors.
.. versionchanged :: 0.15
``_convert`` no longer warns about possible precision or sign
information loss. See discussions on these warnings at:
https://github.com/scikit-image/scikit-image/issues/2602
https://github.com/scikit-image/scikit-image/issues/543#issuecomment-208202228
https://github.com/scikit-image/scikit-image/pull/3575
References
----------
.. [1] DirectX data conversion rules.
https://msdn.microsoft.com/en-us/library/windows/desktop/dd607323%28v=vs.85%29.aspx
.. [2] Data Conversions. In "OpenGL ES 2.0 Specification v2.0.25",
pp 7-8. Khronos Group, 2010.
.. [3] Proper treatment of pixels as integers. A.W. Paeth.
In "Graphics Gems I", pp 249-256. Morgan Kaufmann, 1990.
.. [4] Dirty Pixels. J. Blinn. In "Jim Blinn's corner: Dirty Pixels",
pp 47-57. Morgan Kaufmann, 1998.
"""
image = cp.asarray(image)
dtypeobj_in = image.dtype
if dtype is cp.floating:
dtypeobj_out = cp.dtype("float64")
else:
dtypeobj_out = cp.dtype(dtype)
dtype_in = dtypeobj_in.type
dtype_out = dtypeobj_out.type
kind_in = dtypeobj_in.kind
kind_out = dtypeobj_out.kind
itemsize_in = dtypeobj_in.itemsize
itemsize_out = dtypeobj_out.itemsize
# Below, we do an `issubdtype` check. Its purpose is to find out
# whether we can get away without doing any image conversion. This happens
# when:
#
# - the output and input dtypes are the same or
# - when the output is specified as a type, and the input dtype
# is a subclass of that type (e.g. `cp.floating` will allow
# `float32` and `float64` arrays through)
if cp.issubdtype(dtype_in, cp.obj2sctype(dtype)):
if force_copy:
image = image.copy()
return image
if not (dtype_in in _supported_types and dtype_out in _supported_types):
raise ValueError("Can not convert from {} to {}.".format(
dtypeobj_in, dtypeobj_out))
if kind_in in "ui":
imin_in = cp.iinfo(dtype_in).min
imax_in = cp.iinfo(dtype_in).max
if kind_out in "ui":
imin_out = cp.iinfo(dtype_out).min
imax_out = cp.iinfo(dtype_out).max
# any -> binary
if kind_out == "b":
return image > dtype_in(dtype_range[dtype_in][1] / 2)
# binary -> any
if kind_in == "b":
result = image.astype(dtype_out)
if kind_out != "f":
result *= dtype_out(dtype_range[dtype_out][1])
return result
# float -> any
if kind_in == "f":
if kind_out == "f":
# float -> float
return image.astype(dtype_out)
if cp.min(image) < -1.0 or cp.max(image) > 1.0:
raise ValueError("Images of type float must be between -1 and 1.")
# floating point -> integer
# use float type that can represent output integer type
computation_type = _dtype_itemsize(itemsize_out, dtype_in, cp.float32,
cp.float64)
if not uniform:
if kind_out == "u":
image_out = cp.multiply(image,
imax_out,
dtype=computation_type)
else:
image_out = cp.multiply(image, (imax_out - imin_out) / 2,
dtype=computation_type)
image_out -= 1.0 / 2.0
cp.rint(image_out, out=image_out)
cp.clip(image_out, imin_out, imax_out, out=image_out)
elif kind_out == "u":
image_out = cp.multiply(image,
imax_out + 1,
dtype=computation_type)
cp.clip(image_out, 0, imax_out, out=image_out)
else:
image_out = cp.multiply(image, (imax_out - imin_out + 1.0) / 2.0,
dtype=computation_type)
cp.floor(image_out, out=image_out)
cp.clip(image_out, imin_out, imax_out, out=image_out)
return image_out.astype(dtype_out)
# signed/unsigned int -> float
if kind_out == "f":
# use float type that can exactly represent input integers
computation_type = _dtype_itemsize(itemsize_in, dtype_out, cp.float32,
cp.float64)
if kind_in == "u":
# using cp.divide or cp.multiply doesn't copy the data
# until the computation time
image = cp.multiply(image, 1.0 / imax_in, dtype=computation_type)
# DirectX uses this conversion also for signed ints
# if imin_in:
# cp.maximum(image, -1.0, out=image)
else:
image = cp.add(image, 0.5, dtype=computation_type)
image *= 2 / (imax_in - imin_in)
return cp.asarray(image, dtype_out)
# unsigned int -> signed/unsigned int
if kind_in == "u":
if kind_out == "i":
# unsigned int -> signed int
image = _scale(image, 8 * itemsize_in, 8 * itemsize_out - 1)
return image.view(dtype_out)
else:
# unsigned int -> unsigned int
return _scale(image, 8 * itemsize_in, 8 * itemsize_out)
# signed int -> unsigned int
if kind_out == "u":
image = _scale(image, 8 * itemsize_in - 1, 8 * itemsize_out)
result = cp.empty(image.shape, dtype_out)
cp.maximum(image, 0, out=result, dtype=image.dtype, casting="unsafe")
return result
# signed int -> signed int
if itemsize_in > itemsize_out:
return _scale(image, 8 * itemsize_in - 1, 8 * itemsize_out - 1)
image = image.astype(_dtype_bits("i", itemsize_out * 8))
image -= imin_in
image = _scale(image, 8 * itemsize_in, 8 * itemsize_out, copy=False)
image += imin_out
return image.astype(dtype_out)
def g(x, y, z):
a = x
a += y
cupy.add(x, y, z)
return y
def run_cupy(price, strike, t, rate, vol):
import cupy as cp
# Allocate temporary arrays
size = len(price)
tmp = cp.empty(size, dtype='float64')
vol_sqrt = cp.empty(size, dtype='float64')
rsig = cp.empty(size, dtype='float64')
d1 = cp.empty(size, dtype='float64')
d2 = cp.empty(size, dtype='float64')
# Outputs
call = cp.empty(size, dtype='float64')
put = cp.empty(size, dtype='float64')
# Transfer inputs to the GPU
price = cp.array(price)
strike = cp.array(strike)
t = cp.array(t)
rate = cp.array(rate)
vol = cp.array(vol)
# Create an erf function that doesn't exist
cp_erf = cp.core.create_ufunc('cupyx_scipy_erf', ('f->f', 'd->d'),
'out0 = erf(in0)',
doc='''Error function.
.. seealso:: :meth:`scipy.special.erf`
''')
# Begin computation
c05 = 3.0
c10 = 1.5
invsqrt2 = 1.0 / math.sqrt(2.0)
cp.multiply(vol, vol, out=rsig)
cp.multiply(rsig, c05, out=rsig)
cp.add(rsig, rate, out=rsig)
cp.sqrt(t, out=vol_sqrt)
cp.multiply(vol_sqrt, vol, out=vol_sqrt)
cp.multiply(rsig, t, out=tmp)
cp.divide(price, strike, out=d1)
cp.log2(d1, out=d1)
cp.add(d1, tmp, out=d1)
cp.divide(d1, vol_sqrt, out=d1)
cp.subtract(d1, vol_sqrt, out=d2)
# d1 = c05 + c05 * erf(d1 * invsqrt2)
cp.multiply(d1, invsqrt2, out=d1)
cp_erf(d1, out=d1)
cp.multiply(d1, c05, out=d1)
cp.add(d1, c05, out=d1)
# d2 = c05 + c05 * erf(d2 * invsqrt2)
cp.multiply(d2, invsqrt2, out=d2)
cp_erf(d2, out=d2)
cp.multiply(d2, c05, out=d2)
cp.add(d2, c05, out=d2)
# Reuse existing buffers
e_rt = vol_sqrt
tmp2 = rsig
# e_rt = exp(-rate * t)
cp.multiply(rate, -1.0, out=e_rt)
cp.multiply(e_rt, t, out=e_rt)
cp.exp(e_rt, out=e_rt)
# call = price * d1 - e_rt * strike * d2
#
# tmp = price * d1
# tmp2 = e_rt * strike * d2
# call = tmp - tmp2
cp.multiply(price, d1, out=tmp)
cp.multiply(e_rt, strike, out=tmp2)
cp.multiply(tmp2, d2, out=tmp2)
cp.subtract(tmp, tmp2, out=call)
# put = e_rt * strike * (c10 - d2) - price * (c10 - d1)
# tmp = e_rt * strike
# tmp2 = (c10 - d2)
# put = tmp - tmp2
# tmp = c10 - d1
# tmp = price * tmp
# put = put - tmp
cp.multiply(e_rt, strike, out=tmp)
cp.subtract(c10, d2, out=tmp2)
cp.multiply(tmp, tmp2, out=put)
cp.subtract(c10, d1, out=tmp)
cp.multiply(price, tmp, out=tmp)
cp.subtract(put, tmp, out=put)
# Transfer outputs back to CPU
call = cp.asnumpy(call)
put = cp.asnumpy(put)
return call, put
def g(x, y, z):
x += z
cupy.add(x, y, z)
return z
def __add__(self, other):
return cupy.add(self, other)
def g(x, y, z):
a = x
a += y
cupy.add(x, y, z)
return y
def map_coordinates(input,
coordinates,
output=None,
order=3,
mode='constant',
cval=0.0,
prefilter=True):
"""Map the input array to new coordinates by interpolation.
The array of coordinates is used to find, for each point in the output, the
corresponding coordinates in the input. The value of the input at those
coordinates is determined by spline interpolation of the requested order.
The shape of the output is derived from that of the coordinate array by
dropping the first axis. The values of the array along the first axis are
the coordinates in the input array at which the output value is found.
Args:
input (cupy.ndarray): The input array.
coordinates (array_like): The coordinates at which ``input`` is
evaluated.
output (cupy.ndarray or ~cupy.dtype): The array in which to place the
output, or the dtype of the returned array.
order (int): The order of the spline interpolation, default is 3. Must
be in the range 0-5.
mode (str): Points outside the boundaries of the input are filled
according to the given mode (``'constant'``, ``'nearest'``,
``'mirror'``, ``'reflect'``, ``'wrap'``, ``'grid-mirror'``,
``'grid-wrap'``, ``'grid-constant'`` or ``'opencv'``).
cval (scalar): Value used for points outside the boundaries of
the input if ``mode='constant'`` or ``mode='opencv'``. Default is
0.0
prefilter (bool): It is not used yet. It just exists for compatibility
with :mod:`scipy.ndimage`.
Returns:
cupy.ndarray:
The result of transforming the input. The shape of the output is
derived from that of ``coordinates`` by dropping the first axis.
.. seealso:: :func:`scipy.ndimage.map_coordinates`
"""
_check_parameter('map_coordinates', order, mode)
if mode == 'opencv' or mode == '_opencv_edge':
input = cupy.pad(input, [(1, 1)] * input.ndim,
'constant',
constant_values=cval)
coordinates = cupy.add(coordinates, 1)
mode = 'constant'
ret = _util._get_output(output, input, coordinates.shape[1:])
integer_output = ret.dtype.kind in 'iu'
_util._check_cval(mode, cval, integer_output)
if input.dtype.kind in 'iu':
input = input.astype(cupy.float32)
coordinates = _check_coordinates(coordinates, order)
filtered, nprepad = _filter_input(input, prefilter, mode, cval, order)
large_int = max(_prod(input.shape), coordinates.shape[0]) > 1 << 31
kern = _interp_kernels._get_map_kernel(input.ndim,
large_int,
yshape=coordinates.shape,
mode=mode,
cval=cval,
order=order,
integer_output=integer_output,
nprepad=nprepad)
kern(filtered, coordinates, ret)
return ret
