def backward_pass(x, y, output, hidden_output, W_output):
output_error = -(y - output) # Calculate error
output_over_net = output*(1 - output) # Derivative of sigmoid function
sigmoid_on_error = cp.multiply(output_error, output_over_net) # Calculate the sigmoid function's affect on error
W_output = cp.transpose(W_output)
hidden_error = cp.dot(sigmoid_on_error, W_output) # Calculate the affect of output weights on hidden weights' error
hidden_over_net = hidden_output*(1 - hidden_output) # Derivative of sigmoid function
sigmoid_on_hidden_error = cp.multiply(hidden_error, hidden_over_net) # Calculate the sigmoid function's affect on error
# Correctly arrange matrices for calculations
x = cp.atleast_2d(x)
hidden_output = cp.atleast_2d(hidden_output)
x_transpose = cp.transpose(x)
hidden_output_transpose = cp.transpose(hidden_output)
sigmoid_on_hidden_error = sigmoid_on_hidden_error.reshape(1, sigmoid_on_hidden_error.size)
sigmoid_on_error = sigmoid_on_error.reshape(1, sigmoid_on_error.size)
# Calculate weight changes
W_hidden_c = cp.dot(x_transpose, sigmoid_on_hidden_error)
W_output_c = cp.dot(hidden_output_transpose, sigmoid_on_error)
# Calculate bias changes
B_hidden_c = sigmoid_on_hidden_error
B_output_c = sigmoid_on_error
return W_output_c, W_hidden_c, B_hidden_c, B_output_c
def __truediv__(self, other):
"""Point-wise division by another matrix, vector or scalar"""
if _util.isscalarlike(other):
dtype = self.dtype
if dtype == numpy.float32:
# Note: This is a work-around to make the output dtype the same
# as SciPy. It might be SciPy version dependent.
dtype = numpy.float64
dtype = cupy.result_type(dtype, other)
d = cupy.reciprocal(other, dtype=dtype)
return multiply_by_scalar(self, d)
elif _util.isdense(other):
other = cupy.atleast_2d(other)
check_shape_for_pointwise_op(self.shape, other.shape)
return self.todense() / other
elif base.isspmatrix(other):
# Note: If broadcasting is needed, an exception is raised here for
# compatibility with SciPy, as SciPy does not support broadcasting
# in the "sparse / sparse" case.
check_shape_for_pointwise_op(self.shape,
other.shape,
allow_broadcasting=False)
dtype = numpy.promote_types(self.dtype, other.dtype)
if dtype.char not in 'FD':
dtype = numpy.promote_types(numpy.float64, dtype)
# Note: The following implementation converts two sparse matrices
# into dense matrices and then performs a point-wise division,
# which can use lots of memory.
self_dense = self.todense().astype(dtype, copy=False)
return self_dense / other.todense()
raise NotImplementedError
def __init__(self, arg1, shape=None, dtype=None, copy=False):
if isinstance(arg1, tuple):
data, offsets = arg1
if shape is None:
raise ValueError('expected a shape argument')
else:
raise ValueError('unrecognized form for dia_matrix constructor')
data = cupy.array(data, dtype=dtype, copy=copy)
data = cupy.atleast_2d(data)
offsets = cupy.array(offsets, dtype='i', copy=copy)
offsets = cupy.atleast_1d(offsets)
if offsets.ndim != 1:
raise ValueError('offsets array must have rank 1')
if data.ndim != 2:
raise ValueError('data array must have rank 2')
if data.shape[0] != len(offsets):
raise ValueError(
'number of diagonals (%d) does not match the number of '
'offsets (%d)' % (data.shape[0], len(offsets)))
sorted_offsets = cupy.sort(offsets)
if (sorted_offsets[:-1] == sorted_offsets[1:]).any():
raise ValueError('offset array contains duplicate values')
self.data = data
self.offsets = offsets
self._shape = shape
def _maximum_minimum(self, other, cupy_op, op_name, dense_check):
if _util.isscalarlike(other):
other = cupy.asarray(other, dtype=self.dtype)
if dense_check(other):
dtype = self.dtype
# Note: This is a work-around to make the output dtype the same
# as SciPy. It might be SciPy version dependent.
if dtype == numpy.float32:
dtype = numpy.float64
elif dtype == numpy.complex64:
dtype = numpy.complex128
dtype = cupy.result_type(dtype, other)
other = other.astype(dtype, copy=False)
# Note: The computation steps below are different from SciPy.
new_array = cupy_op(self.todense(), other)
return csr_matrix(new_array)
else:
self.sum_duplicates()
new_data = cupy_op(self.data, other)
return csr_matrix((new_data, self.indices, self.indptr),
shape=self.shape,
dtype=self.dtype)
elif _util.isdense(other):
self.sum_duplicates()
other = cupy.atleast_2d(other)
return cupy_op(self.todense(), other)
elif isspmatrix_csr(other):
self.sum_duplicates()
other.sum_duplicates()
return binopt_csr(self, other, op_name)
raise NotImplementedError
def hilbert2(x, N=None):
"""
Compute the '2-D' analytic signal of `x`
Parameters
----------
x : array_like
2-D signal data.
N : int or tuple of two ints, optional
Number of Fourier components. Default is ``x.shape``
Returns
-------
xa : ndarray
Analytic signal of `x` taken along axes (0,1).
References
----------
.. [1] Wikipedia, "Analytic signal",
https://en.wikipedia.org/wiki/Analytic_signal
"""
x = atleast_2d(x)
if x.ndim > 2:
raise ValueError("x must be 2-D.")
if iscomplexobj(x):
raise ValueError("x must be real.")
if N is None:
N = x.shape
elif isinstance(N, int):
if N <= 0:
raise ValueError("N must be positive.")
N = (N, N)
elif len(N) != 2 or cp.any(cp.asarray(N) <= 0):
raise ValueError(
"When given as a tuple, N must hold exactly two positive integers"
)
Xf = fftpack.fft2(x, N, axes=(0, 1))
h1 = zeros(N[0], "d")
h2 = zeros(N[1], "d")
for p in range(2):
h = eval("h%d" % (p + 1))
N1 = N[p]
if N1 % 2 == 0:
h[0] = h[N1 // 2] = 1
h[1 : N1 // 2] = 2
else:
h[0] = 1
h[1 : (N1 + 1) // 2] = 2
exec("h%d = h" % (p + 1), globals(), locals())
h = h1[:, newaxis] * h2[newaxis, :]
k = x.ndim
while k > 2:
h = h[:, newaxis]
k -= 1
x = fftpack.ifft2(Xf * h, axes=(0, 1))
return x
def sample(self, n_samples=1, random_state=None):
"""
Generate random samples from the model.
Currently, this is implemented only for gaussian and tophat kernels,
and the Euclidean metric.
Parameters
----------
n_samples : int, default=1
Number of samples to generate.
random_state : int, cupy RandomState instance or None, default=None
Returns
-------
X : cupy array of shape (n_samples, n_features)
List of samples.
"""
if not hasattr(self, "X_"):
raise NotFittedError()
supported_kernels = ["gaussian", "tophat"]
if (self.kernel not in supported_kernels
or self.metric != "euclidean"):
raise NotImplementedError(
"Only {} kernels, and the euclidean"
" metric are supported.".format(supported_kernels))
if isinstance(random_state, cp.random.RandomState):
rng = random_state
else:
rng = cp.random.RandomState(random_state)
u = rng.uniform(0, 1, size=n_samples)
if self.sample_weight_ is None:
i = (u * self.X_.shape[0]).astype(np.int64)
else:
cumsum_weight = cp.cumsum(self.sample_weight_)
sum_weight = cumsum_weight[-1]
i = cp.searchsorted(cumsum_weight, u * sum_weight)
if self.kernel == "gaussian":
return cp.atleast_2d(rng.normal(self.X_[i], self.bandwidth))
elif self.kernel == "tophat":
# we first draw points from a d-dimensional normal distribution,
# then use an incomplete gamma function to map them to a uniform
# d-dimensional tophat distribution.
has_scipy(raise_if_unavailable=True)
dim = self.X_.shape[1]
X = rng.normal(size=(n_samples, dim))
s_sq = cp.einsum("ij,ij->i", X, X).get()
# do this on the CPU becaause we don't have
# a gammainc function readily available
correction = cp.array(
gammainc(0.5 * dim, 0.5 * s_sq)**(1.0 / dim) * self.bandwidth /
np.sqrt(s_sq))
return self.X_[i] + X * correction[:, np.newaxis]
def block_diag(*arrs):
"""Create a block diagonal matrix from provided arrays.
Given the inputs ``A``, ``B``, and ``C``, the output will have these
arrays arranged on the diagonal::
[A, 0, 0]
[0, B, 0]
[0, 0, C]
Args:
A, B, C, ... (cupy.ndarray): Input arrays. A 1-D array of length ``n``
is treated as a 2-D array with shape ``(1,n)``.
Returns:
(cupy.ndarray): Array with ``A``, ``B``, ``C``, ... on the diagonal.
Output has the same dtype as ``A``.
.. seealso:: :func:`scipy.linalg.block_diag`
"""
if not arrs:
return cupy.empty((1, 0))
# Convert to 2D and check
if len(arrs) == 1:
arrs = (cupy.atleast_2d(*arrs), )
else:
arrs = cupy.atleast_2d(*arrs)
if any(a.ndim != 2 for a in arrs):
bad = [k for k in range(len(arrs)) if arrs[k].ndim != 2]
raise ValueError('arguments in the following positions have dimension '
'greater than 2: {}'.format(bad))
shapes = tuple(a.shape for a in arrs)
shape = tuple(sum(x) for x in zip(*shapes))
dtype = cupy.find_common_type([a.dtype for a in arrs], [])
out = cupy.zeros(shape, dtype=dtype)
r, c = 0, 0
for arr in arrs:
rr, cc = arr.shape
out[r:r + rr, c:c + cc] = arr
r += rr
c += cc
return out
def _validate_sos(sos):
"""Helper to validate a SOS input"""
sos = cp.atleast_2d(sos)
if sos.ndim != 2:
raise ValueError("sos array must be 2D")
n_sections, m = sos.shape
if m != 6:
raise ValueError("sos array must be shape (n_sections, 6)")
if not (sos[:, 3] == 1).all():
raise ValueError("sos[:, 3] should be all ones")
return sos, n_sections
def __getitem__(self, key):
# For testing- Scipy >= 1.4.0 is needed to guarantee
# results match.
if scipy_available and numpy.lib.NumpyVersion(
scipy.__version__) < '1.4.0':
raise NotImplementedError(
"Sparse __getitem__() requires Scipy >= 1.4.0")
row, col = self._parse_indices(key)
# Dispatch to specialized methods.
if isinstance(row, _int_scalar_types):
if isinstance(col, _int_scalar_types):
return self._get_intXint(row, col)
elif isinstance(col, slice):
return self._get_intXslice(row, col)
elif col.ndim == 1:
return self._get_intXarray(row, col)
raise IndexError('index results in >2 dimensions')
elif isinstance(row, slice):
if isinstance(col, _int_scalar_types):
return self._get_sliceXint(row, col)
elif isinstance(col, slice):
if row == slice(None) and row == col:
return self.copy()
return self._get_sliceXslice(row, col)
elif col.ndim == 1:
return self._get_sliceXarray(row, col)
raise IndexError('index results in >2 dimensions')
elif row.ndim == 1:
if isinstance(col, _int_scalar_types):
return self._get_arrayXint(row, col)
elif isinstance(col, slice):
return self._get_arrayXslice(row, col)
else: # row.ndim == 2
if isinstance(col, _int_scalar_types):
return self._get_arrayXint(row, col)
elif isinstance(col, slice):
raise IndexError('index results in >2 dimensions')
elif row.shape[1] == 1 and (col.ndim == 1 or col.shape[0] == 1):
# special case for outer indexing
return self._get_columnXarray(row[:, 0], col.ravel())
# The only remaining case is inner (fancy) indexing
row, col = cupy.broadcast_arrays(row, col)
if row.shape != col.shape:
raise IndexError('number of row and column indices differ')
if row.size == 0:
return self.__class__(cupy.atleast_2d(row).shape, dtype=self.dtype)
return self._get_arrayXarray(row, col)
def aslinearoperator(A):
"""Return `A` as a LinearOperator.
Args:
A (array-like):
The input array to be converted to a `LinearOperator` object.
It may be any of the following types:
* :class:`cupy.ndarray`
* sparse matrix (e.g. ``csr_matrix``, ``coo_matrix``, etc.)
* :class:`cupyx.scipy.sparse.linalg.LinearOperator`
* object with ``.shape`` and ``.matvec`` attributes
Returns:
cupyx.scipy.sparse.linalg.LinearOperator: `LinearOperator` object
.. seealso:: :func:`scipy.sparse.aslinearoperator``
"""
if isinstance(A, LinearOperator):
return A
elif isinstance(A, cupy.ndarray):
if A.ndim > 2:
raise ValueError('array must have ndim <= 2')
A = cupy.atleast_2d(A)
return MatrixLinearOperator(A)
elif sparse.isspmatrix(A):
return MatrixLinearOperator(A)
else:
if hasattr(A, 'shape') and hasattr(A, 'matvec'):
rmatvec = None
rmatmat = None
dtype = None
if hasattr(A, 'rmatvec'):
rmatvec = A.rmatvec
if hasattr(A, 'rmatmat'):
rmatmat = A.rmatmat
if hasattr(A, 'dtype'):
dtype = A.dtype
return LinearOperator(A.shape,
A.matvec,
rmatvec=rmatvec,
rmatmat=rmatmat,
dtype=dtype)
else:
raise TypeError('type not understood')
def multiply(self, other):
"""Point-wise multiplication by another matrix, vector or scalar"""
if cupy.isscalar(other):
return multiply_by_scalar(self, other)
elif _util.isdense(other):
self.sum_duplicates()
other = cupy.atleast_2d(other)
return multiply_by_dense(self, other)
elif isspmatrix_csr(other):
self.sum_duplicates()
other.sum_duplicates()
return multiply_by_csr(self, other)
else:
msg = 'expected scalar, dense matrix/vector or csr matrix'
raise TypeError(msg)
def hilbert2(x, N=None):
"""
Compute the '2-D' analytic signal of `x`
Parameters
----------
x : array_like
2-D signal data.
N : int or tuple of two ints, optional
Number of Fourier components. Default is ``x.shape``
Returns
-------
xa : ndarray
Analytic signal of `x` taken along axes (0,1).
References
----------
.. [1] Wikipedia, "Analytic signal",
https://en.wikipedia.org/wiki/Analytic_signal
"""
x = cp.atleast_2d(x)
if x.ndim > 2:
raise ValueError("x must be 2-D.")
if cp.iscomplexobj(x):
raise ValueError("x must be real.")
if N is None:
N = x.shape
elif isinstance(N, int):
if N <= 0:
raise ValueError("N must be positive.")
N = (N, N)
elif len(N) != 2 or cp.any(cp.asarray(N) <= 0):
raise ValueError(
"When given as a tuple, N must hold exactly two positive integers")
Xf = cp.fft.fft2(x, N, axes=(0, 1))
h1, h2 = _hilbert2_kernel(size=N[1])
h = h1[:, cp.newaxis] * h2[cp.newaxis, :]
k = x.ndim
while k > 2:
h = h[:, cp.newaxis]
k -= 1
x = cp.fft.ifft2(Xf * h, axes=(0, 1))
return x
def vstack(tup):
"""Stacks arrays vertically.
If an input array has one dimension, then the array is treated as a
horizontal vector and stacked along the additional axis at the head.
Otherwise, the array is stacked along the first axis.
Args:
tup (sequence of arrays): Arrays to be stacked. Each array is converted
by :func:`cupy.atleast_2d` before stacking.
Returns:
cupy.ndarray: Stacked array.
.. seealso:: :func:`numpy.dstack`
"""
return concatenate(cupy.atleast_2d(*tup), 0)
def vstack(tup):
"""Stacks arrays vertically.
If an input array has one dimension, then the array is treated as a
horizontal vector and stacked along the additional axis at the head.
Otherwise, the array is stacked along the first axis.
Args:
tup (sequence of arrays): Arrays to be stacked. Each array is converted
by :func:`cupy.atleast_2d` before stacking.
Returns:
cupy.ndarray: Stacked array.
.. seealso:: :func:`numpy.dstack`
"""
return concatenate(cupy.atleast_2d(*tup), 0)
def __init__(self, arg1, shape=None, dtype=None, copy=False):
if _scipy_available and scipy.sparse.issparse(arg1):
x = arg1.todia()
data = x.data
offsets = x.offsets
shape = x.shape
dtype = x.dtype
copy = False
elif isinstance(arg1, tuple):
data, offsets = arg1
if shape is None:
raise ValueError('expected a shape argument')
else:
raise ValueError(
'unrecognized form for dia_matrix constructor')
data = cupy.array(data, dtype=dtype, copy=copy)
data = cupy.atleast_2d(data)
offsets = cupy.array(offsets, dtype='i', copy=copy)
offsets = cupy.atleast_1d(offsets)
if offsets.ndim != 1:
raise ValueError('offsets array must have rank 1')
if data.ndim != 2:
raise ValueError('data array must have rank 2')
if data.shape[0] != len(offsets):
raise ValueError(
'number of diagonals (%d) does not match the number of '
'offsets (%d)'
% (data.shape[0], len(offsets)))
sorted_offsets = cupy.sort(offsets)
if (sorted_offsets[:-1] == sorted_offsets[1:]).any():
raise ValueError('offset array contains duplicate values')
self.data = data
self.offsets = offsets
if not util.isshape(shape):
raise ValueError('invalid shape (must be a 2-tuple of int)')
self._shape = int(shape[0]), int(shape[1])
def subdivide_polygon(coords, degree=2, preserve_ends=False):
"""Subdivision of polygonal curves using B-Splines.
Note that the resulting curve is always within the convex hull of the
original polygon. Circular polygons stay closed after subdivision.
Parameters
----------
coords : (N, 2) array
Coordinate array.
degree : {1, 2, 3, 4, 5, 6, 7}, optional
Degree of B-Spline. Default is 2.
preserve_ends : bool, optional
Preserve first and last coordinate of non-circular polygon. Default is
False.
Returns
-------
coords : (M, 2) array
Subdivided coordinate array.
References
----------
.. [1] http://mrl.nyu.edu/publications/subdiv-course2000/coursenotes00.pdf
"""
if degree not in _SUBDIVISION_MASKS:
raise ValueError("Invalid B-Spline degree. Only degree 1 - 7 is "
"supported.")
circular = cp.all(coords[0, :] == coords[-1, :])
method = 'valid'
if circular:
# remove last coordinate because of wrapping
coords = coords[:-1, :]
# circular convolution by wrapping boundaries
method = 'same'
mask_even, mask_odd = _SUBDIVISION_MASKS[degree]
# divide by total weight
float_dtype = coords.dtype if coords.dtype.kind == 'f' else cp.float64
mask_even = cp.array(mask_even, float_dtype) / (2**degree)
mask_odd = cp.array(mask_odd, float_dtype) / (2**degree)
even = signal.convolve2d(coords.T,
cp.atleast_2d(mask_even),
mode=method,
boundary='wrap')
odd = signal.convolve2d(coords.T,
cp.atleast_2d(mask_odd),
mode=method,
boundary='wrap')
out = cp.empty((even.shape[1] + odd.shape[1], 2), dtype=float_dtype)
out[1::2] = even.T
out[::2] = odd.T
if circular:
# close polygon
out = cp.vstack([out, out[0, :]])
if preserve_ends and not circular:
out = cp.vstack([coords[0, :], out, coords[-1, :]])
return out
def mi_model_1d_gpu_gd(x, y, biascorrect=False, demeaned=False):
"""Mutual information between a Gaussian and a discrete variable in bits.
This method is based on ANOVA style model comparison.
I = mi_model_gd(x,y) returns the MI between the (possibly multidimensional)
Gaussian variable x and the discrete variable y.
Parameters
----------
x, y : array_like
Gaussian arrays of shape (n_epochs,) or (n_dimensions, n_epochs). y
must be an array of integers
biascorrect : bool | True
Specifies whether bias correction should be applied to the estimated MI
demeaned : bool | False
Specifies whether the input data already has zero mean (true if it has
been copula-normalized)
Returns
-------
i : float
Information shared by x and y (in bits)
"""
# Converting to cupy array
#x, y = cp.array(x), cp.array(y)
x, y = cp.atleast_2d(x), cp.squeeze(y)
if x.ndim > 2:
raise ValueError("x must be at most 2d")
if y.ndim > 1:
raise ValueError("only univariate discrete variables supported")
if not cp.issubdtype(y.dtype, cp.integer):
raise ValueError("y should be an integer array")
nvarx, ntrl = x.shape
ym = cp.unique(y)
if y.size != ntrl:
raise ValueError("number of trials do not match")
if not demeaned:
x = x - x.mean(axis=1)[:, cp.newaxis]
# class-conditional entropies
ntrl_y = cp.zeros(len(ym))
hcond = cp.zeros(len(ym))
for n_yi, yi in enumerate(ym):
idx = y == yi
xm = x[:, idx]
ntrl_y[n_yi] = xm.shape[1]
xm = xm - xm.mean(axis=1)[:, cp.newaxis]
cm = cp.dot(xm, xm.T) / float(ntrl_y[n_yi] - 1)
chcm = cp.linalg.cholesky(cm)
hcond[n_yi] = cp.sum(cp.log(cp.diagonal(chcm)))
# class weights
w = ntrl_y / float(ntrl)
# unconditional entropy from unconditional Gaussian fit
cx = cp.dot(x, x.T) / float(ntrl - 1)
chc = cp.linalg.cholesky(cx)
hunc = cp.sum(cp.log(cp.diagonal(chc))) # + c*nvarx
ln2 = cp.log(2)
if biascorrect:
vars = cp.arange(1, nvarx + 1)
psiterms = psi((ntrl - vars).astype(cp.float) / 2.) / 2.
dterm = (ln2 - cp.log(float(ntrl - 1))) / 2.
hunc = hunc - nvarx * dterm - psiterms.sum()
dterm = (ln2 - cp.log((ntrl_y - 1).astype(cp.float))) / 2.0
psiterms = cp.zeros(len(ym))
for vi in vars:
idx = ntrl_y - vi
psiterms = psiterms + psi(idx.astype(cp.float) / 2.)
hcond = hcond - nvarx * dterm - (psiterms / 2.)
# MI in bits
i = (hunc - cp.sum(w * hcond)) / ln2
return i
def cmi_1d_gpu_ggg(x, y, z, biascorrect=True, demeaned=False):
"""Conditional MI between two Gaussian variables conditioned on a third.
I = cmi_ggg(x,y,z) returns the CMI between two (possibly multidimensional)
Gaussian variables, x and y, conditioned on a third, z, with bias
correction.
Parameters
----------
x, y, z : array_like
Gaussians arrays of shape (n_epochs,) or (n_dimensions, n_epochs).
biascorrect : bool | True
Specifies whether bias correction should be applied to the estimated MI
demeaned : bool | False
Specifies whether the input data already has zero mean (true if it has
been copula-normalized)
Returns
-------
i : float
Information shared by x and y conditioned by z (in bits)
"""
x, y, z = cp.atleast_2d(x), cp.atleast_2d(y), cp.atleast_2d(z)
if x.ndim > 2 or y.ndim > 2 or z.ndim > 2:
raise ValueError("x, y and z must be at most 2d")
ntrl = x.shape[1]
nvarx = x.shape[0]
nvary = y.shape[0]
nvarz = z.shape[0]
nvaryz = nvary + nvarz
nvarxy = nvarx + nvary
nvarxz = nvarx + nvarz
nvarxyz = nvarx + nvaryz
if y.shape[1] != ntrl or z.shape[1] != ntrl:
raise ValueError("number of trials do not match")
# joint variable
xyz = cp.vstack((x, y, z))
if not demeaned:
xyz = xyz - xyz.mean(axis=1)[:, cp.newaxis]
cxyz = cp.dot(xyz, xyz.T) / float(ntrl - 1)
# submatrices of joint covariance
cz = cxyz[nvarxy:, nvarxy:]
cyz = cxyz[nvarx:, nvarx:]
cxz = cp.zeros((nvarxz, nvarxz))
cxz[:nvarx, :nvarx] = cxyz[:nvarx, :nvarx]
cxz[:nvarx, nvarx:] = cxyz[:nvarx, nvarxy:]
cxz[nvarx:, :nvarx] = cxyz[nvarxy:, :nvarx]
cxz[nvarx:, nvarx:] = cxyz[nvarxy:, nvarxy:]
chcz = cp.linalg.cholesky(cz)
chcxz = cp.linalg.cholesky(cxz)
chcyz = cp.linalg.cholesky(cyz)
chcxyz = cp.linalg.cholesky(cxyz)
# entropies in nats
# normalizations cancel for cmi
hz = cp.sum(cp.log(cp.diagonal(chcz)))
hxz = cp.sum(cp.log(cp.diagonal(chcxz)))
hyz = cp.sum(cp.log(cp.diagonal(chcyz)))
hxyz = cp.sum(cp.log(cp.diagonal(chcxyz)))
ln2 = cp.log(2)
if biascorrect:
psiterms = psi(
(ntrl - cp.arange(1, nvarxyz + 1)).astype(cp.float) / 2.) / 2.
dterm = (ln2 - cp.log(ntrl - 1.)) / 2.
hz = hz - nvarz * dterm - psiterms[:nvarz].sum()
hxz = hxz - nvarxz * dterm - psiterms[:nvarxz].sum()
hyz = hyz - nvaryz * dterm - psiterms[:nvaryz].sum()
hxyz = hxyz - nvarxyz * dterm - psiterms[:nvarxyz].sum()
# MI in bits
i = (hxz + hyz - hxyz - hz) / ln2
return i
def mi_1d_gpu_gg(x, y, biascorrect=True, demeaned=False):
"""Mutual information (MI) between two Gaussian variables in bits.
This is the GPU variant of the m1_1d_gg function, using CuPy
I = mi_gg(x,y) returns the MI between two (possibly multidimensional)
Gaussian variables, x and y, with bias correction.
Parameters
----------
x, y : array_like
Gaussian arrays of shape (n_epochs,) or (n_dimensions, n_epochs)
biascorrect : bool | True
Specifies whether bias correction should be applied to the estimated MI
demeaned : bool | False
Specifies whether the input data already has zero mean (true if it has
been copula-normalized)
Returns
-------
i : float
Information shared by x and y (in bits)
"""
x, y = cp.atleast_2d(x), cp.atleast_2d(y)
if (x.ndim > 2) or (y.ndim > 2):
raise ValueError("x and y must be at most 2d")
nvarx, ntrl = x.shape
nvary = y.shape[0]
nvarxy = nvarx + nvary
if y.shape[1] != ntrl:
raise ValueError("number of trials do not match")
# joint variable
xy = cp.vstack((x, y))
if not demeaned:
xy = xy - xy.mean(axis=1)[:, cp.newaxis]
cxy = cp.dot(xy, xy.T) / float(ntrl - 1)
# submatrices of joint covariance
cx = cxy[:nvarx, :nvarx]
cy = cxy[nvarx:, nvarx:]
chcxy = cp.linalg.cholesky(cxy)
chcx = cp.linalg.cholesky(cx)
chcy = cp.linalg.cholesky(cy)
# entropies in nats
# normalizations cancel for mutual information
hx = cp.sum(cp.log(cp.diagonal(chcx)))
hy = cp.sum(cp.log(cp.diagonal(chcy)))
hxy = cp.sum(cp.log(cp.diagonal(chcxy)))
ln2 = cp.log(2)
if biascorrect:
psiterms = psi(
(ntrl - cp.arange(1, nvarxy + 1)).astype(cp.float) / 2.) / 2.
dterm = (ln2 - cp.log(ntrl - 1.)) / 2.
hx = hx - nvarx * dterm - psiterms[:nvarx].sum()
hy = hy - nvary * dterm - psiterms[:nvary].sum()
hxy = hxy - nvarxy * dterm - psiterms[:nvarxy].sum()
# MI in bits
i = (hx + hy - hxy) / ln2
return i
def estimate_local_log_joint_mark_intensity(decoding_marks,
encoding_marks,
mark_std,
occupancy,
mean_rate,
decoding_position=None,
encoding_position=None,
position_std=None,
max_mark_value=6000,
set_diag_zero=False,
position_distance=None,
sample_weights=None):
"""
Parameters
----------
decoding_marks : ndarray, shape (n_decoding_spikes, n_features)
encoding_marks : ndarray, shape (n_encoding_spikes, n_features)
mark_std : float or ndarray, shape (n_features,)
occupancy : ndarray, shape (n_position_bins,)
mean_rate : float
place_bin_centers : ndarray, shape (n_position_bins, n_position_dims)
encoding_positions : ndarray, shape (n_decoding_spikes, n_position_dims)
position_std : float
is_track_interior : None or ndarray, shape (n_position_bins,)
max_mark_value : int
set_diag_zero : bool
Returns
-------
log_joint_mark_intensity : ndarray, shape (n_decoding_spikes, n_position_bins)
"""
n_encoding_spikes, n_marks = encoding_marks.shape
n_decoding_spikes = decoding_marks.shape[0]
if sample_weights is None:
sample_weights = cp.ones((1, n_decoding_spikes), dtype=cp.float32)
denominator = n_encoding_spikes
else:
sample_weights = cp.atleast_2d(sample_weights)
denominator = cp.sum(sample_weights)
mark_distance = cp.ones((n_decoding_spikes, n_encoding_spikes),
dtype=cp.float32) * sample_weights
for mark_ind in range(n_marks):
mark_distance *= normal_pdf_integer_lookup(
cp.expand_dims(decoding_marks[:, mark_ind], axis=1),
cp.expand_dims(encoding_marks[:, mark_ind], axis=0),
std=mark_std,
max_value=max_mark_value)
if set_diag_zero:
diag_ind = cp.diag_indices_from(mark_distance)
mark_distance[diag_ind] = 0.0
if position_distance is None:
position_distance = estimate_position_distance(
decoding_position, encoding_position,
position_std).astype(cp.float32)
return cp.asnumpy(
estimate_log_intensity(
cp.sum(mark_distance * position_distance.T, axis=1) /
denominator, occupancy, mean_rate))
def __init__(self, arg1, shape=None, dtype=None, copy=False):
if shape is not None and len(shape) != 2:
raise ValueError(
'Only two-dimensional sparse arrays are supported.')
if base.issparse(arg1):
x = arg1.asformat(self.format)
data = x.data
row = x.row
col = x.col
if arg1.format != self.format:
# When formats are differnent, all arrays are already copied
copy = False
if shape is None:
shape = arg1.shape
self.has_canonical_format = x.has_canonical_format
elif _util.isshape(arg1):
m, n = arg1
m, n = int(m), int(n)
data = cupy.zeros(0, dtype if dtype else 'd')
row = cupy.zeros(0, dtype='i')
col = cupy.zeros(0, dtype='i')
# shape and copy argument is ignored
shape = (m, n)
copy = False
self.has_canonical_format = True
elif _scipy_available and scipy.sparse.issparse(arg1):
# Convert scipy.sparse to cupyx.scipy.sparse
x = arg1.tocoo()
data = cupy.array(x.data)
row = cupy.array(x.row, dtype='i')
col = cupy.array(x.col, dtype='i')
copy = False
if shape is None:
shape = arg1.shape
self.has_canonical_format = x.has_canonical_format
elif isinstance(arg1, tuple) and len(arg1) == 2:
try:
data, (row, col) = arg1
except (TypeError, ValueError):
raise TypeError('invalid input format')
if not (base.isdense(data) and data.ndim == 1 and base.isdense(row)
and row.ndim == 1 and base.isdense(col) and col.ndim == 1):
raise ValueError('row, column, and data arrays must be 1-D')
if not (len(data) == len(row) == len(col)):
raise ValueError(
'row, column, and data array must all be the same length')
self.has_canonical_format = False
elif base.isdense(arg1):
if arg1.ndim > 2:
raise TypeError('expected dimension <= 2 array or matrix')
dense = cupy.atleast_2d(arg1)
row, col = dense.nonzero()
data = dense[row, col]
shape = dense.shape
self.has_canonical_format = True
else:
raise TypeError('invalid input format')
if dtype is None:
dtype = data.dtype
else:
dtype = numpy.dtype(dtype)
if dtype != 'f' and dtype != 'd' and dtype != 'F' and dtype != 'D':
raise ValueError('Only float32, float64, complex64 and complex128'
' are supported')
data = data.astype(dtype, copy=copy)
row = row.astype('i', copy=copy)
col = col.astype('i', copy=copy)
if shape is None:
if len(row) == 0 or len(col) == 0:
raise ValueError(
'cannot infer dimensions from zero sized index arrays')
shape = (int(row.max()) + 1, int(col.max()) + 1)
if len(data) > 0:
if row.max() >= shape[0]:
raise ValueError('row index exceeds matrix dimensions')
if col.max() >= shape[1]:
raise ValueError('column index exceeds matrix dimensions')
if row.min() < 0:
raise ValueError('negative row index found')
if col.min() < 0:
raise ValueError('negative column index found')
sparse_data._data_matrix.__init__(self, data)
self.row = row
self.col = col
if not _util.isshape(shape):
raise ValueError('invalid shape (must be a 2-tuple of int)')
self._shape = int(shape[0]), int(shape[1])
def nullspace_gpu(A, tol=1e-13):
A = cp.atleast_2d(A)
u, s, vh =svd_gpu(A)
nnz = (s >= tol).sum()
ns = vh[nnz:].conj().T
return ns
