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dict
q35400
KullbackLeibler.gradient
train
def gradient(self): r"""Gradient of the KL functional. The gradient of `KullbackLeibler` with ``prior`` :math:`g` is given as .. math:: \nabla F(x) = 1 - \frac{g}{x}. The gradient is not defined in points where one or more components are non-positive. ...
python
{ "resource": "" }
q35401
KullbackLeiblerCrossEntropyConvexConj._call
train
def _call(self, x): """Return the value in the point ``x``.""" if self.prior is None: tmp = self.domain.element((np.exp(x) - 1)).inner(self.domain.one()) else: tmp = (self.prior * (np.exp(x) - 1)).inner(self.domain.one()) return tmp
python
{ "resource": "" }
q35402
SeparableSum._call
train
def _call(self, x): """Return the separable sum evaluated in ``x``.""" return sum(fi(xi) for xi, fi in zip(x, self.functionals))
python
{ "resource": "" }
q35403
SeparableSum.convex_conj
train
def convex_conj(self): """The convex conjugate functional. Convex conjugate distributes over separable sums, so the result is simply the separable sum of the convex conjugates. """ convex_conjs = [func.convex_conj for func in self.functionals] return SeparableSum(*convex...
python
{ "resource": "" }
q35404
QuadraticForm.convex_conj
train
def convex_conj(self): r"""The convex conjugate functional of the quadratic form. Notes ----- The convex conjugate of the quadratic form :math:`<x, Ax> + <b, x> + c` is given by .. math:: (<x, Ax> + <b, x> + c)^* (x) = <(x - b), A^-1 (x - b)> - c...
python
{ "resource": "" }
q35405
NuclearNorm._asarray
train
def _asarray(self, vec): """Convert ``x`` to an array. Here the indices are changed such that the "outer" indices come last in order to have the access order as `numpy.linalg.svd` needs it. This is the inverse of `_asvector`. """ shape = self.domain[0, 0].shape + self.p...
python
{ "resource": "" }
q35406
NuclearNorm._asvector
train
def _asvector(self, arr): """Convert ``arr`` to a `domain` element. This is the inverse of `_asarray`. """ result = moveaxis(arr, [-2, -1], [0, 1]) return self.domain.element(result)
python
{ "resource": "" }
q35407
NuclearNorm.proximal
train
def proximal(self): """Return the proximal operator. Raises ------ NotImplementedError if ``outer_exp`` is not 1 or ``singular_vector_exp`` is not 1, 2 or infinity """ if self.outernorm.exponent != 1: raise NotImplementedError('`proxim...
python
{ "resource": "" }
q35408
NuclearNorm.convex_conj
train
def convex_conj(self): """Convex conjugate of the nuclear norm. The convex conjugate is the indicator function on the unit ball of the dual norm where the dual norm is obtained by taking the conjugate exponent of both the outer and singular vector exponents. """ return I...
python
{ "resource": "" }
q35409
IndicatorNuclearNormUnitBall.convex_conj
train
def convex_conj(self): """Convex conjugate of the unit ball indicator of the nuclear norm. The convex conjugate is the dual nuclear norm where the dual norm is obtained by taking the conjugate exponent of both the outer and singular vector exponents. """ return NuclearNo...
python
{ "resource": "" }
q35410
Huber.convex_conj
train
def convex_conj(self): """The convex conjugate""" if isinstance(self.domain, ProductSpace): norm = GroupL1Norm(self.domain, 2) else: norm = L1Norm(self.domain) return FunctionalQuadraticPerturb(norm.convex_conj, quadratic...
python
{ "resource": "" }
q35411
TheanoOperator.make_node
train
def make_node(self, x): """Create a node for the computation graph. Parameters ---------- x : `theano.tensor.var.TensorVariable` Input to the node. Returns ------- node : `theano.gof.graph.Apply` Node for the Theano expression graph. Its ...
python
{ "resource": "" }
q35412
TheanoOperator.perform
train
def perform(self, node, inputs, output_storage): """Evaluate this node's computation. Parameters ---------- node : `theano.gof.graph.Apply` The node of this Op in the computation graph. inputs : 1-element list of arrays Contains an array (usually `numpy.n...
python
{ "resource": "" }
q35413
TheanoOperator.infer_shape
train
def infer_shape(self, node, input_shapes): """Return a list of output shapes based on ``input_shapes``. This method is optional. It allows to compute the shape of the output without having to evaluate. Parameters ---------- node : `theano.gof.graph.Apply` Th...
python
{ "resource": "" }
q35414
TheanoOperator.R_op
train
def R_op(self, inputs, eval_points): """Apply the adjoint of the Jacobian at ``inputs`` to ``eval_points``. This is the symbolic counterpart of ODL's :: op.derivative(x).adjoint(v) See `grad` for its usage. Parameters ---------- inputs : 1-element list of ...
python
{ "resource": "" }
q35415
reciprocal_grid
train
def reciprocal_grid(grid, shift=True, axes=None, halfcomplex=False): """Return the reciprocal of the given regular grid. This function calculates the reciprocal (Fourier/frequency space) grid for a given regular grid defined by the nodes:: x[k] = x[0] + k * s, where ``k = (k[0], ..., k[d-1])`...
python
{ "resource": "" }
q35416
realspace_grid
train
def realspace_grid(recip_grid, x0, axes=None, halfcomplex=False, halfcx_parity='even'): """Return the real space grid from the given reciprocal grid. Given a reciprocal grid:: xi[j] = xi[0] + j * sigma, with a multi-index ``j = (j[0], ..., j[d-1])`` in the range ``0 <= j < ...
python
{ "resource": "" }
q35417
dft_preprocess_data
train
def dft_preprocess_data(arr, shift=True, axes=None, sign='-', out=None): """Pre-process the real-space data before DFT. This function multiplies the given data with the separable function:: p(x) = exp(+- 1j * dot(x - x[0], xi[0])) where ``x[0]`` and ``xi[0]`` are the minimum coodinates of ...
python
{ "resource": "" }
q35418
_interp_kernel_ft
train
def _interp_kernel_ft(norm_freqs, interp): """Scaled FT of a one-dimensional interpolation kernel. For normalized frequencies ``-1/2 <= xi <= 1/2``, this function returns:: sinc(pi * xi)**k / sqrt(2 * pi) where ``k=1`` for 'nearest' and ``k=2`` for 'linear' interpolation. Parameters ...
python
{ "resource": "" }
q35419
dft_postprocess_data
train
def dft_postprocess_data(arr, real_grid, recip_grid, shift, axes, interp, sign='-', op='multiply', out=None): """Post-process the Fourier-space data after DFT. This function multiplies the given data with the separable function:: q(xi) = exp(+- 1j * dot(x[0], xi)) * s * ph...
python
{ "resource": "" }
q35420
reciprocal_space
train
def reciprocal_space(space, axes=None, halfcomplex=False, shift=True, **kwargs): """Return the range of the Fourier transform on ``space``. Parameters ---------- space : `DiscreteLp` Real space whose reciprocal is calculated. It must be uniformly discretized. ax...
python
{ "resource": "" }
q35421
_initialize_if_needed
train
def _initialize_if_needed(): """Initialize ``TENSOR_SPACE_IMPLS`` if not already done.""" global IS_INITIALIZED, TENSOR_SPACE_IMPLS if not IS_INITIALIZED: # pkg_resources has long import time from pkg_resources import iter_entry_points for entry_point in iter_entry_points(group='odl....
python
{ "resource": "" }
q35422
tensor_space_impl
train
def tensor_space_impl(impl): """Tensor space class corresponding to the given impl name. Parameters ---------- impl : str Name of the implementation, see `tensor_space_impl_names` for the full list. Returns ------- tensor_space_impl : type Class inheriting from `Ten...
python
{ "resource": "" }
q35423
steepest_descent
train
def steepest_descent(f, x, line_search=1.0, maxiter=1000, tol=1e-16, projection=None, callback=None): r"""Steepest descent method to minimize an objective function. General implementation of steepest decent (also known as gradient decent) for solving .. math:: \min f(x) ...
python
{ "resource": "" }
q35424
adam
train
def adam(f, x, learning_rate=1e-3, beta1=0.9, beta2=0.999, eps=1e-8, maxiter=1000, tol=1e-16, callback=None): r"""ADAM method to minimize an objective function. General implementation of ADAM for solving .. math:: \min f(x) where :math:`f` is a differentiable functional. The alg...
python
{ "resource": "" }
q35425
_approx_equal
train
def _approx_equal(x, y, eps): """Test if elements ``x`` and ``y`` are approximately equal. ``eps`` is a given absolute tolerance. """ if x.space != y.space: return False if x is y: return True try: return x.dist(y) <= eps except NotImplementedError: try: ...
python
{ "resource": "" }
q35426
get_data_dir
train
def get_data_dir(): """Get the data directory.""" base_odl_dir = os.environ.get('ODL_HOME', expanduser(join('~', '.odl'))) data_home = join(base_odl_dir, 'datasets') if not exists(data_home): os.makedirs(data_home) return data_home
python
{ "resource": "" }
q35427
get_data
train
def get_data(filename, subset, url): """Get a dataset with from a url with local caching. Parameters ---------- filename : str Name of the file, for caching. subset : str To what subset the file belongs (e.g. 'ray_transform'). Each subset is saved in a separate subfolder. ...
python
{ "resource": "" }
q35428
forward_backward_pd
train
def forward_backward_pd(x, f, g, L, h, tau, sigma, niter, callback=None, **kwargs): r"""The forward-backward primal-dual splitting algorithm. The algorithm minimizes the sum of several convex functionals composed with linear operators:: min_x f(x) + sum_i g_i(L_i x) + h(x) ...
python
{ "resource": "" }
q35429
samples
train
def samples(*sets): """Generate samples from the given sets using their ``examples`` method. Parameters ---------- set1, ..., setN : `Set` instance Set(s) from which to generate the samples. Returns ------- samples : `generator` Generator that yields tuples of examples from...
python
{ "resource": "" }
q35430
cuboid
train
def cuboid(space, min_pt=None, max_pt=None): """Rectangular cuboid. Parameters ---------- space : `DiscreteLp` Space in which the phantom should be created. min_pt : array-like of shape ``(space.ndim,)``, optional Lower left corner of the cuboid. If ``None`` is given, a quarter ...
python
{ "resource": "" }
q35431
defrise
train
def defrise(space, nellipses=8, alternating=False, min_pt=None, max_pt=None): """Phantom with regularily spaced ellipses. This phantom is often used to verify cone-beam algorithms. Parameters ---------- space : `DiscreteLp` Space in which the phantom should be created, must be 2- or ...
python
{ "resource": "" }
q35432
defrise_ellipses
train
def defrise_ellipses(ndim, nellipses=8, alternating=False): """Ellipses for the standard Defrise phantom in 2 or 3 dimensions. Parameters ---------- ndim : {2, 3} Dimension of the space for the ellipses/ellipsoids. nellipses : int, optional Number of ellipses. If more ellipses are u...
python
{ "resource": "" }
q35433
indicate_proj_axis
train
def indicate_proj_axis(space, scale_structures=0.5): """Phantom indicating along which axis it is projected. The number (n) of rectangles in a parallel-beam projection along a main axis (0, 1, or 2) indicates the projection to be along the (n-1)the dimension. Parameters ---------- space : ...
python
{ "resource": "" }
q35434
_getshapes_2d
train
def _getshapes_2d(center, max_radius, shape): """Calculate indices and slices for the bounding box of a disk.""" index_mean = shape * center index_radius = max_radius / 2.0 * np.array(shape) # Avoid negative indices min_idx = np.maximum(np.floor(index_mean - index_radius), 0).astype(int) max_id...
python
{ "resource": "" }
q35435
_ellipse_phantom_2d
train
def _ellipse_phantom_2d(space, ellipses): """Create a phantom of ellipses in 2d space. Parameters ---------- space : `DiscreteLp` Uniformly discretized space in which the phantom should be generated. If ``space.shape`` is 1 in an axis, a corresponding slice of the phantom is cre...
python
{ "resource": "" }
q35436
ellipsoid_phantom
train
def ellipsoid_phantom(space, ellipsoids, min_pt=None, max_pt=None): """Return a phantom given by ellipsoids. Parameters ---------- space : `DiscreteLp` Space in which the phantom should be created, must be 2- or 3-dimensional. If ``space.shape`` is 1 in an axis, a corresponding ...
python
{ "resource": "" }
q35437
smooth_cuboid
train
def smooth_cuboid(space, min_pt=None, max_pt=None, axis=0): """Cuboid with smooth variations. Parameters ---------- space : `DiscreteLp` Discretized space in which the phantom is supposed to be created. min_pt : array-like of shape ``(space.ndim,)``, optional Lower left corner of th...
python
{ "resource": "" }
q35438
tgv_phantom
train
def tgv_phantom(space, edge_smoothing=0.2): """Piecewise affine phantom. This phantom is taken from [Bre+2010] and includes both linearly varying regions and sharp discontinuities. It is designed to work well with Total Generalized Variation (TGV) type regularization. Parameters ---------- ...
python
{ "resource": "" }
q35439
print_objective
train
def print_objective(x): """Calculate the objective value and prints it.""" value = 0 for minp, maxp in rectangles: x_proj = np.minimum(np.maximum(x, minp), maxp) value += (x - x_proj).norm() print('Point = [{:.4f}, {:.4f}], Value = {:.4f}'.format(x[0], x[1], value))
python
{ "resource": "" }
q35440
sparse_meshgrid
train
def sparse_meshgrid(*x): """Make a sparse `meshgrid` by adding empty dimensions. Parameters ---------- x1,...,xN : `array-like` Input arrays to turn into sparse meshgrid vectors. Returns ------- meshgrid : tuple of `numpy.ndarray`'s Sparse coordinate vectors representing an...
python
{ "resource": "" }
q35441
uniform_grid_fromintv
train
def uniform_grid_fromintv(intv_prod, shape, nodes_on_bdry=True): """Return a grid from sampling an interval product uniformly. The resulting grid will by default include ``intv_prod.min_pt`` and ``intv_prod.max_pt`` as grid points. If you want a subdivision into equally sized cells with grid points in ...
python
{ "resource": "" }
q35442
uniform_grid
train
def uniform_grid(min_pt, max_pt, shape, nodes_on_bdry=True): """Return a grid from sampling an implicit interval product uniformly. Parameters ---------- min_pt : float or sequence of float Vectors of lower ends of the intervals in the product. max_pt : float or sequence of float Ve...
python
{ "resource": "" }
q35443
RectGrid.ndim
train
def ndim(self): """Number of dimensions of the grid.""" try: return self.__ndim except AttributeError: ndim = len(self.coord_vectors) self.__ndim = ndim return ndim
python
{ "resource": "" }
q35444
RectGrid.shape
train
def shape(self): """Number of grid points per axis.""" try: return self.__shape except AttributeError: shape = tuple(len(vec) for vec in self.coord_vectors) self.__shape = shape return shape
python
{ "resource": "" }
q35445
RectGrid.size
train
def size(self): """Total number of grid points.""" # Since np.prod(()) == 1.0 we need to handle that by ourselves return (0 if self.shape == () else int(np.prod(self.shape, dtype='int64')))
python
{ "resource": "" }
q35446
RectGrid.min
train
def min(self, **kwargs): """Return `min_pt`. Parameters ---------- kwargs For duck-typing with `numpy.amin` See Also -------- max odl.set.domain.IntervalProd.min Examples -------- >>> g = RectGrid([1, 2, 5], [-2, 1.5,...
python
{ "resource": "" }
q35447
RectGrid.max
train
def max(self, **kwargs): """Return `max_pt`. Parameters ---------- kwargs For duck-typing with `numpy.amax` See Also -------- min odl.set.domain.IntervalProd.max Examples -------- >>> g = RectGrid([1, 2, 5], [-2, 1.5,...
python
{ "resource": "" }
q35448
RectGrid.stride
train
def stride(self): """Step per axis between neighboring points of a uniform grid. If the grid contains axes that are not uniform, ``stride`` has a ``NaN`` entry. For degenerate (length 1) axes, ``stride`` has value ``0.0``. Returns ------- stride : numpy.array ...
python
{ "resource": "" }
q35449
RectGrid.approx_equals
train
def approx_equals(self, other, atol): """Test if this grid is equal to another grid. Parameters ---------- other : Object to be tested atol : float Allow deviations up to this number in absolute value per vector entry. Returns ...
python
{ "resource": "" }
q35450
RectGrid.approx_contains
train
def approx_contains(self, other, atol): """Test if ``other`` belongs to this grid up to a tolerance. Parameters ---------- other : `array-like` or float The object to test for membership in this grid atol : float Allow deviations up to this number in abso...
python
{ "resource": "" }
q35451
RectGrid.is_subgrid
train
def is_subgrid(self, other, atol=0.0): """Return ``True`` if this grid is a subgrid of ``other``. Parameters ---------- other : `RectGrid` The other grid which is supposed to contain this grid atol : float, optional Allow deviations up to this number in ...
python
{ "resource": "" }
q35452
RectGrid.insert
train
def insert(self, index, *grids): """Return a copy with ``grids`` inserted before ``index``. The given grids are inserted (as a block) into ``self``, yielding a new grid whose number of dimensions is the sum of the numbers of dimensions of all involved grids. Note that no changes...
python
{ "resource": "" }
q35453
RectGrid.points
train
def points(self, order='C'): """All grid points in a single array. Parameters ---------- order : {'C', 'F'}, optional Axis ordering in the resulting point array. Returns ------- points : `numpy.ndarray` The shape of the array is ``size x ...
python
{ "resource": "" }
q35454
RectGrid.corner_grid
train
def corner_grid(self): """Return a grid with only the corner points. Returns ------- cgrid : `RectGrid` Grid with size 2 in non-degenerate dimensions and 1 in degenerate ones Examples -------- >>> g = RectGrid([0, 1], [-1, 0, 2]) ...
python
{ "resource": "" }
q35455
PartialDerivative._call
train
def _call(self, x, out=None): """Calculate partial derivative of ``x``.""" if out is None: out = self.range.element() # TODO: this pipes CUDA arrays through NumPy. Write native operator. with writable_array(out) as out_arr: finite_diff(x.asarray(), axis=self.axis...
python
{ "resource": "" }
q35456
Gradient._call
train
def _call(self, x, out=None): """Calculate the spatial gradient of ``x``.""" if out is None: out = self.range.element() x_arr = x.asarray() ndim = self.domain.ndim dx = self.domain.cell_sides for axis in range(ndim): with writable_array(out[axis]...
python
{ "resource": "" }
q35457
Divergence._call
train
def _call(self, x, out=None): """Calculate the divergence of ``x``.""" if out is None: out = self.range.element() ndim = self.range.ndim dx = self.range.cell_sides tmp = np.empty(out.shape, out.dtype, order=out.space.default_order) with writable_array(out) a...
python
{ "resource": "" }
q35458
Laplacian._call
train
def _call(self, x, out=None): """Calculate the spatial Laplacian of ``x``.""" if out is None: out = self.range.zero() else: out.set_zero() x_arr = x.asarray() out_arr = out.asarray() tmp = np.empty(out.shape, out.dtype, order=out.space.default_ord...
python
{ "resource": "" }
q35459
divide_1Darray_equally
train
def divide_1Darray_equally(ind, nsub): """Divide an array into equal chunks to be used for instance in OSEM. Parameters ---------- ind : ndarray input array nsubsets : int number of subsets to be divided into Returns ------- sub2ind : list list of indices for ea...
python
{ "resource": "" }
q35460
total_variation
train
def total_variation(domain, grad=None): """Total variation functional. Parameters ---------- domain : odlspace domain of TV functional grad : gradient operator, optional Gradient operator of the total variation functional. This may be any linear operator and thereby generali...
python
{ "resource": "" }
q35461
fgp_dual
train
def fgp_dual(p, data, alpha, niter, grad, proj_C, proj_P, tol=None, **kwargs): """Computes a solution to the ROF problem with the fast gradient projection algorithm. Parameters ---------- p : np.array dual initial variable data : np.array noisy data / proximal point alpha : ...
python
{ "resource": "" }
q35462
TotalVariationNonNegative.proximal
train
def proximal(self, sigma): """Prox operator of TV. It allows the proximal step length to be a vector of positive elements. Examples -------- Check that the proximal operator is the identity for sigma=0 >>> import odl.contrib.solvers.spdhg as spdhg, odl, numpy as np ...
python
{ "resource": "" }
q35463
_fields_from_table
train
def _fields_from_table(spec_table, id_key): """Read a specification and return a list of fields. The given specification is assumed to be in `reST grid table format <http://docutils.sourceforge.net/docs/user/rst/quickref.html#tables>`_. Parameters ---------- spec_table : str Specif...
python
{ "resource": "" }
q35464
header_fields_from_table
train
def header_fields_from_table(spec_table, keys, dtype_map): """Convert the specification table to a standardized format. The specification table is assumed to be in `reST grid table format <http://docutils.sourceforge.net/docs/user/rst/quickref.html#tables>`_. It must have the following 5 columns: ...
python
{ "resource": "" }
q35465
FileReaderRawBinaryWithHeader.header_size
train
def header_size(self): """Size of `file`'s header in bytes. The size of the header is determined from `header`. If this is not possible (i.e., before the header has been read), 0 is returned. """ if not self.header: return 0 # Determine header size by findin...
python
{ "resource": "" }
q35466
FileReaderRawBinaryWithHeader.read_header
train
def read_header(self): """Read the header from `file`. The header is also stored in the `header` attribute. Returns ------- header : `OrderedDict` Header from `file`, stored in an ordered dictionary, where each entry has the following form:: ...
python
{ "resource": "" }
q35467
FileReaderRawBinaryWithHeader.read_data
train
def read_data(self, dstart=None, dend=None): """Read data from `file` and return it as Numpy array. Parameters ---------- dstart : int, optional Offset in bytes of the data field. By default, it is taken to be the header size as determined from reading the header...
python
{ "resource": "" }
q35468
FileWriterRawBinaryWithHeader.write_header
train
def write_header(self): """Write `header` to `file`. See Also -------- write_data """ for properties in self.header.values(): value = properties['value'] offset_bytes = int(properties['offset']) self.file.seek(offset_bytes) ...
python
{ "resource": "" }
q35469
RosenbrockFunctional.gradient
train
def gradient(self): """Gradient operator of the Rosenbrock functional.""" functional = self c = self.scale class RosenbrockGradient(Operator): """The gradient operator of the Rosenbrock functional.""" def __init__(self): """Initialize a new inst...
python
{ "resource": "" }
q35470
normalized_scalar_param_list
train
def normalized_scalar_param_list(param, length, param_conv=None, keep_none=True, return_nonconv=False): """Return a list of given length from a scalar parameter. The typical use case is when a single value or a sequence of values is accepted as input. This function makes a ...
python
{ "resource": "" }
q35471
normalized_index_expression
train
def normalized_index_expression(indices, shape, int_to_slice=False): """Enable indexing with almost Numpy-like capabilities. Implements the following features: - Usage of general slices and sequences of slices - Conversion of `Ellipsis` into an adequate number of ``slice(None)`` objects - Fe...
python
{ "resource": "" }
q35472
normalized_nodes_on_bdry
train
def normalized_nodes_on_bdry(nodes_on_bdry, length): """Return a list of 2-tuples of bool from the input parameter. This function is intended to normalize a ``nodes_on_bdry`` parameter that can be given as a single boolean (global) or as a sequence (per axis). Each entry of the sequence can either be a...
python
{ "resource": "" }
q35473
normalized_axes_tuple
train
def normalized_axes_tuple(axes, ndim): """Return a tuple of ``axes`` converted to positive integers. This function turns negative entries into equivalent positive ones according to standard Python indexing "from the right". Parameters ---------- axes : int or sequence of ints Single in...
python
{ "resource": "" }
q35474
safe_int_conv
train
def safe_int_conv(number): """Safely convert a single number to integer.""" try: return int(np.array(number).astype(int, casting='safe')) except TypeError: raise ValueError('cannot safely convert {} to integer'.format(number))
python
{ "resource": "" }
q35475
astra_cpu_forward_projector
train
def astra_cpu_forward_projector(vol_data, geometry, proj_space, out=None): """Run an ASTRA forward projection on the given data using the CPU. Parameters ---------- vol_data : `DiscreteLpElement` Volume data to which the forward projector is applied geometry : `Geometry` Geometry de...
python
{ "resource": "" }
q35476
astra_cpu_back_projector
train
def astra_cpu_back_projector(proj_data, geometry, reco_space, out=None): """Run an ASTRA back-projection on the given data using the CPU. Parameters ---------- proj_data : `DiscreteLpElement` Projection data to which the back-projector is applied geometry : `Geometry` Geometry defin...
python
{ "resource": "" }
q35477
_default_call_out_of_place
train
def _default_call_out_of_place(op, x, **kwargs): """Default out-of-place evaluation. Parameters ---------- op : `Operator` Operator to call x : ``op.domain`` element Point in which to call the operator. kwargs: Optional arguments to the operator. Returns -------...
python
{ "resource": "" }
q35478
_function_signature
train
def _function_signature(func): """Return the signature of a callable as a string. Parameters ---------- func : callable Function whose signature to extract. Returns ------- sig : string Signature of the function. """ if sys.version_info.major > 2: # Python 3...
python
{ "resource": "" }
q35479
Operator.norm
train
def norm(self, estimate=False, **kwargs): """Return the operator norm of this operator. If this operator is non-linear, this should be the Lipschitz constant. Parameters ---------- estimate : bool If true, estimate the operator norm. By default, it is estimated ...
python
{ "resource": "" }
q35480
OperatorSum.derivative
train
def derivative(self, x): """Return the operator derivative at ``x``. The derivative of a sum of two operators is equal to the sum of the derivatives. Parameters ---------- x : `domain` `element-like` Evaluation point of the derivative """ if ...
python
{ "resource": "" }
q35481
OperatorComp.derivative
train
def derivative(self, x): """Return the operator derivative. The derivative of the operator composition follows the chain rule: ``OperatorComp(left, right).derivative(y) == OperatorComp(left.derivative(right(y)), right.derivative(y))`` Parameters -------...
python
{ "resource": "" }
q35482
_indent
train
def _indent(x): """Indent a string by 4 characters.""" lines = x.splitlines() for i, line in enumerate(lines): lines[i] = ' ' + line return '\n'.join(lines)
python
{ "resource": "" }
q35483
ProductSpace.shape
train
def shape(self): """Total spaces per axis, computed recursively. The recursion ends at the fist level that does not have a shape. Examples -------- >>> r2, r3 = odl.rn(2), odl.rn(3) >>> pspace = odl.ProductSpace(r2, r3) >>> pspace.shape (2,) >>> ...
python
{ "resource": "" }
q35484
ProductSpace.dtype
train
def dtype(self): """The data type of this space. This is only well defined if all subspaces have the same dtype. Raises ------ AttributeError If any of the subspaces does not implement `dtype` or if the dtype of the subspaces does not match. """ ...
python
{ "resource": "" }
q35485
ProductSpace.element
train
def element(self, inp=None, cast=True): """Create an element in the product space. Parameters ---------- inp : optional If ``inp`` is ``None``, a new element is created from scratch by allocation in the spaces. If ``inp`` is already an element of this...
python
{ "resource": "" }
q35486
ProductSpace.examples
train
def examples(self): """Return examples from all sub-spaces.""" for examples in product(*[spc.examples for spc in self.spaces]): name = ', '.join(name for name, _ in examples) element = self.element([elem for _, elem in examples]) yield (name, element)
python
{ "resource": "" }
q35487
ProductSpaceElement.asarray
train
def asarray(self, out=None): """Extract the data of this vector as a numpy array. Only available if `is_power_space` is True. The ordering is such that it commutes with indexing:: self[ind].asarray() == self.asarray()[ind] Parameters ---------- out : `nump...
python
{ "resource": "" }
q35488
ProductSpaceElement.real
train
def real(self): """Real part of the element. The real part can also be set using ``x.real = other``, where ``other`` is array-like or scalar. Examples -------- >>> space = odl.ProductSpace(odl.cn(3), odl.cn(2)) >>> x = space.element([[1 + 1j, 2, 3 - 3j], ...
python
{ "resource": "" }
q35489
ProductSpaceElement.real
train
def real(self, newreal): """Setter for the real part. This method is invoked by ``x.real = other``. Parameters ---------- newreal : array-like or scalar Values to be assigned to the real part of this element. """ try: iter(newreal) ...
python
{ "resource": "" }
q35490
ProductSpaceElement.imag
train
def imag(self): """Imaginary part of the element. The imaginary part can also be set using ``x.imag = other``, where ``other`` is array-like or scalar. Examples -------- >>> space = odl.ProductSpace(odl.cn(3), odl.cn(2)) >>> x = space.element([[1 + 1j, 2, 3 - 3...
python
{ "resource": "" }
q35491
ProductSpaceElement.conj
train
def conj(self): """Complex conjugate of the element.""" complex_conj = [part.conj() for part in self.parts] return self.space.element(complex_conj)
python
{ "resource": "" }
q35492
ProductSpaceElement.show
train
def show(self, title=None, indices=None, **kwargs): """Display the parts of this product space element graphically. Parameters ---------- title : string, optional Title of the figures indices : int, slice, tuple or list, optional Display parts of ``self`...
python
{ "resource": "" }
q35493
ProductSpaceArrayWeighting.inner
train
def inner(self, x1, x2): """Calculate the array-weighted inner product of two elements. Parameters ---------- x1, x2 : `ProductSpaceElement` Elements whose inner product is calculated. Returns ------- inner : float or complex The inner pr...
python
{ "resource": "" }
q35494
ProductSpaceArrayWeighting.norm
train
def norm(self, x): """Calculate the array-weighted norm of an element. Parameters ---------- x : `ProductSpaceElement` Element whose norm is calculated. Returns ------- norm : float The norm of the provided element. """ if...
python
{ "resource": "" }
q35495
ProductSpaceConstWeighting.inner
train
def inner(self, x1, x2): """Calculate the constant-weighted inner product of two elements. Parameters ---------- x1, x2 : `ProductSpaceElement` Elements whose inner product is calculated. Returns ------- inner : float or complex The inner...
python
{ "resource": "" }
q35496
ProductSpaceConstWeighting.dist
train
def dist(self, x1, x2): """Calculate the constant-weighted distance between two elements. Parameters ---------- x1, x2 : `ProductSpaceElement` Elements whose mutual distance is calculated. Returns ------- dist : float The distance between...
python
{ "resource": "" }
q35497
euler_matrix
train
def euler_matrix(phi, theta=None, psi=None): """Rotation matrix in 2 and 3 dimensions. Its rows represent the canonical unit vectors as seen from the rotated system while the columns are the rotated unit vectors as seen from the canonical system. Parameters ---------- phi : float or `array...
python
{ "resource": "" }
q35498
axis_rotation
train
def axis_rotation(axis, angle, vectors, axis_shift=(0, 0, 0)): """Rotate a vector or an array of vectors around an axis in 3d. The rotation is computed by `Rodrigues' rotation formula`_. Parameters ---------- axis : `array-like`, shape ``(3,)`` Rotation axis, assumed to be a unit vector. ...
python
{ "resource": "" }
q35499
axis_rotation_matrix
train
def axis_rotation_matrix(axis, angle): """Matrix of the rotation around an axis in 3d. The matrix is computed according to `Rodriguez' rotation formula`_. Parameters ---------- axis : `array-like`, shape ``(3,)`` Rotation axis, assumed to be a unit vector. angle : float or `array-like`...
python
{ "resource": "" }