_id
stringlengths
2
7
title
stringlengths
1
88
partition
stringclasses
3 values
text
stringlengths
75
19.8k
language
stringclasses
1 value
meta_information
dict
q35500
rotation_matrix_from_to
train
def rotation_matrix_from_to(from_vec, to_vec): r"""Return a matrix that rotates ``from_vec`` to ``to_vec`` in 2d or 3d. Since a rotation from one vector to another in 3 dimensions has (at least) one degree of freedom, this function makes deliberate but still arbitrary choices to fix these free paramete...
python
{ "resource": "" }
q35501
transform_system
train
def transform_system(principal_vec, principal_default, other_vecs, matrix=None): """Transform vectors with either ``matrix`` or based on ``principal_vec``. The logic of this function is as follows: - If ``matrix`` is not ``None``, transform ``principal_vec`` and all vectors in `...
python
{ "resource": "" }
q35502
perpendicular_vector
train
def perpendicular_vector(vec): """Return a vector perpendicular to ``vec``. Parameters ---------- vec : `array-like` Vector(s) of arbitrary length. The axis along the vector components must come last. Returns ------- perp_vec : `numpy.ndarray` Array of same shape as...
python
{ "resource": "" }
q35503
is_inside_bounds
train
def is_inside_bounds(value, params): """Return ``True`` if ``value`` is contained in ``params``. This method supports broadcasting in the sense that for ``params.ndim >= 2``, if more than one value is given, the inputs are broadcast against each other. Parameters ---------- value : `array-...
python
{ "resource": "" }
q35504
pyfftw_call
train
def pyfftw_call(array_in, array_out, direction='forward', axes=None, halfcomplex=False, **kwargs): """Calculate the DFT with pyfftw. The discrete Fourier (forward) transform calcuates the sum:: f_hat[k] = sum_j( f[j] * exp(-2*pi*1j * j*k/N) ) where the summation is taken over all ...
python
{ "resource": "" }
q35505
_pyfftw_destroys_input
train
def _pyfftw_destroys_input(flags, direction, halfcomplex, ndim): """Return ``True`` if FFTW destroys an input array, ``False`` otherwise.""" if any(flag in flags or _pyfftw_to_local(flag) in flags for flag in ('FFTW_MEASURE', 'FFTW_PATIENT', 'FFTW_EXHAUSTIVE', 'FFTW_DESTROY_IN...
python
{ "resource": "" }
q35506
_pyfftw_check_args
train
def _pyfftw_check_args(arr_in, arr_out, axes, halfcomplex, direction): """Raise an error if anything is not ok with in and out.""" if len(set(axes)) != len(axes): raise ValueError('duplicate axes are not allowed') if direction == 'forward': out_shape = list(arr_in.shape) if halfcomp...
python
{ "resource": "" }
q35507
admm_linearized
train
def admm_linearized(x, f, g, L, tau, sigma, niter, **kwargs): r"""Generic linearized ADMM method for convex problems. ADMM stands for "Alternating Direction Method of Multipliers" and is a popular convex optimization method. This variant solves problems of the form :: min_x [ f(x) + g(Lx) ] ...
python
{ "resource": "" }
q35508
admm_linearized_simple
train
def admm_linearized_simple(x, f, g, L, tau, sigma, niter, **kwargs): """Non-optimized version of ``admm_linearized``. This function is intended for debugging. It makes a lot of copies and performs no error checking. """ callback = kwargs.pop('callback', None) z = L.range.zero() u = L.range....
python
{ "resource": "" }
q35509
NumericalGradient.derivative
train
def derivative(self, point): """Return the derivative in ``point``. The derivative of the gradient is often called the Hessian. Parameters ---------- point : `domain` `element-like` The point that the derivative should be taken in. Returns ------- ...
python
{ "resource": "" }
q35510
_offset_from_spaces
train
def _offset_from_spaces(dom, ran): """Return index offset corresponding to given spaces.""" affected = np.not_equal(dom.shape, ran.shape) diff_l = np.abs(ran.grid.min() - dom.grid.min()) offset_float = diff_l / dom.cell_sides offset = np.around(offset_float).astype(int) for i in range(dom.ndim):...
python
{ "resource": "" }
q35511
Resampling._call
train
def _call(self, x, out=None): """Apply resampling operator. The element ``x`` is resampled using the sampling and interpolation operators of the underlying spaces. """ if out is None: return x.interpolation else: out.sampling(x.interpolation)
python
{ "resource": "" }
q35512
ResizingOperatorBase.axes
train
def axes(self): """Dimensions in which an actual resizing is performed.""" return tuple(i for i in range(self.domain.ndim) if self.domain.shape[i] != self.range.shape[i])
python
{ "resource": "" }
q35513
ResizingOperator.derivative
train
def derivative(self, point): """Derivative of this operator at ``point``. For the particular case of constant padding with non-zero constant, the derivative is the corresponding zero-padding variant. In all other cases, this operator is linear, i.e. the derivative is equal to ``...
python
{ "resource": "" }
q35514
Strings.contains_all
train
def contains_all(self, other): """Return ``True`` if all strings in ``other`` have size `length`.""" dtype = getattr(other, 'dtype', None) if dtype is None: dtype = np.result_type(*other) dtype_str = np.dtype('S{}'.format(self.length)) dtype_uni = np.dtype('<U{}'.form...
python
{ "resource": "" }
q35515
Strings.element
train
def element(self, inp=None): """Return an element from ``inp`` or from scratch.""" if inp is not None: s = str(inp)[:self.length] s += ' ' * (self.length - len(s)) return s else: return ' ' * self.length
python
{ "resource": "" }
q35516
ComplexNumbers.contains_all
train
def contains_all(self, other): """Return ``True`` if ``other`` is a sequence of complex numbers.""" dtype = getattr(other, 'dtype', None) if dtype is None: dtype = np.result_type(*other) return is_numeric_dtype(dtype)
python
{ "resource": "" }
q35517
ComplexNumbers.element
train
def element(self, inp=None): """Return a complex number from ``inp`` or from scratch.""" if inp is not None: # Workaround for missing __complex__ of numpy.ndarray # for Numpy version < 1.12 # TODO: remove when Numpy >= 1.12 is required if isinstance(inp, n...
python
{ "resource": "" }
q35518
RealNumbers.contains_set
train
def contains_set(self, other): """Return ``True`` if ``other`` is a subset of the real numbers. Returns ------- contained : bool ``True`` if other is an instance of `RealNumbers` or `Integers` False otherwise. Examples -------- >>> real_n...
python
{ "resource": "" }
q35519
RealNumbers.contains_all
train
def contains_all(self, array): """Test if `array` is an array of real numbers.""" dtype = getattr(array, 'dtype', None) if dtype is None: dtype = np.result_type(*array) return is_real_dtype(dtype)
python
{ "resource": "" }
q35520
Integers.contains_all
train
def contains_all(self, other): """Return ``True`` if ``other`` is a sequence of integers.""" dtype = getattr(other, 'dtype', None) if dtype is None: dtype = np.result_type(*other) return is_int_dtype(dtype)
python
{ "resource": "" }
q35521
CartesianProduct.element
train
def element(self, inp=None): """Create a `CartesianProduct` element. Parameters ---------- inp : iterable, optional Collection of input values for the `LinearSpace.element` methods of all sets in the Cartesian product. Returns -------...
python
{ "resource": "" }
q35522
DiscreteFourierTransformBase.adjoint
train
def adjoint(self): """Adjoint transform, equal to the inverse. See Also -------- inverse """ if self.domain.exponent == 2.0 and self.range.exponent == 2.0: return self.inverse else: raise NotImplementedError( 'no adjoint de...
python
{ "resource": "" }
q35523
FourierTransformBase.create_temporaries
train
def create_temporaries(self, r=True, f=True): """Allocate and store reusable temporaries. Existing temporaries are overridden. Parameters ---------- r : bool, optional Create temporary for the real space f : bool, optional Create temporary for th...
python
{ "resource": "" }
q35524
FourierTransform._preprocess
train
def _preprocess(self, x, out=None): """Return the pre-processed version of ``x``. C2C: use ``tmp_r`` or ``tmp_f`` (C2C operation) R2C: use ``tmp_f`` (R2C operation) HALFC: use ``tmp_r`` (R2R operation) The result is stored in ``out`` if given, otherwise in a temporary o...
python
{ "resource": "" }
q35525
FourierTransformInverse.inverse
train
def inverse(self): """Inverse of the inverse, the forward FT.""" sign = '+' if self.sign == '-' else '-' return FourierTransform( domain=self.range, range=self.domain, impl=self.impl, axes=self.axes, halfcomplex=self.halfcomplex, shift=self.shifts, sign=sign, ...
python
{ "resource": "" }
q35526
moveaxis
train
def moveaxis(a, source, destination): """Move axes of an array to new positions. Other axes remain in their original order. This function is a backport of `numpy.moveaxis` introduced in NumPy 1.11. See Also -------- numpy.moveaxis """ import numpy if hasattr(numpy, 'moveaxis')...
python
{ "resource": "" }
q35527
flip
train
def flip(a, axis): """Reverse the order of elements in an array along the given axis. This function is a backport of `numpy.flip` introduced in NumPy 1.12. See Also -------- numpy.flip """ if not hasattr(a, 'ndim'): a = np.asarray(a) indexer = [slice(None)] * a.ndim try: ...
python
{ "resource": "" }
q35528
_read_projections
train
def _read_projections(folder, indices): """Read mayo projections from a folder.""" datasets = [] # Get the relevant file names file_names = sorted([f for f in os.listdir(folder) if f.endswith(".dcm")]) if len(file_names) == 0: raise ValueError('No DICOM files found in {}'.format(folder)) ...
python
{ "resource": "" }
q35529
load_projections
train
def load_projections(folder, indices=None): """Load geometry and data stored in Mayo format from folder. Parameters ---------- folder : str Path to the folder where the Mayo DICOM files are stored. indices : optional Indices of the projections to load. Accepts advanced index...
python
{ "resource": "" }
q35530
load_reconstruction
train
def load_reconstruction(folder, slice_start=0, slice_end=-1): """Load a volume from folder, also returns the corresponding partition. Parameters ---------- folder : str Path to the folder where the DICOM files are stored. slice_start : int Index of the first slice to use. Used for s...
python
{ "resource": "" }
q35531
newtons_method
train
def newtons_method(f, x, line_search=1.0, maxiter=1000, tol=1e-16, cg_iter=None, callback=None): r"""Newton's method for minimizing a functional. Notes ----- This is a general and optimized implementation of Newton's method for solving the problem: .. math:: \min f(x...
python
{ "resource": "" }
q35532
bfgs_method
train
def bfgs_method(f, x, line_search=1.0, maxiter=1000, tol=1e-15, num_store=None, hessinv_estimate=None, callback=None): r"""Quasi-Newton BFGS method to minimize a differentiable function. Can use either the regular BFGS method, or the limited memory BFGS method. Notes ----- This is ...
python
{ "resource": "" }
q35533
broydens_method
train
def broydens_method(f, x, line_search=1.0, impl='first', maxiter=1000, tol=1e-15, hessinv_estimate=None, callback=None): r"""Broyden's first method, a quasi-Newton scheme. Notes ----- This is a general and optimized implementation of Broyden's method, a quasi...
python
{ "resource": "" }
q35534
_axis_in_detector
train
def _axis_in_detector(geometry): """A vector in the detector plane that points along the rotation axis.""" du, dv = geometry.det_axes_init axis = geometry.axis c = np.array([np.vdot(axis, du), np.vdot(axis, dv)]) cnorm = np.linalg.norm(c) # Check for numerical errors assert cnorm != 0 ...
python
{ "resource": "" }
q35535
_rotation_direction_in_detector
train
def _rotation_direction_in_detector(geometry): """A vector in the detector plane that points in the rotation direction.""" du, dv = geometry.det_axes_init axis = geometry.axis det_normal = np.cross(dv, du) rot_dir = np.cross(axis, det_normal) c = np.array([np.vdot(rot_dir, du), np.vdot(rot_dir, ...
python
{ "resource": "" }
q35536
_fbp_filter
train
def _fbp_filter(norm_freq, filter_type, frequency_scaling): """Create a smoothing filter for FBP. Parameters ---------- norm_freq : `array-like` Frequencies normalized to lie in the interval [0, 1]. filter_type : {'Ram-Lak', 'Shepp-Logan', 'Cosine', 'Hamming', 'Hann', cal...
python
{ "resource": "" }
q35537
tam_danielson_window
train
def tam_danielson_window(ray_trafo, smoothing_width=0.05, n_pi=1): """Create Tam-Danielson window from a `RayTransform`. The Tam-Danielson window is an indicator function on the minimal set of data needed to reconstruct a volume from given data. It is useful in analytic reconstruction methods such as F...
python
{ "resource": "" }
q35538
parker_weighting
train
def parker_weighting(ray_trafo, q=0.25): """Create parker weighting for a `RayTransform`. Parker weighting is a weighting function that ensures that oversampled fan/cone beam data are weighted such that each line has unit weight. It is useful in analytic reconstruction methods such as FBP to give a mor...
python
{ "resource": "" }
q35539
fbp_op
train
def fbp_op(ray_trafo, padding=True, filter_type='Ram-Lak', frequency_scaling=1.0): """Create filtered back-projection operator from a `RayTransform`. The filtered back-projection is an approximate inverse to the ray transform. Parameters ---------- ray_trafo : `RayTransform` ...
python
{ "resource": "" }
q35540
walnut_data
train
def walnut_data(): """Tomographic X-ray data of a walnut. Notes ----- See the article `Tomographic X-ray data of a walnut`_ for further information. See Also -------- walnut_geometry References ---------- .. _Tomographic X-ray data of a walnut: https://arxiv.org/abs/1502.0...
python
{ "resource": "" }
q35541
lotus_root_data
train
def lotus_root_data(): """Tomographic X-ray data of a lotus root. Notes ----- See the article `Tomographic X-ray data of a lotus root filled with attenuating objects`_ for further information. See Also -------- lotus_root_geometry References ---------- .. _Tomographic X-ra...
python
{ "resource": "" }
q35542
lotus_root_geometry
train
def lotus_root_geometry(): """Tomographic geometry for the lotus root dataset. Notes ----- See the article `Tomographic X-ray data of a lotus root filled with attenuating objects`_ for further information. See Also -------- lotus_root_geometry References ---------- .. _Tom...
python
{ "resource": "" }
q35543
poisson_noise
train
def poisson_noise(intensity, seed=None): r"""Poisson distributed noise with given intensity. Parameters ---------- intensity : `TensorSpace` or `ProductSpace` element The intensity (usually called lambda) parameter of the noise. Returns ------- poisson_noise : ``intensity.space`` e...
python
{ "resource": "" }
q35544
salt_pepper_noise
train
def salt_pepper_noise(vector, fraction=0.05, salt_vs_pepper=0.5, low_val=None, high_val=None, seed=None): """Add salt and pepper noise to vector. Salt and pepper noise replaces random elements in ``vector`` with ``low_val`` or ``high_val``. Parameters ---------- vector : ...
python
{ "resource": "" }
q35545
uniform_partition_fromintv
train
def uniform_partition_fromintv(intv_prod, shape, nodes_on_bdry=False): """Return a partition of an interval product into equally sized cells. Parameters ---------- intv_prod : `IntervalProd` Interval product to be partitioned shape : int or sequence of ints Number of nodes per axis....
python
{ "resource": "" }
q35546
uniform_partition_fromgrid
train
def uniform_partition_fromgrid(grid, min_pt=None, max_pt=None): """Return a partition of an interval product based on a given grid. This method is complementary to `uniform_partition_fromintv` in that it infers the set to be partitioned from a given grid and optional parameters for ``min_pt`` and ``max...
python
{ "resource": "" }
q35547
uniform_partition
train
def uniform_partition(min_pt=None, max_pt=None, shape=None, cell_sides=None, nodes_on_bdry=False): """Return a partition with equally sized cells. Parameters ---------- min_pt, max_pt : float or sequence of float, optional Vectors defining the lower/upper limits of the int...
python
{ "resource": "" }
q35548
nonuniform_partition
train
def nonuniform_partition(*coord_vecs, **kwargs): """Return a partition with un-equally sized cells. Parameters ---------- coord_vecs1, ... coord_vecsN : `array-like` Arrays of coordinates of the mid-points of the partition cells. min_pt, max_pt : float or sequence of floats, optional ...
python
{ "resource": "" }
q35549
RectPartition.nodes_on_bdry
train
def nodes_on_bdry(self): """Encoding of grid points lying on the boundary. Examples -------- Using global option (default ``False``): >>> part = odl.nonuniform_partition([0, 2, 3], [1, 3]) >>> part.nodes_on_bdry False >>> part = odl.nonuniform_partition(...
python
{ "resource": "" }
q35550
RectPartition.has_isotropic_cells
train
def has_isotropic_cells(self): """``True`` if `grid` is uniform and `cell_sides` are all equal. Always ``True`` for 1D partitions. Examples -------- >>> part = uniform_partition([0, -1], [1, 1], (5, 10)) >>> part.has_isotropic_cells True >>> part = unifo...
python
{ "resource": "" }
q35551
RectPartition.boundary_cell_fractions
train
def boundary_cell_fractions(self): """Return a tuple of contained fractions of boundary cells. Since the outermost grid points can have any distance to the boundary of the partitioned set, the "natural" outermost cell around these points can either be cropped or extended. This p...
python
{ "resource": "" }
q35552
RectPartition.cell_sizes_vecs
train
def cell_sizes_vecs(self): """Return the cell sizes as coordinate vectors. Returns ------- csizes : tuple of `numpy.ndarray`'s The cell sizes per axis. The length of the vectors is the same as the corresponding ``grid.coord_vectors``. For axes with 1 ...
python
{ "resource": "" }
q35553
RectPartition.cell_sides
train
def cell_sides(self): """Side lengths of all 'inner' cells of a uniform partition. Only defined if ``self.grid`` is uniform. Examples -------- We create a partition of the rectangle [0, 1] x [-1, 2] into 3 x 3 cells, where the grid points lie on the boundary. This ...
python
{ "resource": "" }
q35554
RectPartition.approx_equals
train
def approx_equals(self, other, atol): """Return ``True`` in case of approximate equality. Returns ------- approx_eq : bool ``True`` if ``other`` is a `RectPartition` instance with ``self.set == other.set`` up to ``atol`` and ``self.grid == other.other...
python
{ "resource": "" }
q35555
RectPartition.insert
train
def insert(self, index, *parts): """Return a copy with ``parts`` inserted before ``index``. The given partitions are inserted (as a block) into ``self``, yielding a new partition whose number of dimensions is the sum of the numbers of dimensions of all involved partitions. Note ...
python
{ "resource": "" }
q35556
RectPartition.index
train
def index(self, value, floating=False): """Return the index of a value in the domain. Parameters ---------- value : ``self.set`` element Point whose index to find. floating : bool, optional If True, then the index should also give the position inside the ...
python
{ "resource": "" }
q35557
RectPartition.byaxis
train
def byaxis(self): """Object to index ``self`` along axes. Examples -------- Indexing with integers or slices: >>> p = odl.uniform_partition([0, 1, 2], [1, 3, 5], (3, 5, 6)) >>> p.byaxis[0] uniform_partition(0.0, 1.0, 3) >>> p.byaxis[1] uniform_pa...
python
{ "resource": "" }
q35558
DivergentBeamGeometry.det_to_src
train
def det_to_src(self, angle, dparam, normalized=True): """Vector or direction from a detector location to the source. The unnormalized version of this vector is computed as follows:: vec = src_position(angle) - det_point_position(angle, dparam) Parameters ---------- ...
python
{ "resource": "" }
q35559
AxisOrientedGeometry.rotation_matrix
train
def rotation_matrix(self, angle): """Return the rotation matrix to the system state at ``angle``. The matrix is computed according to `Rodrigues' rotation formula <https://en.wikipedia.org/wiki/Rodrigues'_rotation_formula>`_. Parameters ---------- angle : float ...
python
{ "resource": "" }
q35560
elekta_icon_geometry
train
def elekta_icon_geometry(sad=780.0, sdd=1000.0, piercing_point=(390.0, 0.0), angles=None, num_angles=None, detector_shape=(780, 720)): """Tomographic geometry of the Elekta Icon CBCT system. See the [whitepaper]_ for specific descriptio...
python
{ "resource": "" }
q35561
elekta_icon_space
train
def elekta_icon_space(shape=(448, 448, 448), **kwargs): """Default reconstruction space for the Elekta Icon CBCT. See the [whitepaper]_ for further information. Parameters ---------- shape : sequence of int, optional Shape of the space, in voxels. kwargs : Keyword arguments to ...
python
{ "resource": "" }
q35562
elekta_icon_fbp
train
def elekta_icon_fbp(ray_transform, padding=False, filter_type='Hann', frequency_scaling=0.6, parker_weighting=True): """Approximation of the FDK reconstruction used in the Elekta Icon. Parameters ---------- ray_transform : `RayTransform` The ray transform...
python
{ "resource": "" }
q35563
elekta_xvi_space
train
def elekta_xvi_space(shape=(512, 512, 512), **kwargs): """Default reconstruction space for the Elekta XVI CBCT. Parameters ---------- shape : sequence of int, optional Shape of the space, in voxels. kwargs : Keyword arguments to pass to `uniform_discr` to modify the space, e.g. ...
python
{ "resource": "" }
q35564
elekta_xvi_fbp
train
def elekta_xvi_fbp(ray_transform, padding=False, filter_type='Hann', frequency_scaling=0.6): """Approximation of the FDK reconstruction used in the Elekta XVI. Parameters ---------- ray_transform : `RayTransform` The ray transform to be used, should have an Elekta XVI geometr...
python
{ "resource": "" }
q35565
_modified_shepp_logan_ellipsoids
train
def _modified_shepp_logan_ellipsoids(ellipsoids): """Modify ellipsoids to give the modified Shepp-Logan phantom. Works for both 2d and 3d. """ intensities = [1.0, -0.8, -0.2, -0.2, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1] # Add minimal numbers to ensure that the result is nowhere negative. # This is need...
python
{ "resource": "" }
q35566
shepp_logan_ellipsoids
train
def shepp_logan_ellipsoids(ndim, modified=False): """Ellipsoids for the standard Shepp-Logan phantom in 2 or 3 dimensions. Parameters ---------- ndim : {2, 3} Dimension of the space the ellipsoids should be in. modified : bool, optional True if the modified Shepp-Logan phantom shoul...
python
{ "resource": "" }
q35567
shepp_logan
train
def shepp_logan(space, modified=False, min_pt=None, max_pt=None): """Standard Shepp-Logan phantom in 2 or 3 dimensions. Parameters ---------- space : `DiscreteLp` Space in which the phantom is created, must be 2- or 3-dimensional. If ``space.shape`` is 1 in an axis, a corresponding slic...
python
{ "resource": "" }
q35568
_scaling_func_list
train
def _scaling_func_list(bdry_fracs, exponent): """Return a list of lists of scaling functions for the boundary.""" def scaling(factor): def scaling_func(x): return x * factor return scaling_func func_list = [] for frac_l, frac_r in bdry_fracs: func_list_entry = [] ...
python
{ "resource": "" }
q35569
DiscreteLp.interp
train
def interp(self): """Interpolation type of this discretization.""" if self.ndim == 0: return 'nearest' elif all(interp == self.interp_byaxis[0] for interp in self.interp_byaxis): return self.interp_byaxis[0] else: return self.interp_by...
python
{ "resource": "" }
q35570
DiscreteLp.tangent_bundle
train
def tangent_bundle(self): """The tangent bundle associated with `domain` using `partition`. The tangent bundle of a space ``X`` of functions ``R^d --> F`` can be interpreted as the space of vector-valued functions ``R^d --> F^d``. This space can be identified with the power space ``X^d`...
python
{ "resource": "" }
q35571
DiscreteLp.is_uniformly_weighted
train
def is_uniformly_weighted(self): """``True`` if the weighting is the same for all space points.""" try: is_uniformly_weighted = self.__is_uniformly_weighted except AttributeError: bdry_fracs = self.partition.boundary_cell_fractions is_uniformly_weighted = ( ...
python
{ "resource": "" }
q35572
DiscreteLpElement.imag
train
def imag(self, newimag): """Set the imaginary part of this element to ``newimag``. This method is invoked by ``x.imag = other``. Parameters ---------- newimag : array-like or scalar Values to be assigned to the imaginary part of this element. Raises ...
python
{ "resource": "" }
q35573
DiscreteLpElement.conj
train
def conj(self, out=None): """Complex conjugate of this element. Parameters ---------- out : `DiscreteLpElement`, optional Element to which the complex conjugate is written. Must be an element of this element's space. Returns ------- out :...
python
{ "resource": "" }
q35574
_operator_norms
train
def _operator_norms(L): """Get operator norms if needed. Parameters ---------- L : sequence of `Operator` or float The operators or the norms of the operators that are used in the `douglas_rachford_pd` method. For `Operator` entries, the norm is computed with ``Operator.norm(est...
python
{ "resource": "" }
q35575
douglas_rachford_pd_stepsize
train
def douglas_rachford_pd_stepsize(L, tau=None, sigma=None): r"""Default step sizes for `douglas_rachford_pd`. Parameters ---------- L : sequence of `Operator` or float The operators or the norms of the operators that are used in the `douglas_rachford_pd` method. For `Operator` entries, t...
python
{ "resource": "" }
q35576
parallel_beam_geometry
train
def parallel_beam_geometry(space, num_angles=None, det_shape=None): r"""Create default parallel beam geometry from ``space``. This is intended for simple test cases where users do not need the full flexibility of the geometries, but simply want a geometry that works. This default geometry gives a full...
python
{ "resource": "" }
q35577
ParallelBeamGeometry.angles
train
def angles(self): """All angles of this geometry as an array. If ``motion_params.ndim == 1``, the array has shape ``(N,)``, where ``N`` is the number of angles. Otherwise, the array shape is ``(ndim, N)``, where ``N`` is the total number of angles, and ``ndim`` is ``motion_parti...
python
{ "resource": "" }
q35578
ParallelBeamGeometry.det_to_src
train
def det_to_src(self, angle, dparam): """Direction from a detector location to the source. The direction vector is computed as follows:: dir = rotation_matrix(angle).dot(detector.surface_normal(dparam)) Note that for flat detectors, ``surface_normal`` does not depend on the...
python
{ "resource": "" }
q35579
Parallel2dGeometry.frommatrix
train
def frommatrix(cls, apart, dpart, init_matrix, **kwargs): """Create an instance of `Parallel2dGeometry` using a matrix. This alternative constructor uses a matrix to rotate and translate the default configuration. It is most useful when the transformation to be applied is already given ...
python
{ "resource": "" }
q35580
Parallel3dEulerGeometry.det_axes
train
def det_axes(self, angles): """Return the detector axes tuple at ``angles``. Parameters ---------- angles : `array-like` or sequence Euler angles in radians describing the rotation of the detector. The length of the provided argument (along the first axis in ...
python
{ "resource": "" }
q35581
Parallel3dEulerGeometry.rotation_matrix
train
def rotation_matrix(self, angles): """Return the rotation matrix to the system state at ``angles``. Parameters ---------- angles : `array-like` or sequence Euler angles in radians describing the rotation of the detector. The length of the provided argument (along...
python
{ "resource": "" }
q35582
Parallel3dAxisGeometry.frommatrix
train
def frommatrix(cls, apart, dpart, init_matrix, **kwargs): """Create an instance of `Parallel3dAxisGeometry` using a matrix. This alternative constructor uses a matrix to rotate and translate the default configuration. It is most useful when the transformation to be applied is already gi...
python
{ "resource": "" }
q35583
wrap_ufunc_base
train
def wrap_ufunc_base(name, n_in, n_out, doc): """Return ufunc wrapper for implementation-agnostic ufunc classes.""" ufunc = getattr(np, name) if n_in == 1: if n_out == 1: def wrapper(self, out=None, **kwargs): if out is None or isinstance(out, (type(self.elem), ...
python
{ "resource": "" }
q35584
wrap_ufunc_productspace
train
def wrap_ufunc_productspace(name, n_in, n_out, doc): """Return ufunc wrapper for `ProductSpaceUfuncs`.""" if n_in == 1: if n_out == 1: def wrapper(self, out=None, **kwargs): if out is None: result = [getattr(x.ufuncs, name)(**kwargs) ...
python
{ "resource": "" }
q35585
landweber
train
def landweber(op, x, rhs, niter, omega=None, projection=None, callback=None): r"""Optimized implementation of Landweber's method. Solves the inverse problem:: A(x) = rhs Parameters ---------- op : `Operator` Operator in the inverse problem. ``op.derivative(x).adjoint`` must be ...
python
{ "resource": "" }
q35586
conjugate_gradient
train
def conjugate_gradient(op, x, rhs, niter, callback=None): """Optimized implementation of CG for self-adjoint operators. This method solves the inverse problem (of the first kind):: A(x) = y for a linear and self-adjoint `Operator` ``A``. It uses a minimum amount of memory copies by applying ...
python
{ "resource": "" }
q35587
conjugate_gradient_normal
train
def conjugate_gradient_normal(op, x, rhs, niter=1, callback=None): """Optimized implementation of CG for the normal equation. This method solves the inverse problem (of the first kind) :: A(x) == rhs with a linear `Operator` ``A`` by looking at the normal equation :: A.adjoint(A(x)) == A...
python
{ "resource": "" }
q35588
gauss_newton
train
def gauss_newton(op, x, rhs, niter, zero_seq=exp_zero_seq(2.0), callback=None): """Optimized implementation of a Gauss-Newton method. This method solves the inverse problem (of the first kind):: A(x) = y for a (Frechet-) differentiable `Operator` ``A`` using a Gauss-Newton it...
python
{ "resource": "" }
q35589
kaczmarz
train
def kaczmarz(ops, x, rhs, niter, omega=1, projection=None, random=False, callback=None, callback_loop='outer'): r"""Optimized implementation of Kaczmarz's method. Solves the inverse problem given by the set of equations:: A_n(x) = rhs_n This is also known as the Landweber-Kaczmarz's ...
python
{ "resource": "" }
q35590
conjugate_gradient_nonlinear
train
def conjugate_gradient_nonlinear(f, x, line_search=1.0, maxiter=1000, nreset=0, tol=1e-16, beta_method='FR', callback=None): r"""Conjugate gradient for nonlinear problems. Parameters ---------- f : `Functional` Functional with ``...
python
{ "resource": "" }
q35591
tspace_type
train
def tspace_type(space, impl, dtype=None): """Select the correct corresponding tensor space. Parameters ---------- space : `LinearSpace` Template space from which to infer an adequate tensor space. If it has a ``field`` attribute, ``dtype`` must be consistent with it. impl : string ...
python
{ "resource": "" }
q35592
DiscretizedSpace._lincomb
train
def _lincomb(self, a, x1, b, x2, out): """Raw linear combination.""" self.tspace._lincomb(a, x1.tensor, b, x2.tensor, out.tensor)
python
{ "resource": "" }
q35593
DiscretizedSpace._dist
train
def _dist(self, x1, x2): """Raw distance between two elements.""" return self.tspace._dist(x1.tensor, x2.tensor)
python
{ "resource": "" }
q35594
DiscretizedSpace._inner
train
def _inner(self, x1, x2): """Raw inner product of two elements.""" return self.tspace._inner(x1.tensor, x2.tensor)
python
{ "resource": "" }
q35595
DiscretizedSpaceElement.sampling
train
def sampling(self, ufunc, **kwargs): """Sample a continuous function and assign to this element. Parameters ---------- ufunc : ``self.space.fspace`` element The continuous function that should be samplingicted. kwargs : Additional arugments for the sampli...
python
{ "resource": "" }
q35596
_normalize_sampling_points
train
def _normalize_sampling_points(sampling_points, ndim): """Normalize points to an ndim-long list of linear index arrays. This helper converts sampling indices for `SamplingOperator` from integers or array-like objects to a list of length ``ndim``, where each entry is a `numpy.ndarray` with ``dtype=int``...
python
{ "resource": "" }
q35597
PointwiseNorm.derivative
train
def derivative(self, vf): """Derivative of the point-wise norm operator at ``vf``. The derivative at ``F`` of the point-wise norm operator ``N`` with finite exponent ``p`` and weights ``w`` is the pointwise inner product with the vector field :: x --> N(F)(x)^(1-p) * [ F_j(...
python
{ "resource": "" }
q35598
MatrixOperator.adjoint
train
def adjoint(self): """Adjoint operator represented by the adjoint matrix. Returns ------- adjoint : `MatrixOperator` """ return MatrixOperator(self.matrix.conj().T, domain=self.range, range=self.domain, axis=sel...
python
{ "resource": "" }
q35599
MatrixOperator.inverse
train
def inverse(self): """Inverse operator represented by the inverse matrix. Taking the inverse causes sparse matrices to become dense and is generally very heavy computationally since the matrix is inverted numerically (an O(n^3) operation). It is recommended to instead use one of...
python
{ "resource": "" }