aspire.abinitio package

Submodules

aspire.abinitio.J_sync module

class aspire.abinitio.J_sync.JSync(n, epsilon=0.01, max_iters=1000, seed=None)

Bases: object

Class for handling J-synchronization methods.

Initialize JSync object for estimating global handedness synchronization for a set of relative rotations, Rij = Ri @ Rj.T, where i <= j = 0, 1, …, n.

Parameters:

• n – Number of images/rotations.

• epsilon – Tolerance for the power method.

• max_iters – Maximum iterations for the power method.

• seed – Optional seed for power method initial random vector.

global_J_sync(vijs)

Global J-synchronization of all third row outer products. Given 3x3 matrices vijs, each of which might contain a spurious J (ie. vij = J*vi*vj^T*J instead of vij = vi*vj^T), we return vijs that all have either a spurious J or not.

Parameters:

vijs – An (n-choose-2)x3x3 array where each 3x3 slice holds an estimate for the corresponding

outer-product vi*vj^T between the third rows of the rotation matrices Ri and Rj. Each estimate might have a spurious J independently of other estimates.

Returns:

vijs, all of which have a spurious J or not.

power_method(vijs)

Calculate the leading eigenvector of the J-synchronization matrix using the power method.

As the J-synchronization matrix is of size (n-choose-2)x(n-choose-2), we use the power method to compute the eigenvalues and eigenvectors, while constructing the matrix on-the-fly.

Parameters:

vijs – (n-choose-2)x3x3 array of estimates of relative orientation matrices.

Returns:

An array of length n-choose-2 consisting of 1 or -1, where the sign of the i’th entry indicates whether the i’th relative orientation matrix will be J-conjugated.

sync_viis(vijs, viis)

Given a set of synchronized pairwise outer products vijs, J-synchronize the set of outer products viis.

Parameters:

vijs – An (n-choose-2)x3x3 array where each 3x3 slice holds an estimate for the corresponding

outer-product vi*vj^T between the third rows of the rotation matrices Ri and Rj. Each estimate might have a spurious J independently of other estimates.

Parameters:

viis – An n_imgx3x3 array where the i’th slice holds an estimate for the outer product vi*vi^T

between the third row of matrix Ri and itself. Each estimate might have a spurious J independently of other estimates.

Returns:

J-synchronized viis.

aspire.abinitio.commonline_base module

class aspire.abinitio.commonline_base.CLOrient3D(src, n_rad=None, n_theta=360, n_check=None, hist_bin_width=3, full_width=6, max_shift=0.15, shift_step=1, offsets_max_shift=None, offsets_shift_step=None, offsets_max_memory=10000, offsets_equations_factor=1, mask=True)

Bases: object

Define a base class for estimating 3D orientations using common lines methods

Initialize an object for estimating 3D orientations using common lines.

Parameters:

• src – The source object of 2D denoised or class-averaged images.

• n_rad – The number of points in the radial direction. If None, n_rad will default to the ceiling of half the resolution of the source.

• n_theta – The number of points in the theta direction. This value must be even. Default is 360.

• n_check – For each image/projection find its common-lines with n_check images. If n_check is less than the total number of images, a random subset of n_check images is used.

• max_shift – Determines maximum range for shifts for common-line detection as a proportion of the resolution. Default is 0.15.

• shift_step – Resolution of shift estimation for common-line detection in pixels. Default is 1 pixel.

• offsets_max_shift – Determines maximum range for shifts for 2D offset estimation as a proportion of the resolution. Default None inherits from max_shift.

• offsets_shift_step – Resolution of shift estimation for 2D offset estimation in pixels. Default None inherits from shift_step.

• offsets_equations_factor – The factor to rescale the number of shift equations (=1 in default)

• offsets_max_memory – If there are N images and N_check selected to check for common lines, then the exact system of equations solved for the shifts is of size 2N x N(N_check-1)/2 (2N unknowns and N(N_check-1)/2 equations). This may be too big if N is large. The algorithm will use equations_factor times the total number of equations if the resulting total number of memory requirements is less than offsets_max_memory (in megabytes); otherwise it will reduce the number of equations by approximation to fit in offsets_max_memory. For more information see the references in estimate_shifts. Defaults to 10GB.

• hist_bin_width – Bin width in smoothing histogram (degrees).

• full_width – Selection width around smoothed histogram peak (degrees). adaptive will attempt to automatically find the smallest number of `hist_bin_width`s required to find at least one valid image index.

• mask – Option to mask src.images with a fuzzy mask (boolean). Default, True, applies a mask.

build_clmatrix()

Build common-lines matrix from Fourier stack of 2D images

Wrapper for cpu/gpu dispatch.

build_clmatrix_cu()

Build common-lines matrix from Fourier stack of 2D images

build_clmatrix_host()

Build common-lines matrix from Fourier stack of 2D images

property clmatrix

Returns Common Lines Matrix.

Computes if clmatrix is None.

Returns:

Common Lines Matrix

estimate(**kwargs)

Estimate orientation and shifts for all 2D images.

Returns:

(rotations, shifts)

estimate_rotations()

Estimate orientation matrices for all 2D images

Subclasses should implement this function.

estimate_shifts()

Estimate 2D shifts in images

This function computes 2D shifts in x, y of images by solving the least-squares equations to Ax = b. A on the left-hand side is a sparse matrix representing precomputed coefficients of shift equations; and on the right-side, b is estimated 1D shifts along the theta direction between two Fourier rays (one in image i and the other in image j). Each row of shift equations contains four unknowns, shifts in x, y for a pair of images. The detailed implementation can be found in the book chapter as below: Y. Shkolnisky and A. Singer, Center of Mass Operators for Cryo-EM - Theory and Implementation, Modeling Nanoscale Imaging in Electron Microscopy, T. Vogt, W. Dahmen, and P. Binev (Eds.) Nanostructure Science and Technology Series, Springer, 2012, pp. 147–177

property pf

property rotations

Returns estimated rotations.

Computes if rotations is None.

Returns:

Estimated rotations

property shifts

Returns estimated shifts.

Computes if shifts is None.

Returns:

Estimated shifts

aspire.abinitio.commonline_c2 module

class aspire.abinitio.commonline_c2.CLSymmetryC2(src, n_rad=None, n_theta=360, max_shift=0.15, shift_step=1, epsilon=0.001, max_iters=1000, min_dist_cls=25, seed=None, mask=True, **kwargs)

Bases: CLOrient3D

Define a class to estimate 3D orientations using common lines methods for molecules with C2 cyclic symmetry.

The related publications are listed below: X. Cheng, Random Matrices in High-dimensional Data Analysis, PhD thesis, Princeton University, (2013).

G. Pragier and Y. Shkolnisky, A Common Lines Approach for Abinitio Modeling of Cyclically Symmetric Molecules, Inverse Problems, 35, 124005, (2019).

Y. Shkolnisky, and A. Singer, Viewing Direction Estimation in Cryo-EM Using Synchronization, SIAM J. Imaging Sciences, 5, 1088-1110 (2012).

A. Singer, R. R. Coifman, F. J. Sigworth, D. W. Chester, Y. Shkolnisky, Detecting Consistent Common Lines in Cryo-EM by Voting, Journal of Structural Biology, 169, 312-322 (2010).

Initialize object for estimating 3D orientations for molecules with C2 symmetry.

Parameters:

• src – The source object of 2D denoised or class-averaged images with metadata

• n_rad – The number of points in the radial direction

• n_theta – The number of points in the theta direction. Default = 360.

• max_shift – Maximum range for shifts as a proportion of resolution. Default = 0.15.

• shift_step – Resolution of shift estimation in pixels. Default = 1 pixel.

• epsilon – Tolerance for the power method.

• max_iters – Maximum iterations for the power method.

• min_dist_cls – Minimum distance between mutual common-lines. Default = 25 degrees.

• seed – Optional seed for RNG.

• mask – Option to mask src.images with a fuzzy mask (boolean). Default, True, applies a mask.

build_clmatrix()

Build common-lines matrix for molecules with C2 symmetry from Fourier stack of 2D images. This consists of finding for each pair of images the two common-lines induced by the 2-fold symmetry.

estimate_rotations()

Estimate rotation matrices for molecules with C2 symmetry.

aspire.abinitio.commonline_c3_c4 module

class aspire.abinitio.commonline_c3_c4.CLSymmetryC3C4(src, symmetry=None, n_rad=None, n_theta=360, max_shift=0.15, shift_step=1, epsilon=0.01, max_iters=1000, degree_res=1, seed=None, mask=True, **kwargs)

Bases: CLOrient3D

Define a class to estimate 3D orientations using common lines methods for molecules with C3 and C4 cyclic symmetry.

The related publications are listed below: G. Pragier and Y. Shkolnisky, A Common Lines Approach for Abinitio Modeling of Cyclically Symmetric Molecules, Inverse Problems, 35, 124005, (2019).

Y. Shkolnisky, and A. Singer, Viewing Direction Estimation in Cryo-EM Using Synchronization, SIAM J. Imaging Sciences, 5, 1088-1110 (2012).

A. Singer, R. R. Coifman, F. J. Sigworth, D. W. Chester, Y. Shkolnisky, Detecting Consistent Common Lines in Cryo-EM by Voting, Journal of Structural Biology, 169, 312-322 (2010).

Initialize object for estimating 3D orientations for molecules with C3 and C4 symmetry.

Parameters:

• src – The source object of 2D denoised or class-averaged images with metadata

• symmetry – A string, ‘C3’ or ‘C4’, indicating the symmetry type.

• n_rad – The number of points in the radial direction

• n_theta – The number of points in the theta direction. Default = 360.

• max_shift – Maximum range for shifts as a proportion of resolution. Default = 0.15.

• shift_step – Resolution of shift estimation in pixels. Default = 1 pixel.

• epsilon – Tolerance for the power method.

• max_iter – Maximum iterations for the power method.

• degree_res – Degree resolution for estimating in-plane rotations.

• seed – Optional seed for RNG.

• mask – Option to mask src.images with a fuzzy mask (boolean). Default, True, applies a mask.

estimate_rotations()

Estimate rotation matrices for molecules with C3 or C4 symmetry.

Returns:

Array of rotation matrices, size n_imgx3x3.

aspire.abinitio.commonline_cn module

class aspire.abinitio.commonline_cn.CLSymmetryCn(src, symmetry=None, n_rad=None, n_theta=360, max_shift=0.15, shift_step=1, epsilon=0.001, max_iters=1000, degree_res=1, n_points_sphere=500, equator_threshold=10, seed=None, mask=True, **kwargs)

Bases: CLOrient3D

Define a class to estimate 3D orientations using common lines methods for molecules with Cn cyclic symmetry, with n>4.

Initialize object for estimating 3D orientations for molecules with Cn symmetry, n>4.

Parameters:

• src – The source object of 2D denoised or class-averaged images with metadata

• symmetry – A string, ‘Cn’, indicating the symmetry type.

• n_rad – The number of points in the radial direction.

• n_theta – The number of points in the theta direction. Default = 360.

• max_shift – Maximum range for shifts as a proportion of resolution. Default = 0.15.

• shift_step – Resolution of shift estimation in pixels. Default = 1 pixel.

• epsilon – Tolerance for the power method.

• max_iter – Maximum iterations for the power method.

• degree_res – Degree resolution for estimating in-plane rotations.

• n_points_sphere – The number of candidate rotations used to estimate viewing directions.

• equator_threshold – Threshold for removing candidate rotations within equator_threshold degrees of being an equator image. Default is 10 degrees.

• seed – Optional seed for RNG.

• mask – Option to mask src.images with a fuzzy mask (boolean). Default, True, applies a mask.

estimate_rotations()

Estimate rotation matrices for molecules with Cn symmetry, n > 4.

Returns:

Array of rotation matrices, size n_imgx3x3.

static generate_candidate_rots(n, equator_threshold, order, degree_res, seed)

Generate random rotations that exclude rotations inducing equator images for use as candidates in the CLSymmetryCn algorithm.

Parameters:

• n – Number of rotations to generate.

• equator_threshold – Angular distance from equator (in degrees).

• order – Cyclic order of underlying molecule.

• degree_res – Degree resolution for in-plane rotations.

• seed – Random seed.

Returns:

Candidate rotations, In-plane rotations

static relative_rots_to_cl_indices(relative_rots, n_theta)

Given a set of relative rotations between pairs of images produce the common-line indices for each pair.

Parameters:

• relative_rots – The n x 3 x 3 relative rotations between pairs of images.

• n_theta – The theta resolution for common-line indices.

Returns:

Common-line indices c1s, c2s each length n.

class aspire.abinitio.commonline_cn.MeanOuterProductEstimator

Bases: object

Incrementally accumulate outer product entries of unknown conjugation.

dtype

alias of float64

push(V)

Given V, accumulate entries into a running sum of J-synchronized entries.

synchronized_mean()

Calculate the mean of synchronized outer product estimates.

aspire.abinitio.commonline_d2 module

class aspire.abinitio.commonline_d2.CLSymmetryD2(src, n_rad=None, n_theta=360, max_shift=0.15, shift_step=1, grid_res=1200, inplane_res=5, eq_min_dist=7, epsilon=0.01, seed=None, mask=True, **kwargs)

Bases: CLOrient3D

Define a class to estimate 3D orientations using common lines methods for molecules with D2 (dihedral) symmetry.

Corresponding publication: E. Rosen and Y. Shkolnisky, Common lines ab-initio reconstruction of D2-symmetric molecules, SIAM Journal on Imaging Sciences, volume 13-4, p. 1898-1994, 2020

Initialize object for estimating 3D orientations for molecules with D2 symmetry.

Parameters:

• src – The source object of 2D denoised or class-averaged images with metadata

• n_rad – The number of points in the radial direction of Fourier image.

• n_theta – The number of points in the theta direction of Fourier image. Default = 360.

• max_shift – Maximum range for shifts as a proportion of resolution. Default = 0.15.

• shift_step – Resolution of shift estimation in pixels. Default = 1 pixel.

• grid_res – Number of sampling points on sphere for projetion directions. These are generated using the Saaf-Kuijlaars algorithm. Default value is 1200.

• inplane_res – The sampling resolution of in-plane rotations for each projection direction. Default value is 5 degrees.

• eq_min_dist – Width of strip around equator projection directions from which we do not sample directions. Default value is 7 degrees.

• epsilon – Tolerance for J-synchronization power method.

• seed – Optional seed for RNG.

• mask – Option to mask src.images with a fuzzy mask (boolean). Default, True, applies a mask.

estimate_rotations()

Estimate rotation matrices for molecules with D2 symmetry. Sets the attribute self.rotations with an array of estimated rotation matrices, size src.nx3x3.

aspire.abinitio.commonline_ev module

class aspire.abinitio.commonline_ev.CommLineEV(src)

Bases: CLOrient3D

Class to estimate 3D orientations using Eigenvector method [SS11]

constructor of an object for estimating 3D orientations

estimate()

perform estimation of orientations

output()

Output the 3D orientations

aspire.abinitio.commonline_gcar module

class aspire.abinitio.commonline_gcar.CommLineGCAR(src)

Bases: CLOrient3D

Define a derived class to estimate 3D orientations using Globally Consistent Angular Reconstitution described as below: R. Coifman, Y. Shkolnisky, F. J. Sigworth, and A. Singer, Reference Free Structure Determination through Eigenvestors of Center of Mass Operators, Applied and Computational Harmonic Analysis, 28, 296-312 (2010).

constructor of an object for estimating 3D oreintations

estimate()

perform estimation of orientations

output()

Output the 3D orientations

aspire.abinitio.commonline_irls module

class aspire.abinitio.commonline_irls.CommonlineIRLS(src, *args, num_itrs=10, eps_weighting=0.001, alpha=None, max_rankZ=None, max_rankW=None, **kwargs)

Bases: CommonlineLUD

Estimate 3D orientations using Iteratively Reweighted Least Squares (IRLS) as described in the following publication: L. Wang, A. Singer, and Z. Wen, Orientation Determination of Cryo-EM Images Using Least Unsquared Deviations, SIAM J. Imaging Sciences, 6, 2450-2483 (2013).

Initialize a class for estimating 3D orientations using an IRLS-based optimization. See CommonlineLUD for additional arguments.

Parameters:

• num_itrs – Number of iterations for iterative reweighting. Default is 10.

• eps_weighting – Regularization value for reweighting factor. Default is 1e-3.

• alpha – Spectral norm constraint for IRLS algorithm. Default is None, which does not apply a spectral norm constraint. To apply a spectral norm constraint provide a value in the range [2/3, 1), 2/3 is recommended.

• max_rankZ – Maximum rank used for projecting the Z matrix (for adaptive projection). If None, defaults to max(6, n_img // 4).

• max_rankW – Maximum rank used for projecting the W matrix (for adaptive projection). If None, defaults to max(6, n_img // 4).

estimate_rotations()

Estimate rotation matrices using the common lines method with IRLS optimization.

aspire.abinitio.commonline_lud module

class aspire.abinitio.commonline_lud.CommonlineLUD(src, alpha=None, tol=0.001, mu=1, gam=1.618, eps=None, maxit=1000, adp_proj=True, max_rankZ=None, max_rankW=None, adp_mu=True, dec_mu=0.5, inc_mu=2, mu_min=0.0001, mu_max=10000.0, min_mu_itr=5, max_mu_itr=20, delta_mu_l=0.1, delta_mu_u=10, **kwargs)

Bases: CommonlineSDP

Define a derived class to estimate 3D orientations using Least Unsquared Deviations as described in the following publication: L. Wang, A. Singer, and Z. Wen, Orientation Determination of Cryo-EM Images Using Least Unsquared Deviations, SIAM J. Imaging Sciences, 6, 2450-2483 (2013).

Initialize a class for estimating 3D orientations using a Least Unsquared Deviations algorithm.

This class extends the CLOrient3D class, inheriting its initialization parameters. Additional parameters detailed below.

Parameters:

• alpha – Spectral norm constraint for ADMM algorithm. Default is None, which does not apply a spectral norm constraint. To apply a spectral norm constraint provide a value in the range [2/3, 1), 2/3 is recommended.

• tol – Tolerance for convergence. The algorithm stops when conditions reach this threshold. Default is 1e-3.

• mu – The penalty parameter (or dual variable scaling factor) in the optimization problem. Default is 1.

• gam – Relaxation factor for updating variables in the algorithm (typically between 1 and 2). Default is 1.618.

• eps – Small positive value used to filter out negligible eigenvalues. Default is 1e-5 if src.dtype is singles, otherwise 1e-12.

• maxit – Maximum number of iterations allowed for the algorithm. Default is 1000.

• adp_proj – Flag for using adaptive projection during eigenvalue computation: - True: Adaptive rank selection (Default). - False: Full eigenvalue decomposition.

• max_rankZ – Maximum rank used for projecting the Z matrix (for adaptive projection). If None, defaults to max(6, n_img // 2).

• max_rankW – Maximum rank used for projecting the W matrix (for adaptive projection). If None, defaults to max(6, n_img // 2).

• adp_mu – Adaptive adjustment of the penalty parameter mu: - True: Enabled (Default). - False: Disabled.

• dec_mu – Scaling factor for decreasing mu. Default is 0.5.

• inc_mu – Scaling factor for increasing mu. Default is 2.

• mu_min – Minimum allowable value for mu. Default is 1e-4.

• mu_max – Maximum allowable value for mu. Default is 1e4.

• min_mu_itr – Minimum number of iterations before mu is adjusted. Default is 5.

• max_mu_itr – Maximum number of iterations allowed for mu adjustment. Default is 20.

• delta_mu_l – Lower bound for relative drop ratio to trigger a decrease in mu. Default is 0.1.

• delta_mu_u – Upper bound for relative drop ratio to trigger an increase in mu. Default is 10.

estimate_rotations()

Estimate rotation matrices using the common lines method with LUD optimization.

aspire.abinitio.commonline_sdp module

class aspire.abinitio.commonline_sdp.CommonlineSDP(src, n_rad=None, n_theta=360, n_check=None, hist_bin_width=3, full_width=6, max_shift=0.15, shift_step=1, offsets_max_shift=None, offsets_shift_step=None, offsets_max_memory=10000, offsets_equations_factor=1, mask=True)

Bases: CLOrient3D

Class to estimate 3D orientations using semi-definite programming.

See the following publication for more details:

A. Singer and Y. Shkolnisky, “Three-Dimensional Structure Determination from Common Lines in Cryo-EM

by Eigenvectors and Semidefinite Programming”

SIAM J. Imaging Sciences, Vol. 4, No. 2, (2011): 543-572. doi:10.1137/090767777

Initialize an object for estimating 3D orientations using common lines.

Parameters:

• src – The source object of 2D denoised or class-averaged images.

• n_rad – The number of points in the radial direction. If None, n_rad will default to the ceiling of half the resolution of the source.

• n_theta – The number of points in the theta direction. This value must be even. Default is 360.

• n_check – For each image/projection find its common-lines with n_check images. If n_check is less than the total number of images, a random subset of n_check images is used.

• max_shift – Determines maximum range for shifts for common-line detection as a proportion of the resolution. Default is 0.15.

• shift_step – Resolution of shift estimation for common-line detection in pixels. Default is 1 pixel.

• offsets_max_shift – Determines maximum range for shifts for 2D offset estimation as a proportion of the resolution. Default None inherits from max_shift.

• offsets_shift_step – Resolution of shift estimation for 2D offset estimation in pixels. Default None inherits from shift_step.

• offsets_equations_factor – The factor to rescale the number of shift equations (=1 in default)

• offsets_max_memory – If there are N images and N_check selected to check for common lines, then the exact system of equations solved for the shifts is of size 2N x N(N_check-1)/2 (2N unknowns and N(N_check-1)/2 equations). This may be too big if N is large. The algorithm will use equations_factor times the total number of equations if the resulting total number of memory requirements is less than offsets_max_memory (in megabytes); otherwise it will reduce the number of equations by approximation to fit in offsets_max_memory. For more information see the references in estimate_shifts. Defaults to 10GB.

• hist_bin_width – Bin width in smoothing histogram (degrees).

• full_width – Selection width around smoothed histogram peak (degrees). adaptive will attempt to automatically find the smallest number of `hist_bin_width`s required to find at least one valid image index.

• mask – Option to mask src.images with a fuzzy mask (boolean). Default, True, applies a mask.

estimate_rotations()

Estimate rotation matrices using the common lines method with semi-definite programming.

aspire.abinitio.commonline_sync module

class aspire.abinitio.commonline_sync.CLSyncVoting(src, n_rad=None, n_theta=360, max_shift=0.15, shift_step=1, hist_bin_width=3, full_width=6, mask=True, **kwargs)

Bases: CLOrient3D

Define a class to estimate 3D orientations using synchronization matrix and voting method.

The related publications are listed as below: Y. Shkolnisky, and A. Singer, Viewing Direction Estimation in Cryo-EM Using Synchronization, SIAM J. Imaging Sciences, 5, 1088-1110 (2012).

A. Singer, R. R. Coifman, F. J. Sigworth, D. W. Chester, Y. Shkolnisky, Detecting Consistent Common Lines in Cryo-EM by Voting, Journal of Structural Biology, 169, 312-322 (2010).

Initialize an object for estimating 3D orientations using synchronization matrix

Parameters:

• src – The source object of 2D denoised or class-averaged images with metadata

• n_rad – The number of points in the radial direction

• n_theta – The number of points in the theta direction. Default is 360.

• max_shift – Determines maximum range for shifts as a proportion of the resolution. Default is 0.15.

• shift_step – Resolution for shift estimation in pixels. Default is 1 pixel.

• hist_bin_width – Bin width in smoothing histogram (degrees).

• full_width – Selection width around smoothed histogram peak (degrees). adaptive will attempt to automatically find the smallest number of `hist_bin_width`s required to find at least one valid image index.

• mask – Option to mask src.images with a fuzzy mask (boolean). Default, True, applies a mask.

estimate_rotations()

Estimate orientation matrices for all 2D images using synchronization matrix

syncmatrix_vote()

Construct the synchronization matrix using voting method

A pre-computed common line matrix is required as input.

aspire.abinitio.commonline_sync3n module

class aspire.abinitio.commonline_sync3n.CLSync3N(src, n_rad=None, n_theta=360, max_shift=0.15, shift_step=1, hist_bin_width=1, full_width='adaptive', epsilon=0.01, max_iters=1000, sigma=3, seed=None, mask=True, S_weighting=False, J_weighting=False, hist_intervals=100, disable_gpu=False, **kwargs)

Bases: CLOrient3D

Define a class to estimate 3D orientations using common lines Sync3N methods (2017).

Ido Greenberg, Yoel Shkolnisky, Common lines modeling for reference free Ab-initio reconstruction in cryo-EM, Journal of Structural Biology, Volume 200, Issue 2, 2017, Pages 106-117, ISSN 1047-8477, https://doi.org/10.1016/j.jsb.2017.09.007.

Initialize object for estimating 3D orientations.

Parameters:

• src – The source object of 2D denoised or class-averaged images with metadata

• n_rad – The number of points in the radial direction

• n_theta – The number of points in the theta direction

• max_shift – Maximum range for shifts as a proportion of box size. Default = 0.15.

• shift_step – Step size of shift estimation in pixels. Default = 1 pixel.

• hist_bin_width – Bin width in smoothing histogram (degrees).

• full_width – Selection width around smoothed histogram peak (degrees). adaptive will attempt to automatically find the smallest number of `hist_bin_width`s required to find at least one valid image index.

• epsilon – Tolerance for the power method.

• max_iter – Maximum iterations for the power method.

• sigma – Voting contribution smoothing factor.

• seed – Optional seed for RNG.

• mask – Option to mask src.images with a fuzzy mask (boolean). Default, True, applies a mask.

• S_weighting – Optionally apply probabilistic weighting to the S matrix.

• J_weighting – Optionally use J weights instead of signs when computing signs_times_v.

• hist_intervals – Number of histogram bins used to compute triangle scores when S_weighting enabled.

• disable_gpu – Disables GPU acceleration; forces CPU only code for this module. Defaults to automatically using GPU when available.

estimate_rotations()

Estimate rotation matrices.

Returns:

Array of rotation matrices, size n_imgx3x3.

aspire.abinitio.commonline_utils module

aspire.abinitio.commonline_utils.build_outer_products(n, dtype)

Builds sets of outer products of 3rd rows of rotation matrices. This is a helper function used in commonline testing.

Parameters:

• n – Number of 3rd rows to construct outer product from.

• dtype – dtype of outputs

Returns:

tuple of (vijs, viis, gt_vis), where vijs are the pairwise outer products of gt_vis and viis are self outer products of gt_vis.

aspire.abinitio.commonline_utils.g_sync(rots, order, rots_gt)

Given ground truth rotations, synchronize estimated rotations over symmetry group elements.

Every estimated rotation might be a version of the ground truth rotation rotated by g^{s_i}, where s_i = 0, 1, …, order. This method synchronizes the ground truth rotations so that only a single global rotation need be applied to all estimates for error analysis.

Parameters:

• rots – Estimated rotation matrices

• order – The cyclic order asssociated with the symmetry of the underlying molecule.

• rots_gt – Ground truth rotation matrices.

Returns:

g-synchronized ground truth rotations.

aspire.abinitio.sync_voting module

Module contents