U Xe @sddlZddlZddlmZddlmZddlm Z e ddZ ej dddej j ej j ej jej jdd d d Zd d ZddZd%ddZddZdddejddddfddZddZdddejddddfddZddZd&d#d$ZdS)'N) tau_rand_int)tqdmcCs |dkr dS|dkrdS|SdS)zStandard clamping of a value into a fixed range (in this case -4.0 to 4.0) Parameters ---------- val: float The value to be clamped. Returns ------- The clamped value, now fixed to be in the range -4.0 to 4.0. g@gN)valrr+lib/python3.8/site-packages/umap/layouts.pyclips rzf4(f4[::1],f4[::1])T)resultdiffdimi)fastmathcachelocalscCs<d}|jd}t|D] }||||}|||7}q|S)zReduced Euclidean distance. Parameters ---------- x: array of shape (embedding_dim,) y: array of shape (embedding_dim,) Returns ------- The squared euclidean distance between x and y r)shaperange)xyrr r r rrrrdists   rc0Cs(t|jdD]}|||kr||}||}||}||}t||} |r\dd|t| |}!||t| |dd|t| |}"|!||}#|!||}$|#d|d|!t|||"}%|$d|d|!t|||"}&||}'|||||||'}(|||||||'})|||(|%|)|&||||}*| dkrd||t| |d}+|+|t| |d}+nd}+t| D]t},t|+||,||,}-|r|-td|*||,||,7}-||,|-| 7<| r||,|- | 7<q||||7<t |||| |}.t|.D]}/t ||}||}t||} | dkrd| |}+|+d| |t| |d}+n||krqNnd}+t| D]B},|+dkrt|+||,||,}-nd}-||,|-| 7<qqN|||.| |7<qdS) Nr?r@MbP?) numbaprangerrpownpexprrintr)0head_embeddingtail_embeddingheadtail n_verticesepochs_per_sampleab rng_stategammar move_otheralphaepochs_per_negative_sampleepoch_of_next_negative_sampleepoch_of_next_samplen densmap_flag dens_phi_sum dens_re_sum dens_re_cov dens_re_std dens_re_mean dens_lambdadens_Rdens_mu dens_mu_totr jkcurrentother dist_squaredphiZ dphi_termZq_jkZq_kjZdrkZdrjZ re_std_sqZweight_kZweight_jZgrad_cor_coeff grad_coeffdgrad_d n_neg_samplesprrr'_optimize_layout_euclidean_single_epoch>s  &                 rFcCs|d|dt|jD]}||} ||} || } || } t| | } dd|t| |}|| || 7<|| || 7<|| |7<|| |7<q d}t|jD]"}t|||||||<qdS)Nrrg:0yE>) Zfillrrsizerrrrlog)r!r"r#r$r'r(Zre_sumZphi_sumr r;r<r=r>r?r@epsilonrrr-_optimize_layout_euclidean_densmap_epoch_inits   rJr@Fc(Cs|jd}| }|| }|}|}tjtd| d}|dkrBi}|dkrNi}|rtjtd| d}t|dd}|d}|d}|d }tj|tj d }tj|tj d }|d } nHd }d }tjdtj d }tjdtj d }tjdtj d }tjdtj d }d}!g}"t |t r|}!t |!}d |kr2| |d <t t|f|D]4}#|ov|dd kov|#dt|d|dk}$|$r|||||||||tt|| }%t|}&t|||d}'n d }%d }&d }'|||||||||| | |||||||#|$|||'|%|&||||| dt|#t|}|rT|#t|dd krTtd|#d|d|!dk rB|#|!krB|"|qB|!dk r|"||!dkr|S|"S)a^ Improve an embedding using stochastic gradient descent to minimize the fuzzy set cross entropy between the 1-skeletons of the high dimensional and low dimensional fuzzy simplicial sets. In practice this is done by sampling edges based on their membership strength (with the (1-p) terms coming from negative sampling similar to word2vec). Parameters ---------- head_embedding: array of shape (n_samples, n_components) The initial embedding to be improved by SGD. tail_embedding: array of shape (source_samples, n_components) The reference embedding of embedded points. If not embedding new previously unseen points with respect to an existing embedding this is simply the head_embedding (again); otherwise it provides the existing embedding to embed with respect to. head: array of shape (n_1_simplices) The indices of the heads of 1-simplices with non-zero membership. tail: array of shape (n_1_simplices) The indices of the tails of 1-simplices with non-zero membership. n_epochs: int, or list of int The number of training epochs to use in optimization, or a list of epochs at which to save the embedding. In case of a list, the optimization will use the maximum number of epochs in the list, and will return a list of embedding in the order of increasing epoch, regardless of the order in the epoch list. n_vertices: int The number of vertices (0-simplices) in the dataset. epochs_per_sample: array of shape (n_1_simplices) A float value of the number of epochs per 1-simplex. 1-simplices with weaker membership strength will have more epochs between being sampled. a: float Parameter of differentiable approximation of right adjoint functor b: float Parameter of differentiable approximation of right adjoint functor rng_state: array of int64, shape (3,) The internal state of the rng gamma: float (optional, default 1.0) Weight to apply to negative samples. initial_alpha: float (optional, default 1.0) Initial learning rate for the SGD. negative_sample_rate: int (optional, default 5) Number of negative samples to use per positive sample. parallel: bool (optional, default False) Whether to run the computation using numba parallel. Running in parallel is non-deterministic, and is not used if a random seed has been set, to ensure reproducibility. verbose: bool (optional, default False) Whether to report information on the current progress of the algorithm. densmap: bool (optional, default False) Whether to use the density-augmented densMAP objective densmap_kwds: dict (optional, default None) Auxiliary data for densMAP tqdm_kwds: dict (optional, default None) Keyword arguments for tqdm progress bar. move_other: bool (optional, default False) Whether to adjust tail_embedding alongside head_embedding Returns ------- embedding: array of shape (n_samples, n_components) The optimized embedding. rTr parallelNZmu_sumrlambdaRZmu)ZdtypeZ var_shiftrdisableZfracr z completed z / Zepochs)rcopyrnjitrFrJrsumZzerosfloat32 isinstancelistmaxrrfloatZsqrtvarZmeandotr printappend)(r!r"r#r$n_epochsr%r&r'r(r)r* initial_alphanegative_sample_raterMverboseZdensmapZ densmap_kwds tqdm_kwdsr+r r,r-r.r/ optimize_fnZ dens_init_fnr:r7r8r9r2r3Zdens_var_shiftZ epochs_listZembedding_listr0r1r5r6r4rrroptimize_layout_euclideansR         rdc" Cst|jdD]}||| kr||}||}||}||}|||f|\}}|||f|\}}|dkrtd|t|d|d}nd}d||d|d}t|D]P}t|||}|||| 7<| rt|||}|||| 7<q||||7<t| | || |} t| D]}!t||}||}|||f|\}}|dkrtd|t|d|d}n||krq8nd}|d|||d}t|D]*}t|||}|||| 7<qq8| || | |7<q|| fS)Nrrrrrư>)rrrrr r)"r&r/r#r$r!r" output_metricoutput_metric_kwdsr r,r+r0r.r-r)r%r'r(r*r r;r<r=r> dist_outputgrad_dist_output_Zrev_grad_dist_outputw_lrArBrCrDrErrr%_optimize_layout_generic_single_epochsb          rmrcCs|jd}| }|| }|}|}tjtdd}|dkr@i}d|krR| |d<tt|f|D]H}|||||||| |||||||| |||| | dt|t|}qb|S)a Improve an embedding using stochastic gradient descent to minimize the fuzzy set cross entropy between the 1-skeletons of the high dimensional and low dimensional fuzzy simplicial sets. In practice this is done by sampling edges based on their membership strength (with the (1-p) terms coming from negative sampling similar to word2vec). Parameters ---------- head_embedding: array of shape (n_samples, n_components) The initial embedding to be improved by SGD. tail_embedding: array of shape (source_samples, n_components) The reference embedding of embedded points. If not embedding new previously unseen points with respect to an existing embedding this is simply the head_embedding (again); otherwise it provides the existing embedding to embed with respect to. head: array of shape (n_1_simplices) The indices of the heads of 1-simplices with non-zero membership. tail: array of shape (n_1_simplices) The indices of the tails of 1-simplices with non-zero membership. n_epochs: int The number of training epochs to use in optimization. n_vertices: int The number of vertices (0-simplices) in the dataset. epochs_per_sample: array of shape (n_1_simplices) A float value of the number of epochs per 1-simplex. 1-simplices with weaker membership strength will have more epochs between being sampled. a: float Parameter of differentiable approximation of right adjoint functor b: float Parameter of differentiable approximation of right adjoint functor rng_state: array of int64, shape (3,) The internal state of the rng gamma: float (optional, default 1.0) Weight to apply to negative samples. initial_alpha: float (optional, default 1.0) Initial learning rate for the SGD. negative_sample_rate: int (optional, default 5) Number of negative samples to use per positive sample. verbose: bool (optional, default False) Whether to report information on the current progress of the algorithm. tqdm_kwds: dict (optional, default None) Keyword arguments for tqdm progress bar. move_other: bool (optional, default False) Whether to adjust tail_embedding alongside head_embedding Returns ------- embedding: array of shape (n_samples, n_components) The optimized embedding. rTr NrPr)rrRrrSrmrrrY)r!r"r#r$r^r%r&r'r(r)r*r_r`rgrhrarbr+r r,r-r.r/rcr0rrroptimize_layout_genericsJV  roc"Cst|jdD]}||| kr||}||}||}||}|||f|\}}||}d|| |d }t| D]B}t|||}|||| 7<| rz||| | 7<qz||||7<t| ||||}t|D]} t||}||}|||f|\}}tt|||d | |d}!| d|!d|!| |d}t| D]*}t|||}|||| 7<qnq|||||7<qdS)Nrrrf)rrrr rrrrX)"r&r/r#r$r!r"rgrhweightsigmasr r,r+r0r.r-r)r%rhosr*r r;r<r=r>rirjrlrArBrCrDrEZw_hrrr%_optimize_layout_inverse_single_epoch~sP      &"  rscCs|jd}|}| |}|}| }tjtdd}|dkr@i}d|krR| |d<tt|f|D]J}|| |||||||||||||||| ||| |dt|t|}qb|S)a Improve an embedding using stochastic gradient descent to minimize the fuzzy set cross entropy between the 1-skeletons of the high dimensional and low dimensional fuzzy simplicial sets. In practice this is done by sampling edges based on their membership strength (with the (1-p) terms coming from negative sampling similar to word2vec). Parameters ---------- head_embedding: array of shape (n_samples, n_components) The initial embedding to be improved by SGD. tail_embedding: array of shape (source_samples, n_components) The reference embedding of embedded points. If not embedding new previously unseen points with respect to an existing embedding this is simply the head_embedding (again); otherwise it provides the existing embedding to embed with respect to. head: array of shape (n_1_simplices) The indices of the heads of 1-simplices with non-zero membership. tail: array of shape (n_1_simplices) The indices of the tails of 1-simplices with non-zero membership. weight: array of shape (n_1_simplices) The membership weights of the 1-simplices. sigmas: rhos: n_epochs: int The number of training epochs to use in optimization. n_vertices: int The number of vertices (0-simplices) in the dataset. epochs_per_sample: array of shape (n_1_simplices) A float value of the number of epochs per 1-simplex. 1-simplices with weaker membership strength will have more epochs between being sampled. a: float Parameter of differentiable approximation of right adjoint functor b: float Parameter of differentiable approximation of right adjoint functor rng_state: array of int64, shape (3,) The internal state of the rng gamma: float (optional, default 1.0) Weight to apply to negative samples. initial_alpha: float (optional, default 1.0) Initial learning rate for the SGD. negative_sample_rate: int (optional, default 5) Number of negative samples to use per positive sample. verbose: bool (optional, default False) Whether to report information on the current progress of the algorithm. tqdm_kwds: dict (optional, default None) Keyword arguments for tqdm progress bar. move_other: bool (optional, default False) Whether to adjust tail_embedding alongside head_embedding Returns ------- embedding: array of shape (n_samples, n_components) The optimized embedding. rTrnNrPr)rrRrrSrsrrrY)r!r"r#r$rprqrrr^r%r&r'r(r)r*r_r`rgrhrarbr+r r,r-r.r/rcr0rrroptimize_layout_inversesL`  rtc( Cst|}|jddd}d}|D]}|jd|kr"|jd}q"t|tj}tjt| dtj |t |D]t}|D]h}|||jdkr||||kr|||}|||}|||}|||}t ||}|dkr"d||t ||d}||t ||d}nd}t | D]} t ||| || }!t | |D]}"||"}#||#krdkr|"krXnnh|||"||f}$|$dkrX|!t | tt|"d |||"||f|| ||#|$| f8}!qX|| t |!|7<| r.t ||| || }%t | |D]}"||"}#||#krjdkrj|"kr:nnh|||"||f}$|$dkr:|%t | tt|"d |||"||f|| ||#|$| f8}%q:|| t |%|7<q.||||||7<|||dkrFt|||||||}&nd}&t |&D]x}'t| ||jd}|||}t ||}|dkrd| |}|d||t ||d}n||krʐqRnd}t | D]} |dkrt ||| || }!nd}!t | |D]}"||"}#||#kr>dkr>|"krnnh|||"||f}$|$dkr|!t | tt|"d |||"||f|| ||#|$| f8}!q|| t |!|7<q֐qR||||&|||7<qqzdS) Nrrrrrrrr)lenrrZarangeastypeZint32ZrandomZseedabsZshufflerrrrrr r)(head_embeddingstail_embeddingsheadstailsr&r'r(regularisation_weights relationsr)r*lambda_r r+r,r-r.r/r0Z n_embeddingsZ window_sizeZ max_n_edgesZe_p_sZembedding_orderr mr;r<r=r>r?rArBrCoffsetZ neighbor_mZidentified_indexZ other_grad_drDrErrr/_optimize_layout_aligned_euclidean_single_epochTs   "      (  (           (    rP);?V?{Gzt?cCsJ|djd}| }tjjtjjddd}tjjtjjddd}tjjtjjddd}tt|D]J}| || t j|| || t j| || t jqrtj t d|d}|dkri}d|kr| |d<tt|f|D]H}||||||| | |||| | |||||||| dt|t|}q|S)NrrTrLrPr)rrtypedZListZ empty_listtypesrUrrur]rvrrSrrrY)rxryrzr{r^r&r|r}r)r'r(r*r~r_r`rMrarbr+r r,r-r.r/rrcr0rrr!optimize_layout_aligned_euclideans` r) rrrKFFFNNF) rrrrrrKTFNF)ZnumpyrrZumap.distancesZ distancesZdistZ umap.utilsrZ tqdm.autorrSrrrUZintprrFrJrdrmZ euclideanrorsrtrrrrrrs     ~, M] V "