o Xεiʆ @sFddlZddlZddlmZddlmZddlm Z e ddZ ej dddej j ej j ej jej jdd d d Zd d ZddZej edddZej edddZd)defddZ         d*ddZddZdddejddddfddZddZdddejddddfd d!Zd"d#Z $ %  &      d+d'd(ZdS),N)tqdm) tau_rand_intcCs|dkrdS|dkr dS|S)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@g)valrr@/home/ubuntu/.local/lib/python3.10/site-packages/umap/layouts.pyclip s 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$t|jdD]}|||kr||}||}||}||}t||} |rdd|t| |}!||t| |dd|t| |}"|!||}#|!||}$|#d|d|!t|||"}%|$d|d|!t|||"}&||}'|||||||'}(|||||||'})|||(|%|)|&||||}*| dkrd||t| |d}+|+|t| |d}+nd}+t| D]8},t|+||,||,}-|r|-td|*||,||,7}-||,|-| 7<| r ||,|- | 7<q||||7<t |||| |}.t|.D]^}/t |||}||}t||} | dkrRd| |}+|+d| |t| |d}+n ||krYq$d}+t| D]!},|+dkrst|+||,||,}-nd}-||,|-| 7<q_q$|||.| |7<qdS) Nr?r@MbP?) numbaprangerrpownpexprrintr)0head_embeddingtail_embeddingheadtail n_verticesepochs_per_sampleabrng_state_per_samplegammar move_otheralphaepochs_per_negative_sampleepoch_of_next_negative_sampleepoch_of_next_samplen densmap_flag dens_phi_sum dens_re_sum dens_re_cov dens_re_std dens_re_mean dens_lambdadens_Rdens_mu dens_mu_totr jkcurrentother dist_squaredphi dphi_termq_jkq_kjdrkdrj re_std_sqweight_kweight_jgrad_cor_coeff grad_coeffdgrad_d n_neg_samplesprrr'_optimize_layout_euclidean_single_epoch?s &               rOcCs|d|dt|jD]F}||} ||} || } || } t| | } dd|t| |}|| || 7<|| || 7<|| |7<|| |7<qd}t|jD]}t|||||||<q^dS)Nrrg:0yE>) fillrrsizerrrrlog)r!r"r#r$r'r(re_sumphi_sumr r;r<r=r>r?r@epsilonrrr-_optimize_layout_euclidean_densmap_epoch_inits"   rVFr parallelrXcCs |rtStS)N)3_nb_optimize_layout_euclidean_single_epoch_parallel*_nb_optimize_layout_euclidean_single_epoch)rXrrr._get_optimize_layout_euclidean_single_epoch_fnsr[r@c)Cs|jd}| }|| }|}|}t| }|duri}|dur#i}|rWtjtd| d}t|dd}|d}|d}|d }tj|tj d }tj|tj d }|d } n$d }d }tjdtj d }tjdtj d }tjdtj d }tjdtj d }d}!g}"t |t r|}!t |!}d |vr| |d <tj |jd t| f| tjd |ddd ftjtjdd}#tt|fi|D]}$|o|dd ko|$dt|d|dk}%|%r|||||||||tt|| }&t|}'t|||d}(nd }&d }'d }(||||||||||#| |||||||$|%|||(|&|'||||| dt|$t|}|rG|$t|dd krGtd|$d|d|!durX|$|!vrX|"|q|!dure|"||!durl|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. rNTrWmu_sumrlambdaRmudtype var_shiftrdisablefracr z completed z / epochs)rcopyr[rnjitrVrsumzerosfloat32 isinstancelistmaxfulllenint64astypefloat64viewreshaperrfloatsqrtvarmeandotr printappend))r!r"r#r$n_epochsr%r&r'r( rng_stater* initial_alphanegative_sample_raterXverbosedensmap densmap_kwds tqdm_kwdsr+r r,r-r.r/ optimize_fn dens_init_fnr:r7r8r9r2r3dens_var_shift epochs_listembedding_listr)r0r1r5r6r4rrroptimize_layout_euclideans R   &   rc" Cst|jdD]}||| kr||}||}||}||}|||g|R\}}|||g|R\}}|dkrItd|t|d|d}nd}d||d|d}t|D](}t|||}|||| 7<| rt|||}|||| 7<q[||||7<t| | || |} t| D]X}!t|||}||}|||g|R\}}|dkrtd|t|d|d}n||krqd}|d|||d}t|D]}t|||}|||| 7<qq| || | |7<q|| fS)Nrrrrrerư>)rrrrr r)"r&r/r#r$r!r" output_metricoutput_metric_kwdsr r,r+r0r.r-r)r%r'r(r*r r;r<r=r> dist_outputgrad_dist_output_rev_grad_dist_outputw_lrJrKrLrMrNrrr%_optimize_layout_generic_single_epochsd      rrcCs|jd}| }|| }|}|}tjtdd}|dur i}d|vr)| |d<tj|jdt| f| tjd|dddf tj  tj dd}t t|fi|D]$}|||||||| |||||||||||| | d t|t|}qW|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 Nrdrrarer)rrirrjrrrqrrrsrtrurvrwrrrx)r!r"r#r$rr%r&r'r(rr*rrrrrrr+r r,r-r.r/rr)r0rrroptimize_layout_genericsT V &rc"Cst|jdD]}||| kr||}||}||}||}|||g|R\}}||}d|| |d }t| D]!}t|||}|||| 7<| r^||| | 7<q=||||7<t| ||||}t|D]T} t||}||}|||g|R\}}tt|||d | |d}!| d|!d|!| |d}t| D]}t|||}|||| 7<qqy|||||7<qdS)Nrrr)rrrr rrrrp)"r&r/r#r$r!r"rrweightsigmasr r,r+r0r.r-rr%rhosr*r r;r<r=r>rrrrJrKrLrMrNw_hrrr%_optimize_layout_inverse_single_epochsT      &"  rcCs|jd}|}| |}|}| }tjtdd}|dur i}d|vr)| |d<tt|fi|D]%}|| |||||||||||||||| ||| |dt|t|}q3|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. 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