J-jdZddlmZmZmZddlZddlmZddlZ ddl m Z m Z ddl mZddlmZ[[[d ZGd d eZGd d eZGddeZGddeZy)aCollection of classes that sample from parametrized distributions and provide an update mechanism of the distribution parameters. All classes are supposed to follow the base class `StatisticalModelSamplerWithZeroMeanBaseClass` interface in module `interfaces`. )absolute_importdivisionprint_functionN)range)rglen print_warning)Hessian),StatisticalModelSamplerWithZeroMeanBaseClassTc\eZdZdZd dZdZdZdZedZ edZ ed Z y) GaussSamplercd|_y)z-declarative init, doesn't need to be executedN) dimensionselfs Y/Users/jameslopez/projects/TradingBot25/.venv/lib/python3.12/site-packages/cma/sampler.py__init__zGaussSampler.__init__s Nc<|jt|||y)abset Hessian from f at x0. >>> import numpy as np, cma >>> es = cma.CMAEvolutionStrategy(3 * [1], 1, {'verbose':-9}) >>> es.sm.set_H_by_f(cma.ff.elli, 3 * [0]) # Hessian of cma.ff.elli Now the eigen spectrum of H^1/2 C H^1/2 where H is the Hessian of ``cma.ff.elli`` is given by the `spectrum` property. N)set_H_Hessian)rfx0epss r set_H_by_fzGaussSampler.set_H_by_fs 8Ar3'(rctjj|\}}t|dkr2t j dj t|dk|y|dz|z|_|jj|_ y)z@set Hessian w.r.t. which to compute the eigen spectrum. rzcThe Hessian has {0} negative eigenvalues: {1} Hence, no (new) Hessian is set as spectrum reference.N?) nplinalgeighanywarningswarnformatsum_rightT_left)rHDBs rrzGaussSampler.set_H#soyy~~a 1 q1u: MM$VCAJ2 4 fqj [[]] rcyzdo nothing by defaultNrargskwargss rupdatezGaussSampler.update/ rcyr.r/r0s r update_nowzGaussSampler.update_now2r4rc pt|ds |jdzSt j t tjjt jt j|j|j|jS#t$rY|jSwxYw)z5return eigen spectrum w.r.t. H like sqrt(H) C sqrt(H)r)) hasattrr+AttributeError variancesrasarraysortedr eigvalshdotr)covariance_matrixr'rs r eigenspectrumzGaussSampler.eigenspectrum5stW% vvqy zz&!3!3BFF266 JJ..<0155>"?@A A" >> ! sB B54B5cy)*condition number of the correlation matrixrr/rs rcorr_conditionzGaussSampler.corr_condition@rcddddd} ||j}|S#t$r-|j}|dzddd |zz z dd |d zzz zz}Y|SwxYw) aJapproximation of the expected length when isotropic with variance 1. The exact value could be computed by:: from scipy.special import gamma return 2**0.5 * gamma((self.dimension+1) / 2) / gamma(self.dimension / 2) The approximation obeys ``chin < chin_hat < (1 + 5e-5) * chin``. gS63E?g( ?gz63E?g:\?)rr8rr?rHr8)rKeyError)rvaluesvalNs rchinzGaussSampler.chinDs(O%,<> A(C   AAS&Aa!e ,rR!Q$Y/??@C  As2AAN) __name__ __module__ __qualname__rrrr3r6propertyrArDrOr/rrr r sY ) #   A Arr ceZdZdZej j dfdZedZ ddZ dZ dZ dZ d Zed Zed Zed Zy )GaussStandardConstantzqStandard Multi-variate normal distribution with zero mean. No update/change of distribution parameters. Fc t||_tj||_||_||_y#t $r ||_Y!wxYwrP)lenrrr<standard_deviations TypeErrorrandn quadratic)rrr[r\r2s rrzGaussStandardConstant.__init___sK ' ^DN')zz)'>* *''**rc6|j||j}|r_|dur |j}n|}t|D]>}t ||dz}ddks||jdzkDs,||xx||dzz zcc<@t |dr||j z}|S)NTr8rrG333333$@rrY)r[rrOrr&r9rY)rnumber same_lengtharzlen_isss rsamplezGaussStandardConstant.sampleqsjj0 d"yy"3ZQ^q5B$!66FdRWn,F  4. / 4++ +C rc<t|dr|j|zS|SNrYr9rYrxs r transformzGaussStandardConstant.transforms# 4. /++a/ /rc<t|dr||jz S|Srirjrks rtransform_inversez'GaussStandardConstant.transform_inverses# 4. /t/// /rcvtjtj|j|dzSNr8)rsqrtr&rorks rnormzGaussStandardConstant.norms*wwrvvd44Q7:;<>23 3 4s!1;A/.A/c|jr2tjtj|jSdSrP)r\rr}r^rrs rcorrelation_matrixz(GaussStandardConstant.correlation_matrixs)37>>rwwrwwt~~./KtKrNF)rQrRrS__doc__rrandomr[rrTr;rgrmrorsrwr{r@rr/rrrVrVZs yy  #++   = 44LLrrVcLeZdZdZdddej j ejjfdZ ddZ e dZ e dZ e d Zdd Zd d Zdd Zd ZdZdZddZdZdZd!dZd!dZe dZe dZdZdZdZdZe dZ dZ!dZ"y)"GaussFullSampleraMulti-variate normal distribution with zero mean. Provides methods to `sample` from and `update` a multi-variate normal distribution with zero mean and full covariance matrix. :param dimension: (required) define the dimensionality (attribute ``dimension``) of the normal distribution. If ``dimension`` is a vector, it sets the diagonal of the initial covariance matrix. :param lazy_update_gap=0: is the number of iterations to wait between the O(n^3) updates of the sampler. All values <=1 behave identically. :param constant_trace='': 'arithmetic'/'aeigen' or 'geometric' or 'geigen' (geometric mean of eigenvalues) are available to be constant. :param randn=np.random.randn: is used to generate N(0,1) numbers. :param eigenmethod=np.linalg.eigh: function returning eigenvalues and -vectors of symmetric matrix >>> import cma, numpy as np >>> g = cma.sampler.GaussFullSampler(np.ones(4)) >>> z = g.sample(1)[0] >>> assert g.norm([1,0,0,0]) == 1 >>> g.update([[1., 0., 0., 0]], [.9]) >>> g.update_now() >>> assert g.norm([1,0,0,0]) == 1 >>> g.update([[4., 0., 0.,0]], [.5]) >>> g.update_now() >>> g *= 2 >>> assert cma.utilities.math.Mh.equals_approximately(g.variances[0], 17) >>> assert cma.utilities.math.Mh.equals_approximately(g.D[-1]**2, 17) TODO ---- o Clean up CMAEvolutionStrategy attributes related to sampling (like usage of B, C, D, dC, sigma_vec, these are pretty substantial changes). In particular this should become compatible with any StatisticalModelSampler. Plan: keep B, C, D, dC for the time being as output-info attributes, DONE: keep sigma_vec (55 appearances) as a class. o combination of sigma_vec and C: - update sigma_vec with y (this is wrong: use "z") - rescale y according to the inverse update of sigma_vec (as if y is expressed in the new sigma_vec while C in the old) - update C with the "new" y. rNc  t||_tj|}t||jk(sJtj |dztjd|jz tj|jzz|_ ||_ ||_ |r|ntj|_ ||_||_tj |j|_ tj |jdz|_|j$j'}|j$||_|j"dd|f|_ d|_d|_d|_d|_d|_d|_d|_y#t$r ||_tj |}YwxYw)Nr8g-C6?rrr)rXrrr<rZr^r}exparangeClazy_update_gapconstant_traceinfcondition_limitr[ eigenmethodeyer,r+argsort_inverse_root_C_corr_condition_corr_condition_count_eigen_beta_diagonal_acceleration last_update count_tell count_eigen) rrrrrr[rrYidxs rrzGaussFullSampler.__init__s|  5 ^DN"$**Y"7 &'4>>999,a/ffdT^^3YYt~~67889 .,2Arvv &';#%ffnn34# +,(+,(9 5&DN"$'')"4  5s%F%GGc|tj|j}|j||j|j |j |jy)zreset distribution while keeping all other parameters. If `standard_deviations` is not given, `np.ones` is used, which might not be the original initial setting. N)rrr[r)rr^rrrrr[r)rrYs rresetzGaussFullSampler.resetsS  &"$''$.."9  )&*&:&:%)%8%8 JJ"&"2"2  4rc@tj|jSrP)rr}rrs rr;zGaussFullSampler.variancesswwtvvrc|j|jk(r*|jdk\s|jdkr |jS|j|_tj j |j|_|jS)rCrg333333?)rrr{rrr condrrs rrDzGaussFullSampler.corr_conditionst  + +t/?/? ?    !T%:%:S%@'' '+/+;+;(!yy~~d.E.EF###rcdtd|jdzdz dzf|_|jS)zbeta from Algorithm 1 line 16 in https://direct.mit.edu/evco/article/28/3/405/94999/Diagonal-Acceleration-for-Covariance-Matrixrrr8)ryrDrrs rbeta_diagonal_accelerationz+GaussFullSampler.beta_diagonal_accelerations8,/43F3F3Ka3ORS3S/T+U(///rc|j||j||j}|r_|dur |j}n|}t |D]>}t ||dz}ddks||jdzkDs,||xx||dzz zcc<@t j|j|j|zjj}|SNTr8rrGr`r) r6r[rrOrr&rr?r,r+r() rrarrbrcrdrerfarys rrgzGaussFullSampler.sample$s (jj0 d"yy"3ZQ^q5B$!66FdRWn,F ffTVVdffsl--.00 rctj|d}tj|}tj|ddsJt |t |k(sJ|xj d|zt |z zc_tj|dkdD]i}|j||}tj|sJ||xxt |||dzdzz zcc<tj||riJ|xj tj||jz|z c_|xjdz c_ y)aBupdate/learn by natural gradient ascent. The natural gradient used for the update is:: np.dot(weights * vectors.T, vectors) and equivalently:: sum([outer(weights[i] * vec, vec) for i, vec in enumerate(vectors)], axis=0) Details: - The weights include the learning rate and ``-1 <= sum( weights[idx]) <= 1`` must be `True` for ``idx = weights > 0`` and for ``idx = weights < 0``. - The content (length) of ``vectors`` with negative weights is changed! Tcopyrr& .>r8N) rarrayr<isfiniterXrr&nonzerorsr?r(rrvectorsweightsc1_times_delta_hsigmakrss rr3zGaussFullSampler.update6s,((7.**W%{{71:a=)))7|s7|+++ !++c'l::GaK(+A 99WQZ(D;;t$ $$ AJ#gaj/TD[1,<< zB is not orthogonal) rrr_updateC _decompose_C_assertions_quadraticr"absr&r,rprintr+)rrs rr6zGaussFullSampler.update_nowas)  ""22O OOd..@ @ t1A1AA FQ F  G   ?? SSq!DNNQ.../&&AB-()*.,*-/3*4&5 ' ( $&&M #dffQ$..1"4 445q!"u EqI J &5 rcyrPr/rs rrzGaussFullSampler._updateC~s rc0tj|j}|j||_|jdd|f|_t |jt |jf|jd|jdfk(sJy)z4sort columns of B and D according to the values in DNrr)rrr+r,rzry)rrs r_sortBDzGaussFullSampler._sortBDsnjj 3DFF S[)dffQi-DDDDrc||j|jjzdz |_|j} |j|j\|_|_t |jdkr!t dt|jz |xjdz c_ttj|jsJddkr|j|j |jsd}n|jdvs|jjdr$dtj |j"z }n3|jjdrGtj$tj tj&|j" }n|jjd r#dtj |jz }n|jjd rGtj$tj tj&|j }n1t)d t+|jzd d|j d}|dk7r*|xj|zc_|xj|zc_|xjdzc_ttj|jsJd|_ddkrrtj:|j|jz |jj|_|j<|j<jzdz |_yy#t,$r"t dt+|jzwxYw#t0$r}t)dt3|zdzt|dz}t5|j6D]}|j||xx|z cc<|dz|zdz|_|j9Yd}~1d}~wwxYw)zeigen-decompose self.C thereby updating self.B and self.D. self.C is made symmetric. Know bugs: if update is not called before decompose, the state variables can get into an inconsistent state. r8rzLcovariance matrix was not positive definite with a minimal eigenvalue of %e.rrG)rT)armeangeoaeiggeigz6trace normalization option setting '%s' not recognizedr) class_namemaxwarns iterationz1Value '%s' not allowed for constant trace settingrNz3covariance matrix eigen decomposition failed with z/ Consider to reformulate the objective function )rr(r+rr,r" ValueErrorrzrallrrrlimit_conditionr startswithrr;rlogr reprr:r Exceptionstrrrrr?inverse_root_C)rD_oldsemin_di2res rrzGaussFullSampler._decompose_Cs\&&46688#q(0 (!--dff5NDFDF466Q; 8:=dff+FGG "    ! r{{466*+ ++1u   " r**A((I59L9L9W9WXf9gBGGDNN33A((33U<t~~(> ??@A((33F;BGGDFFO+A((33F;tvv 778A!"Z"&t':':";#<-?!W[WgWgiAAv! !  FFsNFr{{466*+ ++#'D  6"$&&$&&$&&(("CD #'#6#69L9L9N9N#NRS"SD  " r !TW[\`\o\oWp!pqq rG Fa&BC D %j!mG4>>*q ! ' +Qh(3.DF      s&A!N+FM==+N(+ P;4A>> import cma >>> es = cma.CMAEvolutionStrategy(3 * [1], 1, {'CMA_diagonal_decoding':False, 'verbose':-9}) >>> _ = es.optimize(cma.ff.elli) >>> assert es.sm.condition_number > 1e4 >>> es.sm.limit_condition(1e4 - 1) >>> assert es.sm.condition_number < 1e4 Nrz*condition limit was %f<=1 but should be >1rr8rzcond=%e, limit=%e, eps=%er) rrrrr{r+RuntimeWarningrrr)rlimitrres rrz GaussFullSampler.limit_conditions$ =((E aZI$%& &{{5!T%:%:e%C vvbz1}utvvay!|33 B !8 !<&&s3"45 5t~~&A FF1IaLC L' 1  #  3rcf|jtj|rG|xj|zc_|xj|dzzc_ |xj |dzzc_yttj|jdk(r:|xjtj||zc_|jyt|jdk(r&|xj|zc_|jytt|#t $rYywxYw)a(multiply ``self.C`` with ``factor`` updating internal states. ``factor`` can be a scalar, a vector or a matrix. The vector is used as outer product and multiplied element-wise, i.e., ``multiply_C(diag(C)**-0.5)`` generates a correlation matrix. Details: rrr8N)rrisscalarrr+rr:rXr<shapeouterrrrrus r multiply_CzGaussFullSampler.multiply_Cs  ;;v  FFf F FFfck !F ##vs{2#F#)) *a / FFbhhvv. .F      ! # FFf F    S[) )"  sD$$ D0/D0c(|j||Sz``sm *= factor`` is a shortcut for ``sm = sm.__imul__(factor)``. Multiplies the covariance matrix with `factor`. rrus rrwzGaussFullSampler.__imul__   rctj|j|jz|jj}|r|j |S)a]return associated linear transformation. If ``B = sm.to_linear_transformation()`` and z ~ N(0, I), then np.dot(B, z) ~ Normal(0, sm.C) and sm.C and B have the same eigenvectors. With `reset=True`, ``np.dot(B, sm.sample(1)[0])`` obeys the same distribution after the call. See also: `to_unit_matrix` rr?r,r+r(rrrtfs rto_linear_transformationz)GaussFullSampler.to_linear_transformation9VVDFFTVVOTVVXX .  JJL rctj|j|jz |jj}|r|j |S)abreturn inverse of associated linear transformation. If ``B = sm.to_linear_transformation_inverse()`` and z ~ Normal(0, sm.C), then np.dot(B, z) ~ Normal(0, I) and sm.C and B have the same eigenvectors. With `reset=True`, also ``sm.sample(1)[0] ~ Normal(0, I)`` after the call. See also: `to_unit_matrix` rrs r to_linear_transformation_inversez1GaussFullSampler.to_linear_transformation_inverse$rrc|jSrPrrs rr@z"GaussFullSampler.covariance_matrix3 vv rc|jj}t|jdD].}|||fdz}|dd|fxx|zcc<||ddfxx|zcc<0||jzdz }|S)7return correlation matrix of the distribution. rrNg@)rrrrr()rcrefacs rrz#GaussFullSampler.correlation_matrix7su FFKKMqwwqz"AAqD'3,C adGsNG adGsNG#WOrc|jdtj|jdz}|j|_|j |S)"re-scale" C to a correlation matrix and return the scaling factors as standard deviations. See also: `to_linear_transformation`. rr)r6rr}rrrr sigma_vecs rto_correlation_matrixz&GaussFullSampler.to_correlation_matrixCsE GGDFFOS( (( rcx|j|||j|||j||zdzz S)6return correlation between variables i and j. rrrrejs r correlationzGaussFullSampler.correlationOs=vvay|tvvay|dffQil:S@@@rctj|j|jtj|jj|zS).apply linear transformation ``C**0.5`` to `x`.)rr?r,r+r(rks rrmzGaussFullSampler.transformTs3vvdffdffrvvdffhh'::;;rcddkrjqtjjjz jj _jjj zdz _tjj|Sfd}||}tj tj|s%tjdj|||S)7apply inverse linear transformation ``C**-0.5`` to `x`.rGr8ctjjtjjj|jz SrP)rr?r,r(r+)rlrs rinvz/GaussFullSampler.transform_inverse..inv`s466$&&"&&1"5">? ?rzinv(x={0}) = {1} is not finite) rrr?r,r+r(rrr#r$r%)rrlrxinverses` rroz"GaussFullSampler.transform_inverseXs 6##+')vvdfftvvotvvxx'H$(,(<(>> import cma, numpy as np >>> sm = cma.sampler.GaussFullSampler(np.ones(10)) >>> x = np.random.randn(10) >>> d = sm.norm(x) `d` is the norm "in" the true sample distribution, sampled points have a typical distance of ``sqrt(2*sm.dim)``, where ``sm.dim`` is the dimension, and an expected distance of close to ``dim**0.5`` to the sample mean zero. In the example, `d` is the Euclidean distance, because C = I. r8r)r&rr?r,r(r+rks rrszGaussFullSampler.normqs5&BFF46688Q'$&&0145s::rcd}|||z|jdz|jdzz ||||z|jdz|jdzzg}|Dcgc] }|| }}|tcc}w)N r)r+r,NotImplementedError)rrsigmarrXrlFs r!inverse_hessian_scalar_correctionz2GaussFullSampler.inverse_hessian_scalar_corrections C%K$&&)+dffQi7 7 C%K$&&)+dffQi7 7 9 1aQqT1  !! sA1rP)NFrr)#rQrRrSrrrr[r r!rrrTr;rDrrgr3r6rrrrrrwrrr@rrrrmror{rsrr/rrrrs2h"# "!%yyYY^^ %N 4 $$00 $)VK: EATF$L*6     A <(++;*"rrceZdZdZdej j dfdZdZe dZ ddZ ddZ d Z d Zdd Zdd Ze d Ze dZdZdZdZdZe dZdZy)GaussDiagonalSamplera-Multi-variate normal distribution with zero mean and diagonal covariance matrix. Provides methods to `sample` from and `update` a multi-variate normal distribution with zero mean and diagonal covariance matrix. Arguments to `__init__` ----------------------- `standard_deviations` (required) define the diagonal of the initial covariance matrix, and consequently also the dimensionality (attribute `dim`) of the normal distribution. If `standard_deviations` is an `int`, ``np.ones(standard_deviations)`` is used. `constant_trace='None'`: 'arithmetic' or 'geometric' or 'aeigen' or 'geigen' (geometric mean of eigenvalues) are available to be constant. `randn=np.random.randn` is used to generate N(0,1) numbers. >>> import cma, numpy as np >>> s = cma.sampler.GaussDiagonalSampler(np.ones(4)) >>> z = s.sample(1)[0] >>> assert s.norm([1,0,0,0]) == 1 >>> s.update([[1., 0., 0., 0]], [.9]) >>> assert s.norm([1,0,0,0]) == 1 >>> s.update([[4., 0., 0.,0]], [.5]) >>> g *= 2 TODO ---- o DONE implement CMA_diagonal with samplers o Clean up CMAEvolutionStrategy attributes related to sampling (like usage of B, C, D, dC, sigma_vec, these are pretty substantial changes). In particular this should become compatible with any StatisticalModelSampler. Plan: keep B, C, D, dC for the time being as output-info attributes, keep sigma_vec (55 appearances) either as constant scaling or as a class. Current favorite: make a class (DONE) . o combination of sigma_vec and C: - update sigma_vec with y (this is wrong: use "z") - rescale y according to the inverse update of sigma_vec (as if y is expressed in the new sigma_vec while C in the old) - update C with the "new" y. NoneFc \ t||_tj|}|jt|k(sJt||jk(sJ|dz|_ ||_||_||_ d|_ y#t$r||_tj |}YwxYw)Nr8r) rXrrr<rZr^rrr[r\r)rrrr[r\r2rYs rrzGaussDiagonalSampler.__init__s  5 ^DN"$**Y"7 ~~%8!9999&'4>>999$a'$, " 5&DN"$'')"4  5s%B%B+*B+c~|j|j|j|j|jy)z>reset distribution while keeping all other parameters )rr[r\N)rrrr[r\rs rrzGaussDiagonalSampler.resets2 dnn%)%8%8 JJ $  0rc|jSrPrrs rr;zGaussDiagonalSampler.variancesrrc$|j||j}|r_|dur |j}n|}t|D]>}t ||dz}ddks||jdzkDs,||xx||dzz zcc<@|j dz|z}|Sr)r[rrOrr&r)rrarbrcrdrerfrs rrgzGaussDiagonalSampler.samplesjj0 d"yy"3ZQ^q5B$!66FdRWn,F ffckC rctj|d}tj|}tj|ddsJt |t |k(sJ|xj d|zt |z zc_tj|dkdD]i}|j||}tj|sJ||xxt |||dzdzz zcc<tj||riJ|xj tj||dzz c_|xjdz c_ y)aupdate/learn by natural gradient ascent. The natural gradient used for the update of the coordinate-wise variances is:: np.dot(weights, vectors**2) Details: The weights include the learning rate and ``-1 <= sum(weights[idx]) <= 1`` must be `True` for ``idx = weights > 0`` and for ``idx = weights < 0``. The content of `vectors` with negative weights is changed. Trrrrr8N) rrr<rrXrr&rrsr?rrs rr3zGaussDiagonalSampler.updates((7.**W%{{71:a=)))7|s7|+++ !++c'l::GaK(+A 99WQZ(D;;t$ $$ AJ#gaj/TD[1,<< r"spA@(1/DX~C?CLLLLLL^e"|e"Nl3<l3r