J-jHH6dZddlmZmZddlZGddeZy)a\`RecombinationWeights` is a list of recombination weights for the CMA-ES. The most delicate part is the correct setting of negative weights depending on learning rates to prevent negative definite matrices when using the weights in the covariance matrix update. The dependency chain is lambda -> weights -> mueff -> c1, cmu -> negative weights )divisionprint_functionNceZdZdZddZdZdZddZddZdZ d Z d Z d Z e d Ze d Ze dZe dZy)RecombinationWeightsaa list of decreasing (recombination) weight values. To be used in the update of the covariance matrix C in CMA-ES as ``w_i``:: C <- (1 - c1 - cmu * sum w_i) C + c1 ... + cmu sum w_i y_i y_i^T After calling `finalize_negative_weights`, the weights ``w_i`` let ``1 - c1 - cmu * sum w_i = 1`` and guaranty positive definiteness of C if ``y_i^T C^-1 y_i <= dimension`` for all ``w_i < 0``. Class attributes/properties: - ``lambda_``: number of weights, alias for ``len(self)`` - ``mu``: number of strictly positive weights, i.e. ``sum([wi > 0 for wi in self])`` - ``mueff``: variance effective number of positive weights, i.e. ``1 / sum([self[i]**2 for i in range(self.mu)])`` where ``1 == sum([self[i] for i in range(self.mu)])**2`` - `mueffminus`: variance effective number of negative weights - `positive_weights`: `np.array` of the strictly positive weights - ``finalized``: `True` if class instance is ready to use Class methods not inherited from `list`: - `finalize_negative_weights`: main method - `zero_negative_weights`: set negative weights to zero, leads to ``finalized`` to be `True`. - `set_attributes_from_weights`: useful when weight values are "manually" changed, removed or inserted - `asarray`: alias for ``np.asarray(self)`` - `do_asserts`: check consistency of weight values, passes also when not yet ``finalized`` Usage: >>> # from recombination_weights import RecombinationWeights >>> from cma.recombination_weights import RecombinationWeights >>> dimension, popsize = 5, 7 >>> weights = RecombinationWeights(popsize) >>> c1 = 2. / (dimension + 1)**2 # caveat: __future___ division >>> cmu = weights.mueff / (weights.mueff + dimension**2) >>> weights.finalize_negative_weights(dimension, c1, cmu) >>> print('weights = [%s]' % ', '.join("%.2f" % w for w in weights)) weights = [0.59, 0.29, 0.12, 0.00, -0.31, -0.57, -0.79] >>> print("sum=%.2f, c1+cmu*sum=%.2f" % (sum(weights), ... c1 + cmu * sum(weights))) sum=-0.67, c1+cmu*sum=0.00 >>> print('mueff=%.1f, mueffminus=%.1f, mueffall=%.1f' % ( ... weights.mueff, ... weights.mueffminus, ... sum(abs(w) for w in weights)**2 / ... sum(w**2 for w in weights))) mueff=2.3, mueffminus=2.7, mueffall=4.8 >>> weights = RecombinationWeights(popsize) >>> print("sum=%.2f, mu=%d, sumpos=%.2f, sumneg=%.2f" % ( ... sum(weights), ... weights.mu, ... sum(weights[:weights.mu]), ... sum(weights[weights.mu:]))) sum=0.00, mu=3, sumpos=1.00, sumneg=-1.00 >>> print('weights = [%s]' % ', '.join("%.2f" % w for w in weights)) weights = [0.59, 0.29, 0.12, 0.00, -0.19, -0.34, -0.47] >>> weights = RecombinationWeights(21) >>> weights.finalize_negative_weights(3, 0.081, 0.28) >>> weights.insert(weights.mu, 0) # add zero weight in the middle >>> weights = weights.set_attributes_from_weights() # change lambda_ >>> assert weights.lambda_ == 22 >>> print("sum=%.2f, mu=%d, sumpos=%.2f" % ... (sum(weights), weights.mu, sum(weights[:weights.mu]))) sum=0.24, mu=10, sumpos=1.00 >>> print('weights = [%s]%%' % ', '.join(["%.1f" % (100*weights[i]) ... for i in range(0, 22, 5)])) weights = [27.0, 6.8, 0.0, -6.1, -11.7]% >>> weights.zero_negative_weights() # doctest:+ELLIPSIS [0.270... >>> "%.2f, %.2f" % (sum(weights), sum(weights[weights.mu:])) '1.00, 0.00' >>> mu = int(weights.mu / 2) >>> for i in range(len(weights)): ... weights[i] = 1. / mu if i < mu else 0 >>> weights = weights.set_attributes_from_weights() >>> 5 * "%.1f " % (sum(w for w in weights if w > 0), ... sum(w for w in weights if w < 0), ... weights.mu, ... weights.mueff, ... weights.mueffminus) '1.0 0.0 5.0 5.0 0.0 ' The optimal weights on the sphere and other functions are closer to exponent 0.75: >>> for expo, w in [(expo, RecombinationWeights(5, exponent=expo)) ... for expo in [1, 0.9, 0.8, 0.7, 0.6, 0.5]]: ... assert all([len(w(i)) == i for i in range(3, 8)]) ... print(7 * "%.2f " % tuple([expo, w.mueff] + w)) 1.00 1.65 0.73 0.27 0.00 -0.36 -0.64 0.90 1.70 0.71 0.29 0.00 -0.37 -0.63 0.80 1.75 0.69 0.31 0.00 -0.39 -0.61 0.70 1.80 0.67 0.33 0.00 -0.40 -0.60 0.60 1.84 0.65 0.35 0.00 -0.41 -0.59 0.50 1.89 0.62 0.38 0.00 -0.43 -0.57 >>> for lam in [8, 8**2, 8**3, 8**4]: ... if lam == 8: ... print(" lam expo mueff w[i] / w[i](1)") ... print(" /mu(1) 1 2 3 4 5 6 7 8") ... w1 = RecombinationWeights(lam, exponent=1) ... for expo, w in [(expo, RecombinationWeights(lam, exponent=expo)) ... for expo in [1, 0.8, 0.6]]: ... print('%4d ' % lam + 10 * "%.2f " % tuple([expo, w.mueff / w1.mueff] + [w[i] / w1[i] for i in range(8)])) lam expo mueff w[i] / w[i](1) /mu(1) 1 2 3 4 5 6 7 8 8 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 8 0.80 1.11 0.90 1.02 1.17 1.50 1.30 1.07 0.98 0.93 8 0.60 1.24 0.80 1.02 1.35 2.21 1.68 1.13 0.95 0.85 64 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 64 0.80 1.17 0.82 0.86 0.88 0.91 0.93 0.95 0.97 0.98 64 0.60 1.36 0.65 0.72 0.76 0.80 0.84 0.87 0.91 0.94 512 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 512 0.80 1.20 0.76 0.78 0.79 0.80 0.81 0.82 0.83 0.83 512 0.60 1.42 0.56 0.59 0.61 0.63 0.64 0.65 0.67 0.68 4096 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 4096 0.80 1.21 0.71 0.73 0.74 0.74 0.75 0.75 0.76 0.76 4096 0.60 1.44 0.50 0.52 0.53 0.54 0.55 0.55 0.56 0.56 Reference: Hansen 2016, arXiv:1604.00772. c |}||_|d|_ t|}|dkrtd|zd|_tj|||jdt||jd}|d k7r2t |jt|D]}||xx| zcc<|jd|_y#t$r tt|}nt#t$rhd}t d|dzDcgc]D}|t j |dzdz t j |z |jFncc}w}}YnwxYwY?wxYw) areturn recombination weights `list`, post condition is ``sum(self) == 0 and sum(self.positive_weights) == 1``. Positive and negative weights sum to 1 and -1, respectively. The number of positive weights, ``self.mu``, is about ``len_/2``. Weights are strictly decreasing. `finalize_negative_weights` (...) or `zero_negative_weights` () should be called to finalize the negative weights. :param `len_`: AKA ``lambda`` is the number of weights, see attribute `lambda_` which is an alias for ``len(self)``. Alternatively, a list of "raw" weights can be provided. Ncd|dk(r|S|dk7|dkrdndz}|tj||zzS)Nrr)mathfabs)xexposs g/Users/jameslopez/projects/TradingBot25/.venv/lib/python3.12/site-packages/cma/recombination_weights.py signed_powerz3RecombinationWeights.__init__..signed_powers;qy(a!a%BQ7Atyy|T111g@z%number of weights must be >=2, was %dF) do_assertsr)exponentlen TypeErrorlistranger log ValueErrordebug__init__set_attributes_from_weightssummur finalized)selflen_rweightsrisum_negs rrzRecombinationWeights.__init__s\    DM 8w ! T\\ !>D7):);$<< < T\\ !>Wt||%;s$BBT$''(^S S rc||jk\r||S|dkrt|dgzSt|dz }|dkDsJ|d||d|zkDdgzz|| dzS)aFreturn weight list of len `lambda_` from the extreme weights. This obeys the constraint ``sign(w[i]) == sign((lambda_-1)/2 - i)`` if the original weights do. >>> import cma >>> for lam in [2, 3, 5, 11, 33]: ... w = cma.recombination_weights.RecombinationWeights(lam) ... for i in range(1, len(w) + 2): ... w2 = w.trim_middle(i) ... assert len(w2) == i, (len(w2), i) ... if i > 1: ... assert w2[0] == w[0], (w2, w) ... assert w2[-1] == w[-1], (w2, w) ... i_middle = (i - 1) / 2 ... assert i > len(w) or ( ... w2[int(i_middle - .1)] * w2[int(i_middle + 1.1)] < 0), ( ... lam, i, i_middle) rgrN)r(int)r"r(mu_s r trim_middlez RecombinationWeights.trim_middlesy* dll "= Q;w<2$& &'A+QwwDSzWq3w.2$66sdeDDrNcn7ddkDstddzddkDrtddz|dd|tfdttdz DsJt dD|_t d|j }|dkDsJtt|D]}||xx|zcc<dt d d|j Dz |_t |j d}|t d Dz d zd ksJ| xs|j|S) amake the class attribute values consistent with weights, in case after (re-)setting the weights from input parameter ``weights``, post condition is also ``sum(self.postive_weights) == 1``. This method allows to set or change the weight list manually, e.g. like ``weights[:] = new_list`` or using the `pop`, `insert` etc. generic `list` methods to change the list. Currently, weights must be non-increasing and the first weight must be strictly positive and the last weight not larger than zero. Then all ``weights`` are normalized such that the positive weights sum to one. Nrz&the first weight must be >0 but was %fr z&the last weight must be <=0 but was %fc3:K|]}||dzk\ywrN.0r%r$s r zCRecombinationWeights.set_attributes_from_weights..*:!8A1:1-!8rc3&K|] }|dkD ywrNr1r3ws rr4zCRecombinationWeights.set_attributes_from_weights..s-Wa!eWc3&K|] }|dz ywrNr1r9s rr4zCRecombinationWeights.set_attributes_from_weights.. s 6#4*+1#4r;c3,K|] }|dks |ywr8r1r9s rr4zCRecombinationWeights.set_attributes_from_weights.. 7gQ1g rdy=)rallrrrr mueffr)r"r$rsposr%snegs ` rrz0RecombinationWeights.set_attributes_from_weightssc  1:>  >G ^,- - 8a<QwS=DI&'..q28|<44a"fslc5I7@6AB  , ,QT__1D04 Q2@.@ A  :: (3t94 5 rcttt|D]}||xx||dkrdndzcc<d|_|S)z0finalize by setting all negative weights to zerorrT)rrr!)r"ks rzero_negative_weightsz*RecombinationWeights.zero_negative_weightsHs;s4y!A GDGaKqQ .G" rc |}t|}||jdksJ|ddks^t|jt|jdz f}t ||jD]}| |j|z z ||<t|t ||jdz }t |j|jD]}||xx|zcc<d|z dz t |cxkr d|z dzksJJ|jr1tdt |t ||jd fzyy)aset sum of negative weights to ``-abs(value)`` Precondition: the last weight must no be greater than zero. Details: if no negative weight exists, all zero weights with index lambda / 2 or greater become uniformely negative. rr rNrh㈵>zsum w = %.2f, sum w^- = %.2f) absr maxr+r(rrrrK)r"valuer$istartr%factors rrLz.RecombinationWeights._negative_weights_set_sumOs5E tww1$$$r{Q$''3t||a'7#89:F64<<0#Vt||f'<= 1US!2334tww -A AJ& J.5y4#g,AUT1AAAAAA :: 0w<#gdggh&7"8!89: ; rc|}t|}t||jd| k\ry|ddkr||jdksJt|t||jdz }|dkrWt|j|jD]}||xx|zcc<|j rt dt||fzt|dzd|z k\sJy)zDlower bound the sum of negative weights to ``-abs(value)``. Nr rrz#sum w = %.2f (with correction %.2f)rX)rYrr rr(rrK)r"r[r$r]r%s rrMz0RecombinationWeights._negative_weights_limit_sumisE  wtwwx !eV + r{Q7477#3q#888US!2334 A:477DLL1 f$ 2zz;7|U+,-7|d"a%i///rc|ddcxk\rdkDsJJddksJt|jk(sJtfdttdz DsJ|jdkDsJ|jdz dcxkDr|jk\sJJdt dd|jDcxkrdksJJ|j dz t d|jd zt d d|jDz cxkrd|j zksJJ|jdcxk(rt |jdk(sfn|jdz t |jdd zt d |jdDz cxkrd|jzksJJyy) zassert consistency. Assert: - attribute values of ``lambda_, mu, mueff, mueffminus`` - value of first and last weight - monotonicity of weights - sum of positive weights to be one rrr c3:K|]}||dzk\ywr0r1r2s rr4z2RecombinationWeights.do_asserts..r5r6g+?c3 K|]}|yw)Nr1r9s rr4z2RecombinationWeights.do_asserts..s8&71&7s Ngjt?rc3&K|] }|dz ywr=r1r9s rr4z2RecombinationWeights.do_asserts../P>O1>Or;c3&K|] }|dz ywr=r1r9s rr4z2RecombinationWeights.do_asserts..rcr;)rr(rBrr rrCrN)r"r$s @rrzRecombinationWeights.do_assertszsGAJ""""""r{a7|t||+++:!&s7|a'7!8:: ::ww{{twwqy!A9)999999s8ghtww&788@5@@@@@ U"GHTWW%&)C/Pghtww>O/P,PP# "# $# $#1>GDGGH,=(>>%'GDGGH%&)C/Pgdggh>O/P,PP('( )(( )((?rct|S)zalias for ``len(self)``)r)r"s rr(zRecombinationWeights.lambda_s4yrc|}t||jd}|td|Dz dzdksJ|dk(rdS|dztd||jdDz S)Nc3,K|] }|dks |ywr8r1r9s rr4z2RecombinationWeights.mueffminus..r?r@rrArc3&K|] }|dz ywr=r1r9s rr4z2RecombinationWeights.mueffminus..s>,=qad,=r;)rr )r"r$rEs rrNzRecombinationWeights.mueffminussv74778$%s7g777!;eCCCQY @a#>GDGGH,=>>> @rcf ddlm}||d|jS#|d|jcYSxYw)z}all (strictly) positive weights as ``np.array``. Useful to implement recombination for the new mean vector. rasarrayN)numpyrkr r"rks rpositive_weightsz%RecombinationWeights.positive_weightss6  " %4>* * "> !s0cddlm}||S)zreturn weights as numpy arrayrrj)rlrkrms rrkzRecombinationWeights.asarrays "t}r)r)NT)T)__name__ __module__ __qualname____doc__rr)r-rrSrVrLrMrpropertyr(rNrnrkr1rrrrs@B/bE:$L56n;40")8@@  " "rr)rs __future__rrr rrr1rrrvs  0 _4_r