ó Z_Sc@ sÙddlmZmZddlZddlmZmZmZddlZ ddlm Z m Z m Z m Z mZmZmZmZmZddlTdefd„ƒYZdefd „ƒYZddd d d „ZdS( iÿÿÿÿ(tdivisiontprint_functionN(tlogtsqrttexp( tarraytasarraytfloat64tonestzerostint32talltanytshape(t*t DirichletcB sweZdZdZd„Zd„Zd„Zd„Zd„Zd „Z d „Z d „Z d „Z d „Z d„ZRS(s^The Dirichlet probability distribution. The Dirichlet is a continuous multivariate probability distribution across non-negative unit length vectors. In other words, the Dirichlet is a probability distribution of probability distributions. It is conjugate to the multinomial distribution and is widely used in Bayesian statistics. The Dirichlet probability distribution of order K-1 is p(theta_1,...,theta_K) d theta_1 ... d theta_K = (1/Z) prod_i=1,K theta_i^{alpha_i - 1} delta(1 -sum_i=1,K theta_i) The normalization factor Z can be expressed in terms of gamma functions: Z = {prod_i=1,K Gamma(alpha_i)} / {Gamma( sum_i=1,K alpha_i)} The K constants, alpha_1,...,alpha_K, must be positive. The K parameters, theta_1,...,theta_K are nonnegative and sum to 1. Status: Alpha talphat_totalt_meancC s.t|tƒ|_t|ƒ|_d|_dS(s¤ Args: - alpha -- The parameters of the Dirichlet prior distribution. A vector of non-negative real numbers. N(RRRtsumRtNoneR(tselfR((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pyt__init__NscC sl|j}t|ƒ}t|ftƒ}x.t|ƒD] }tj||dƒ|| (2002) gð?(RtlenR Rtrangetrandomt gammavariateR(RRtKtthetatk((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pytsample\s  cC s,|jdkr%|j|j|_n|jS(N(RRRR(R((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pytmeanqscC sù|j}t|ƒ}t|ƒ}t||ftƒ}xDt|ƒD]6}||d|||||d|||fR?RtmaxtGammatfrom_mean_variancet inverse_cdf( RR<tfracRtvariancetsdtgt low_limitt high_limit((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pytinterval_relative_entropyès #(salphas_totals_mean(t__name__t __module__t__doc__t __slots__RRRR%R(R-R2R;R>R?RJ(((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pyR3s       +  RAcB sqeZdZd Zd„Zed„ƒZed„ƒZd„Zd„Z d„Z d „Z d „Z d „Z RS( sdThe gamma probability distribution. (Not to be confused with the gamma function.) RtbetacC sL|dkrtdƒ‚n|dkr6tdƒ‚n||_||_dS(Ngsalpha must be positivesbeta must be positive(R&RRO(RRRO((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pyRs    cC s||d|ƒS(Ngð?((tclsR tscale((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pytfrom_shape_scale scC s%|d|}||}|||ƒS(Ni((RPRRERRO((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pyRB s cC s|j|jS(N(RRO(R((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pyRscC s|j|jdS(Ni(RRO(R((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pyREscC stj|jd|jƒS(Ngð?(RRRRO(R((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pyRscC sO|dkrdS|j}|j}||dt| |ƒ||t|ƒS(Nggð?(RRORtgamma(RR'R1tb((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pytpdfs    cC sdt|j|j|ƒS(Ngð?(tnormalized_incomplete_gammaRRO(RR'((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pytcdf"sc s1‡‡fd†}tt|tˆjƒƒƒƒS(Nc sˆjt|ƒƒˆS(N(RWR(R'(tpR(s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pytrootof&s(Rt find_rootRR(RRXRY((RXRs=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pyRC%s(salphasbeta(RKRLRMRNRt classmethodRRRBRRERRURWRC(((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pyRAùs      g`sáÓbÈO>i2c  s|d„}‡fd†}d„}|dk rC||ˆ|||ƒS|dk re||ˆ|||ƒS||ˆ||ƒSdS(sˆReturn argument 'x' of the function f(x), such that f(x)=0 to within the given tolerance. f : The function to optimize, f(x) x : The initial guess y : An optional second guess that shoudl bracket the root. fprime : The derivate of f'(x) (Optional) tolerance : The error bounds max_iterations : Maximum number of iterations Raises: ArithmeticError : Failure to converge to the given tolerence Notes: Uses Newton-Raphson algorihtm if f'(x) is given, else uses bisect if y is given and brackets the root, else uses secant. Status : Beta (Not fully tested) c S s±|}|d}||ƒ}||ƒ}d}xft|ƒD]X} ||||||}t||ƒ|kru|S|}|}|}||ƒ}q;Wtd||fƒ‚dS(Ng-Cëâ6?is3Failed to converge after %d iterations, value is %f(RtabstArithmeticError( tfR't tolerancetmax_iterationstx0tx1tv0tv1tx2R"((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pytsecantDs    c  sç||ƒ}||ƒ}|dkr(|S|dkr8|S||dkrWtdƒ‚nxst|ƒD]e}||}|d|} || ƒ} ||krž| S| |dkr½| }| }qd| }| }qdWtd|ˆfƒ‚dS(Nis!Start points do not bracket root.gà?s3Failed to converge after %d iterations, value is %f(R]R( R^R1RTR_R`tfatfbR"tdeltatxmtfm(R'(s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pytbisectYs,         cS sq|}xNt|ƒD]@}|||ƒ||ƒ}t||ƒ|krM|S|}qWtd||fƒ‚dS(Ns3Failed to converge after %d iterations, value is %f(RR\R](R^R'tfprimeR_R`RaR"Rb((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pytnewtonvs N(R( R^R'tyRmR_R`RfRlRn((R's=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pyRZ-s   (t __future__RRRtmathRRRtnumpyR)RRRRR R R R R tcorebio.moremathtobjectRRARRZ(((s=/home/psgendb/BIRCHDEV/pkg/weblogo-3.4/weblogolib/logomath.pyt(s  @ Æ4