B d4@s`ddlmZmZmZddlZddlZddlZddlTddlZ ddl Z ddl m Z ddl m Z ddlmZddlmZddlmZd e_d d ZGd d d eZddZddZddZd9ddZd:ddZGdddeZGdddeZd;d!d"Zdd)d*Z"Gd+d,d,eZ#d-d.Z$d?d/d0Z%d1d2Z&Gd3d4d4eZ'd5d6Z(d7d8Z)dS)@)absolute_importdivisionprint_functionN)*)matrix)flex)rational)range)zipa Fits a gaussian function to a list of points. Parameters ---------- x : scitbx.array_family.flex.double y : scitbx.array_family.flex.double Returns ------- scitbx.math.gaussian_fit_1d_analytical Examples -------- >>> from scitbx.array_family import flex >>> from scitbx.math import gaussian_fit_1d_analytical >>> x, y = flex.double(), flex.double() >>> x.append(-1) ; y.append(.1) >>> x.append(0) ; y.append(1) >>> x.append(1) ; y.append(.1) >>> fit = gaussian_fit_1d_analytical(x, y) >>> print fit.a, fit.b 1.0 2.30258509299 cCs tj|S)N)rmedianZ dispersion)datar s/mnt/filia/a/genomebrowser/www/genomebrowser/fleming/tools/molprobity/modules/cctbx_project/scitbx/math/__init__.pymedian_statistics)src@s$eZdZddZddZddZdS)line_given_pointscCs:dd|D|_|jd|jd|_t|j|_dS)NcSsg|]}t|qSr )rcol).0pointr r r /sz.line_given_points.__init__..r)pointsdeltafloatnorm_sq delta_norm_sq)selfrr r r__init__.szline_given_points.__init__cCs<|jdkr||jdS|j||jd|jS)zAhttp://mathworld.wolfram.com/Point-LineDistance3-Dimensional.htmlr)rrrrcross)rrr r r distance_sq3s zline_given_points.distance_sqcCs6|jd||j |j}|jd|j|S)Nr)rdotrr)rrtr r rperp_xyz:s"zline_given_points.perp_xyzN)__name__ __module__ __qualname__rrr!r r r rr,srcCs,tt|d|d|dddddS)Nrg?g@g)maxmin)rr r r*r3_rotation_cos_rotation_angle_from_matrix>s$r*cCsBt|}|dkr*t|}|t|}nd}d|||S)z Chirikjian, G. Stochastic models, information theory, and Lie groups. Volume 2, pp 39-40. Applied and Numerical Harmonic Analysis, Birkhauser g?g?)r*mathacossin transpose)r)Z cos_thetathetaZa1r r rr3_rotation_matrix_logarithmEs  r0cs<|s tdddlttjfdd|D}t|S)z Calculates an approximation of the Riemannian (geometric) mean through quaternion averaging Arithmetic and geometric solutions for average rigid-body rotation (2010). I Sharf, A Wolf & M.B. Rubin, Mechanism and Machine Theory, 45, 1239-1251 zAverage of empty sequencerNcsg|]}jt|qSr )rr%r3_rotation_matrix_as_unit_quaternion)re)scitbxr rrgszEr3_rotation_average_rotation_matrix_from_matrices..) 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Special case of generalized_inverse(a) * b taking advantage of the fact that a is real and symmetric. Opportunistic algorithm: first assumes that a has full rank. If this is true, solves a*x=b for x using simple back-substitution. Only if a is rank-deficient: To obtain the x with minimum norm, transforms a to a basis formed by its eigenvectors, solves a*x=b in this basis, then transforms x back to the original basis system. Returns None if a*x=b has no solution. rNr)a_workb_work min_abs_pivot)Z free_valuesrq)rrmax_rank)r{rrecas_flex_double_matrix n_columnsr]rdoubler'allr^ deep_copyZrow_echelon_full_pivotingZnullityZback_substitutionZis_square_matrixr3linalg eigensystemreal_symmetricvectorsZmatrix_transposeZmatrix_multiplyZrank)rMbZrelative_min_abs_pivotZabsolute_min_abs_pivotZ back_substitution_epsilon_factorrrqZawZbwZefraesrSZctrr r r)solve_a_x_eq_b_min_norm_given_a_sym_b_cols@           rc@s eZdZdZddZddZdS)finite_difference_computationa Computing the derivative of a scalar function f(x, ...) wrt x, where x may be a vector, involves computing f(x + h, ...) where h is suitably chosen a delta. So as to keep numerical accuracy, it is best to follow a well known recipe to choose h knowing its direction. When using that value, a finite difference computation typically reaches a precision of self.precision Reference: chap 5.7 of Numerical Recipes in C cCs ttjjj}t||_dS)N)r+rnr3Zdouble_numeric_limitsrq precision)rr2r r rrWsz&finite_difference_computation.__init__cCs0||j}}|t|}||}|||}|S)z Compute the value h in the given direction that is most suitable for use in finite difference computation around the given point x. The vector 'direction' may not be a unit-vector. )rr^)rr directionrarTuhr r r best_delta[s    z(finite_difference_computation.best_deltaN)r"r#r$__doc__rrr r r rrLs rc Cs~tj}tj}|tjd}|tjd}|d|||||}|d|||||} |d|||} || | fS)zj Returns a point on sphere of radius r: see definition of polar (sperical) coordinate system in 3D. rKrrrO)r+r-rNrL) r)Zs_degZt_degrxr-rNrTr rayzr r rpoint_on_spherefsrc Cs||gddkst|d|d|d|d|d|dg}t|g}|dk rf|dkstnF|dksrtt|dd|dd|dd}t||d}|dt|d}t}x&t|dD]} | || |qW| ||S)NrrrO) countr]rr|r+rnintrr extendro) startendnstepZvecr)Z vec_lengthZdrrrIr r requally_spaced_points_on_vectorts.  * rcCs.yt|}Wntk r*t|}YnXt|}|drn||d}|d|dd}||dd}n@||d||ddd}|d|d}||dd}t|}|dr||d}||d}n@||d||ddd}||d||ddd}|d||||dfS)z Returns the Tukey five number summary (min, lower hinge, median, upper hinge, max) for a sequence of observations. This function gives the same results as R's fivenum function. rONrr)rsortedAttributeErrorrE)r ZsortsrZmedr[upperZlhingeZuhinger r rfive_number_summarys&     rc@seZdZdZddZdS) sin_cos_tablez8 Always evaludate performance when it is important! cCst||_dtj|j|_t|_t|_xBt|jD]4}|j t ||j|j t ||jq8WdS)NrO) rr+rLrrrZ sin_tableZ cos_tabler ror-rN)rrrIr r rrs  zsin_cos_table.__init__N)r"r#r$rrr r r rrsrc Csg}xZt|D]N\}}g}x.t|D]"\}}t|||kr$||q$W||kr||qW|dd}x*t|D]\}}x|D] } ||| <qWqvW|S)aB Best explained by examples: for array [0.232, 0.002, 0.45, 1.2, 0.233, 1.2, 0.5, 0.231, 0,0,0,0,0] return [0, 1, 2, 3, 0, 3, 4, 0, 1,1,1,1,1] if eps=0.01. Other examples: [0, 2, 0, 2] [0, 1, 0, 1] [0, 0, 0, 0] [0, 0, 0, 0] [1, 2, 3, 4] [0, 1, 2, 3] N) enumerater^ro) raepsZii_allrIZxiiijZxjrZiiir r rsimilarity_indicess  rcCs|ddkrtd||||}||||}xRtd|dD]B}|ddkrl|d||||7}qB|d||||7}qBW||dS)z< Integral of f on [a,b] using composite Simpson's rule. rOrzn must be evenrr%)rCr )r`rMrrrrTrIr r rsimpsons   r)r=r>)F)Nrrz)NNN)NN)rrr)NN)* __future__rrrr5r+r7Zscitbx.math.extZscitbx.linalg.eigensystemr3Zscitbx.math.gaussianrscitbx.array_familyrboost_adaptbx.boostr six.movesr r Zgaussian_fit_1d_analyticalrrobjectrr*r0r<rJrUrVrer~rrrrrrrrrrr r r rsN      $ 7    8