B da@sdZddlmZmZmZddlmZddlmZdaddZ da dd Z dd l Z dd l Z Gd d d eZGd ddeZGdddeZGdddeeZGdddeeZGdddeZGdddeeZGdddeeZGdddeZGdddeZGdd d eZGd!d"d"eZGd#d$d$eZdWd%d&Zd'd(Zd)d*Zd+d,Zd-d.Z d/d0Z!dXd1d2Z"dYd3d4Z#d5d6Z$d7d8Z%d9d:Z&d;d<Z'd=d>Z(dZd?d@Z)GdAdBdBeZ*dCdDZ+dEdFZ,d[dHdIZ-d\dJdKZ.dLdMZ/dNdOZ0dPdQZ1dRdSZ2dTdUZ3e4dVkre2e3d S)]a Note: this module can be used in isolation (without the rest of scitbx). All external dependencies (other than plain Python) are optional. The primary purpose of this module is to provide compact implementations of essential matrix/vector algorithms with minimal external dependencies. Optimizations for execution performance are used only if compactness is not affected. The scitbx/math module provides faster C++ alternatives to some algorithms included here. )absolute_importdivisionprint_function)range)zipFcCs6tdkr2yddlmaWntk r0daYnXtS)NFr)flex)_flex_importedscitbx.array_familyr ImportErrorr r u/mnt/filia/a/genomebrowser/www/genomebrowser/fleming/tools/molprobity/modules/cctbx_project/scitbx/matrix/__init__.py flex_proxys  r cCs6tdkr2y ddl}Wntk r,daYnX|atS)NFr)_numpy_importedZ numpy.linalgr )numpyr r r numpy_proxys  rNc@seZdZdZeZddZddZddZdd Z d d Z d d Z ddZ ddZ dddZddZddZddZddZddZdd Zd!d"Zd#d$Zd%d&Zdd(d)Zd*d+Zd,d-Zdd/d0Zd1d2Zd3d4Zd5d6Zd7d8Zd9d:Z d;d<Z!d=d>Z"d?d@Z#dAdBZ$dCdDZ%e#Z&e%Z'dEdFZ(ddGdHZ)dIdJZ*dKdLZ+ddNdOZ,dPdQZ-dRdSZ.dTdUZ/dVdWZ0dXdYZ1dd[d\Z2d]d^Z3d_d`Z4dadbZ5ddcddZ6ddedfZ7ddgdhZ8ddidjZ9ddkdlZ:dmdnZ;ddodpZddvdwZ?ddxdyZ@ddzd{ZAdd|d}ZBdddZCdddZDddZEddZFddZGddZHddZIddZJdddZKdddZLddZMddZNddZOddZPddZQddZRddZSdddZTddZUddZVddZWdS)recz Base rectangle object, used to store 2-dimensional data. Examples -------- >>> from scitbx.matix import rec >>> m = rec((1, 2, 3, 4), (2, 2)) >>> print m.trace() 5 >>> other = rec((1, 1, 1, 1), (2, 2)) >>> print m.dot(other) 10 cCsVt|dkstt||js&||}t||d|dksBt||_t||_dS)Nr)lenAssertionError isinstancecontainer_typeelemstuplen)selfrrr r r __init__5s   z rec.__init__cCs |jdS)Nr)r)rr r r n_rows=sz rec.n_rowscCs |jdS)Nr)r)rr r r n_columns@sz rec.n_columnscCstdd|jD|jS)NcSsg|] }| qSr r ).0er r r Dszrec.__neg__..)rrr)rr r r __neg__Csz rec.__neg__cs@|j|jkst|j|jtfddttD|jS)Ncsg|]}||qSr r )ri)abr r r!Jszrec.__add__..)rrrrrr)rotherr )r$r%r __add__Fsz rec.__add__cs@|j|jkst|j|jtfddttD|jS)Ncsg|]}||qSr r )rr#)r$r%r r r!Pszrec.__sub__..)rrrrrr)rr&r )r$r%r __sub__Lsz rec.__sub__c s2tds.z2Incompatible matrices: self.n: %s other.n: %sr)r)hasattrrlistrrrrcolrr RuntimeErrorstrrappendsqr) rr&r$aracr%bcresultr#ksjr )r&r __mul__Rs2  ( z rec.__mul__cCst|tr||S||S)zscalar * matrix)rrr8)rr&r r r __rmul__os  z rec.__rmul__Nc Csv|j}|}|}|dkrdg||}d}xlt|D]`}d}xNt|D]B} xt| D]2} ||||| | | | 7<|d7}qWqW||7}| | 7} qW|| krht|St||| fS)NrrzIncompatible matrices.)rrrrr0rr)rr&r$r1r2r4Zjacr7ikr#r5r%r3Zjbcr r r transpose_multiplyus>$ $  zrec.transpose_multiplycstfdd|jD|jS)Ncsg|] }|qSr r )rr )r&r r r!szrec.__div__..)rrr)rr&r )r&r __div__sz rec.__div__cstfdd|jD|jS)Ncsg|] }|qSr r )rr )r&r r r!sz#rec.__truediv__..)rrr)rr&r )r&r __truediv__szrec.__truediv__cstfdd|jD|jS)Ncsg|] }|qSr r )rr )r&r r r!sz$rec.__floordiv__..)rrr)rr&r )r&r __floordiv__szrec.__floordiv__cstfdd|jD|jS)Ncsg|] }|qSr r )rr )r&r r r!szrec.__mod__..)rrr)rr&r )r&r __mod__sz rec.__mod__cCs|j|||S)N)rr)riricr r r __call__sz rec.__call__cCs t|jS)N)rr)rr r r __len__sz rec.__len__cCs |j|S)N)r)rr#r r r __getitem__szrec.__getitem__cCstdd|jD|jS)NcSsg|] }t|qSr )float)rr r r r r!sz rec.as_float..)rrr)rr r r as_floatsz rec.as_floatcs(ddlmtfdd|jD|jS)Nr)rationalcsg|]}|qSr )int)rr )rGr r r!sz)rec.as_boost_rational..)boost_adaptbx.boostrGrrr)rr )rGr as_boost_rationals zrec.as_boost_rationalTcCs8|rtdd|jD|jStdd|jD|jSdS)NcSsg|]}tt|qSr )rHround)rr r r r r!szrec.as_int..cSsg|] }t|qSr )rH)rr r r r r!s)rrr)rZroundingr r r as_intsz rec.as_intcCs&t}|dk st||j|jS)N)rrZarrayrreshaper)rrr r r as_numpy_arrays zrec.as_numpy_arraycCstdd|jD|jS)NcSsg|] }t|qSr )abs)rr r r r r!sz rec.each_abs..)rrr)rr r r each_abssz rec.each_absrcs2dfddtfdd|jD|jS)Ng@cs4t|}| kr |7}n|kr0|8}|S)N)mathfmod)r r)halfperiodr r mod_shorts   z%rec.each_mod_short..mod_shortcsg|] }|qSr r )rr )rVr r r!sz&rec.each_mod_short..)rrr)rrUr )rTrVrUr each_mod_shortszrec.each_mod_shortcCs,d}x"|jD]}|dks ||kr |}q W|S)N)r)rr4r r r r mins  zrec.mincCs,d}x"|jD]}|dks ||kr |}q W|S)N)r)rr4r r r r maxs  zrec.maxcCs@d}x6tt|jD]$}|dks4|j||j|kr|}qW|S)N)rrr)rr4r#r r r min_indexs z rec.min_indexcCs@d}x6tt|jD]$}|dks4|j||j|kr|}qW|S)N)rrr)rr4r#r r r max_indexs z rec.max_indexcCs d}x|jD] }||7}q W|S)Nr)r)rr4r r r r sums  zrec.sumcCs d}x|jD] }||9}q W|S)Nr)r)rr4r r r r products  z rec.productcCsL||kst|}d}x&t|D]}||j|||7}q*W|S)Nr)rrrrr)rrr4r#r r r traces z rec.tracecCs$d}x|jD]}|||7}q W|S)Nr)r)rr4r r r r norm_sqs z rec.norm_sqcstfdd|jD|jS)Ncsg|]}t|qSr )rK)rr))digitsr r r!szrec.round..)rrr)rr`r )r`r rKsz rec.roundcCs*|dks|dkstt|S)Nr)rrrrQsqrtr_)rr r r __abs__sz rec.__abs__cCs |t|S)N)rO)rr r r normalize sz rec.normalizecCsd}|j}|dkr>xrtt|D]}||}|||7}q WnHt|jt|jksVt|j}x(tt|D]}|||||7}qjW|S)Nr)rrrr)rr&r4r$r#vr%r r r dot szrec.dotcCs|jdkst|j|jkst|j}|j}t|d|d|d|d|d|d|d|d|d|d|d|df|jS)N))r)rrfrrr)rrrr)rr&r$r%r r r crosssz rec.crosscCs0|jdkrtd|}|tdddS)N)rfrfzNot a 3x3 matrix.rf)rg?)rr-r;identityr_)rZrtrr r r is_r3_rotation_matrix_rms$s zrec.is_r3_rotation_matrix_rms:0yE>cCs ||kotd||kS)Nr)rirO determinant)r rms_tolerancer r r is_r3_rotation_matrix)s zrec.is_r3_rotation_matrixcCs |jdkS)N) g?gggg?gggg?)r)rr r r is_r3_identity_matrix-szrec.is_r3_identity_matrixcCs |jdkS)z Is the translation vector zero )ggg)r)rr r r is_col_zero0szrec.is_col_zerocCstdd|jDdkS)z Are all elements zero cSsg|]}|dkrdqS)rrr )rr)r r r r!6szrec.is_zero..r)rr)rr r r is_zero4sz rec.is_zerocstfdd|jDdkS)z Are all elements zero csg|]}t|krdqS)r)rO)rr))epsr r r!:sz&rec.is_approx_zero..r)rr)rrqr )rqr is_approx_zero8szrec.is_approx_zeroc Cs|jdkst|j\}}}}td||||dd||||d||||d||||d||||dd||||d||||d||||d||||df S)N))r)rsrrr)rrrr0)rq0q1q2q3r r r %unit_quaternion_as_r3_rotation_matrix<s ::z)rec.unit_quaternion_as_r3_rotation_matrixFc Cs |jdkrtd|j\ }}}}}}} } } |dkrt|} |rJtj| } t| t| | t| } t| t| |t| }nT|dkrtjd} t||} d}n0|dkrtj d} t| |} d}ntd|rd | tjd | tjd |tjfS| | |fSd S) ab Get the rotation angles around the axis x,y,z for rotation r Such that r = Rx*Ry*Rz Those angles are the Tait-Bryan angles form of Euler angles Note that typically there are two solutions, and this function will return only one. In the case that cos(beta) == 0 there are infinite number of solutions, the function returns the one where gamma = 0 Args: deg : When False use radians, when True use degrees alternate_solution: return the alternate solution for the angles Returns: angles: containing rotation angles in the form (rotx, roty, rotz) )rfrfzNot a 3x3 matrix.)rrrrryzCan't calculate rotation anglesN) rr-rrQasinpiatan2cosArithmeticError)rdegZalternate_solutionZRxxZRxyZRxzZRyxZRyyZRyzZRzxZRzyZRzzbetaalphagammar r r "r3_rotation_matrix_as_x_y_z_anglesDs.   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Please update the code calling this method.r)messagecategory stacklevel)rrr)warningswarnDeprecationWarningr)rrrrrr r r rotates z rec.rotate绽|=c Cs|jdkst|j\}}}||||}t|||d|krJtdt|}||krt|dkrltdStdS|}| } ||} | |} d|} t|| | | | | | | | | | || | | | | ||f S)N))rfr)rrfrzself is not a normal vector.r) rrrrrrrrr) rrrrryrrrry)rrrrOr-rQrar0) rZsin_angle_is_zero_thresholdZis_normal_vector_thresholdr)rrZxxyyr6usZvsrrdocr r r vector_to_001_rotations   zrec.vector_to_001_rotationcCs|dkr |}|jddks,|jddks,t|jddksL|jddksLtg}x,|jD]"}x|jD]}|||qdWqXWt|t|jt|jfS)Nrr)rrrr/rr)rr&r4r$r%r r r r$s    zrec.outer_productcCsP|}|dkr|S|}|dkr(|S||}|dkr<|S||t|S)Nr)r_rerQra)rr&value_if_undefinedZ self_norm_sqZ other_norm_sqrr r r cos_angle.sz rec.cos_anglecCsD|j|d}|dkr|Sttdtd|}|r@|dtj9}|S)N)r&ryrrz)rrQrrYrXr|)rr&rrrr4r r r r7s z rec.angleư>cCs|j|dst|dd}|dkrNt|dkrNtdt|dkrNd}n,|dkrzt|dkrztdt|dkrzd}t|dtjS) zB Assuming it is a rotation matrix, tr(m) = 1+2*cos(alpha) )rlg?rrrgư>ggf@)rmrr^rOrQrr|)rrqargr r r rotation_angle>s((zrec.rotation_anglecCsN|j|d}|dkr|S|dkr(|d9}ttd|}|rJ|dtj9}|S)N)r&rryrrz)rrQrrXr|)rr&rrrr4r r r accute_angleHs zrec.accute_anglecCs|jd|jdkS)Nrr)r)rr r r is_squarePsz rec.is_squarecCs|s t|j}|jd}|dkr,|dS|dkrT|d|d|d|dS|dkr|d|d|d|d|d|d|d|d|d|d |d|d|d|d|d St}|dk r||}|||j|St |d S) Nrrrrfrs)m) rrrrr doubleresizegridZmatrix_determinant_via_ludeterminant_via_lu)rrrrr r r rkSs   x  zrec.determinantc Cs|j}|dkrtd|dS|dkr.td|dS|j}|dkrdt|d|d |d  |d f|dS|d krt|d |d |d|d|d |d |d |d|d|d|d |d |d |d |d|d|d |d |d |d|d  |d|d |d|d|d|d |d|d  |d|d|d|d |d |d|df |dS|sttddS)N)rrr )rr)rr)r)rrrfrrr)rfrfrsrrrrzNot implemented.)rrrrrr-)rrrr r r co_factor_matrix_transposedfs*  (     (zrec.co_factor_matrix_transposedcCs|s t|j}|ddkr>|}|dks2t||St}|dk r|||j}|| || t ||dSt }|dk r| |j}||_||j|}t ||dSt|dS)Nrrs)rr)r)rrrrkrr rrrrZmatrix_inversion_in_placerrZasarrayshapeZravelZlinalginvinverse_via_lu)rrrkrrrr r r inverse}s&        z rec.inversecCsVg}x:t|D]*}x$t|D]}||||q$WqWt|||fS)N)rrrr/r)rrr7r#r r r transposes z rec.transposec Cs|} |} | } | } |r<| |d7} | dt|d7} | |7} | dkrxt| D]}| |7} xtt| D]h}|dkr| t|||7} n| ||||7} |d| kr| d7} qn|d| kst|dkrn| |7} qnW|d| krX| |7} |r| d7} | | 7} | d7} qXW| |S)N= rrz,  )rrrrr.)r outer_open outer_close inner_open inner_closeinner_close_followlabelone_row_per_lineformatprefixnrncr6indentr@rAr r r _mathematica_or_matlab_forms4      zrec._mathematica_or_matlab_formc Cs8|jddddd||||d }|r(|d7}|dd}|S)N{},) rrrrrrrrrz //MatrixFormr z*^)rreplace)rrrrrZ matrix_formr4r r r mathematica_forms zrec.mathematica_formc Cs|jddddd||||d S)N[]r;) rrrrrrrrr)r)rrrrrr r r matlab_formszrec.matlab_formcCsP|j\}}|j}t|dkr&t|}ndt|dt|df}d|||fS)Nrfz (%s, ..., %s)rryzmatrix.rec(elems=%s, n=(%d,%d)))rrrr.)rZn0Zn1r r r r __repr__s    z rec.__repr__cCs |jddS)NT)r)r)rr r r __str__sz rec.__str__cCsHg}|j\}}x4t|D](}|t|j|||d|qW|S)Nr)rrr/r+r)rr4rrr@r r r as_list_of_listss  (zrec.as_list_of_listscCs`|jdkst|j}|d|d|d|d|dd|d|d d|d |d dfS) N)rfrfrrsrrrfg@rrrr)rrr)rrr r r as_sym_mat3s zrec.as_sym_mat3cCs|jdkst|jS)N)rfrf)rrr)rr r r as_mat3sz rec.as_mat3cCs4t}|dk st||j}|||j|S)N)r rrrrMrr)rrr4r r r as_flex_double_matrixs   zrec.as_flex_double_matrixcCs4t}|dk st||j}|||j|S)N)r rrHrrMrr)rrr4r r r as_flex_int_matrixs   zrec.as_flex_int_matrixrrrrc Csd|dkr|jdks$ntd|dkrB|jdksHntt|d|d|d}t|d|d|d}g}x*|D]"}x|D]}||||qWqWt|t|t|fS)Nrr)rrrr/rr) rstopstartstepZi_rowsZi_columsr4r@rAr r r extract_blocks$$  zrec.extract_blockcCs|||kr dS|dkrdStt|tr2|j|jkSxDt|D]4}x.t|D]}||||||fkrRdSqRWq@WdS)NTF) issubclasstyperrrrr)rr&r@rAr r r __eq__s  z rec.__eq__cCs || S)N)r)rr&r r r __ne__sz rec.__ne__cCs|j\}}d}xlt|D]`}d}xNt|D]B}|||}t|tsFt|dkrZ|jd}q*|jd|ks*tq*W||7}qWd}x^t|D]R}d} x@t|D]4}|||}|dkr|jd} q|jd| kstqW|| 7}qWdg||} d} xt|D]}d} xt|D]v}|||}|j\}} d} xNt|D]B}| ||| }x*t| D]}|| | ||<| d7} qRWq4W| | 7} qW| |kst| |7} qW| |kstt| ||fdS)Nrr)rr)rrrrr)rrrZ result_nrr@Zpart_nrrApartZ result_ncZpart_ncZ result_elemsZ result_irZ result_icZi_partZpart_irZi_resultZpart_icr r r resolve_partitionssL          zrec.resolve_partitions)N)T)r)N)rj)FF)F)F)F)FF)F)F)F)F)rr)N)N)NF)r)NF)rFNrF)rFNr)rr)X__name__ __module__ __qualname____doc__rrrrrr"r'r(r8r9r;r<r=r>r?rBrCrDrFrJrLrNrPrWrXrYrZr[r\r]r^r_rKrb length_sqrrcrergrirmrnrorprrrxrrrrrrrrrrrrrrrrrrrrrkrrrrrrrrrrrrrrrrrr r r r r$s  !      /4         "     rc@seZdZeZddZdS) mutable_reccCs||j|<dS)N)r)rr#r)r r r __setitem__Fszmutable_rec.__setitem__N)rrrr+rrr r r r rCsrcseZdZfddZZS) row_mixincstt||dt|fdS)Nr)superrrr)rr) __class__r r rKszrow_mixin.__init__)rrrr __classcell__r r )rr rIsrc@s eZdZdS)rowN)rrrr r r r rNsrc@s eZdZdS) mutable_rowN)rrrr r r r rOsrcs,eZdZfddZddZeeZZS) col_mixincstt||t|dfdS)Nr)rrrr)rr)rr r rSszcol_mixin.__init__cs$tj|fddt|DS)Ncsg|]}qSr r )rr#)r$r%uniformr r r!Xsz$col_mixin.random..)randomrr)clsrr$r%r )r$r%rr rVszcol_mixin.random)rrrrr classmethodrr r )rr rQs rc@seZdZdZdS)r,a8 Class type built on top of rec and col_mixin, allows for single-dimensional vectors. This is especially convenient when working with 3D coordinate data in Python. Examples -------- >>> from scitbx.matrix import col >>> vector = col([3, 0, 4]) >>> print abs(vector) 5.0 N)rrrrr r r r r,[s r,c@s eZdZdS) mutable_colN)rrrr r r r rjsrc@seZdZddZdS)r0cCs>t|}t|dd}|||ks(tt||||fdS)Ng?)rrHrrr)rrlrr r r rnsz sqr.__init__N)rrrrr r r r r0lsr0c@seZdZddZdS)diagcCsZt|}ddt||D}x$t|D]}|||||d<q(Wt||||fdS)NcSsg|]}dqS)rr )rr#r r r r!xsz!diag.__init__..r)rrrr)rZ diag_elemsrrr#r r r rvs z diag.__init__N)rrrrr r r r rtsrcseZdZfddZZS)rhcstt|d|dS)N)r)rrhr)rr)rr r rszidentity.__init__)rrrrrr r )rr rh}srhcseZdZfddZZS) inversioncstt|d|dS)N)ry)rrr)rr)rr r rszinversion.__init__)rrrrrr r )rr rsrc@seZdZdddZdS)symNc Csl|dkstdt|dks t|}t||d|d|d|d|d|d|d|d|df d dS) NzNot implemented.rrrfrsrrr)rfrf)rrrr)rrsym_mat3rr r r rs z sym.__init__)NN)rrrrr r r r rsrcCsR|rtt}}n tt}}t|tr2|d|dS|\}}|d||||fdS)N)r)r)rr)rrr,rrrH)rmutableZcol_tZrec_trrr r r zeross   r cCs t|ddS)NT)r)r )rr r r mutable_zerossr cCs*t|}t|}x|D] }||7}qW|S)z+ The sum of the given sequence of matrices )iternext)iterablesequencer4rr r r r\s   r\c Cs*|\}}}td| ||d| | |df S)zMatrix associated with vector cross product: a.cross(b) is equivalent to cross_product_matrix(a) * b Useful for simplification of equations. Used frequently in robotics and classical mechanics literature. r)r0)ZvvvZv0Zv1Zv2r r r rs  rcCst|t|kstd}xZt||D]L\}}|dkrB|dkrpdSq$|dkrNdS||}|dkrd|}q$||kr$dSq$W|dkrdS|S)Nr)rrr)vector_1vector_2r4e1e2rr r r &linearly_dependent_pair_scaling_factors rc Cst|dkst|d|d}|d|d}|d|d}||}|}||}|}|dkst|dkrxdStdtd||||d} t| } |||dkr| d 9} |r| d tj 9} | S) Nrsrrrrfgg?g?ryrz) rrrgrrYrXrerQrr|) sitesrZd_01Zd_21Zd_23Zn_0121Z n_0121_normZn_2123Z n_2123_normrr4r r r _dihedral_angles$   rcCs2t}|dkrt||dSddlm}|||dS)N)rrr)dihedral_angle)r rZ scitbx.mathr)rrrrr r r rs   rcCs8t|}t||}|j||d}|t|||jS)zAbout 6 times slower than the implementation below. Interestingly, a C++ implementation is still 2 times slower than the implementation below, due to the tuple-vec3 conversion overhead. )rr)r,rr) axis_point_1 axis_point_2rrrpivotrrSr r r __rotate_point_around_axiss  rcCs4||||}|\}}}|| }||||fS)N)rgre)point_1point_2point_3rr$r%rrr r r plane_equations  rc Cst|dksttt|dt|dt|dd\}}}}|\}}}t|d|d|d} | dkrrdSt|||||||| S)z http://mathworld.wolfram.com/Point-PlaneDistance.html Given three points describing a plane and a fourth point outside the plane, return the distance from the fourth point to the plane. rfrrr)rrrN)rrrr,rQrarO) xyzpointsr$r%rrr)rrZdenr r r distance_from_planes   r!cCsJt|dkstx4|ddD]$}t||ddd}||krdSqWdS)Nrf)rr FT)rrr!)r  tolerancerrr r r all_in_planes r#c Cs`ddlm}||g}||g}||g}||}||}||||||} | S)z' Slow version based on flex arrays r)r)r r vec3_doublere) rrrrr$r%pabapprojr r r __project_point_on_axis s    r)cCs|\}}}|\}}}|\} } } ||||||} } }| || || |}}}|| || ||}| | | | ||}||}||| ||| |||f}|S)a Project a 3D coordinate on a given arbitrary axis. :param axis_point_1: tuple representing 3D coordinate at one end of the axis :param axis_point_2: tuple representing 3D coordinate at other end of the axis :param point: tuple representing 3D coordinate of starting point to rotate :param deg: Python boolean (default=False), specifies whether the angle is in degrees :returns: Python tuple (len=3) of rotated point r )rrrZaxZayazZbxZbyZbzZpxpyZpzZabxZabyZabzZapxZapyZapzZ ap_dot_abZ ab_dot_abbracketsr(r r r project_point_on_axiss   "r-c+Cs|r|tjd9}|\}}}|\}} } |\} } } ||| || |}}}|d}|d}|d}|||}|d}t|}t||}d||}|||}|||}|||}| || || |}}}|||}|||} |||}!|||}"|||}#|||}$|||}%|||}&|||}'|||| ||!|}(||"||#||$|})||%||&||'|}*|(|)|*fS)a Rotate a 3D coordinate about a given arbitrary axis by the specified angle. :param axis_point_1: tuple representing 3D coordinate at one end of the axis :param axis_point_2: tuple representing 3D coordinate at other end of the axis :param point: tuple representing 3D coordinate of starting point to rotate :param angle: rotation angle (defaults to radians) :param deg: Python boolean (default=False), specifies whether the angle is in degrees :returns: Python tuple (len=3) of rotated point gf@rg?r)rQr|r~r)+rrrrrZxaZyaZzaxbZybZzbr)rrZxlZylZzlZxlsqZylsqZzlsqZdlsqZdlcaZdsaZocaZxlyloZxlzloZylzloZxmaZymaZzmaZm1Zm2Zm3Zm4Zm5Zm6Zm7Zm8Zm9Zx_newZy_newZz_newr r r rotate_point_around_axis.s>                  r0c@sPeZdZdZddZddZddZdd Zd d Zd d Z ddZ ddZ dS)ra Object for representing associated rotation and translation matrices. These will usually be a 3x3 matrix and a 1x3 matrix, internally represented by objects of type :py:class:`scitbx.matrix.sqr` and :py:class:`scitbx.matrix.col`. Transformations may be applied to :py:mod:`scitbx.array_family.flex` arrays using the overloaded multiplication operator. Examples -------- >>> from scitbx.matrix import rt >>> symop = rt((-1,0,0,0,1,0,0,0,-1), (0,0.5,0)) # P21 symop >>> from scitbx.array_family import flex >>> sites_frac = flex.vec3_double([(0.1,0.1,0.1), (0.1,0.2,0.3)]) >>> sites_symm = symop * sites_frac >>> print list(sites_symm) [(-0.1, 0.6, -0.1), (-0.1, 0.7, -0.3)] cCsxt|ddr t|dj|_nt|d|_t|ddrNt|dj|_nt|d|_|j|jksttdS)Nrrr)r*r0rrSr,trr)rZ tuple_r_tr r r rrsz rt.__init__cCs>t|tr&t|j|j|j|jfSt|j|j|fSdS)N)rrrSr1)rr&r r r r'}s z rt.__add__cCs>t|tr&t|j|j|j|jfSt|j|j|fSdS)N)rrrSr1)rr&r r r r(s z rt.__sub__cCsbt|tr,t|j|j|j|j|jfSt|tr|j|jjkrXt|j||jfS|j|jjkrv|j||jStdt|t|ft|jj }t|t t fr t||kr|jt ||jSt|||krt|jt ||jfStdt|t|f|dkrFt}|dk rFt||jrF|jj ||jj Stdt|t|fdS)Nz@cannot multiply %s by %s: incompatible number of rows or columnsz9cannot multiply %s by %s: incompatible number of elementsrfzcannot multiply %s by %s)rrrSr1rr ValueErrorreprrrr+rr,r0r r$ TypeError)rr&rrr r r r8s0 "    z rt.__mul__cCs|j}t|||j fS)N)rSrrr1)rr_invr r r rs z rt.inversecCs|j}t|||j fS)N)rSrrr1)rr5r r r inverse_assuming_orthogonal_rs z rt.inverse_assuming_orthogonal_rcCst|j|jfS)N)rrSrFr1)rr r r rFsz rt.as_floatcCs|j|jkst|j}g}xBt|D]6}||jj|||d|||j|q0W|dg||dt ||d|dfS)Nrr) rSrrrrextendrr/r1r)rrr4Zi_rowr r r as_augmented_matrixs " zrt.as_augmented_matrixN) rrrrrr'r(r8rr6rFr8r r r r r^s rcCsdd|DS)NcSsg|] }t|qSr )r,)relemr r r r!szcol_list..r )seqr r r col_listr;cCsdd|DS)NcSsg|] }t|qSr )r)rr9r r r r!szrow_list..r )r:r r r row_listr<r=TcCsd}t|||kstdg|}dg|d}xtt|D]h}d}x:t|D].}||||} | dkrn| } | |krL| }qLW|dkr|rt|dSd|||<q:Wd} x t|D]}xft|D]Z}||||} x4t|D](} | |||| || ||8} qW| ||||<qWd}xt||D]}||||} x6t|D]*} | |||| || ||8} qRW| ||||<| dkr| } ||| } | |kr4| }|} q4W|| kr2xFt|D]:} | || ||| } }|||| || <||<qW||d7<|||| <| ||<||||dkrb|r^t|dS|d|krd||||} x0t|d|D]}||||| 9<qWqW|S)Nz*lu_decomposition_in_place: singular matrixgrrg?)rrrr-)r$rraise_if_singularZis_singular_messageZvv pivot_indicesr#Zbigr7ZdumZimaxr\r5r:Zjkr r r lu_decomposition_in_placesh (*        "r@c Cst|||kst|}xt|D]}||}||krF|rBtddS||}||||<||krx8t||D] } ||||| || 8}qnWn|r|}|||<q"Wxlt|dddD]X}||}x2t|d|D] } ||||| || 8}qW|||||||<qWdS)Nz3lu_back_substitution: pivot_indices[i] out of rangeFrryT)rrrr-) r$rr?r%r>iir#Zpivot_indices_ir\r7r r r lu_back_substitutions. "  rBcCs|s t|jd}|dkr&tgSt|j}t||d}dg||}xXt|D]L}dg|}d||<t||||dx$t|D]}||||||<qWqTWt|S)Nr)r$rgg?)r$rr?r%) rrrr0r+rr@rrB)rrr$r?rSr7r%r#r r r rs     rcCs|s t|jd}|dkr"dSt|j}t||dd}|dkrFdSd}x$t|D]}|||||9}qTW|ddr| }|S)NrrF)r$rr>ryr)rrrr+rr@r)rrr$r?r4r#r r r rs    rc Cs |jdkstt|dks"t||}ddlm}||}t | }t | }t |d|d|dgdd}t |d |d |d gdd}t |d |d |dgdd}dt |d||dt |d||dt |d||} || } | S)a Return nearest orthonormal matrix, R, of M from R := M*(M^t * M)^{-1/2} where ^t means transpose of matrix or vector e1, e2, e3, lambda1, lambda2, lambda3 are eigenvectors and respective eigenvalues of (M^t * M ) (M^t * M )^{-1/2} = 1/sqrt(lambda1) * e1*e1^t + 1/sqrt(lambda2) * e2*e2^t + 1/sqrt(lambda3) * e3*e3^t http://people.csail.mit.edu/bkph/articles/Nearest_Orthonormal_Matrix.pdf )rfrfg:0yE>r) eigensystemrr)rrf)rrfrsrrrrg?)rrrOrkrZ scitbx.linalgrCZreal_symmetricrr+valuesZvectorsrrQra) ZMmxZMtMmxrCesZevaluesZevectorsZevec1Zevec2Zevec3Z MtMinvsqrtmxZRmxr r r find_nearest_orthonormal_matrix"s    : rFcJs yddlm}Wn,tk 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