R1ioRdZddlmZmZmZmZmZmZmZm Z m Z m Z m Z m Z ddlmZddlmZeej$ZGddeZeZdZdZd Zd Zd Zeeeef\ZZZZd Zd Z dZ!dZ"dZ#e!Z$e#Z%dZ&dZ'dZ(dZ)dZ*dZ+ ddl,m-Z-dZ/y#ddl.m.Z-YdZ/yxYw)z@Basic operations that are needed repeatedly throughout Skyfield.) arcsinarctan2arraycoseinsumfinfofloat64 full_likeloadrollaxissinsqrt)get_data)tauceZdZdZeZy)Az8Allow literal NumPy arrays to be spelled ``A[1, 2, 3]``.N)__name__ __module__ __qualname____doc__r __getitem__V/home/cursorai/projects/iching/venv/lib/python3.12/site-packages/skyfield/functions.pyrr s BKrrc,||zjdS)zGiven one or more vectors in `v` and `u`, return their dot products. This works whether `v` and `u` each have the shape ``(3,)``, or whether they are each whole arrays of corresponding x, y, and z coordinates and have shape ``(3, N)``. raxis)sum)vus rdotsr!s E;;A; rct|dS)z*Swap the first two dimensions of an array.)r )Ms rTr%s Aq>rctd||S)z8Matrix times vector: multiply an NxN matrix by a vector.zij...,j...->i...r)r$rs rmxvr(s $a ++rctd||S)z/Matrix times matrix: multiply two NxN matrices.zij...,jk...->ik...r')M1M2s rmxmr,#s &B //rctd|||S)zCMatrix times matrix times matrix: multiply 3 NxN matrices together.zij...,jk...,kl...->il...r')r*r+M3s rmxmxmr/'s ,b"b 99rc>t||zjdS)zGiven a 3-element array |xyz|, return its length. The three elements can be simple scalars, or the array can be two dimensions and offer three whole series of x, y, and z coordinates. rr)rr)xyzs r length_ofr2-s sQ' ((rc|t|z}|t|z}dtt||z t||zzS)aGiven two vectors `v` and `u`, return the radian angle separating them. This works whether `v` and `u` each have the shape ``(3,)``, or whether they are each whole arrays of corresponding x, y, and z coordinates with shape ``(3, N)``. The returned angle will be between 0 and tau/2. This formula is from Section 12 of: https://people.eecs.berkeley.edu/~wkahan/Mindless.pdf g@)r2r)r rabs r angle_betweenr66sD IaLA IaLA 1q5)9QU+;< <rxys rfrom_sphericalrPks; c%j.C #C.#C.!c%j.A BBrcrt|}t|}|dz}|dz}t|||f||| f|||ffSNg?rr rr=cszeroones rrot_xrZsM E A E A 3;D *C 3d#dAr]T1aLA BBrcrt|}t|}|dz}|dz}t|||f|||f| ||ffSrRrTrUs rrot_yr\sM E A E A 3;D *C 1dA,sD 1QBa=A BBrcrt|}t|}|dz}|dz}t|| |f|||f|||ffSrRrTrUs rrot_zr^sM E A E A 3;D *C 1qb$-!QdC/@A BBrcL|\}}}|dz}t|| |f||| f| ||ffS)NrS)r)angular_velocity_vectorr:r;r<rXs rangular_velocity_matrixras@%GAq! s7D 4!Q-!TA2!Q > ??rcbt|dr|St|dr t|St|S)aSConvert plain Python sequences into NumPy arrays. This lets users pass plain old Python lists and tuples to Skyfield, instead of always having to remember to build NumPy arrays. We pass any kind of generic sequence to the NumPy ``array()`` constructor and wrap any other kind of value in a NumPy ``float64`` object. shape__len__)hasattrrr )values r _to_arrayrgs1ug  "U|u~rct|dd}t|dd}||z }|dkDr.|r|xjd|zz c_||fSt||}||fS|dkr+|r|xjd| zz c_||fSt||}||fS)zECoerce two NumPy generics-or-arrays to the same number of dimensions.ndimr)r#)getattrrcr )r4r5anbn differences r _reconcilerns FA B FA BbJA~ GGtj( (G a4K !QA a4K a GGtzk) )G a4K!QA a4Kr)BytesIO)StringIOc`tddj|}tt|S)z=Load a binary NumPy array file that is bundled with Skyfield.skyfieldzdata/{0})rformatr ro)filenamedatas rload_bundled_npyrvs( J 1 1( ; rsF"g++C,0:Ce+D$)= $<& C"   CCC@  "--,s BB&