ó Ąź™\c@ sŤddlmZmZddlmZddlmZddlmZddl m Z ddl m Z m Z ddlZdefd „ƒYZd eefd „ƒYZdS( i˙˙˙˙(tprint_functiontdivision(tBasic(tExpr(tInteger(tsympify(t SYMPY_INTStIterableNt NDimArraycB sŻeZdZeZd)d„Zd„Zd„Zd„Z d„Z e d„ƒZ e d)d)d„ƒZ d„Zed „ƒZd „Zd „Zd „Zd „Zd„Zd„Zd„Zd„Zd„Zd„Zd„ZeZd„Zd„Zd„Zd„Z d„Z!d„Z"d„Z#d„Z$d„Z%d„Z&e"Z'e#Z(d„Z)d „Z*d!„Z+d"„Z,d#„Z-d$„Z.d%„Z/d&„Z0d'„Z1e d(„ƒZ2RS(*sŠ Examples ======== Create an N-dim array of zeros: >>> from sympy import MutableDenseNDimArray >>> a = MutableDenseNDimArray.zeros(2, 3, 4) >>> a [[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]] Create an N-dim array from a list; >>> a = MutableDenseNDimArray([[2, 3], [4, 5]]) >>> a [[2, 3], [4, 5]] >>> b = MutableDenseNDimArray([[[1, 2], [3, 4], [5, 6]], [[7, 8], [9, 10], [11, 12]]]) >>> b [[[1, 2], [3, 4], [5, 6]], [[7, 8], [9, 10], [11, 12]]] Create an N-dim array from a flat list with dimension shape: >>> a = MutableDenseNDimArray([1, 2, 3, 4, 5, 6], (2, 3)) >>> a [[1, 2, 3], [4, 5, 6]] Create an N-dim array from a matrix: >>> from sympy import Matrix >>> a = Matrix([[1,2],[3,4]]) >>> a Matrix([ [1, 2], [3, 4]]) >>> b = MutableDenseNDimArray(a) >>> b [[1, 2], [3, 4]] Arithmetic operations on N-dim arrays >>> a = MutableDenseNDimArray([1, 1, 1, 1], (2, 2)) >>> b = MutableDenseNDimArray([4, 4, 4, 4], (2, 2)) >>> c = a + b >>> c [[5, 5], [5, 5]] >>> a - b [[-3, -3], [-3, -3]] cK s ddlm}||||S(Ni˙˙˙˙(tImmutableDenseNDimArray(tsympy.tensor.arrayR (tclstiterabletshapetkwargsR ((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt__new__BscC sĚt|ttfƒr7||jkr3tdƒ‚n|St|ƒ|jkr[tdƒ‚nd}xdt|jƒD]S}|||j|krŤtdt |ƒdƒ‚n||j|||}qqW|S(Nsindex out of rangesWrong number of array axesisIndex s out of border( t isinstanceRRt _loop_sizet ValueErrortlent_ranktrangeR tstr(tselftindext real_indexti((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt _parse_indexFscC s[g}x>tt|jƒƒD]'\}}|j||ƒ||}qW|jƒt|ƒS(N(t enumeratetreversedR tappendtreversettuple(Rt integer_indexRRtsh((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt_get_tuple_indexYs " cC sÇt|tƒr|n|f}tg|D]}t|tƒoD|j ^q(ƒrĂxSt||jƒD]?\}}|dktks“||ktkrctdƒ‚qcqcWddl m }|||ŒSdS(Nisindex out of rangei˙˙˙˙(tIndexed( RR tanyRt is_numbertzipR tTrueRt sympy.tensorR$tNone(RRt tuple_indexRtnth_dimR$((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt_check_symbolic_indexas2$ cC s5ddlm}t|t|tfƒr1t‚ndS(Ni˙˙˙˙(t MatrixBase(tsympy.matrices.matricesR.RRRtNotImplementedError(RtvalueR.((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt_setter_iterable_checklsc s‡fd†‰ˆ|ƒS(Nc s­t|tƒs|gdfSg}tg|D]}ˆ|ƒ^q,Œ\}}tt|ƒƒdkrttdƒ‚nx|D]}|j|ƒq{W|t|ƒf|dfS(Nis'could not determine shape unambiguouslyi((RRR'RtsetRtextend(tpointertresultRtelemstshapes(tf(s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyR9ss + ((R R ((R9s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt_scan_iterable_shapeqs cK sxddlm}|dkr7|dkr7d}d}nŇ|dkrjt|tƒrj|j}t|ƒ}nŸ|dkrt|tƒr|j|ƒ\}}nl|dkrÄt||ƒrÄ|j}nE|dkrët|tƒrë|j}n|dk rúnd}|f}t|t t fƒr*|f}nt g|D]}t|t t fƒ ^q4ƒrht dƒ‚nt |ƒ|fS(Ni˙˙˙˙(R.s#Shape should contain integers only.((((R/R.R*RRR tlistRR:RRR%t TypeErrorR (R R R RR.tdim((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt_handle_ndarray_creation_inputss,       /cC s|jS(s-Overload common function len(). Returns number of elements in array. Examples ======== >>> from sympy import MutableDenseNDimArray >>> a = MutableDenseNDimArray.zeros(3, 3) >>> a [[0, 0, 0], [0, 0, 0], [0, 0, 0]] >>> len(a) 9 (R(R((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt__len__¨scC s|jS(sŕ Returns array shape (dimension). Examples ======== >>> from sympy import MutableDenseNDimArray >>> a = MutableDenseNDimArray.zeros(3, 3) >>> a.shape (3, 3) (t_shape(R((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyR ¸scC s|jS(s× Returns rank of array. Examples ======== >>> from sympy import MutableDenseNDimArray >>> a = MutableDenseNDimArray.zeros(3,4,5,6,3) >>> a.rank() 5 (R(R((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pytrankČs cO s6ddlm}|jdtƒ||jƒ||ŽS(s5 Calculate the derivative of each element in the array. Examples ======== >>> from sympy import ImmutableDenseNDimArray >>> from sympy.abc import x, y >>> M = ImmutableDenseNDimArray([[x, y], [1, x*y]]) >>> M.diff(x) [[1, 0], [0, y]] i˙˙˙˙(t Derivativetevaluate(tsympyRBt setdefaultR(t as_immutable(RtargsRRB((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pytdiff×scC s |j|ƒS(N(t_visit_eval_derivative_array(Rts((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt_accept_eval_derivativeésc s|j‡fd†ƒS(Nc s ˆj|ƒS(N(RH(tx(tbase(s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pytît(t applyfunc(RRM((RMs<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt_visit_eval_derivative_scalarěscC sddlm}|||ƒS(Ni˙˙˙˙(tderive_by_array(RDRR(RRMRR((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyRIđscC stj|||ƒS(N(Rt_eval_derivative_n_times(RRJtn((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyRSősc srddlm}ddlm}ddlm}tˆt||tfƒrX||ˆƒS|j‡fd†ƒSdS(Ni˙˙˙˙(RR(tTuple(t MatrixCommonc s |jˆƒS(N(RH(RL(targ(s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyRN˙RO( RDRRRUtsympy.matrices.commonRVRRRRP(RRWRRRURV((RWs<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt_eval_derivativeřs  cC st|ƒt||ƒ|jƒS(s[Apply a function to each element of the N-dim array. Examples ======== >>> from sympy import ImmutableDenseNDimArray >>> m = ImmutableDenseNDimArray([i*2+j for i in range(2) for j in range(2)], (2, 2)) >>> m [[0, 1], [2, 3]] >>> m.applyfunc(lambda i: 2*i) [[0, 2], [4, 6]] (ttypetmapR (RR9((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyRPs c sN‡‡fd†‰ˆjƒdkr2ˆdjƒSˆˆjˆjdˆjƒS(sţReturns string, allows to use standard functions print() and str(). Examples ======== >>> from sympy import MutableDenseNDimArray >>> a = MutableDenseNDimArray.zeros(2, 2) >>> a [[0, 0], [0, 0]] c  s´t|ƒdkrMddjgt||ƒD]}tˆ|ƒ^q+ƒdS||d}ddjgt|dƒD]3}ˆ||d|||||d|ƒ^quƒdS(Nit[s, t]i(RtjoinRR(R"t shape_leftRtjte(R9R(s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyR9s;i((RAt__str__RR (R((R9Rs<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyRbs cC s |jƒS(N(Rb(R((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt__repr__(scC s*ddlm}||ddƒ}d|S(s^ IPython/Jupyter LaTeX printing To change the behavior of this (e.g., pass in some settings to LaTeX), use init_printing(). init_printing() will also enable LaTeX printing for built in numeric types like ints and container types that contain SymPy objects, like lists and dictionaries of expressions. i˙˙˙˙(tlatextmodetplains$\displaystyle %s$(tsympy.printing.latexRd(RRdRJ((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt _repr_latex_/s c s.‡‡fd†‰ˆˆjˆjdˆjƒS(s? Converting MutableDenseNDimArray to one-dim list Examples ======== >>> from sympy import MutableDenseNDimArray >>> a = MutableDenseNDimArray([1, 2, 3, 4], (2, 2)) >>> a [[1, 2], [3, 4]] >>> b = a.tolist() >>> b [[1, 2], [3, 4]] c  st|ƒdkr6gt||ƒD]}ˆ|^q"Sg}||d}xLt|dƒD]:}|jˆ||d|||||d|ƒƒq[W|S(Nii(RRR(R"R_RR`RaR6(R9R(s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyR9Ns$8i(RR (R((R9Rs<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyttolist>s cC s‡t|tƒs$tt|ƒƒ‚n|j|jkrEtdƒ‚ngt||ƒD]\}}||^qU}t|ƒ||jƒS(Nsarray shape mismatch(RRR<RR RR'RZ(RtotherRR`t result_list((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt__add__Ys ,cC s‡t|tƒs$tt|ƒƒ‚n|j|jkrEtdƒ‚ngt||ƒD]\}}||^qU}t|ƒ||jƒS(Nsarray shape mismatch(RRR<RR RR'RZ(RRjRR`Rk((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt__sub__cs ,cC svddlm}t|tt|fƒr7tdƒ‚nt|ƒ}g|D]}||^qJ}t|ƒ||jƒS(Ni˙˙˙˙(R.s=scalar expected, use tensorproduct(...) for tensorial product( R/R.RRRRRRZR (RRjR.RRk((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt__mul__ms  cC svddlm}t|tt|fƒr7tdƒ‚nt|ƒ}g|D]}||^qJ}t|ƒ||jƒS(Ni˙˙˙˙(R.s=scalar expected, use tensorproduct(...) for tensorial product( R/R.RRRRRRZR (RRjR.RRk((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt__rmul__vs  cC svddlm}t|tt|fƒr7tdƒ‚nt|ƒ}g|D]}||^qJ}t|ƒ||jƒS(Ni˙˙˙˙(R.sscalar expected( R/R.RRRRRRZR (RRjR.RRk((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt__div__s  cC stdƒ‚dS(Ns"unsupported operation on NDimArray(R0(RRj((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt__rdiv__ˆscC s0g|D] }| ^q}t|ƒ||jƒS(N(RZR (RRRk((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt__neg__‹scC s;t|tƒstS|j|jko:t|ƒt|ƒkS(sę NDimArray instances can be compared to each other. Instances equal if they have same shape and data. Examples ======== >>> from sympy import MutableDenseNDimArray >>> a = MutableDenseNDimArray.zeros(2, 3) >>> b = MutableDenseNDimArray.zeros(2, 3) >>> a == b True >>> c = a.reshape(3, 2) >>> c == b False >>> a[0,0] = 1 >>> b[0,0] = 2 >>> a == b False (RRtFalseR R;(RRj((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt__eq__scC s ||k S(N((RRj((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt__ne__¨scC s>|jƒdkr!tdƒ‚nddlm}||dƒS(Nisarray rank not 2i(t permutedimsi(ii(RARtarrayopRv(RRv((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt_eval_transposeŽscC s |jƒS(N(Rx(R((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt transpose´scC s,|jg|D]}|jƒ^q |jƒS(N(tfunct conjugateR (RR((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt_eval_conjugateˇscC s |jƒS(N(R|(R((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyR{şscC s|jƒjƒS(N(RyR{(R((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt _eval_adjoint˝scC s |jƒS(N(R}(R((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pytadjointŔscC s[t|tƒs|fS|j|ƒ\}}}gt|||ƒD]}|||^qCS(N(RtslicetindicesR(RRJR=tstarttstoptstepR((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt _slice_expandĂscC sPgt||jƒD]\}}|j||ƒ^q}tj|Œ}||fS(N(R'R R„t itertoolstproduct(RRRR=t sl_factorsteindices((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt _get_slice_data_for_array_accessÉs7cC szt|tƒs$t|ƒ|ƒ}n|j|ƒ\}}g|D]'}t|tƒrat|ƒnd^q@}|||fS(N(RRRZR‰R;tminR*(RRR1R‡RˆRt slice_offsets((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt$_get_slice_data_for_array_assignmentÎs 4cC s^|dkr-t|ƒdkr-tdƒ‚n|dkrZt|ƒdkrZtdƒ‚ndS(Nis*arrays without shape need one scalar valueis/if array shape is (0,) there cannot be elements((i(RR(R t flat_listR ((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt_check_special_boundsÖsN(3t__name__t __module__t__doc__R(t _diff_wrtR*RRR#R-R2t classmethodR:R>R?tpropertyR RARHRKRQRIRSRYRPRbRcRht_repr_latex_origRiRlRmRnRoRpRqRrRtRut __truediv__t __rtruediv__RxRyR|R{R}R~R„R‰RŒRŽ(((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyR s\3    &                         tImmutableNDimArraycB s)eZdZd„Zd„Zd„ZRS(g&@cC s tj|ƒS(N(Rt__hash__(R((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyR™áscC s|S(N((R((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyRFäscC stdƒ‚dS(Nsabstract method(R0(R((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyt as_mutableçs(RRt _op_priorityR™RFRš(((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyR˜Ţs  (t __future__RRRDRtsympy.core.exprRtsympy.core.numbersRtsympy.core.sympifyRtsympy.core.compatibilityRRR…tobjectRR˜(((s<lib/python2.7/site-packages/sympy/tensor/array/ndim_array.pyts ˙Ô