U L?h.G@s\ddlmZmZmZddlmZddlmZddl m Z dgZ GdddeeZ ddZ d S) )sympifyAddImmutableMatrix) EvalfMixin) Printable) prec_to_dpsDyadicc@seZdZdZdZddZeddZddZeZ d d Z e Z d d Z e Z d dZddZddZddZddZddZddZddZddZdd ZeZd4d"d#Zd5d$d%Zd&d'Zd(d)Zd*d+Zd,d-Zd.d/Zd0d1Z d2d3Z!d!S)6rayA Dyadic object. See: https://en.wikipedia.org/wiki/Dyadic_tensor Kane, T., Levinson, D. Dynamics Theory and Applications. 1985 McGraw-Hill A more powerful way to represent a rigid body's inertia. While it is more complex, by choosing Dyadic components to be in body fixed basis vectors, the resulting matrix is equivalent to the inertia tensor. FcCsbg|_|dkrg}t|dkrd}t|jD]\}}t|ddt|j|dkr,t|ddt|j|dkr,|j|d|dd|dd|ddf|j|<||dd}qq,|dkr|j|d||dqd}|t|jkr^|j|ddk|j|ddkB|j|ddkBrT|j|j||d8}|d7}qdS)a2 Just like Vector's init, you should not call this unless creating a zero dyadic. zd = Dyadic(0) Stores a Dyadic as a list of lists; the inner list has the measure number and the two unit vectors; the outerlist holds each unique unit vector pair. rN)argslen enumeratestrremoveappend)selfinlistaddedivrM/var/www/html/venv/lib/python3.8/site-packages/sympy/physics/vector/dyadic.py__init__s6  "  "zDyadic.__init__cCstS)zReturns the class Dyadic. )rrrrrfunc@sz Dyadic.funccCst|}t|j|jS)zThe add operator for Dyadic. ) _check_dyadicrr rotherrrr__add__EszDyadic.__add__cCsVt|j}t|}t|D]2\}}|||d||d||df||<qt|S)aMultiplies the Dyadic by a sympifyable expression. Parameters ========== other : Sympafiable The scalar to multiply this Dyadic with Examples ======== >>> from sympy.physics.vector import ReferenceFrame, outer >>> N = ReferenceFrame('N') >>> d = outer(N.x, N.x) >>> 5 * d 5*(N.x|N.x) rr r )listr rr r)rrZnewlistrrrrr__mul__Ls  zDyadic.__mul__cCsddlm}m}t|tr|t|}td}|jD]H}|jD]<}||d|d|d|d|d|d7}q:q0n>||}|d}|jD]&}||d|d|d|7}q|S)aThe inner product operator for a Dyadic and a Dyadic or Vector. Parameters ========== other : Dyadic or Vector The other Dyadic or Vector to take the inner product with Examples ======== >>> from sympy.physics.vector import ReferenceFrame, outer >>> N = ReferenceFrame('N') >>> D1 = outer(N.x, N.y) >>> D2 = outer(N.y, N.y) >>> D1.dot(D2) (N.x|N.y) >>> D1.dot(N.y) N.x r)Vector _check_vectorr r ) sympy.physics.vector.vectorr!r" isinstancerrr dotouter)rrr!r"olrZv2rrrr%hs   > $z Dyadic.dotcCs|d|S)z0Divides the Dyadic by a sympifyable expression. r )r rrrr __truediv__szDyadic.__truediv__cCs\|dkrtd}t|}|jgkr0|jgkr0dS|jgksD|jgkrHdSt|jt|jkS)z[Tests for equality. Is currently weak; needs stronger comparison testing rTF)rrr setrrrr__eq__sz Dyadic.__eq__cCs ||k S)Nrrrrr__ne__sz Dyadic.__ne__cCs|dSNrrrrr__neg__szDyadic.__neg__c Cs|j}t|dkrtdSg}t|D]$\}}||ddkrt|d|||dd|||dq&||ddkr|d|||dd|||dq&||ddkr&|||d}t||dtrd|}|d r|dd}d}nd}||||||dd|||dq&d |}|drr|d d}n|d r|dd}|S) Nrr  + z\otimes r r- - (%s)- ) r r rr r_printr$r startswithjoin rprinterarr'rrarg_str str_startoutstrrrr_latexsH       z Dyadic._latexcs|Gfddd}|S)NcseZdZdZfddZdS)zDyadic._pretty..Fakerc sj}}t|dkrtdSjr(dnd}g}t|D].\}}||ddkr|d|||d||||dgq8||ddkr|d|||d||||dgq8||ddkr8t||dtr| ||d d} n|||d} | d r2| dd} d} nd} || | d |||d||||dgq8d |} | dr| d d} n| d r| dd} | S) Nru⊗|r r/r r-r0r2r5r3r4) r r rZ _use_unicoder extendZdoprintr$rr6Zparensr7r8) rr kwargsr;Zmppbarr'rrr<r=r>er:rrrendersT         z#Dyadic._pretty..Fake.renderN)__name__ __module__ __qualname__ZbaselinerFrrDrrFakesrJr)rr:rJrrDr_prettys1zDyadic._prettycCs d||Sr,rrrrr__rsub__szDyadic.__rsub__c Cs|j}t|dkr|dSg}t|D]8\}}||ddkrz|d|||dd|||ddq(||ddkr|d|||dd|||ddq(||ddkr(|||d}t||dtrd |}|dd kr |dd }d }nd }|||d|||dd|||ddq(d|}|d r|dd }n|dr|dd }|S)zPrinting method. rr z + (r@r )r-z - (r1r2Nr0r/z*(r3r4r5) r r r6r rr$rr8r7r9rrr _sympystrsP       zDyadic._sympystrcCs||dS)zThe subtraction operator. r-)rrrrr__sub__*szDyadic.__sub__cCsPddlm}||}td}|jD](}||d|d|d|7}q"|S)aReturns the dyadic resulting from the dyadic vector cross product: Dyadic x Vector. Parameters ========== other : Vector Vector to cross with. Examples ======== >>> from sympy.physics.vector import ReferenceFrame, outer, cross >>> N = ReferenceFrame('N') >>> d = outer(N.x, N.x) >>> cross(d, N.y) (N.x|N.z) r)r"r r )r#r"rr r&cross)rrr"r'rrrrrP.s   &z Dyadic.crossNcCsddlm}||||S)aExpresses this Dyadic in alternate frame(s) The first frame is the list side expression, the second frame is the right side; if Dyadic is in form A.x|B.y, you can express it in two different frames. If no second frame is given, the Dyadic is expressed in only one frame. Calls the global express function Parameters ========== frame1 : ReferenceFrame The frame to express the left side of the Dyadic in frame2 : ReferenceFrame If provided, the frame to express the right side of the Dyadic in Examples ======== >>> from sympy.physics.vector import ReferenceFrame, outer, dynamicsymbols >>> from sympy.physics.vector import init_vprinting >>> init_vprinting(pretty_print=False) >>> N = ReferenceFrame('N') >>> q = dynamicsymbols('q') >>> B = N.orientnew('B', 'Axis', [q, N.z]) >>> d = outer(N.x, N.x) >>> d.express(B, N) cos(q)*(B.x|N.x) - sin(q)*(B.y|N.x) r)express)sympy.physics.vector.functionsrQ)rZframe1Zframe2rQrrrrQJs zDyadic.expresscs,dkr |tfdd|DddS)aReturns the matrix form of the dyadic with respect to one or two reference frames. Parameters ---------- reference_frame : ReferenceFrame The reference frame that the rows and columns of the matrix correspond to. If a second reference frame is provided, this only corresponds to the rows of the matrix. second_reference_frame : ReferenceFrame, optional, default=None The reference frame that the columns of the matrix correspond to. Returns ------- matrix : ImmutableMatrix, shape(3,3) The matrix that gives the 2D tensor form. Examples ======== >>> from sympy import symbols, trigsimp >>> from sympy.physics.vector import ReferenceFrame >>> from sympy.physics.mechanics import inertia >>> Ixx, Iyy, Izz, Ixy, Iyz, Ixz = symbols('Ixx, Iyy, Izz, Ixy, Iyz, Ixz') >>> N = ReferenceFrame('N') >>> inertia_dyadic = inertia(N, Ixx, Iyy, Izz, Ixy, Iyz, Ixz) >>> inertia_dyadic.to_matrix(N) Matrix([ [Ixx, Ixy, Ixz], [Ixy, Iyy, Iyz], [Ixz, Iyz, Izz]]) >>> beta = symbols('beta') >>> A = N.orientnew('A', 'Axis', (beta, N.x)) >>> trigsimp(inertia_dyadic.to_matrix(A)) Matrix([ [ Ixx, Ixy*cos(beta) + Ixz*sin(beta), -Ixy*sin(beta) + Ixz*cos(beta)], [ Ixy*cos(beta) + Ixz*sin(beta), Iyy*cos(2*beta)/2 + Iyy/2 + Iyz*sin(2*beta) - Izz*cos(2*beta)/2 + Izz/2, -Iyy*sin(2*beta)/2 + Iyz*cos(2*beta) + Izz*sin(2*beta)/2], [-Ixy*sin(beta) + Ixz*cos(beta), -Iyy*sin(2*beta)/2 + Iyz*cos(2*beta) + Izz*sin(2*beta)/2, -Iyy*cos(2*beta)/2 + Iyy/2 - Iyz*sin(2*beta) + Izz*cos(2*beta)/2 + Izz/2]]) Ncs&g|]}D]}||q qSr)r%).0rjsecond_reference_framerrr sz$Dyadic.to_matrix..r4)MatrixZreshape)rZreference_framerVrrUr to_matrixms +zDyadic.to_matrixc stfdd|jDtdS)z(Calls .doit() on each term in the Dyadiccs0g|](}t|djf|d|dfgqSrr r )rdoitrSrhintsrrrWszDyadic.doit..rsumr r)rr^rr]rr[s  z Dyadic.doitcCsddlm}|||S)aTake the time derivative of this Dyadic in a frame. This function calls the global time_derivative method Parameters ========== frame : ReferenceFrame The frame to take the time derivative in Examples ======== >>> from sympy.physics.vector import ReferenceFrame, outer, dynamicsymbols >>> from sympy.physics.vector import init_vprinting >>> init_vprinting(pretty_print=False) >>> N = ReferenceFrame('N') >>> q = dynamicsymbols('q') >>> B = N.orientnew('B', 'Axis', [q, N.z]) >>> d = outer(N.x, N.x) >>> d.dt(B) - q'*(N.y|N.x) - q'*(N.x|N.y) r)time_derivative)rRra)rframerarrrdts z Dyadic.dtcCs<td}|jD](}|t|d|d|dfg7}q|S)zReturns a simplified Dyadic.rr r )rr simplify)routrrrrrds &zDyadic.simplifycs tfdd|jDtdS)a5Substitution on the Dyadic. Examples ======== >>> from sympy.physics.vector import ReferenceFrame >>> from sympy import Symbol >>> N = ReferenceFrame('N') >>> s = Symbol('s') >>> a = s*(N.x|N.x) >>> a.subs({s: 2}) 2*(N.x|N.x) cs0g|](}t|dj|d|dfgqSrZ)rsubsr\r rBrrrWszDyadic.subs..rr_)rr rBrrgrrfs z Dyadic.subscCsDt|stdtd}|jD] \}}}|||||7}q|S)z/Apply a function to each component of a Dyadic.z`f` must be callable.r)callable TypeErrorrr r&)rfreabcrrr applyfuncs zDyadic.applyfunccCsT|js |Sg}t|}|jD].}t|}|dj|d|d<|t|qt|S)Nr)n)r rrZevalfrtupler)rprecnew_argsZdpsr new_inlistrrr _eval_evalfs zDyadic._eval_evalfcCs@g}|jD],}t|}|d||d<|t|q t|S)a Replace occurrences of objects within the measure numbers of the Dyadic. Parameters ========== rule : dict-like Expresses a replacement rule. Returns ======= Dyadic Result of the replacement. Examples ======== >>> from sympy import symbols, pi >>> from sympy.physics.vector import ReferenceFrame, outer >>> N = ReferenceFrame('N') >>> D = outer(N.x, N.x) >>> x, y, z = symbols('x y z') >>> ((1 + x*y) * D).xreplace({x: pi}) (pi*y + 1)*(N.x|N.x) >>> ((1 + x*y) * D).xreplace({x: pi, y: 2}) (1 + 2*pi)*(N.x|N.x) Replacements occur only if an entire node in the expression tree is matched: >>> ((x*y + z) * D).xreplace({x*y: pi}) (z + pi)*(N.x|N.x) >>> ((x*y*z) * D).xreplace({x*y: pi}) x*y*z*(N.x|N.x) r)r rxreplacerrpr)rrulerrrrsrrrrus ( zDyadic.xreplace)N)N)"rGrHrI__doc__Z is_numberrpropertyrr__radd__r __rmul__r%__and__r(r*r+r.r?rKrLrNrOrP__xor__rQrYr[rcrdrfrnrtrurrrrr s> & %$6$ # 1  cCst|tstd|S)NzA Dyadic must be supplied)r$rri)rrrrrs rN)ZsympyrrrrXZsympy.core.evalfrZsympy.printing.defaultsrZmpmath.libmp.libmpfr__all__rrrrrrs