U L?h @sddlmZddlmZddlmZmZddlmZm Z ddl m Z ddl m Z mZddlmZddlmZmZmZmZmZmZmZmZmZmZmZmZmZdd lm Z dd d d d ddd d d dddZ!ddZ"d defd dddZ#d S))Tuple)oo)GtLt)DummySymbol)Abs)MinMax)And) AssignmentAddAugmentedAssignmentbreak_ CodeBlock DeclarationFunctionDefinitionPrintReturnScopeWhileVariablePointerreal)isnan-q=NgؗҼr!)rtoldebugitermaxcounterdelta_fncse handle_nanboundscCs|dkrt}t} d} ndd} |j} |||}| rtddlm} | |g\}\}dd|D}|t||g7}n t||g}| dk r|tt|t | t g7}|t ||g7}| dk r|t|t t || d| d g7}|rt||gd |j| }||g7}tt|||t|}tt|ttd g}|dk r|pLtd d }t|d}|t||t |d t|t||}t|t |}|}|r|t|gd|j||g7}| t |S)a Generates an AST for Newton-Raphson method (a root-finding algorithm). Explanation =========== Returns an abstract syntax tree (AST) based on ``sympy.codegen.ast`` for Netwon's method of root-finding. Parameters ========== expr : expression wrt : Symbol With respect to, i.e. what is the variable. atol : number or expression Absolute tolerance (stopping criterion) rtol : number or expression Relative tolerance (stopping criterion) delta : Symbol Will be a ``Dummy`` if ``None``. debug : bool Whether to print convergence information during iterations itermax : number or expr Maximum number of iterations. counter : Symbol Will be a ``Dummy`` if ``None``. delta_fn: Callable[[Expr, Symbol], Expr] computes the step, default is newtons method. For e.g. Halley's method use delta_fn=lambda e, x: -2*e*e.diff(x)/(2*e.diff(x)**2 - e*e.diff(x, 2)) cse: bool Perform common sub-expression elimination on delta expression handle_nan: Token How to handle occurrence of not-a-number (NaN). bounds: Optional[tuple[Expr, Expr]] Perform optimization within bounds Examples ======== >>> from sympy import symbols, cos >>> from sympy.codegen.ast import Assignment >>> from sympy.codegen.algorithms import newtons_method >>> x, dx, atol = symbols('x dx atol') >>> expr = cos(x) - x**3 >>> algo = newtons_method(expr, x, atol=atol, delta=dx) >>> algo.has(Assignment(dx, -expr/expr.diff(x))) True References ========== .. [1] https://en.wikipedia.org/wiki/Newton%27s_method NdeltacSs|Srr)rrrr r!Pr"z newtons_method..r)r(cSsg|]\}}t||qSr)r ).0ZdumZsub_errr Wsz"newtons_method..z{}=%12.5g {}=%12.5g\n)typevalueT)integerz {}=%12.5g\n)rrnameZsympy.simplify.cse_mainr(factorr rrrrr r r rformatrrrrrrZdeducedappendr r)exprwrtZatolr+r#r$r%r&r'r(r)r*ZWrapperZname_dZ delta_exprZcsesredZwhl_bdyZprntreqdeclarsZ v_counterZwhlZblckrrr newtons_methodsF;   $    r;cCs(t|tr|jj}nt|tr$|j}|Sr) isinstancervariablesymbolr)argrrr _symbol_ofss    r@Znewton)r+c Ks|dkr|f}dd|D}|dkr@td|j}||r@d}t||fd|i||}t|trl|j}|j dd|D} | rt dd t t | td d |D} t|t|} tt|| | |d S) a Generates an AST for a function implementing the Newton-Raphson method. Parameters ========== expr : expression wrt : Symbol With respect to, i.e. what is the variable params : iterable of symbols Symbols appearing in expr that are taken as constants during the iterations (these will be accepted as parameters to the generated function). func_name : str Name of the generated function. attrs : Tuple Attribute instances passed as ``attrs`` to ``FunctionDefinition``. \*\*kwargs : Keyword arguments passed to :func:`sympy.codegen.algorithms.newtons_method`. Examples ======== >>> from sympy import symbols, cos >>> from sympy.codegen.algorithms import newtons_method_function >>> from sympy.codegen.pyutils import render_as_module >>> x = symbols('x') >>> expr = cos(x) - x**3 >>> func = newtons_method_function(expr, x) >>> py_mod = render_as_module(func) # source code as string >>> namespace = {} >>> exec(py_mod, namespace, namespace) >>> res = eval('newton(0.5)', namespace) >>> abs(res - 0.865474033102) < 1e-12 True See Also ======== sympy.codegen.algorithms.newtons_method NcSs*i|]"}t|tr|jtd|jjqS)z(*%s))r<rr>rr2r,prrr s z+newtons_method_function..Zd_r+cSsh|] }t|qSr)r@rArrr sz*newtons_method_function..zMissing symbols in params: %sz, css|]}t|tVqdSr)rrrArrr sz*newtons_method_function..)attrs)rr2hasr;Zxreplacer<rbodyZ free_symbols difference ValueErrorjoinmapstrtuplerrrr) r6r7params func_namerFr+kwargsZ pointer_subsalgoZ not_in_paramsr:rHrrr newtons_method_function{s$)  rS)rN)$Zsympy.core.containersrZsympy.core.numbersrZsympy.core.relationalrrZsympy.core.symbolrrZ$sympy.functions.elementary.complexesrZ(sympy.functions.elementary.miscellaneousr r Zsympy.logic.boolalgr Zsympy.codegen.astr r rrrrrrrrrrrZsympy.codegen.cfunctionsrr;r@rSrrrr s$    <  c