o o 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=NgؗҼsr!)rtoldebugitermaxcounterdelta_fncse handle_nanboundscCs|dur t}t} d} ndd} |j} |||}| r:ddlm} | |g\}\}dd|D}|t||g7}nt||g}| durQ|tt|t | t g7}|t ||g7}| duro|t|t t || d| d g7}|rt||gd |j| }||g7}tt|||t|}tt|ttd g}|dur|ptd 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!Psz newtons_method..r)r'cSsg|] \}}t||qSr)r ).0dumsub_errr Wsz"newtons_method..z{}=%12.5g {}=%12.5g\n)typevalueT)integerz {}=%12.5g\n)rrnamesympy.simplify.cse_mainr'factorr rrrrr r r rformatrrrrrrdeducedappendr r)exprwrtatolr*r"r#r$r%r&r'r(r)Wrappername_d delta_exprcsesredwhl_bdyprntreqdeclars v_counterwhlblckrrr newtons_methodsF;   $    rHcCs*t|tr |jj}|St|tr|j}|Sr) isinstancervariablesymbolr)argrrr _symbol_ofss  rMnewton)r*c Ks|dur|f}dd|D}|dur td|j}||r d}t||fd|i||}t|tr6|j}|j dd|D} | rOt 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))rIrrKrr3r+prrr s z+newtons_method_function..d_r*cSsh|]}t|qSr)rMrOrrr sz*newtons_method_function..zMissing symbols in params: %sz, css|]}t|tVqdSr)rrrOrrr sz*newtons_method_function..)attrs)rr3hasrHxreplacerIrbody free_symbols difference ValueErrorjoinmapstrtuplerrrr) r9r:params func_namerUr*kwargs pointer_subsalgo not_in_paramsrDrXrrr newtons_method_function{s$)  rf)rN)$sympy.core.containersrsympy.core.numbersrsympy.core.relationalrrsympy.core.symbolrr$sympy.functions.elementary.complexesr(sympy.functions.elementary.miscellaneousr r sympy.logic.boolalgr sympy.codegen.astr r rrrrrrrrrrrsympy.codegen.cfunctionsrrHrMrfrrrr s"   <   c