g ddlmZddlmZddlmZmZddlmZm Z ddl m Z ddl m Z mZddlmZddlmZmZmZmZmZmZmZmZmZmZmZmZmZdd lm Z  dd d d d dd d d ddZ!dZ"d defd ddZ#d S))Tuple)oo)GtLt)DummySymbol)Abs)MinMax)And) AssignmentAddAugmentedAssignmentbreak_ CodeBlock DeclarationFunctionDefinitionPrintReturnScopeWhileVariablePointerreal)isnan-q=NgؗҼr"saRq \)rtoldebugitermaxcounterdelta_fncse handle_nanboundsc <|t}t} d} n d} |j} |||}| rJddlm} | |g\}\}d|D}|t ||gz }nt ||g}| 4|tt|t| tgz }|t||gz }| <|t |tt|| d| dgz }|r1t||gd|j| }||gz }t!t#|||t#|zz}t%t'|t(t* g}||ptd }t'j|d}|t%||t|dt1|t3||}t|t|}|}|r<|t|gd |j||gz }| 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 Ndeltac|Sr)r s r!r"z newtons_method..PsAr#r)r)c4g|]\}}t||Sr/)r ).0dumsub_es r! z"newtons_method..Ws&AAAjc5:c5))AAAr#z{}=%12.5g {}=%12.5g\n)typevalueT)integerz {}=%12.5g\n)rrnamesympy.simplify.cse_mainr)factorr rrrrrr r rformatrr rrrrdeducedappendr r)exprwrtatolr-r$r%r&r'r(r)r*r+Wrappername_d delta_exprcsesredwhl_bdyprntreqdeclars v_counterwhlblcks r!newtons_methodrNsv }+$$$J 2//////sJ--//011 fsAADAAAJuc**++eZ001E%,, *f(E(EFFGG &sE2233G JsCC(;(;VAY$G$GHHII c5\#;#B#B38V#T#TUUD6 SZZSXX - . .C8EB???@@AG0U4000$Wa00 {9--...-gq99:::#r'7++,, Y( ) )C D C E3%!6!6sx!@!@AABBBSEMD 79d# $ $$r#ct|tr |jj}nt|tr|j}|Sr) isinstancervariablesymbolr)args r! _symbol_ofrTss>#{##l! C " "j Jr#newton)r-c \||f}d|D}|.td|jz}||rd}t||fd|i||}t |t r|j}|j d|D} | r8tdd tt| ztd|D} t|t!|} t#t$|| | | 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 Nc|i|]9}t|t|jtd|jjz:S)z(*%s))rPrrRrr9r1ps r! z+newtons_method_function..sK???z!W'='=?AHfWqx}%<==???r#d_r-c,h|]}t|Sr/)rTrXs r! z*newtons_method_function..s1P1P1PA*Q--1P1P1Pr#zMissing symbols in params: %sz, c3@K|]}t|tVdSr)rrrXs r! z*newtons_method_function..s,66!HQ%%666666r#)attrs)rr9hasrNxreplacerPrbody free_symbols difference ValueErrorjoinmapstrtuplerrrr) r?r@params func_namer`r-kwargs pointer_subsalgo not_in_paramsrJrcs r!newtons_method_functionrq{sCR~??#???L }tch'' 88E?? E $ ; ;5 ;F ; ; D D\ R RD$y%001P1P1P1P1PQQM_8499SmE\E\;];]]^^^66v66666G T6#;; ' 'D dIwE J J JJr#)rN)$sympy.core.containersrsympy.core.numbersrsympy.core.relationalrrsympy.core.symbolrr$sympy.functions.elementary.complexesr (sympy.functions.elementary.miscellaneousr r sympy.logic.boolalgr sympy.codegen.astr rrrrrrrrrrrrsympy.codegen.cfunctionsrrNrTrqr/r#r!r{s''''''!!!!!!********--------444444========######+*****U`%e58Q8Q`%`%`%`%`%F/3heegg9K`d9K9K9K9K9K9K9Kr#