o o h/@sbddlZddlmZddlmZmZddlmZddlm Z  GdddeZ Gdd d eZ dS) N)Interval) is_increasing is_decreasing) Optimization)UndefinedFunctioncs8eZdZdZfddZddZddZdd ZZS) SumApproxa8 Approximates sum by neglecting small terms. Explanation =========== If terms are expressions which can be determined to be monotonic, then bounds for those expressions are added. Parameters ========== bounds : dict Mapping expressions to length 2 tuple of bounds (low, high). reltol : number Threshold for when to ignore a term. Taken relative to the largest lower bound among bounds. Examples ======== >>> from sympy import exp >>> from sympy.abc import x, y, z >>> from sympy.codegen.rewriting import optimize >>> from sympy.codegen.approximations import SumApprox >>> bounds = {x: (-1, 1), y: (1000, 2000), z: (-10, 3)} >>> sum_approx3 = SumApprox(bounds, reltol=1e-3) >>> sum_approx2 = SumApprox(bounds, reltol=1e-2) >>> sum_approx1 = SumApprox(bounds, reltol=1e-1) >>> expr = 3*(x + y + exp(z)) >>> optimize(expr, [sum_approx3]) 3*(x + y + exp(z)) >>> optimize(expr, [sum_approx2]) 3*y + 3*exp(z) >>> optimize(expr, [sum_approx1]) 3*y c s"tjdi|||_||_dS)N)super__init__boundsreltol)selfr r kwargs __class__rp/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/codegen/approximations.pyr 6s zSumApprox.__init__c|jfddS)Nc |SNvalueargr rr< z$SumApprox.__call__..factorreplacequeryr exprrrr__call__;zSumApprox.__call__cCs|jSr)is_Addr rrrr>szSumApprox.queryc s|jD]j}|js|jvst|jdkrq|j\}|jvrqtj|}t|||rH||j|di||j|difj|<qt|||rj||j|di||j|difj|<q|St fdd|jDr͇fdd|jD}d}|D]\}}|dkr|krnnqt |t t |t |}qg} t |j|D]\}\}}t t |t ||jkr| |q|j| S|S)Nrc3s |] }|jp |jvVqdSr is_numberr .0termrrr Vsz"SumApprox.value..cs$g|]}|jr ||fnj|qSrr&r(rrr Ws$z#SumApprox.value..)argsr'r len free_symbolsrrsubsrallmaxminabszipr appendfunc) r addr*fsintrvlr largest_abs_guaranteelohi new_termsrrrrAs@        zSumApprox.value __name__ __module__ __qualname____doc__r r"rr __classcell__rrrrrs  'rcs:eZdZdZd fdd ZddZddZd d ZZS) SeriesApproxa  Approximates functions by expanding them as a series. Parameters ========== bounds : dict Mapping expressions to length 2 tuple of bounds (low, high). reltol : number Threshold for when to ignore a term. Taken relative to the largest lower bound among bounds. max_order : int Largest order to include in series expansion n_point_checks : int (even) The validity of an expansion (with respect to reltol) is checked at discrete points (linearly spaced over the bounds of the variable). The number of points used in this numerical check is given by this number. Examples ======== >>> from sympy import sin, pi >>> from sympy.abc import x, y >>> from sympy.codegen.rewriting import optimize >>> from sympy.codegen.approximations import SeriesApprox >>> bounds = {x: (-.1, .1), y: (pi-1, pi+1)} >>> series_approx2 = SeriesApprox(bounds, reltol=1e-2) >>> series_approx3 = SeriesApprox(bounds, reltol=1e-3) >>> series_approx8 = SeriesApprox(bounds, reltol=1e-8) >>> expr = sin(x)*sin(y) >>> optimize(expr, [series_approx2]) x*(-y + (y - pi)**3/6 + pi) >>> optimize(expr, [series_approx3]) (-x**3/6 + x)*sin(y) >>> optimize(expr, [series_approx8]) sin(x)*sin(y) c sXtjdi|||_||_||_|ddkrtd||_tt |j |_ dS)Nr%z7Checking the solution at expansion point is not helpfulr) r r r r max_order ValueErrorn_point_checksmathceillog10_prec)r r r rHrJrrrrr s zSeriesApprox.__init__cr)Ncrrrrrrrrrz'SeriesApprox.__call__..rr rrrr"r#zSeriesApprox.__call__cCs |jot|t ot|jdkS)Nr%) is_Function isinstancerr.r-r rrrrs zSeriesApprox.querycCs|j}t|dkr |S|\}||jvr|S|j|\}}||d}d}t|jdddD]I}|j|||d} d} t|jD]0} || |||jd} | || i} ||| i}t d| | |j |j krpd} nq@| rv| }q-|dur}|S|S)Nr%rGr)x0nTF) r/r.r rangerHseriesremoveOrJxreplacer4evalfrNr )r fexprr/symbr<r=rRcheapestrSfserin_okidxxvalrefrrrrs4   zSeriesApprox.value)rFrFr?rrrrrEgs % rE) rKsympy.sets.setsrsympy.calculus.singularitiesrrsympy.codegen.rewritingrsympy.core.functionrrrErrrrs   Y