<p>编辑:重读我的答案->;我想我会填补一些缺失的部分,作为对某一天实际使用这个工具的人的服务。下面我标记了如何命名我的库,以及需要什么导入。我现在没有时间成为sympy的真正贡献者,但是我觉得这个功能肯定会被其他数学/物理教授/学生使用。在</p>
<p>注意,由于空间原因,省略了以下两个库,我将在以后的某个日期抛出指向回购的链接。在</p>
<pre><code>import Library_SympyExpressionToPythonFunction
</code></pre>
<p>创建一个python可调用函数对象,其参数(数字和名称)与sympy表达式中的自由变量相同。在</p>
^{pr2}$
<p>字面上就是str(SympyExpression)</p>
<pre><code># -
</code></pre>
<p>图书馆代谢比斯法:</p>
<pre><code># -
import pprint
import Library_SympyExpressionToPythonFunction
import Library_SympyExpressionToStringExpression
import sympy
import sympy.core
def Main(
ApproximationSymbol = sympy.Symbol('x'),
ResultType = 'sympy',
Kind= None,
Order= None,
ReturnAll = False,
CheckArguments = True,
PrintExtra = False,
):
Result = None
if (CheckArguments):
ArgumentErrorMessage = ""
if (len(ArgumentErrorMessage) > 0 ):
if(PrintExtra):
print "ArgumentErrorMessage:\n", ArgumentErrorMessage
raise Exception(ArgumentErrorMessage)
ChebyChevPolynomials = []
ChebyChevPolynomials.append(sympy.sympify(1.))
ChebyChevPolynomials.append(ApproximationSymbol)
#Generate the polynomial with sympy:
for Term in range(Order + 1)[2:]:
Tn = ChebyChevPolynomials[Term - 1]
Tnminus1 = ChebyChevPolynomials[Term - 2]
Tnplus1 = 2*ApproximationSymbol*Tn - Tnminus1
ChebyChevPolynomials.append(Tnplus1.simplify().expand().trigsimp())
if(PrintExtra): print 'ChebyChevPolynomials'
if(PrintExtra): pprint.pprint(ChebyChevPolynomials)
if (ReturnAll):
Result = []
for SympyChebyChevPolynomial in ChebyChevPolynomials:
if (ResultType == 'python'):
Result.append(Library_SympyExpressionToPythonFunction.Main(SympyChebyChevPolynomial))
elif (ResultType == 'string'):
Result.append(Library_SympyExpressionToStringExpression.Main(SympyChebyChevPolynomial))
else:
Result.append(SympyChebyChevPolynomial)
else:
SympyExpression = ChebyChevPolynomials[Order] #the last one
#If the result type is something other than sympy, we can cast it into that type here:
if (ResultType == 'python'):
Result = Library_SympyExpressionToPythonFunction.Main(SympyExpression)
elif (ResultType == 'string'):
Result = Library_SympyExpressionToStringExpression.Main(SympyExpression)
else:
Result = SympyExpression
return Result
# -
</code></pre>
<p>图书馆协方差近似维数</p>
<pre><code># -
import numpy
import sympy
import sympy.mpmath
import pprint
import Library_SympyExpressionToPythonFunction
import Library_GenerateChebyShevPolynomial
def Main(
SympyExpression= None,
DomainMinimumPoint= None,
DomainMaximumPoint= None,
ApproximationOrder= None,
CheckArguments = True,
PrintExtra = False,
):
#Tsymb = sympy.Symbol('t')
Xsymb = sympy.Symbol('x')
DomainStart = DomainMinimumPoint[0]
print 'DomainStart', DomainStart
DomainEnd = DomainMaximumPoint[0]
print 'DomainEnd', DomainEnd
#Transform the coefficients and the result to be on arbitrary inverval instead of from 0 to 1
DomainWidth = DomainEnd - DomainStart
DomainCenter = (DomainEnd - DomainStart) / 2.
t = (Xsymb*(DomainWidth) + DomainStart + DomainEnd) / 2.
x = (2.*Xsymb - DomainStart - DomainEnd) / (DomainWidth)
SympyExpression = SympyExpression.subs(Xsymb, t)
#GET THE COEFFICIENTS:
Coefficients = []
for CoefficientNumber in range(ApproximationOrder):
if(PrintExtra): print 'CoefficientNumber', CoefficientNumber
Coefficient = 0.0
for k in range(1, ApproximationOrder + 1):
if(PrintExtra): print ' k', k
CoefficientFunctionPart = SympyExpression.subs(Xsymb, sympy.cos( sympy.pi*( float(k) - .5 )/ float(ApproximationOrder) ) )
if(PrintExtra): print ' CoefficientFunctionPart', CoefficientFunctionPart
CeofficientCosArg = float(CoefficientNumber)*( float(k) - .5 )/ float( ApproximationOrder)
if(PrintExtra): print ' ',CoefficientNumber,'*','(',k,'-.5)/(', ApproximationOrder ,') == ', CeofficientCosArg
CoefficientCosPart = sympy.cos( sympy.pi*CeofficientCosArg )
if(PrintExtra): print ' CoefficientCosPart', CoefficientCosPart
Coefficient += CoefficientFunctionPart*CoefficientCosPart
if(PrintExtra): print 'Coefficient==', Coefficient
Coefficient = (2./ApproximationOrder)*Coefficient.evalf(10)
if(PrintExtra): print 'Coefficient==', Coefficient
Coefficients.append(Coefficient)
print '\n\nCoefficients'
pprint.pprint( Coefficients )
#GET THE POLYNOMIALS:
ChebyShevPolynomials = Library_GenerateChebyShevPolynomial.Main(
ResultType = 'sympy',
Kind= 1,
Order= ApproximationOrder-1,
ReturnAll = True,
)
print '\nChebyShevPolynomials'
pprint.pprint( ChebyShevPolynomials )
Result = 0.0 -.5*(Coefficients[0])
for Coefficient, ChebyShevPolynomial in zip(Coefficients, ChebyShevPolynomials):
Result += Coefficient*ChebyShevPolynomial
#Transform the coefficients and the result to be on arbitrary inverval instead of from 0 to 1
Result = Result.subs(Xsymb, x)
return Result
</code></pre>
<h2>在</h2>
<p>示例:Sympychebysheva近似尺寸:</p>
<pre><code>#
import sympy
import sympy.mpmath
import matplotlib.pyplot as plt
import json
import pprint
import Library_GenerateBesselFunction
import Library_SympyChebyShevApproximationOneDimension
import Library_SympyExpressionToPythonFunction
import Library_GraphOneDimensionalFunction
ApproximationOrder = 10
#CREATE THE EXAMPLE EXRESSION:
Kind = 1
Order = 2
ExampleSympyExpression = sympy.sin(sympy.Symbol('x'))
"""
Library_GenerateBesselFunction.Main(
ResultType = 'sympy',
Kind = Kind,
Order = Order,
VariableNames = ['x'],
)
"""
PythonOriginalFunction = Library_SympyExpressionToPythonFunction.Main(
ExampleSympyExpression ,
FloatPrecision = 100,
)
#CREATE THE NATIVE CHEBY APPROXIMATION
ChebyDomainMin = 5.
ChebyDomainMax = 10.
ChebyDomain = [ChebyDomainMin, ChebyDomainMax]
ChebyExpandedPolynomialCoefficients, ChebyError = sympy.mpmath.chebyfit(
PythonOriginalFunction,
ChebyDomain,
ApproximationOrder,
error=True
)
print 'ChebyExpandedPolynomialCoefficients'
pprint.pprint( ChebyExpandedPolynomialCoefficients )
def PythonChebyChevApproximation(Point):
Result = sympy.mpmath.polyval(ChebyExpandedPolynomialCoefficients, Point)
return Result
#CREATE THE GENERIC ONE DIMENSIONAL CHEBY APPROXIMATION:
SympyChebyApproximation = Library_SympyChebyShevApproximationOneDimension.Main(
SympyExpression = ExampleSympyExpression*sympy.cos( sympy.Symbol('a') ),
ApproximationSymbol = sympy.Symbol('x'),
DomainMinimumPoint = [ChebyDomainMin],
DomainMaximumPoint = [ChebyDomainMax],
ApproximationOrder = ApproximationOrder
)
print 'SympyChebyApproximation', SympyChebyApproximation
SympyChebyApproximation = SympyChebyApproximation.subs(sympy.Symbol('a'), 0.0)
print 'SympyChebyApproximation', SympyChebyApproximation
PythonCastedChebyChevApproximationGeneric = Library_SympyExpressionToPythonFunction.Main(
SympyChebyApproximation ,
FloatPrecision = 100,
)
print 'PythonCastedChebyChevApproximationGeneric(1)', PythonCastedChebyChevApproximationGeneric(1.)
</code></pre>