From 95d73a8407d9431dbe37b48a5461e90225c88b8b Mon Sep 17 00:00:00 2001 From: Antonio Jimenez Pastor Date: Mon, 3 Sep 2018 15:56:34 +0200 Subject: [PATCH] Updated the Struve example Started the example of Legendre elliptic integrals --- ajpastor/dd_functions/ddExamples.py | 59 ++++++++++++++++++--- releases/diff_defined_functions__0.5.zip | Bin 111226 -> 111685 bytes ...f_defined_functions__0.5__18.09.03_15:56:33.zip | Bin 0 -> 111685 bytes 3 files changed, 52 insertions(+), 7 deletions(-) create mode 100644 releases/old/diff_defined_functions__0.5__18.09.03_15:56:33.zip diff --git a/ajpastor/dd_functions/ddExamples.py b/ajpastor/dd_functions/ddExamples.py index 4137183..9e5e582 100644 --- a/ajpastor/dd_functions/ddExamples.py +++ b/ajpastor/dd_functions/ddExamples.py @@ -10,7 +10,6 @@ _sage_const_3 = Integer(3); _sage_const_2 = Integer(2); _sage_const_1 = Integer( from ajpastor.dd_functions.ddFunction import *; from ajpastor.misc.dinamic_string import *; -#from ajpastor.dd_functions.ddParametrizedFunction import *; ## Global variables (PUBLIC) DFinite_examples = {}; @@ -46,7 +45,8 @@ def DD_EXAMPLES_LOAD(): DFinite_examples['sinh'] = sh; DFinite_examples['cosh'] = ch; P = DFiniteP.parameters()[_sage_const_0 ]; - DFinite_examples['bessel'] = DFiniteP.element([x**_sage_const_2 -P**_sage_const_2 ,x,x**_sage_const_2 ], name=DinamicString("bessel_J(_1,_2)", ["P","x"])); + DFinite_examples['bessel'] = DFiniteP.element([x**2-P**2,x,x**2], name=DinamicString("bessel_J(_1,_2)", ["P","x"])); + DFinite_examples['struve'] = DFiniteP.element([(1-P)*x**2+P**2*(P+1),x*(x**2-P**2-P),(2-P)*x**2,x**3], name=DinamicString("pi*struve_H(_1,_2)", ["P","x"])); DFinite_examples['legendre'] = DFiniteP.element([P*(P+_sage_const_1 ), -_sage_const_2 *x,_sage_const_1 -x**_sage_const_2 ], name=DinamicString("legendre_P(_1,_2)", ["P","x"])); DFinite_examples['chebyshev1'] = DFiniteP.element([P**_sage_const_2 ,-x,(_sage_const_1 -x**_sage_const_2 )], name=DinamicString("chebyshev_T(_1,_2)", ["P","x"])); DFinite_examples['chebyshev2'] = DFiniteP.element([P*(P+_sage_const_2 ),-_sage_const_3 *x,_sage_const_1 -x**_sage_const_2 ], name=DinamicString("chebyshev_U(_1,_2)", ["P","x"])); @@ -490,16 +490,28 @@ def AiryD(init=()): ### Struve's functions @cached_function -def StruveD(mu,kind=1): - raise NotImplementedError("Struve functions not yet implemented"); +def StruveD(mu=None,kind=1): + _sage_const_1 = ZZ(1); _sage_const_2 = ZZ(2); _sage_const_3 = ZZ(3); if(kind != 1): raise TypeError("Only struve_H functions are implemented"); + + f = DFinite_examples['struve']; + if(mu is None): + return f; elif((mu < 0) or (mu not in ZZ)): raise TypeError("Parameter must be greater or equal to -1 to have a power series (got %d)" %mu); + + P = f.parent().parameters()[0]; + num = factorial(mu+_sage_const_1)*pi*(_sage_const_1/_sage_const_2)**(mu+_sage_const_1); + den = gamma(_sage_const_3/_sage_const_2)*gamma(mu+_sage_const_3/_sage_const_2); + val = QQ(num/den); + + print num,den,val; - name=DinamicString("(%s)*struve_H(%s,_1)" %((1/(struve_H(mu,x).derivative(mu+1)(x=0))),mu), ["x"]); - init = [0 for i in range(mu+1)] + [1]; - return DFinite.element([x**2*(1-mu)-mu**2,x*(x**2-mu**2-mu),-(mu-2)*x**2,x**3], init, name=name); + f = f(P=mu); + f = f.change_init_values([0 for i in range(mu+1)] + [val], name=f._DDFunction__name); + + return f; ### Parabolic Cylinder Functions @cached_function @@ -531,6 +543,39 @@ def ParabolicCylinderD(a=None,b=None,c=None, init=()): rc = destiny_ring.parameters()[0]; return destiny_ring.element([(rc+rb*x+ra*x**2),0,1], init, name=DinamicString("ParabolicCylinder(_1,_2,_3;_4)", [repr(ra), repr(rb), repr(rc), "x"])); +## Elliptic integrals +## Legendre elliptic integrals +def EllipticLegendreD(kind,var='phi'): + if(kind not in [0,1,2]): + raise ValueError("The kind of legendre elliptic integral is not valid. Required 0,1 or 2"); + if(str(var) not in ['m','phi']): + raise ValueError("The variable for taking the equation must be 'm' or 'phi'"); + + var = str(var); + if(var == 'm'): + if(kind == 1): + name = DinamicString("(2/pi)*elliptic_f(pi/2,_1)", ["x"]); + return DFinite.elemetn([-x,(1-3*x**2), x*(1-x**2)],[1], name=name); + elif(kind == 2): + name = DinamicString("(2/pi)*elliptic_e(pi/2,_1)", ["x"]); + return DFinite.elemetn([x,(1-x**2), x*(1-x**2)],[1], name=name); + else: + return (EllipticLegendreD(1,var)-EllipticLegendreD(2,var))/x**2; + + if(var == 'phi'): + DDFiniteP = DFiniteP.to_depth(2); + P = DDFiniteP.parameters()[0]; + s = DFiniteP(Sin(x)); + c = DFiniteP(Cos(x)); + if(kind == 1): + name = DinamicString("(2/pi)*elliptic_f(_2,_1)", [repr(P),"x"]); + return DDFiniteP.element([0,-P**2*s*c,1-P**2*s**2], [0,1], name=name); + elif(kind == 2): + name = DinamicString("(2/pi)*elliptic_e(_2,_1)", [repr(P),"x"]); + return DDFiniteP.element([0,P**2*s*c,1-P**2*s**2], [0,1], name=name); + 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