def gradient_set( self, x, degree, a = None, b = None ):
if ( ( a is not None ) and ( b is not None ) ):
x = ( 2. * x - b - a ) / ( b - a );
if ( degree == 0 ):
grad = 0.;
elif ( degree == 1 ):
grad = (self.alpha_poly + self.beta_poly + 2.)/2.;
elif ( degree == 2 ):
xm1 = x - 1.;
grad = ( (self.alpha_poly + self.beta_poly + 3.) *
(self.alpha_poly + self.beta_poly + 4.)*xm1 +
2.*(self.alpha_poly + self.beta_poly + 3.) *
(self.alpha_poly + 2.) ) / 4.;
else:
# Support higher degree polynomials using the 3 point recursion
#formula:
xm1 = x - 1.
dPabdx_n = ( (self.alpha_poly + self.beta_poly + 3.) *
(self.alpha_poly + self.beta_poly + 4.)*xm1 +
2.*(self.alpha_poly + self.beta_poly + 3.) *
(self.alpha_poly + 2.) ) / 4.
dPabdx_nm1 = (self.alpha_poly + self.beta_poly + 2.)/2.;
for i in xrange( 2, degree ):
ab2i = self.alpha_poly + self.beta_poly + 2.*i
pab2i3 = pochhammer(ab2i, 3);
grad = ( ( (ab2i+1.)*(self.alpha_poly*self.alpha_poly-self.beta_poly*self.beta_poly) + x*pab2i3 ) * dPabdx_n + pab2i3*type1_value(x,i)- 2.*(i+self.alpha_poly)*(i+self.beta_poly)*(ab2i+2.)*dPabdx_nm1 ) / ( 2.*(i+1.)*(i+self.alpha_poly+self.beta_poly+1.)*ab2i );
if ( i != degree-1 ):
dPabdx_nm1 = dPabdx_n;
dPabdx_n = grad;
return grad
def value_set( self, x, degree, a = None, b = None ):
if ( ( a is not None ) and ( b is not None ) ):
x = ( 2. * x - b - a ) / ( b - a );
if ( degree == 0 ):
value = 1.;
elif ( degree == 1 ):
value = (self.alpha_poly + self.beta_poly + 2.)*(x-1.)/2. + \
self.alpha_poly + 1.;
elif ( degree == 2 ):
xm1 = x - 1.;
value = ( (self.alpha_poly + self.beta_poly + 3.) *
(self.alpha_poly + self.beta_poly + 4.)*xm1*xm1 +
4.*(self.alpha_poly + self.beta_poly + 3.) *
(self.alpha_poly + 2.)*xm1 +
4.*(self.alpha_poly + 1.)*(self.alpha_poly + 2.) ) / 8.;
else:
# Support higher degree polynomials using the 3 point recursion
# formula:
xm1 = x - 1.
Pab_n = ( (self.alpha_poly + self.beta_poly + 3.) *
(self.alpha_poly + self.beta_poly + 4.)*xm1*xm1
+ 4*(self.alpha_poly + self.beta_poly + 3.) *
(self.alpha_poly + 2.)*xm1
+ 4.*(self.alpha_poly + 1.)*(self.alpha_poly + 2.) ) / 8.
Pab_nm1 = (self.alpha_poly + self.beta_poly + 2.)*xm1/2. + \
self.alpha_poly + 1.;
for i in xrange( 2, degree ):
ab2i = self.alpha_poly + self.beta_poly + 2.*i;
value = ( ( (ab2i+1.)*(self.alpha_poly*self.alpha_poly-self.beta_poly*self.beta_poly) + x*pochhammer(ab2i,3) )*Pab_n - 2.*(i+self.alpha_poly)*(i+self.beta_poly)*(ab2i+2.)*Pab_nm1 ) / ( 2.*(i+1.)*(i+self.alpha_poly+self.beta_poly+1.)*ab2i );
if ( i != degree-1 ):
Pab_nm1 = Pab_n;
Pab_n = value;
return value;
