Ejemplo n.º 1
0
 def evaluate_at_box(self,k,coeff,n,l,nn,ll,x):
     if isinstance(x,list) or isinstance(x,Vector):
         value_list = []
         for i in range(len(x)):
             coordinate = (x[i]+ll)*(2.0**(n-nn))-l
             p = Vector(phi(coordinate,k))                                                                                                  
             value_list.append(coeff.inner(p)*math.sqrt(2.0**n))
         return Vector(value_list)
     else:
         coordinate = (x + ll)*(2.0**(n-nn))-l
         p = Vector(phi(coordinate,self.k))                                                                                                  
         value = coeff.inner(p)*math.sqrt(2.0**n)
         return value
Ejemplo n.º 2
0
 def evaluate_at_box(self, k, coeff, n, l, nn, ll, x):
     if isinstance(x, list) or isinstance(x, Vector):
         value_list = []
         for i in range(len(x)):
             coordinate = (x[i] + ll) * (2.0**(n - nn)) - l
             p = Vector(phi(coordinate, k))
             value_list.append(coeff.inner(p) * math.sqrt(2.0**n))
         return Vector(value_list)
     else:
         coordinate = (x + ll) * (2.0**(n - nn)) - l
         p = Vector(phi(coordinate, self.k))
         value = coeff.inner(p) * math.sqrt(2.0**n)
         return value
Ejemplo n.º 3
0
 def init_quadrature(self, order):
     x, w = gauss_legendre(order)
     self.quad_w = Vector(w)
     self.quad_x = Vector(x)
     self.quad_npt = npt = len(w)
     self.quad_phi = Matrix(npt, self.k)  # phi[point,i]
     self.quad_phiT = Matrix(self.k, npt)  # phi[point,i] transpose
     self.quad_phiw = Matrix(npt, self.k)  # phi[point,i]*weight[point]
     for i in xrange(npt):
         p = phi(self.quad_x[i], self.k)
         for m in xrange(self.k):
             self.quad_phi[i, m] = p[m]
             self.quad_phiT[m, i] = p[m]
             self.quad_phiw[i, m] = w[i] * p[m]
Ejemplo n.º 4
0
 def init_quadrature(self, order):
     x, w = gauss_legendre(order)
     self.quad_w = Vector(w)
     self.quad_x = Vector(x)
     self.quad_npt = npt = len(w)
     self.quad_phi  = Matrix(npt, self.k) # phi[point,i]
     self.quad_phiT = Matrix(self.k, npt) # phi[point,i] transpose
     self.quad_phiw = Matrix(npt, self.k) # phi[point,i]*weight[point]
     for i in xrange(npt):
         p = phi(self.quad_x[i], self.k)
         for m in xrange(self.k):
             self.quad_phi[i, m] = p[m]
             self.quad_phiT[m, i] = p[m]
             self.quad_phiw[i, m] = w[i] * p[m]
Ejemplo n.º 5
0
    def __evaluate(self, n, l, x):
        '''
        eval f(x) using adaptively refined numerical representation of f(x)
        answer should be within tolerance of the analytical f(x)

        Descend tree looking for box (n,l) with scaling function
        coefficients containing the point x.
        '''
        if self.s[n].has_key(l):
            p = Vector(phi(x, self.k))
            return self.s[n][l].inner(p) * math.sqrt(2.0**n)
        else:
            n, l, x = n + 1, 2 * l, 2 * x
            if x >= 1: l, x = l + 1, x - 1
            return self.__evaluate(n, l, x)
Ejemplo n.º 6
0
    def __evaluate(self, n, l, x):
        '''
        eval f(x) using adaptively refined numerical representation of f(x)
        answer should be within tolerance of the analytical f(x)

        Descend tree looking for box (n,l) with scaling function
        coefficients containing the point x.
        '''
        if self.s[n].has_key(l):
            p = Vector(phi(x, self.k))
            return self.s[n][l].inner(p)*math.sqrt(2.0**n)
        else:
            n, l, x = n + 1, 2 * l, 2 * x
            if x >= 1:  l, x = l + 1, x - 1
            return self.__evaluate(n, l, x)