def __mul__(self,g): '''inner product of two basis functions''' # calculate the inner product. assert (g.base == 'scale' or g.base=='wavelet'), 'inner product error' if ((g.base is 'scale' and self.j>=g.j) or (g.base is 'wavelet' and self.j<>g.j)):temp_mul=0; return temp_mul elif max((self.Supp()[0],g.Supp()[0])) >= min((self.Supp()[1],g.Supp()[1])):temp_mul=0; return temp_mul else: j_max=np.max((self.j,g.j)) j_min=np.min((self.j,g.j)) if j_min==self.j:k_max=self.k;k_min=g.k else: k_min=self.k;k_max=g.k self_temp=TransformCoefficients['TQ'+str(j_max+1-self.j)] g_temp= TransformCoefficients['T'+g.name+str(j_max+1-g.j)] temp_len_min=np.min((self_temp.shape[1],g_temp.shape[1])) temp_len_max=np.max((self_temp.shape[1],g_temp.shape[1])) if temp_len_min==self_temp.shape[1]:Matrix_In=self_temp;Matrix_out=g_temp else:Matrix_In=g_temp;Matrix_out=self_temp Incoefs_temp=np.zeros((temp_len_min+temp_len_max-1,temp_len_max)) for n in range(temp_len_max): m=0 for i in range(n,n+temp_len_min): Incoefs_temp[i,n]=Matrix_In[0,m] m+=1 Incoefs=np.dot(Incoefs_temp,Matrix_out.T) #Calculate inner product start=5-Matrix_In.shape[1] stop=4+Matrix_out.shape[1] temp_mul=0 b8=spline.spline8(0,0) for i in range(start,stop): temp_mul+=Incoefs[i-start]*b8(i+(2**(j_max+1-j_min))*(k_max)-2*k_min) return float(temp_mul*(1./(2**(j_max+1)))*(2**(self.j/2.))*(2**(g.j/2.)))
def __call__(self,s): #This is to find maximum resolution. j_max=np.max((self.j1,self.j2)) #This is to find minimum resolution. j_min=np.min((self.j1,self.j2)) if j_min==self.j1:k_max=self.k1;k_min=self.k2 else: k_min=self.k1;k_max=self.k2 temp_1=TransformCoefficients['T'+self.name1+str(j_max+1-self.j1)] temp_2=TransformCoefficients['T'+self.name2+str(j_max+1-self.j2)] temp_len_min=np.min((temp_1.shape[1],temp_2.shape[1])) temp_len_max=np.max((temp_1.shape[1],temp_2.shape[1])) if temp_len_min==temp_1.shape[1]:Matrix_In=temp_1;Matrix_out=temp_2 else:Matrix_In=temp_2;Matrix_out=temp_1 Concoefs_temp=np.zeros((temp_len_min+temp_len_max-1,temp_len_max)) for n in range(temp_len_max): m=0 for i in range(n,n+temp_len_min): Concoefs_temp[i,n]=Matrix_In[0,m] m+=1 Concoefs=np.dot(Concoefs_temp,Matrix_out.T) weights=Concoefs l=(2**(j_max+1-j_min))*(k_max)+2*k_min f=[spline.spline8(j_max+1,j+l) for j in range(weights.shape[0])] k=IDEComponents.spline8(1,f,weights) return (1./2**(j_max+1))*k(s)*(2**(self.j1/2.))*(2**(self.j2/2.))
