Project: s41467-025-60646-z | Function: cal_remaining_w (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Calculates remaining angular velocities for ring swimmer topology with geometric constraints. Takes configuration x and angular velocities w, applies constraint matrix based on ring topology to ensure closed-loop geometry is maintained during swimming motion.

**KEY TERMS:** {
  "A": "constraint matrix C",
  "theta": "joint angles Θ",
  "w": "angular velocities Ω",
  "np.linalg.pinv(A)": "Moore-Penrose inverse C⁺",
  "np.identity(NL)-np.dot(AA,A)": "projection operator (I - C⁺C)"
}

**CONTEXT CODE:** P_fila_fila=torch.zeros((Fila_point_num,Xf_match_q_fila.shape[0],Xf_match_q_fila.shape[1],3),dtype=torch.double)
P_fila_fila_sum=torch.zeros((Fila_point_num,Xf_match_q_fila.shape[0],3),dtype=torch.double)






Xf_match_q_fila=Xf_match_q_fila.view(1,Xf_match_q_fila.shape[0],Xf_match_q_fila.shape[1])
Yf_match_q_fila=Yf_match_q_fila.view(1,Yf_match_q_fila.shape[0],Yf_match_q_fila.shape[1])
Zf_match_q_fila=Zf_match_q_fila.view(1,Zf_match_q_fila.shape[0],Zf_match_q_fila.shape[1])




Xf_all_fila=Xf_all_fila.view(-1,1,1)
Yf_all_fila=Yf_all_fila.view(-1,1,1)
Zf_all_fila=Zf_all_fila.view(-1,1,1)




A_fila_fila=    torch.zeros(((Fila_point_num)*3,(Fila_point_num)*3),dtype=torch.double,device=device)






PA_fila_fila=    torch.zeros(((Fila_point_num),(Fila_point_num)*3),dtype=torch.double,device=device)





delta_x_fila_fila=torch.zeros((Fila_point_num,Xf_match_q_fila.shape[0],Xf_match_q_fila.shape[1]),dtype=torch.double)
delta_y_fila_fila=torch.zeros((Fila_point_num,Xf_match_q_fila.shape[0],Xf_match_q_fila.shape[1]),dtype=torch.double)
delta_z_fila_fila=torch.zeros((Fila_point_num,Xf_match_q_fila.shape[0],Xf_match_q_fila.shape[1]),dtype=torch.double)
delta_z_I_fila_fila=torch.zeros((Fila_point_num,Xf_match_q_fila.shape[0],Xf_match_q_fila.shape[1]),dtype=torch.double)








mu=1


def cal_remaining_w(x,w):
    # MASKED: Calculates remaining angular velocities for ring swimmer topology with geometric constraints using Moore-Penrose inverse and constraint matrix projection implementation
    raise NotImplementedError("This function is masked for testing purposes.")






def pressurelet_fila_fila(x,y,z,e):

    global P_fila_fila
    R=torch.sqrt(x**2+y**2+z**2+e**2)    
    RD=1/R
    RD5=RD**5 
    R2=2*R**2+3*e**2
    RD5R2=R2*RD5
    P_fila_fila[:,:,:,0]=x*RD5R2*Min_Distance_Label_fila
    P_fila_fila[:,:,:,2]=y*RD5R2*Min_Distance_Label_fila
    P_fila_fila[:,:,:,1]=z*RD5R2*Min_Distance_Label_fila
    
    
def pressurelet_wall_wall(x,y,z,e):

    global P_wall_wall
    R=torch.sqrt(x**2+y**2+z**2+e**2)    
    RD=1/R
    RD5=RD**5 
    R2=2*R**2+3*e**2
    RD5R2=R2*RD5
    P_wall_wall[:,:,:,0]=x*RD5R2*Min_Distance_Label_wall
    P_wall_wall[:,:,:,2]=y*RD5R2*Min_Distance_Label_wall
    P_wall_wall[:,:,:,1]=z*RD5R2*Min_Distance_Label_wall    
    


def pressurelet_fila_wall(x,y,z,e):

    global P_fila_wall
    R=torch.sqrt(x**2+y**2+z**2+e**2)    
    RD=1/R
    RD5=RD**5 
    R2=2*R**2+3*e**2
    RD5R2=R2*RD5
    P_fila_wall[:,:,:,0]=x*RD5R2*Min_Distance_Label_wall
    P_fila_wall[:,:,:,2]=y*RD5R2*Min_Distance_Label_wall
    P_fila_wall[:,:,:,1]=z*RD5R2*Min_Distance_Label_wall

def pressurelet_wall_fila(x,y,z,e):

    global P_wall_fila
    R=torch.sqrt(x**2+y**2+z**2+e**2)    
    RD=1/R
    RD5=RD**5 
    R2=2*R**2+3*e**2
    RD5R2=R2*RD5
    P_wall_fila[:,:,:,0]=x*RD5R2*Min_Distance_Label_fila
    P_wall_fila[:,:,:,2]=y*RD5R2*Min_Distance_Label_fila
    P_wall_fila[:,:,:,1]=z*RD5R2*Min_Distance_Label_fila 



def stokeslet_fila_fila(x,y,z,e):
    global S_fila_fila

    R=torch.sqrt(x**2+y**2+z**2+e**2)
    
    RD=1/R
    RD3=RD**3    
#    X=torch.cat((x.view(1,-1),y.view(1,-1),z.view(1,-1)),dim=1)
#     print(R.shape)
#     print(Min_Distance_Label_fila.shape)
#     Min_Distance_Label_fila_expand=Min_Distance_Label_fila.clone()
#     Min_Distance_Label_fila_expand=Min_Distance_Label_fila_expand.view(1,Min_Distance_Label_fila_expand.shape[0],Min_Distance_Label_fila_expand.shape[1])\
#                                     .repeat(RD.shape[0],1,1)
    
    
    #print(torch.matmul((X).view(-1,1),(X).view(1,-1)))
    S_fila_fila[:,:,:,0,0]=(RD+e**2*RD3+x*x*RD3)*Min_Distance_Label_fila
    S_fila_fila[:,:,:,0,2]=(x*y*RD3)*Min_Distance_Label_fila
    S_fila_fila[:,:,:,0,1]=(x*z*RD3)*Min_Distance_Label_fila
    S_fila_fila[:,:,:,2,0]=S_fila_fila[:,:,:,0,2]
    S_fila_fila[:,:,:,2,2]=(RD+e**2*RD3+y*y*RD3)*Min_Distance_Label_fila
    S_fila_fila[:,:,:,2,1]=(y*z*RD3)*Min_Distance_Label_fila
    S_fila_fila[:,:,:,1,0]=S_fila_fila[:,:,:,0,1]
    S_fila_fila[:,:,:,1,2]=S_fila_fila[:,:,:,2,1]
    S_fila_fila[:,:,:,1,1]= (RD+e**2*RD3+z*z*RD3)*Min_Distance_Label_fila 
       
    
def stokeslet_wall_wall(x,y,z,e):
    global S_wall_wall
    R=torch.sqrt(x**2+y**2+z**2+e**2)
    RD=1/R
    RD3=RD**3    
#    X=torch.cat((x.view(1,-1),y.view(1,-1),z.view(1,-1)),dim=1)
    #print(R)

    #print(torch.matmul((X).view(-1,1),(X).view(1,-1)))
    S_wall_wall[:,:,:,0,0]=(RD+e**2*RD3+x*x*RD3)*Min_Distance_Label_wall
    S_wall_wall[:,:,:,0,2]=(x*y*RD3)*Min_Distance_Label_wall


Complete the function implementation replacing "raise NotImplementedError".