import numpy as np

# Delete the ith row and jth column from x

# returns a copy of x with row,column deleted
def numpy_delete_ij(x, i, j):
    x = np.delete(x, i, axis=0)
    x = np.delete(x, j, axis=1)
    return x

# returns a view to x with row,column deleted
def my_delete1_ij(x, i, j):
    x[:,j:-1] = x[:,j+1:] 
    x[i:-1,:] = x[i+1:,:] 
    return x[:-1,:-1] 

# returns a view to x with row,column deleted
def my_delete2_ij(x, i, j):
    Nj,Ni = x.shape    
    if j>Nj/2:
        # move right half one step left
        cj = 0
        if j < Nj:
            x[:,j:-1] = x[:,j+1:] 
    else:
        # move left half one step right
        cj = 1
        if j > 0:
            x[:,1:j+1] = x[:,:j]
    if i>Ni/2:
        ci = 0
        # move lower half one step up
        if i < Ni:
            x[i:-1,:] = x[i+1:,:] 
    else:
        # move upper half one step down
        ci = 1
        if i > 0:
            x[1:i+1,:] = x[:i,:]
    # pick the correct corner of x and return the view
    if cj == 0 :
        if ci == 0:
            return x[:-1,:-1]  # up left 
        else:
            return x[1:,:-1]   # down left 
    else:
        if ci == 0:
            return x[:-1,1:]  # up right
        else:
            return x[1:,1:]  # down right