def hadamard(n, dtype=int):
 if (n < 1):
  lg2 = 0
 else:
  lg2 = int(math.log(n, 2))
 if ((2 ** lg2) != n):
  raise ValueError('n must be an positive integer, and n must be a power of 2')
 H = np.array([[1]], dtype=dtype)
 for i in range(0, lg2):
  H = np.vstack((np.hstack((H, H)), np.hstack((H, (- H)))))
 return H

def hadamard ( n , dtype = int ) : if ( n < 1 ) : lg2 = 0 else : lg2 = int ( math . log ( n , 2 ) ) if ( ( 2 ** lg2 ) != n ) : raise ValueError ( 'n must be an positive integer, and n must be a power of 2' ) H = np . array ( [ [ 1 ] ] , dtype = dtype ) for i in range ( 0 , lg2 ) : H = np . vstack ( ( np . hstack ( ( H , H ) ) , np . hstack ( ( H , ( - H ) ) ) ) ) return H
construct a hadamard matrix .