tensor_expend.py

## approach-1
#--------------------------------------------------------------------#
def taylor_func(x, func_type='sin(x)', n_terms=2):
    
    # f(a) + 0.5 * f`(a)(x - a) + f``(a)(x - a)^2
    if func_type == 'sin(x)':
        
        c = tf.constant([1, -1/6, 1/120, -1/5040], dtype=tf.float32)
        p = tf.constant([1,3,5,7], dtype=tf.float32)

    if func_type == 'ln(1+x)':
        
        c = tf.constant([1, -1/2, 1/3, -1/4, 1/5, -1/6], dtype=tf.float32)
        p = tf.constant([1,2,3,4,5,6], dtype=tf.float32)

    new_x = [x] + [i * tf.math.pow(x, j) for i, j in zip(c, p)]
    new_x = tf.stack(new_x, axis=-1)

    return new_x

#--------------------------------------------------------------------#
## aproach-2
def taylor_expend(x):
  c = tf.constant([1, -1/6, 1/120, -1/5040], dtype=tf.float32)
  p = tf.constant([1, 3, 5, 7], dtype=tf.float32)
  exp = []
  def loop(i):
    if i > 3:
      return
    pp = tf.gather(p, i)
    cc = tf.gather(c, i)
    t = (x ** pp) * cc
    exp.append(t)
    loop(i + 1)
  loop(0)
  exp = tf.stack(exp, axis=-1)
  return exp

#--------------------------------------------------------------------#
## aproach-3

inputs = tf.keras.Input(shape=(32,32,3))

conv_1 = Conv2D(64, (3, 3), input_shape=(32,32,3), padding='same')(inputs)
BN_1 = BatchNormalization(axis=-1)(conv_1)
pool_1 = MaxPooling2D(strides=(1,1), pool_size=(3,3), padding='same')(BN_1)
PEN_1 = taylor_func(pool_1, func_type="sin(x)", n_terms=2)
PEN_1 = tf.stack([pool_1, - (1/6) * tf.math.pow(pool_1, 3), (1/120) * tf.math.pow(pool_1, 5)], axis=1) ## 3 expansion terms of sin(x)
PEN_1 =tf.reshape(PEN_1, (-1, PEN_1.shape[2], PEN_1.shape[2], PEN_1.shape[1]*PEN_1.shape[-1]))