Created
February 19, 2021 20:30
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## 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])) |
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