import numpy as np

#functions
#sigmoid
def  sigmoid(x):
    return 1 / (1 + np.exp(-x) )

#Relu
def relu(x):
    return np.maximum(0, x)


#softmax
def softmax(x):
    if x.ndim == 2:
        x = x.T
        x = x - np.max(x, axis=0)
        y = np.exp(x) / np.sum(np.exp(x), axis=0)
        return y.T
    x = x -np.max(x, axis=0)
    return np.exp(x) / np.sum(np.exp(x), axis=0)

def cross_entropy_error(y, t):
    if y.ndim == 1:
        t = t.reshape(1, t.size)
        y = y.reshape(1, y.size)

    if t.size == y.size:
        t = t.argmax(axis=1)

    batch_size = y.shape[0]
    return -np.sum(np.log(y[np.arange(batch_size), t] + 1e-7)) / batch_size


def softmax_loss(X, t):
    y = softmax(X)
    return cross_entropy_error(y, t)
