import math


def _generate_cosine_lr(lr_init, lr_end, lr_max, total_steps, warmup_steps):
    """
    Applies cosine decay to generate learning rate array.

    Args:
       lr_init(float): init learning rate.
       lr_end(float): end learning rate
       lr_max(float): max learning rate.
       total_steps(int): all steps in training.
       warmup_steps(int): all steps in warmup epochs.

    Returns:
       np.array, learning rate array.
    """
    decay_steps = total_steps - warmup_steps
    lr_each_step = []
    for i in range(total_steps):
        if i < warmup_steps:
            lr_inc = (float(lr_max) - float(lr_init)) / float(warmup_steps)
            lr = float(lr_init) + lr_inc * (i + 1)
        else:
            linear_decay = (total_steps - i) / decay_steps
            cosine_decay = 0.5 * (1 + math.cos(math.pi * 2 * 0.47 * i / decay_steps))
            decayed = linear_decay * cosine_decay + 0.00001
            lr = lr_max * decayed
        lr_each_step.append(lr)
    return lr_each_step