import torch


def sequence_loss(flow_preds, flow_gt, valid, gamma=0.8, max_flow=400):
    """Loss function defined over sequence of flow predictions, from RAFT."""

    n_predictions = len(flow_preds)
    flow_loss = 0.0

    # exlude invalid pixels and extremely large diplacements
    mag = torch.sum(flow_gt**2, dim=1).sqrt()
    valid = (valid >= 0.5) & (mag < max_flow)

    for i in range(n_predictions):
        i_weight = gamma**(n_predictions - i - 1)
        i_loss = (flow_preds[i] - flow_gt).abs()
        flow_loss += i_weight * (valid[:, None] * i_loss).mean()

    epe = torch.sum((flow_preds[-1] - flow_gt)**2, dim=1).sqrt()
    epe = epe.view(-1)[valid.view(-1)]

    metrics = {
        'epe': epe.mean().item(),
        '1px': (epe < 1).float().mean().item(),
        '3px': (epe < 3).float().mean().item(),
        '5px': (epe < 5).float().mean().item(),
    }

    return flow_loss, metrics