"""Differentiable conditional logical likelihood through exact DEM elimination."""
import jax
import jax.numpy as jnp


def make_loss_and_grad(width):
    indices=jnp.arange(1<<width,dtype=jnp.int32)
    @jax.jit
    def evaluate(dets,labels,probabilities,masks,measured):
        # Per-shot error probabilities have shape [operations,batch].
        f=jnp.zeros((len(dets),1<<width),jnp.float32).at[:,0].set(1)
        def forward(f,args):
            p,mask,d=args
            def error(f):
                return (1-p[:,None])*f+p[:,None]*f[:,indices^mask],jnp.ones(len(dets))
            def project(f):
                dst=(indices[None,:]&~mask)|(dets[:,d,None].astype(jnp.int32)*mask)
                g=jnp.take_along_axis(f,dst,axis=1)*((indices&mask)==0)
                norm=jnp.maximum(g.sum(axis=1),1e-30)
                return g/norm[:,None],norm
            out,norm=jax.lax.cond(d<0,error,project,f)
            return out,(f,norm)
        f,(history,norms)=jax.lax.scan(forward,f,(probabilities,masks,measured))
        indicator=((indices[None,:]&1)==labels[:,None])
        correct=jnp.maximum(jnp.sum(f*indicator,axis=1),1e-10)
        predicted=jnp.sum(f[:,1::2],axis=1)
        initial=1-indicator/correct[:,None]
        def backward(b,args):
            p,mask,d,old,norm=args
            def error(b):
                flipped=b[:,indices^mask]
                grad=jnp.sum(old*(flipped-b),axis=1)
                return (1-p[:,None])*b+p[:,None]*flipped,grad
            def project(b):
                obs=((indices[None,:]&mask)==dets[:,d,None].astype(jnp.int32)*mask)
                values=b[:,indices&~mask]
                mean=jnp.sum(old*obs*values,axis=1)/norm
                prior=(values-mean[:,None])*obs/norm[:,None]
                return prior,jnp.zeros(len(dets))
            return jax.lax.cond(d<0,error,project,b)
        _,grad=jax.lax.scan(backward,initial,(probabilities,masks,measured,history,norms),reverse=True)
        return -jnp.log(correct),predicted,grad
    return evaluate