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#include "cnf.h"
#include <stdlib.h>
/* Compute tr(df/dz) via central finite differences.
* Uses z_p (D) as scratch; writes intermediate outputs to f_p and f_m (D). */
static double compute_trace_fd(const DynMLP *net, const double *theta,
const double *z, double t, Workspace *ws,
double eps, double *z_p, double *f_p, double *f_m) {
int D = net->D;
double tr = 0.0;
for (int i = 0; i < D; i++) {
vec_copy(z, z_p, D);
z_p[i] += eps;
dynmlp_forward(net, theta, z_p, t, f_p, ws);
z_p[i] = z[i] - eps;
dynmlp_forward(net, theta, z_p, t, f_m, ws);
tr += (f_p[i] - f_m[i]) / (2.0 * eps);
}
return tr;
}
/* ---- Forward augmented ODE ---- */
typedef struct {
DynMLP net;
const double *theta;
int D;
Workspace *ws;
double eps;
double *z_p, *f_p, *f_m; /* D */
} CNFFwdCtx;
static void cnf_fwd_rhs(const double *aug, double t, const double *params,
int aug_dim, double *out, void *ctx) {
(void)params; (void)aug_dim;
CNFFwdCtx *c = (CNFFwdCtx *)ctx;
int D = c->D;
dynmlp_forward(&c->net, c->theta, aug, t, out, c->ws);
out[D] = -compute_trace_fd(&c->net, c->theta, aug, t, c->ws,
c->eps, c->z_p, c->f_p, c->f_m);
}
/* aug_state = [z(D), a_z(D), g(nparams)]
* a_logp (= dL/d(logdet)) is a constant stored in ctx since d(logdet)/dt
* does not depend on logdet itself. */
typedef struct {
DynMLP net;
const double *theta;
int D;
int nparams;
Workspace *ws;
double eps;
double a_logp;
/* scratch buffers */
double *z_oj; /* D: outer perturbation (trace grad z & theta) */
double *z_p2, *f_p2, *f_m2; /* D: inner scratch for nested compute_trace_fd */
double *neg_a_z; /* D */
double *dg_tmp; /* nparams */
double *da_z_tmp; /* D (vjp_z scratch, not used as output) */
double *v_ei; /* D: one-hot for trace grad theta */
double *vjp_z_tmp; /* D */
double *vjp_th_p; /* nparams */
double *vjp_th_m; /* nparams */
} CNFAdjCtx;
static void cnf_adj_rhs(const double *aug, double t, const double *params,
int aug_dim, double *out, void *ctx) {
(void)params; (void)aug_dim;
CNFAdjCtx *cc = (CNFAdjCtx *)ctx;
int D = cc->D;
int nparams = cc->nparams;
const double *z = aug;
const double *a_z = aug + D;
dynmlp_forward(&cc->net, cc->theta, z, t, out, cc->ws);
for (int i = 0; i < D; i++) cc->neg_a_z[i] = -a_z[i];
vec_zero(cc->dg_tmp, nparams);
dynmlp_vjp(&cc->net, cc->theta, z, t, cc->neg_a_z,
out + D, cc->dg_tmp, cc->ws);
vec_copy(cc->dg_tmp, out + 2 * D, nparams);
if (cc->a_logp == 0.0) return; /* no trace gradient terms needed */
for (int j = 0; j < D; j++) {
vec_copy(z, cc->z_oj, D);
cc->z_oj[j] += cc->eps;
double tr_p = compute_trace_fd(&cc->net, cc->theta, cc->z_oj, t, cc->ws,
cc->eps, cc->z_p2, cc->f_p2, cc->f_m2);
cc->z_oj[j] = z[j] - cc->eps;
double tr_m = compute_trace_fd(&cc->net, cc->theta, cc->z_oj, t, cc->ws,
cc->eps, cc->z_p2, cc->f_p2, cc->f_m2);
out[D + j] += cc->a_logp * (tr_p - tr_m) / (2.0 * cc->eps);
}
vec_zero(cc->v_ei, D);
for (int i = 0; i < D; i++) {
cc->v_ei[i] = 1.0;
vec_copy(z, cc->z_oj, D);
cc->z_oj[i] += cc->eps;
vec_zero(cc->vjp_th_p, nparams);
dynmlp_vjp(&cc->net, cc->theta, cc->z_oj, t, cc->v_ei,
cc->vjp_z_tmp, cc->vjp_th_p, cc->ws);
cc->z_oj[i] = z[i] - cc->eps;
vec_zero(cc->vjp_th_m, nparams);
dynmlp_vjp(&cc->net, cc->theta, cc->z_oj, t, cc->v_ei,
cc->vjp_z_tmp, cc->vjp_th_m, cc->ws);
cc->v_ei[i] = 0.0;
double scale = cc->a_logp / (2.0 * cc->eps);
for (int k = 0; k < nparams; k++)
out[2 * D + k] += scale * (cc->vjp_th_p[k] - cc->vjp_th_m[k]);
}
}
/* ---- Public API ---- */
void cnf_init(CNF *cnf, int D, int H, double *theta, RNG *r) {
dynmlp_init(&cnf->net, D, H, theta, r);
cnf->nparams = dynmlp_nparams(D, H);
cnf->trace_eps = 1e-5;
}
CNFSampleResult cnf_sample(const CNF *cnf, const double *theta,
const double *z0, double t0, double t1,
double atol, double rtol) {
int D = cnf->net.D;
Workspace ws = workspace_alloc(D, cnf->net.H, cnf->nparams);
double *z_p = vec_alloc(D), *f_p = vec_alloc(D), *f_m = vec_alloc(D);
CNFFwdCtx ctx = { cnf->net, theta, D, &ws, cnf->trace_eps, z_p, f_p, f_m };
double *aug0 = vec_zeros(D + 1);
vec_copy(z0, aug0, D);
ODEResult res = ode_solve(cnf_fwd_rhs, aug0, t0, t1,
NULL, D + 1, atol, rtol, &ctx);
free(aug0);
free(z_p); free(f_p); free(f_m);
workspace_free(&ws);
CNFSampleResult out;
out.z1 = vec_alloc(D);
vec_copy(res.y, out.z1, D);
out.delta_logp = res.y[D];
out.nfe = res.nfe;
free(res.y);
return out;
}
CNFLogProbResult cnf_log_prob(const CNF *cnf, const double *theta,
const double *z1, double t0, double t1,
double atol, double rtol) {
int D = cnf->net.D;
Workspace ws = workspace_alloc(D, cnf->net.H, cnf->nparams);
double *z_p = vec_alloc(D), *f_p = vec_alloc(D), *f_m = vec_alloc(D);
CNFFwdCtx ctx = { cnf->net, theta, D, &ws, cnf->trace_eps, z_p, f_p, f_m };
double *aug1 = vec_zeros(D + 1);
vec_copy(z1, aug1, D);
ODEResult res = ode_solve(cnf_fwd_rhs, aug1, t1, t0,
NULL, D + 1, atol, rtol, &ctx);
free(aug1);
free(z_p); free(f_p); free(f_m);
workspace_free(&ws);
/* Backward integral gives ∫_{t1}^{t0} -tr dt = -delta_logp_fwd,
* so delta_logp = log p(z1) - log p(z0) = -res.y[D]. */
CNFLogProbResult out;
out.z0 = vec_alloc(D);
vec_copy(res.y, out.z0, D);
out.delta_logp = -res.y[D];
out.nfe = res.nfe;
free(res.y);
return out;
}
CNFBackwardResult cnf_backward(const CNF *cnf, const double *theta,
const double *z1,
double dL_dlogp, const double *dL_dz1_in,
double t0, double t1,
double atol, double rtol) {
int D = cnf->net.D;
int nparams = cnf->nparams;
int aug_dim = 2 * D + nparams;
Workspace ws = workspace_alloc(D, cnf->net.H, nparams);
CNFAdjCtx ctx;
ctx.net = cnf->net;
ctx.theta = theta;
ctx.D = D;
ctx.nparams = nparams;
ctx.ws = &ws;
ctx.eps = cnf->trace_eps;
ctx.a_logp = dL_dlogp;
ctx.z_oj = vec_alloc(D);
ctx.z_p2 = vec_alloc(D);
ctx.f_p2 = vec_alloc(D);
ctx.f_m2 = vec_alloc(D);
ctx.neg_a_z = vec_alloc(D);
ctx.dg_tmp = vec_alloc(nparams);
ctx.da_z_tmp = vec_alloc(D);
ctx.v_ei = vec_zeros(D);
ctx.vjp_z_tmp = vec_alloc(D);
ctx.vjp_th_p = vec_alloc(nparams);
ctx.vjp_th_m = vec_alloc(nparams);
double *aug = vec_zeros(aug_dim);
vec_copy(z1, aug, D);
vec_copy(dL_dz1_in, aug + D, D);
ODEResult res = ode_solve(cnf_adj_rhs, aug, t1, t0,
NULL, aug_dim, atol, rtol, &ctx);
free(aug);
CNFBackwardResult out;
out.dL_dz0 = vec_alloc(D);
out.dL_dtheta = vec_alloc(nparams);
vec_copy(res.y + D, out.dL_dz0, D);
vec_copy(res.y + 2 * D, out.dL_dtheta, nparams);
out.nfe = res.nfe;
free(res.y);
free(ctx.z_oj); free(ctx.z_p2); free(ctx.f_p2); free(ctx.f_m2);
free(ctx.neg_a_z); free(ctx.dg_tmp); free(ctx.da_z_tmp);
free(ctx.v_ei); free(ctx.vjp_z_tmp); free(ctx.vjp_th_p); free(ctx.vjp_th_m);
workspace_free(&ws);
return out;
}
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