aboutsummaryrefslogtreecommitdiff
path: root/src
diff options
context:
space:
mode:
Diffstat (limited to 'src')
-rw-r--r--src/adam.c35
-rw-r--r--src/adjoint.c255
-rw-r--r--src/dynmlp.c94
-rw-r--r--src/main.c105
-rw-r--r--src/ode_solver.c137
-rw-r--r--src/spiral.c73
-rw-r--r--src/tests.c345
-rw-r--r--src/train.c47
-rw-r--r--src/utils.c106
9 files changed, 1197 insertions, 0 deletions
diff --git a/src/adam.c b/src/adam.c
new file mode 100644
index 0000000..2d37bab
--- /dev/null
+++ b/src/adam.c
@@ -0,0 +1,35 @@
+#include "adam.h"
+#include "utils.h"
+
+#include <math.h>
+#include <stdlib.h>
+
+Adam adam_init(int nparams, double lr, double beta1, double beta2, double eps) {
+ Adam a;
+ a.m = vec_zeros(nparams);
+ a.v = vec_zeros(nparams);
+ a.nparams = nparams;
+ a.lr = lr;
+ a.beta1 = beta1;
+ a.beta2 = beta2;
+ a.eps = eps;
+ a.t = 0;
+ return a;
+}
+
+void adam_update(Adam *a, double *theta, const double *grad) {
+ a->t++;
+ double bc1 = 1.0 - pow(a->beta1, (double)a->t);
+ double bc2 = 1.0 - pow(a->beta2, (double)a->t);
+ double alpha = a->lr * sqrt(bc2) / bc1;
+ for (int i = 0; i < a->nparams; i++) {
+ a->m[i] = a->beta1 * a->m[i] + (1.0 - a->beta1) * grad[i];
+ a->v[i] = a->beta2 * a->v[i] + (1.0 - a->beta2) * grad[i] * grad[i];
+ theta[i] -= alpha * a->m[i] / (sqrt(a->v[i]) + a->eps);
+ }
+}
+
+void adam_free(Adam *a) {
+ free(a->m);
+ free(a->v);
+}
diff --git a/src/adjoint.c b/src/adjoint.c
new file mode 100644
index 0000000..df62927
--- /dev/null
+++ b/src/adjoint.c
@@ -0,0 +1,255 @@
+#include "adjoint.h"
+
+#include <stdlib.h>
+
+typedef struct {
+ double *dL_dz0;
+ double *dL_dtheta;
+ int nfe;
+} AdjointResult;
+
+typedef struct {
+ int num_checkpoints;
+ double *times;
+ double **states;
+ double *z1;
+ int nfe;
+} ForwardResult;
+
+typedef struct {
+ double *dL_dz0;
+ double *dL_dtheta;
+ int nfe;
+} MultiObsAdjointResult;
+
+void neural_ode_rhs(const double *state, double t, const double *params,
+ int dim, double *out, void *ctx) {
+ (void)params;
+ (void)dim;
+
+ AdjointCtx *ac = (AdjointCtx *)ctx;
+ dynmlp_forward(&ac->net, ac->theta, state, t, out, ac->ws);
+}
+
+static void adjoint_dynamics(const double *aug_state, double t, const double *params,
+ int aug_dim, double *aug_out, void *ctx) {
+ (void)params;
+ (void)aug_dim;
+
+ AdjointCtx *ac = (AdjointCtx *)ctx;
+ int D = ac->state_dim;
+ int nparams = ac->nparams;
+ const double *z = aug_state;
+ const double *a = aug_state + D;
+
+ dynmlp_forward(&ac->net, ac->theta, z, t, aug_out, ac->ws);
+
+ double *neg_a = ac->ws->neg_a;
+ double *vjp_z = ac->ws->vjp_z;
+ double *vjp_theta = ac->ws->vjp_theta;
+ vec_zero(vjp_theta, nparams);
+ for (int i = 0; i < D; i++) neg_a[i] = -a[i];
+
+ dynmlp_vjp(&ac->net, ac->theta, z, t, neg_a, vjp_z, vjp_theta, ac->ws);
+
+ vec_copy(vjp_z, aug_out + D, D);
+ vec_copy(vjp_theta, aug_out + 2 * D, nparams);
+}
+
+static void forward_result_free(ForwardResult *fr) {
+ free(fr->times);
+ for (int i = 0; i <= fr->num_checkpoints; i++)
+ free(fr->states[i]);
+ free(fr->states);
+ free(fr->z1);
+}
+
+static ForwardResult forward_solve(const DynMLP *net, const double *theta,
+ const double *z0, double t0, double t1,
+ double atol, double rtol, int num_checkpoints) {
+ int D = net->D;
+ Workspace ws = workspace_alloc(D, net->H, net->nparams);
+ AdjointCtx ac = { *net, theta, D, net->nparams, &ws };
+
+ ForwardResult fr;
+ fr.num_checkpoints = num_checkpoints;
+ fr.nfe = 0;
+
+ fr.times = vec_alloc(num_checkpoints + 1);
+ fr.states = (double **)xmalloc((size_t)(num_checkpoints + 1) * sizeof(double *));
+ for (int i = 0; i <= num_checkpoints; i++)
+ fr.states[i] = vec_alloc(D);
+
+ for (int i = 0; i <= num_checkpoints; i++)
+ fr.times[i] = t0 + (t1 - t0) * (double)i / (double)num_checkpoints;
+
+ vec_copy(z0, fr.states[0], D);
+
+ for (int i = 0; i < num_checkpoints; i++) {
+ ODEResult seg = ode_solve(neural_ode_rhs, fr.states[i],
+ fr.times[i], fr.times[i + 1],
+ NULL, D, atol, rtol, &ac);
+ vec_copy(seg.y, fr.states[i + 1], D);
+ fr.nfe += seg.nfe;
+ free(seg.y);
+ }
+
+ fr.z1 = vec_alloc(D);
+ vec_copy(fr.states[num_checkpoints], fr.z1, D);
+
+ workspace_free(&ws);
+ return fr;
+}
+
+static AdjointResult adjoint_solve(const DynMLP *net, const double *theta,
+ const ForwardResult *fr, const double *dL_dz1,
+ double atol, double rtol) {
+ int D = net->D;
+ int nparams = net->nparams;
+ int aug_dim = 2 * D + nparams;
+
+ double *aug = vec_zeros(aug_dim);
+ vec_copy(fr->z1, aug, D);
+ vec_copy(dL_dz1, aug + D, D);
+
+ Workspace ws = workspace_alloc(D, net->H, nparams);
+ AdjointCtx ac = { *net, theta, D, nparams, &ws };
+ int total_nfe = 0;
+
+ for (int k = fr->num_checkpoints; k >= 1; k--) {
+ /* Replace z with stored checkpoint to prevent numerical drift */
+ vec_copy(fr->states[k], aug, D);
+
+ ODEResult seg = ode_solve(adjoint_dynamics, aug,
+ fr->times[k], fr->times[k - 1],
+ NULL, aug_dim, atol, rtol, &ac);
+ vec_copy(seg.y, aug, aug_dim);
+ total_nfe += seg.nfe;
+ free(seg.y);
+ }
+
+ AdjointResult ar;
+ ar.dL_dz0 = vec_alloc(D);
+ ar.dL_dtheta = vec_alloc(nparams);
+ ar.nfe = total_nfe;
+ vec_copy(aug + D, ar.dL_dz0, D);
+ vec_copy(aug + 2 * D, ar.dL_dtheta, nparams);
+
+ workspace_free(&ws);
+ free(aug);
+ return ar;
+}
+
+NeuralODEOutput neural_ode_forward_backward(const DynMLP *net, const double *theta,
+ const double *z0, double t0, double t1,
+ const double *target, double atol, double rtol,
+ int num_checkpoints) {
+ int D = net->D;
+
+ ForwardResult fr = forward_solve(net, theta, z0, t0, t1, atol, rtol, num_checkpoints);
+
+ double *dL_dz1 = vec_alloc(D);
+ for (int i = 0; i < D; i++) dL_dz1[i] = fr.z1[i] - target[i];
+
+ AdjointResult ar = adjoint_solve(net, theta, &fr, dL_dz1, atol, rtol);
+
+ NeuralODEOutput out;
+ out.z1 = vec_alloc(D);
+ vec_copy(fr.z1, out.z1, D);
+ out.dL_dz0 = ar.dL_dz0;
+ out.dL_dtheta = ar.dL_dtheta;
+ out.nfe_forward = fr.nfe;
+ out.nfe_backward = ar.nfe;
+
+ forward_result_free(&fr);
+ free(dL_dz1);
+ return out;
+}
+
+static MultiObsAdjointResult adjoint_solve_multi(
+ const DynMLP *net,
+ const double *theta,
+ const double *z_traj,
+ const double *times,
+ const double *dL_dz_each,
+ int ntimes,
+ double atol,
+ double rtol)
+{
+ int D = net->D;
+ int nparams = net->nparams;
+ int aug_dim = 2 * D + nparams;
+
+ Workspace ws = workspace_alloc(D, net->H, nparams);
+ AdjointCtx ac = { *net, theta, D, nparams, &ws };
+
+ double *a = vec_alloc(D);
+ double *dtheta = vec_zeros(nparams);
+ double *aug = vec_alloc(aug_dim);
+ int total_nfe = 0;
+
+ vec_copy(dL_dz_each + (ntimes - 1) * D, a, D);
+
+ for (int i = ntimes - 1; i >= 1; i--) {
+ vec_copy(z_traj + i * D, aug, D);
+ vec_copy(a, aug + D, D);
+ vec_copy(dtheta, aug + 2 * D, nparams);
+
+ ODEResult seg = ode_solve(adjoint_dynamics, aug,
+ times[i], times[i - 1],
+ NULL, aug_dim, atol, rtol, &ac);
+ vec_copy(seg.y, aug, aug_dim);
+ total_nfe += seg.nfe;
+ free(seg.y);
+
+ vec_copy(aug + D, a, D);
+ vec_copy(aug + 2 * D, dtheta, nparams);
+
+ /* Kick: add per-observation loss gradient at time t_{i-1} */
+ vec_add_scaled(a, 1.0, dL_dz_each + (i - 1) * D, D);
+ }
+
+ MultiObsAdjointResult result;
+ result.dL_dz0 = a;
+ result.dL_dtheta = dtheta;
+ result.nfe = total_nfe;
+
+ workspace_free(&ws);
+ free(aug);
+ return result;
+}
+
+MultiObsNeuralODEOutput neural_ode_forward_backward_multi(
+ const DynMLP *net,
+ const double *theta,
+ const double *z0,
+ const double *times,
+ const double *targets,
+ int ntimes,
+ double atol,
+ double rtol)
+{
+ int D = net->D;
+ Workspace ws = workspace_alloc(D, net->H, net->nparams);
+ AdjointCtx ac = { *net, theta, D, net->nparams, &ws };
+
+ ODEResult fwd = ode_solve_times(neural_ode_rhs, z0, times, ntimes,
+ NULL, D, atol, rtol, &ac);
+ workspace_free(&ws);
+
+ double *dL_dz_each = vec_alloc(ntimes * D);
+ for (int i = 0; i < ntimes * D; i++)
+ dL_dz_each[i] = fwd.y[i] - targets[i];
+
+ MultiObsAdjointResult ar = adjoint_solve_multi(net, theta, fwd.y, times,
+ dL_dz_each, ntimes, atol, rtol);
+ free(dL_dz_each);
+
+ MultiObsNeuralODEOutput out;
+ out.z_traj = fwd.y;
+ out.dL_dz0 = ar.dL_dz0;
+ out.dL_dtheta = ar.dL_dtheta;
+ out.nfe_forward = fwd.nfe;
+ out.nfe_backward = ar.nfe;
+ return out;
+}
diff --git a/src/dynmlp.c b/src/dynmlp.c
new file mode 100644
index 0000000..70c9b75
--- /dev/null
+++ b/src/dynmlp.c
@@ -0,0 +1,94 @@
+#include "dynmlp.h"
+
+#include <math.h>
+
+static void xavier_init(double *w, int fan_in, int fan_out, RNG *r) {
+ double limit = sqrt(6.0 / (fan_in + fan_out));
+ int n = fan_in * fan_out;
+ for (int i = 0; i < n; i++)
+ w[i] = (2.0 * rng_uniform(r) - 1.0) * limit;
+}
+
+int dynmlp_nparams(int D, int H) {
+ return (D + 1) * H + H + H * D + D;
+}
+
+void dynmlp_init(DynMLP *net, int D, int H, double *theta, RNG *r) {
+ net->D = D;
+ net->H = H;
+ net->nparams = dynmlp_nparams(D, H);
+ xavier_init(theta + DYNMLP_W1(D, H), D + 1, H, r);
+ vec_zero(theta + DYNMLP_b1(D, H), H);
+ xavier_init(theta + DYNMLP_W2(D, H), H, D, r);
+ vec_zero(theta + DYNMLP_b2(D, H), D);
+}
+
+void dynmlp_forward(const DynMLP *net, const double *theta,
+ const double *z, double t, double *out,
+ Workspace *ws) {
+ int D = net->D, H = net->H;
+ const double *W1 = theta + DYNMLP_W1(D, H);
+ const double *b1 = theta + DYNMLP_b1(D, H);
+ const double *W2 = theta + DYNMLP_W2(D, H);
+ const double *b2 = theta + DYNMLP_b2(D, H);
+
+ double *x = ws->x;
+ double *h_pre = ws->h_pre;
+ double *h = ws->h;
+
+ vec_copy(z, x, D);
+ x[D] = t;
+
+ mat_vec(W1, x, h_pre, H, D + 1);
+ vec_add_scaled(h_pre, 1.0, b1, H);
+
+ for (int i = 0; i < H; i++) h[i] = tanh(h_pre[i]);
+
+ mat_vec(W2, h, out, D, H);
+ vec_add_scaled(out, 1.0, b2, D);
+}
+
+void dynmlp_vjp(const DynMLP *net, const double *theta,
+ const double *z, double t, const double *v,
+ double *vjp_z, double *vjp_theta,
+ Workspace *ws) {
+ int D = net->D;
+ int H = net->H;
+ const double *W1 = theta + DYNMLP_W1(D, H);
+ const double *b1 = theta + DYNMLP_b1(D, H);
+ const double *W2 = theta + DYNMLP_W2(D, H);
+ double *dW1 = vjp_theta + DYNMLP_W1(D, H);
+ double *db1 = vjp_theta + DYNMLP_b1(D, H);
+ double *dW2 = vjp_theta + DYNMLP_W2(D, H);
+ double *db2 = vjp_theta + DYNMLP_b2(D, H);
+
+ double *x = ws->x;
+ double *h_pre = ws->h_pre;
+ double *h = ws->h;
+ vec_copy(z, x, D);
+ x[D] = t;
+ mat_vec(W1, x, h_pre, H, D + 1);
+ vec_add_scaled(h_pre, 1.0, b1, H);
+
+ for (int i = 0; i < H; i++)
+ h[i] = tanh(h_pre[i]);
+
+ double *dh = ws->dh;
+ double *dh_pre = ws->dh_pre;
+ double *dx = ws->dx;
+ vec_zero(dh, H);
+ vec_zero(dx, D + 1);
+
+ mat_vec_T(W2, v, dh, D, H);
+ mat_outer_add(dW2, 1.0, v, h, D, H);
+ vec_add_scaled(db2, 1.0, v, D);
+
+ for (int i = 0; i < H; i++)
+ dh_pre[i] = (1.0 - h[i] * h[i]) * dh[i];
+
+ mat_vec_T(W1, dh_pre, dx, H, D + 1);
+ mat_outer_add(dW1, 1.0, dh_pre, x, H, D + 1);
+ vec_add_scaled(db1, 1.0, dh_pre, H);
+
+ vec_copy(dx, vjp_z, D);
+}
diff --git a/src/main.c b/src/main.c
new file mode 100644
index 0000000..2cae095
--- /dev/null
+++ b/src/main.c
@@ -0,0 +1,105 @@
+#include "utils.h"
+#include "dynmlp.h"
+#include "ode_solver.h"
+#include "adjoint.h"
+#include "adam.h"
+#include "train.h"
+#include "spiral.h"
+#include "tests.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <time.h>
+
+int main(void) {
+ RNG r = rng_init(42);
+
+ /* --- sanity checks --- */
+ test_ode_solver();
+ test_dynmlp_gradients(&r);
+ test_adjoint_gradients(&r);
+ test_multi_obs_adjoint(&r);
+ test_training(&r);
+
+ printf("\n--- Training demo (spiral) ---\n\n");
+
+ r = rng_init((uint64_t)time(NULL));
+
+ const double t0 = 0.0, t1 = 1.5;
+ const double noise_std = 0.1;
+ const double atol_train = 1e-3, rtol_train = 1e-3;
+ const double atol_eval = 1e-5, rtol_eval = 1e-5;
+ const int TRAIN_N = 200, TEST_N = 50;
+ const int ITERS = 500, BATCH = 16, LOG_EVERY = 25;
+
+ Dataset train_ds = generate_spiral_dataset(TRAIN_N, t0, t1, noise_std, &r);
+ Dataset test_ds = generate_spiral_dataset(TEST_N, t0, t1, noise_std, &r);
+
+ const int D = 2, H = 32;
+ DynMLP net;
+ int nparams = dynmlp_nparams(D, H);
+ double *theta = vec_alloc(nparams);
+ dynmlp_init(&net, D, H, theta, &r);
+
+ Adam adam = adam_init(nparams, 1e-3, 0.9, 0.999, 1e-8);
+
+ printf("%-6s %-12s %-12s %-10s %-10s",
+ "Iter", "Train Loss", "Test Loss", "Fwd NFE", "Bwd NFE");
+ printf("\n--------------------------------------------------\n");
+
+ const double **batch_z0 = (const double **)xmalloc(BATCH * sizeof(double *));
+ const double **batch_tgt = (const double **)xmalloc(BATCH * sizeof(double *));
+
+ for (int iter = 1; iter <= ITERS; iter++) {
+ for (int b = 0; b < BATCH; b++) {
+ int idx = (int)(rng_next(&r) % (uint64_t)TRAIN_N);
+ batch_z0[b] = train_ds.z0[idx];
+ batch_tgt[b] = train_ds.target[idx];
+ }
+
+ TrainStepResult res = train_step(&net, theta, batch_z0, batch_tgt,
+ t0, t1, BATCH, &adam,
+ atol_train, rtol_train, 10);
+
+ if (iter % LOG_EVERY == 0) {
+ double test_loss = evaluate(&net, theta, &test_ds,
+ t0, t1, atol_eval, rtol_eval);
+ printf("%-6d %-12.6f %-12.6f %-10d %-10d\n",
+ iter, res.loss, test_loss,
+ res.nfe_fwd, res.nfe_bwd);
+ fflush(stdout);
+ }
+ }
+
+ free(batch_z0);
+ free(batch_tgt);
+
+ printf("\n--------------------------------------------------\n");
+ double final_test_loss = evaluate(&net, theta, &test_ds,
+ t0, t1, atol_eval, rtol_eval);
+ printf("Final test loss : %.6f\n", final_test_loss);
+ printf("Total parameters: %d\n", nparams);
+
+ printf("\nSample predictions:\n");
+ Workspace ws = workspace_alloc(D, H, nparams);
+ AdjointCtx ac = { net, theta, D, nparams, &ws };
+ for (int s = 0; s < 5; s++) {
+ int idx = (int)(rng_next(&r) % (uint64_t)TEST_N);
+ ODEResult fwd = ode_solve(neural_ode_rhs,
+ test_ds.z0[idx], t0, t1,
+ NULL, D, atol_eval, rtol_eval, &ac);
+ printf(" z0=(%.4f, %.4f) predicted=(%.4f, %.4f) target=(%.4f, %.4f)\n",
+ test_ds.z0[idx][0], test_ds.z0[idx][1],
+ fwd.y[0], fwd.y[1],
+ test_ds.target[idx][0], test_ds.target[idx][1]);
+ free(fwd.y);
+ }
+ workspace_free(&ws);
+
+ free(theta);
+ adam_free(&adam);
+ dataset_free(&train_ds);
+ dataset_free(&test_ds);
+
+ return 0;
+}
diff --git a/src/ode_solver.c b/src/ode_solver.c
new file mode 100644
index 0000000..566cb2a
--- /dev/null
+++ b/src/ode_solver.c
@@ -0,0 +1,137 @@
+#include "ode_solver.h"
+#include "utils.h"
+
+#include <math.h>
+#include <stdlib.h>
+
+static const double dp_c[7] = { 0.0, 1.0/5.0, 3.0/10.0, 4.0/5.0, 8.0/9.0, 1.0, 1.0 };
+static const double dp_a2[1] = { 1.0/5.0 };
+static const double dp_a3[2] = { 3.0/40.0, 9.0/40.0 };
+static const double dp_a4[3] = { 44.0/45.0, -56.0/15.0, 32.0/9.0 };
+static const double dp_a5[4] = { 19372.0/6561.0, -25360.0/2187.0, 64448.0/6561.0, -212.0/729.0 };
+static const double dp_a6[5] = { 9017.0/3168.0, -355.0/33.0, 46732.0/5247.0, 49.0/176.0, -5103.0/18656.0 };
+static const double dp_b[7] = { 35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0, 0.0 };
+static const double dp_e[7] = {
+ 35.0/384.0 - 5179.0/57600.0,
+ 0.0,
+ 500.0/1113.0 - 7571.0/16695.0,
+ 125.0/192.0 - 393.0/640.0,
+ -2187.0/6784.0 + 92097.0/339200.0,
+ 11.0/84.0 - 187.0/2100.0,
+ -1.0/40.0
+};
+
+ODEResult ode_solve(ode_rhs_fn f, const double *y0, double t0, double t1,
+ const double *params, int dim, double atol, double rtol,
+ void *ctx) {
+ double **k = (double **)xmalloc(7 * sizeof(double *));
+ for (int i = 0; i < 7; i++) k[i] = vec_alloc(dim);
+ double *y = vec_alloc(dim);
+ double *y5 = vec_alloc(dim);
+ double *err = vec_alloc(dim);
+ double *stg = vec_alloc(dim);
+
+ ODEResult res = { vec_alloc(dim), 0 };
+ vec_copy(y0, y, dim);
+
+ double t = t0;
+ double h = 0.01 * (t1 - t0);
+ int k1_fresh = 0;
+
+ for (int step = 0; step < 1000000; step++) {
+ if (t1 > t0) {
+ if (t >= t1) break;
+ if (t + h > t1) h = t1 - t;
+ } else {
+ if (t <= t1) break;
+ if (t + h < t1) h = t1 - t;
+ }
+
+ if (!k1_fresh) { f(y, t, params, dim, k[0], ctx); res.nfe++; k1_fresh = 1; }
+
+ for (int i = 0; i < dim; i++)
+ stg[i] = y[i] + h * dp_a2[0]*k[0][i];
+ f(stg, t + dp_c[1]*h, params, dim, k[1], ctx); res.nfe++;
+
+ for (int i = 0; i < dim; i++)
+ stg[i] = y[i] + h * (dp_a3[0]*k[0][i] + dp_a3[1]*k[1][i]);
+ f(stg, t + dp_c[2]*h, params, dim, k[2], ctx); res.nfe++;
+
+ for (int i = 0; i < dim; i++)
+ stg[i] = y[i] + h * (dp_a4[0]*k[0][i] + dp_a4[1]*k[1][i] + dp_a4[2]*k[2][i]);
+ f(stg, t + dp_c[3]*h, params, dim, k[3], ctx); res.nfe++;
+
+ for (int i = 0; i < dim; i++)
+ stg[i] = y[i] + h * (dp_a5[0]*k[0][i] + dp_a5[1]*k[1][i]
+ + dp_a5[2]*k[2][i] + dp_a5[3]*k[3][i]);
+ f(stg, t + dp_c[4]*h, params, dim, k[4], ctx); res.nfe++;
+
+ for (int i = 0; i < dim; i++)
+ stg[i] = y[i] + h * (dp_a6[0]*k[0][i] + dp_a6[1]*k[1][i]
+ + dp_a6[2]*k[2][i] + dp_a6[3]*k[3][i] + dp_a6[4]*k[4][i]);
+ f(stg, t + dp_c[5]*h, params, dim, k[5], ctx); res.nfe++;
+
+ for (int i = 0; i < dim; i++)
+ y5[i] = y[i] + h * (dp_b[0]*k[0][i] + dp_b[2]*k[2][i]
+ + dp_b[3]*k[3][i] + dp_b[4]*k[4][i] + dp_b[5]*k[5][i]);
+ f(y5, t + h, params, dim, k[6], ctx); res.nfe++;
+
+ for (int i = 0; i < dim; i++)
+ err[i] = h * (dp_e[0]*k[0][i] + dp_e[2]*k[2][i] + dp_e[3]*k[3][i]
+ + dp_e[4]*k[4][i] + dp_e[5]*k[5][i] + dp_e[6]*k[6][i]);
+
+ double err_sq = 0.0;
+ for (int i = 0; i < dim; i++) {
+ double sc = atol + rtol * fmax(fabs(y[i]), fabs(y5[i]));
+ double e = err[i] / sc;
+ err_sq += e * e;
+ }
+ double err_norm = sqrt(err_sq / (double)dim);
+
+ double factor;
+ if (err_norm == 0.0) {
+ factor = 5.0;
+ } else {
+ factor = 0.9 * pow(err_norm, -0.2);
+ if (factor < 0.2) factor = 0.2;
+ if (factor > 5.0) factor = 5.0;
+ }
+
+ if (err_norm <= 1.0) {
+ vec_copy(y5, y, dim);
+ t += h;
+ double *tmp = k[0]; k[0] = k[6]; k[6] = tmp;
+ h *= factor;
+ } else {
+ if (factor > 1.0) factor = 1.0;
+ h *= factor;
+ }
+ }
+
+ vec_copy(y, res.y, dim);
+ for (int i = 0; i < 7; i++) free(k[i]);
+
+ free(k);
+ free(y);
+ free(y5);
+ free(err);
+ free(stg);
+
+ return res;
+}
+
+ODEResult ode_solve_times(ode_rhs_fn f, const double *y0, const double *times,
+ int ntimes, const double *params, int dim,
+ double atol, double rtol, void *ctx) {
+ ODEResult res = { vec_alloc(dim * ntimes), 0 };
+ vec_copy(y0, res.y, dim);
+ for (int i = 1; i < ntimes; i++) {
+ ODEResult seg = ode_solve(f, res.y + (i-1)*dim, times[i-1], times[i],
+ params, dim, atol, rtol, ctx);
+ vec_copy(seg.y, res.y + i * dim, dim);
+ res.nfe += seg.nfe;
+
+ free(seg.y);
+ }
+ return res;
+}
diff --git a/src/spiral.c b/src/spiral.c
new file mode 100644
index 0000000..5d5cc00
--- /dev/null
+++ b/src/spiral.c
@@ -0,0 +1,73 @@
+#include "spiral.h"
+#include "adjoint.h"
+#include "ode_solver.h"
+
+#include <math.h>
+#include <stdlib.h>
+
+static void spiral_rhs(const double *state, double t, const double *params,
+ int dim, double *out, void *ctx) {
+ (void)t; (void)dim; (void)ctx;
+ double alpha = params[0];
+ out[0] = alpha * state[1];
+ out[1] = -alpha * state[0];
+}
+
+Dataset generate_spiral_dataset(int num_samples, double t0, double t1,
+ double noise_std, RNG *r) {
+ Dataset ds;
+ ds.num_samples = num_samples;
+ ds.z0 = (double **)xmalloc(num_samples * sizeof(double *));
+ ds.target = (double **)xmalloc(num_samples * sizeof(double *));
+
+ for (int i = 0; i < num_samples; i++) {
+ double alpha = 1.0;
+ double angle = 2.0 * M_PI * rng_uniform(r);
+ double radius = 0.5 + 1.0 * rng_uniform(r);
+
+ ds.z0[i] = vec_alloc(2);
+ ds.target[i] = vec_alloc(2);
+
+ ds.z0[i][0] = radius * cos(angle);
+ ds.z0[i][1] = radius * sin(angle);
+
+ ODEResult res = ode_solve(spiral_rhs, ds.z0[i], t0, t1,
+ &alpha, 2, 1e-8, 1e-8, NULL);
+ vec_copy(res.y, ds.target[i], 2);
+ free(res.y);
+
+ /* add noise to the initial observation */
+ ds.z0[i][0] += noise_std * rng_normal(r);
+ ds.z0[i][1] += noise_std * rng_normal(r);
+ }
+ return ds;
+}
+
+void dataset_free(Dataset *ds) {
+ for (int i = 0; i < ds->num_samples; i++) {
+ free(ds->z0[i]);
+ free(ds->target[i]);
+ }
+ free(ds->z0);
+ free(ds->target);
+}
+
+double evaluate(const DynMLP *net, const double *theta,
+ const Dataset *ds, double t0, double t1,
+ double atol, double rtol) {
+ int D = net->D;
+ Workspace ws = workspace_alloc(D, net->H, net->nparams);
+ AdjointCtx ac = { *net, theta, D, net->nparams, &ws };
+ double total_loss = 0.0;
+ for (int i = 0; i < ds->num_samples; i++) {
+ ODEResult fwd = ode_solve(neural_ode_rhs, ds->z0[i], t0, t1,
+ NULL, D, atol, rtol, &ac);
+ for (int j = 0; j < D; j++) {
+ double d = fwd.y[j] - ds->target[i][j];
+ total_loss += 0.5 * d * d;
+ }
+ free(fwd.y);
+ }
+ workspace_free(&ws);
+ return total_loss / (double)ds->num_samples;
+}
diff --git a/src/tests.c b/src/tests.c
new file mode 100644
index 0000000..7d42a5c
--- /dev/null
+++ b/src/tests.c
@@ -0,0 +1,345 @@
+#include "tests.h"
+#include "dynmlp.h"
+#include "ode_solver.h"
+#include "adjoint.h"
+#include "adam.h"
+#include "train.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+static void rhs_decay(const double *y, double t, const double *p, int d, double *out, void *ctx) {
+ (void)t; (void)p; (void)d; (void)ctx;
+ out[0] = -y[0];
+}
+
+static void rhs_rotation(const double *y, double t, const double *p, int d, double *out, void *ctx) {
+ (void)t; (void)p; (void)d; (void)ctx;
+ out[0] = -y[1]; out[1] = y[0];
+}
+
+void test_ode_solver(void) {
+ const double atol = 1e-8, rtol = 1e-8, tol = 1e-6;
+
+ { double y0 = 1.0;
+ ODEResult r = ode_solve(rhs_decay, &y0, 0.0, 1.0, NULL, 1, atol, rtol, NULL);
+ double err = fabs(r.y[0] - exp(-1.0));
+ printf("ODE test 1 (decay): err=%.2e nfe=%d %s\n", err, r.nfe, err < tol ? "PASS" : "FAIL");
+ free(r.y); }
+
+ { double y0[2] = {1.0, 0.0};
+ ODEResult r = ode_solve(rhs_rotation, y0, 0.0, 2.0 * M_PI, NULL, 2, atol, rtol, NULL);
+ double err = sqrt((r.y[0]-1.0)*(r.y[0]-1.0) + r.y[1]*r.y[1]);
+ printf("ODE test 2 (rotation): err=%.2e nfe=%d %s\n", err, r.nfe, err < tol ? "PASS" : "FAIL");
+ free(r.y); }
+
+ { double y0 = exp(-1.0);
+ ODEResult r = ode_solve(rhs_decay, &y0, 1.0, 0.0, NULL, 1, atol, rtol, NULL);
+ double err = fabs(r.y[0] - 1.0);
+ printf("ODE test 3 (backward): err=%.2e nfe=%d %s\n", err, r.nfe, err < tol ? "PASS" : "FAIL");
+ free(r.y); }
+}
+
+void test_dynmlp_gradients(RNG *r) {
+ const int D = 3, H = 8;
+ const double EPS = 1e-7, TOL = 1e-5;
+
+ int np = dynmlp_nparams(D, H);
+ double *theta = vec_alloc(np);
+ double *z = vec_alloc(D);
+ double *v = vec_alloc(D);
+ double *out_p = vec_alloc(D);
+ double *out_m = vec_alloc(D);
+
+ DynMLP net;
+ dynmlp_init(&net, D, H, theta, r);
+ for (int i = 0; i < D; i++) z[i] = rng_normal(r);
+ for (int i = 0; i < D; i++) v[i] = rng_normal(r);
+ double t = rng_normal(r);
+
+ Workspace ws = workspace_alloc(D, H, np);
+
+ double *vjp_z = vec_zeros(D);
+ double *vjp_theta = vec_zeros(np);
+ dynmlp_vjp(&net, theta, z, t, v, vjp_z, vjp_theta, &ws);
+
+ double *num_vjp_z = vec_alloc(D);
+ for (int i = 0; i < D; i++) {
+ double zi = z[i];
+ z[i] = zi + EPS; dynmlp_forward(&net, theta, z, t, out_p, &ws);
+ z[i] = zi - EPS; dynmlp_forward(&net, theta, z, t, out_m, &ws);
+ z[i] = zi;
+ num_vjp_z[i] = (vec_dot(v, out_p, D) - vec_dot(v, out_m, D)) / (2.0 * EPS);
+ }
+ double max_err_z = 0.0;
+ for (int i = 0; i < D; i++) {
+ double e = fabs(vjp_z[i] - num_vjp_z[i]);
+ if (e > max_err_z) max_err_z = e;
+ }
+
+ double *num_vjp_theta = vec_alloc(np);
+ for (int k = 0; k < np; k++) {
+ double tk = theta[k];
+ theta[k] = tk + EPS; dynmlp_forward(&net, theta, z, t, out_p, &ws);
+ theta[k] = tk - EPS; dynmlp_forward(&net, theta, z, t, out_m, &ws);
+ theta[k] = tk;
+ num_vjp_theta[k] = (vec_dot(v, out_p, D) - vec_dot(v, out_m, D)) / (2.0 * EPS);
+ }
+ double max_err_theta = 0.0;
+ for (int k = 0; k < np; k++) {
+ double e = fabs(vjp_theta[k] - num_vjp_theta[k]);
+ if (e > max_err_theta) max_err_theta = e;
+ }
+
+ printf("dL/dz: max_err=%.2e %s\n", max_err_z, max_err_z < TOL ? "PASS" : "FAIL");
+ printf("dL/dtheta: max_err=%.2e %s\n", max_err_theta, max_err_theta < TOL ? "PASS" : "FAIL");
+
+ workspace_free(&ws);
+ free(theta); free(z); free(v); free(out_p); free(out_m);
+ free(vjp_z); free(vjp_theta); free(num_vjp_z); free(num_vjp_theta);
+}
+
+void test_adjoint_gradients(RNG *r) {
+ const int D = 2, H = 8;
+ const double EPS = 1e-5, atol = 1e-7, rtol = 1e-7;
+ const double t0 = 0.0, t1 = 1.0;
+
+ int np = dynmlp_nparams(D, H);
+ double *theta = vec_alloc(np);
+ double *z0 = vec_alloc(D);
+ double *target = vec_alloc(D);
+
+ DynMLP net;
+ dynmlp_init(&net, D, H, theta, r);
+ for (int i = 0; i < D; i++) z0[i] = rng_normal(r);
+ for (int i = 0; i < D; i++) target[i] = rng_normal(r);
+
+ NeuralODEOutput out = neural_ode_forward_backward(&net, theta, z0, t0, t1,
+ target, atol, rtol, 10);
+
+ Workspace ws = workspace_alloc(D, H, np);
+
+#define FWD_LOSS(z0_, theta_) ({ \
+ AdjointCtx ac_ = { net, (theta_), D, np, &ws }; \
+ ODEResult r_ = ode_solve(neural_ode_rhs, (z0_), t0, t1, NULL, D, atol, rtol, &ac_); \
+ double l_ = 0.0; \
+ for (int _i = 0; _i < D; _i++) { double _d = r_.y[_i] - target[_i]; l_ += 0.5*_d*_d; } \
+ free(r_.y); l_; \
+})
+
+ double *num_dL_dtheta = vec_alloc(np);
+ for (int k = 0; k < np; k++) {
+ double tk = theta[k];
+ theta[k] = tk + EPS; double lp = FWD_LOSS(z0, theta);
+ theta[k] = tk - EPS; double lm = FWD_LOSS(z0, theta);
+ theta[k] = tk;
+ num_dL_dtheta[k] = (lp - lm) / (2.0 * EPS);
+ }
+ double max_num_theta = 0.0;
+ for (int k = 0; k < np; k++)
+ if (fabs(num_dL_dtheta[k]) > max_num_theta) max_num_theta = fabs(num_dL_dtheta[k]);
+ double max_err_theta = 0.0;
+ for (int k = 0; k < np; k++) {
+ double e = fabs(out.dL_dtheta[k] - num_dL_dtheta[k]);
+ if (e > max_err_theta) max_err_theta = e;
+ }
+ double rel_theta = max_err_theta / (max_num_theta + 1e-8);
+ printf("adjoint dL/dtheta: max_rel_err=%.2e nfe_fwd=%d nfe_bwd=%d %s\n",
+ rel_theta, out.nfe_forward, out.nfe_backward, rel_theta < 1e-3 ? "PASS" : "FAIL");
+
+ double *num_dL_dz0 = vec_alloc(D);
+ for (int i = 0; i < D; i++) {
+ double zi = z0[i];
+ z0[i] = zi + EPS; double lp = FWD_LOSS(z0, theta);
+ z0[i] = zi - EPS; double lm = FWD_LOSS(z0, theta);
+ z0[i] = zi;
+ num_dL_dz0[i] = (lp - lm) / (2.0 * EPS);
+ }
+ double max_num_z0 = 0.0;
+ for (int i = 0; i < D; i++)
+ if (fabs(num_dL_dz0[i]) > max_num_z0) max_num_z0 = fabs(num_dL_dz0[i]);
+ double max_err_z0 = 0.0;
+ for (int i = 0; i < D; i++) {
+ double e = fabs(out.dL_dz0[i] - num_dL_dz0[i]);
+ if (e > max_err_z0) max_err_z0 = e;
+ }
+ double rel_z0 = max_err_z0 / (max_num_z0 + 1e-8);
+ printf("adjoint dL/dz0: max_rel_err=%.2e %s\n", rel_z0, rel_z0 < 1e-3 ? "PASS" : "FAIL");
+
+#undef FWD_LOSS
+
+ workspace_free(&ws);
+ free(out.z1); free(out.dL_dz0); free(out.dL_dtheta);
+ free(num_dL_dtheta); free(num_dL_dz0);
+ free(theta); free(z0); free(target);
+}
+
+void test_multi_obs_adjoint(RNG *r) {
+ const int D = 2, H = 8;
+ const double EPS = 1e-5, atol = 1e-7, rtol = 1e-7;
+ const int ntimes = 5;
+
+ double times[5] = { 0.0, 0.5, 1.0, 1.5, 2.0 };
+
+ int np = dynmlp_nparams(D, H);
+ double *theta = vec_alloc(np);
+ double *z0 = vec_alloc(D);
+ double *targets = vec_alloc(ntimes * D);
+
+ DynMLP net;
+ dynmlp_init(&net, D, H, theta, r);
+ for (int i = 0; i < D; i++) z0[i] = rng_normal(r);
+ for (int i = 0; i < ntimes * D; i++) targets[i] = rng_normal(r);
+
+ MultiObsNeuralODEOutput out = neural_ode_forward_backward_multi(
+ &net, theta, z0, times, targets, ntimes, atol, rtol);
+
+ Workspace ws = workspace_alloc(D, H, np);
+ AdjointCtx ac = { net, theta, D, np, &ws };
+
+ /* Numerical dL/dtheta */
+ double *num_dL_dtheta = vec_alloc(np);
+ for (int k = 0; k < np; k++) {
+ double tk = theta[k];
+
+ theta[k] = tk + EPS;
+ ODEResult rp = ode_solve_times(neural_ode_rhs, z0, times, ntimes,
+ NULL, D, atol, rtol, &ac);
+ double lp = 0.0;
+ for (int i = 0; i < ntimes * D; i++) {
+ double d = rp.y[i] - targets[i]; lp += 0.5 * d * d;
+ }
+ free(rp.y);
+
+ theta[k] = tk - EPS;
+ ODEResult rm = ode_solve_times(neural_ode_rhs, z0, times, ntimes,
+ NULL, D, atol, rtol, &ac);
+ double lm = 0.0;
+ for (int i = 0; i < ntimes * D; i++) {
+ double d = rm.y[i] - targets[i]; lm += 0.5 * d * d;
+ }
+ free(rm.y);
+
+ theta[k] = tk;
+ num_dL_dtheta[k] = (lp - lm) / (2.0 * EPS);
+ }
+
+ double max_num_theta = 0.0;
+ for (int k = 0; k < np; k++)
+ if (fabs(num_dL_dtheta[k]) > max_num_theta) max_num_theta = fabs(num_dL_dtheta[k]);
+ double max_err_theta = 0.0;
+ for (int k = 0; k < np; k++) {
+ double e = fabs(out.dL_dtheta[k] - num_dL_dtheta[k]);
+ if (e > max_err_theta) max_err_theta = e;
+ }
+ double rel_theta = max_err_theta / (max_num_theta + 1e-8);
+ printf("multi-obs adjoint dL/dtheta: max_rel_err=%.2e nfe_fwd=%d nfe_bwd=%d %s\n",
+ rel_theta, out.nfe_forward, out.nfe_backward, rel_theta < 1e-3 ? "PASS" : "FAIL");
+
+ /* Numerical dL/dz0 */
+ double *num_dL_dz0 = vec_alloc(D);
+ for (int i = 0; i < D; i++) {
+ double zi = z0[i];
+
+ z0[i] = zi + EPS;
+ ODEResult rp = ode_solve_times(neural_ode_rhs, z0, times, ntimes,
+ NULL, D, atol, rtol, &ac);
+ double lp = 0.0;
+ for (int j = 0; j < ntimes * D; j++) {
+ double d = rp.y[j] - targets[j]; lp += 0.5 * d * d;
+ }
+ free(rp.y);
+
+ z0[i] = zi - EPS;
+ ODEResult rm = ode_solve_times(neural_ode_rhs, z0, times, ntimes,
+ NULL, D, atol, rtol, &ac);
+ double lm = 0.0;
+ for (int j = 0; j < ntimes * D; j++) {
+ double d = rm.y[j] - targets[j]; lm += 0.5 * d * d;
+ }
+ free(rm.y);
+
+ z0[i] = zi;
+ num_dL_dz0[i] = (lp - lm) / (2.0 * EPS);
+ }
+
+ double max_num_z0 = 0.0;
+ for (int i = 0; i < D; i++)
+ if (fabs(num_dL_dz0[i]) > max_num_z0) max_num_z0 = fabs(num_dL_dz0[i]);
+ double max_err_z0 = 0.0;
+ for (int i = 0; i < D; i++) {
+ double e = fabs(out.dL_dz0[i] - num_dL_dz0[i]);
+ if (e > max_err_z0) max_err_z0 = e;
+ }
+ double rel_z0 = max_err_z0 / (max_num_z0 + 1e-8);
+ printf("multi-obs adjoint dL/dz0: max_rel_err=%.2e %s\n",
+ rel_z0, rel_z0 < 1e-3 ? "PASS" : "FAIL");
+
+ workspace_free(&ws);
+ free(out.z_traj); free(out.dL_dz0); free(out.dL_dtheta);
+ free(num_dL_dtheta); free(num_dL_dz0);
+ free(theta); free(z0); free(targets);
+}
+
+void test_training(RNG *r) {
+ const int D = 2, H = 16;
+ const int N = 50, BATCH = 10, ITERS = 300;
+ const double t0 = 0.0, t1 = 1.0;
+ const double atol = 1e-4, rtol = 1e-4;
+
+ DynMLP net;
+ int nparams = dynmlp_nparams(D, H);
+ double *theta = vec_alloc(nparams);
+ dynmlp_init(&net, D, H, theta, r);
+ Adam adam = adam_init(nparams, 1e-3, 0.9, 0.999, 1e-8);
+
+ double **z0s = (double **)xmalloc(N * sizeof(double *));
+ double **targets = (double **)xmalloc(N * sizeof(double *));
+ for (int i = 0; i < N; i++) {
+ double angle = 2.0 * M_PI * rng_uniform(r);
+ z0s[i] = vec_alloc(D);
+ targets[i] = vec_alloc(D);
+ z0s[i][0] = cos(angle);
+ z0s[i][1] = sin(angle);
+ targets[i][0] = -z0s[i][1];
+ targets[i][1] = z0s[i][0];
+ }
+
+ const double **batch_z0 = (const double **)xmalloc(BATCH * sizeof(double *));
+ const double **batch_tgt = (const double **)xmalloc(BATCH * sizeof(double *));
+
+ printf("\n--- Training test (D=2, H=16, 90-deg rotation) ---\n");
+ for (int iter = 0; iter < ITERS; iter++) {
+ for (int b = 0; b < BATCH; b++) {
+ int idx = (int)(rng_next(r) % (uint64_t)N);
+ batch_z0[b] = z0s[idx];
+ batch_tgt[b] = targets[idx];
+ }
+ TrainStepResult res = train_step(&net, theta, batch_z0, batch_tgt,
+ t0, t1, BATCH, &adam, atol, rtol, 10);
+ if ((iter + 1) % 50 == 0)
+ printf("iter %3d loss=%.4f nfe_fwd=%d\n", iter + 1, res.loss, res.nfe_fwd);
+ }
+
+ Workspace ws = workspace_alloc(D, H, nparams);
+ AdjointCtx ac = { net, theta, D, nparams, &ws };
+ double final_loss = 0.0;
+ for (int i = 0; i < N; i++) {
+ ODEResult fwd = ode_solve(neural_ode_rhs, z0s[i], t0, t1, NULL, D, atol, rtol, &ac);
+ for (int j = 0; j < D; j++) {
+ double d = fwd.y[j] - targets[i][j];
+ final_loss += 0.5 * d * d;
+ }
+ free(fwd.y);
+ }
+ final_loss /= (double)N;
+ printf("Loss: %.4f\n", final_loss);
+
+ workspace_free(&ws);
+ adam_free(&adam);
+ free(batch_z0); free(batch_tgt);
+ for (int i = 0; i < N; i++) { free(z0s[i]); free(targets[i]); }
+ free(z0s); free(targets);
+ free(theta);
+}
diff --git a/src/train.c b/src/train.c
new file mode 100644
index 0000000..ebaf7cd
--- /dev/null
+++ b/src/train.c
@@ -0,0 +1,47 @@
+#include "train.h"
+#include "adjoint.h"
+#include "utils.h"
+
+#include <stdlib.h>
+
+static double train_one(const DynMLP *net, const double *theta,
+ const double *z0, double t0, double t1,
+ const double *target, double *grad_accum,
+ double atol, double rtol, int num_checkpoints,
+ int *nfe_fwd, int *nfe_bwd) {
+ NeuralODEOutput out = neural_ode_forward_backward(net, theta, z0, t0, t1,
+ target, atol, rtol, num_checkpoints);
+ double loss = 0.0;
+ int D = net->D;
+ for (int i = 0; i < D; i++) {
+ double d = out.z1[i] - target[i];
+ loss += 0.5 * d * d;
+ }
+ for (int i = 0; i < net->nparams; i++) grad_accum[i] += out.dL_dtheta[i];
+ *nfe_fwd += out.nfe_forward;
+ *nfe_bwd += out.nfe_backward;
+ free(out.z1);
+ free(out.dL_dz0);
+ free(out.dL_dtheta);
+ return loss;
+}
+
+TrainStepResult train_step(const DynMLP *net, double *theta,
+ const double **z0s, const double **targets,
+ double t0, double t1, int batch_size,
+ Adam *adam, double atol, double rtol, int num_checkpoints) {
+ int nparams = net->nparams;
+ double *grad_accum = vec_zeros(nparams);
+ TrainStepResult res = { 0.0, 0, 0 };
+
+ for (int b = 0; b < batch_size; b++) {
+ res.loss += train_one(net, theta, z0s[b], t0, t1, targets[b],
+ grad_accum, atol, rtol, num_checkpoints,
+ &res.nfe_fwd, &res.nfe_bwd);
+ }
+ res.loss /= (double)batch_size;
+ for (int i = 0; i < nparams; i++) grad_accum[i] /= (double)batch_size;
+ adam_update(adam, theta, grad_accum);
+ free(grad_accum);
+ return res;
+}
diff --git a/src/utils.c b/src/utils.c
new file mode 100644
index 0000000..c10e9da
--- /dev/null
+++ b/src/utils.c
@@ -0,0 +1,106 @@
+#include "utils.h"
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+
+RNG rng_init(uint64_t seed) {
+ RNG r;
+ r.state = seed ? seed : 1;
+ return r;
+}
+
+uint64_t rng_next(RNG *r) {
+ uint64_t x = r->state;
+ x ^= x << 13;
+ x ^= x >> 7;
+ x ^= x << 17;
+ r->state = x;
+ return x;
+}
+
+double rng_uniform(RNG *r) {
+ return (double)(rng_next(r) >> 11) / (double)(UINT64_C(1) << 53);
+}
+
+double rng_normal(RNG *r) {
+ double u1 = rng_uniform(r);
+ double u2 = rng_uniform(r);
+ if (u1 < 1e-300) u1 = 1e-300;
+ return sqrt(-2.0 * log(u1)) * cos(2.0 * M_PI * u2);
+}
+
+void *xmalloc(size_t n) {
+ void *p = malloc(n);
+ if (!p) { fprintf(stderr, "fatal: malloc(%zu) failed\n", n); abort(); }
+ return p;
+}
+
+void *xcalloc(size_t count, size_t size) {
+ void *p = calloc(count, size);
+ if (!p) { fprintf(stderr, "fatal: calloc(%zu, %zu) failed\n", count, size); abort(); }
+ return p;
+}
+
+double *vec_alloc(int n) { return (double *)xmalloc((size_t)n * sizeof(double)); }
+double *vec_zeros(int n) { return (double *)xcalloc((size_t)n, sizeof(double)); }
+void vec_zero(double *v, int n) { memset(v, 0, (size_t)n * sizeof(double)); }
+void vec_copy(const double *src, double *dst, int n) { memcpy(dst, src, (size_t)n * sizeof(double)); }
+
+void vec_add_scaled(double *dst, double alpha, const double *v, int n) {
+ for (int i = 0; i < n; i++) dst[i] += alpha * v[i];
+}
+
+double vec_dot(const double *a, const double *b, int n) {
+ double s = 0.0;
+ for (int i = 0; i < n; i++) s += a[i] * b[i];
+ return s;
+}
+
+void mat_vec(const double *M, const double *x, double *dst, int rows, int cols) {
+ for (int i = 0; i < rows; i++) {
+ double s = 0.0;
+ for (int j = 0; j < cols; j++) s += M[i * cols + j] * x[j];
+ dst[i] = s;
+ }
+}
+
+void mat_vec_T(const double *M, const double *v, double *dst, int rows, int cols) {
+ for (int i = 0; i < rows; i++)
+ for (int j = 0; j < cols; j++)
+ dst[j] += M[i * cols + j] * v[i];
+}
+
+void mat_outer_add(double *M, double alpha,
+ const double *a, const double *b, int rows, int cols) {
+ for (int i = 0; i < rows; i++)
+ for (int j = 0; j < cols; j++)
+ M[i * cols + j] += alpha * a[i] * b[j];
+}
+
+Workspace workspace_alloc(int D, int H, int nparams) {
+ Workspace ws;
+ ws.x = vec_alloc(D + 1);
+ ws.h_pre = vec_alloc(H);
+ ws.h = vec_alloc(H);
+ ws.dh = vec_alloc(H);
+ ws.dh_pre = vec_alloc(H);
+ ws.dx = vec_alloc(D + 1);
+ ws.neg_a = vec_alloc(D);
+ ws.vjp_z = vec_alloc(D);
+ ws.vjp_theta = vec_alloc(nparams);
+ return ws;
+}
+
+void workspace_free(Workspace *ws) {
+ free(ws->x);
+ free(ws->h_pre);
+ free(ws->h);
+ free(ws->dh);
+ free(ws->dh_pre);
+ free(ws->dx);
+ free(ws->neg_a);
+ free(ws->vjp_z);
+ free(ws->vjp_theta);
+}
generated by cgit v1.2.3 (git 2.51.0) at 2026-09-01 21:17:57 +0000