Merge pull request #73 from MatthewSZhang/multi-output

1. Output intercept when no poly term is assign to that output. It should be mean value for that output.
2. Update the warning message. We allow no poly term for some outputs, but at least one poly term should be assigned to one output.
3. For Jacobian of NARX, it should skip to compute dynamic part when no y in terms.

Author: MatthewSZhang

fastcan/narx.py

@@ -760,7 +760,8 @@ def fit(self, X, y, sample_weight=None, coef_init=None, **params):
             warnings.warn(
                 f"output_ids got {self.output_ids_}, which does not "
                 f"contain all values from 0 to {self.n_outputs_ - 1}."
-                "The predicted outputs for the missing values will be 0.",
+                "The prediction for the missing outputs will be a constant"
+                "(i.e., intercept).",
                 UserWarning,
             )
 
@@ -783,6 +784,7 @@ def fit(self, X, y, sample_weight=None, coef_init=None, **params):
             for i in range(self.n_outputs_):
                 output_i_mask = self.output_ids_ == i
                 if np.sum(output_i_mask) == 0:
+                    intercept[i] = np.mean(y_masked[:, i])
                     continue
                 osa_narx.fit(
                     poly_terms_masked[:, output_i_mask],
@@ -974,8 +976,8 @@ def _update_dydx(
             dydx[k, y_ids, x_ids] = terms
 
             # Update dynamic terms of Jacobian
-            cfd = np.zeros((n_y, n_y, max_delay), dtype=float)
-            if max_delay > 0:
+            if max_delay > 0 and grad_yyd_ids.size > 0:
+                cfd = np.zeros((n_y, n_y, max_delay), dtype=float)
                 _update_cfd(
                     X,
                     y_hat,