From 70536ac4408c9d9f4b55e3fea018abb97a3d43de Mon Sep 17 00:00:00 2001
From: SIKAI ZHANG <34108862+MatthewSZhang@users.noreply.github.com>
Date: Wed, 9 Apr 2025 15:48:14 +0800
Subject: [PATCH 1/3] ENH speed up grad computation via Cython

---
 fastcan/_cancorr_fast.pyx |   6 +-
 fastcan/_fastcan.py       |   2 +-
 fastcan/_narx_fast.pyx    | 113 ++++++++++++++
 fastcan/meson.build       |   8 +
 fastcan/narx.py           | 202 +++++++++++++++----------
 pixi.lock                 | 302 ++++++++++++++++++--------------------
 tests/test_narx_jac.py    |  49 ++++---
 7 files changed, 420 insertions(+), 262 deletions(-)
 create mode 100644 fastcan/_narx_fast.pyx

diff --git a/fastcan/_cancorr_fast.pyx b/fastcan/_cancorr_fast.pyx
index ba3fb4d..5d8cea4 100644
--- a/fastcan/_cancorr_fast.pyx
+++ b/fastcan/_cancorr_fast.pyx
@@ -11,7 +11,7 @@ from cython.parallel import prange
 from scipy.linalg.cython_blas cimport isamax, idamax
 from sklearn.utils._cython_blas cimport ColMajor, NoTrans
 from sklearn.utils._cython_blas cimport _dot, _scal, _nrm2, _gemm, _axpy
-from sklearn.utils._typedefs cimport int32_t, uint8_t
+from sklearn.utils._typedefs cimport uint8_t
 
 
 @final
@@ -106,7 +106,7 @@ cdef floating _sscvm(
 cdef void _mgsvv(
     const floating* w,          # IN
     const floating* x,          # IN/OUT
-    int n_samples,     # IN
+    int n_samples,              # IN
 ) noexcept nogil:
     """
     Modified Gram-Schmidt process. x = x - w*w.T*x
@@ -133,7 +133,7 @@ cpdef int _forward_search(
     int num_threads,                  # IN
     int verbose,                      # IN
     uint8_t[::1] mask,                # IN/TEMP
-    int32_t[::1] indices,             # OUT
+    int[::1] indices,                 # OUT
     floating[::1] scores,             # OUT
 ) except -1 nogil:
     """
diff --git a/fastcan/_fastcan.py b/fastcan/_fastcan.py
index 2441858..01af376 100644
--- a/fastcan/_fastcan.py
+++ b/fastcan/_fastcan.py
@@ -293,7 +293,7 @@ def _get_support_mask(self):
 
 def _prepare_search(n_features, n_features_to_select, indices_include, indices_exclude):
     # initiated with -1
-    indices = np.full(n_features_to_select, -1, dtype=np.intc, order="F")
+    indices = np.full(n_features_to_select, -1, dtype=np.int32, order="F")
     indices[: indices_include.size] = indices_include
     scores = np.zeros(n_features_to_select, dtype=float, order="F")
     mask = np.zeros(n_features, dtype=np.ubyte, order="F")
diff --git a/fastcan/_narx_fast.pyx b/fastcan/_narx_fast.pyx
new file mode 100644
index 0000000..85d46ca
--- /dev/null
+++ b/fastcan/_narx_fast.pyx
@@ -0,0 +1,113 @@
+"""
+Fast gradient computation for narx
+"""
+# Authors: The fastcan developers
+# SPDX-License-Identifier: MIT
+
+from cython cimport floating, final
+
+
+@final
+cpdef void _update_terms(
+    const floating[:, ::1] X,       # IN
+    const floating[:, ::1] y_hat,   # IN
+    floating[::1] terms,            # OUT
+    const int[:, ::1] feat_ids,     # IN
+    const int[:, ::1] delay_ids,    # IN
+    const int k,                    # IN
+) noexcept nogil:
+    """
+    Evaluate all terms for the given features and delays at timestep k.
+    """
+    cdef:
+        int i
+        int n_coefs = feat_ids.shape[0]
+
+    for i in range(n_coefs):
+        terms[i] = _evaluate_term(
+            X, y_hat, feat_ids[i], delay_ids[i], k
+        )
+
+
+@final
+cpdef void _predict_step(
+    const floating[:, ::1] X,       # IN
+    const floating[:, ::1] y_hat,   # IN
+    floating[::1] y_pred,           # OUT
+    const floating[::1] coef,       # IN
+    const int[:, ::1] feat_ids,     # IN
+    const int[:, ::1] delay_ids,    # IN
+    const int[::1] output_ids,      # IN
+    const int k,                    # IN
+) noexcept nogil:
+    """
+    Evaluate the expression for all outputs at timestep k.
+    """
+    cdef:
+        int n_terms = feat_ids.shape[0]
+        int i, output_i
+
+    # Add all terms
+    for i in range(n_terms):
+        output_i = output_ids[i]
+        y_pred[output_i] += coef[i] * _evaluate_term(
+            X, y_hat, feat_ids[i], delay_ids[i], k
+        )
+
+
+@final
+cdef floating _evaluate_term(
+    const floating[:, ::1] X,       # IN
+    const floating[:, ::1] y_hat,   # IN
+    const int[::1] feat_ids,        # IN
+    const int[::1] delay_ids,       # IN
+    const int k,                    # IN
+) noexcept nogil:
+    """
+    Evaluate a term based on feature and delay IDs.
+    """
+    cdef:
+        int n_feats = X.shape[1]
+        int n_vars = feat_ids.shape[0]
+        floating term = 1.0
+        int i, feat_id
+
+    for i in range(n_vars):
+        feat_id = feat_ids[i]
+        if feat_id != -1:
+            if feat_id < n_feats:
+                term *= X[k - delay_ids[i], feat_id]
+            else:
+                term *= y_hat[k - delay_ids[i], feat_id - n_feats]
+
+    return term
+
+
+@final
+cpdef void _update_cfd(
+    const floating[:, ::1] X,           # IN
+    const floating[:, ::1] y_hat,       # IN
+    floating[:, :, ::1] cfd,            # OUT
+    const floating[::1] coef,           # IN
+    const int[:, ::1] grad_yyd_ids,     # IN
+    const int[::1] grad_coef_ids,       # IN
+    const int[:, ::1] grad_feat_ids,    # IN
+    const int[:, ::1] grad_delay_ids,   # IN
+    const int k,                        # IN
+) noexcept nogil:
+    """
+    Updates CFD matrix based on the current state.
+    """
+    cdef:
+        int n_grad_terms = grad_yyd_ids.shape[0]
+        int i, row_y_id, col_y_id, delay_id_1
+
+    for i in range(n_grad_terms):
+        row_y_id = grad_yyd_ids[i, 0]
+        col_y_id = grad_yyd_ids[i, 1]
+        delay_id_1 = grad_yyd_ids[i, 2]
+
+        cfd[row_y_id, col_y_id, delay_id_1] += coef[grad_coef_ids[i]] * \
+            _evaluate_term(
+                X, y_hat, grad_feat_ids[i], grad_delay_ids[i], k
+            )
diff --git a/fastcan/meson.build b/fastcan/meson.build
index 934ad7a..402f933 100644
--- a/fastcan/meson.build
+++ b/fastcan/meson.build
@@ -13,4 +13,12 @@ py.extension_module(
     subdir: 'fastcan',
     cython_args: cython_args,
     install: true
+)
+
+py.extension_module(
+    '_narx_fast',
+    '_narx_fast.pyx',
+    subdir: 'fastcan',
+    cython_args: cython_args,
+    install: true
 )
\ No newline at end of file
diff --git a/fastcan/narx.py b/fastcan/narx.py
index 288f11b..f5299f7 100644
--- a/fastcan/narx.py
+++ b/fastcan/narx.py
@@ -25,6 +25,7 @@
 )
 
 from ._fastcan import FastCan
+from ._narx_fast import _predict_step, _update_cfd, _update_terms  # type: ignore
 from ._refine import refine
 
 
@@ -342,7 +343,8 @@ def _validate_feat_delay_ids(
     feat_ids_ = check_array(
         feat_ids,
         ensure_2d=True,
-        dtype=int,
+        dtype=np.int32,
+        order="C",
     )
     if (feat_ids_.min() < -1) or (feat_ids_.max() > n_features + n_outputs - 1):
         raise ValueError(
@@ -353,7 +355,8 @@ def _validate_feat_delay_ids(
     delay_ids_ = check_array(
         delay_ids,
         ensure_2d=True,
-        dtype=int,
+        dtype=np.int32,
+        order="C",
     )
     if delay_ids_.shape != feat_ids_.shape:
         raise ValueError(
@@ -692,9 +695,9 @@ def fit(self, X, y, sample_weight=None, coef_init=None, **params):
         self : object
             Fitted Estimator.
         """
-        check_X_params = dict(dtype=float, ensure_all_finite="allow-nan")
+        check_X_params = dict(dtype=float, order="C", ensure_all_finite="allow-nan")
         check_y_params = dict(
-            ensure_2d=False, dtype=float, ensure_all_finite="allow-nan"
+            ensure_2d=False, dtype=float, order="C", ensure_all_finite="allow-nan"
         )
         X, y = validate_data(
             self, X, y, validate_separately=(check_X_params, check_y_params)
@@ -732,11 +735,11 @@ def fit(self, X, y, sample_weight=None, coef_init=None, **params):
         n_terms = self.feat_ids_.shape[0]
         # Validate output_ids
         if self.output_ids is None:
-            self.output_ids_ = np.zeros(n_terms, dtype=int)
+            self.output_ids_ = np.zeros(n_terms, dtype=np.int32)
         else:
             self.output_ids_ = column_or_1d(
                 self.output_ids,
-                dtype=int,
+                dtype=np.int32,
                 warn=True,
             )
             if len(self.output_ids_) != n_terms:
@@ -806,7 +809,7 @@ def fit(self, X, y, sample_weight=None, coef_init=None, **params):
                     f"({(n_coef_intercept,)}), but got {coef_init.shape}."
                 )
 
-        cfd_ids = NARX._get_cfd_ids(
+        grad_yyd_ids, grad_coef_ids, grad_feat_ids, grad_delay_ids = NARX._get_cfd_ids(
             self.feat_ids_, self.delay_ids_, self.output_ids_, X.shape[1]
         )
         sample_weight_sqrt = np.sqrt(sample_weight).reshape(-1, 1)
@@ -815,14 +818,17 @@ def fit(self, X, y, sample_weight=None, coef_init=None, **params):
             x0=coef_init,
             jac=NARX._grad,
             args=(
-                NARX._expression,
+                _predict_step,
                 X,
                 y,
                 self.feat_ids_,
                 self.delay_ids_,
                 self.output_ids_,
                 sample_weight_sqrt,
-                cfd_ids,
+                grad_yyd_ids,
+                grad_coef_ids,
+                grad_feat_ids,
+                grad_delay_ids,
             ),
             **params,
         )
@@ -830,31 +836,16 @@ def fit(self, X, y, sample_weight=None, coef_init=None, **params):
         self.intercept_ = res.x[-self.n_outputs_ :]
         return self
 
-    @staticmethod
-    def _evaluate_term(feat_ids, delay_ids, X, y_hat, k):
-        n_features_in = X.shape[1]
-        term = 1
-        for i, feat_id in enumerate(feat_ids):
-            if feat_id != -1:
-                if feat_id < n_features_in:
-                    term *= X[k - delay_ids[i], feat_id]
-                else:
-                    term *= y_hat[k - delay_ids[i], feat_id - n_features_in]
-        return term
-
-    @staticmethod
-    def _expression(X, y_hat, coef, intercept, feat_ids, delay_ids, output_ids, k):
-        y_pred = np.copy(intercept)
-        for i, feat_id in enumerate(feat_ids):
-            output_i = output_ids[i]
-            y_pred[output_i] += coef[i] * NARX._evaluate_term(
-                feat_id, delay_ids[i], X, y_hat, k
-            )
-        return y_pred
-
     @staticmethod
     def _predict(
-        expression, X, y_ref, coef, intercept, feat_ids, delay_ids, output_ids
+        expression,
+        X,
+        y_ref,
+        coef,
+        intercept,
+        feat_ids,
+        delay_ids,
+        output_ids,
     ):
         n_samples = X.shape[0]
         n_ref, n_outputs = y_ref.shape
@@ -874,8 +865,16 @@ def _predict(
             if at_init:
                 y_hat[k] = y_ref[k % n_ref]
             else:
-                y_hat[k] = expression(
-                    X, y_hat, coef, intercept, feat_ids, delay_ids, output_ids, k
+                y_hat[k] = intercept
+                expression(
+                    X,
+                    y_hat,
+                    y_hat[k],
+                    coef,
+                    feat_ids,
+                    delay_ids,
+                    output_ids,
+                    k,
                 )
             if np.any(y_hat[k] > 1e20):
                 y_hat[k:] = 1e20
@@ -888,58 +887,50 @@ def _get_cfd_ids(feat_ids, delay_ids, output_ids, n_features_in):
         Get ids of CFD (Coef, Feature, and Delay) matrix to update dyn(k)/dx.
         Maps coefficients to their corresponding features and delays.
         """
-        n_outputs = np.max(output_ids) + 1
-        max_delay = np.max(delay_ids)
 
         # Initialize cfd_ids as a list of lists n_outputs *  n_outputs * max_delay
         # axis-0 (i): [dy0(k)/dx, dy1(k)/dx, ..., dyn(k)/dx]
         # axis-1 (j): [dy0(k-d)/dx, dy1(k-d)/dx, ..., dyn(k-d)/dx]
         # axis-2 (d): [dyj(k-1)/dx, dyj(k-2)/dx, ..., dyj(k-max_delay)/dx]
-        cfd_ids = [
-            [[[] for _ in range(max_delay)] for _ in range(n_outputs)]
-            for _ in range(n_outputs)
-        ]
+        grad_yyd_ids = []
+        grad_coef_ids = []
+        grad_feat_ids = []
+        grad_delay_ids = []
 
         for coef_id, (term_feat_ids, term_delay_ids) in enumerate(
             zip(feat_ids, delay_ids)
         ):
-            row_y_id = output_ids[coef_id]
+            row_y_id = output_ids[coef_id]  # y(k, id)
             for var_id, (feat_id, delay_id) in enumerate(
                 zip(term_feat_ids, term_delay_ids)
             ):
                 if feat_id >= n_features_in and delay_id > 0:
-                    col_y_id = feat_id - n_features_in
-                    cfd_ids[row_y_id][col_y_id][delay_id - 1].append(
-                        [
-                            coef_id,
-                            np.delete(term_feat_ids, var_id),
-                            np.delete(term_delay_ids, var_id),
-                        ]
-                    )
-
-        return cfd_ids
-
-    @staticmethod
-    def _update_cfd(X, y_hat, coef, cfd_ids, k):
-        """
-        Updates CFD matrix based on the current state.
-        """
-        n_outputs, max_delay = y_hat.shape[1], len(cfd_ids[0][0])
-        cfd = np.zeros((n_outputs, n_outputs, max_delay))
-
-        for i, yi_ids in enumerate(cfd_ids):
-            for j, yiyj in enumerate(yi_ids):
-                for d, yiyjd in enumerate(yiyj):
-                    if yiyjd:
-                        cfd[i, j, d] = sum(
-                            coef[coef_id]
-                            * NARX._evaluate_term(feat_id, delay_id, X, y_hat, k)
-                            for coef_id, feat_id, delay_id in yiyjd
-                        )
-        return cfd
+                    col_y_id = feat_id - n_features_in  # y(k-1, id)
+                    grad_yyd_ids.append([row_y_id, col_y_id, delay_id - 1])
+                    grad_coef_ids.append(coef_id)
+                    grad_feat_ids.append(np.delete(term_feat_ids, var_id))
+                    grad_delay_ids.append(np.delete(term_delay_ids, var_id))
+
+        return (
+            np.array(grad_yyd_ids, dtype=np.int32),
+            np.array(grad_coef_ids, dtype=np.int32),
+            np.array(grad_feat_ids, dtype=np.int32),
+            np.array(grad_delay_ids, dtype=np.int32),
+        )
 
     @staticmethod
-    def _update_dydx(X, y_hat, coef, feat_ids, delay_ids, output_ids, cfd_ids):
+    def _update_dydx(
+        X,
+        y_hat,
+        coef,
+        feat_ids,
+        delay_ids,
+        output_ids,
+        grad_yyd_ids,
+        grad_coef_ids,
+        grad_feat_ids,
+        grad_delay_ids,
+    ):
         """
         Computation of the Jacobian matrix dydx.
 
@@ -970,15 +961,32 @@ def _update_dydx(X, y_hat, coef, feat_ids, delay_ids, output_ids, cfd_ids):
                 continue
             # Compute terms for time step k
             terms = np.ones(n_x, dtype=float)
-            for j in range(n_coefs):
-                terms[j] = NARX._evaluate_term(feat_ids[j], delay_ids[j], X, y_hat, k)
+            _update_terms(
+                X,
+                y_hat,
+                terms,
+                feat_ids,
+                delay_ids,
+                k,
+            )
 
             # Update constant terms of Jacobian
             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:
-                cfd = NARX._update_cfd(X, y_hat, coef, cfd_ids, k)
+                _update_cfd(
+                    X,
+                    y_hat,
+                    cfd,
+                    coef,
+                    grad_yyd_ids,
+                    grad_coef_ids,
+                    grad_feat_ids,
+                    grad_delay_ids,
+                    k,
+                )
                 for d in range(max_delay):
                     dydx[k] += cfd[:, :, d] @ dydx[k - d - 1]
 
@@ -1007,7 +1015,14 @@ def _loss(
         intercept = coef_intercept[-n_outputs:]
 
         y_hat = NARX._predict(
-            expression, X, y, coef, intercept, feat_ids, delay_ids, output_ids
+            expression,
+            X,
+            y,
+            coef,
+            intercept,
+            feat_ids,
+            delay_ids,
+            output_ids,
         )
 
         y_masked, y_hat_masked, sample_weight_sqrt_masked = _mask_missing_value(
@@ -1026,7 +1041,10 @@ def _grad(
         delay_ids,
         output_ids,
         sample_weight_sqrt,
-        cfd_ids,
+        grad_yyd_ids,
+        grad_coef_ids,
+        grad_feat_ids,
+        grad_delay_ids,
     ):
         # Sum of squared errors
         n_outputs = y.shape[1]
@@ -1034,10 +1052,26 @@ def _grad(
         intercept = coef_intercept[-n_outputs:]
 
         y_hat = NARX._predict(
-            expression, X, y, coef, intercept, feat_ids, delay_ids, output_ids
+            expression,
+            X,
+            y,
+            coef,
+            intercept,
+            feat_ids,
+            delay_ids,
+            output_ids,
         )
         dydx = NARX._update_dydx(
-            X, y_hat, coef, feat_ids, delay_ids, output_ids, cfd_ids
+            X,
+            y_hat,
+            coef,
+            feat_ids,
+            delay_ids,
+            output_ids,
+            grad_yyd_ids,
+            grad_coef_ids,
+            grad_feat_ids,
+            grad_delay_ids,
         )
 
         mask_nomissing = _mask_missing_value(
@@ -1075,7 +1109,14 @@ def predict(self, X, y_init=None):
         """
         check_is_fitted(self)
 
-        X = validate_data(self, X, reset=False, ensure_all_finite="allow-nan")
+        X = validate_data(
+            self,
+            X,
+            dtype=float,
+            order="C",
+            reset=False,
+            ensure_all_finite="allow-nan",
+        )
         if y_init is None:
             y_init = np.zeros((self.max_delay_, self.n_outputs_))
         else:
@@ -1093,9 +1134,8 @@ def predict(self, X, y_init=None):
                     f"`y_init` should have {self.n_outputs_} outputs "
                     f"but got {y_init.shape[1]}."
                 )
-
         y_hat = NARX._predict(
-            NARX._expression,
+            _predict_step,
             X,
             y_init,
             self.coef_,
diff --git a/pixi.lock b/pixi.lock
index 8ed8c9e..c2ecfcd 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -37,7 +37,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/ncurses-6.5-h2d0b736_3.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/ninja-1.12.1-h297d8ca_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/numpy-2.2.4-py313h17eae1a_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/openssl-3.4.1-h7b32b05_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/openssl-3.5.0-h7b32b05_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/packaging-24.2-pyhd8ed1ab_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/pyproject-metadata-0.9.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/python-3.13.2-hf636f53_101_cp313.conda
@@ -57,11 +57,11 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/osx-64/ca-certificates-2025.1.31-h8857fd0_0.conda
       - conda: https://conda.anaconda.org/conda-forge/osx-64/cctools-1010.6-ha66f10e_6.conda
       - conda: https://conda.anaconda.org/conda-forge/osx-64/cctools_osx-64-1010.6-hd19c6af_6.conda
-      - conda: https://conda.anaconda.org/conda-forge/osx-64/clang-18-18.1.8-default_h3571c67_8.conda
-      - conda: https://conda.anaconda.org/conda-forge/osx-64/clang-18.1.8-default_h576c50e_8.conda
+      - conda: https://conda.anaconda.org/conda-forge/osx-64/clang-18-18.1.8-default_h3571c67_9.conda
+      - conda: https://conda.anaconda.org/conda-forge/osx-64/clang-18.1.8-default_h576c50e_9.conda
       - conda: https://conda.anaconda.org/conda-forge/osx-64/clang_impl_osx-64-18.1.8-h6a44ed1_24.conda
       - conda: https://conda.anaconda.org/conda-forge/osx-64/clang_osx-64-18.1.8-h7e5c614_24.conda
-      - conda: https://conda.anaconda.org/conda-forge/osx-64/clangxx-18.1.8-default_heb2e8d1_8.conda
+      - conda: https://conda.anaconda.org/conda-forge/osx-64/clangxx-18.1.8-default_heb2e8d1_9.conda
       - conda: https://conda.anaconda.org/conda-forge/osx-64/clangxx_impl_osx-64-18.1.8-h4b7810f_24.conda
       - conda: https://conda.anaconda.org/conda-forge/osx-64/clangxx_osx-64-18.1.8-h7e5c614_24.conda
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@@ -3472,35 +3456,35 @@ packages:
   - pkg:pypi/h2?source=hash-mapping
   size: 53888
   timestamp: 1738578623567
-- conda: https://conda.anaconda.org/conda-forge/linux-64/harfbuzz-11.0.0-h76408a6_0.conda
-  sha256: 9d33201d3e12a61d4ea4b1252a3468afb18b11a418f095dceffdf09bc6792f59
-  md5: 347cb348bfc8d77062daee11c326e518
+- conda: https://conda.anaconda.org/conda-forge/linux-64/harfbuzz-11.0.1-h2c12942_0.conda
+  sha256: 5013bfd767f7fa00e1cd103d76800c10542953f6dc5f225e538c7c35d5aaf1c7
+  md5: c90105cecb8bf8248f6666f1f5a40bbb
   depends:
   - __glibc >=2.17,<3.0.a0
   - cairo >=1.18.4,<2.0a0
   - freetype >=2.13.3,<3.0a0
   - graphite2
   - icu >=75.1,<76.0a0
-  - libexpat >=2.6.4,<3.0a0
+  - libexpat >=2.7.0,<3.0a0
   - libgcc >=13
-  - libglib >=2.84.0,<3.0a0
+  - libglib >=2.84.1,<3.0a0
   - libstdcxx >=13
   - libzlib >=1.3.1,<2.0a0
   license: MIT
   license_family: MIT
   purls: []
-  size: 1720702
-  timestamp: 1743082646624
-- conda: https://conda.anaconda.org/conda-forge/win-64/harfbuzz-11.0.0-h9e37d49_0.conda
-  sha256: f1ab5960a52a11186f528249bec5ce5e43bb4c44c87ffa24334255f07c3fd4b8
-  md5: b7648427f5b6797ae3904ad76e4c7f19
+  size: 2029831
+  timestamp: 1744033845291
+- conda: https://conda.anaconda.org/conda-forge/win-64/harfbuzz-11.0.1-h078c0c3_0.conda
+  sha256: a908178119ed98bdb1b46817be8c843416e10dd8f928148acd9ec861d611374a
+  md5: 81b86b68c534852535acc9c5cfce7469
   depends:
   - cairo >=1.18.4,<2.0a0
   - freetype >=2.13.3,<3.0a0
   - graphite2
   - icu >=75.1,<76.0a0
-  - libexpat >=2.6.4,<3.0a0
-  - libglib >=2.84.0,<3.0a0
+  - libexpat >=2.7.0,<3.0a0
+  - libglib >=2.84.1,<3.0a0
   - libzlib >=1.3.1,<2.0a0
   - ucrt >=10.0.20348.0
   - vc >=14.2,<15
@@ -3508,8 +3492,8 @@ packages:
   license: MIT
   license_family: MIT
   purls: []
-  size: 1125019
-  timestamp: 1743083466989
+  size: 1119818
+  timestamp: 1744035191347
 - conda: https://conda.anaconda.org/conda-forge/noarch/hpack-4.1.0-pyhd8ed1ab_0.conda
   sha256: 6ad78a180576c706aabeb5b4c8ceb97c0cb25f1e112d76495bff23e3779948ba
   md5: 0a802cb9888dd14eeefc611f05c40b6e
@@ -3731,9 +3715,9 @@ packages:
   - pkg:pypi/ipykernel?source=hash-mapping
   size: 119568
   timestamp: 1719845667420
-- conda: https://conda.anaconda.org/conda-forge/noarch/ipython-9.0.2-pyhca29cf9_0.conda
-  sha256: 72ad5d59719d7639641f21032de870fadd43ec2349229161728b736f1df720d1
-  md5: e5ba968166136311157765e8b2ccb9d0
+- conda: https://conda.anaconda.org/conda-forge/noarch/ipython-9.1.0-pyhca29cf9_0.conda
+  sha256: 330d452de42f10537bff1490f6ff08bf4e6c0c7288255be43f9e895e15dd2969
+  md5: 4f71690ae510b365a22bb1cb926e6df2
   depends:
   - __win
   - colorama
@@ -3753,12 +3737,12 @@ packages:
   license: BSD-3-Clause
   license_family: BSD
   purls:
-  - pkg:pypi/ipython?source=hash-mapping
-  size: 614763
-  timestamp: 1741457145171
-- conda: https://conda.anaconda.org/conda-forge/noarch/ipython-9.0.2-pyhfb0248b_0.conda
-  sha256: 98f14471e0f492d290c4882f1e2c313fffc67a0f9a3a36e699d7b0c5d42a5196
-  md5: b031bcd65b260a0a3353531eab50d465
+  - pkg:pypi/ipython?source=compressed-mapping
+  size: 619172
+  timestamp: 1744033183734
+- conda: https://conda.anaconda.org/conda-forge/noarch/ipython-9.1.0-pyhfb0248b_0.conda
+  sha256: 24cabcd711d03d2865a67ebc17941bc9bde949b3f0c9a34655c4153dce1c34c3
+  md5: b6c7f97b71c0f670dd9e585d3f65e867
   depends:
   - __unix
   - pexpect >4.3
@@ -3779,8 +3763,8 @@ packages:
   license_family: BSD
   purls:
   - pkg:pypi/ipython?source=hash-mapping
-  size: 615519
-  timestamp: 1741457126430
+  size: 619977
+  timestamp: 1744033187813
 - conda: https://conda.anaconda.org/conda-forge/noarch/ipython_pygments_lexers-1.1.1-pyhd8ed1ab_0.conda
   sha256: 894682a42a7d659ae12878dbcb274516a7031bbea9104e92f8e88c1f2765a104
   md5: bd80ba060603cc228d9d81c257093119
@@ -4720,9 +4704,9 @@ packages:
   purls: []
   size: 3733549
   timestamp: 1740088502127
-- conda: https://conda.anaconda.org/conda-forge/osx-64/libclang-cpp18.1-18.1.8-default_h3571c67_8.conda
-  sha256: 9e9af164c1ddfd114a786aceacf64df0041c3528a97cc96c06f3bf1040485e29
-  md5: 1444a2cd1f78fccea7dacb658f8aeb39
+- conda: https://conda.anaconda.org/conda-forge/osx-64/libclang-cpp18.1-18.1.8-default_h3571c67_9.conda
+  sha256: a3453cf08393f4a369a70795036d60dd8ea0de1efbf683594cbcaba49d8e3e74
+  md5: ef1a444913775b76f3391431967090a9
   depends:
   - __osx >=10.13
   - libcxx >=18.1.8
@@ -4730,11 +4714,11 @@ packages:
   license: Apache-2.0 WITH LLVM-exception
   license_family: Apache
   purls: []
-  size: 13905920
-  timestamp: 1742266347128
-- conda: https://conda.anaconda.org/conda-forge/osx-arm64/libclang-cpp18.1-18.1.8-default_hf90f093_8.conda
-  sha256: b736c4c3a32d4aa16b4af7b2094b4f3786ea34723cccb9918579206706000f90
-  md5: a5f883cd77dcc0f62a0eca8445d9e147
+  size: 13908110
+  timestamp: 1744061729284
+- conda: https://conda.anaconda.org/conda-forge/osx-arm64/libclang-cpp18.1-18.1.8-default_hf90f093_9.conda
+  sha256: 23eb5b180fadbe0b9a1d1aa123e44ef7ff774174b8a43fa40495c4ecc80f1328
+  md5: 88893bbbccb1400d677f747b0c8f226f
   depends:
   - __osx >=11.0
   - libcxx >=18.1.8
@@ -4742,8 +4726,8 @@ packages:
   license: Apache-2.0 WITH LLVM-exception
   license_family: Apache
   purls: []
-  size: 13330731
-  timestamp: 1742265504673
+  size: 13330734
+  timestamp: 1744062341062
 - conda: https://conda.anaconda.org/conda-forge/linux-64/libclang-cpp20.1-20.1.2-default_hb5137d0_0.conda
   sha256: d87e9fd20c05be07c236fd56ff1b559614648d4848d0ea9334221e71db55e556
   md5: 729198eae19e9dbf8e0ffe355d416bde
@@ -6621,9 +6605,9 @@ packages:
   license_family: MIT
   size: 10854
   timestamp: 1733230986902
-- conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-common-9.0.1-h266115a_5.conda
-  sha256: df9e895e8933ade7d362ab42bfe97e52a6b93d4d30df517324d60f6f35da1540
-  md5: 6cf2f0c19b0b7ff3d5349c9826c26a9e
+- conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-common-9.0.1-h266115a_6.conda
+  sha256: 9c2e3f9e9883e4b8d7e9e6abf7b235dc00bdcd5ef66640a360464a9f5756294d
+  md5: 94116b69829e90b72d566e64421e1bff
   depends:
   - __glibc >=2.17,<3.0.a0
   - libgcc >=13
@@ -6632,24 +6616,24 @@ packages:
   license: GPL-2.0-or-later
   license_family: GPL
   purls: []
-  size: 633439
-  timestamp: 1741896463089
-- conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-libs-9.0.1-he0572af_5.conda
-  sha256: f37303d2fb453bbc47d1e09d56ef06b20570d0eaf375115707ffc1e609c9b508
-  md5: d13932a2a61de7c0fb7864b592034a6e
+  size: 616215
+  timestamp: 1744124836761
+- conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-libs-9.0.1-he0572af_6.conda
+  sha256: 274467a602944d12722f757f660ad034de6f5f5d7d2ea1b913ef6fd836c1b8ce
+  md5: 9802ae6d20982f42c0f5d69008988763
   depends:
   - __glibc >=2.17,<3.0.a0
   - libgcc >=13
   - libstdcxx >=13
   - libzlib >=1.3.1,<2.0a0
-  - mysql-common 9.0.1 h266115a_5
+  - mysql-common 9.0.1 h266115a_6
   - openssl >=3.4.1,<4.0a0
   - zstd >=1.5.7,<1.6.0a0
   license: GPL-2.0-or-later
   license_family: GPL
   purls: []
-  size: 1371634
-  timestamp: 1741896565103
+  size: 1369369
+  timestamp: 1744124916632
 - conda: https://conda.anaconda.org/conda-forge/noarch/nbclient-0.10.2-pyhd8ed1ab_0.conda
   sha256: a20cff739d66c2f89f413e4ba4c6f6b59c50d5c30b5f0d840c13e8c9c2df9135
   md5: 6bb0d77277061742744176ab555b723c
@@ -6995,9 +6979,9 @@ packages:
   purls: []
   size: 784483
   timestamp: 1732674189726
-- conda: https://conda.anaconda.org/conda-forge/linux-64/openssl-3.4.1-h7b32b05_0.conda
-  sha256: cbf62df3c79a5c2d113247ddea5658e9ff3697b6e741c210656e239ecaf1768f
-  md5: 41adf927e746dc75ecf0ef841c454e48
+- conda: https://conda.anaconda.org/conda-forge/linux-64/openssl-3.5.0-h7b32b05_0.conda
+  sha256: 38285d280f84f1755b7c54baf17eccf2e3e696287954ce0adca16546b85ee62c
+  md5: bb539841f2a3fde210f387d00ed4bb9d
   depends:
   - __glibc >=2.17,<3.0.a0
   - ca-certificates
@@ -7005,33 +6989,33 @@ packages:
   license: Apache-2.0
   license_family: Apache
   purls: []
-  size: 2939306
-  timestamp: 1739301879343
-- conda: https://conda.anaconda.org/conda-forge/osx-64/openssl-3.4.1-hc426f3f_0.conda
-  sha256: 505a46671dab5d66df8e684f99a9ae735a607816b12810b572d63caa512224df
-  md5: a7d63f8e7ab23f71327ea6d27e2d5eae
+  size: 3121673
+  timestamp: 1744132167438
+- conda: https://conda.anaconda.org/conda-forge/osx-64/openssl-3.5.0-hc426f3f_0.conda
+  sha256: 7ee137b67f2de89d203e5ac2ebffd6d42252700005bf6af2bbf3dc11a9dfedbd
+  md5: e06e13c34056b6334a7a1188b0f4c83c
   depends:
   - __osx >=10.13
   - ca-certificates
   license: Apache-2.0
   license_family: Apache
   purls: []
-  size: 2591479
-  timestamp: 1739302628009
-- conda: https://conda.anaconda.org/conda-forge/osx-arm64/openssl-3.4.1-h81ee809_0.conda
-  sha256: 4f8e2389e1b711b44182a075516d02c80fa7a3a7e25a71ff1b5ace9eae57a17a
-  md5: 75f9f0c7b1740017e2db83a53ab9a28e
+  size: 2737547
+  timestamp: 1744140967264
+- conda: https://conda.anaconda.org/conda-forge/osx-arm64/openssl-3.5.0-h81ee809_0.conda
+  sha256: 53f825acb8d3e13bdad5c869f6dc7df931941450eea7f6473b955b0aaea1a399
+  md5: 3d2936da7e240d24c656138e07fa2502
   depends:
   - __osx >=11.0
   - ca-certificates
   license: Apache-2.0
   license_family: Apache
   purls: []
-  size: 2934522
-  timestamp: 1739301896733
-- conda: https://conda.anaconda.org/conda-forge/win-64/openssl-3.4.1-ha4e3fda_0.conda
-  sha256: 56dcc2b4430bfc1724e32661c34b71ae33a23a14149866fc5645361cfd3b3a6a
-  md5: 0730f8094f7088592594f9bf3ae62b3f
+  size: 3067649
+  timestamp: 1744132084304
+- conda: https://conda.anaconda.org/conda-forge/win-64/openssl-3.5.0-ha4e3fda_0.conda
+  sha256: 43dd7f56da142ca83c614c8b0085589650ae9032b351a901c190e48eefc73675
+  md5: 4ea7db75035eb8c13fa680bb90171e08
   depends:
   - ca-certificates
   - ucrt >=10.0.20348.0
@@ -7040,8 +7024,8 @@ packages:
   license: Apache-2.0
   license_family: Apache
   purls: []
-  size: 8515197
-  timestamp: 1739304103653
+  size: 8999138
+  timestamp: 1744135594688
 - conda: https://conda.anaconda.org/conda-forge/noarch/overrides-7.7.0-pyhd8ed1ab_1.conda
   sha256: 1840bd90d25d4930d60f57b4f38d4e0ae3f5b8db2819638709c36098c6ba770c
   md5: e51f1e4089cad105b6cac64bd8166587
diff --git a/tests/test_narx_jac.py b/tests/test_narx_jac.py
index 850b456..9405815 100644
--- a/tests/test_narx_jac.py
+++ b/tests/test_narx_jac.py
@@ -5,6 +5,7 @@
 from scipy.integrate import odeint
 from sklearn.metrics import r2_score
 
+from fastcan._narx_fast import _predict_step  # type: ignore
 from fastcan.narx import NARX, make_narx
 
 
@@ -18,16 +19,16 @@ def test_simple():
     X = np.array([1.5, 1.5, 1.5]).reshape(-1, 1)
     y = np.array([1, 2.9, 3.66]).reshape(-1, 1)
 
-    feat_ids = np.array([1, 0]).reshape(-1, 1)
-    delay_ids = np.array([1, 1]).reshape(-1, 1)
-    output_ids = np.array([0, 0])
+    feat_ids = np.array([1, 0], dtype=np.int32).reshape(-1, 1)
+    delay_ids = np.array([1, 1], dtype=np.int32).reshape(-1, 1)
+    output_ids = np.array([0, 0], dtype=np.int32)
     coef = np.array([0.4, 1])
     intercept = np.array([1], dtype=float)
     sample_weight = np.array([1, 1, 1], dtype=float)
 
 
     y_hat = NARX._predict(
-        NARX._expression,
+        _predict_step,
         X=X,
         y_ref=y,
         coef=coef,
@@ -43,7 +44,7 @@ def test_simple():
     coef_1 = np.array([0.4+delta_w, 1])
 
     y_hat_1 = NARX._predict(
-        NARX._expression,
+        _predict_step,
         X=X,
         y_ref=y,
         coef=coef_1,
@@ -60,17 +61,22 @@ def test_simple():
     ])
 
 
-    cfd_ids = NARX._get_cfd_ids(feat_ids, delay_ids, output_ids, 1)
+    grad_yyd_ids, grad_coef_ids, grad_feat_ids, grad_delay_ids = NARX._get_cfd_ids(
+        feat_ids, delay_ids, output_ids, 1
+    )
     grad = NARX._grad(
         np.r_[coef_1, intercept],
-        NARX._expression,
+        _predict_step,
         X,
         y,
         feat_ids,
         delay_ids,
         output_ids,
-        sample_weight_sqrt=np.sqrt(sample_weight),
-        cfd_ids=cfd_ids,
+        np.sqrt(sample_weight),
+        grad_yyd_ids,
+        grad_coef_ids,
+        grad_feat_ids,
+        grad_delay_ids,
     )
 
     assert_almost_equal(grad.sum(axis=0), grad_truth, decimal=4)
@@ -117,7 +123,8 @@ def test_complex():
             [2, 3],
             [1, 1],
             [1, 0],
-        ]
+        ],
+        dtype=np.int32
     )
 
     delay_ids = np.array(
@@ -131,10 +138,11 @@ def test_complex():
             [1, 2],
             [0, 0],
             [2, 3],
-        ]
+        ],
+        dtype=np.int32
     )
 
-    output_ids = np.array([0, 0, 0, 0, 0, 1, 1, 1, 1])
+    output_ids = np.array([0, 0, 0, 0, 0, 1, 1, 1, 1], dtype=np.int32)
 
     coef = np.array(
         [
@@ -153,22 +161,27 @@ def test_complex():
     intercept = np.array([1, 0.5])
 
     # NARX Jacobian
-    cfd_ids = NARX._get_cfd_ids(feat_ids, delay_ids, output_ids, X.shape[1])
+    grad_yyd_ids, grad_coef_ids, grad_feat_ids, grad_delay_ids = NARX._get_cfd_ids(
+        feat_ids, delay_ids, output_ids, X.shape[1]
+    )
     grad = NARX._grad(
         np.r_[coef, intercept],
-        NARX._expression,
+        _predict_step,
         X,
         y,
         feat_ids,
         delay_ids,
         output_ids,
-        sample_weight_sqrt=np.sqrt(np.ones((y.shape[0], 1))),
-        cfd_ids=cfd_ids,
+        np.sqrt(np.ones((y.shape[0], 1))),
+        grad_yyd_ids,
+        grad_coef_ids,
+        grad_feat_ids,
+        grad_delay_ids,
     )
 
     # Numerical gradient
     y_hat_0 = NARX._predict(
-        NARX._expression,
+        _predict_step,
         X=X,
         y_ref=y,
         coef=coef,
@@ -191,7 +204,7 @@ def test_complex():
             intercept_1[i-len(coef)] += delta_w
 
         y_hat_1 = NARX._predict(
-            NARX._expression,
+            _predict_step,
             X=X,
             y_ref=y,
             coef=coef_1,

From 74ed9b20aa98d16c49d10a9c7532a42bffb90d30 Mon Sep 17 00:00:00 2001
From: SIKAI ZHANG <34108862+MatthewSZhang@users.noreply.github.com>
Date: Wed, 9 Apr 2025 16:23:25 +0800
Subject: [PATCH 2/3] MNT fix time-narx put all code in setup and timing empty

---
 pixi.lock      | 2 +-
 pyproject.toml | 6 +++---
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/pixi.lock b/pixi.lock
index c2ecfcd..5717f3b 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -3034,7 +3034,7 @@ packages:
 - pypi: .
   name: fastcan
   version: 0.3.2
-  sha256: 91dc839be1251db991da3b261369f5f145a325c33fc7a7f2b08dc9f56cda574a
+  sha256: 47bb0010fe7a5d9799f463daa4ad6f2e5b26021750c245afd3ff45c84f72895e
   requires_dist:
   - scikit-learn>=1.6.0
   - furo ; extra == 'docs'
diff --git a/pyproject.toml b/pyproject.toml
index 8b03d29..629ae6e 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -92,10 +92,10 @@ compilers = "*"
 compilers = "*"
 
 [tool.pixi.tasks]
-time-h = "python -m timeit -n 5 -s 'import numpy as np; from fastcan import FastCan; X = np.random.rand(3000, 100); y = np.random.rand(3000, 20); s = FastCan(100, verbose=0).fit(X, y)'"
-time-eta = "python -m timeit -n 5 -s 'import numpy as np; from fastcan import FastCan; X = np.random.rand(3000, 100); y = np.random.rand(3000, 20); s = FastCan(100, eta=True, verbose=0).fit(X, y)'"
+time-h = "python -m timeit -n 5 -s 'import numpy as np; from fastcan import FastCan; X = np.random.rand(3000, 100); y = np.random.rand(3000, 20)' 's = FastCan(100, verbose=0).fit(X, y)'"
+time-eta = "python -m timeit -n 5 -s 'import numpy as np; from fastcan import FastCan; X = np.random.rand(3000, 100); y = np.random.rand(3000, 20)' 's = FastCan(100, eta=True, verbose=0).fit(X, y)'"
 profile-minibatch = { cmd = '''python -c "import cProfile; import numpy as np; from fastcan import minibatch; X = np.random.rand(100, 3000); y = np.random.rand(100, 20); cProfile.run('minibatch(X, y, 1000, 10, verbose=0)', sort='$SORT')"''', env = { SORT = "cumtime" } }
-time-narx = '''python -m timeit -n 1 -s "import numpy as np; from fastcan.narx import make_narx; rng = np.random.default_rng(5); X = rng.random((1000, 10)); y = rng.random((1000, 2)); s = make_narx(X, y, 10, max_delay=2, poly_degree=2, verbose=0).fit(X, y, coef_init='one_step_ahead', verbose=1)"'''
+time-narx = '''python -m timeit -n 1 -s "import numpy as np; from fastcan.narx import make_narx; rng = np.random.default_rng(5); X = rng.random((1000, 10)); y = rng.random((1000, 2)); m = make_narx(X, y, 10, max_delay=2, poly_degree=2, verbose=0)" "m.fit(X, y, coef_init='one_step_ahead', verbose=1)"'''
 
 [tool.pixi.feature.test.tasks]
 test = { cmd = "pytest", cwd = "tests" }

From b96534ea560a531ccedf3dd73b66b4b010cfa63f Mon Sep 17 00:00:00 2001
From: SIKAI ZHANG <34108862+MatthewSZhang@users.noreply.github.com>
Date: Wed, 9 Apr 2025 16:32:12 +0800
Subject: [PATCH 3/3] MNT fix nogil-h, nogil-eta put all code in setup and
 timing empty

---
 pixi.lock      | 2 +-
 pyproject.toml | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/pixi.lock b/pixi.lock
index 5717f3b..87d8e2c 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -3034,7 +3034,7 @@ packages:
 - pypi: .
   name: fastcan
   version: 0.3.2
-  sha256: 47bb0010fe7a5d9799f463daa4ad6f2e5b26021750c245afd3ff45c84f72895e
+  sha256: e5bb5ff118a28f9e719f00a46fa3048c6d70304835a57046fbc32f79ec576a05
   requires_dist:
   - scikit-learn>=1.6.0
   - furo ; extra == 'docs'
diff --git a/pyproject.toml b/pyproject.toml
index 629ae6e..144a2f7 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -121,10 +121,10 @@ doc-clean = { cmd = "rm -rf $BUILDDIR generated auto_examples", cwd = "doc", env
 
 [tool.pixi.feature.nogil.tasks]
 nogil-build = { cmd = "pip install --editable . --verbose --no-build-isolation --config-settings editable-verbose=true" }
-nogil-h = { cmd = "python -Xgil=0 -m timeit -n 5 -s 'import numpy as np; from fastcan import FastCan; X = np.random.rand(3000, 100); y = np.random.rand(3000, 20); s = FastCan(100, verbose=0).fit(X, y)'", depends-on = [
+nogil-h = { cmd = "python -Xgil=0 -m timeit -n 5 -s 'import numpy as np; from fastcan import FastCan; X = np.random.rand(3000, 100); y = np.random.rand(3000, 20)' 's = FastCan(100, verbose=0).fit(X, y)'", depends-on = [
     "nogil-build",
 ] }
-nogil-eta = { cmd = "python -Xgil=0 -m timeit -n 5 -s 'import numpy as np; from fastcan import FastCan; X = np.random.rand(3000, 100); y = np.random.rand(3000, 20); s = FastCan(100, eta=True, verbose=0).fit(X, y)'", depends-on = [
+nogil-eta = { cmd = "python -Xgil=0 -m timeit -n 5 -s 'import numpy as np; from fastcan import FastCan; X = np.random.rand(3000, 100); y = np.random.rand(3000, 20)' 's = FastCan(100, eta=True, verbose=0).fit(X, y)'", depends-on = [
     "nogil-build",
 ] }