From 727a676cb8bccc0679b7516d88c73d01fdc346ec Mon Sep 17 00:00:00 2001
From: SIKAI ZHANG <34108862+MatthewSZhang@users.noreply.github.com>
Date: Thu, 10 Apr 2025 16:41:12 +0800
Subject: [PATCH] MNT output proper constant when some outputs only have
 intercepts

---
 fastcan/narx.py    |   8 +-
 pixi.lock          | 234 ++++++++++++++++-----------------------------
 tests/test_narx.py |  44 +++++++--
 3 files changed, 124 insertions(+), 162 deletions(-)

diff --git a/fastcan/narx.py b/fastcan/narx.py
index f5299f7..e65ebd9 100644
--- a/fastcan/narx.py
+++ b/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,
diff --git a/pixi.lock b/pixi.lock
index 87d8e2c..761afa4 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -329,7 +329,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_events-0.12.0-pyh29332c3_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_server-2.15.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_server_terminals-0.5.3-pyhd8ed1ab_1.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-4.3.6-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-4.4.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_pygments-0.3.0-pyhd8ed1ab_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_server-2.27.3-pyhd8ed1ab_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/keyutils-1.6.1-h166bdaf_0.tar.bz2
@@ -393,15 +393,15 @@ environments:
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       - conda: https://conda.anaconda.org/conda-forge/noarch/mistune-3.1.3-pyh29332c3_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/munkres-1.1.4-pyh9f0ad1d_0.tar.bz2
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-common-9.0.1-h266115a_6.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-libs-9.0.1-he0572af_6.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-common-9.2.0-h266115a_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-libs-9.2.0-he0572af_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/nbclient-0.10.2-pyhd8ed1ab_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/noarch/nbformat-5.10.4-pyhd8ed1ab_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/ncurses-6.5-h2d0b736_3.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/nest-asyncio-1.6.0-pyhd8ed1ab_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/ninja-1.12.1-h297d8ca_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-7.3.3-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-7.4.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-shim-0.2.4-pyhd8ed1ab_1.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/openjpeg-2.5.3-h5fbd93e_0.conda
@@ -446,7 +446,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/pyyaml-6.0.2-py313h8060acc_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/pyzmq-26.4.0-py313h8e95178_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/qhull-2020.2-h434a139_5.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/qt6-main-6.9.0-h6441bc3_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/qt6-main-6.9.0-h6441bc3_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/readline-8.2-h8c095d6_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/referencing-0.36.2-pyh29332c3_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/requests-2.32.3-pyhd8ed1ab_1.conda
@@ -611,7 +611,7 @@ environments:
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       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_server-2.15.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_server_terminals-0.5.3-pyhd8ed1ab_1.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-4.3.6-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-4.4.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_pygments-0.3.0-pyhd8ed1ab_2.conda
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       - conda: https://conda.anaconda.org/conda-forge/osx-64/kiwisolver-1.4.7-py313h0c4e38b_0.conda
@@ -669,7 +669,7 @@ environments:
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       - conda: https://conda.anaconda.org/conda-forge/osx-64/ninja-1.12.1-h3c5361c_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-7.3.3-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-7.4.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-shim-0.2.4-pyhd8ed1ab_1.conda
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       - conda: https://conda.anaconda.org/conda-forge/osx-64/openjpeg-2.5.3-h7fd6d84_0.conda
@@ -857,7 +857,7 @@ environments:
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       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_server_terminals-0.5.3-pyhd8ed1ab_1.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-4.3.6-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-4.4.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_pygments-0.3.0-pyhd8ed1ab_2.conda
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@@ -915,7 +915,7 @@ environments:
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+      - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-7.4.0-pyhd8ed1ab_0.conda
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@@ -1097,7 +1097,7 @@ environments:
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-      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-4.3.6-pyhd8ed1ab_0.conda
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@@ -1147,7 +1147,7 @@ environments:
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-      - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-7.3.3-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-7.4.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-shim-0.2.4-pyhd8ed1ab_1.conda
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@@ -1191,7 +1191,7 @@ environments:
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@@ -1299,31 +1299,32 @@ environments:
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       osx-64:
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@@ -1787,21 +1788,6 @@ packages:
   license_family: MIT
   size: 172678
   timestamp: 1742502887437
-- conda: https://conda.anaconda.org/conda-forge/osx-64/black-25.1.0-py312hb401068_0.conda
-  sha256: e937f18e36e23ecf0ec9ab89fc3ef5263308e88b645c4278fe8807fd95bef4c1
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-  - python_abi 3.12.* *_cp312
-  license: MIT
-  license_family: MIT
-  size: 393484
-  timestamp: 1738616259890
 - conda: https://conda.anaconda.org/conda-forge/noarch/bleach-6.2.0-pyh29332c3_4.conda
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@@ -2807,18 +2793,6 @@ packages:
   - pkg:pypi/cython?source=hash-mapping
   size: 3766349
   timestamp: 1739228643862
-- conda: https://conda.anaconda.org/conda-forge/osx-64/cython-3.0.12-py312hdfbeeba_0.conda
-  sha256: a186d286aedb2230dcdcaf2a8602c098112eaacdf9d8af39da2a474950bf1b98
-  md5: 5801a15eece1bd00c7f6dc0c68640a9f
-  depends:
-  - __osx >=10.13
-  - libcxx >=18
-  - python >=3.12,<3.13.0a0
-  - python_abi 3.12.* *_cp312
-  license: Apache-2.0
-  license_family: APACHE
-  size: 3455381
-  timestamp: 1739228540351
 - conda: https://conda.anaconda.org/conda-forge/osx-64/cython-3.0.12-py313h9efc8c2_0.conda
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   md5: ddace7cae5c3073c031ad08ef01881da
@@ -4081,9 +4055,9 @@ packages:
   - pkg:pypi/jupyter-server-terminals?source=hash-mapping
   size: 19711
   timestamp: 1733428049134
-- conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-4.3.6-pyhd8ed1ab_0.conda
-  sha256: cf10c9b4158c4ef2796fde546f2bbe45f43c1402a0c2a175939ebbb308846ada
-  md5: 8b91a10c966aa65b9ad1a2702e6ef121
+- conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-4.4.0-pyhd8ed1ab_0.conda
+  sha256: 4d225d094d1e5a8e95c2bde0f9c9bbc5aac52d9abf7fd597dd7af0f467b44347
+  md5: 2da6a5e2c788a1b1998b24c50a18572a
   depends:
   - async-lru >=1.0.0
   - httpx >=0.25.0
@@ -4097,7 +4071,7 @@ packages:
   - notebook-shim >=0.2
   - packaging
   - python >=3.9
-  - setuptools >=40.8.0
+  - setuptools >=41.1.0
   - tomli >=1.2.2
   - tornado >=6.2.0
   - traitlets
@@ -4105,8 +4079,8 @@ packages:
   license_family: BSD
   purls:
   - pkg:pypi/jupyterlab?source=compressed-mapping
-  size: 7641308
-  timestamp: 1741964212957
+  size: 8402007
+  timestamp: 1743711353203
 - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_pygments-0.3.0-pyhd8ed1ab_2.conda
   sha256: dc24b900742fdaf1e077d9a3458fd865711de80bca95fe3c6d46610c532c6ef0
   md5: fd312693df06da3578383232528c468d
@@ -6551,20 +6525,20 @@ packages:
   license_family: MIT
   size: 17058016
   timestamp: 1738767732637
-- conda: https://conda.anaconda.org/conda-forge/osx-64/mypy-1.15.0-py312h01d7ebd_0.conda
-  sha256: 38132c4b5de6686965f21b51a1656438e83b2a53d6f50e9589e73fb57a43dd49
-  md5: 0251bb4d6702b729b06fd5c7918e9242
+- conda: https://conda.anaconda.org/conda-forge/osx-64/mypy-1.15.0-py313h63b0ddb_0.conda
+  sha256: ec50dc7be70eff5008d73b4bd29fba72e02e499e9b60060a49ece4c1e12a9d55
+  md5: e9dc60a2c2c62f4d2e24f61603f00bdc
   depends:
   - __osx >=10.13
   - mypy_extensions >=1.0.0
   - psutil >=4.0
-  - python >=3.12,<3.13.0a0
-  - python_abi 3.12.* *_cp312
+  - python >=3.13,<3.14.0a0
+  - python_abi 3.13.* *_cp313
   - typing_extensions >=4.1.0
   license: MIT
   license_family: MIT
-  size: 12384787
-  timestamp: 1738768017667
+  size: 11022410
+  timestamp: 1738768159908
 - conda: https://conda.anaconda.org/conda-forge/osx-arm64/mypy-1.15.0-py313h90d716c_0.conda
   sha256: 4dc7a5a30017c742c204311afd078c639ca434b7f44835dfba789a5fb972ea6c
   md5: d01a9742c8e3c425d3c3d5e412a43872
@@ -6605,9 +6579,9 @@ packages:
   license_family: MIT
   size: 10854
   timestamp: 1733230986902
-- conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-common-9.0.1-h266115a_6.conda
-  sha256: 9c2e3f9e9883e4b8d7e9e6abf7b235dc00bdcd5ef66640a360464a9f5756294d
-  md5: 94116b69829e90b72d566e64421e1bff
+- conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-common-9.2.0-h266115a_0.conda
+  sha256: 571b6a2bffaf186ab92cdb06852fc5b6b5b7c6605de2b397fb13cfb0bb05c375
+  md5: db22a0962c953e81a2a679ecb1fc6027
   depends:
   - __glibc >=2.17,<3.0.a0
   - libgcc >=13
@@ -6616,24 +6590,24 @@ packages:
   license: GPL-2.0-or-later
   license_family: GPL
   purls: []
-  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
+  size: 653477
+  timestamp: 1743939199519
+- conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-libs-9.2.0-he0572af_0.conda
+  sha256: 41cd870c04961591eabe7a43283d2bbc80a382e007f766edb8396ffd2bdfa418
+  md5: 93340b072c393d23c4700a1d40565dca
   depends:
   - __glibc >=2.17,<3.0.a0
   - libgcc >=13
   - libstdcxx >=13
   - libzlib >=1.3.1,<2.0a0
-  - mysql-common 9.0.1 h266115a_6
+  - mysql-common 9.2.0 h266115a_0
   - openssl >=3.4.1,<4.0a0
   - zstd >=1.5.7,<1.6.0a0
   license: GPL-2.0-or-later
   license_family: GPL
   purls: []
-  size: 1369369
-  timestamp: 1744124916632
+  size: 1371585
+  timestamp: 1743939293417
 - conda: https://conda.anaconda.org/conda-forge/noarch/nbclient-0.10.2-pyhd8ed1ab_0.conda
   sha256: a20cff739d66c2f89f413e4ba4c6f6b59c50d5c30b5f0d840c13e8c9c2df9135
   md5: 6bb0d77277061742744176ab555b723c
@@ -6778,13 +6752,12 @@ packages:
   purls: []
   size: 285150
   timestamp: 1715441052517
-- conda: https://conda.anaconda.org/conda-forge/noarch/notebook-7.3.3-pyhd8ed1ab_0.conda
-  sha256: 5086c70ff352a72b9d47fcf73d37a1be583cf5b416c9729295a9b3710330d781
-  md5: 3b04a08fc654590f45e0a713982f898b
+- conda: https://conda.anaconda.org/conda-forge/noarch/notebook-7.4.0-pyhd8ed1ab_0.conda
+  sha256: d3f70987bc1e1a20b122726a49a24e5e6f09d00c9862bb399cd1682cd59a1e1e
+  md5: 7e82caa4495c513bcfb33a159e1222d4
   depends:
-  - importlib_resources >=5.0
   - jupyter_server >=2.4.0,<3
-  - jupyterlab >=4.3.6,<4.4
+  - jupyterlab >=4.4.0,<4.5
   - jupyterlab_server >=2.27.1,<3
   - notebook-shim >=0.2,<0.3
   - python >=3.9
@@ -6793,8 +6766,8 @@ packages:
   license_family: BSD
   purls:
   - pkg:pypi/notebook?source=hash-mapping
-  size: 9705127
-  timestamp: 1741968301453
+  size: 10473675
+  timestamp: 1744236307330
 - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-shim-0.2.4-pyhd8ed1ab_1.conda
   sha256: 7b920e46b9f7a2d2aa6434222e5c8d739021dbc5cc75f32d124a8191d86f9056
   md5: e7f89ea5f7ea9401642758ff50a2d9c1
@@ -7403,17 +7376,6 @@ packages:
   - pkg:pypi/psutil?source=hash-mapping
   size: 475101
   timestamp: 1740663284505
-- conda: https://conda.anaconda.org/conda-forge/osx-64/psutil-7.0.0-py312h01d7ebd_0.conda
-  sha256: bdfa40a1ef3a80c3bec425a5ed507ebda2bdebce2a19bccb000db9d5c931750c
-  md5: fcad6b89f4f7faa999fa4d887eab14ba
-  depends:
-  - __osx >=10.13
-  - python >=3.12,<3.13.0a0
-  - python_abi 3.12.* *_cp312
-  license: BSD-3-Clause
-  license_family: BSD
-  size: 473946
-  timestamp: 1740663466925
 - conda: https://conda.anaconda.org/conda-forge/osx-64/psutil-7.0.0-py313h63b0ddb_0.conda
   sha256: b117f61eaf3d5fb640d773c3021f222c833a69c2ac123d7f4b028b3e5d638dd4
   md5: 2c8969aaee2cf24bc8931f5fc36cccfd
@@ -7807,28 +7769,6 @@ packages:
   size: 33233150
   timestamp: 1739803603242
   python_site_packages_path: lib/python3.13/site-packages
-- conda: https://conda.anaconda.org/conda-forge/osx-64/python-3.12.9-h9ccd52b_1_cpython.conda
-  build_number: 1
-  sha256: c394f7068a714cad7853992f18292bb34c6d99fe7c21025664b05069c86b9450
-  md5: b878567b6b749f993dbdbc2834115bc3
-  depends:
-  - __osx >=10.13
-  - bzip2 >=1.0.8,<2.0a0
-  - libexpat >=2.6.4,<3.0a0
-  - libffi >=3.4,<4.0a0
-  - liblzma >=5.6.4,<6.0a0
-  - libsqlite >=3.49.1,<4.0a0
-  - libzlib >=1.3.1,<2.0a0
-  - ncurses >=6.5,<7.0a0
-  - openssl >=3.4.1,<4.0a0
-  - readline >=8.2,<9.0a0
-  - tk >=8.6.13,<8.7.0a0
-  - tzdata
-  constrains:
-  - python_abi 3.12.* *_cp312
-  license: Python-2.0
-  size: 13833024
-  timestamp: 1741129416409
 - conda: https://conda.anaconda.org/conda-forge/osx-64/python-3.13.2-h2267d90_1_cp313t.conda
   build_number: 1
   sha256: 95abaeed4b827aa209f89a2fa18e219c89b913a82510f0fbe729ef2e04a68b7d
@@ -8072,16 +8012,6 @@ packages:
   purls: []
   size: 6858
   timestamp: 1743483201023
-- conda: https://conda.anaconda.org/conda-forge/osx-64/python_abi-3.12-6_cp312.conda
-  build_number: 6
-  sha256: abbe800dc60cfe459be68a4f3fd946b09ae573c586efb3396ee48634ee3723ad
-  md5: e6096b1328952bbe07342f8927940ea9
-  constrains:
-  - python 3.12.* *_cpython
-  license: BSD-3-Clause
-  license_family: BSD
-  size: 6929
-  timestamp: 1743483235505
 - conda: https://conda.anaconda.org/conda-forge/osx-64/python_abi-3.13-5_cp313t.conda
   build_number: 5
   sha256: a96553de64be6441400e88c2c6ad7123d91cbcea4898b5966a653163f30d9f55
@@ -8359,9 +8289,9 @@ packages:
   purls: []
   size: 1377020
   timestamp: 1720814433486
-- conda: https://conda.anaconda.org/conda-forge/linux-64/qt6-main-6.9.0-h6441bc3_0.conda
-  sha256: 5f04a118f6f4124bf0f3a7b7ca2510954860c764db8c25a62bcfa91f51693073
-  md5: d3df16592e15a3f833cfc4d19ae58677
+- conda: https://conda.anaconda.org/conda-forge/linux-64/qt6-main-6.9.0-h6441bc3_1.conda
+  sha256: 0485df0e29daf02023b98b0d7f5f4f97bd23650582d8c64d80f22cdb1ad01676
+  md5: 4029a8dcb1d97ea241dbe5abfda1fad6
   depends:
   - __glibc >=2.17,<3.0.a0
   - alsa-lib >=1.2.13,<1.3.0a0
@@ -8370,19 +8300,19 @@ packages:
   - fontconfig >=2.15.0,<3.0a0
   - fonts-conda-ecosystem
   - freetype >=2.13.3,<3.0a0
-  - harfbuzz >=11.0.0,<12.0a0
+  - harfbuzz >=11.0.1
   - icu >=75.1,<76.0a0
   - krb5 >=1.21.3,<1.22.0a0
-  - libclang-cpp20.1 >=20.1.1,<20.2.0a0
-  - libclang13 >=20.1.1
+  - libclang-cpp20.1 >=20.1.2,<20.2.0a0
+  - libclang13 >=20.1.2
   - libcups >=2.3.3,<2.4.0a0
   - libdrm >=2.4.124,<2.5.0a0
   - libegl >=1.7.0,<2.0a0
   - libgcc >=13
   - libgl >=1.7.0,<2.0a0
-  - libglib >=2.84.0,<3.0a0
+  - libglib >=2.84.1,<3.0a0
   - libjpeg-turbo >=3.0.0,<4.0a0
-  - libllvm20 >=20.1.1,<20.2.0a0
+  - libllvm20 >=20.1.2,<20.2.0a0
   - libpng >=1.6.47,<1.7.0a0
   - libpq >=17.4,<18.0a0
   - libsqlite >=3.49.1,<4.0a0
@@ -8393,8 +8323,8 @@ packages:
   - libxkbcommon >=1.8.1,<2.0a0
   - libxml2 >=2.13.7,<2.14.0a0
   - libzlib >=1.3.1,<2.0a0
-  - mysql-libs >=9.0.1,<9.1.0a0
-  - openssl >=3.4.1,<4.0a0
+  - mysql-libs >=9.2.0,<9.3.0a0
+  - openssl >=3.5.0,<4.0a0
   - pcre2 >=10.44,<10.45.0a0
   - wayland >=1.23.1,<2.0a0
   - xcb-util >=0.4.1,<0.5.0a0
@@ -8419,25 +8349,25 @@ packages:
   license: LGPL-3.0-only
   license_family: LGPL
   purls: []
-  size: 51884819
-  timestamp: 1743632133306
-- conda: https://conda.anaconda.org/conda-forge/win-64/qt6-main-6.9.0-h83cda92_0.conda
-  sha256: 84ff37de3c72a612dfbf9b317d5501231a87582f2edf4959ff706b84b4aa9246
-  md5: d92e5a0de3263315551d54d5574f5193
+  size: 51522155
+  timestamp: 1744201848686
+- conda: https://conda.anaconda.org/conda-forge/win-64/qt6-main-6.9.0-h83cda92_1.conda
+  sha256: 40bb84f5898e60dd7ee27a504c0403ea5dae514ce0638b763bb00ff4d73ab611
+  md5: 412f970fc305449b6ee626fe9c6638a8
   depends:
   - double-conversion >=3.3.1,<3.4.0a0
-  - harfbuzz >=11.0.0,<12.0a0
+  - harfbuzz >=11.0.1
   - icu >=75.1,<76.0a0
   - krb5 >=1.21.3,<1.22.0a0
-  - libclang13 >=20.1.1
-  - libglib >=2.84.0,<3.0a0
+  - libclang13 >=20.1.2
+  - libglib >=2.84.1,<3.0a0
   - libjpeg-turbo >=3.0.0,<4.0a0
   - libpng >=1.6.47,<1.7.0a0
   - libsqlite >=3.49.1,<4.0a0
   - libtiff >=4.7.0,<4.8.0a0
   - libwebp-base >=1.5.0,<2.0a0
   - libzlib >=1.3.1,<2.0a0
-  - openssl >=3.4.1,<4.0a0
+  - openssl >=3.5.0,<4.0a0
   - pcre2 >=10.44,<10.45.0a0
   - ucrt >=10.0.20348.0
   - vc >=14.3,<15
@@ -8448,8 +8378,8 @@ packages:
   license: LGPL-3.0-only
   license_family: LGPL
   purls: []
-  size: 94992566
-  timestamp: 1743635306726
+  size: 94780444
+  timestamp: 1744204470975
 - conda: https://conda.anaconda.org/conda-forge/linux-64/readline-8.2-h8c095d6_2.conda
   sha256: 2d6d0c026902561ed77cd646b5021aef2d4db22e57a5b0178dfc669231e06d2c
   md5: 283b96675859b20a825f8fa30f311446
@@ -8626,20 +8556,20 @@ packages:
   license_family: MIT
   size: 9001038
   timestamp: 1743819292575
-- conda: https://conda.anaconda.org/conda-forge/osx-64/ruff-0.11.4-py312h60e8e2e_0.conda
-  sha256: 6f2a267f074d65a8b198971c0f55648be9d5a36e9b77cc7f201b7011125d20a1
-  md5: 5ac88d878ce5ec735befa59dce14d0bf
+- conda: https://conda.anaconda.org/conda-forge/osx-64/ruff-0.11.4-py313h837c616_0.conda
+  sha256: 6eeb0acc7868ac46186e8317154df5403d19687665114fced5aae45c522e8d00
+  md5: 164585e6a4b12fd29517c940602c265d
   depends:
   - __osx >=10.13
   - libcxx >=18
-  - python >=3.12,<3.13.0a0
-  - python_abi 3.12.* *_cp312
+  - python >=3.13,<3.14.0a0
+  - python_abi 3.13.* *_cp313
   constrains:
   - __osx >=10.13
   license: MIT
   license_family: MIT
-  size: 8403708
-  timestamp: 1743820004397
+  size: 8406832
+  timestamp: 1743819610560
 - conda: https://conda.anaconda.org/conda-forge/osx-arm64/ruff-0.11.4-py313hd3a9b03_0.conda
   sha256: 7b7fe29220adb5b40210956dd25e05b77ce3e1a3eb89e5c867724d74eb4e8d01
   md5: 4543a37cc5e13195d08611d1a154c38f
@@ -8722,7 +8652,7 @@ packages:
   - ruff>=0.11.0 ; extra == 'tests'
   - black>=24.3.0 ; extra == 'tests'
   - mypy>=1.15 ; extra == 'tests'
-  - pyamg>=5.0.0 ; extra == 'tests'
+  - pyamg>=4.2.1 ; extra == 'tests'
   - polars>=0.20.30 ; extra == 'tests'
   - pyarrow>=12.0.0 ; extra == 'tests'
   - numpydoc>=1.2.0 ; extra == 'tests'
@@ -8783,7 +8713,7 @@ packages:
   - ruff>=0.11.0 ; extra == 'tests'
   - black>=24.3.0 ; extra == 'tests'
   - mypy>=1.15 ; extra == 'tests'
-  - pyamg>=5.0.0 ; extra == 'tests'
+  - pyamg>=4.2.1 ; extra == 'tests'
   - polars>=0.20.30 ; extra == 'tests'
   - pyarrow>=12.0.0 ; extra == 'tests'
   - numpydoc>=1.2.0 ; extra == 'tests'
@@ -8844,7 +8774,7 @@ packages:
   - ruff>=0.11.0 ; extra == 'tests'
   - black>=24.3.0 ; extra == 'tests'
   - mypy>=1.15 ; extra == 'tests'
-  - pyamg>=5.0.0 ; extra == 'tests'
+  - pyamg>=4.2.1 ; extra == 'tests'
   - polars>=0.20.30 ; extra == 'tests'
   - pyarrow>=12.0.0 ; extra == 'tests'
   - numpydoc>=1.2.0 ; extra == 'tests'
@@ -8905,7 +8835,7 @@ packages:
   - ruff>=0.11.0 ; extra == 'tests'
   - black>=24.3.0 ; extra == 'tests'
   - mypy>=1.15 ; extra == 'tests'
-  - pyamg>=5.0.0 ; extra == 'tests'
+  - pyamg>=4.2.1 ; extra == 'tests'
   - polars>=0.20.30 ; extra == 'tests'
   - pyarrow>=12.0.0 ; extra == 'tests'
   - numpydoc>=1.2.0 ; extra == 'tests'
diff --git a/tests/test_narx.py b/tests/test_narx.py
index 685bcda..c8139cf 100644
--- a/tests/test_narx.py
+++ b/tests/test_narx.py
@@ -2,7 +2,7 @@
 
 import numpy as np
 import pytest
-from numpy.testing import assert_array_equal
+from numpy.testing import assert_almost_equal, assert_array_equal
 from sklearn.metrics import r2_score
 from sklearn.utils.estimator_checks import check_estimator
 
@@ -243,17 +243,48 @@ def test_narx(nan, multi_output):
         ).fit(X, y)
 
 
-def test_mulit_output_warn_error():
+def test_mulit_output_warn():
+    X = np.random.rand(10, 2)
+    y = np.random.rand(10, 2)
+    for i in range(2):
+        if i == 0:
+            # X only, grad does not have dynamic part
+            time_shift_ids = np.array([[0, 1], [1, 1]])
+            poly_ids = np.array([[1, 1], [2, 2]])
+        else:
+            time_shift_ids = np.array([[0, 0], [1, 1], [2, 1]])
+            poly_ids = np.array([[1, 1], [2, 2], [0, 3]])
+        feat_ids, delay_ids = tp2fd(time_shift_ids, poly_ids)
+
+        with pytest.warns(UserWarning, match="output_ids got"):
+            narx = NARX(feat_ids=feat_ids, delay_ids=delay_ids)
+            narx.fit(X, y)
+        y_pred = narx.predict(X)
+        assert_almost_equal(np.std(y_pred[narx.max_delay_:, 1] - np.mean(y[:, 1])), 0.0)
+
+        X_nan = np.copy(X)
+        y_nan = np.copy(y)
+        X_nan[4, 0] = np.nan
+        y_nan[4, 1] = np.nan
+        for coef_init in [None, "one_step_ahead"]:
+            with pytest.warns(UserWarning, match="output_ids got"):
+                y_pred = narx.fit(X_nan, y_nan, coef_init=coef_init).predict(X_nan)
+            y_nan_masked, y_pred_masked = _mask_missing_value(y_nan, y_pred)
+            assert_almost_equal(
+                np.std(
+                    y_pred_masked[y_pred_masked[:, 0]!=0, 1] -\
+                    np.mean(y_nan_masked[:, 1])
+                ),
+                0.0,
+            )
+
+def test_mulit_output_error():
     X = np.random.rand(10, 2)
     y = np.random.rand(10, 2)
     time_shift_ids = np.array([[0, 1], [1, 1]])
     poly_ids = np.array([[1, 1], [2, 2]])
     feat_ids, delay_ids = tp2fd(time_shift_ids, poly_ids)
 
-    with pytest.warns(UserWarning, match="output_ids got"):
-        narx = NARX(feat_ids=feat_ids, delay_ids=delay_ids)
-        narx.fit(X, y)
-
     with pytest.raises(ValueError, match="The length of output_ids should"):
         narx = NARX(
         feat_ids=feat_ids,
@@ -281,7 +312,6 @@ def test_mulit_output_warn_error():
         narx.predict(X, y_init=[1, 1, 1])
 
 
-
 def test_sample_weight():
     rng = np.random.default_rng(12345)
     n_samples = 100