regularization towards initial guess

.github/workflows/test_src.yml

@@ -22,11 +22,11 @@ jobs:
           - windows-latest
           - macos-latest
         python-version:
-          - "3.9"
           - "3.10"
           - "3.11"
           - "3.12"
           - "3.13"
+          - "3.14"
     runs-on: ${{ matrix.os }}
     steps:
       - uses: actions/checkout@v4
@@ -39,5 +39,8 @@ jobs:
           python -m pip install --upgrade pip
           python -m pip install tox
       - name: Run tests
+        if: runner.os == 'Windows'
+        env:
+          MPLBACKEND: Agg  # Fix a bug in GitHub Actions for Windows
         run: |
           python -m tox -e py${{ matrix.python-version }}

.github/workflows/test_style.yml

@@ -19,7 +19,7 @@ jobs:
       - name: Install Python
         uses: actions/setup-python@v5
         with:
-          python-version: 3.12
+          python-version: 3.14
       - name: Install tox
         run: |
           python -m pip install --upgrade pip

docs/source/contributing/how_to_contribute.md

@@ -58,7 +58,7 @@ Style checks, unit tests, and documentation builds are managed with [`tox`](http
 For each of these tasks, `tox` creates a new virtual environment, installs the dependencies (e.g., `pytest` for running unit tests), and executes the task recipe.
 
 :::{note}
-Unit tests are executed for Python 3.9 through 3.12 if they are installed on your system.
+Unit tests are executed for Python 3.10 through 3.14 if they are installed on your system.
 The best way to install multiple Python versions varies by platform; for MacOS, [we suggest](https://stackoverflow.com/questions/36968425/how-can-i-install-multiple-versions-of-python-on-latest-os-x-and-use-them-in-par#answer-65094122) using [Homebrew](https://brew.sh/).
 
 ```shell

docs/source/contributing/testing.md

@@ -176,8 +176,8 @@ If all tests pass, a line coverage report will be generated.
 Open `htmlcov/index.html` in a browser to view the report.
 
 :::{note}
-Running `tox` without any arguments tests the code for Python 3.9 through 3.12 (if they are installed on your system).
-To test a single Python version, use `tox -e py310` for Python 3.10, `tox -e py311` for Python3.11, and so on.
+Running `tox` without any arguments tests the code for Python 3.10 through 3.14 (if they are installed on your system).
+To test a single Python version, use `tox -e py314` for Python 3.14, `tox -e py313` for Python3.13, and so on.
 :::
 
 ## GitHub Actions

docs/source/opinf/changelog.md

@@ -5,6 +5,15 @@
 New versions may introduce substantial new features or API adjustments.
 :::
 
+## Version 0.5.17
+
+- Dropped support for Python 3.9, added test coverage for Python 3.14.
+- Tikhonov / L2 least-squares now take an initial guess
+- Expansion of operators to larger or smaller bases (for nested OpInf)
+- Parametric and nonparametric polynomial operators of arbitrary order
+- Bases now have a `fit_compress()` method
+- Update `utils.TimedBlock` to use `time.process_time()`
+
 ## Version 0.5.16
 
 Backend improvements to the regularization selection procedure.

pyproject.toml

@@ -11,7 +11,7 @@ authors = [
 ]
 maintainers = [{ name = "Shane A. McQuarrie", email = "[email protected]" }]
 readme = { file = "README.md", content-type = "text/markdown" }
-requires-python = ">=3.9"
+requires-python = ">=3.10"
 license = { file = "LICENSE" }
 keywords = [
     "operator inference",

src/opinf/__init__.py

@@ -7,7 +7,7 @@
     https://github.com/Willcox-Research-Group/rom-operator-inference-Python3
 """
 
-__version__ = "0.5.16"
+__version__ = "0.5.17"
 
 from . import (
     basis,

src/opinf/basis/_pod.py

@@ -120,17 +120,64 @@ def method_of_snapshots(
     eigvals = eigvals[::-1]
     eigvecs = eigvecs[:, ::-1]
 
+    # can at most have as many non-zero eigenvalues as there was data
+    if eigvals.shape[0] > states.shape[0]:
+        eigvals[states.shape[0] :] = 0
+    if eigvals.shape[0] > states.shape[1]:
+        eigvals[states.shape[1] :] = 0
+
     # By definition the Gramian is symmetric positive semi-definite.
     # If any eigenvalues are smaller than zero, they are only measuring
     # numerical error and can be truncated.
     positives = eigvals > max(minthresh, abs(np.min(eigvals)))
+
+    if sum(positives) > states.shape[0]:
+        print(eigvals)
+        print(positives)
+        raise RuntimeError(
+            f"""selected more non-zero singular values {sum(positives)}
+            than there are state dimensions ({states.shape[0]})"""
+        )
+
+    # can at most have as many non-zero entries as there were state dofs
     eigvecs = eigvecs[:, positives]
     eigvals = eigvals[positives]
 
     # Rescale and square root eigenvalues to get singular values.
     svals = np.sqrt(eigvals * n_states)
     V = states @ (eigvecs / svals)
 
+    # if basis functions are not orthonormal, apply Gram-Schmidt
+    counter = 0
+
+    def inner_product(V):
+        if inner_product_matrix is None:
+            return V.T @ V
+        return V.T @ _Wmult(inner_product_matrix, V)
+
+    while (
+        not np.isclose(inner_product(V), np.eye(V.shape[1])).all()
+    ) and counter < 10:
+        for i in range(V.shape[1]):
+            v_i = V[:, i]
+            for j in range(i):
+                v_i = (
+                    v_i
+                    - (v_i.T @ _Wmult(inner_product_matrix, V[:, j])) * V[:, j]
+                )
+            norm_vi = np.sqrt(v_i.T @ _Wmult(inner_product_matrix, v_i))
+            V[:, i] = v_i / norm_vi
+
+        if V.shape[0] != states.shape[0]:
+            print(V.shape, counter)
+            raise RuntimeError(
+                "something went seriously wrong in computation of V"
+            )
+        counter += 1
+
+    if not np.isclose(inner_product(V), np.eye(V.shape[1])).all():
+        raise RuntimeWarning("Computed basis functions are not orthonormal.")
+
     return V, svals, eigvecs.T
 
 

src/opinf/ddt/_base.py

@@ -144,7 +144,6 @@ def estimate(self, states, inputs=None):
         """
         raise NotImplementedError  # pragma: no cover
 
-    @abc.abstractmethod
     def mask(self, arr):
         """Map an array from the training time domain to the domain of the
         estimated time derivatives.
@@ -171,7 +170,7 @@ def mask(self, arr):
         >>> Q3.shape == Q.shape
         True
         """
-        raise NotImplementedError  # pragma: no cover
+        return arr
 
     # Verification ------------------------------------------------------------
     def verify_shapes(self, r: int = 5, m: int = 3):  # pragma: no cover