.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/02_resize/01_resize_module_1d.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code or to run this example in your browser via Binder. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_02_resize_01_resize_module_1d.py: Resize Module 1D ================ Starting from a 1D signal :math:`f[k]` on a unit grid, we perform a 1D resize directly on the samples and compare: - a coarse spline built from ``resize(..., method="cubic")``, - a coarse spline built from ``resize(..., method="cubic-antialiasing")``, - the interpolating spline :math:`f(x)` of the original samples for reference. We build up the visualization step-by-step: 1. Only the original samples :math:`f[k]`. 2. The fine interpolating spline :math:`f(x)`. 3. The coarse spline from ``resize(..., "cubic")``. 4. The coarse spline from ``resize(..., "cubic-antialiasing")``. 5. Everything together on one plot. .. GENERATED FROM PYTHON SOURCE LINES 26-28 Imports ------- .. GENERATED FROM PYTHON SOURCE LINES 28-41 .. code-block:: Python import numpy as np import matplotlib.pyplot as plt from splineops.resize import resize # core 1-D spline resizer from splineops.spline_interpolation.tensor_spline import TensorSpline plt.rcParams.update({ "font.size": 14, "axes.titlesize": 18, "axes.labelsize": 16, }) .. GENERATED FROM PYTHON SOURCE LINES 43-52 1D Resize-Based Coarsening -------------------------- Starting again from a 1D signal f[k] on a unit grid, we perform a 1D resize directly on the samples. We then compare: - a coarse spline built from `resize(..., method="cubic")`, - a coarse spline built from `resize(..., method="cubic-antialiasing")`, - the interpolating spline f(x) of the original samples for reference. .. GENERATED FROM PYTHON SOURCE LINES 52-64 .. code-block:: Python # 1) Original 1D samples f[k] (same as in 02_01 / 02_02) number_of_samples = 27 f_support_1d = np.arange(number_of_samples, dtype=np.float64) f_samples_1d = np.array([ -0.657391, -0.641319, -0.613081, -0.518523, -0.453829, -0.385138, -0.270688, -0.179849, -0.11805, -0.0243016, 0.0130667, 0.0355389, 0.0901577, 0.219599, 0.374669, 0.384896, 0.301386, 0.128646, -0.00811776, 0.0153119, 0.106126, 0.21688, 0.347629, 0.419532, 0.50695, 0.544767, 0.555373 ], dtype=np.float64) .. GENERATED FROM PYTHON SOURCE LINES 65-69 Original Samples ---------------- We start by visualizing only the discrete samples :math:`f[k]` on the unit grid. .. GENERATED FROM PYTHON SOURCE LINES 69-80 .. code-block:: Python plt.figure(figsize=(10, 4)) plt.title("Original samples f[k]") plt.stem(f_support_1d, f_samples_1d, basefmt=" ") plt.axhline(0, color="black", linewidth=1, zorder=0) plt.xlabel("k") plt.ylabel("f[k]") plt.grid(True) plt.tight_layout() plt.show() .. image-sg:: /auto_examples/02_resize/images/sphx_glr_01_resize_module_1d_001.png :alt: Original samples f[k] :srcset: /auto_examples/02_resize/images/sphx_glr_01_resize_module_1d_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 81-86 Fine Spline f(x) ---------------- Next, we build the fine interpolating spline :math:`f(x)` on the unit grid using cubic B-splines, and sample it densely for visualization. .. GENERATED FROM PYTHON SOURCE LINES 86-123 .. code-block:: Python # Fine spline f(x) on Vā‚ (unit grid) plot_points_per_unit_1d = 12 base_1d = "bspline3" mode_1d = "mirror" f_1d = TensorSpline( data=f_samples_1d, coordinates=f_support_1d, bases=base_1d, modes=mode_1d, ) # Dense evaluation grid for the fine spline f_coords_1d = np.array([ q / plot_points_per_unit_1d for q in range(plot_points_per_unit_1d * number_of_samples) ]) f_data_1d = f_1d(coordinates=(f_coords_1d,), grid=False) plt.figure(figsize=(10, 4)) plt.title("Fine spline f(x) interpolating f[k]") plt.stem(f_support_1d, f_samples_1d, basefmt=" ", label="f[k] samples") plt.axhline(0, color="black", linewidth=1, zorder=0) plt.plot( f_coords_1d, f_data_1d, linewidth=2, label="fine spline f(x)", ) plt.xlabel("x") plt.ylabel("Amplitude") plt.grid(True) plt.legend() plt.tight_layout() plt.show() .. image-sg:: /auto_examples/02_resize/images/sphx_glr_01_resize_module_1d_002.png :alt: Fine spline f(x) interpolating f[k] :srcset: /auto_examples/02_resize/images/sphx_glr_01_resize_module_1d_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 124-129 Coarse Grid and Resize ---------------------- We now choose a coarser grid and obtain coarse samples by resizing the original discrete signal with two different methods. .. GENERATED FROM PYTHON SOURCE LINES 129-185 .. code-block:: Python # 2) Choose a coarse length: round(27 // Ļ€) val_T = np.pi K = number_of_samples g_support_length = round(K // val_T) # e.g., 27 // Ļ€ ā‰ˆ 8 # Express this as a zoom factor for resize zoom_1d = g_support_length / K # e.g., 8 / 27 # 3) Coarse samples via resize: cubic and cubic-antialiasing g_samples_cubic = resize( f_samples_1d, zoom_factors=(zoom_1d,), method="cubic", ).astype(np.float64) g_samples_aa = resize( f_samples_1d, zoom_factors=(zoom_1d,), method="cubic-antialiasing", ).astype(np.float64) L = g_samples_cubic.shape[0] # 4) Reconstruct the continuous coarse grid used by resize for pure interpolation: # # step = (K - 1) / (L - 1) # x_l = step * l # step = (K - 1) / (L - 1) if L > 1 else 0.0 g_support_x = step * np.arange(L, dtype=np.float64) # Build TensorSplines on that coarse grid g_cubic_ts = TensorSpline( data=g_samples_cubic, coordinates=g_support_x, bases=base_1d, modes=mode_1d, ) g_aa_ts = TensorSpline( data=g_samples_aa, coordinates=g_support_x, bases=base_1d, modes=mode_1d, ) # Evaluate both coarse splines on the same dense grid as f(x) g_coords_dense = f_coords_1d g_cubic_data = g_cubic_ts(coordinates=(g_coords_dense,), grid=False) g_aa_data = g_aa_ts(coordinates=(g_coords_dense,), grid=False) # Optional sanity check at the coarse nodes: resize(cubic) vs fine spline sampled at x_l f_at_xg = f_1d(coordinates=(g_support_x,), grid=False) mse_cubic_nodes = np.mean((g_samples_cubic - f_at_xg) ** 2) print(f"MSE at coarse nodes: resize(cubic) vs f(x_l) = {mse_cubic_nodes:.6e}") .. rst-class:: sphx-glr-script-out .. code-block:: none MSE at coarse nodes: resize(cubic) vs f(x_l) = 3.046348e-14 .. GENERATED FROM PYTHON SOURCE LINES 186-191 Coarse Cubic Spline ------------------- We now show the coarse spline built from the ``"cubic"`` resize together with the original samples and fine spline. .. GENERATED FROM PYTHON SOURCE LINES 191-243 .. code-block:: Python plt.figure(figsize=(10, 4)) plt.title("Coarse cubic spline") plt.stem(f_support_1d, f_samples_1d, basefmt=" ", label="f[k] samples") plt.axhline(0, color="black", linewidth=1, zorder=0) plt.plot( f_coords_1d, f_data_1d, linewidth=2, alpha=0.5, label="fine spline f(x)", ) plt.plot( g_coords_dense, g_cubic_data, linewidth=2, label="coarse spline (cubic)", ) # vertical red stems from coarse samples plt.vlines( x=g_support_x, ymin=0, ymax=g_samples_cubic, color="red", linewidth=2.0, ) # (optionally change "s" -> "rs" to make markers red squares) plt.plot( g_support_x, g_samples_cubic, "rs", mfc="none", markersize=10, markeredgewidth=2, label="coarse samples (cubic)", ) # --- coarse-grid x-axis, like in 02_02 --- coarse_indices = np.arange(L, dtype=int) plt.xlim(0, K - 1) plt.xticks(g_support_x, [str(k) for k in coarse_indices]) plt.xlabel("x") plt.ylabel("Amplitude") plt.grid(True) plt.legend() plt.tight_layout() plt.show() .. image-sg:: /auto_examples/02_resize/images/sphx_glr_01_resize_module_1d_003.png :alt: Coarse cubic spline :srcset: /auto_examples/02_resize/images/sphx_glr_01_resize_module_1d_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 244-249 Coarse Cubic Antialiasing Spline -------------------------------- Similarly, we show the coarse spline obtained with the antialiasing preset, which inserts a low-pass step before decimation. .. GENERATED FROM PYTHON SOURCE LINES 249-300 .. code-block:: Python plt.figure(figsize=(10, 4)) plt.title("Coarse cubic antialiasing spline") plt.stem(f_support_1d, f_samples_1d, basefmt=" ", label="f[k] samples") plt.axhline(0, color="black", linewidth=1, zorder=0) plt.plot( f_coords_1d, f_data_1d, linewidth=2, alpha=0.5, label="fine spline f(x)", ) plt.plot( g_coords_dense, g_aa_data, linewidth=2, label="coarse spline (cubic-antialiasing)", ) # vertical red stems from coarse AA samples plt.vlines( x=g_support_x, ymin=0, ymax=g_samples_aa, color="red", linewidth=2.0, ) plt.plot( g_support_x, g_samples_aa, "ro", # red circles, hollow mfc="none", markersize=8, markeredgewidth=2, label="coarse samples (cubic-antialiasing)", ) # --- coarse-grid x-axis --- coarse_indices = np.arange(L, dtype=int) plt.xlim(0, K - 1) plt.xticks(g_support_x, [str(k) for k in coarse_indices]) plt.xlabel("x") plt.ylabel("Amplitude") plt.grid(True) plt.legend() plt.tight_layout() plt.show() .. image-sg:: /auto_examples/02_resize/images/sphx_glr_01_resize_module_1d_004.png :alt: Coarse cubic antialiasing spline :srcset: /auto_examples/02_resize/images/sphx_glr_01_resize_module_1d_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 301-306 All Splines Together -------------------- Finally, we overlay both coarse splines on top of the fine spline and original samples for a direct comparison. .. GENERATED FROM PYTHON SOURCE LINES 306-378 .. code-block:: Python plt.figure(figsize=(10, 4)) plt.title("1D resize on f[k]: cubic vs cubic-antialiasing") # Original samples f[k] plt.stem(f_support_1d, f_samples_1d, basefmt=" ", label="f[k] samples") plt.axhline(0, color="black", linewidth=1, zorder=0) # Fine spline f(x) for reference plt.plot( f_coords_1d, f_data_1d, linewidth=2, alpha=0.5, label="fine f(x) (reference)", ) # Coarse spline from resize(..., "cubic") plt.plot( g_coords_dense, g_cubic_data, linewidth=2, label="coarse spline (cubic)", ) # red stems for cubic coarse samples plt.vlines( x=g_support_x, ymin=0, ymax=g_samples_cubic, color="red", linewidth=2.0, ) plt.plot( g_support_x, g_samples_cubic, "rs", mfc="none", markersize=10, markeredgewidth=2, label="coarse samples (cubic)", ) # Coarse spline from resize(..., "cubic-antialiasing") plt.plot( g_coords_dense, g_aa_data, linewidth=2, label="coarse spline (cubic-antialiasing)", ) plt.plot( g_support_x, g_samples_aa, "ro", mfc="none", markersize=8, markeredgewidth=2, label="coarse samples (cubic-antialiasing)", ) # --- coarse-grid x-axis --- coarse_indices = np.arange(L, dtype=int) plt.xlim(0, K - 1) plt.xticks(g_support_x, [str(k) for k in coarse_indices]) plt.xlabel("x") plt.ylabel("Amplitude") plt.grid(True) plt.legend() plt.tight_layout() plt.show() .. image-sg:: /auto_examples/02_resize/images/sphx_glr_01_resize_module_1d_005.png :alt: 1D resize on f[k]: cubic vs cubic-antialiasing :srcset: /auto_examples/02_resize/images/sphx_glr_01_resize_module_1d_005.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.587 seconds) .. _sphx_glr_download_auto_examples_02_resize_01_resize_module_1d.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/splineops/splineops.github.io/main?urlpath=lab/tree/notebooks_binder/auto_examples/02_resize/01_resize_module_1d.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: 01_resize_module_1d.ipynb <01_resize_module_1d.ipynb>` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: 01_resize_module_1d.py <01_resize_module_1d.py>` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: 01_resize_module_1d.zip <01_resize_module_1d.zip>` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_