{ "cells": [ { "cell_type": "markdown", "id": "77f3ae5b", "metadata": {}, "source": [ "# Data Analysis via Interpolation\n", "\n", "## Overview, Objectives, and Key Terms\n", "\n", "In [Lesson 24](L24_ModelingDataWithLeastSquaresFits.ipynb), we treated measured data as\n", "\n", "$$\n", "\\mathbf{y} = \\mathbf{A}\\mathbf{x} + \\boldsymbol{\\epsilon},\n", "$$\n", "\n", "where $\\mathbf{A}$ is the design matrix, $\\mathbf{x}$ contains model parameters, and $\\boldsymbol{\\epsilon}$ is the measurement or modeling error. Least squares is natural when those deviations behave like samples of a zero-mean error process. With normal errors, the least-squares solution also has a statistical interpretation, and nonlinear models can be interpreted locally by linearizing around the best-fit parameters.\n", "\n", "Interpolation answers a different question. It says: suppose the tabulated values are the model, at least at the tabulated points. How should we estimate values between them?\n", "\n", "### Objectives\n", "\n", "By the end of this lesson, you should be able to\n", "\n", "- interpret linear interpolation as a weighted sum,\n", "- compute 1-D interpolation weights and connect them to `np.interp`,\n", "- use `CubicSpline` when a smooth 1-D interpolant is appropriate,\n", "- recognize regular grid interpolation as repeated 1-D interpolation,\n", "- use `RegularGridInterpolator` for rectilinear 2-D and 3-D grid data,\n", "- recognize unstructured interpolation as interpolation over triangles or tetrahedra,\n", "- use `LinearNDInterpolator` for scattered points.\n", "\n", "### Key Terms\n", "\n", "- interpolation\n", "- extrapolation\n", "- convex combination\n", "- barycentric weights\n", "- rectilinear grid\n", "- triangulation\n", "- `np.interp`\n", "- `CubicSpline`\n", "- `RegularGridInterpolator`\n", "- `LinearNDInterpolator`" ] }, { "cell_type": "code", "execution_count": null, "id": "87e35d6b", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib.tri import Triangulation\n", "from scipy.interpolate import CubicSpline, LinearNDInterpolator, RegularGridInterpolator\n", "\n", "COLORS = {\n", " \"ink\": \"#1f2937\",\n", " \"muted\": \"#64748b\",\n", " \"grid\": \"#e5e7eb\",\n", " \"panel\": \"#fafaf7\",\n", " \"purple\": \"#512888\",\n", " \"orange\": \"#D55E00\",\n", " \"blue\": \"#2563eb\",\n", " \"green\": \"#059669\",\n", " \"red\": \"#dc2626\",\n", "}\n", "\n", "plt.rcParams.update({\n", " \"figure.facecolor\": \"white\",\n", " \"axes.facecolor\": COLORS[\"panel\"],\n", " \"axes.edgecolor\": COLORS[\"muted\"],\n", " \"axes.labelcolor\": COLORS[\"ink\"],\n", " \"axes.titlecolor\": COLORS[\"ink\"],\n", " \"xtick.color\": COLORS[\"ink\"],\n", " \"ytick.color\": COLORS[\"ink\"],\n", " \"grid.color\": COLORS[\"grid\"],\n", " \"font.size\": 11,\n", "})\n", "\n", "\n", "def style_axes(ax):\n", " ax.grid(True, alpha=0.5)\n", " ax.spines[\"top\"].set_visible(False)\n", " ax.spines[\"right\"].set_visible(False)" ] }, { "cell_type": "markdown", "id": "096b9131", "metadata": {}, "source": [ "## The Teeter-Totter: Two Points, Two Weights\n", "\n", "Start with two trusted points $(x_0,y_0)$ and $(x_1,y_1)$. We want the value at $x_*$ between them. Instead of first writing a slope and intercept, write the interpolated value as a weighted sum:\n", "\n", "$$\n", "y_* = w_0 y_0 + w_1 y_1.\n", "$$\n", "\n", "The weights have two jobs. First, they must add to one:\n", "\n", "$$\n", "w_0 + w_1 = 1.\n", "$$\n", "\n", "Second, they must balance the horizontal location:\n", "\n", "$$\n", "w_0 x_0 + w_1 x_1 = x_*.\n", "$$\n", "\n", "Two equations, two unknowns. The solution is\n", "\n", "$$\n", "w_0 = \\frac{x_1-x_*}{x_1-x_0},\n", "\\qquad\n", "w_1 = \\frac{x_*-x_0}{x_1-x_0}.\n", "$$\n", "\n", "This is the teeter-totter picture: the point closer to $x_*$ gets more weight." ] }, { "cell_type": "code", "execution_count": null, "id": "163a499f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Input\n", "points: (2.0, 1.5), (8.0, 5.0)\n", "target x*: 4.5\n", "Output\n", "weights: w0=0.583, w1=0.417, sum=1.000\n", "interpolated y*: 2.958\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x0, x1 = 2.0, 8.0\n", "y0, y1 = 1.5, 5.0\n", "x_star = 4.5\n", "w0 = (x1 - x_star)/(x1 - x0)\n", "w1 = (x_star - x0)/(x1 - x0)\n", "y_star = w0*y0 + w1*y1\n", "\n", "print(\"Input\")\n", "print(f\"points: ({x0:.1f}, {y0:.1f}), ({x1:.1f}, {y1:.1f})\")\n", "print(f\"target x*: {x_star:.1f}\")\n", "print(\"Output\")\n", "print(f\"weights: w0={w0:.3f}, w1={w1:.3f}, sum={w0+w1:.3f}\")\n", "print(f\"interpolated y*: {y_star:.3f}\")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(10, 3.2), constrained_layout=True)\n", "ax = axes[0]\n", "ax.plot([x0, x1], [y0, y1], color=COLORS[\"muted\"], lw=2)\n", "ax.scatter([x0, x1], [y0, y1], color=[COLORS[\"blue\"], COLORS[\"orange\"]], s=70, zorder=3, label=\"known data\")\n", "ax.scatter([x_star], [y_star], marker=\"*\", color=COLORS[\"green\"], edgecolor=COLORS[\"ink\"], s=180, zorder=4, label=\"interpolated\")\n", "ax.vlines(x_star, min(y0, y1), y_star, color=COLORS[\"green\"], ls=\":\", lw=2)\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"y\")\n", "ax.set_title(\"line segment view\")\n", "ax.legend(fontsize=8)\n", "style_axes(ax)\n", "\n", "ax = axes[1]\n", "ax.hlines(0, x0, x1, color=COLORS[\"ink\"], lw=3)\n", "ax.scatter([x0, x1, x_star], [0, 0, 0], color=[COLORS[\"blue\"], COLORS[\"orange\"], COLORS[\"green\"]], s=[80, 80, 140], zorder=3)\n", "ax.text(x0, 0.12, f\"x0\\nw0={w0:.2f}\", ha=\"center\", color=COLORS[\"blue\"])\n", "ax.text(x1, 0.12, f\"x1\\nw1={w1:.2f}\", ha=\"center\", color=COLORS[\"orange\"])\n", "ax.text(x_star, -0.18, \"x*\", ha=\"center\", color=COLORS[\"green\"])\n", "ax.set_ylim(-0.35, 0.45)\n", "ax.set_yticks([])\n", "ax.set_xlabel(\"position\")\n", "ax.set_title(\"teeter-totter weights\")\n", "style_axes(ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c1fc6be5", "metadata": {}, "source": [ "## The 1-D Tool: `np.interp`\n", "\n", "For 1-D linear interpolation, `np.interp` is the right first tool. It implements exactly the weighted-sum idea above, interval by interval.\n", "\n", "Use it when:\n", "\n", "- the data are 1-D,\n", "- the $x$ values are ordered,\n", "- linear segments are appropriate,\n", "- you want a simple, dependable interpolation rather than a fitted model." ] }, { "cell_type": "code", "execution_count": null, "id": "59dd1eba", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Input\n", "number of table points: 6\n", "evaluation points : 300\n", "Output\n", "linear interpolation at x=3.0: -0.4066\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Input: a small table sampled from a smooth function.\n", "x = np.array([0.0, 1.0, 2.5, 4.0, 6.0, 8.0])\n", "y = np.exp(-0.18*x)*np.cos(1.2*x)\n", "x_eval = np.linspace(x[0], x[-1], 300)\n", "\n", "# Tool: 1-D linear interpolation.\n", "y_linear = np.interp(x_eval, x, y)\n", "\n", "print(\"Input\")\n", "print(f\"number of table points: {len(x)}\")\n", "print(f\"evaluation points : {len(x_eval)}\")\n", "print(\"Output\")\n", "print(f\"linear interpolation at x=3.0: {np.interp(3.0, x, y): .4f}\")\n", "\n", "fig, ax = plt.subplots(figsize=(7, 3.2), constrained_layout=True)\n", "ax.plot(x_eval, y_linear, color=COLORS[\"purple\"], lw=2.5, label=\"np.interp\")\n", "ax.scatter(x, y, color=COLORS[\"ink\"], s=45, zorder=3, label=\"table values\")\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"y\")\n", "ax.set_title(\"linear interpolation preserves the tabulated values\")\n", "ax.legend(fontsize=8)\n", "style_axes(ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "977dcbcb", "metadata": {}, "source": [ "## Smooth 1-D Interpolation: `CubicSpline`\n", "\n", "Sometimes straight segments are too angular for the task. A cubic spline still interpolates the data exactly, but it uses piecewise cubic polynomials with smooth connections between intervals.\n", "\n", "That is not automatically better. A smoother curve is a stronger assumption. If the table is monotone and overshoot would be physically awkward, a shape-preserving tool such as `PchipInterpolator` is often preferable. The main point is to choose the tool that matches what you believe about the data." ] }, { "cell_type": "code", "execution_count": null, "id": "af2af80d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Tool: smooth 1-D interpolation.\n", "spline = CubicSpline(x, y)\n", "y_cubic = spline(x_eval)\n", "\n", "fig, ax = plt.subplots(figsize=(7, 3.2), constrained_layout=True)\n", "ax.plot(x_eval, y_linear, color=COLORS[\"purple\"], lw=2.2, label=\"linear\")\n", "ax.plot(x_eval, y_cubic, color=COLORS[\"orange\"], lw=2.2, label=\"CubicSpline\")\n", "ax.scatter(x, y, color=COLORS[\"ink\"], s=45, zorder=3, label=\"table values\")\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"y\")\n", "ax.set_title(\"same data, different interpolation assumptions\")\n", "ax.legend(fontsize=8)\n", "style_axes(ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a21c3d73", "metadata": {}, "source": [ "## Regular Grids: Repeat the Same Idea\n", "\n", "On a rectangular or rectilinear grid, 2-D linear interpolation is naturally sequential 1-D interpolation.\n", "\n", "For a point inside one grid cell:\n", "\n", "1. interpolate in $x$ along the lower row,\n", "2. interpolate in $x$ along the upper row,\n", "3. interpolate those two intermediate values in $y$.\n", "\n", "In 3-D, repeat the same idea one more time. This is why the modern SciPy tool is named `RegularGridInterpolator`: it works for 1-D, 2-D, 3-D, and higher-dimensional rectilinear grids." ] }, { "cell_type": "code", "execution_count": null, "id": "32fcb1cf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Input\n", "grid shape: (7, 6)\n", "target point: (2.60, 1.70)\n", "Output\n", "manual sequential interpolation: 1.524157\n", "RegularGridInterpolator : 1.524157\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def response(x, y):\n", " return np.sin(0.7*x) + 0.15*y**2 - 0.4*np.cos(1.2*y)\n", "\n", "xg = np.linspace(0.0, 6.0, 7)\n", "yg = np.linspace(0.0, 4.0, 6)\n", "Xg, Yg = np.meshgrid(xg, yg, indexing=\"ij\")\n", "Zg = response(Xg, Yg)\n", "point = np.array([2.6, 1.7])\n", "\n", "# Manual sequential interpolation inside the containing cell.\n", "ix = np.searchsorted(xg, point[0]) - 1\n", "iy = np.searchsorted(yg, point[1]) - 1\n", "x_left, x_right = xg[ix], xg[ix+1]\n", "y_low, y_high = yg[iy], yg[iy+1]\n", "\n", "z_low = np.interp(point[0], [x_left, x_right], [Zg[ix, iy], Zg[ix+1, iy]])\n", "z_high = np.interp(point[0], [x_left, x_right], [Zg[ix, iy+1], Zg[ix+1, iy+1]])\n", "z_manual = np.interp(point[1], [y_low, y_high], [z_low, z_high])\n", "\n", "# Tool: regular-grid interpolation. Values have shape (len(xg), len(yg)).\n", "rgi = RegularGridInterpolator((xg, yg), Zg, method=\"linear\")\n", "z_tool = float(rgi([point])[0])\n", "\n", "print(\"Input\")\n", "print(f\"grid shape: {Zg.shape}\")\n", "print(f\"target point: ({point[0]:.2f}, {point[1]:.2f})\")\n", "print(\"Output\")\n", "print(f\"manual sequential interpolation: {z_manual:.6f}\")\n", "print(f\"RegularGridInterpolator : {z_tool:.6f}\")\n", "\n", "fig, ax = plt.subplots(figsize=(6.2, 4.2), constrained_layout=True)\n", "levels = ax.contourf(Xg, Yg, Zg, levels=16, cmap=\"viridis\", alpha=0.78)\n", "ax.plot(Xg, Yg, color=\"white\", lw=0.8, alpha=0.65)\n", "ax.plot(Xg.T, Yg.T, color=\"white\", lw=0.8, alpha=0.65)\n", "ax.scatter(Xg, Yg, s=18, color=COLORS[\"ink\"], label=\"grid data\")\n", "ax.scatter([point[0]], [point[1]], marker=\"*\", s=180, color=COLORS[\"orange\"], edgecolor=COLORS[\"ink\"], label=\"query point\")\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"y\")\n", "ax.set_title(\"regular grid interpolation\")\n", "ax.legend(fontsize=8, loc=\"upper left\")\n", "fig.colorbar(levels, ax=ax, label=\"z\")\n", "style_axes(ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "638b1d45", "metadata": {}, "source": [ "## Unstructured Points: Barycentric Weights\n", "\n", "Not all data arrive on a grid. In 2-D, scattered points can be triangulated. Inside one triangle, linear interpolation is still a weighted sum:\n", "\n", "$$\n", "z_* = w_0 z_0 + w_1 z_1 + w_2 z_2,\n", "$$\n", "\n", "with\n", "\n", "$$\n", "w_0 + w_1 + w_2 = 1.\n", "$$\n", "\n", "The extra equations make the weighted average land at the query point in both $x$ and $y$. These are barycentric weights. In 3-D, the same idea uses tetrahedra and four weights.\n", "\n", "The matching SciPy tool for piecewise-linear interpolation on scattered points is `LinearNDInterpolator`. In 2-D, it triangulates the points; in 3-D, it uses tetrahedra." ] }, { "cell_type": "code", "execution_count": null, "id": "e13781bd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Input\n", "scattered points: 24\n", "query point : (3.00, 2.20)\n", "Output\n", "LinearNDInterpolator value: 1.885130\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rng = np.random.default_rng(415)\n", "points = rng.random((24, 2))\n", "points[:, 0] *= 6.0\n", "points[:, 1] *= 4.0\n", "values = response(points[:, 0], points[:, 1])\n", "query = np.array([3.0, 2.2])\n", "\n", "# Tool: scattered-data interpolation by triangulation.\n", "scattered_interp = LinearNDInterpolator(points, values)\n", "z_query = float(scattered_interp([query])[0])\n", "tri = Triangulation(points[:, 0], points[:, 1])\n", "\n", "print(\"Input\")\n", "print(f\"scattered points: {len(points)}\")\n", "print(f\"query point : ({query[0]:.2f}, {query[1]:.2f})\")\n", "print(\"Output\")\n", "print(f\"LinearNDInterpolator value: {z_query:.6f}\")\n", "\n", "fig, ax = plt.subplots(figsize=(6.2, 4.2), constrained_layout=True)\n", "ax.triplot(tri, color=COLORS[\"muted\"], lw=1.0)\n", "sc = ax.scatter(points[:, 0], points[:, 1], c=values, cmap=\"viridis\", s=55, edgecolor=COLORS[\"ink\"], label=\"scattered data\")\n", "ax.scatter([query[0]], [query[1]], marker=\"*\", s=190, color=COLORS[\"orange\"], edgecolor=COLORS[\"ink\"], label=\"query point\")\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"y\")\n", "ax.set_title(\"unstructured interpolation uses triangles\")\n", "ax.legend(fontsize=8, loc=\"upper left\")\n", "fig.colorbar(sc, ax=ax, label=\"z\")\n", "style_axes(ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ebf4649f", "metadata": {}, "source": [ "## Tool Choice\n", "\n", "A useful decision rule is:\n", "\n", "- **1-D table, linear segments**: use `np.interp`.\n", "- **1-D table, smooth curve**: use `CubicSpline` or a shape-preserving spline such as `PchipInterpolator`.\n", "- **2-D, 3-D, or higher rectilinear grid**: use `RegularGridInterpolator`.\n", "- **Unstructured 2-D or 3-D points**: use `LinearNDInterpolator` for piecewise-linear interpolation.\n", "- **Old `interp2d` code**: do not copy it into new work. It has been removed from SciPy; use `RegularGridInterpolator` for regular grids and scattered-data interpolators for unstructured points.\n", "\n", "Interpolation is not fitting. It passes through the data. That is a feature when the table is the model, and a liability when the table is noisy." ] }, { "cell_type": "markdown", "id": "a09c1d3e", "metadata": {}, "source": [ "## Further Reading\n", "\n", "- SciPy, [interp2d transition guide](https://docs.scipy.org/doc/scipy/tutorial/interpolate/interp_transition_guide.html)\n", "- SciPy, [RegularGridInterpolator](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.RegularGridInterpolator.html)\n", "- SciPy, [LinearNDInterpolator](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.LinearNDInterpolator.html)\n", "- SciPy, [CubicSpline](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.CubicSpline.html)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 5 }