docs/notebooks/demo_basis.ipynb

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 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from splinebasis import Msplines, ISplineBasis"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
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   "source": [
    "### Plot Some M-Splines and their derivatives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "spline = Msplines(order=3,lower=0,upper=1,num_knots=10)\n",
    "x = np.linspace(0,1,100)\n",
    "for i in range(1,spline.n+1):\n",
    "    plt.plot(x,spline(x,i),label=f'$M_{i}$')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(1,spline.n+1):\n",
    "    plt.plot(x,spline.derivatives(x,i),label=f'$M\\'_{i}$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Use the Spline basis class to plot I-splines and their Sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "basis = ISplineBasis(num_basis=10,order=3,lower=0,upper=1, n_grid=100)\n",
    "\n",
    "for i in basis.basis_vectors:\n",
    "    plt.plot(x,i)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights = np.ones(basis.num_basis)\n",
    "weights /= np.sum(weights)\n",
    "\n",
    "plt.plot(x,basis(weights))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights = np.ones(basis.num_basis)\n",
    "weights /= np.sum(weights)\n",
    "\n",
    "plt.plot(x,basis.derivatives(weights))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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