notebooks/01a-python-fem-basis-func.ipynb

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    "ChEn-5310: Computational Continuum Transport Phenomena Fall 2021 UMass Lowell; Prof. V. F. de Almeida **28Oct21**\n",
    "\n",
    "# 01a. Python FEM Basis Functions\n",
    "$  \n",
    "  \\newcommand{\\Amtrx}{\\boldsymbol{\\mathsf{A}}}\n",
    "  \\newcommand{\\Gmtrx}{\\boldsymbol{\\mathsf{G}}}\n",
    "  \\newcommand{\\Bmtrx}{\\boldsymbol{\\mathsf{B}}}\n",
    "  \\newcommand{\\Mmtrx}{\\boldsymbol{\\mathsf{M}}}\n",
    "  \\newcommand{\\Imtrx}{\\boldsymbol{\\mathsf{I}}}\n",
    "  \\newcommand{\\Pmtrx}{\\boldsymbol{\\mathsf{P}}}\n",
    "  \\newcommand{\\Lmtrx}{\\boldsymbol{\\mathsf{L}}}\n",
    "  \\newcommand{\\Umtrx}{\\boldsymbol{\\mathsf{U}}}\n",
    "  \\newcommand{\\Smtrx}{\\boldsymbol{\\mathsf{S}}}\n",
    "  \\newcommand{\\xvec}{\\boldsymbol{\\mathsf{x}}}\n",
    "  \\newcommand{\\avec}{\\boldsymbol{\\mathsf{a}}}\n",
    "  \\newcommand{\\bvec}{\\boldsymbol{\\mathsf{b}}}\n",
    "  \\newcommand{\\cvec}{\\boldsymbol{\\mathsf{c}}}\n",
    "  \\newcommand{\\rvec}{\\boldsymbol{\\mathsf{r}}}\n",
    "  \\newcommand{\\fvec}{\\boldsymbol{\\mathsf{f}}}\n",
    "  \\newcommand{\\mvec}{\\boldsymbol{\\mathsf{m}}}\n",
    "  \\newcommand{\\gvec}{\\boldsymbol{\\mathsf{g}}}\n",
    "  \\newcommand{\\zerovec}{\\boldsymbol{\\mathsf{0}}}\n",
    "  \\newcommand{\\norm}[1]{\\bigl\\lVert{#1}\\bigr\\rVert}\n",
    "  \\newcommand{\\transpose}[1]{{#1}^\\top}\n",
    "  \\DeclareMathOperator{\\rank}{rank}\n",
    "  \\newcommand{\\Reals}{\\mathbb{R}}\n",
    "  \\newcommand{\\thetavec}{\\boldsymbol{\\theta}}\n",
    "$"
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    "---\n",
    "\n",
    "## Table of Contents<a id=\"toc\"></a>\n",
    "* [Objectives](#obj)\n",
    "* [Finite Element Lagrange Polynomial Basis Functions](#fem-lagrange-basis)\n",
    " 1. [Domain Partition](#dom-part)\n",
    " 2. [Parent Mapping](#parent-map)\n",
    " 3. [Parent Basis Functions (or also called shape functions)](#parent-basis)\n",
    " 4. [Global Basis Functions](#global-basis)\n",
    " 5. [Testing](#test)\n",
    "* [Function Approximation](#func-approx)\n",
    " + [Inner Product](#inner-prod)\n",
    " + [Gram Matrix](#gram-matrix)\n",
    " + [Load Vector](#load-vector)\n",
    " + [Optimal Combination Coefficients](#cont-optimal-coeff)\n",
    " + [Results](#cont-res)\n",
    "---"
   ]
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    "## [Objectives](#toc)<a id=\"obj\"></a>\n",
    "\n",
    " + Present basic `python` code that implements finite element basis functions mathematical structures (notes: [OneNote Engy-5310-fem-basis-func](https://studentuml-my.sharepoint.com/:o:/g/personal/valmor_dealmeida_uml_edu/Evw7drHQs_ZMqvRqjb762w8BtVaiw2QrQKjQwYf6qCN4Sg?e=v6nG9O); [PDF](https://studentuml-my.sharepoint.com/:b:/g/personal/valmor_dealmeida_uml_edu/EXFVW-nIPxhKjRDTKVqur1QBfwlaeCfa7hiayzAkR4g_ow?e=KjHEyI)).\n",
    " + Review the fundamental mathematical elements of the finite element basis functions theory.\n",
    " + Demonstrate function approximation via Lagrange finite element basis functions of degree 1. It is left as an exercise to extend the `python` functions below to degrees 2 and 3. Note: only minor modification is needed beyond coding the parent basis functions for higher-order degree."
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    "## [Finite Element Lagrange Basis Functions](#toc)<a id=\"fem-lagrange-basis\"></a>\n",
    "\n",
    "The following subsections follow the ordered presentation of the theory. \n",
    "The `python` code below can be extended to higher degree Lagrange polynomials. It is left as an exercise for the reader.\n",
    "Only minor changes are needed. The point of the implementation below is to present the major components of a program that implements the basic theory of the finite element method. The course notes should be reviewed in addition to the `python` code below."
   ]
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    "### [1) Domain Partition](#toc)<a id=\"dom-part\"></a>\n",
    "\n",
    "The very first structure needed is the domain partition. Build the domain partition artifacts. This can be easily extended to higher order partitions (higher degree) to include interior nodes in the domain patches (or elements). Therefore a partition needs to be aware of the degree of polynomials to be distributed over the domain. Also, here the boundary conditions should be used to flag nodes where no basis functions will be placed."
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    "'''Domain partition'''\n",
    "def get_domain_partition(degree, n_elem, x_min, x_max, bc_x_min='flux', bc_x_max='flux'):\n",
    "    assert degree == 1\n",
    "    # Local node numbering on parent domain\n",
    "    # --0--------------1---->\n",
    "    #  -1      0      +1    zeta\n",
    "    gnodes_x = np.linspace(x_min, x_max, n_elem+1, dtype=np.float64)\n",
    "    patches = list()\n",
    "    local_to_global_node_id_map = list()\n",
    "    for e in range(n_elem):\n",
    "        gnode_id_2 = e + 1            # right\n",
    "        gnode_id_1 = gnode_id_2 - 1   # left\n",
    "        x1 = gnodes_x[gnode_id_1]\n",
    "        x2 = gnodes_x[gnode_id_2]\n",
    "        # Local node id:  0   1\n",
    "        patches.append((x1, x2))\n",
    "        # Local node id:                        0           1\n",
    "        local_to_global_node_id_map.append([gnode_id_1, gnode_id_2])\n",
    "    if bc_x_min == 'essential':\n",
    "        local_to_global_node_id_map[0][0] = -1\n",
    "    if bc_x_max == 'essential':\n",
    "        local_to_global_node_id_map[-1][-1] = -1\n",
    "    return (patches, gnodes_x, local_to_global_node_id_map)"
   ]
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    "### [2) Parent Mapping](#toc)<a id=\"parent-map\"></a>\n",
    "\n",
    "The parent mapping is not a function of the degree of the Lagrange polynomials unless the domain is curved and an isoparametric mapping is used (this is not covered in this course yet). The foregoing makes the parent mapping the second structured needed."
   ]
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    "'''Parent mapping'''\n",
    "def get_parent_mapping():\n",
    "    # zeta in [-1,1]\n",
    "    parent_mapping = lambda zeta, x_e_bar, h_e: x_e_bar + h_e/2*zeta # compute x\n",
    "    parent_mapping_prime = lambda h_e: h_e/2                           # compute mapping derivative wrt zeta\n",
    "    # x in Omega_e\n",
    "    inverse_parent_mapping = lambda x, x_e_bar, h_e: (x - x_e_bar)*2/h_e # compute zeta\n",
    "    return (parent_mapping, parent_mapping_prime, inverse_parent_mapping)"
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    "### [3) Parent Basis Functions](#toc)<a id=\"parent-basis\"></a>\n",
    "\n",
    "Construct the parent basis functions. Again, the course notes should be followed to extend this to higher degree Lagrange polynomials, and/or h-p adaptivity."
   ]
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    "'''Parent basis functions'''\n",
    "def get_parent_basis_functions():\n",
    "    parent_basis_func_list = list()\n",
    "    parent_basis_func_prime_list = list()\n",
    "    parent_basis_func_list.append(lambda zeta: -(zeta-1)/2)  # left\n",
    "    parent_basis_func_list.append(lambda zeta:  (zeta+1)/2)  # right\n",
    "    parent_basis_func_prime_list.append(lambda zeta: -1/2) # left\n",
    "    parent_basis_func_prime_list.append(lambda zeta:  1/2) # right\n",
    "    \n",
    "    return (parent_basis_func_list, parent_basis_func_prime_list)"
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    "### [4) Global Basis Functions](#toc)<a id=\"global-basis\"></a>\n",
    "\n",
    "A global finite element basis function is never constructed but here it is demonstrated how it can be done so the theory is proven numerically. The `python` functions below requires only minor changes when extended for higher degree Lagrange polynomials, and/or rudimentary h-p adaptivity."
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    "'''Any global basis function'''\n",
    "def global_basis_function(i, x, domain_partition, parent_mapping, parent_basis_functions):\n",
    "    \"\"\"Evaluate the ith global FE basis function and its derivative on x points.\n",
    "    \n",
    "    This is never needed in practice. It is here for demonstrating the theory.\n",
    "    \"\"\"\n",
    "  \n",
    "    try:\n",
    "        len(x)\n",
    "    except TypeError:\n",
    "        x = np.array([x])\n",
    "  \n",
    "    if not isinstance(x, np.ndarray):\n",
    "       assert isinstance(x, list) or isinstance(x, tuple)\n",
    "       x = np.array(x)\n",
    "  \n",
    "    phi_i_x = np.copy(x) * 0.0 # initialization\n",
    "    phi_prime_i_x = np.copy(x) * 0.0 # initialization\n",
    "        \n",
    "    patches = domain_partition[0]\n",
    "    local_to_global_node_id_map = domain_partition[2]\n",
    "    inverse_parent_mapping = parent_mapping[2]\n",
    "    parent_basis_func_list = parent_basis_functions[0]\n",
    "  \n",
    "    # expensive reverse lookup\n",
    "    for j, x_j in enumerate(x):\n",
    "        for e, nodes_x in enumerate(patches):\n",
    "            if nodes_x[0] <= x_j <= nodes_x[1]:\n",
    "                n_lnodes = len(nodes_x)\n",
    "                for I in range(n_lnodes):\n",
    "                    if local_to_global_node_id_map[e][I] == i:\n",
    "                        x_e_bar = (nodes_x[0] + nodes_x[1])/2\n",
    "                        h_e = nodes_x[1] - nodes_x[0]\n",
    "                        zetta = inverse_parent_mapping(x_j, x_e_bar, h_e)\n",
    "                        phi_i_x[j] = parent_basis_func_list[I](zetta)\n",
    "                break\n",
    "    return phi_i_x"
   ]
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    "Here the entire set of global basis functions is created; again, the `python` function below requires only minor changes for higher degree Lagrange polynomials, and/or when used with rudimentary h-p adaptivity."
   ]
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    "'''All global basis functions'''\n",
    "def get_global_basis_functions(domain_partition, parent_mapping, parent_basis_functions, global_basis_function):\n",
    "    \n",
    "    basis_func_list = list()\n",
    "    n_gnodes = domain_partition[1].size\n",
    "    local_to_global_node_id_map = domain_partition[2]\n",
    "    phi_i = lambda i, x: global_basis_function(i,x, domain_partition, parent_mapping, parent_basis_functions)\n",
    "  \n",
    "    visited = [False]*n_gnodes\n",
    "    for e in range(n_elem):\n",
    "        for I in range(len(local_to_global_node_id_map[e])):\n",
    "            gnode_id = local_to_global_node_id_map[e][I]\n",
    "            if gnode_id >= 0 and not visited[gnode_id]:\n",
    "                      basis_func_list.append(lambda x, i=gnode_id: phi_i(i,x))\n",
    "                      visited[gnode_id] = True\n",
    "  \n",
    "    assert len(basis_func_list) >= 1, 'There are no basis functions to build.'\n",
    "    \n",
    "    return basis_func_list"
   ]
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    "### [5) Testing](#toc)<a id=\"test\"></a>\n",
    "\n",
    "See below for choices of boundary conditions and global basis functions."
   ]
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    "'''Plot global basis functions'''\n",
    "def plot(npts=200, title='Lagrange Basis Functions'):\n",
    "    \n",
    "    import matplotlib.pyplot as plt\n",
    "    #%matplotlib inline\n",
    "    plt.style.use('classic')\n",
    "    plt.figure(1, figsize=(14, 5))\n",
    "\n",
    "    x_pts = np.linspace(x_min, x_max, npts)\n",
    "    for (i,phi_i) in enumerate(phi_list):\n",
    "        plt.plot(x_pts, phi_i(x_pts),'-',label=r'$\\phi_%i$'%i)\n",
    "\n",
    "    gnodes_x = domain_partition[1]\n",
    "    plt.scatter(gnodes_x, np.zeros(gnodes_x.size), color='red', marker='x', s=80, label='nodes')\n",
    "\n",
    "    plt.title(title, fontsize=20)\n",
    "    plt.ylabel(r'$\\phi_i(x)$', fontsize=18)\n",
    "    plt.xlabel(r'$x$', fontsize=18)\n",
    "    plt.xticks(fontsize=16)\n",
    "    plt.yticks(fontsize=16)\n",
    "    plt.legend(loc='best',fontsize=12)\n",
    "    plt.grid(True)\n",
    "    plt.show()"
   ]
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    "'''Test'''\n",
    "import numpy as np\n",
    "x_min = -2\n",
    "x_max = 10\n",
    "\n",
    "degree = 1\n",
    "n_elem = 200\n",
    "\n",
    "# It is implied here the boundary conditions are of type: flux\n",
    "domain_partition = get_domain_partition(degree, n_elem, x_min, x_max)\n",
    "parent_mapping = get_parent_mapping()\n",
    "parent_basis_functions = get_parent_basis_functions()\n",
    "\n",
    "phi_list = get_global_basis_functions(domain_partition, parent_mapping, parent_basis_functions, global_basis_function)\n",
    "\n",
    "#plot(npts=800, title=r'Lagrange Basis Functions (w/ Flux Boundary Conditions) (degree = %i; dim =%i'%(degree, len(phi_list))+')')"
   ]
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     "text": [
      "Help on function plot in module __main__:\n",
      "\n",
      "plot(npts=200, title='Lagrange Basis Functions')\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(plot)"
   ]
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    "## [Function Approximation](#toc)<a id=\"func-approx\"></a>\n",
    "\n",
    "This section covers implementation `python` code for function approximation using Lagrange finite element basis functions and the continuous least-squares residual covered in previous notebooks in this course."
   ]
  },
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   "source": [
    "### [Target Function](#toc)<a id=\"f\"></a>\n",
    "\n",
    "Given a *well-behaved* target function $f:[a,b]\\rightarrow\\Reals$, compute an approximant $g:[a,b]\\rightarrow\\Reals$."
   ]
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     "text": [
      "# shape pts =  12\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1120x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Generate the target function'''\n",
    "\n",
    "try:    \n",
    "    from engy_5310.toolkit import TargetFunction   \n",
    "except ModuleNotFoundError:\n",
    "    assert False, 'You need to provide your own code here. Bailing out.'\n",
    "\n",
    "shape_pts = [(-2,-10), (-1,10), (0,-18), (1,14), (2,0), (3,28), (5,-23), (6, -1), (6.5, -15), (7,12), (9,1), (10,-10)]\n",
    "print('# shape pts = ', len(shape_pts))\n",
    "\n",
    "f = TargetFunction(shape_pts, type='linear')\n",
    "  \n",
    "f.plot(n_plot_pts=200, show_shape_pts=True, title='Target Function')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Inner Product](#toc)<a id=\"inner-prod\"></a>\n",
    "\n",
    "The inner products $(\\phi_i,\\phi_j)$ and $(f,\\phi_i)$ are used repetitively when approximating a function via the continuous least-squares method. It pays off to implement a general `python` function for this operation. It can be readily computed using the global basis functions. This is rarely done this way since it is expensive. A much more effective element-by-element integration method will be described next in the course. For now the code below is a pedagogical way of demonstrating the implementation. In addition, the code below is independent of the degree of the Lagrange polynomial basis functions; no change in this code is needed when using higher-order degree polynomials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T03:58:39.120888Z",
     "start_time": "2021-11-08T03:58:39.117362Z"
    },
    "code_folding": [
     2
    ]
   },
   "outputs": [],
   "source": [
    "'''Pedagogical inner product'''\n",
    "from scipy.integrate import quad\n",
    "def inner_product(u, v, patches):\n",
    "    integrand = lambda x: u(x) * v(x)          \n",
    "    inner_product = 0.0\n",
    "    for nodes_x in patches:\n",
    "        (inner_product_e, _) = quad(integrand, nodes_x[0], nodes_x[1])\n",
    "        inner_product += inner_product_e           \n",
    "    return inner_product"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Gram Matrix](#toc)<a id=\"gram-matrix\"></a>\n",
    "\n",
    "Build the matrix of inner products of the basis functions, the *Gram matrix* or also called the *mass matrix*: ${(\\Gmtrx)}_{i,j} = (\\phi_i, \\phi_j)$. The implementation below is expensive and provide here for pedagogical purposes. A much faster way will covered later, however it will be less direct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T03:58:46.699739Z",
     "start_time": "2021-11-08T03:58:46.696522Z"
    },
    "code_folding": [
     1
    ]
   },
   "outputs": [],
   "source": [
    "'''Pedagogical Gram matrix'''\n",
    "def get_gram_matrix(basis_func_list, domain_partition, inner_product):\n",
    "    N = len(basis_func_list)\n",
    "    patches = domain_partition[0]\n",
    "    a_mtrx = np.zeros((N, N), dtype=np.float64)\n",
    "    for i,phi_i in enumerate(basis_func_list):\n",
    "        for j,phi_j in enumerate(basis_func_list):\n",
    "            a_mtrx[i,j] = inner_product(phi_i, phi_j, patches)    \n",
    "    return a_mtrx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:00:00.749860Z",
     "start_time": "2021-11-08T03:58:48.681145Z"
    }
   },
   "outputs": [],
   "source": [
    "'''Compute the Pedagogical Gram matrix'''\n",
    "gram_mtrx = get_gram_matrix(phi_list, domain_partition, inner_product)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:00:00.757757Z",
     "start_time": "2021-11-08T04:00:00.751600Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.08, 0.04, 0.  , 0.  , 0.  , 0.  , ..., 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.04, 0.16, 0.04, 0.  , 0.  , 0.  , ..., 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.04, 0.16, 0.04, 0.  , 0.  , ..., 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.04, 0.16, 0.04, 0.  , ..., 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.04, 0.16, 0.04, ..., 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.04, 0.16, ..., 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       ...,\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.  , 0.  , ..., 0.16, 0.04, 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.  , 0.  , ..., 0.04, 0.16, 0.04, 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.  , 0.  , ..., 0.  , 0.04, 0.16, 0.04, 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.  , 0.  , ..., 0.  , 0.  , 0.04, 0.16, 0.04, 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.  , 0.  , ..., 0.  , 0.  , 0.  , 0.04, 0.16, 0.04],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.  , 0.  , ..., 0.  , 0.  , 0.  , 0.  , 0.04, 0.08]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions(precision=2, edgeitems=6, threshold=200, linewidth=150)\n",
    "gram_mtrx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:16:52.254879Z",
     "start_time": "2021-11-08T04:16:52.249539Z"
    },
    "code_folding": [
     1
    ]
   },
   "outputs": [],
   "source": [
    "'''Element-by-element assembly of the Gram matrix'''\n",
    "def assemble_gram_matrix(a_mtrx, domain_partition, parent_mapping, parent_basis_func_list):\n",
    "    \n",
    "    n = len(parent_basis_func_list)\n",
    "    \n",
    "    local_to_global_node_id_map = domain_partition[2]\n",
    "    \n",
    "    local_a_mtrx = np.zeros((n, n), dtype=np.float64)\n",
    "    \n",
    "    for I in range(n):\n",
    "        parent_basis_func_I = parent_basis_func_list[0][I]\n",
    "        for J in range(n):\n",
    "            integrand = lambda zeta: parent_basis_func_I(zeta) * parent_basis_func_list[0][J](zeta)\n",
    "            (local_a_mtrx[I,J], _) = quad(integrand, -1, 1)\n",
    "            \n",
    "    for (e, gnode_ids) in enumerate(local_to_global_node_id_map):\n",
    "        (x_0, x_1) = domain_partition[0][e]\n",
    "        h_e = x_1 - x_0\n",
    "        parent_mapping_jacobian = parent_mapping[1](h_e)\n",
    "        for (I, i) in enumerate(gnode_ids):\n",
    "            for (J, j) in enumerate(gnode_ids):\n",
    "                a_mtrx[i,j] += local_a_mtrx[I,J] * parent_mapping_jacobian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:24:21.661732Z",
     "start_time": "2021-11-08T04:24:21.657882Z"
    }
   },
   "outputs": [],
   "source": [
    "'''Compute the Gram matrix'''\n",
    "\n",
    "N = len(phi_list) # this needs to be changed to the number of degrees of freedom or effective global basis functions\n",
    "\n",
    "g_mtrx = np.zeros((N,N), dtype=np.float64)\n",
    "\n",
    "assemble_gram_matrix(g_mtrx, domain_partition, parent_mapping, parent_basis_functions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:18:45.145700Z",
     "start_time": "2021-11-08T04:18:45.140812Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.08, 0.04, 0.  , 0.  , 0.  , 0.  , ..., 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.04, 0.16, 0.04, 0.  , 0.  , 0.  , ..., 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.04, 0.16, 0.04, 0.  , 0.  , ..., 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.04, 0.16, 0.04, 0.  , ..., 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.04, 0.16, 0.04, ..., 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.04, 0.16, ..., 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       ...,\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.  , 0.  , ..., 0.16, 0.04, 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.  , 0.  , ..., 0.04, 0.16, 0.04, 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.  , 0.  , ..., 0.  , 0.04, 0.16, 0.04, 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.  , 0.  , ..., 0.  , 0.  , 0.04, 0.16, 0.04, 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.  , 0.  , ..., 0.  , 0.  , 0.  , 0.04, 0.16, 0.04],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.  , 0.  , ..., 0.  , 0.  , 0.  , 0.  , 0.04, 0.08]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_mtrx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:18:52.299201Z",
     "start_time": "2021-11-08T04:18:52.295666Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "||gram_mtrx - g_mtrx|| =  6.0332475458014115e-16\n"
     ]
    }
   ],
   "source": [
    "print('||gram_mtrx - g_mtrx|| = ', np.linalg.norm(gram_mtrx-g_mtrx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Load Vector](#toc)<a id=\"load-vector\"></a>\n",
    "\n",
    "Build the load vector ${(\\bvec)}_{i} = (f, \\phi_i)$ by computing the inner product of $f$ with each basis function member."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:19:04.668232Z",
     "start_time": "2021-11-08T04:19:00.289543Z"
    }
   },
   "outputs": [],
   "source": [
    "'''Build the pedagogical load vector'''\n",
    "\n",
    "b_vec = np.zeros(len(phi_list), dtype=np.float64)\n",
    "patches = domain_partition[0]\n",
    "for i, phi_i in enumerate(phi_list):\n",
    "    b_vec[i] = inner_product(f, phi_i, patches)      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:19:04.674873Z",
     "start_time": "2021-11-08T04:19:04.669657Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.01, -1.25, -0.1 ,  1.06,  1.94,  1.05, -0.56, -2.17, -3.61, -3.07, -1.25,  0.6 ,  2.38,  2.9 ,  2.15,  1.34,  0.55,  0.66,  2.15,  3.76,\n",
       "        5.37,  6.18,  5.01,  3.54,  2.07,  0.6 , -0.87, -2.34, -3.81, -5.01, -4.46, -3.2 , -1.93, -0.8 , -1.33, -2.77, -1.73,  1.25,  2.65,  2.4 ,\n",
       "        2.09,  1.77,  1.45,  1.14,  0.82,  0.5 ,  0.1 , -0.5 , -1.13, -1.77, -1.09])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:20:41.368032Z",
     "start_time": "2021-11-08T04:20:41.362626Z"
    },
    "code_folding": [
     2
    ]
   },
   "outputs": [],
   "source": [
    "'''Element-by-element assembly of the load vector'''\n",
    "\n",
    "def assemble_load_vector(b_vec, domain_partition, parent_mapping, parent_basis_func_list):\n",
    "    \n",
    "    n = len(parent_basis_func_list)\n",
    "    local_to_global_node_id_map = domain_partition[2]\n",
    "    \n",
    "    local_b_vec = np.zeros(n, dtype=np.float64)\n",
    "            \n",
    "    for (e, gnode_ids) in enumerate(local_to_global_node_id_map):\n",
    "        (x_0, x_1) = domain_partition[0][e]\n",
    "        h_e = x_1 - x_0\n",
    "        parent_mapping_jacobian = parent_mapping[1](h_e)\n",
    "        x_e_bar = (x_0 + x_1)/2.0\n",
    "        \n",
    "        for I in range(n):\n",
    "            parent_basis_func_I = parent_basis_func_list[0][I]\n",
    "            f_parent = lambda zeta, x_e_bar=x_e_bar, h_e=h_e: f(parent_mapping[0](zeta, x_e_bar, h_e))\n",
    "            integrand = lambda zeta: f_parent(zeta) * parent_basis_func_I(zeta)\n",
    "            (local_b_vec[I], _) = quad(integrand, -1, 1)\n",
    "        \n",
    "        for (I, i) in enumerate(gnode_ids):\n",
    "                b_vec[i] += local_b_vec[I] * parent_mapping_jacobian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:24:35.506050Z",
     "start_time": "2021-11-08T04:24:34.757222Z"
    }
   },
   "outputs": [],
   "source": [
    "'''Assemble load vector'''\n",
    "\n",
    "load_vec = np.zeros(len(phi_list))\n",
    "assemble_load_vector(load_vec, domain_partition, parent_mapping, parent_basis_functions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:22:03.726648Z",
     "start_time": "2021-11-08T04:22:03.721518Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.01, -1.25, -0.1 ,  1.06,  1.94,  1.05, -0.56, -2.17, -3.61, -3.07, -1.25,  0.6 ,  2.38,  2.9 ,  2.15,  1.34,  0.55,  0.66,  2.15,  3.76,\n",
       "        5.37,  6.18,  5.01,  3.54,  2.07,  0.6 , -0.87, -2.34, -3.81, -5.01, -4.46, -3.2 , -1.93, -0.8 , -1.33, -2.77, -1.73,  1.25,  2.65,  2.4 ,\n",
       "        2.09,  1.77,  1.45,  1.14,  0.82,  0.5 ,  0.1 , -0.5 , -1.13, -1.77, -1.09])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "load_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:22:39.998173Z",
     "start_time": "2021-11-08T04:22:39.995000Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "||b_vec - load_vec|| =  1.5236066710304134e-14\n"
     ]
    }
   ],
   "source": [
    "print('||b_vec - load_vec|| = ', np.linalg.norm(b_vec-load_vec))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Optimal Combination Coefficients](#toc)<a id=\"cont-optimal-coeff\"></a>\n",
    "\n",
    "Compute the optimal coefficient vector by solving\n",
    "\n",
    "\\begin{equation*}\n",
    " \\overset{(n\\times n)}{\\Gmtrx}\\,\\cvec^* = \\bvec ,\n",
    "\\end{equation*}\n",
    "\n",
    "which has a unique solution since the Gram matrix, $\\Gmtrx$, is always full rank (linear independent basis functions)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:24:39.599238Z",
     "start_time": "2021-11-08T04:24:39.595013Z"
    }
   },
   "outputs": [],
   "source": [
    "'''Compute optimal coefficient vector'''\n",
    "\n",
    "#c_star_vec = np.linalg.solve(gram_mtrx, b_vec)\n",
    "c_star_vec = np.linalg.solve(g_mtrx, load_vec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Results](#toc)<a id=\"cont-res\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-11-08T04:24:43.441512Z",
     "start_time": "2021-11-08T04:24:42.620180Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1120x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Plot comparison of f and g_best_vec'''\n",
    "\n",
    "n_pts = 300\n",
    "x_pts = np.linspace(x_min, x_max, n_pts)\n",
    "\n",
    "eval_mtrx = np.zeros((n_pts,len(phi_list)), dtype=np.float64)\n",
    "for (j,phi_j) in enumerate(phi_list):\n",
    "    eval_mtrx[:,j] = phi_j(x_pts)\n",
    "    \n",
    "g_best = eval_mtrx@c_star_vec\n",
    "\n",
    "f.plot(g=(x_pts,g_best), n_plot_pts=n_pts, g_line_style='plain', f_line_style='dashed', title=r'Compare $f$ and $g$ Functions ($m\\rightarrow\\infty$, N='+str(len(phi_list))+')')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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