{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5796054b",
   "metadata": {},
   "source": [
    "\n",
    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "### Interactive Simple Machine Learning Artificial Neural Network (ANN)\n",
    "\n",
    "\n",
    "#### Michael Pyrcz, Professor, The University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e41c1943",
   "metadata": {},
   "source": [
    "#### Neural Networks\n",
    "\n",
    "Machine learning method for supervised learning for classification and regression analysis.  Here are some key aspects of support vector machines.\n",
    "\n",
    "**Basic Design** *\"...a computing system made up of a number of simple, highly interconnected processing elements, which process information by their dynamic state response to external inputs.\"* Caudill (1989). \n",
    "\n",
    "**Nature-inspire Computing** based on the neuronal structure in the brain, including many interconnected simple, processing units, known as nodes that are capable of complicated emergent pattern detection due to a large number of nodes and interconnectivity.\n",
    "\n",
    "**Training and Testing** just like and other predictive model (e.g. linear regression, decision trees and support vector machines) we perform training to fit parameters and testing to tune hyperparameters.  Here we observe the error with training and testing datasets, but do not demonstrate tuning of the hyperparameters.  \n",
    "\n",
    "**Parameters** are the weights applied to each connection and a bias term applied to each node.  For a single node in an artificial neural network, this includes the slope terms, $\\beta_i$, and the bias term, $\\beta_{0}$.\n",
    "\n",
    "\\begin{equation}\n",
    "Y = \\sum_{i=1}^m \\beta_i X + \\beta_0\n",
    "\\end{equation}\n",
    "\n",
    "it can be seen that the number of parameters increases rapidly as we increase the number of nodes and the connectivity between the nodes.\n",
    "\n",
    "**Layers** the typical artificial neural net is structured with an **input layer**, with one node for each $m$ predictor feature, $X_1,\\ldots,X_m$. There is an **ouput layer**, with one node for each $r$ response feature, $Y_1,\\ldots,Y_r$.  There may be one or more layers of nodes between the input and output layers, known as **hidden layer(s)**.  \n",
    "\n",
    "**Connections** are the linkages between the nodes in adjacent layers.  For example, in a fully connected artificial neural network, all the input nodes are connected to all of the nodes in the first layer, then all of the nodes in the first layer are connected to the next layer and so forth. Each connection includes a weight parameter as indicated above.\n",
    "\n",
    "**Nodes** receive the weighted signal from the connected previous layer nodes, sum and then apply this result to the **activation** function in the node. Some example activation functions include:\n",
    "\n",
    "* **Binary** the node fires or not.  This is represented by a Heaviside step function.\n",
    "\n",
    "* **Identify** the input is passed to the output $f(x) = x$\n",
    "\n",
    "* **Linear** the node passes a signal that increases linearly with the weighted input.\n",
    "\n",
    "* **Logistic** also known as sigmoid or soft step $f(x) = \\frac{1}{1+e^{-x}}$\n",
    "\n",
    "the node output is the nonlinear activiation function applied to the linearly weighted inputs. This is fed to all nodes in the next layer.\n",
    "\n",
    "**Training Cycles** - the presentation of a batch of data, forward application of the current prediction model to make estimates, calculation of error and then backpropagation of error to correct the artificial neural network parameters to reduce the error over all of the batches.\n",
    "\n",
    "**Batch** is the set of training data for each training cycle of forward prediction and back propagation of error, drawn to train for each iteration. There is a trade-off, a larger batch results in more computational time per iteration, but a more accurate estimate of the error to adjust the weights.  Smaller batches result in a nosier estimate of the error, but faster epochs, this results in faster learning and even possibly more robust models.\n",
    "\n",
    "**Epochs** - is a set of training cycles, batches covering all available training data.  \n",
    "\n",
    "**Local Minimums** - if one calculated the error hypersurface over the range of model parameters it would be hyparabolic, there is a global minimium error solution.  But this error hyper surface is rough and it is possible to be stuck in a local minimum. **Learning Rate** and **Mommentum** coefficients are introduced to avoid getting stuck in local minimums.\n",
    "\n",
    "* **Mommentum** is a hyperparameter to control the use of information from the weight update over the last epoch for consideration in the current epoch.  This can be accomplished with an update vector, $v_i$, a mommentum parameter, $\\alpha$, to calculate the current weight update, $v_{i+1}$ given the new update $\\theta_{i+1}$.\n",
    "\n",
    "\\begin{equation}\n",
    "v_{i+1} = \\alpha v_i + \\theta_{i+1}\n",
    "\\end{equation}\n",
    "\n",
    "* **Learning Rate** is a hyperparameter that controls the adjustment of the weights in response to the gradient indicated by backpropagation of error \n",
    "\n",
    "##### Applications to subsurface modeling\n",
    "\n",
    "We demonstrate the estimation of normal score transformed porosity from depth.  This would be useful for building a vertical trend model. \n",
    "\n",
    "* modeling the complicated relationship between porosity and depth.\n",
    "\n",
    "#### Limitations of Neural Network Estimation\n",
    "\n",
    "Since we demonstrate the use of an artificial neural network to estimate porosity from sparsely sampled data over depth, we should comment on limitations of our artificial neural networks for this estimation problem:\n",
    "\n",
    "* does not honor the well data\n",
    "\n",
    "* does not honor the histogram of the data\n",
    "\n",
    "* does not honor spatial correlation \n",
    "\n",
    "* does not honor the multivariate relationship\n",
    "\n",
    "* generally low interpretability models\n",
    "\n",
    "* requires a large number of data for effective training\n",
    "\n",
    "* high model complexity with high model variance\n",
    "\n",
    "#### Import Required Packages\n",
    "\n",
    "We will also need some standard packages. These should have been installed with Anaconda 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "877ffa62",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import (MultipleLocator, AutoMinorLocator, AutoLocator) # control of axes ticks\n",
    "plt.rc('axes', axisbelow=True)                            # set axes and grids in the background for all plots\n",
    "from ipywidgets import interactive                        # widgets and interactivity\n",
    "from ipywidgets import widgets                            \n",
    "from ipywidgets import Layout\n",
    "from ipywidgets import Label\n",
    "from ipywidgets import VBox, HBox\n",
    "import math\n",
    "seed = 13"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a27fea49",
   "metadata": {},
   "source": [
    "If you get a package import error, you may have to first install some of these packages. This can usually be accomplished by opening up a command window on Windows and then typing 'python -m pip install [package-name]'. More assistance is available with the respective package docs.  \n",
    "\n",
    "#### Declare Functions\n",
    "\n",
    "I just added a convenience function for adding major and minor gridlines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8abbc843",
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_grid():\n",
    "    plt.gca().grid(True, which='major',linewidth = 1.0); plt.gca().grid(True, which='minor',linewidth = 0.2) # add y grids\n",
    "    plt.gca().tick_params(which='major',length=7); plt.gca().tick_params(which='minor', length=4)\n",
    "    plt.gca().xaxis.set_minor_locator(AutoMinorLocator()); plt.gca().yaxis.set_minor_locator(AutoMinorLocator()) # turn on minor ticks   \n",
    "\n",
    "def calculate_angle_rads(x1, y1, x2, y2):\n",
    "    dx = x2 - x1     # Calculate the differences\n",
    "    dy = y2 - y1\n",
    "    angle_rads = math.atan2(dy, dx)    # Calculate the angle in radians\n",
    "    #angle_degrees = math.degrees(angle_radians)    # Convert the angle to degrees\n",
    "    return angle_rads\n",
    "    \n",
    "def offset(pto, distance, angle_deg): # modified from ChatGPT 4.o generated\n",
    "    angle_rads = math.radians(angle_deg) # Convert angle from degrees to radians\n",
    "    x_new = pto[0] + distance * math.cos(angle_rads) # Calculate the new coordinates\n",
    "    y_new = pto[1] + distance * math.sin(angle_rads)\n",
    "    return np.array((x_new, y_new))\n",
    "\n",
    "def offsetx(xo, distance, angle_deg): # modified from ChatGPT 4.o generated\n",
    "    angle_rads = math.radians(angle_deg) # Convert angle from degrees to radians\n",
    "    x_new = xo + distance * math.cos(angle_rads) # Calculate the new coordinates\n",
    "    return np.array((xo, x_new))\n",
    "\n",
    "def offset_arrx(xo, distance, angle_deg,size): # modified from ChatGPT 4.o generated\n",
    "    angle_rads = math.radians(angle_deg) # Convert angle from degrees to radians\n",
    "    x_new = xo + distance * math.cos(angle_rads) # Calculate the new coordinates\n",
    "    x_arr = x_new + size * math.cos(angle_rads+2.48) # Calculate the new coordinates\n",
    "    return np.array((x_new, x_arr))\n",
    "\n",
    "def offsety(yo, distance, angle_deg): # modified from ChatGPT 4.o generated\n",
    "    angle_rads = math.radians(angle_deg) # Convert angle from degrees to radians\n",
    "    y_new = yo + distance * math.sin(angle_rads) # Calculate the new coordinates\n",
    "    return np.array((yo, y_new))\n",
    "\n",
    "def offset_arry(yo, distance, angle_deg,size): # modified from ChatGPT 4.o generated\n",
    "    angle_rads = math.radians(angle_deg) # Convert angle from degrees to radians\n",
    "    y_new = yo + distance * math.sin(angle_rads) # Calculate the new coordinates\n",
    "    y_arr = y_new + size * math.sin(angle_rads+2.48) # Calculate the new coordinates\n",
    "    return np.array((y_new, y_arr))\n",
    "\n",
    "def lint(x1, y1, x2, y2, t):\n",
    "    # Calculate the interpolated coordinates\n",
    "    x = x1 + t * (x2 - x1)\n",
    "    y = y1 + t * (y2 - y1)\n",
    "    return np.array((x, y))\n",
    "\n",
    "def lintx(x1, y1, x2, y2, t):\n",
    "    # Calculate the interpolated coordinates\n",
    "    x = x1 + t * (x2 - x1)\n",
    "    return x\n",
    "\n",
    "def linty(x1, y1, x2, y2, t):\n",
    "    # Calculate the interpolated coordinates\n",
    "    y = y1 + t * (y2 - y1)\n",
    "    return y\n",
    "\n",
    "def lint_intx(x1, y1, x2, y2, ts, te):\n",
    "    # Calculate the interpolated coordinates\n",
    "    xs = x1 + ts * (x2 - x1)\n",
    "    xe = x1 + te * (x2 - x1)\n",
    "    return np.array((xs,xe))\n",
    "\n",
    "def lint_inty(x1, y1, x2, y2, ts, te):\n",
    "    # Calculate the interpolated coordinates\n",
    "    ys = y1 + ts * (y2 - y1)\n",
    "    ye = y1 + te * (y2 - y1)\n",
    "    return np.array((ys,ye))\n",
    "\n",
    "def lint_int_arrx(x1, y1, x2, y2, ts, te, size):\n",
    "    # Calculate the interpolated coordinates\n",
    "    xe = x1 + te * (x2 - x1)\n",
    "    line_angle_rads = calculate_angle_rads(x1, y1, x2, y2)\n",
    "    x_arr = xe + size * math.cos(line_angle_rads+2.48) # Calculate the new coordinates\n",
    "    return np.array((xe,x_arr))\n",
    "\n",
    "def lint_int_arry(x1, y1, x2, y2, ts, te, size):\n",
    "    # Calculate the interpolated coordinates\n",
    "    ye = y1 + te * (y2 - y1)\n",
    "    line_angle_rads = calculate_angle_rads(x1, y1, x2, y2)\n",
    "    y_arr = ye + size * math.sin(line_angle_rads+2.48) # Calculate the new coordinates\n",
    "    return np.array((ye,y_arr))\n",
    "\n",
    "def as_si(x, ndp): # from xnx on StackOverflow https://stackoverflow.com/questions/31453422/displaying-numbers-with-x-instead-of-e-scientific-notation-in-matplotlib \n",
    "    s = '{x:0.{ndp:d}e}'.format(x=x, ndp=ndp)\n",
    "    m, e = s.split('e')\n",
    "    return r'{m:s}\\times 10^{{{e:d}}}'.format(m=m, e=int(e))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7913b84d",
   "metadata": {},
   "source": [
    "#### The Simple ANN\n",
    "\n",
    "I wrote this code to specify a simple ANN:\n",
    "\n",
    "- three input nodes, 2 hidden nodes and 1 output node\n",
    "\n",
    "and to train the ANN by interatively performing the forward calculation and backpropagation. I calculate:\n",
    "\n",
    "- the error and then propagate it to each node\n",
    "- solve for the partial derivatives of the error with respect to each weight and bias\n",
    "\n",
    "all weights, biases and partial derivatives for all epoch are recorded in vectors for plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "183d883f",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = 0.5; x2 = 0.2; x3 = 0.7; y = 0.3 # training data\n",
    "lr = 0.2 # learning rate\n",
    "\n",
    "np.random.seed(seed=seed)\n",
    "\n",
    "nepoch = 1000\n",
    "\n",
    "y4 = np.zeros(nepoch); y5 = np.zeros(nepoch); y6 = np.zeros(nepoch)\n",
    "\n",
    "w14 = np.zeros(nepoch); w24 = np.zeros(nepoch); w34 = np.zeros(nepoch)\n",
    "w15 = np.zeros(nepoch); w25 = np.zeros(nepoch); w35 = np.zeros(nepoch)\n",
    "w46 = np.zeros(nepoch); w56 = np.zeros(nepoch)\n",
    "\n",
    "dw14 = np.zeros(nepoch); dw24 = np.zeros(nepoch); dw34 = np.zeros(nepoch)\n",
    "dw15 = np.zeros(nepoch); dw25 = np.zeros(nepoch); dw35 = np.zeros(nepoch)\n",
    "dw46 = np.zeros(nepoch); dw56 = np.zeros(nepoch)\n",
    "\n",
    "db4 = np.zeros(nepoch); db5 = np.zeros(nepoch); db6 = np.zeros(nepoch)\n",
    "\n",
    "b4 = np.zeros(nepoch); b5 = np.zeros(nepoch); b6 = np.zeros(nepoch)\n",
    "y4 = np.zeros(nepoch); y5 = np.zeros(nepoch); y6 = np.zeros(nepoch)\n",
    "d4 = np.zeros(nepoch); d5 = np.zeros(nepoch); d6 = np.zeros(nepoch)\n",
    "\n",
    "# initialize the weights - Xavier Weight Initialization \n",
    "lower, upper = -(1.0 / np.sqrt(3.0)), (1.0 / np.sqrt(3.0)) # lower and upper bound for the weights, uses inputs to node\n",
    "#lower, upper = -(sqrt(6.0) / sqrt(3.0 + 2.0)), (sqrt(6.0) / sqrt(3.0 + 2.0)) # Normalized Xavier weights, integrates ouputs also\n",
    "w14[0] = lower + np.random.random() * (upper - lower); \n",
    "w24[0] = lower + np.random.random() * (upper - lower); \n",
    "w34[0] = lower + np.random.random() * (upper - lower);\n",
    "w15[0] = lower + np.random.random() * (upper - lower); \n",
    "w25[0] = lower + np.random.random() * (upper - lower); \n",
    "w35[0] = lower + np.random.random() * (upper - lower);\n",
    "\n",
    "lower, upper = -(1.0 / np.sqrt(2.0)), (1.0 / np.sqrt(2.0))\n",
    "#lower, upper = -(sqrt(6.0) / sqrt(2.0 + 1.0)), (sqrt(6.0) / sqrt(2.0 + 1.0)) # Normalized Xavier weights, integrates ouputs also\n",
    "\n",
    "w46[0] = lower + np.random.random() * (upper - lower); \n",
    "w56[0] = lower + np.random.random() * (upper - lower);     \n",
    "\n",
    "#b4[0] = np.random.random(); b5[0] = np.random.random(); b6[0] = np.random.random()\n",
    "b4[0] = (np.random.random()-0.5)*0.5; b5[0] = (np.random.random()-0.5)*0.5; b6[0] = (np.random.random()-0.5)*0.5; # small random value    \n",
    "\n",
    "\n",
    "for i in range(0,nepoch):\n",
    "\n",
    "# forward pass of model\n",
    "    y4[i] = w14[i]*x1 + w24[i]*x2 + w34[i]*x3 + b4[i]; \n",
    "    y4[i] = 1.0/(1 + math.exp(-1*y4[i]))\n",
    "    \n",
    "    y5[i] = w15[i]*x1 + w25[i]*x2 + w35[i]*x3 + b5[i]\n",
    "    y5[i] = 1.0/(1 + math.exp(-1*y5[i]))\n",
    "    \n",
    "    y6[i] = w46[i]*y4[i] + w56[i]*y5[i] + b6[i]\n",
    "#    y6[i] = 1.0/(1 + math.exp(-1*y6[i])) # sgimoid / logistic activation at o6 \n",
    "\n",
    "# back propagate the error through the nodes\n",
    "#    d6[i] = y6[i]*(1-y6[i])*(y-y6[i]) # sgimoid / logistic activation at o6 \n",
    "    d6[i] = (y-y6[i]) # identity activation o at o6\n",
    "    d5[i] = y5[i]*(1-y5[i])*w56[i]*d6[i]; d4[i] = y4[i]*(1-y4[i])*w46[i]*d6[i]\n",
    "\n",
    "# calculate the change in weights\n",
    "    if i < nepoch - 1:\n",
    "        dw14[i] = lr*d4[i]*x1; dw24[i] = lr*d4[i]*x2; dw34[i] = lr*d4[i]*x3\n",
    "        dw15[i] = lr*d5[i]*x1; dw25[i] = lr*d5[i]*x2; dw35[i] = lr*d5[i]*x3\n",
    "        dw46[i] = lr*d6[i]*y4[i]; dw56[i] = lr*d6[i]*y5[i] \n",
    "        \n",
    "        db4[i] = lr*d4[i]; db5[i] = lr*d5[i]; db6[i] = lr*d6[i];\n",
    "\n",
    "        w14[i+1] = w14[i] + dw14[i]; w24[i+1] = w24[i] + dw24[i]; w34[i+1] = w34[i] + dw34[i] \n",
    "        w15[i+1] = w15[i] + dw15[i]; w25[i+1] = w25[i] + dw25[i]; w35[i+1] = w35[i] + dw35[i] \n",
    "        w46[i+1] = w46[i] + dw46[i]; w56[i+1] = w56[i] + dw56[i]\n",
    "\n",
    "        b4[i+1] = b4[i] + db4[i]; b5[i+1] = b5[i] + db5[i]; b6[i+1] = b6[i] + db6[i] "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf37b61d",
   "metadata": {},
   "source": [
    "#### Interactive Artificial Neural Network (ANN)\n",
    "\n",
    "The interactive inputs include:\n",
    "\n",
    "* **$n_{epoch}$** - number of cycles through the data, coupled forward prediction and back propagation\n",
    "\n",
    "* **$\\eta$** - learning rate, applied to the weight and bias derivatives\n",
    "\n",
    "* **$S$** - random number seed\n",
    "\n",
    "* **Weights** - show the network weights\n",
    "\n",
    "* **Forward Pass** - show the contributions and node outputs\n",
    "\n",
    "* **Back Propogation** - show the error partial derivatives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d270c12b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# widgets and dashboard\n",
    "l = widgets.Text(value='                                             Machine Learning Simple Artificial Neural Network, Prof. Michael Pyrcz, The University of Texas at Austin',layout=Layout(width='950px', height='30px'))\n",
    "\n",
    "nepoch = widgets.IntSlider(min=0, max = 100, value=0, step = 1, description = '$n_{epoch}$',orientation='horizontal', style = {'description_width': 'initial'},\n",
    "                           continuous_update=False,layout=Layout(width='300px', height='30px'))\n",
    "\n",
    "lr = widgets.FloatLogSlider(min=-2, max = 0, value=0.1, step = 1.0, description = '$\\eta$',orientation='horizontal', style = {'description_width': 'initial'},\n",
    "                           continuous_update=False,layout=Layout(width='300px', height='30px'),readout_format='.2f')\n",
    "\n",
    "seed = widgets.IntSlider(min=0, max = 100, value=1, step = 1, description = '$S$',orientation='horizontal', style = {'description_width': 'initial'},\n",
    "                           continuous_update=False,layout=Layout(width='300px', height='30px'))\n",
    "\n",
    "weights = widgets.Checkbox(value=True,description='Weights',disabled=False,layout=Layout(width='300px', height='30px'))\n",
    "\n",
    "forward = widgets.Checkbox(value=True,description='Forward Pass',disabled=False,layout=Layout(width='300px', height='30px'))\n",
    "\n",
    "back = widgets.Checkbox(value=True,description='Back Propogation',disabled=False,layout=Layout(width='300px', height='30px'))\n",
    "\n",
    "ui1 = widgets.HBox([nepoch,lr,seed],)\n",
    "ui2 = widgets.HBox([weights,forward,back],)\n",
    "ui = widgets.VBox([l,ui1,ui2],)\n",
    "\n",
    "def run_plot(nepoch,lr,weights,forward,back,seed):                       # make data, fit models and plot\n",
    "    min_lw = 0.5; node_r = 0.2; min_node_r = 0.20\n",
    "    lw = 2.0 - min_lw; min_alpha = 0.1\n",
    "    alpha = 1.0 - min_alpha\n",
    "    iepoch = nepoch\n",
    "    np.random.seed(seed=seed)\n",
    "    x1 = 0.5; x2 = 0.2; x3 = 0.7; y = 0.3 # training data\n",
    "    \n",
    "    np.random.seed(seed=seed)\n",
    "    \n",
    "    nepoch = 1000\n",
    "    \n",
    "    y4 = np.zeros(nepoch); y5 = np.zeros(nepoch); y6 = np.zeros(nepoch)\n",
    "    \n",
    "    w14 = np.zeros(nepoch); w24 = np.zeros(nepoch); w34 = np.zeros(nepoch)\n",
    "    w15 = np.zeros(nepoch); w25 = np.zeros(nepoch); w35 = np.zeros(nepoch)\n",
    "    w46 = np.zeros(nepoch); w56 = np.zeros(nepoch)\n",
    "    \n",
    "    dw14 = np.zeros(nepoch); dw24 = np.zeros(nepoch); dw34 = np.zeros(nepoch)\n",
    "    dw15 = np.zeros(nepoch); dw25 = np.zeros(nepoch); dw35 = np.zeros(nepoch)\n",
    "    dw46 = np.zeros(nepoch); dw56 = np.zeros(nepoch)\n",
    "    \n",
    "    db4 = np.zeros(nepoch); db5 = np.zeros(nepoch); db6 = np.zeros(nepoch)\n",
    "    \n",
    "    b4 = np.zeros(nepoch); b5 = np.zeros(nepoch); b6 = np.zeros(nepoch)\n",
    "    y4 = np.zeros(nepoch); y5 = np.zeros(nepoch); y6 = np.zeros(nepoch)\n",
    "    y4in = np.zeros(nepoch); y5in = np.zeros(nepoch); y6in = np.zeros(nepoch)\n",
    "    d4 = np.zeros(nepoch); d5 = np.zeros(nepoch); d6 = np.zeros(nepoch)\n",
    "    d1 = np.zeros(nepoch); d2 = np.zeros(nepoch); d3 = np.zeros(nepoch)\n",
    "    \n",
    "    # initialize the weights - Xavier Weight Initialization \n",
    "    lower, upper = -(1.0 / np.sqrt(3.0)), (1.0 / np.sqrt(3.0)) # lower and upper bound for the weights, uses inputs to node\n",
    "    #lower, upper = -(sqrt(6.0) / sqrt(3.0 + 2.0)), (sqrt(6.0) / sqrt(3.0 + 2.0)) # Normalized Xavier weights, integrates ouputs also\n",
    "    w14[0] = lower + np.random.random() * (upper - lower); \n",
    "    w24[0] = lower + np.random.random() * (upper - lower); \n",
    "    w34[0] = lower + np.random.random() * (upper - lower);\n",
    "    w15[0] = lower + np.random.random() * (upper - lower); \n",
    "    w25[0] = lower + np.random.random() * (upper - lower); \n",
    "    w35[0] = lower + np.random.random() * (upper - lower);\n",
    "    \n",
    "    lower, upper = -(1.0 / np.sqrt(2.0)), (1.0 / np.sqrt(2.0))\n",
    "    #lower, upper = -(sqrt(6.0) / sqrt(2.0 + 1.0)), (sqrt(6.0) / sqrt(2.0 + 1.0)) # Normalized Xavier weights, integrates ouputs also\n",
    "\n",
    "    w46[0] = lower + np.random.random() * (upper - lower); \n",
    "    w56[0] = lower + np.random.random() * (upper - lower);     \n",
    "\n",
    "    #b4[0] = np.random.random(); b5[0] = np.random.random(); b6[0] = np.random.random()\n",
    "    b4[0] = (np.random.random()-0.5)*0.5; b5[0] = (np.random.random()-0.5)*0.5; b6[0] = (np.random.random()-0.5)*0.5; # small random value    \n",
    "\n",
    "    for i in range(0,nepoch):\n",
    "    \n",
    "    # forward pass of model\n",
    "        y4in[i] = w14[i]*x1 + w24[i]*x2 + w34[i]*x3 + b4[i]; \n",
    "        y4[i] = 1.0/(1 + math.exp(-1*y4in[i]))\n",
    "        \n",
    "        y5in[i] = w15[i]*x1 + w25[i]*x2 + w35[i]*x3 + b5[i]\n",
    "        y5[i] = 1.0/(1 + math.exp(-1*y5in[i]))\n",
    "        \n",
    "        y6in[i] = w46[i]*y4[i] + w56[i]*y5[i] + b6[i]\n",
    "        y6[i] = y6in[i]\n",
    "    #    y6[i] = 1.0/(1 + math.exp(-1*y6in[i])) # sgimoid / logistic activation at o6 \n",
    "    \n",
    "    # back propagate the error through the nodes\n",
    "    #    d6[i] = y6[i]*(1-y6[i])*(y-y6[i]) # sgimoid / logistic activation at o6 \n",
    "        d6[i] = (y-y6[i]) # identity activation o at o6\n",
    "        d5[i] = y5[i]*(1-y5[i])*w56[i]*d6[i]; d4[i] = y4[i]*(1-y4[i])*w46[i]*d6[i]\n",
    "        d1[i] = w14[i]*d4[i] + w15[i]*d5[i]; d2[i] = w24[i]*d4[i] + w25[i]*d5[i]; d3[i] = w34[i]*d4[i] + w35[i]*d5[i] # identity and 2 paths\n",
    "    \n",
    "    # calculate the change in weights\n",
    "        if i < nepoch - 1:\n",
    "            dw14[i] = lr*d4[i]*x1; dw24[i] = lr*d4[i]*x2; dw34[i] = lr*d4[i]*x3 \n",
    "            dw15[i] = lr*d5[i]*x1; dw25[i] = lr*d5[i]*x2; dw35[i] = lr*d5[i]*x3\n",
    "            dw46[i] = lr*d6[i]*y4[i]; dw56[i] = lr*d6[i]*y5[i] \n",
    "            \n",
    "            db4[i] = lr*d4[i]; db5[i] = lr*d5[i]; db6[i] = lr*d6[i];\n",
    "    \n",
    "            w14[i+1] = w14[i] + dw14[i]; w24[i+1] = w24[i] + dw24[i]; w34[i+1] = w34[i] + dw34[i] \n",
    "            w15[i+1] = w15[i] + dw15[i]; w25[i+1] = w25[i] + dw25[i]; w35[i+1] = w35[i] + dw35[i] \n",
    "            w46[i+1] = w46[i] + dw46[i]; w56[i+1] = w56[i] + dw56[i]\n",
    "    \n",
    "            b4[i+1] = b4[i] + db4[i]; b5[i+1] = b5[i] + db5[i]; b6[i+1] = b6[i] + db6[i] \n",
    "    \n",
    "    dx = -0.21; dy = -0.09; edge = 1.0\n",
    "    \n",
    "    o6x = 17; o6y =5; h5x = 10; h5y = 3.5; h4x = 10; h4y = 6.5\n",
    "    i1x = 3; i1y = 9.0; i2x = 3; i2y = 5; i3x = 3; i3y = 1.0; buffer = 0.5\n",
    "    \n",
    "    max_x = np.max(np.abs([x1,x2,x3]))\n",
    "    max_y = np.max(np.abs([y4[iepoch],y5[iepoch],y6[iepoch]]))\n",
    "    max_dO = np.max(np.abs([d1[iepoch],d2[iepoch],d3[iepoch]]))\n",
    "    max_d = np.max(np.abs([d1[iepoch],d2[iepoch],d3[iepoch],d4[iepoch],d5[iepoch],d6[iepoch]]))\n",
    "    max_d_trans = 1.0/abs(math.log(max_d)+0.00001)\n",
    "    max_signal = np.max(np.abs([x1*w14[iepoch],x2*w24[iepoch],x3*w34[iepoch],\n",
    "                                x1*w15[iepoch],x2*w25[iepoch],x3*w35[iepoch],\n",
    "                                y4[iepoch],y5[iepoch],y6[iepoch]]))\n",
    "    \n",
    "    plt.subplot(111)\n",
    "    plt.gca().set_axis_off()\n",
    "    \n",
    "    if (weights == True and forward == False and back == False) or (weights == False and forward == True and back == False):\n",
    "        \n",
    "        circle_i1 = plt.Circle((i1x,i1y), node_r*abs(x1)/max_x+min_node_r, fill=False, edgecolor = 'black',lw=2,zorder=100); plt.annotate(r' $I_1$',(i1x+dx,i1y+dy),zorder=110) \n",
    "        circle_i1b = plt.Circle((i1x,i1y), node_r*1.5*abs(x1)/max_x+min_node_r, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10)\n",
    "        plt.gca().add_patch(circle_i1); plt.gca().add_patch(circle_i1b)\n",
    "    \n",
    "        circle_i2 = plt.Circle((i2x,i2y), node_r*abs(x2)/max_x+min_node_r, fill=False, edgecolor = 'black',lw=2,zorder=100); plt.annotate(r' $I_2$',(i2x+dx,i2y+dy),zorder=110) \n",
    "        circle_i2b = plt.Circle((i2x,i2y), node_r*1.5*abs(x2)/max_x+min_node_r, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10)\n",
    "        plt.gca().add_patch(circle_i2); plt.gca().add_patch(circle_i2b)\n",
    "    \n",
    "        circle_i3 = plt.Circle((i3x,i3y), node_r*abs(x3)/max_x+min_node_r, fill=False, edgecolor = 'black',lw=2,zorder=100); plt.annotate(r' $I_3$',(i3x+dx,i3y+dy),zorder=110) \n",
    "        circle_i3b = plt.Circle((i3x,i3y), node_r*1.5*abs(x3)/max_x+min_node_r, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10)\n",
    "        plt.gca().add_patch(circle_i3); plt.gca().add_patch(circle_i3b)\n",
    "        \n",
    "        circle_h4 = plt.Circle((h4x,h4y), node_r*abs(y4[iepoch])/max_y+min_node_r,fill=True,facecolor = 'red',alpha=0.5,edgecolor = 'black',lw=2,zorder=100); plt.annotate(r'$H_4$',(h4x+dx,h4y+dy),zorder=110)\n",
    "        circle_h4o = plt.Circle((h4x,h4y), node_r*abs(y4[iepoch])/max_y+min_node_r,fill=False,alpha=1.0,edgecolor = 'black',lw=2,zorder=105) \n",
    "        circle_h4b = plt.Circle((h4x,h4y), node_r*1.5*abs(y4[iepoch])/max_y+min_node_r, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10)\n",
    "        plt.gca().add_patch(circle_h4); plt.gca().add_patch(circle_h4b); plt.gca().add_patch(circle_h4o)\n",
    "    \n",
    "        circle_h5 = plt.Circle((h5x,h5y), node_r*abs(y5[iepoch])/max_y+min_node_r, fill=True,facecolor = 'blue',alpha=0.5,edgecolor = 'black',lw=2,zorder=100); plt.annotate(r'$H_5$',(h5x+dx,h5y+dy),zorder=110)\n",
    "        circle_h5o = plt.Circle((h5x,h5y), node_r*abs(y5[iepoch])/max_y+min_node_r, fill=False,alpha=1.0,edgecolor = 'black',lw=2,zorder=105) \n",
    "        circle_h5b = plt.Circle((h5x,h5y), node_r*1.5*abs(y5[iepoch])/max_y+min_node_r, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10);\n",
    "        plt.gca().add_patch(circle_h5); plt.gca().add_patch(circle_h5b); plt.gca().add_patch(circle_h5o)\n",
    "    \n",
    "        circle_o6 = plt.Circle((o6x,o6y), node_r*abs(y6[iepoch])/max_y+min_node_r,fill=True,facecolor = 'orange',alpha=0.5,edgecolor = 'black',lw=2,zorder=100); plt.annotate(r'$O_6$',(o6x+dx,o6y+dy),zorder=110)\n",
    "        circle_o6o = plt.Circle((o6x,o6y), node_r*abs(y6[iepoch])/max_y+min_node_r,fill=False,alpha=1.0,edgecolor = 'black',lw=2,zorder=105)\n",
    "        circle_o6b = plt.Circle((o6x,o6y), node_r*1.5*abs(y6[iepoch])/max_y+min_node_r, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10);\n",
    "        plt.gca().add_patch(circle_o6); plt.gca().add_patch(circle_o6b); plt.gca().add_patch(circle_o6o)\n",
    "  \n",
    "    if weights == False and forward == False and back == True:\n",
    "        i1_r = (1.0/abs(math.log(abs(d1[iepoch]))+0.00001)/max_d_trans)*node_r+min_node_r\n",
    "        circle_i1 = plt.Circle((i1x,i1y), i1_r, fill=False, edgecolor = 'black',lw=2,zorder=100); plt.annotate(r' $I_1$',(i1x+dx,i1y+dy),zorder=110) \n",
    "        circle_i1b = plt.Circle((i1x,i1y), i1_r*1.5, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10)\n",
    "        plt.gca().add_patch(circle_i1); plt.gca().add_patch(circle_i1b)\n",
    "\n",
    "        i2_r = (1.0/abs(math.log(abs(d2[iepoch]))+0.00001)/max_d_trans)*node_r+min_node_r\n",
    "        circle_i2 = plt.Circle((i2x,i2y), i2_r, fill=False, edgecolor = 'black',lw=2,zorder=100); plt.annotate(r' $I_2$',(i2x+dx,i2y+dy),zorder=110) \n",
    "        circle_i2b = plt.Circle((i2x,i2y), i2_r*1.5, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10)\n",
    "        plt.gca().add_patch(circle_i2); plt.gca().add_patch(circle_i2b)\n",
    "    \n",
    "        i3_r = (1.0/abs(math.log(abs(d3[iepoch]))+0.00001)/max_d_trans)*node_r+min_node_r\n",
    "        circle_i3 = plt.Circle((i3x,i3y), i3_r, fill=False, edgecolor = 'black',lw=2,zorder=100); plt.annotate(r' $I_3$',(i3x+dx,i3y+dy),zorder=110) \n",
    "        circle_i3b = plt.Circle((i3x,i3y), i3_r*1.5*abs(x3)/max_x+min_node_r, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10)\n",
    "        plt.gca().add_patch(circle_i3); plt.gca().add_patch(circle_i3b)\n",
    "        \n",
    "        h4_r = (1.0/abs(math.log(abs(d4[iepoch]))+0.00001)/max_d_trans)*node_r+min_node_r\n",
    "        circle_h4 = plt.Circle((h4x,h4y), h4_r,fill=True,facecolor = 'red',alpha=0.5,edgecolor = 'black',lw=2,zorder=100); plt.annotate(r'$H_4$',(h4x+dx,h4y+dy),zorder=110)\n",
    "        circle_h4o = plt.Circle((h4x,h4y), h4_r,fill=False,alpha=1.0,edgecolor = 'black',lw=2,zorder=105) \n",
    "        circle_h4b = plt.Circle((h4x,h4y), h4_r*1.5, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10)\n",
    "        plt.gca().add_patch(circle_h4); plt.gca().add_patch(circle_h4b); plt.gca().add_patch(circle_h4o)\n",
    "    \n",
    "        h5_r = (1.0/abs(math.log(abs(d5[iepoch]))+0.00001)/max_d_trans)*node_r+min_node_r\n",
    "        circle_h5 = plt.Circle((h5x,h5y), h5_r, fill=True,facecolor = 'blue',alpha=0.5,edgecolor = 'black',lw=2,zorder=100); plt.annotate(r'$H_5$',(h5x+dx,h5y+dy),zorder=110)\n",
    "        circle_h5o = plt.Circle((h5x,h5y), h5_r, fill=False,alpha=1.0,edgecolor = 'black',lw=2,zorder=105) \n",
    "        circle_h5b = plt.Circle((h5x,h5y), h5_r*1.5, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10);\n",
    "        plt.gca().add_patch(circle_h5); plt.gca().add_patch(circle_h5b); plt.gca().add_patch(circle_h5o)\n",
    "    \n",
    "        h6_r = (1.0/abs(math.log(abs(d6[iepoch]))+0.00001)/max_d_trans)*node_r+min_node_r\n",
    "        circle_o6 = plt.Circle((o6x,o6y), h6_r,fill=True,facecolor = 'orange',alpha=0.5,edgecolor = 'black',lw=2,zorder=100); plt.annotate(r'$O_6$',(o6x+dx,o6y+dy),zorder=110)\n",
    "        circle_o6o = plt.Circle((o6x,o6y), h6_r,fill=False,alpha=1.0,edgecolor = 'black',lw=2,zorder=105)\n",
    "        circle_o6b = plt.Circle((o6x,o6y), h6_r*1.5, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10);\n",
    "        plt.gca().add_patch(circle_o6); plt.gca().add_patch(circle_o6b); plt.gca().add_patch(circle_o6o)\n",
    "   \n",
    "    if (weights == True and forward == True and back == True) or (weights == False and forward == False and back == False):\n",
    "\n",
    "        circle_i1 = plt.Circle((i1x,i1y), node_r, fill=False, edgecolor = 'black',lw=2,zorder=100); plt.annotate(r' $I_1$',(i1x+dx,i1y+dy),zorder=110) \n",
    "        circle_i1b = plt.Circle((i1x,i1y), node_r*1.5, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10)\n",
    "        plt.gca().add_patch(circle_i1); plt.gca().add_patch(circle_i1b)\n",
    "    \n",
    "        circle_i2 = plt.Circle((i2x,i2y), node_r, fill=False, edgecolor = 'black',lw=2,zorder=100); plt.annotate(r' $I_2$',(i2x+dx,i2y+dy),zorder=110) \n",
    "        circle_i2b = plt.Circle((i2x,i2y), node_r*1.5, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10)\n",
    "        plt.gca().add_patch(circle_i2); plt.gca().add_patch(circle_i2b)\n",
    "    \n",
    "        circle_i3 = plt.Circle((i3x,i3y), node_r, fill=False, edgecolor = 'black',lw=2,zorder=100); plt.annotate(r' $I_3$',(i3x+dx,i3y+dy),zorder=110) \n",
    "        circle_i3b = plt.Circle((i3x,i3y), node_r*1.5, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10)\n",
    "        plt.gca().add_patch(circle_i3); plt.gca().add_patch(circle_i3b)\n",
    "        \n",
    "        circle_h4 = plt.Circle((h4x,h4y), node_r,fill=True,facecolor = 'red',alpha=0.5,edgecolor = 'black',lw=2,zorder=100); plt.annotate(r'$H_4$',(h4x+dx,h4y+dy),zorder=110)\n",
    "        circle_h4o = plt.Circle((h4x,h4y), node_r,fill=False,alpha=1.0,edgecolor = 'black',lw=2,zorder=105) \n",
    "        circle_h4b = plt.Circle((h4x,h4y), node_r*1.5, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10)\n",
    "        plt.gca().add_patch(circle_h4); plt.gca().add_patch(circle_h4b); plt.gca().add_patch(circle_h4o)\n",
    "    \n",
    "        circle_h5 = plt.Circle((h5x,h5y), node_r, fill=True,facecolor = 'blue',alpha=0.5,edgecolor = 'black',lw=2,zorder=100); plt.annotate(r'$H_5$',(h5x+dx,h5y+dy),zorder=110)\n",
    "        circle_h5o = plt.Circle((h5x,h5y), node_r, fill=False,alpha=1.0,edgecolor = 'black',lw=2,zorder=105) \n",
    "        circle_h5b = plt.Circle((h5x,h5y), node_r*1.5, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10);\n",
    "        plt.gca().add_patch(circle_h5); plt.gca().add_patch(circle_h5b); plt.gca().add_patch(circle_h5o)\n",
    "    \n",
    "        circle_o6 = plt.Circle((o6x,o6y), node_r,fill=True,facecolor = 'orange',alpha=0.5,edgecolor = 'black',lw=2,zorder=100); plt.annotate(r'$O_6$',(o6x+dx,o6y+dy),zorder=110)\n",
    "        circle_o6o = plt.Circle((o6x,o6y), node_r,fill=False,alpha=1.0,edgecolor = 'black',lw=2,zorder=105)\n",
    "        circle_o6b = plt.Circle((o6x,o6y), node_r*1.5, fill=True, facecolor = 'white',edgecolor = None,lw=1,zorder=10);\n",
    "        plt.gca().add_patch(circle_o6); plt.gca().add_patch(circle_o6b); plt.gca().add_patch(circle_o6o)\n",
    "        \n",
    "    plt.plot([i1x-edge,i1x],[i1y,i1y],color='grey',lw=1.0,zorder=1)\n",
    "    plt.plot([i2x-edge,i2x],[i2y,i2y],color='grey',lw=1.0,zorder=1)\n",
    "    plt.plot([i3x-edge,i3x],[i3y,i3y],color='grey',lw=1.0,zorder=1)\n",
    "    \n",
    "    plt.annotate(r'$x_1$ = ' + str(np.round(x1,2)),(i1x-buffer-1.6,i1y-0.05),size=8,zorder=200,color='grey',\n",
    "                 bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=0,ha='left') \n",
    "    plt.annotate(r'$x_2$ = ' + str(np.round(x2,2)),(i2x-buffer-1.6,i2y-0.05),size=8,zorder=200,color='grey',\n",
    "                 bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=0) \n",
    "    plt.annotate(r'$x_3$ = ' + str(np.round(x3,2)),(i3x-buffer-1.6,i3y-0.05),size=8,zorder=200,color='grey',\n",
    "                 bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=0) \n",
    "    \n",
    "    min_wt = np.min(np.abs([w14[iepoch],w24[iepoch],w34[iepoch],w15[iepoch],w25[iepoch],w35[iepoch],w46[iepoch],w56[iepoch]]))\n",
    "    max_wt = np.max(np.abs([w14[iepoch],w24[iepoch],w34[iepoch],w15[iepoch],w25[iepoch],w35[iepoch],w46[iepoch],w56[iepoch]]))\n",
    "  \n",
    "    min_dwt = np.min(np.abs([dw14[iepoch],dw24[iepoch],dw34[iepoch],dw15[iepoch],dw25[iepoch],dw35[iepoch],dw46[iepoch],dw56[iepoch]]))\n",
    "    max_dwt = np.max(np.abs([dw14[iepoch],dw24[iepoch],dw34[iepoch],dw15[iepoch],dw25[iepoch],dw35[iepoch],dw46[iepoch],dw56[iepoch]]))\n",
    " \n",
    "    if (weights == True and forward == False and back == False):\n",
    "        plt.plot([i1x,h4x],[i1y,h4y],color='orangered',alpha = alpha*abs(w14[iepoch]/max_wt)+min_alpha,lw=lw*abs(w14[iepoch]/max_wt)+min_lw,zorder=1)\n",
    "        plt.plot([i2x,h4x],[i2y,h4y],color='red',alpha = alpha*abs(w24[iepoch]/max_wt)+min_alpha,lw=lw*abs(w24[iepoch]/max_wt)+min_lw,zorder=1)\n",
    "        plt.plot([i3x,h4x],[i3y,h4y],color='darkred',alpha = alpha*abs(w34[iepoch]/max_wt)+min_alpha,lw=lw*abs(w34[iepoch]/max_wt)+min_lw,zorder=1)\n",
    "    \n",
    "        plt.plot([i1x,h5x],[i1y,h5y],color='dodgerblue',alpha = alpha*abs(w15[iepoch]/max_wt)+min_alpha,lw=lw*abs(w15[iepoch]/max_wt)+min_lw,zorder=1)\n",
    "        plt.plot([i2x,h5x],[i2y,h5y],color='blue',alpha = alpha*abs(w25[iepoch]/max_wt)+min_alpha,lw=lw*abs(w25[iepoch]/max_wt)+min_lw,zorder=1)\n",
    "        plt.plot([i3x,h5x],[i3y,h5y],color='darkblue',alpha = alpha*abs(w35[iepoch]/max_wt)+min_alpha,lw=lw*abs(w35[iepoch]/max_wt)+min_lw,zorder=1)\n",
    "    \n",
    "        plt.plot([h4x,o6x],[h4y,o6y],color='orange',alpha = alpha*abs(w46[iepoch]/max_wt)+min_alpha,lw=lw*abs(w46[iepoch]/max_wt)+min_lw,zorder=1)\n",
    "        plt.plot([h5x,o6x],[h5y,o6y],color='darkorange',alpha = alpha*abs(w56[iepoch]/max_wt)+min_alpha,lw=lw*abs(w56[iepoch]/max_wt)+min_lw,zorder=1)\n",
    " \n",
    "    if (weights == False and forward == True and back == False):\n",
    "        plt.plot([i1x,h4x],[i1y,h4y],color='orangered',alpha = alpha*abs(x1*w14[iepoch]/max_signal)+min_alpha,lw=lw*abs(x1*w14[iepoch]/max_signal)+min_lw,zorder=1)\n",
    "        plt.plot([i2x,h4x],[i2y,h4y],color='red',alpha = alpha*abs(x2*w24[iepoch]/max_signal)+min_alpha,lw=lw*abs(x2*w24[iepoch]/max_signal)+min_lw,zorder=1)\n",
    "        plt.plot([i3x,h4x],[i3y,h4y],color='darkred',alpha = alpha*abs(x3*w34[iepoch]/max_signal)+min_alpha,lw=lw*abs(x3*w34[iepoch]/max_signal)+min_lw,zorder=1)\n",
    "    \n",
    "        plt.plot([i1x,h5x],[i1y,h5y],color='dodgerblue',alpha = alpha*abs(x1*w15[iepoch]/max_signal)+min_alpha,lw=lw*abs(x1*w15[iepoch]/max_signal)+min_lw,zorder=1)\n",
    "        plt.plot([i2x,h5x],[i2y,h5y],color='blue',alpha = alpha*abs(x2*w25[iepoch]/max_signal)+min_alpha,lw=lw*abs(x2*w25[iepoch]/max_signal)+min_lw,zorder=1)\n",
    "        plt.plot([i3x,h5x],[i3y,h5y],color='darkblue',alpha = alpha*abs(x3*w35[iepoch]/max_signal)+min_alpha,lw=lw*abs(x3*w35[iepoch]/max_signal)+min_lw,zorder=1)\n",
    "    \n",
    "        plt.plot([h4x,o6x],[h4y,o6y],color='orange',alpha = alpha*abs(y4[iepoch]*w46[iepoch]/max_signal)+min_alpha,lw=lw*abs(y4[iepoch]*w46[iepoch]/max_signal)+min_lw,zorder=1)\n",
    "        plt.plot([h5x,o6x],[h5y,o6y],color='darkorange',alpha = alpha*abs(y5[iepoch]*w56[iepoch]/max_signal)+min_alpha,lw=lw*abs(y5[iepoch]*w56[iepoch]/max_signal)+min_lw,zorder=1)\n",
    "\n",
    "    if (weights == False and forward == False and back == True):\n",
    "\n",
    "        plt.plot([i1x,h4x],[i1y,h4y],color='orangered',alpha = alpha*abs(dw14[iepoch]/max_dwt)+min_alpha,lw=lw*abs(dw14[iepoch]/max_dwt)+min_lw,zorder=1)\n",
    "        plt.plot([i2x,h4x],[i2y,h4y],color='red',alpha = alpha*abs(dw24[iepoch]/max_dwt)+min_alpha,lw=lw*abs(dw24[iepoch]/max_dwt)+min_lw,zorder=1)\n",
    "        plt.plot([i3x,h4x],[i3y,h4y],color='darkred',alpha = alpha*abs(dw34[iepoch]/max_dwt)+min_alpha,lw=lw*abs(dw34[iepoch]/max_dwt)+min_lw,zorder=1)\n",
    "    \n",
    "        plt.plot([i1x,h5x],[i1y,h5y],color='dodgerblue',alpha = alpha*abs(dw15[iepoch]/max_dwt)+min_alpha,lw=lw*abs(dw15[iepoch]/max_dwt)+min_lw,zorder=1)\n",
    "        plt.plot([i2x,h5x],[i2y,h5y],color='blue',alpha = alpha*abs(dw25[iepoch]/max_dwt)+min_alpha,lw=lw*abs(dw25[iepoch]/max_dwt)+min_lw,zorder=1)\n",
    "        plt.plot([i3x,h5x],[i3y,h5y],color='darkblue',alpha = alpha*abs(dw35[iepoch]/max_dwt)+min_alpha,lw=lw*abs(dw35[iepoch]/max_dwt)+min_lw,zorder=1)\n",
    "    \n",
    "        plt.plot([h4x,o6x],[h4y,o6y],color='orange',alpha = alpha*abs(dw46[iepoch]/max_dwt)+min_alpha,lw=lw*abs(dw46[iepoch]/max_dwt)+min_lw,zorder=1)\n",
    "        plt.plot([h5x,o6x],[h5y,o6y],color='darkorange',alpha = alpha*abs(dw56[iepoch]/max_dwt)+min_alpha,lw=lw*abs(dw56[iepoch]/max_dwt)+min_lw,zorder=1)\n",
    "    \n",
    "    if (weights == True and forward == True and back == True) or (weights == False and forward == False and back == False):\n",
    "    \n",
    "        plt.plot([i1x,h4x],[i1y,h4y],color='orangered',lw=lw+min_lw,zorder=1)\n",
    "        plt.plot([i2x,h4x],[i2y,h4y],color='red',lw=lw+min_lw,zorder=1)\n",
    "        plt.plot([i3x,h4x],[i3y,h4y],color='darkred',lw=lw+min_lw,zorder=1)\n",
    "    \n",
    "        plt.plot([i1x,h5x],[i1y,h5y],color='dodgerblue',lw=lw+min_lw,zorder=1)\n",
    "        plt.plot([i2x,h5x],[i2y,h5y],color='blue',lw=lw+min_lw,zorder=1)\n",
    "        plt.plot([i3x,h5x],[i3y,h5y],color='darkblue',lw=lw+min_lw,zorder=1)\n",
    "    \n",
    "        plt.plot([h4x,o6x],[h4y,o6y],color='orange',lw=lw+min_lw,zorder=1)\n",
    "        plt.plot([h5x,o6x],[h5y,o6y],color='darkorange',lw=lw+min_lw,zorder=1)\n",
    "    \n",
    "    if forward == True:\n",
    "    \n",
    "        plt.plot(offsetx(i1x,2,-20),offsety(i1y,2,-20)+0.1,color='orangered',lw=1.0,zorder=1)\n",
    "        plt.plot(offset_arrx(i1x,2,-20,0.2),offset_arry(i1y,2,-20,0.2)+0.1,color='orangered',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$I_{1}$ = ' + str(np.round(x1,2)),(lintx(i1x,i1y,h4x,h4y,0.1),linty(i1x,i1y,h4x,h4y,0.1)),size=8,zorder=200,color='orangered',\n",
    "                 bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-20)\n",
    "    \n",
    "        plt.plot(offsetx(i2x,2,12),offsety(i2y,2,12)+0.1,color='red',lw=1.0,zorder=1)\n",
    "        plt.plot(offset_arrx(i2x,2,12,0.2),offset_arry(i2y,2,12,0.2)+0.1,color='red',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$I_{2}$ = ' + str(np.round(x2,2)),(lintx(i2x,i2y,h4x,h4y,0.1),linty(i2x,i2y,h4x,h4y,0.1)+0.24),size=8,zorder=200,color='red',\n",
    "                 bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=12)\n",
    "    \n",
    "        plt.plot(offsetx(i3x,2,38),offsety(i3y,2,38)+0.1,color='darkred',lw=1.0,zorder=1)\n",
    "        plt.plot(offset_arrx(i3x,2,38,0.2),offset_arry(i3y,2,38,0.2)+0.1,color='darkred',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$I_{3}$ = ' + str(np.round(x3,2)),(lintx(i3x,i3y,h4x,h4y,0.08)-0.2,linty(i3x,i3y,h4x,h4y,0.08)+0.2),size=8,zorder=200,color='darkred',\n",
    "                 bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=38)\n",
    "    \n",
    "        plt.plot(offsetx(h4x,2,-12),offsety(h4y,2,-12)+0.1,color='orange',lw=1.0,zorder=1)\n",
    "        plt.plot(offset_arrx(h4x,2,-12,0.2),offset_arry(h4y,2,-12,0.2)+0.1,color='orange',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$H_{4}$ = ' + str(np.round(y4[iepoch],2)),(lintx(h4x,h4y,o6x,o6y,0.08),linty(h4x,h4y,o6x,o6y,0.08)-0.0),size=8,zorder=200,color='orange',\n",
    "                 bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-12)\n",
    "        \n",
    "        plt.annotate(r'$H_{4_{in}}$ = ' + str(np.round(y4in[iepoch],2)),(lintx(h4x,h4y,o6x,o6y,0.08)-0.5,linty(h4x,h4y,o6x,o6y,0.08)+0.5),size=8,zorder=200,color='orange',\n",
    "                 bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-12)\n",
    "    \n",
    "        plt.plot(offsetx(h5x,2,12),offsety(h5y,2,12)+0.1,color='darkorange',lw=1.0,zorder=1)\n",
    "        plt.plot(offset_arrx(h5x,2,12,0.2),offset_arry(h5y,2,12,0.2)+0.1,color='darkorange',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$H_{5}$ = ' + str(np.round(y5[iepoch],2)),(lintx(h5x,h5y,o6x,o6y,0.07),linty(h5x,h5y,o6x,o6y,0.07)+0.25),size=8,zorder=200,color='darkorange',\n",
    "                 bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=12)\n",
    "\n",
    "        plt.annotate(r'$H_{5_{in}}$ = ' + str(np.round(y5in[iepoch],2)),(lintx(h5x,h5y,o6x,o6y,0.08)-0.5,linty(h5x,h5y,o6x,o6y,0.08)+0.5),size=8,zorder=200,color='darkorange',\n",
    "                 bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=12)\n",
    "        \n",
    "        plt.plot([o6x+edge,o6x],[o6y,o6y],color='grey',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$\\hat{y}$ = ' + str(np.round(y6[iepoch],2)),(o6x+buffer+0.7,o6y-0.05),size=8,zorder=300,color='grey',\n",
    "                 bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=0) \n",
    "\n",
    "#        plt.annotate(r'$\\frac{\\partial P}{\\partial \\hat{y}}$ = ' + str(np.round(d6[iepoch],2)),(o6x,o6y-1.2),size=10,\n",
    "#                bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),zorder=200)\n",
    "\n",
    "        plt.annotate(r'$y$ = ' + str(np.round(y,2)),(o6x+buffer+0.7,o6y+0.5),size=8,zorder=300,color='grey',\n",
    "                 bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=0) \n",
    "\n",
    "    plt.plot([h4x,h4x-0.5],[h4y,h4y+1.0],color='red',zorder=5)\n",
    "    plt.annotate(r'$b_{4}$ = ' + str(np.round(b4[iepoch],2)),(h4x-0.7,h4y+1.2),size=8,zorder=200,color='red',\n",
    "        bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=0)  \n",
    "    \n",
    "    plt.plot([h5x,h5x-0.5],[h5y,h5y+1.0],color='blue',zorder=5)\n",
    "    plt.annotate(r'$b_{5}$ = ' + str(np.round(b5[iepoch],2)),(h5x-0.7,h5y+1.2),size=8,zorder=200,color='blue',\n",
    "        bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=0)  \n",
    "    \n",
    "    plt.plot([o6x,o6x-0.5],[o6y,o6y+1.0],color='orange',zorder=5)\n",
    "    plt.annotate(r'$b_{6}$ = ' + str(np.round(b6[iepoch],2)),(o6x-0.7,o6y+1.2),size=8,zorder=200,color='orange',\n",
    "        bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=0)  \n",
    "    \n",
    "    plt.plot([o6x+edge,o6x],[o6y,o6y],color='grey',lw=1.0,zorder=1)\n",
    "    plt.annotate(r'$y$ = ' + str(np.round(y,2)),(o6x+buffer+0.7,o6y-0.05),size=8,zorder=200,color='grey',\n",
    "        bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=0) \n",
    "    \n",
    "    if back == True:\n",
    "    \n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial O_{6_{in}}}$ = ' + str(np.round(d6[iepoch],2)),(o6x-0.5,o6y-1.2),size=10,zorder=100)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial H_{4_{in}}}$ = ' + str(np.round(d4[iepoch],2)),(h4x-0.5,h4y-0.7),size=10,zorder=100)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial H_{5_{in}}}$ = ' + str(np.round(d5[iepoch],2)),(h5x-0.5,h5y-0.7),size=10,zorder=100)\n",
    "    \n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial \\hat{y}}$ = ' + str(np.round(d6[iepoch],2)),(o6x,o6y-1.8),size=10,zorder=100)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial H_{4_{out}}}$ = ' + str(np.round(w46[iepoch]*d6[iepoch],2)),(h4x,h4y-1.2),size=10,zorder=100)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial H_{5_{out}}}$ = ' + str(np.round(w56[iepoch]*d6[iepoch],2)),(h5x,h5y-1.2),size=10,zorder=100)\n",
    "   \n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial X_1}$ = ' + r'${0:s}$'.format(as_si(d1[iepoch],2)),(i1x-2.0,i1y-0.9),size=10,zorder=100)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial X_2}$ = ' + r'${0:s}$'.format(as_si(d2[iepoch],2)),(i2x-2.0,i2y-0.9),size=10,zorder=100)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial X_3}$ = ' + r'${0:s}$'.format(as_si(d3[iepoch],2)),(i3x-2.0,i3y-0.9),size=10,zorder=100)\n",
    "        \n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial I_1}$ = ' + r'${0:s}$'.format(as_si(d1[iepoch],2)),(i1x-1.5,i1y-1.4),size=10,zorder=100)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial I_2}$ = ' + r'${0:s}$'.format(as_si(d2[iepoch],2)),(i2x-1.5,i2y-1.4),size=10,zorder=100)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial I_3}$ = ' + r'${0:s}$'.format(as_si(d3[iepoch],2)),(i3x-1.5,i3y-1.4),size=10,zorder=100)\n",
    "\n",
    "        plt.plot(lint_intx(h4x, h4y, o6x, o6y,0.4,0.6),lint_inty(h4x,h4y,o6x,o6y,0.4,0.6)-0.1,color='orange',lw=1.0,zorder=1)\n",
    "        plt.plot(lint_int_arrx(o6x,o6y,h4x,h4y,0.4,0.6,0.2),lint_int_arry(o6x,o6y,h4x,h4y,0.4,0.6,0.2)-0.1,color='orange',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial \\lambda_{4,6}} =$' + r'${0:s}$'.format(as_si(dw46[iepoch]/lr,2)),(lintx(h4x,h4y,o6x,o6y,0.5)-0.6,linty(h4x,h4y,o6x,o6y,0.5)-0.72),size=7,zorder=200,color='orange',\n",
    "                  bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-11)\n",
    "    \n",
    "        plt.plot(lint_intx(h5x, h5y, o6x, o6y,0.4,0.6),lint_inty(h5x,h5y,o6x,o6y,0.4,0.6)-0.1,color='darkorange',lw=1.0,zorder=1)\n",
    "        plt.plot(lint_int_arrx(o6x,o6y,h5x,h5y,0.4,0.6,0.2),lint_int_arry(o6x,o6y,h5x,h5y,0.4,0.6,0.2)-0.1,color='darkorange',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial \\lambda_{5,6}} =$' + r'${0:s}$'.format(as_si(dw56[iepoch]/lr,2)),(lintx(h5x,h5y,o6x,o6y,0.5)-0.4,linty(h5x,h5y,o6x,o6y,0.5)-0.6),size=7,zorder=200,color='darkorange',\n",
    "                  bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=12)\n",
    "\n",
    "        plt.plot(lint_intx(i1x, i1y, h4x, h4y,0.4,0.6),lint_inty(i1x,i1y,h4x,h4y,0.4,0.6)-0.1,color='orangered',lw=1.0,zorder=1)\n",
    "        plt.plot(lint_int_arrx(h4x,h4y,i1x,i1y,0.4,0.6,0.2),lint_int_arry(h4x,h4y,i1x,i1y,0.4,0.6,0.2)-0.1,color='orangered',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial \\lambda_{1,4}} =$' + r'${0:s}$'.format(as_si(dw14[iepoch]/lr,2)),(lintx(i1x,i1y,h4x,h4y,0.5)-0.6,linty(i1x,i1y,h4x,h4y,0.5)-1.0),size=7,zorder=200,color='orangered',\n",
    "                  bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-20)\n",
    "    \n",
    "        plt.plot(lint_intx(i2x, i2y, h4x, h4y,0.3,0.5),lint_inty(i2x,i2y,h4x,h4y,0.3,0.5)-0.1,color='red',lw=1.0,zorder=1)\n",
    "        plt.plot(lint_int_arrx(h4x,h4y,i2x,i2y,0.5,0.7,0.2),lint_int_arry(h4x,h4y,i2x,i2y,0.5,0.7,0.2)-0.12,color='red',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial \\lambda_{2,4}} =$' + r'${0:s}$'.format(as_si(dw24[iepoch]/lr,2)),(lintx(i2x,i2y,h4x,h4y,0.5)-1.05,linty(i2x,i2y,h4x,h4y,0.5)-0.7),size=7,zorder=200,color='red',\n",
    "                  bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=12)\n",
    "    \n",
    "        plt.plot(lint_intx(i3x, i3y, h4x, h4y,0.2,0.4),lint_inty(i3x,i3y,h4x,h4y,0.2,0.4)-0.1,color='darkred',lw=1.0,zorder=1)\n",
    "        plt.plot(lint_int_arrx(h4x,h4y,i3x,i3y,0.5,0.8,0.2),lint_int_arry(h4x,h4y,i3x,i3y,0.5,0.8,0.2)-0.12,color='darkred',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial \\lambda_{3,4}} =$' + r'${0:s}$'.format(as_si(dw34[iepoch]/lr,2)),(lintx(i3x,i3y,h4x,h4y,0.5)-1.7,linty(i3x,i3y,h4x,h4y,0.5)-1.7),size=7,zorder=200,color='darkred',\n",
    "                  bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=38)\n",
    "    \n",
    "        plt.plot(lint_intx(i3x, i3y, h5x, h5y,0.4,0.6),lint_inty(i3x,i3y,h5x,h5y,0.4,0.6)-0.1,color='darkblue',lw=1.0,zorder=1)\n",
    "        plt.plot(lint_int_arrx(h5x,h5y,i3x,i3y,0.4,0.6,0.2),lint_int_arry(h5x,h5y,i3x,i3y,0.4,0.6,0.2)-0.12,color='darkblue',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial \\lambda_{3,5}} =$' + r'${0:s}$'.format(as_si(dw35[iepoch]/lr,2)),(lintx(i3x,i3y,h5x,h5y,0.5)-0.4,linty(i3x,i3y,h5x,h5y,0.5)-0.6),size=7,zorder=200,color='darkblue',\n",
    "                  bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=20)\n",
    "    \n",
    "        plt.plot(lint_intx(i2x, i2y, h5x, h5y,0.3,0.5),lint_inty(i2x,i2y,h5x,h5y,0.3,0.5)-0.1,color='blue',lw=1.0,zorder=1)\n",
    "        plt.plot(lint_int_arrx(h5x,h5y,i2x,i2y,0.3,0.7,0.2),lint_int_arry(h5x,h5y,i2x,i2y,0.3,0.7,0.2)-0.12,color='blue',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial \\lambda_{2,5}} =$' + r'${0:s}$'.format(as_si(dw25[iepoch]/lr,2)),(lintx(i2x,i2y,h5x,h5y,0.5)-1.2,linty(i2x,i2y,h5x,h5y,0.5)-0.65),size=7,zorder=200,color='blue',\n",
    "                  bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-12)\n",
    "    \n",
    "        plt.plot(lint_intx(i1x, i1y, h5x, h5y,0.2,0.4),lint_inty(i1x,i1y,h5x,h5y,0.2,0.4)-0.1,color='dodgerblue',lw=1.0,zorder=1)\n",
    "        plt.plot(lint_int_arrx(h5x,h5y,i1x,i1y,0.2,0.8,0.2),lint_int_arry(h5x,h5y,i1x,i1y,0.2,0.8,0.2)-0.12,color='dodgerblue',lw=1.0,zorder=1)\n",
    "        plt.annotate(r'$\\frac{\\partial P}{\\partial \\lambda_{1,5}} =$' + r'${0:s}$'.format(as_si(dw15[iepoch]/lr,2)),(lintx(i1x,i1y,h5x,h5y,0.5)-2.2,linty(i1x,i1y,h4x,h4y,0.5)-0.2),size=7,zorder=200,color='dodgerblue',\n",
    "                  bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-36,xycoords = 'data',va=\"top\",ha=\"left\")\n",
    "    \n",
    "    if forward == False:\n",
    "    \n",
    "        plt.annotate(r'$\\lambda_{1,4}$ = ' + str(np.round(w14[iepoch],2)),((i1x+h4x)*0.45,(i1y+h4y)*0.5+0.7),size=8,zorder=200,color='orangered',\n",
    "                     bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-18,xycoords = 'data',va=\"top\",ha=\"left\") \n",
    "        plt.annotate(r'$\\lambda_{2,4}$ = ' + str(np.round(w24[iepoch],2)),((i2x+h4x)*0.45-0.3,(i2y+h4y)*0.5-0.03),size=8,zorder=200,color='red',\n",
    "                     bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=12) \n",
    "        plt.annotate(r'$\\lambda_{3,4}$ = ' + str(np.round(w34[iepoch],2)),((i3x+h4x)*0.45-1.2,(i3y+h4y)*0.5-1.1),size=8,zorder=200,color='darkred',\n",
    "                     bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=38) \n",
    "        \n",
    "        plt.annotate(r'$\\lambda_{1,5}$ = ' + str(np.round(w15[iepoch],2)),((i1x+h5x)*0.55-2.5,(i1y+h5y)*0.5+0.7),size=8,zorder=200,color='dodgerblue',\n",
    "            bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-36) \n",
    "        plt.annotate(r'$\\lambda_{2,5}$ = ' + str(np.round(w25[iepoch],2)),((i2x+h5x)*0.55-1.5,(i2y+h5y)*0.5+0.05),size=8,zorder=200,color='blue',\n",
    "                     bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-12) \n",
    "        plt.annotate(r'$\\lambda_{3,5}$ = ' + str(np.round(w35[iepoch],2)),((i3x+h5x)*0.55-1.0,(i3y+h5y)*0.5+0.1),size=8,zorder=200,color='darkblue',\n",
    "                     bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=18) \n",
    "        \n",
    "        plt.annotate(r'$\\lambda_{4,6}$ = ' + str(np.round(w46[iepoch],2)),((h4x+o6x)*0.47,(h4y+o6y)*0.47+0.39),size=8,zorder=200,color='orange',\n",
    "            bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-12) \n",
    "        plt.annotate(r'$\\lambda_{5,6}$ = ' + str(np.round(w56[iepoch],2)),((h5x+o6x)*0.47,(h5y+o6y)*0.47+0.26),size=8,zorder=200,color='darkorange',\n",
    "            bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=12) \n",
    "        \n",
    "    if forward == True:\n",
    "     \n",
    "        plt.annotate(r'$\\lambda_{1,4} \\times X_1$ = ' + str(np.round(x1*w14[iepoch],2)),((i1x+h4x)*0.45,(i1y+h4y)*0.5+0.70),size=8,zorder=200,color='orangered',\n",
    "                     bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-18,xycoords = 'data',va=\"top\",ha=\"left\") \n",
    "        plt.annotate(r'$\\lambda_{2,4} \\times X_2$ = ' + str(np.round(x2*w24[iepoch],2)),((i2x+h4x)*0.45-0.3,(i2y+h4y)*0.5+0.70),size=8,zorder=200,color='red',\n",
    "                     bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=10,xycoords = 'data',va=\"top\",ha=\"left\") \n",
    "        plt.annotate(r'$\\lambda_{3,4} \\times X_3$ = ' + str(np.round(x3*w34[iepoch],2)),((i3x+h4x)*0.45-1.4,(i3y+h4y)*0.5-1.3),size=8,zorder=200,color='darkred',\n",
    "                     bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=36,xycoords = 'data',va=\"bottom\",ha=\"left\") \n",
    "        \n",
    "        plt.annotate(r'$\\lambda_{1,5} \\times X_1$ = ' + str(np.round(x1*w15[iepoch],2)),((i1x+h5x)*0.55-2.5,(i1y+h5y)*0.5+1.9),size=8,zorder=200,color='dodgerblue',\n",
    "            bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-36,xycoords = 'data',va=\"top\",ha=\"left\") \n",
    "        plt.annotate(r'$\\lambda_{2,5} \\times X_2$ = ' + str(np.round(x2*w25[iepoch],2)),((i2x+h5x)*0.55-1.5,(i2y+h5y)*0.5+0.7),size=8,zorder=200,color='blue',\n",
    "                     bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-12,xycoords = 'data',va=\"top\",ha=\"left\") \n",
    "        plt.annotate(r'$\\lambda_{3,5} \\times X_3$ = ' + str(np.round(x3*w35[iepoch],2)),((i3x+h5x)*0.55-1.0,(i3y+h5y)*0.5+1.1),size=8,zorder=200,color='darkblue',\n",
    "                     bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=18,xycoords = 'data',va=\"top\",ha=\"left\") \n",
    "        \n",
    "        plt.annotate(r'$\\lambda_{4,6} \\times Y_4$ = ' + str(np.round(y4[iepoch]*w46[iepoch],2)),((h4x+o6x)*0.47,(h4y+o6y)*0.47+1.0),size=8,zorder=200,color='orange',\n",
    "            bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=-12,xycoords = 'data',va=\"top\",ha=\"left\") \n",
    "        plt.annotate(r'$\\lambda_{5,6} \\times Y_5$ = ' + str(np.round(y5[iepoch]*w56[iepoch],2)),((h5x+o6x)*0.47,(h5y+o6y)*0.47+1.0),size=8,zorder=200,color='darkorange',\n",
    "            bbox=dict(boxstyle=\"round,pad=0.0\", edgecolor='white', facecolor='white', alpha=1.0),rotation=12,xycoords = 'data',va=\"top\",ha=\"left\") \n",
    "    \n",
    "\n",
    "    \n",
    "    plt.plot([0.5,20,20,0.5,0.5],[-1,-1,10,10,-1],color='black')\n",
    "    #plt.scatter(0,10,color='yellow')\n",
    "    \n",
    "    plt.subplots_adjust(left=0.0, bottom=0.0, right=1.5, top=1.0, wspace=0.2, hspace=0.2); plt.show()\n",
    "       \n",
    "# connect the function to make the samples and plot to the widgets    \n",
    "interactive_plot = widgets.interactive_output(run_plot, {'nepoch':nepoch,'lr':lr,'weights':weights,'forward':forward,'back':back,'seed':seed})\n",
    "interactive_plot.clear_output(wait = True)               # reduce flickering by delaying plot updating   "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "554bb4ff",
   "metadata": {},
   "source": [
    "### Interactive Machine Learning Norms Demonstation \n",
    "\n",
    "#### Michael Pyrcz, Professor, The University of Texas at Austin \n",
    "\n",
    "Interactive artificial neural network dashboard built from scratch to demonstrate, parameter initialization and training. \n",
    "\n",
    "### The Inputs\n",
    "\n",
    "* **$n_{epoch}$** - number of training cycles, **$\\eta$** - learning rate, **$S$** - random number seed\n",
    "* **Weights** - show the network weights, **Forward Pass** - show the contributions and node outputs, **Back Propogation** - show the partial derivatives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "873fbf10",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "216f8e52f67c4bcb97fc44095878244e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(Text(value='                                             Machine Learning Simple Artificial Neu…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "171d9decfc7c4081aa909f60fe582969",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(ui, interactive_plot)                           # display the interactive plot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d3a38fd",
   "metadata": {},
   "source": [
    "Note, I am still making improvements. For now it is best to select weights, forward pass or back propogation and not a combination of two of the choices."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1b27996",
   "metadata": {},
   "source": [
    "#### Comments\n",
    "\n",
    "This was an interactive demonstration of an artifial neural network. Providing students an opportunity to play with machine learning, deep learning for experiential learning.\n",
    "  \n",
    "#### The Author:\n",
    "\n",
    "### Michael Pyrcz, Professor, The University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Professor, Cockrell School of Engineering and The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)  \n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "dd58c977",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-3,3,1000)\n",
    "y_sigmoid = 1.0/(1.0+np.exp(-1*x))\n",
    "dy_sigmoid = y_sigmoid*(1.0-y_sigmoid)\n",
    "\n",
    "y_tanh = (np.exp(x) - np.exp(-1*x))/(np.exp(x) + np.exp(-1*x))\n",
    "dy_tanh = 1 - (np.exp(x) - np.exp(-1*x))**2.0/(np.exp(x) + np.exp(-1*x))**2.0\n",
    "\n",
    "y_relu = np.clip(x, a_min = 0,a_max = None)\n",
    "dy_relu = np.where(y_relu == 0,0,1.0)\n",
    "\n",
    "major_ticks = np.array([-2,-1,0,1,2])\n",
    "\n",
    "plt.subplot(321)\n",
    "plt.plot(x,y_sigmoid,color='red',lw=3,label=r'$f(x)$',zorder=10)\n",
    "plt.gca().set_yticks(major_ticks); plt.title('Sigmoid / Logistic Activation'); plt.xlabel(r'$H_{j_{in}}$'); plt.ylabel(r'$H_{j}$')\n",
    "plt.plot([-3,3],[0,0],color='black',zorder=1); plt.plot([-3,3],[1,1],color='black',zorder=1)\n",
    "add_grid(); plt.xlim([-3,3]); plt.ylim([-3,3]); plt.legend(loc='lower right')\n",
    "\n",
    "plt.subplot(322)\n",
    "plt.plot(x,dy_sigmoid,color='blue',lw=3,label=r'$\\frac{\\partial f}{\\partial x}(x)$',zorder=1)\n",
    "plt.gca().set_yticks(major_ticks); plt.title('Sigmoid / Logistic Activation Derivative'); plt.xlabel(r'$H_{j_{in}}$'); plt.ylabel(r'$\\frac{\\partial H_{j}}{\\partial H_{j_{in}}}$')\n",
    "plt.plot([-3,3],[0,0],color='black',zorder=1)\n",
    "add_grid(); plt.xlim([-3,3]); plt.ylim([-3,3]); plt.legend(loc='lower right')\n",
    "\n",
    "plt.subplot(323)\n",
    "plt.plot(x,y_tanh,color='red',lw=3,label=r'$f(x)$',zorder=10)\n",
    "plt.gca().set_yticks(major_ticks); plt.title('Tanh Activation'); plt.xlabel(r'$H_{j_{in}}$'); plt.ylabel(r'$H_{j}$')\n",
    "plt.plot([-3,3],[-1,-1],color='black',zorder=1); plt.plot([-3,3],[1,1],color='black',zorder=1)\n",
    "add_grid(); plt.xlim([-3,3]); plt.ylim([-3,3]); plt.legend(loc='lower right')\n",
    "\n",
    "plt.subplot(324)\n",
    "plt.plot(x,dy_tanh,color='blue',lw=3,label=r'$\\frac{\\partial f}{\\partial x}(x)$',zorder=1)\n",
    "plt.gca().set_yticks(major_ticks); plt.title('Sigmoid / Logistic Activation Derivative'); plt.xlabel(r'$H_{j_{in}}$'); plt.ylabel(r'$\\frac{\\partial H_{j}}{\\partial H_{j_{in}}}$')\n",
    "plt.plot([-3,3],[0,0],color='black',zorder=1)\n",
    "add_grid(); plt.xlim([-3,3]); plt.ylim([-3,3]); plt.legend(loc='lower right')\n",
    "\n",
    "plt.subplot(325)\n",
    "plt.plot(x,y_relu,color='red',lw=3,label=r'$f(x)$',zorder=10); plt.xlabel(r'$H_{j_{in}}$'); plt.ylabel(r'$H_{j}$')\n",
    "plt.gca().set_yticks(major_ticks); plt.title('Rectified Linear Unit (ReLU) Activation')\n",
    "plt.plot([-3,3],[0,0],color='black',zorder=1)\n",
    "add_grid(); plt.xlim([-3,3]); plt.ylim([-3,3]); plt.legend(loc='lower right')\n",
    "\n",
    "plt.subplot(326)\n",
    "plt.plot(x,dy_relu,color='blue',lw=3,label=r'$\\frac{\\partial f}{\\partial x}(x)$',zorder=1)\n",
    "plt.gca().set_yticks(major_ticks); plt.title('Rectified Linear Unit (ReLU) Activation Derivative'); plt.xlabel(r'$H_{j_{in}}$'); plt.ylabel(r'$\\frac{\\partial H_{j}}{\\partial H_{j_{in}}}$')\n",
    "plt.plot([-3,3],[0,0],color='black',zorder=1)\n",
    "add_grid(); plt.xlim([-3,3]); plt.ylim([-3,3]); plt.legend(loc='lower right')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.5, wspace=0.2, hspace=0.5); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "82cd5982",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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