3d gradient descent plot

Polynomial Regression.ipynb

@@ -582,6 +582,92 @@
     "plot_cost_function(logs_5)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Wizualizacja metody najszybszego spadku dla wielomianu drugiego stopnia"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "degree = 1\n",
+    "initial_theta = np.matrix([0] * (degree + 1)).reshape(degree + 1, 1)\n",
+    "m, n_plus_1 = data_matrix.shape\n",
+    "n = n_plus_1 - 1\n",
+    "X = (np.ones((m, 1)))\n",
+    "\n",
+    "for i in range(1, degree + 1):\n",
+    "    Xn = np.power(data_matrix[:, 0:n], i)\n",
+    "    Xn /= np.amax(Xn, axis=0)\n",
+    "    X = np.concatenate((X, Xn), axis=1)\n",
+    "\n",
+    "X = np.matrix(X).reshape(m, degree * n + 1)\n",
+    "Y = np.matrix(data_matrix[:, -1])\n",
+    "\n",
+    "\n",
+    "steepest_descent_deg_2, logs_deg_2 = steepest_descent(X, Y, initial_theta, epochs = 60)\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cost_history = [row[0] for row in logs_deg_2]\n",
+    "all_thetas = [row[1] for row in logs_deg_2]\n",
+    "theta0_history = [row[0].item() for row in all_thetas]\n",
+    "theta1_history = [row[1].item() for row in all_thetas]\n",
+    "\n",
+    "cost_history = np.array(cost_history)\n",
+    "theta0_history = np.array(theta0_history)\n",
+    "theta1_history = np.array(theta1_history)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "theta0_vals = theta0_history\n",
+    "theta1_vals = theta1_history\n",
+    "J_vals = np.zeros((len(theta0_vals), len(theta1_vals)))\n",
+    "\n",
+    "c1=0\n",
+    "c2=0\n",
+    "pom = 0\n",
+    "for i in theta0_vals:\n",
+    "    for j in theta1_vals:\n",
+    "        t = np.array([i, j])\n",
+    "        J_vals[c1][c2] = cost_history[pom]\n",
+    "        c2=c2+1\n",
+    "    c1=c1+1\n",
+    "    pom += 1\n",
+    "    c2=0"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import plotly.graph_objects as go\n",
+    "\n",
+    "fig = go.Figure(data=[go.Surface(x=theta0_vals, y=theta1_vals, z=J_vals)])\n",
+    "fig.update_layout(title='Loss function for different thetas', autosize=True,\n",
+    "                  width=600, height=600, xaxis_title='theta0', \n",
+    "                 yaxis_title='theta1')\n",
+    "fig.show()"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},