finished exercises for intro to numpy

projects/intro-to-economic-modeling-and-ds/scientific-computing/intro-to-numpy.ipynb

@@ -1105,9 +1105,179 @@
     "# Exercises"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 62,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x_3d: \n",
+      " [[[ 1  2  3]\n",
+      "  [ 4  5  6]]\n",
+      "\n",
+      " [[10 20 30]\n",
+      "  [40 50 60]]]\n",
+      "\n",
+      "x_3d[:, 1] \n",
+      " [[ 4  5  6]\n",
+      " [40 50 60]]\n",
+      "\n",
+      "x_3d[:, 0, :1]: \n",
+      " [[ 1]\n",
+      " [10]]\n",
+      "\n",
+      "x_3d[1, 1, 2:]: \n",
+      " [60]\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "# 1.  Try indexing into another element of your choice from the 3-dimensional array.\n",
+    "# \n",
+    "# Building an understanding of indexing means working through this type of operation \n",
+    "# several times – without skipping steps!\n",
+    "\n",
+    "\n",
+    "x_3d_list = [[[1, 2, 3], [4, 5, 6]], \n",
+    "             [[10, 20, 30], [40, 50, 60]]]\n",
+    "x_3d = np.array(x_3d_list)\n",
+    "\n",
+    "print(f\"x_3d: \\n {x_3d}\\n\")\n",
+    "print(f\"x_3d[:, 1] \\n {x_3d[:, 1]}\\n\")\n",
+    "print(f\"x_3d[:, 0, :1]: \\n {x_3d[:, 0, :1]}\\n\")\n",
+    "print(f\"x_3d[1, 1, 2:]: \\n {x_3d[1, 1, 2:]}\\n\") # the 0  in 0:2 is optional"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 65,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[1 2 3]\n",
+      " [4 5 6]\n",
+      " [7 8 9]]\n",
+      "inner is the column, example column 1 is [2 5 8]\n",
+      "outer is the row, example row 1 is [4 5 6]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# 2. Look at the 2-dimensional array x_2d.\n",
+    "\n",
+    "x_2d = np.array([[1, 2, 3], \n",
+    "                 [4, 5, 6], \n",
+    "                 [7, 8, 9]])\n",
+    "print(x_2d)\n",
+    "\n",
+    "# Does the inner-most index correspond to rows or columns? \n",
+    "# What does the outer-most index correspond to? \n",
+    "\n",
+    "# Write your thoughts.\n",
+    "column_number = 1\n",
+    "row_number = 1\n",
+    "\n",
+    "inner = x_2d[:,column_number]\n",
+    "outer = x_2d[1]\n",
+    "\n",
+    "print(f'inner is the column, example column 1 is {inner}')\n",
+    "print(f'outer is the row, example row 1 is {outer}')\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 68,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 5  6]\n",
+      " [50 60]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# 3. What would you do to extract the array [[5, 6], [50, 60]] from \n",
+    "# [[[1, 2, 3], [4, 5, 6]], [[10, 20, 30], [40, 50, 60]]]?\n",
+    "\n",
+    "arr = [[[1, 2, 3], [4, 5, 6]], \n",
+    "       [[10, 20, 30], [40, 50, 60]]]\n",
+    "\n",
+    "arr = np.array(arr)\n",
+    "\n",
+    "e_arr = arr[:,1,1:]\n",
+    "print(e_arr)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
+   "source": [
+    "Let’s revisit a bond pricing example we saw in Control flow.\n",
+    "\n",
+    "Recall that the equation for pricing a bond with coupon payment $C$, face value $M$, yield to maturity $i$, and periods to maturity $N$ is\n",
+    "\n",
+    "$$\n",
+    "\\begin{align}\n",
+    "    P &= \\left(\\sum_{n=1}^N \\frac{C}{(i+1)^n}\\right) + \\frac{M}{(1+i)^N} \\\\\n",
+    "      &= C \\left(\\frac{1 - (1+i)^{-N}}{i} \\right) + M(1+i)^{-N}\n",
+    "\\end{align}\n",
+    "$$\n",
+    "\n",
+    "In the code cell below, we have defined variables for `i`, `M` and `C`.\n",
+    "1. You have two tasks:\n",
+    "1. Define a numpy array N that contains all maturities between 1 and 10"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 80,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "array calculation: price of our bound is $117.06\n",
+      "direct calculation: price of our bound is $117.06\n"
+     ]
+    }
+   ],
+   "source": [
+    "i = 0.03\n",
+    "M = 100\n",
+    "C = 5\n",
+    "\n",
+    "# Define array here\n",
+    "x = np.arange(1,11)\n",
+    "N = len(x)\n",
+    "# price bonds here\n",
+    "face_val_discount = M/(1+i)**N\n",
+    "discounts = C/(i+1)**x\n",
+    "P = discounts.sum() + face_val_discount\n",
+    "P = round(P,2)\n",
+    "\n",
+    "P_direct = C*(1-(1+i)**(-N))/i + face_val_discount\n",
+    "P_direct = round(P_direct, 2)\n",
+    "\n",
+    "print(f'array calculation: price of our bound is ${P}')\n",
+    "print(f'direct calculation: price of our bound is ${P_direct}')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": []
   }
  ],