Merge branch 'master' into gaspar

# Conflicts:
#	07-LinearAlgebra&Learning.ipynb

05-NumPy&Pandas.ipynb

@@ -978,10 +978,124 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Inversa(C)=\n",
+      " [[-2.         -2.07692308 -0.38461538]\n",
+      " [ 1.          1.07692308  0.38461538]\n",
+      " [-0.         -0.23076923 -0.15384615]]\n",
+      "\n",
+      "np.linalg.inv(C)=\n",
+      " [[-2.         -2.07692308 -0.38461538]\n",
+      " [ 1.          1.07692308  0.38461538]\n",
+      " [-0.         -0.23076923 -0.15384615]]\n",
+      "Trying:\n",
+      "    A = np.array([[2, 4, 3], [0, 1, -1], [3, 5, 7]])\n",
+      "Expecting nothing\n",
+      "ok\n",
+      "Trying:\n",
+      "    Inversa(A)\n",
+      "Expecting:\n",
+      "    array([[ 4.        , -4.33333333, -2.33333333],\n",
+      "           [-1.        ,  1.66666667,  0.66666667],\n",
+      "           [-1.        ,  0.66666667,  0.66666667]])\n",
+      "ok\n",
+      "Trying:\n",
+      "    C = np.array([[1, 3, 5], [-2, -4, -5], [3, 6, 1]])\n",
+      "Expecting nothing\n",
+      "ok\n",
+      "Trying:\n",
+      "    Inversa(C)\n",
+      "Expecting:\n",
+      "    array([[-2.        , -2.07692308, -0.38461538],\n",
+      "           [ 1.        ,  1.07692308,  0.38461538],\n",
+      "           [-0.        , -0.23076923, -0.15384615]])\n",
+      "ok\n",
+      "1 items had no tests:\n",
+      "    __main__\n",
+      "1 items passed all tests:\n",
+      "   4 tests in __main__.Inversa\n",
+      "4 tests in 2 items.\n",
+      "4 passed and 0 failed.\n",
+      "Test passed.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "TestResults(failed=0, attempted=4)"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "\n",
+    "import numpy as np\n",
+    "import sys\n",
+    "\n",
+    "def Inversa(A):\n",
+    "    '''Función que calcula la inversa (si existe) de una matriz de n x n mediante el metodo de eliminación\n",
+    "        de Gauss-Jordan.\n",
+    "        \n",
+    "        Args: \n",
+    "            A (np.array): Lista de Arreglos que representa la matriz con valores tipo float.\n",
+    "            Se dice que la matriz inversa A-1 tiene inversa, si A-1*A = I, donde I es la matriz identidad   \n",
+    "        \n",
+    "        Returns:\n",
+    "            np.array: La matriz inversa de A\n",
+    "        \n",
+    "        Ejemplos:\n",
+    "        >>> A = np.array([[2, 4, 3], [0, 1, -1], [3, 5, 7]])\n",
+    "        >>> Inversa(A)\n",
+    "        array([[ 4.        , -4.33333333, -2.33333333],\n",
+    "               [-1.        ,  1.66666667,  0.66666667],\n",
+    "               [-1.        ,  0.66666667,  0.66666667]])\n",
+    "       \n",
+    "        >>> C = np.array([[1, 3, 5], [-2, -4, -5], [3, 6, 1]])\n",
+    "        >>> Inversa(C)\n",
+    "        array([[-2.        , -2.07692308, -0.38461538],\n",
+    "               [ 1.        ,  1.07692308,  0.38461538],\n",
+    "               [-0.        , -0.23076923, -0.15384615]])\n",
+    "    '''\n",
+    "    if len(A) != len(A[0]):\n",
+    "        print('La matriz no es cuadrada, por lo tanto NO INVERTIBLE estrictamente')\n",
+    "    else:\n",
+    "        A = np.array(A, dtype=np.float64)\n",
+    "        n = len(A)\n",
+    "        Inver = np.eye(n, dtype=np.float64)\n",
+    "        #Método L por eliminación de Gauss, p es el pivote\n",
+    "        for p in range(n-1):\n",
+    "            if A[p,p] == 0: #Verifica que el pivote no sea cero\n",
+    "                sys.exit('La matriz es singular, por lo tanto NO INVERTIBLE')\n",
+    "            A[p,:], Inver[p,:] = A[p,:] / A[p,p], Inver[p,:] / A[p,p]\n",
+    "            for k in range(p+1,n):\n",
+    "                A[k,:], Inver[k,:] = A[p,:] * A[k,p] - A[k,:], Inver[p,:] * A[k,p] - Inver[k,:]\n",
+    "        #Método U por eliminación de Gauss\n",
+    "        for p in reversed(range(1,n)):\n",
+    "            if A[p,p] == 0: #Verifica que el pivote no sea cero\n",
+    "                sys.exit('La matriz es singular, por lo tanto NO INVERTIBLE')\n",
+    "            A[p,:], Inver[p,:] = A[p,:] / A[p,p], Inver[p,:] / A[p,p]\n",
+    "            for k in reversed(range(p)):\n",
+    "                A[k,:], Inver[k,:] = A[p,:] * A[k,p] - A[k,:], Inver[p,:] * A[k,p] - Inver[k,:]\n",
+    "        return Inver\n",
+    "\n",
+    "C = np.array([[1, 3, 5],\n",
+    "              [-2, -4, -5],\n",
+    "              [3, 6, 1]], dtype=float)\n",
+    "\n",
+    "print('Inversa(C)=\\n',Inversa(C))\n",
+    "print('\\nnp.linalg.inv(C)=\\n', np.linalg.inv(C))\n",
+    "import doctest\n",
+    "doctest.testmod(verbose=True)\n"
+   ]
   },
   {
    "cell_type": "markdown",