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Commit 50761a23 authored by Alan Christian Chan Godinez's avatar Alan Christian Chan Godinez
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"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# 2.SciPy\n", "![scipy](https://cdn-images-1.medium.com/max/1600/1*Y2v3PrF1rUQRUHwOcXJznA.png)\n",
"## 2.1 NumPy" "\n",
"# 5.SciPy\n",
"SciPy es un ecosistema para computo cientifico en python, esta constriuido sobre los arreglos de NumPy. Scipy incluye herramientas como Matplotlib, pandas , SymPy y scikit-learn. \n",
"\n",
"## 5.1 NumPy\n",
"NumPy es la base para todos los paquetes de computo científico en python, provee soporte para arreglos multidimensionales y matrices, junto con una amplia coleccion de funciones matematicas de alto nivel para operar con estos arreglos.\n",
"\n",
"### 5.1.1 numpy.array \n",
"El tipo de dato mas importante de numpy es **numpy.array** sus atibutos mas importantes son:\n",
"* numpy.array.**ndim**: -numero de dimensiones del arreglo.\n",
"* numpy.array.**shape**: Un tupla indicando el tamaño del arreglo en cada dimension.\n",
"* numpy.array.**size**: El numero total elementos en el arreglo.\n",
"* numpy.array.**dtype**: El tipo de elemenos en el arreglo e.g. numpy.int32, numpy.int16, and numpy.float64.\n",
"* numpy.array.**itemsize**: el tamaño en bytes de cada elemento del arrglo.\n",
"* numpy.array.**data**: El bloque de memoria que contiene los datos del arreglo.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 0 1 2 3 4]\n",
" [ 5 6 7 8 9]\n",
" [10 11 12 13 14]]\n",
"(3, 5)\n",
"2\n",
"int32\n"
]
}
],
"source": [
"import numpy as np\n",
"a = np.array([[ 0, 1, 2, 3, 4],\n",
" [ 5, 6, 7, 8, 9],\n",
" [10, 11, 12, 13, 14]])\n",
"print(a)\n",
"print(a.shape)\n",
"print(a.ndim)\n",
"print(a.dtype)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1.+0.j, 2.+0.j],\n",
" [3.+0.j, 4.+0.j]])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = np.array( [ [1,2], [3,4] ], dtype=complex )\n",
"c"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
" np.zeros( (3,4) )\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1., 1., 1., 1.],\n",
" [1., 1., 1., 1.],\n",
" [1., 1., 1., 1.]])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.ones( (3,4)) "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1., 1., 1., 1.],\n",
" [1., 1., 1., 1.],\n",
" [1., 1., 1., 1.]])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.empty( (3,4) ) "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1., 0., 0., 0., 0.],\n",
" [0., 1., 0., 0., 0.],\n",
" [0., 0., 1., 0., 0.],\n",
" [0., 0., 0., 1., 0.],\n",
" [0., 0., 0., 0., 1.]])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.eye(5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Operaciones Basicas"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"a = np.array([20,30,40,50] )\n",
"b = np.arange( 4 )"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([20, 29, 38, 47])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Suma\n",
"a-b"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 40, 60, 80, 100])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Multiplicacion por Escalar\n",
"a*2"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 1, 4, 9])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Potencia\n",
"b**2"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ True, True, True, False])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#Operadores Boleanos\n",
"a<50"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0, 30, 80, 150])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#Multiplicacion por elemento\n",
"a*b"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"66"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c= np.arange(12).reshape(3,4)\n",
"c.sum()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([12, 15, 18, 21])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c.sum(axis=0) # Suma por Columna"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 6, 22, 38])"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c.sum(axis=1) #Suma por Fila"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[**Producto punto**](https://en.wikipedia.org/wiki/Dot_product) y [**Multiplicacion Matricial**](https://en.wikipedia.org/wiki/Matrix_multiplication)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a@b == a.dot(b)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"A = np.array([[1, 0], [0, 1]])\n",
"B = np.array([[4, 1], [2, 2]]) "
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ True, True],\n",
" [ True, True]])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.matmul(A, B) == A.dot(B)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Elementos, filas, columnas y submatrices."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0, 1, 2, 3],\n",
" [10, 11, 12, 13],\n",
" [20, 21, 22, 23],\n",
" [30, 31, 32, 33],\n",
" [40, 41, 42, 43]])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def f(x,y):\n",
" return 10*x+y\n",
"B = np.fromfunction(f,(5,4),dtype=int)\n",
"B"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"B[0,3]"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([10, 11, 12, 13])"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"B[1,:]"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1, 11, 21, 31, 41])"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"B[:,1]"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1, 2],\n",
" [11, 12]])"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"B[:2,1:3]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Iterando elementos"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0 1 2 3]\n",
"[10 11 12 13]\n",
"[20 21 22 23]\n",
"[30 31 32 33]\n",
"[40 41 42 43]\n"
]
}
],
"source": [
"for row in B:\n",
" print(row)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0\n",
"1\n",
"2\n",
"3\n",
"10\n",
"11\n",
"12\n",
"13\n",
"20\n",
"21\n",
"22\n",
"23\n",
"30\n",
"31\n",
"32\n",
"33\n",
"40\n",
"41\n",
"42\n",
"43\n"
]
}
],
"source": [
"for element in B.flat:\n",
" print(element)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Cambio de forma"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[2., 9., 8., 6.],\n",
" [8., 4., 2., 9.],\n",
" [1., 1., 4., 5.]])"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a = np.floor(10*np.random.random((3,4)))\n",
"a"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(3, 4)"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a.shape"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[2., 9.],\n",
" [8., 6.],\n",
" [8., 4.],\n",
" [2., 9.],\n",
" [1., 1.],\n",
" [4., 5.]])"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a.reshape(6,2)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[2., 8., 1.],\n",
" [9., 4., 1.],\n",
" [8., 2., 4.],\n",
" [6., 9., 5.]])"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a.T"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ True, True, True],\n",
" [ True, True, True],\n",
" [ True, True, True],\n",
" [ True, True, True]])"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a.transpose()==a.T"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(4, 3)"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a.T.shape"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[2., 9., 8., 6.],\n",
" [8., 4., 2., 9.],\n",
" [1., 1., 4., 5.]])"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# La dimensión con -1 se calcula automaticamente\n",
"a.reshape(3,-1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 5.2 Ejercicos\n",
"\n",
"### 5.2.1 Sin utilizar numpy escribe una funcion para obten el producto punto de dos vectores."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"166.39999999999998\n"
]
}
],
"source": [
"a = [2, 5.6, 9, 8, 10]\n",
"b = [1, 3, 2.4, 2, 11]\n",
"\n",
"def ProductoPunto(a,b):\n",
" '''Encontrar el producto punto de dos vectores dados a y b, sin usar arreglos de Numpy. \n",
" \n",
" Args: \n",
" a(), b(): son los vectores que se multiplicaran, los cuales son de la misma longitud.\n",
" \n",
" Returns:\n",
" float, int: El resultado del producto punto entre a y b.\n",
" \n",
" Ejemplos: \n",
" \n",
" >>> a = [2, 5.6, 9, 8, 10] \n",
" >>> b = [1, 3, 2.4, 2, 11]\n",
" >>> ProdPunto(a, b)\n",
" el Resultado debe ser: 166.39999999999998\n",
" '''\n",
" \n",
" return sum( map((lambda V1, V2: V1*V2), a, b) )\n",
" \n",
" \n",
"\n",
"print (ProductoPunto(a,b))\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.2.2 Sin utilizar numpy escribe una funcion que obtenga la multiplicacion de dos matrices.\n"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[23, -5, 2, 5]\n",
"[15, 6, 26, 39]\n",
"None\n"
]
}
],
"source": [
"# A = [[1,2,3],[4,5,6]]\n",
"# B = [[7,8],[9,10],[11,12]]\n",
"\n",
"def MultiplicacionMatrices(a,b):\n",
" \n",
" '''Multiplicar dos matrices dadas A y B, sena A una de 3x2 y B una de 2x3. \n",
" \n",
" Args: \n",
" a(), b(): sonlas matrices dadas de diferente longitud.\n",
" \n",
" Returns:\n",
" una matriz de 4x2.\n",
" \n",
" Ejemplo 01: \n",
" \n",
" >>> A = [[1,2,3],[4,5,6]]\n",
" >>> B = [[7,8],[9,10],[11,12]]\n",
" >>> la matriz obtenida debe ser de :\n",
" el Resultado debe ser: \n",
" \n",
" Ejemplo 02:\n",
" \n",
" Sea una Matriz de 3x2 \n",
" >>> X = [[2,0,-3], [4,1,5]]\n",
" \n",
" Sea una Matriz de 4x3 \n",
" Y = [[7, -1, 4, 7],[2, 5, 0,-4],[-3, 1, 2, 3]]\n",
" \n",
" Resultado es un aMatriz de $x2\n",
" [23, -5, 2, 5]\n",
" [15, 6, 26, 39]\n",
" '''\n",
" \n",
" A = [[1,2,3],[4,5,6]]\n",
" B = [[7,8],[9,10],[11,12]]\n",
"\n",
" X = [[2,0,-3],[4,1,5]]\n",
" # 4x3 matrix\n",
" Y = [[7, -1, 4, 7],[2, 5, 0,-4],[-3, 1, 2, 3]]\n",
" # result is 4x2\n",
" result = [[0,0,0,0],[0,0,0,0]]\n",
"\n",
" #se itera a través de filas de X\n",
" for i in range(len(X)):\n",
" # Se itera a traves de las colmnas de Y\n",
" for j in range(len(Y[0])):\n",
" # iterar a través de filas de Y\n",
" for k in range(len(Y)):\n",
" result[i][j] += X[i][k] * Y[k][j]\n",
"\n",
" for r in result:\n",
" print (r)\n",
" \n",
"#return r\n",
"\n",
"print (MultiplicacionMatrices(a,b))"
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[58, 64]\n",
"[139, 154]\n",
"None\n"
]
}
],
"source": [
"# A = [[1,2,3],[4,5,6]]\n",
"# B = [[7,8],[9,10],[11,12]]\n",
"\n",
"def MultiplicacionMatrices(a,b):\n",
" \n",
" '''Multiplicar dos matrices dadas A y B, sena A una de 3x2 y B una de 2x3. \n",
" \n",
" Args: \n",
" a(), b(): sonlas matrices dadas de diferente longitud.\n",
" \n",
" Returns:\n",
" una matriz de 4x2.\n",
" \n",
" Ejemplo 01: \n",
" \n",
" >>> A = [[1,2,3],[4,5,6]]\n",
" >>> B = [[7,8],[9,10],[11,12]]\n",
" >>> la matriz obtenida debe ser de :\n",
" el Resultado debe ser: \n",
" \n",
" Ejemplo 02:\n",
" \n",
" Sea una Matriz de 3x2 \n",
" >>> X = [[2,0,-3], [4,1,5]]\n",
" \n",
" Sea una Matriz de 4x3 \n",
" Y = [[7, -1, 4, 7],[2, 5, 0,-4],[-3, 1, 2, 3]]\n",
" \n",
" Resultado es un aMatriz de $x2\n",
" [23, -5, 2, 5]\n",
" [15, 6, 26, 39]\n",
" '''\n",
" # 3x2\n",
" a = [[1,2,3],[4,5,6]]\n",
" #2x3\n",
" b = [[7,8],[9,10],[11,12]]\n",
"\n",
" result = [[0,0],[0,0]]\n",
"\n",
" #se itera a través de filas de a\n",
" for i in range(len(a)):\n",
" # Se itera a traves de las columnas de b\n",
" for j in range(len(b[0])):\n",
" # iterar a través de filas de b\n",
" for k in range(len(b)):\n",
" result[i][j] += a[i][k] * b[k][j]\n",
"\n",
" for r in result:\n",
" print (r)\n",
" \n",
" \n",
"#return (r)\n",
"\n",
"print (MultiplicacionMatrices(a,b))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.2.3 Utiliza numpy para probar que las dos funciones anteriores dan el resultado correcto."
]
},
{
"cell_type": "code",
"execution_count": 116,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"166.4\n"
]
},
{
"data": {
"text/plain": [
"matrix([[ 1, 0],\n",
" [ 2, -1]])"
]
},
"execution_count": 116,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#Sean \n",
"a = [2, 5.6, 9, 8, 10]\n",
"b = [1, 3, 2.4, 2, 11]\n",
"\n",
"\n",
"#Comprobacion con Numpy ejercicio 1\n",
"print(np.matmul(a, b))\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 145,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sea A:\n",
"[[1 2 3]\n",
" [4 5 6]]\n",
"Sea B:\n",
"[[ 7 8]\n",
" [ 9 10]\n",
" [11 12]]\n",
"El Producto de A por B es:\n",
"[[ 58 64]\n",
" [139 154]]\n"
]
}
],
"source": [
"#Comprobar la Multiplicacion de Matrices usndo Numpy Sean \n",
"# A = [[1,2,3],[4,5,6]]\n",
"# B = [[7,8],[9,10],[11,12]]\n",
"\n",
"\n",
"import numpy as np\n",
"A = np.matrix('1 2 3 ; 4 5 6')\n",
"print ('Sea A:')\n",
"print (A)\n",
"B = np.matrix('7 8; 9 10 ; 11 12')\n",
"\n",
"print ('Sea B:')\n",
"print (B) \n",
"\n",
"print ('El Producto de A por B es:')\n",
"print (A*B)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.2.4 Utilizando solo lo visto hasta el momento de numpy escribe una funcion que encuentre la inversa de una matriz por el metodo de Gauss-Jordan.\n",
"[Wikipedia](https://en.wikipedia.org/wiki/Gaussian_elimination): En matemáticas, la eliminación de Gauss Jordan, llamada así en honor de Carl Friedrich Gauss y Wilhelm Jordan es un algoritmo del álgebra lineal que se usa para determinar las soluciones de un sistema de ecuaciones lineales, para encontrar matrices e inversas. Un sistema de ecuaciones se resuelve por el método de Gauss cuando se obtienen sus soluciones mediante la reducción del sistema dado a otro equivalente en el que cada ecuación tiene una incógnita menos que la anterior. El método de Gauss transforma la matriz de coeficientes en una matriz triangular superior. El método de Gauss-Jordan continúa el proceso de transformación hasta obtener una matriz diagonal"
]
},
{
"cell_type": "code",
"execution_count": 159,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sea A:\n",
"[[1 2 3]\n",
" [4 5 6]]\n"
]
},
{
"data": {
"text/plain": [
"matrix([[-0.94444444, 0.44444444],\n",
" [-0.11111111, 0.11111111],\n",
" [ 0.72222222, -0.22222222]])"
]
},
"execution_count": 159,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from numpy import matrix\n",
"import numpy as np\n",
"A = np.matrix('1 2 3 ; 4 5 6')\n",
"print ('Sea A:')\n",
"print (A)\n",
"\n",
"A.I"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.2.5 Utilizando la funcion anterior escribe otra que obtenga la pseduo-inversa de una matriz."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 5.3 Pandas\n",
"En python, pandas es una biblioteca de software escrita como extensión de NumPy para manipulación y análisis de datos. En particular, ofrece estructuras de datos y operaciones para manipular tablas numéricas y series temporales.\n",
"and expressive data structures designed to make working with “relational” or “labeled” data both easy and intuitive. Su objetivo es ser un bloque de construccion fundamental para realizar analisis de datos en el mundo real.\n",
"El nombre de la biblioteca deriva del término \"datos de panel\" (PANel DAta), término de econometría que designa datos que combinan una dimensión temporal con otra dimensión transversal.\n",
"\n",
"Pandas tiene dos typos de datos principales, **Series** (1D) y **DataFrame** (2D), *Dataframe* es un contenedr para *Series* y *Series* es un contenedor de escalares. \n",
"\n",
"### 5.3.1 Series\n",
"Series es un arreglo unidimensional etiquetado capaz de contener cualquier tipo de dato (Enteros, cadenas, punto flotante, objetos, etc), El eje de etiquetas es llamado indice (**index**).\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"a 1.085164\n",
"b 0.684054\n",
"c -3.137046\n",
"d -0.780916\n",
"e 0.497413\n",
"dtype: float64"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s = pd.Series(np.random.randn(5), index=['a', 'b', 'c', 'd', 'e'])\n",
"s"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0 -0.165303\n",
"1 0.089697\n",
"2 -1.680879\n",
"3 -0.160729\n",
"4 0.235082\n",
"dtype: float64"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pd.Series(np.random.randn(5))"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"a 0\n",
"b 1\n",
"c 2\n",
"dtype: int64"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d = {'b': 1, 'a': 0, 'c': 2}\n",
"pd.Series(d)"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"b 1.0\n",
"c 2.0\n",
"d NaN\n",
"a 0.0\n",
"dtype: float64"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d = {'a': 0., 'b': 1., 'c': 2.}\n",
"pd.Series(d, index=['b', 'c', 'd', 'a'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Las Series son compatibles con *numpy.array* y *dict*"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0851635954341003"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s[0]"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"a 1.085164\n",
"b 0.684054\n",
"c -3.137046\n",
"dtype: float64"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s[:3]"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"a 1.085164\n",
"b 0.684054\n",
"e 0.497413\n",
"dtype: float64"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s[s>s.mean()]"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"a 2.170327\n",
"b 1.368108\n",
"c -6.274092\n",
"d -1.561832\n",
"e 0.994826\n",
"dtype: float64"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s*2"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"a True\n",
"b True\n",
"c False\n",
"d False\n",
"e False\n",
"dtype: bool"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s>s.median()"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0851635954341003"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s[\"a\"]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Alieneacion Automatica"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [],
"source": [
"a = np.array(range(10))\n",
"s = pd.Series(a)"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0 0\n",
"1 1\n",
"2 2\n",
"3 3\n",
"4 4\n",
"5 5\n",
"6 6\n",
"7 7\n",
"8 8\n",
"9 9\n",
"dtype: int64"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 4, 6, 8, 10, 12, 14])"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(a[:6]+a[4:])"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0 NaN\n",
"1 NaN\n",
"2 NaN\n",
"3 NaN\n",
"4 8.0\n",
"5 10.0\n",
"6 NaN\n",
"7 NaN\n",
"8 NaN\n",
"9 NaN\n",
"dtype: float64"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(s[:6]+s[4:])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.3.2 DataFrame\n",
"DataFrame es un estructura bidimensional etiquetada con columnas que pueden ser de diferentes tipos, es el objeto mas usado en pandas, se puede pensar en ella como un diccionario de **Series**. **DataFrame** acepta diferentes tipos de entradas como:\n",
"* Diccionarios de arreglos unidimensionales, listas dicionarios o series. \n",
"* 2-D numpy.ndarray\n",
"* Series\n",
"* Otro **DataFrame**"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [],
"source": [
"d = {'one': pd.Series([1., 2., 3.], index=['a', 'b', 'c']),\n",
" 'two': pd.Series([1., 2., 3., 4.], index=['a', 'x', 'c', 'd'])}"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [],
"source": [
"df = pd.DataFrame(d)"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>one</th>\n",
" <th>two</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>a</th>\n",
" <td>1.0</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>b</th>\n",
" <td>2.0</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>c</th>\n",
" <td>3.0</td>\n",
" <td>3.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>d</th>\n",
" <td>NaN</td>\n",
" <td>4.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>x</th>\n",
" <td>NaN</td>\n",
" <td>2.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" one two\n",
"a 1.0 1.0\n",
"b 2.0 NaN\n",
"c 3.0 3.0\n",
"d NaN 4.0\n",
"x NaN 2.0"
]
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Seleccionar, Añadir y Borrar Columnas"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"a 1.0\n",
"b 2.0\n",
"c 3.0\n",
"d NaN\n",
"x NaN\n",
"Name: one, dtype: float64"
]
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df[\"one\"]"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>one</th>\n",
" <th>two</th>\n",
" <th>three</th>\n",
" <th>flag</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>a</th>\n",
" <td>1.0</td>\n",
" <td>1.0</td>\n",
" <td>1.0</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>b</th>\n",
" <td>2.0</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>c</th>\n",
" <td>3.0</td>\n",
" <td>3.0</td>\n",
" <td>9.0</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>d</th>\n",
" <td>NaN</td>\n",
" <td>4.0</td>\n",
" <td>NaN</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>x</th>\n",
" <td>NaN</td>\n",
" <td>2.0</td>\n",
" <td>NaN</td>\n",
" <td>False</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" one two three flag\n",
"a 1.0 1.0 1.0 False\n",
"b 2.0 NaN NaN False\n",
"c 3.0 3.0 9.0 True\n",
"d NaN 4.0 NaN False\n",
"x NaN 2.0 NaN False"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df['three'] = df['one'] * df['two']\n",
"df['flag'] = df['one'] > 2\n",
"df"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [],
"source": [
"del df['two']"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [],
"source": [
"three = df.pop('three')"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>one</th>\n",
" <th>flag</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>a</th>\n",
" <td>1.0</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>b</th>\n",
" <td>2.0</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>c</th>\n",
" <td>3.0</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>d</th>\n",
" <td>NaN</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>x</th>\n",
" <td>NaN</td>\n",
" <td>False</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" one flag\n",
"a 1.0 False\n",
"b 2.0 False\n",
"c 3.0 True\n",
"d NaN False\n",
"x NaN False"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>one</th>\n",
" <th>two</th>\n",
" <th>flag</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>a</th>\n",
" <td>1.0</td>\n",
" <td>1.0</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>b</th>\n",
" <td>2.0</td>\n",
" <td>NaN</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>c</th>\n",
" <td>3.0</td>\n",
" <td>9.0</td>\n",
" <td>True</td>\n",
" </tr>\n",
" <tr>\n",
" <th>d</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>x</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>False</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" one two flag\n",
"a 1.0 1.0 False\n",
"b 2.0 NaN False\n",
"c 3.0 9.0 True\n",
"d NaN NaN False\n",
"x NaN NaN False"
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# inserta la columna three en la posición 1 bajo el nombre two\n",
"df.insert(1, \"two\", three)\n",
"df"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Indexado y Selección\n",
"\n",
"| Operación | Sintaxis | Resultado |\n",
"|:----------|:--------:|:----------|\n",
"| Selección de Columna | df[col] | Series |\n",
"| Selección de fila por etiqueta | df.loc[label] | Series |\n",
"| Selección de fila por posición | df.iloc[loc] | Series |\n",
"| Rango de filas | df[5:10] | DataFrame |\n",
"| Selección de filas por vector booleano | df[bool_vec] | DataFrame |\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"one 1\n",
"two 1\n",
"flag False\n",
"Name: a, dtype: object"
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.loc['a']"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"one 3\n",
"two 9\n",
"flag True\n",
"Name: c, dtype: object"
]
},
"execution_count": 62,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.iloc[2]"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>one</th>\n",
" <th>two</th>\n",
" <th>flag</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>a</th>\n",
" <td>1.0</td>\n",
" <td>1.0</td>\n",
" <td>False</td>\n",
" </tr>\n",
" <tr>\n",
" <th>b</th>\n",
" <td>2.0</td>\n",
" <td>NaN</td>\n",
" <td>False</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" one two flag\n",
"a 1.0 1.0 False\n",
"b 2.0 NaN False"
]
},
"execution_count": 63,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df[:2]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 5.4 Ejercicios\n",
"Los siguentes ejercicios de realizann con los dato de *iris.csv*"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>sepal_length</th>\n",
" <th>sepal_width</th>\n",
" <th>petal_length</th>\n",
" <th>petal_width</th>\n",
" <th>species</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>5.1</td>\n",
" <td>3.5</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>4.9</td>\n",
" <td>3.0</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>4.7</td>\n",
" <td>3.2</td>\n",
" <td>1.3</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>4.6</td>\n",
" <td>3.1</td>\n",
" <td>1.5</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>5.0</td>\n",
" <td>3.6</td>\n",
" <td>1.4</td>\n",
" <td>0.2</td>\n",
" <td>setosa</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" sepal_length sepal_width petal_length petal_width species\n",
"0 5.1 3.5 1.4 0.2 setosa\n",
"1 4.9 3.0 1.4 0.2 setosa\n",
"2 4.7 3.2 1.3 0.2 setosa\n",
"3 4.6 3.1 1.5 0.2 setosa\n",
"4 5.0 3.6 1.4 0.2 setosa"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"iris = pd.read_csv('data/iris.csv')\n",
"iris.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.4.1 ¿Cual es el numero de observaciones en el conjunto de datos?"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.4.2 ¿Cual es el numero de columnas en el conjunto de datos?"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.4.3 Imprime el nombre de todas las columnas"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.4.4 ¿Cual es el nombre de la columna 4?"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.4.5 Selecciona las columnas, \"sepal_length\" y \"petal_length\""
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.4.6 Selecciona las filas en donde \"sepal_length\" sea mayor a 4.8"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5.4.7 Agrega una nueva columna que sea la muliplicacion de \"petal_length\" por \"petal_width\""
] ]
}, },
{ {
...@@ -19,7 +2251,7 @@ ...@@ -19,7 +2251,7 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## 2.2 Pandas" "### 5.4.8 Encuentra el promedio por especie de cada columna."
] ]
}, },
{ {
...@@ -46,7 +2278,7 @@ ...@@ -46,7 +2278,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.6.8rc1" "version": "3.7.1"
} }
}, },
"nbformat": 4, "nbformat": 4,
......
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