Utilitzar tensors i numpy (contracció de tensors i indexat)

tensors_i_numpy.ipynb

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     "cell_type": "markdown",
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     "source": [
      "# Definici\u00f3 i manipulaci\u00f3 (slicing) de tensors en numpy:\n",
      "\n",
      "Nota que a python els \u00edndex comencen a zero i els intervals \"0:2\" s'interpreten [0,2)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "print \"Definim un vector unidimensional:\"\n",
      "A = np.array(range(0,24))\n",
      "print A\n",
      "print \"El convertim en un tensor 3x4x2\"\n",
      "A.shape = (3,4,2)\n",
      "print A\n",
      "print \"Accedim a la component A[0,2,1]\"\n",
      "print A[0,2,1]\n",
      "print \"Accedim a la component A[0,:,:]\"\n",
      "print A[0,:,:]\n",
      "print \"Volem agafar la component i=1, les components j={0,1} i la component k=0\"\n",
      "print A[1,0:2,0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Definim un vector unidimensional:\n",
        "[ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23]\n",
        "El convertim en un tensor 3x4x2\n",
        "[[[ 0  1]\n",
        "  [ 2  3]\n",
        "  [ 4  5]\n",
        "  [ 6  7]]\n",
        "\n",
        " [[ 8  9]\n",
        "  [10 11]\n",
        "  [12 13]\n",
        "  [14 15]]\n",
        "\n",
        " [[16 17]\n",
        "  [18 19]\n",
        "  [20 21]\n",
        "  [22 23]]]\n",
        "Accedim a la component A[0,2,1]\n",
        "5\n",
        "Accedim a la component A[0,:,:]\n",
        "[[0 1]\n",
        " [2 3]\n",
        " [4 5]\n",
        " [6 7]]\n",
        "Volem agafar la component i=1, les components j={0,1} i la component k=0\n",
        "[ 8 10]\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Una contracci\u00f3 tensorial senzilla:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B = np.array([[4,7,2],[2,3,4],[6,4,2], [5,6,7],[1,2,4]])\n",
      "print \"B \u00e9s una matriu 5x3:\"\n",
      "print B\n",
      "print \"Segur? Mida de B:\"\n",
      "print B.shape\n",
      "print \"Clar que s\u00ed\"\n",
      "print \"Fem la contracci\u00f3 dels tensors A,B. Contraurem el primer \u00edndex de A amb el segon \u00edndex de B\"\n",
      "C = np.tensordot(A, B, [0,1])\n",
      "print C\n",
      "print \"Dimensions de C:\"\n",
      "print C.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "B \u00e9s una matriu 5x3:\n",
        "[[4 7 2]\n",
        " [2 3 4]\n",
        " [6 4 2]\n",
        " [5 6 7]\n",
        " [1 2 4]]\n",
        "Segur? Mida de B:\n",
        "(5, 3)\n",
        "Clar que s\u00ed\n",
        "Fem la contracci\u00f3 dels tensors A,B. Contraurem el primer \u00edndex de A amb el segon \u00edndex de B\n",
        "[[[ 88  88  64 160  80]\n",
        "  [101  97  76 178  87]]\n",
        "\n",
        " [[114 106  88 196  94]\n",
        "  [127 115 100 214 101]]\n",
        "\n",
        " [[140 124 112 232 108]\n",
        "  [153 133 124 250 115]]\n",
        "\n",
        " [[166 142 136 268 122]\n",
        "  [179 151 148 286 129]]]\n",
        "Dimensions de C:\n",
        "(4, 2, 5)\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Podem contraure m\u00e9s d'un \u00edndex simult\u00e0niament:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Ara farem servir el tensor C 4x2x5 i el contraurem amb el tensor A 3x4x2.\"\n",
      "print \"Contraurem el primer \u00edndex de C amb el segon de A i el segon \u00edndex de C amb el tercer de A\"\n",
      "D = np.tensordot(C,A,[ [0,1],[1,2]]) # els \u00edndex els comencem a comptar des de zero!\n",
      "print \"Resultat:\"\n",
      "print D\n",
      "print \"Dimensions:\"\n",
      "print D.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Ara farem servir el tensor C 4x2x5 i el contraurem amb el tensor A 3x4x2.\n",
        "Contraurem el primer \u00edndex de C amb el segon de A i el segon \u00edndex de C amb el tercer de A\n",
        "Resultat:\n",
        "[[ 4284 12828 21372]\n",
        " [ 3724 11372 19020]\n",
        " [ 3472 10256 17040]\n",
        " [ 7000 21272 35544]\n",
        " [ 3220  9908 16596]]\n",
        "Dimensions:\n",
        "(5, 3)\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Definir amb un bucle for un tensor numpy \u00e9s possible:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Un apunt: la funcio range(10) torna una llista amb els n\u00fameros enters en l'interval [0,10):\"\n",
      "print range(10)\n",
      "print \"La farem servir per iterar pel nostre tensor\"\n",
      "dimensions_tensor = (3,2,4)\n",
      "print \"Inicialitzem un tensor de la mida que volem a zeros:\"\n",
      "tensor = np.zeros(dimensions_tensor) # Tot el tensor s\u00f3n zeros\n",
      "print tensor\n",
      "print \"Les dimensions del tensor\", tensor.shape\n",
      "print \"Li donem valors a voluntat:\"\n",
      "for i in range(dimensions_tensor[0]):\n",
      "    for j in range(dimensions_tensor[1]):\n",
      "        for k in range(dimensions_tensor[2]):\n",
      "            if i==j and k==1:\n",
      "                tensor[i,j,k] = 1\n",
      "            elif i==k and j==0:\n",
      "                tensor[i,j,k] = 2\n",
      "            else:\n",
      "                tensor[i,j,k] = 3\n",
      "print tensor"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Un apunt: la funcio range(10) torna una llista amb els n\u00fameros enters en l'interval [0,10):\n",
        "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
        "La farem servir per iterar pel nostre tensor\n",
        "Inicialitzem un tensor de la mida que volem a zeros:\n",
        "[[[ 0.  0.  0.  0.]\n",
        "  [ 0.  0.  0.  0.]]\n",
        "\n",
        " [[ 0.  0.  0.  0.]\n",
        "  [ 0.  0.  0.  0.]]\n",
        "\n",
        " [[ 0.  0.  0.  0.]\n",
        "  [ 0.  0.  0.  0.]]]\n",
        "Les dimensions del tensor (3, 2, 4)\n",
        "Li donem valors a voluntat:\n",
        "[[[ 2.  1.  3.  3.]\n",
        "  [ 3.  3.  3.  3.]]\n",
        "\n",
        " [[ 3.  2.  3.  3.]\n",
        "  [ 3.  1.  3.  3.]]\n",
        "\n",
        " [[ 3.  3.  2.  3.]\n",
        "  [ 3.  3.  3.  3.]]]\n"
       ]
      }
     ],
     "prompt_number": 50
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