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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Introduzione al Python per il calcolo scientifico."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "05/12/2014\n",
      "\n",
      "docente: Francesca Mazzia\n",
      "\n",
      "Il materiale \u00e8 distribuito con licenza Creative Commons Attribuzione-Non commerciale-Non Opere Derivate 2.5 Italy License http://creativecommons.org/licenses/by-nc-nd/2.5/it/"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Matrici e Vettori"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Scriviamo una matrice casuale con 3 righe  4 colonne \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "# np.random.rand genera numeri casuali appartenenti a una distribuzione uniforme\n",
      "A = np.random.rand(3,4)*10\n",
      "print(A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.99560353  7.67272576  0.49584679  9.31424283]\n",
        " [ 6.66089124  4.21645872  2.89825974  4.63601822]\n",
        " [ 3.66089621  9.64700287  1.08335531  5.12058017]]\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# questa e' una matrice rettangolare\n",
      "# scriviamo una matrice quadrata con elementi casuali interi\n",
      "A = np.random.randint(10,size=(3,3))\n",
      "print(A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[0 6 7]\n",
        " [5 6 3]\n",
        " [3 5 2]]\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# gli elementi delle matrici si denotano\n",
      "# usando l'indice di riga e di colonna\n",
      "print(A[0,0])\n",
      "print(A[1,1])\n",
      "print(A[2,2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0\n",
        "6\n",
        "2\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(type(A))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<class 'numpy.ndarray'>\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Trasposta"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('trasposta\\n',A.T)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "trasposta\n",
        " [[0 5 3]\n",
        " [6 6 5]\n",
        " [7 3 2]]\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Prodotto riga per colonne e prodotto fra matrici"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(np.dot(A,A))\n",
      "print(A*A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[51 71 32]\n",
        " [39 81 59]\n",
        " [31 58 40]]\n",
        "[[ 0 36 49]\n",
        " [25 36  9]\n",
        " [ 9 25  4]]\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Tipo matrix"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A = np.asmatrix(A)\n",
      "print(A)    \n",
      "print(type(A)) # A di tipo matrix\n",
      "print(A.I)     # A.I inversa di A\n",
      "print(A.I*A)    # il * e' il prodotto riga per colonne\n",
      "print(np.dot(A.I,A))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[0 6 7]\n",
        " [5 6 3]\n",
        " [3 5 2]]\n",
        "<class 'numpy.matrixlib.defmatrix.matrix'>\n",
        "[[-0.06976744  0.53488372 -0.55813953]\n",
        " [-0.02325581 -0.48837209  0.81395349]\n",
        " [ 0.1627907   0.41860465 -0.69767442]]"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "[[  1.00000000e+00   0.00000000e+00  -2.22044605e-16]\n",
        " [  0.00000000e+00   1.00000000e+00   0.00000000e+00]\n",
        " [  4.44089210e-16  -4.44089210e-16   1.00000000e+00]]\n",
        "[[  1.00000000e+00   0.00000000e+00  -2.22044605e-16]\n",
        " [  0.00000000e+00   1.00000000e+00   0.00000000e+00]\n",
        " [  4.44089210e-16  -4.44089210e-16   1.00000000e+00]]\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U=np.triu(A)   # operazioni con in input matrix in output array\n",
      "print(type(U))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<class 'numpy.ndarray'>\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A.shape  # numero di righe e colonne"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "(3, 3)"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A.ndim  # dimensione della matrice, possiamo avere array a piu' dimensioni"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "2"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "O = np.zeros( (3,3) ) # matrice nulla\n",
      "print(O)\n",
      "print(type(O))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.  0.  0.]\n",
        " [ 0.  0.  0.]\n",
        " [ 0.  0.  0.]]\n",
        "<class 'numpy.ndarray'>\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "I = np.eye(3) # matrice identit\u00e0\n",
      "print(type(I))\n",
      "print(I)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<class 'numpy.ndarray'>\n",
        "[[ 1.  0.  0.]\n",
        " [ 0.  1.  0.]\n",
        " [ 0.  0.  1.]]\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "d = np.diag(np.array([1, 2, 3, 4])) # array con elementi sulla diagonale\n",
      "print(d)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[1 0 0 0]\n",
        " [0 2 0 0]\n",
        " [0 0 3 0]\n",
        " [0 0 0 4]]\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "narray = np.arange(1,10,2) # arange array\n",
      "print(narray)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1 3 5 7 9]\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B = np.empty((3,4) ) # array vuoto non inizializzato\n",
      "print(B)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.  0.  0.  0.]\n",
        " [ 0.  0.  0.  0.]\n",
        " [ 0.  0.  0.  0.]]\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline\n",
      "image = np.random.rand(30, 30)\n",
      "plt.imshow(image, cmap=plt.cm.hot)    \n",
      "plt.colorbar()   "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "<matplotlib.colorbar.Colorbar at 0x6982e10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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j1ZyKatBY6DYQsyJrg7QWvekwc0/jBzKbQktzC8kUehhTZeyPmFWbUVpju44+bNj6C1zY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\naI/2rbBHsHq0R3u0b4X9/+9F98Fef3y0AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4ec4f10>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.arange(10) \n",
      "a[::-1]      # ordine inverso"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.arange(10000)\n",
      "%timeit a + 1  "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10000 loops, best of 3: 38.5 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l = range(10000)\n",
      "%timeit [i+1 for i in l] "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100 loops, best of 3: 2.46 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      " a = np.array([1, 2, 3, 4])\n",
      " b = np.array([4, 2, 2, 4])\n",
      " a == b\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "array([False,  True, False,  True], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a > b\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "array([False, False,  True, False], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.array_equal(a,b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      " np.sin(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "array([ 0.84147098,  0.90929743,  0.14112001, -0.7568025 ])"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.sin(a[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "0.8414709848078965"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f = np.random.randint(10,size=(2,2,2))\n",
      "print(f)\n",
      "print(f.ndim)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[[3 9]\n",
        "  [7 5]]\n",
        "\n",
        " [[3 9]\n",
        "  [1 2]]]\n",
        "3\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f[0,0,:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "array([3, 9])"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f[0,:,0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "array([3, 7])"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.sum(f,axis=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "array([[12, 12],\n",
        "       [12,  3]])"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy as sp\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import  linalgmod\n",
      "import  time\n",
      "\n",
      "dim=100\n",
      "A=np.random.rand(dim,dim)\n",
      "B=np.random.rand(dim,dim)\n",
      "#import importlib as imp\n",
      "#imp.reload(linalgmod)  #per ricaricare il modulo se si fanno modifiche"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t1=time.clock()\n",
      "C1=linalgmod.prodmatmat(A,B)\n",
      "t2=time.clock()-t1\n",
      "print( \"clock = \", t2 )\n",
      "\n",
      " \n",
      "# A e B sono array il prodotto riga per colonne si esegue utilizzando \n",
      "# np.dot\n",
      "t1=time.clock()\n",
      "C2=np.dot(A,B)\n",
      "t2d=time.clock()-t1\n",
      "print( \"clock = \", t2d )\n",
      "\n",
      "\n",
      "print( \"errore\", np.max(np.abs(C1-C2)) )\n",
      "\n",
      "# C1 e C2 contengono gli stessi elementi\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "clock =  2.6231819965945533\n",
        "clock =  0.01525054161902517\n",
        "errore 0.0\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.linalg as la\n",
      "# la function inv calcola l'inversa di A \n",
      "AI = la.inv(A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print( np.dot(AI,A) ) \n",
      "\n",
      "# una matrice che non ha inversa si dice\n",
      "# singolare\n",
      "print(la.det(A)) #  det calcola il determinate di A\n",
      "\n",
      "A = np.random.rand(3,4)\n",
      "# norma di Frobenious\n",
      "print('norma frobenious= ',la.norm(A) )\n",
      "# norma 1\n",
      "n1 = la.norm(A,1)\n",
      "print('norma 1 = ',n1)\n",
      "\n",
      "# norma infinito\n",
      "ninf = la.norm(A,np.inf)\n",
      "print('norma infinito = ',ninf)\n",
      "# norma 2\n",
      "n2= la.norm(A,2)\n",
      "print('norma 2 = ',n2 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[  1.00000000e+00  -2.22044605e-16  -6.59194921e-17 ...,  -3.77475828e-15\n",
        "   -8.60422844e-16  -2.22044605e-15]\n",
        " [  3.33066907e-16   1.00000000e+00   1.54390389e-15 ...,  -5.55111512e-16\n",
        "    1.16573418e-15   7.77156117e-16]\n",
        " [  1.66533454e-16   1.11022302e-16   1.00000000e+00 ...,  -3.10862447e-15\n",
        "   -3.63598041e-15  -2.22044605e-15]\n",
        " ..., \n",
        " [  2.22044605e-16  -8.32667268e-17  -3.22658567e-16 ...,   1.00000000e+00\n",
        "   -2.73392420e-15  -1.49880108e-15]\n",
        " [  5.68989300e-16   4.57966998e-16  -1.73038667e-16 ...,   1.94289029e-16\n",
        "    1.00000000e+00   3.33066907e-15]\n",
        " [ -6.66133815e-16  -6.66133815e-16  -4.30211422e-16 ...,   3.33066907e-15\n",
        "    6.27276009e-15   1.00000000e+00]]\n",
        "2.604858322799237e+25\n",
        "norma frobenious=  2.24160295425\n",
        "norma 1 =  2.26212171885\n",
        "norma infinito =  2.65610113131\n",
        "norma 2 =  2.0883589504\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a=np.array([-4, -3, -2, -1,  0,  1,  2,  3,  4])\n",
      "b = a.reshape((3, 3))\n",
      "print(b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[-4 -3 -2]\n",
        " [-1  0  1]\n",
        " [ 2  3  4]]\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Sistema lineare: trovare  x tale che A*x = b"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.lookfor('solve linear system')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Search results for 'solve linear system'\n",
        "----------------------------------------\n",
        "numpy.linalg.solve\n",
        "    Solve a linear matrix equation, or system of linear scalar equations.\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A = np.random.rand(3,3)\n",
      "b = np.array([1,2,3])\n",
      "x = np.linalg.solve(A,b)\n",
      "print(x)\n",
      "type(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-15.57501659  11.8153128    6.31760386]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "numpy.ndarray"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(type(A))\n",
      "print(np.dot(A,x)-b) # residuo"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<class 'numpy.ndarray'>\n",
        "[  2.22044605e-16   0.00000000e+00   0.00000000e+00]\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(x.shape)\n",
      "y = x.T\n",
      "print(y.shape)\n",
      "print(A*x-b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(3,)\n",
        "(3,)\n",
        "[[ -1.66639368  -0.68171654  -2.65188978]\n",
        " [ -5.4209156    2.33786283  -0.91694723]\n",
        " [-10.13776455   8.62832522  -1.49056068]]\n"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Risolviamo un sistema lineare con matrice dei coefficienti\n",
      "la matrice di Hilbert.La matrice viene costruita nel modulo linalgmod.\n",
      "Il termine noto lo scegliamo in modo che la soluzione x\n",
      "sia il vettore di tutti  uno."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 7\n",
      "A = linalgmod.hilb(n)\n",
      "#print(A)\n",
      "x = np.ones( (n,1))\n",
      "b = np.dot(A,x)\n",
      "#print(b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "risolviamo il sistema, calcoliamo il residuo e l'errore assoluto"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xa = np.linalg.solve(A,b)\n",
      "xb = la.solve(A,b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(la.norm(x-xa,2))\n",
      "print(la.norm(x-xb,2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "4.03300396553e-08\n",
        "4.03300396553e-08\n"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Stampiamo il numero di condizione di A. Il numero di condizione nella soluzione di un sistema lineare ci dice come una perturbazione sui dati di input (A e b) si ripercuote sul risultato (xa). Il numero di condizione $$\\kappa(A) = \\| A \\| \\| A^{-1}\\|$$ "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.linalg.cond(A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 55,
       "text": [
        "475367356.59218162"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "la matrice di Hilbert \u00e8 mal condizionata"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Possiamo anche prima fattorizzare la matrice a poi risolvere i sistemi\n",
      "lineari usando la fattorizzazione. La fattorizzazione usata dagli \n",
      "algoritmi classici \u00e8 la fattorizzazione LU con pivot"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#%%\n",
      "# function lu di scipy\n",
      "p,l,u=la.lu(A)\n",
      "la.norm(A-np.dot(np.dot(p,l),u),1)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 56,
       "text": [
        "4.163336342344337e-17"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.linalg.cond(l)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 57,
       "text": [
        "6.8625619731504957"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.linalg.cond(u)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 58,
       "text": [
        "208813266.86136585"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# function lu della libreria lapack\n",
      "x1=la.solve(A,b)\n",
      "lu,piv=la.lu_factor(A)\n",
      "# piv contiene il vettore delle permutazioni\n",
      "# la riga i e' stata cambiata con la riga piv[i\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x2=la.lu_solve((lu,piv),b)\n",
      "la.norm(x2-x,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 61,
       "text": [
        "4.0330039655283455e-08"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "visualizziamo il residuo. Un residuo piccolo non implica un errore piccolo se la matrice \u00e8 mal condizionata."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "la.norm(np.dot(A,x2)-b,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 62,
       "text": [
        "2.4825341532472731e-16"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Matrici Sparse"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import scipy.sparse as sparse\n",
      "A = sparse.csr_matrix([[1, 2, 0], [0, 0, 3], [4, 0, 5]])\n",
      "print(A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "  (0, 0)\t1\n",
        "  (0, 1)\t2\n",
        "  (1, 2)\t3\n",
        "  (2, 0)\t4\n",
        "  (2, 2)\t5\n"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      " v = np.array([1, 0, -1])\n",
      " A.dot(v)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 65,
       "text": [
        "array([ 1, -3, -1], dtype=int32)"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "per eseguire il prodotto riga per colonne bisogna utilizzare metodi speciali"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.dot(A, v)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "ValueError",
       "evalue": "setting an array element with a sequence.",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-66-0b2385270cf1>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mA\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mv\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;31mValueError\u001b[0m: setting an array element with a sequence."
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "oppure trasformare la matrice in matrice densa, operazione che non conviene fare."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A = sparse.coo_matrix( ([1,2,3,4],([0,1,2,3],[1,2,3,0]) ) )\n",
      "print(A)\n",
      "print(A.todense())\n",
      "print(type(A.todense()))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "  (0, 1)\t1\n",
        "  (1, 2)\t2\n",
        "  (2, 3)\t3\n",
        "  (3, 0)\t4\n",
        "[[0 1 0 0]\n",
        " [0 0 2 0]\n",
        " [0 0 0 3]\n",
        " [4 0 0 0]]\n",
        "<class 'numpy.matrixlib.defmatrix.matrix'>\n"
       ]
      }
     ],
     "prompt_number": 70
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "numero degli elementi diversi da zero in A"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A.nnz"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 71,
       "text": [
        "4"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "esistono vari formati di rappresentazione, fra cui:\n",
      "il formato per coordinate(coo), il formato compresso per colonne (csc) \n",
      "e il formato compresso per righe (csr)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B=sparse.csc_matrix(A)\n",
      "print(B)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "  (3, 0)\t4\n",
        "  (0, 1)\t1\n",
        "  (1, 2)\t2\n",
        "  (2, 3)\t3\n"
       ]
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "l'algebra lineare per le matrici sparse \u00e8 implementata nel pacchetto\n",
      "scipy.sparse.linalg,  risulta ottimizzata per matrici nel formato csc e csr"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.sparse.linalg as sla\n",
      "b = np.random.rand(4,1)\n",
      "x = sla.spsolve(A,b)\n",
      "print(x)\n",
      "x = sla.spsolve(B,b)\n",
      "print(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.07157297  0.39450702  0.33304688  0.02639068]\n",
        "[ 0.07157297  0.39450702  0.33304688  0.02639068]\n"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B.dot(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 75,
       "text": [
        "array([ 0.39450702,  0.66609376,  0.07917204,  0.28629188])"
       ]
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 100000;\n",
      "I = np.arange(0,N)\n",
      "J = I+1\n",
      "J[N-1]=0\n",
      "A = sparse.coo_matrix( (np.arange(1,N+1),(I,J) ) )\n",
      "b = I[:]\n",
      "B=sparse.csc_matrix(A)\n",
      "x1 = sla.spsolve(A,b)\n",
      "x2 = sla.spsolve(B,b)\n",
      "print(la.norm(x1-x2,np.inf))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.0\n"
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.dot(A.todense(), v)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "ValueError",
       "evalue": "array is too big.",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-77-1725d607ad69>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mA\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtodense\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mv\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;32mC:\\Programmi\\Anaconda\\envs\\python3\\lib\\site-packages\\scipy\\sparse\\base.py\u001b[0m in \u001b[0;36mtodense\u001b[1;34m(self, order, out)\u001b[0m\n\u001b[0;32m    603\u001b[0m             \u001b[0;31m`\u001b[0m\u001b[0mnumpy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmatrix\u001b[0m\u001b[0;31m`\u001b[0m \u001b[0mobject\u001b[0m \u001b[0mthat\u001b[0m \u001b[0mshares\u001b[0m \u001b[0mthe\u001b[0m \u001b[0msame\u001b[0m \u001b[0mmemory\u001b[0m\u001b[1;33m.\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    604\u001b[0m         \"\"\"\n\u001b[1;32m--> 605\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0masmatrix\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtoarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0morder\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0morder\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mout\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mout\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    606\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    607\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mtoarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0morder\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mout\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32mC:\\Programmi\\Anaconda\\envs\\python3\\lib\\site-packages\\scipy\\sparse\\coo.py\u001b[0m in \u001b[0;36mtoarray\u001b[1;34m(self, order, out)\u001b[0m\n\u001b[0;32m    267\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mtoarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0morder\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mout\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    268\u001b[0m         \u001b[1;34m\"\"\"See the docstring for `spmatrix.toarray`.\"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 269\u001b[1;33m         \u001b[0mB\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_process_toarray_args\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0morder\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mout\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    270\u001b[0m         \u001b[0mfortran\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mB\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mflags\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mf_contiguous\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    271\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mfortran\u001b[0m \u001b[1;32mand\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mB\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mflags\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mc_contiguous\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32mC:\\Programmi\\Anaconda\\envs\\python3\\lib\\site-packages\\scipy\\sparse\\base.py\u001b[0m in \u001b[0;36m_process_toarray_args\u001b[1;34m(self, order, out)\u001b[0m\n\u001b[0;32m    787\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mout\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    788\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 789\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0morder\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0morder\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    790\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    791\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m__numpy_ufunc__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpos\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minputs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mValueError\u001b[0m: array is too big."
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Interpolazione\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "%run spline_dem.py"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "grafico di una funzione bidimensionale"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x, y = np.mgrid[-1:1:20j, -1:1:20j]\n",
      "z = (x+y) * np.exp(-6.0*(x*x+y*y))\n",
      "\n",
      "plt.figure()\n",
      "plt.pcolor(x, y, z)\n",
      "plt.colorbar()\n",
      "plt.title(\"funzione con elementi sparsi.\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "\n",
      "fig = plt.figure()\n",
      "ax = fig.gca(projection='3d')\n",
      "surf = ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap=cm.coolwarm,\n",
      "        linewidth=0, antialiased=False)\n",
      "\n",
      "ax.set_zlim(-0.3, 0.3)\n",
      "\n",
      "ax.zaxis.set_major_locator(LinearLocator(10))\n",
      "ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
      "\n",
      "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
      "\n",
      "plt.show()\n",
      "ax.zaxis.set_major_locator(LinearLocator(20))\n",
      "\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import interpolate\n",
      "xnew, ynew = np.mgrid[-1:1:70j, -1:1:70j]\n",
      "tck = interpolate.bisplrep(x, y, z, s=0)\n",
      "znew = interpolate.bisplev(xnew[:,0], ynew[0,:], tck)\n",
      "\n",
      "plt.figure()\n",
      "plt.pcolor(xnew, ynew, znew)\n",
      "plt.colorbar()\n",
      "plt.title(\"Interpolated function.\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "fig = plt.figure()\n",
      "ax = fig.gca(projection='3d')\n",
      "surf = ax.plot_surface(xnew, ynew, znew, rstride=1, cstride=1, cmap=cm.coolwarm,\n",
      "        linewidth=0, antialiased=False)\n",
      "\n",
      "ax.set_zlim(-0.3, 0.3)\n",
      "\n",
      "ax.zaxis.set_major_locator(LinearLocator(10))\n",
      "ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n",
      "\n",
      "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
      "\n",
      "plt.show()\n",
      "ax.zaxis.set_major_locator(LinearLocator(20))\n",
      "\n",
      "\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}