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   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 3, 5, 7]\n"
     ]
    }
   ],
   "source": [
    "print(list(filter(lambda x: x % 2 == 1, l)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "36\n"
     ]
    }
   ],
   "source": [
    "from functools import reduce\n",
    "print(reduce(lambda a, b: a + b, l))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    }
   ],
   "source": [
    "print(reduce(lambda a, b: a if a > b else b, l))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## == vs. is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "print(5 == 5)\n",
    "print(5 is 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "False\n",
      "True\n"
     ]
    }
   ],
    "a = b = [1,2,3]\n",
    "print([1,2,3] == [1,2,3])\n",
    "print([1,2,3] is [1,2,3])\n",
    "print(a is b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NumPy Grundlagen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NumPy Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4 5 6]\n",
      "1\n",
      "6\n",
      "[2 3 4]\n",
      "[1 2]\n",
      "[6 5 4 3 2 1]\n",
      "[2 4 6]\n",
      "[1 3 4 5]\n",
      "[1 3 6]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([1, 2, 3, 4, 5, 6])\n",
    "print(a)\n",
    "print(a[0])\n",
    "print(a[-1])\n",
    "print(a[1:4])\n",
    "print(a[:2])\n",
    "print(a[::-1])\n",
    "print(a[1::2])\n",
    "print(a[[0, 2, 3, 4]]) # Liste von Indizes\n",
    "print(a[[True, False, True, False, False, True]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Operatoren auf NumPy Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 4 5 6 7 8]\n",
      "[ 3  6  9 12 15 18]\n",
      "[ 1  4  9 16 25 36]\n",
      "[ 2  4  8 16 32 64]\n"
     ]
    }
   ],
    "print(a + 2)\n",
    "print(3 * a)\n",
    "print(a**2)\n",
    "print(2**a)"
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = np.array([6, 5, 4, 3, 2, 1]) # b = a[::-1]"
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7 7 7 7 7 7]\n",
      "[ 6 10 12 12 10  6]\n",
      "[ 1 32 81 64 25  6]\n"
     ]
    }
   ],
   "source": [
    "print(a + b)\n",
    "print(a * b)\n",
    "print(a**b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zweidimensionale Arrays (Matrizen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n",
      "1 6\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "print(A)\n",
    "print(A[0,0], A[1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n",
      "[1 4 7]\n"
     ]
    }
   ],
   "source": [
    "print(A[0])\n",
    "print(A[:, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [4 5]]\n"
     ]
    }
   ],
   "source": [
    "print(A[:2, :2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 1]\n",
      " [5 4]]\n"
     ]
    }
   ],
   "source": [
    "print(A[:2, 1::-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4 5]\n",
      " [1 2]]\n"
     ]
    }
   ],
   "source": [
    "print(A[1::-1, :2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Werte überschreiben"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n"
     ]
    }
   ],
   "source": [
    "B = A.copy()\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[12 12 12]\n",
      " [ 4  5  6]\n",
      " [ 7  8  9]]\n"
     ]
    }
   ],
   "source": [
    "B[0] = 12\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[12 -5 12]\n",
      " [ 4 -5  6]\n",
      " [ 7 -5  9]]\n"
     ]
    }
   ],
   "source": [
    "B[:, 1] = -5\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[12 -5 12]\n",
      " [ 4 -5  6]\n",
      " [ 5  6  7]]\n"
     ]
    }
   ],
   "source": [
    "B[2] = [5, 6, 7]\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[12 12 12]\n",
      " [ 4 -5  6]\n",
      " [ 5 12  7]]\n"
     ]
    }
   ],
   "source": [
    "B[:, 1] = B[0]\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dimensionen hinzufügen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[1 2 3]\n",
      "  [4 5 6]\n",
      "  [7 8 9]]]\n"
     ]
    }
   ],
   "source": [
    "print(A[None])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[1 2 3]]\n",
      "\n",
      " [[4 5 6]]\n",
      "\n",
      " [[7 8 9]]]\n"
     ]
    }
   ],
   "source": [
    "print(A[:, None])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[1]\n",
      "  [2]\n",
      "  [3]]\n",
      "\n",
      " [[4]\n",
      "  [5]\n",
      "  [6]]\n",
      "\n",
      " [[7]\n",
      "  [8]\n",
      "  [9]]]\n"
     ]
    }
   ],
   "source": [
    "print(A[:, :, None])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 0 -1]\n",
      "  [-1 -1]\n",
      "  [-2 -4]]\n",
      "\n",
      " [[-1  0]\n",
      "  [-2  0]\n",
      "  [-3 -3]]]\n",
      "[[[ 0 -1]\n",
      "  [-1  0]]\n",
      "\n",
      " [[-1 -1]\n",
      "  [-2  0]]\n",
      "\n",
      " [[-2 -4]\n",
      "  [-3 -3]]]\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[1,0],[0,1]])\n",
    "Y = np.array([[1,1],[2,1],[3,4]])\n",
    "print(X[:, None] - Y[None, :])\n",
    "print(X[None, :] - Y[:, None])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Boolesche Funktionen auf NumPy Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = np.array([1, 0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ True False  True]\n"
     ]
    }
   ],
   "source": [
    "print(b == 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[False  True False]\n"
     ]
    }
   ],
   "source": [
    "print(b < 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [7 8 9]]\n"
     ]
    }
   ],
   "source": [
    "print(A[b == 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [7 8 9]]\n"
     ]
    }
   ],
   "source": [
    "print(A[[True, False, True]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[False False False]\n",
      " [False False  True]\n",
      " [ True  True  True]]\n"
     ]
    }
   ],
   "source": [
    "print(A > 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "print(A[A > 5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nützliche NumPy Funktionen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.ndarray((4,4))\n",
    "A = np.zeros((3, 4))\n",
    "B = np.ones((3,4))\n",
    "c = np.arange(0, 1, .1)\n",
    "d = np.linspace(0, 1, 10)\n",
    "I = np.identity(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4.67296746e-307 1.69121096e-306 8.01092457e-307 1.24610994e-306]\n",
      " [1.42418987e-306 1.37961641e-306 1.60220528e-306 1.24611266e-306]\n",
      " [9.34598925e-307 1.24612081e-306 1.11260755e-306 1.60220393e-306]\n",
      " [1.51320640e-306 9.34609790e-307 1.24610723e-306 1.24610723e-306]]\n"
     ]
    }
   ],
   "source": [
    "print(X) # zufällige Werte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1. 1. 1.]\n",
      " [1. 1. 1. 1.]\n",
      " [1. 1. 1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]\n"
     ]
    }
   ],
   "source": [
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.         0.11111111 0.22222222 0.33333333 0.44444444 0.55555556\n",
      " 0.66666667 0.77777778 0.88888889 1.        ]\n"
     ]
    }
   ],
   "source": [
    "print(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 0.]\n",
      " [0. 1. 0. 0.]\n",
      " [0. 0. 1. 0.]\n",
      " [0. 0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "print(I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  2.  3.  4.]\n",
      " [ 5.  6.  7.  8.]\n",
      " [ 9. 10. 11. 12.]\n",
      " [13. 14. 15. 16.]]\n"
     ]
    }
   ],
   "source": [
    "M = np.linspace(1, 16, 16).reshape((4,4))\n",
    "print(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  5.  9. 13.]\n",
      " [ 2.  6. 10. 14.]\n",
      " [ 3.  7. 11. 15.]\n",
      " [ 4.  8. 12. 16.]]\n"
     ]
    }
   ],
   "source": [
    "print(M.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "136.0 8.5 20922789888000.0\n"
     ]
    }
   ],
   "source": [
    "print(M.sum(), M.mean(), M.prod())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[28. 32. 36. 40.] [ 7.  8.  9. 10.] [ 585. 1680. 3465. 6144.]\n"
     ]
    }
   ],
   "source": [
    "print(M.sum(0), M.mean(0), M.prod(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10. 26. 42. 58.] [ 2.5  6.5 10.5 14.5] [2.400e+01 1.680e+03 1.188e+04 4.368e+04]\n"
     ]
    }
   ],
   "source": [
    "print(M.sum(1), M.mean(1), M.prod(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 2. 3. 4.]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(1,4, 4)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 30.  70. 110. 150.]\n"
     ]
    }
   ],
   "source": [
    "print(M.dot(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 30.  70. 110. 150.]\n"
     ]
    }
   ],
   "source": [
    "print(M @ x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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