mp574_lecture_003.ipynb

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    "## Lecture 2: Intro to Optimization\n",
    "\n",
    "Goal: to motivate the use of an optimization framework in imaging. "
   ]
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    "## MP 574 Lecture 2: Intro to optimization\n",
    "##\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import scipy.linalg as la\n",
    "import numpy.random as rnd\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display, Image\n",
    "import matplotlib.image as mpimg\n",
    "from os.path import dirname, join as pjoin\n",
    "import scipy.io as sio"
   ]
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   "source": [
    "A = [[1, 4, 5, 12], \n",
    "    [-5, 8, 9, 0],\n",
    "    [-6, 7, 11, 19]]\n"
   ]
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   "cell_type": "code",
   "execution_count": 184,
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    {
     "data": {
      "text/plain": [
       "array([[-0.23174056],\n",
       "       [ 0.65590855],\n",
       "       [-0.71177458],\n",
       "       [ 0.09724827]])"
      ]
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     "execution_count": 184,
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    "la.null_space(A)"
   ]
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   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [],
   "source": [
    "b= np.array([0, 1, 2, 3])\n",
    "y = np.array([-1, 0.2, 0.9, 2.1])\n",
    "b = np.random.rand(3,1)\n",
    "A = np.random.rand(3,2)\n",
    "x = np.linalg.lstsq(A, b, rcond=None)"
   ]
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   "execution_count": 201,
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     "data": {
      "text/plain": [
       "(array([[-0.29783349],\n",
       "        [ 1.97790238]]),\n",
       " array([0.18282723]),\n",
       " 2,\n",
       " array([1.5246864 , 0.25989249]))"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "x"
   ]
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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