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     "text": [
      "Running sanity checks...\n",
      "Gradient check passed!\n",
      "Gradient check passed!\n",
      "Gradient check passed!\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "\n",
    "\n",
    "# First implement a gradient checker by filling in the following functions\n",
    "def gradcheck_naive(f, x):\n",
    "    \"\"\" Gradient check for a function f.\n",
    "\n",
    "    Arguments:\n",
    "    f -- a function that takes a single argument and outputs the\n",
    "         cost and its gradients\n",
    "    x -- the point (numpy array) to check the gradient at\n",
    "    \"\"\"\n",
    "\n",
    "    rndstate = random.getstate()\n",
    "    random.setstate(rndstate)\n",
    "    fx, grad = f(x) # Evaluate function value at original point\n",
    "    h = 1e-4        # Do not change this!\n",
    "\n",
    "    # Iterate over all indexes in x\n",
    "    it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])\n",
    "    while not it.finished:\n",
    "        ix = it.multi_index\n",
    "        # Try modifying x[ix] with h defined above to compute\n",
    "        # numerical gradients. Make sure you call random.setstate(rndstate)\n",
    "        # before calling f(x) each time. This will make it possible\n",
    "        # to test cost functions with built in randomness later.\n",
    "\n",
    "        ### YOUR CODE HERE:\n",
    "        x[ix] += h\n",
    "        random.setstate(rndstate)\n",
    "        new_f1 = f(x)[0]\n",
    "        x[ix] -= 2*h\n",
    "        random.setstate(rndstate)\n",
    "        new_f2 = f(x)[0]\n",
    "        x[ix] += h\n",
    "        numgrad = (new_f1 - new_f2) / (2 * h)\n",
    "        ### END YOUR CODE\n",
    "\n",
    "        # Compare gradients\n",
    "        reldiff = abs(numgrad - grad[ix]) / max(1, abs(numgrad), abs(grad[ix]))\n",
    "        if reldiff > 1e-5:\n",
    "            print(\"Gradient check failed.\")\n",
    "            print(\"First gradient error found at index %s\" % str(ix))\n",
    "            print(\"Your gradient: %f \\t Numerical gradient: %f\" % (\n",
    "                grad[ix], numgrad))\n",
    "            return\n",
    "\n",
    "        it.iternext() # Step to next dimension\n",
    "\n",
    "    print(\"Gradient check passed!\")\n",
    "\n",
    "\n",
    "def sanity_check():\n",
    "    \"\"\"\n",
    "    Some basic sanity checks.\n",
    "    \"\"\"\n",
    "    quad = lambda x: (np.sum(x ** 2), x * 2)\n",
    "\n",
    "    print(\"Running sanity checks...\")\n",
    "    gradcheck_naive(quad, np.array(123.456))      # scalar test\n",
    "    gradcheck_naive(quad, np.random.randn(3,))    # 1-D test\n",
    "    gradcheck_naive(quad, np.random.randn(4,5))   # 2-D test\n",
    "    print(\"\")\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    sanity_check()"
   ]
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