numpy_lesson9-ix_( ), Linear Algebra, Repeat, Stack.ipynb

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    "import numpy as np"
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      "matrix_a=>\n",
      " [[ 0  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]\n",
      " [20 21 22 23 24]]\n",
      "\n",
      "np.ix_([1,3],[2,4]))\n",
      "ix_()=>\n",
      "(array([[1],\n",
      "       [3]]), array([[2, 4]]))\n",
      "\n",
      "Seperate the return value of ix_(): rows, cols = np.ix_([1,3],[2,4])\n",
      "rows=>\n",
      "[[1]\n",
      " [3]]\n",
      "cols=>\n",
      "[[2 4]]\n",
      "\n",
      "Get values by ix_():\n",
      "a_ix = martix_a[ np.ix_([1,3],[2,4]) ]\n",
      "a_ix=>\n",
      "[[ 7  9]\n",
      " [17 19]]\n"
     ]
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   "source": [
    "##ix_()\n",
    "\n",
    "martix_a = np.arange(0, 25).reshape(5, 5)\n",
    "print('matrix_a=>\\n', martix_a)\n",
    "\n",
    "# ix_() will return a tuple what is composed by array [1,3] and array [2,4].\n",
    "# ix_() 會回傳一個由[1,3]和[2,4]兩個輸入值而組成的tuple.\n",
    "print()\n",
    "print('np.ix_([1,3],[2,4]))')\n",
    "print('ix_()=>\\n{0}'.format(np.ix_([1,3],[2,4])))\n",
    "\n",
    "# We can seperate the return value of ix_() as two different array.\n",
    "# 我們可以分別將ix_()的回傳值以兩個不同的陣列取出.\n",
    "print()\n",
    "print('Seperate the return value of ix_(): rows, cols = np.ix_([1,3],[2,4])')\n",
    "rows, cols = np.ix_([1,3],[2,4])\n",
    "print('rows=>\\n{0}\\ncols=>\\n{1}'.format(rows, cols))\n",
    "\n",
    "# The return value of ix_() can divide into two part:\n",
    "# The first part will is composed by the first input array,\n",
    "# and the first part will become a column vector.\n",
    "# The second part is composed by the second input array,\n",
    "# and it will become a row vector.\n",
    "# Therefor, we can use the return value of ix_() as an index set\n",
    "# to get values from a 2-dimension matrix directly.\n",
    "# ix_()的回傳值分為兩個部分：\n",
    "# 第一部分由第一個輸入陣列組成, 它會變成一個column vector. \n",
    "# 第二部分由第二個輸入陣列組成, 它會變成一個row vector. \n",
    "# 因此, 我們可以利用ix_()的回傳值形成一組索引集, 直接從一個二維陣列中取值.\n",
    "print()\n",
    "print('Get values by ix_():')\n",
    "print('a_ix = martix_a[ np.ix_([1,3],[2,4]) ]')\n",
    "a_ix = martix_a[np.ix_([1,3],[2,4])]\n",
    "print('a_ix=>\\n{0}'.format(a_ix))"
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      "x1=>\n",
      "[[1. 2.]\n",
      " [3. 4.]]\n",
      "x2=>\n",
      "[[5.]\n",
      " [6.]]\n",
      "\n",
      "x1 product x2=>\n",
      "[[17.]\n",
      " [39.]]\n",
      "\n",
      "x1 times x2=>\n",
      "[[ 5. 10.]\n",
      " [18. 24.]]\n",
      "\n",
      "transpose x1=>\n",
      "[[1. 3.]\n",
      " [2. 4.]]\n",
      "\n",
      "identify matrix I=>\n",
      "[[1. 0. 0.]\n",
      " [0. 1. 0.]\n",
      " [0. 0. 1.]]\n"
     ]
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   "source": [
    "##Linear Algebra\n",
    "x1 = np.array([[1, 2], [3, 4]], dtype=np.float32).reshape(2,2)\n",
    "x2 = np.array([5, 6], dtype=np.float32).reshape(2,1)\n",
    "print('x1=>\\n{0}\\nx2=>\\n{1}'.format(x1, x2))\n",
    "\n",
    "# matrix product\n",
    "# 矩陣相乘\n",
    "print()\n",
    "print('x1 product x2=>\\n{0}'.format(np.dot(x1, x2)))\n",
    "\n",
    "# element-by-element multiplication\n",
    "# 矩陣內元素相乘\n",
    "print()\n",
    "print('x1 times x2=>\\n{0}'.format(x1*x2))\n",
    "\n",
    "# transpose\n",
    "# 轉置矩陣\n",
    "print()\n",
    "print('transpose x1=>\\n{0}'.format(np.transpose(x1)))\n",
    "\n",
    "# identity matrix\n",
    "# 單位矩陣\n",
    "print()\n",
    "print('identify matrix I=>\\n{0}'.format(np.eye(3)))\n",
    "\n"
   ]
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     "text": [
      "col=>\n",
      "[[0]\n",
      " [1]\n",
      " [2]]\n",
      "\n",
      "repeat col for 5 times=>\n",
      "[[0 0 0 0 0]\n",
      " [1 1 1 1 1]\n",
      " [2 2 2 2 2]]\n",
      "\n",
      "repeat col like [2,4]=>\n",
      "[[0 0 0 0]\n",
      " [1 1 1 1]\n",
      " [2 2 2 2]\n",
      " [0 0 0 0]\n",
      " [1 1 1 1]\n",
      " [2 2 2 2]]\n",
      "\n",
      "hstack col=>\n",
      "[[0 0]\n",
      " [1 1]\n",
      " [2 2]]\n",
      "\n",
      "vstack col=>\n",
      "[[0]\n",
      " [1]\n",
      " [2]\n",
      " [0]\n",
      " [1]\n",
      " [2]]\n"
     ]
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   ],
   "source": [
    "##Repeat / Tile / hstack / vstack\n",
    "col = np.arange(0,3).reshape(3,1)\n",
    "print('col=>\\n{0}'.format(col))\n",
    "\n",
    "# Repeat col for 5 times along the 2nd axis.\n",
    "# 沿著第2軸，重製col 5次\n",
    "a = np.repeat(col, 5, axis=1)\n",
    "print()\n",
    "print('repeat col for 5 times=>\\n{0}'.format(a))\n",
    "\n",
    "# Repeat col 2 times along the direction of 1st dimension,\n",
    "# and repeat col 4 times along the direction of 2nd dimension.\n",
    "# 沿著第一個維度的方向重複col 2次, 沿著第二個維度的方向重複col 4次.\n",
    "a = np.tile(col, (2,4))\n",
    "print()\n",
    "print('repeat col like [2,4]=>\\n{0}'.format(a))\n",
    "\n",
    "# Stack col with horizontal line.\n",
    "# 將col沿著水平線堆疊.\n",
    "print()\n",
    "print('hstack col=>\\n{0}'.format(np.hstack([col, col])))\n",
    "\n",
    "# Stack col with vertical line.\n",
    "# 將col沿著垂直線堆疊.\n",
    "print()\n",
    "print('vstack col=>\\n{0}'.format(np.vstack([col, col])))"
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