05.3.4 Matrix-matrix multiplication via rank-1 updates.ipynb

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      "Matrix-matrix multiplication via rank-1 updates"
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     "source": [
      "We continue to look at how the FLAMEPy API can be used to implement different matrix-matrix multiplication algorithms.  "
     ]
    },
    {
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     "source": [
      "First, we create some matrices."
     ]
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     "input": [
      "import numpy as np\n",
      "\n",
      "m = 4\n",
      "n = 3\n",
      "k = 5\n",
      "\n",
      "C = np.matrix( np.random.random( (m, n) ) )\n",
      "print( 'C = ' )\n",
      "print( C )\n",
      "\n",
      "Cold = np.matrix( np.zeros( (m,n ) ) )\n",
      "Cold = np.matrix( np.copy( C ) )           # an alternative way of doing a \"hard\" copy, in this case of a matrix\n",
      "    \n",
      "A = np.matrix( np.random.random( (m, k) ) )\n",
      "print( 'A = ' )\n",
      "print( A )\n",
      "\n",
      "B = np.matrix( np.random.random( (k, n) ) )\n",
      "print( 'B = ' )\n",
      "print( B )"
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      "<h2>The algorithm  </h2>\n",
      "\n",
      "<image src=\"https://studio.edx.org/c4x/UTAustinX/UT.5.01x/asset/Gemm_nn_unb_var3.png\" alt=\"Matrix-matrix multiplication via rank-1 updates picture\" width=\"80%\">\n"
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      "<h2> The routine <code> Gemm_nn_unb_var3( A, B, C ) </code> </h2>\n",
      "\n",
      "This routine computes $ C := A B + C $ via rank-1 updates.  The \"\\_nn\\_\" means that this is the \"No transpose, No transpose\" case of matrix multiplication.  \n",
      "The reason for this is that the operations $ C := A^T B + C $ (\"\\_tn\\_\" or \"Transpose, No transpose\"), $ C := A B^T + C $ (\"\\_nt\\_\" or \"No transpose, Transpose\"), and $ C := A^T B^T + C $ (\"\\_tt\\_\" or \"Transpose, Transpose\") are also encountered.  \n",
      "    \n",
      "The specific laff function we will use is\n",
      "<ul>\n",
      "<li> <code> laff.ger( alpha, x, y, A ) </code> which computes the rank-1 update (adds a multiple of an outer product to a matrix)\n",
      "$ A := \\alpha x y^T + A $. \n",
      "    </li>\n",
      "</ul>\n",
      "\n",
      "Use the <a href=\"https://studio.edx.org/c4x/UTAustinX/UT.5.01x/asset/index.html\"> Spark webpage</a> to generate a code skeleton.  (Make sure you adjust the name of the routine.)"
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      "C = np.matrix( np.copy( Cold ) )               # restore C \n",
      "\n",
      "Gemm_nn_unb_var3( A, B, C )\n",
      "\n",
      "print( 'C - ( Cold + A * B )' )\n",
      "print( C - ( Cold + A * B ) )"
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     "source": [
      "Bingo! It works!"
     ]
    },
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     "level": 2,
     "metadata": {},
     "source": [
      "Watch the algorithm at work!"
     ]
    },
    {
     "cell_type": "markdown",
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     "source": [
      "Copy and paste the code into <a href=\"http://edx-org-utaustinx.s3.amazonaws.com/UT501x/PictureFlame/PictureFLAME.html\"> PictureFLAME </a>, a webpage where you can watch your routine in action.  Just cut and paste into the box.  \n",
      "\n",
      "Disclaimer: we implemented a VERY simple interpreter.  If you do something wrong, we cannot guarantee the results.  But if you do it right, you are in for a treat.\n",
      "\n",
      "If you want to reset the problem, just click in the box into which you pasted the code and hit \"next\" again."
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