Latin Squares Experimental Design Generator

latin_squares_experimental_design.ipynb

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      "source": "# Latin Square Experimental Design\n\nLatin squares have the property that every number appears before and after every other number and equal number of times. \n\n\nThis makes latin squares useful experimental designs.  They can provide a balanced and randomized trial sequence. \n\nI've given an example below.  \n\nThe goal of this notebook is to generate a set of pre-made latin squares for javascript experiments. It probably could have been programmed in JS, but I'm faster with python. \n\nI implemented the algorithm [described here](http://rintintin.colorado.edu/~chathach/balancedlatinsquares.html),\nwhich is an instantiation of \n\n\n> `Bradley, J. V. \n> Complete counterbalancing of immediate sequential effects in a Latin square design. \n> Journal of American Statistical Association, 1958, 53, 525-528.`\n\n\n### Note\nThis algorithm only works for even numbers.  Odd numbers require some extra trickiness"
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      "source": "generate_one(10)",
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([[ 1,  2, 10,  3,  9,  4,  8,  5,  7,  6],\n       [ 2,  3,  1,  4, 10,  5,  9,  6,  8,  7],\n       [ 3,  4,  2,  5,  1,  6, 10,  7,  9,  8],\n       [ 4,  5,  3,  6,  2,  7,  1,  8, 10,  9],\n       [ 5,  6,  4,  7,  3,  8,  2,  9,  1, 10],\n       [ 6,  7,  5,  8,  4,  9,  3, 10,  2,  1],\n       [ 7,  8,  6,  9,  5, 10,  4,  1,  3,  2],\n       [ 8,  9,  7, 10,  6,  1,  5,  2,  4,  3],\n       [ 9, 10,  8,  1,  7,  2,  6,  3,  5,  4],\n       [10,  1,  9,  2,  8,  3,  7,  4,  6,  5]], dtype=int32)"
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          "execution_count": 2
        }
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      "source": "print(base.format(\n                spacer.join([\n                    entry_template.format(i, make_matrix(generate_one(i))) for i in range(4,10,2)\n                ])\n            ))",
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": "\nvar latin_squares = {\n\n    \"4\": [[ 1,  2,  4,  3],\n           [ 2,  3,  1,  4],\n           [ 3,  4,  2,  1],\n           [ 4,  1,  3,  2]],\n           \n    \"6\": [[ 1,  2,  6,  3,  5,  4],\n           [ 2,  3,  1,  4,  6,  5],\n           [ 3,  4,  2,  5,  1,  6],\n           [ 4,  5,  3,  6,  2,  1],\n           [ 5,  6,  4,  1,  3,  2],\n           [ 6,  1,  5,  2,  4,  3]],\n           \n    \"8\": [[ 1,  2,  8,  3,  7,  4,  6,  5],\n           [ 2,  3,  1,  4,  8,  5,  7,  6],\n           [ 3,  4,  2,  5,  1,  6,  8,  7],\n           [ 4,  5,  3,  6,  2,  7,  1,  8],\n           [ 5,  6,  4,  7,  3,  8,  2,  1],\n           [ 6,  7,  5,  8,  4,  1,  3,  2],\n           [ 7,  8,  6,  1,  5,  2,  4,  3],\n           [ 8,  1,  7,  2,  6,  3,  5,  4]]\n}\n\n",
          "name": "stdout"
        }
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      "source": "import numpy as np\n\ndef generate_one(n):\n    out = np.empty((n,n)).astype(np.int32)\n    out[0, 0] = 1\n    forward = list(range(1, n, 2))\n    backward = sorted(set(range(1,n))-set(forward), reverse=True)\n    \n    for latin_number, index in enumerate(forward+backward, 2):\n        out[0, index] = latin_number\n    for column_index in range(n):\n        out[1:, column_index] = np.arange(out[0, column_index]+1, out[0, column_index] + n) % n\n    out[out==0] = n\n    return out\n\nbase = \"\"\"\nvar latin_squares = {{\n{}\n}}\n\"\"\"\n\nentry_template =     \"\"\"\n    \"{}\": {}\"\"\"\n\nspacer = \"\"\",\n           \"\"\"\n\nrow_template = \"[{}]\"\n\nmake_row = lambda row: row_template.format(\", \".join([\"{:>2}\".format(i) for i in row]))\nmake_matrix = lambda mat:\"[\"+spacer.join([make_row(mat[i]) \n                                          for i in range(mat.shape[0])])+\"]\"\n\nfilepath = \"latin_squares.js\"\nwith open(filepath, \"w\") as fp:\n    fp.write(base.format(\n                spacer.join([\n                    entry_template.format(i, make_matrix(generate_one(i))) for i in range(4,40,2)\n                ])\n            ))",
      "execution_count": 6,
      "outputs": []
    }
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        "description": "Latin Squares Experimental Design Generator",
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