subspace

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{
  "coordinateSystems": [
      {
          "name": "in",
          "axes": [
              { "name": "0", "type": "array" },
              { "name": "1", "type": "array" },
              { "name": "2", "type": "array" },
              { "name": "3", "type": "array" },
              { "name": "4", "type": "array" }
          ]
      },
      {
          "name": "out",
          "axes": [
              { "name": "x", "type": "space" },
              { "name": "y", "type": "space" },
              { "name": "z", "type": "space" }
          ]
      }
  ],
  "coordinateTransformations": [
    {
      "type": "byDimension",
      "name": "5D-to-3D-not-contiguous",
      "input": "in",
      "output": "out",
      "transformations": [
        {
          "type": "mapAxis",
          "mapAxis": { "0": "x", "2": "z" },
          "input": [ "0", "2" ],
          "output": [ "x", "z" ]
        },
        {
          "type": "scale",
          "scale": [ 2 ],
          "input": [ "1" ],
          "output": [ "y" ]
        }
      ]
    }
  ]
}

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{
    "coordinateSystems" : [
        { "name" : "in", "axes" : [ {"name" : "i"}, {"name" : "j" } ]},
        { "name" : "out", "axes" : [ {"name" : "x"}, {"name" : "y" } ]}
    ],
    "coordinateTransformations" : [
        { 
            "type" : "byDimension",
            "input" : "in",
            "output" : "out",
            "transformations" : [
                {
                    "type": "identity",
                    "input" : ["j"],
                    "output" : ["x"]
                },
                {
                    "type": "scale",
                    "scale" : [2],
                    "input" : ["i"],
                    "output" : ["y"]
                }
            ]
        }
    ]
}