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Clear["Global`*"]

Rx[\[Phi]_] := MatrixExp[-I \[Phi] {{0, 0, 0}, {0, 0, -I}, {0, I, 0}}]

Ry[\[Phi]_] := MatrixExp[-I \[Phi] {{0, 0, I}, {0, 0, 0}, {-I, 0, 0}}]

Rz[\[Phi]_] := MatrixExp[-I \[Phi] {{0, -I, 0}, {I, 0, 0}, {0, 0, 0}}]

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git config --global alias.lg "log --graph --pretty=format:'%Cred%h%Creset -%C(yellow)%d%Creset %s %Cgreen(%cr) %C(bold blue)<%an>%Creset'"

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function meshgrid(xArray, yArray, zArray) {
    /*
     Here xArray, yArray, zArray should all be 1d arrays.
     Then it returns 3 fortran-style 3D arrays, that is,
     they are all column-major order:
     http://www.wikiwand.com/en/Row-_and_column-major_order.
     The returned xMesh, yMesh, and zMesh are all of shape
     [zNum, xNum, yNum].
     */
    let xNum = xArray.size;

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function flatten(arr) {
    return arr.reduce(function (flat, toFlatten) {
        return flat.concat(Array.isArray(toFlatten) ? flatten(toFlatten) : toFlatten);
    }, []);
}

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function reshape(oldNdarr, newShape) {
    /*
     Here oldNdarray is a ndarray, newShape is an array spcifying the newer one's shape.
     */
    return ndarray(oldNdarr.data, newShape);
}

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function meshgrid(xArray, yArray) {
    /*
     Here xArray, yArray should all be 1d arrays.
     Then it returns 2 fortran-style 2D arrays, that is,
     they are all column-major order:
     http://www.wikiwand.com/en/Row-_and_column-major_order.
     The returned xMesh and yMesh are all of shape [xNum, yNum].
     */
    let xNum = xArray.size;
    let yNum = yArray.size;

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-- from [StackOverflow](https://stackoverflow.com/questions/4597820/does-haskell-have-list-slices-i-e-python)
takeStep :: Int -> [a] -> [a]
takeStep _ [] = []
takeStep n (x:xs) = x : takeStep n (drop (n-1) xs)

slice :: Int -> Int -> Int -> [a] -> [a]
slice start stop step = takeStep step . take (stop - start) . drop start

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function linspace(shape, start, end, options) {
    /*
     If we use ndarray-linspace package,
     it returns a ndarray with dtype='array',
     but this dtype cannot be used by ndarray-tile package, it needs 'float'.
     So we need to transform dtype manually.
     */
    let tmp = linspace(ndarray([], shape), start, end, options);
    return reshape(ndarray(new Float64Array(tmp.data)), shape);
}

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fib[n_] := Which[n == 0, 0, n == 1, 1, n > 1, fib[n - 1] + fib[n - 2]]

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def iter_islast(iterable):
    """
    iter_islast(iterable) -> generates (item, islast) pairs

    Generates pairs where the first element is an item from the iterable
    source and the second element is a boolean flag indicating if it is
    the last item in the sequence.

    Referenced from
    `here <http://code.activestate.com/recipes/392015-finding-the-last-item-in-a-loop/>`_.