Construct braids from complex array

[jeanluct]

In finishing the book I realized it would be easy/useful to allow

b = braid(Z)

where Z is a K x N array of complex numbers describing the orbit of N particles.

This is easy to implement, but there's one small catch. There's logic in the braid constructor to allow for

b = braid(XY)

when XY is K x 2. In that case a warning is issued (BRAIDLAB:braid:braid:onetraj), and a braid of 1 particle is created (identity), assuming the user means K x 2 x 1.

In Matlab there is no way to have a singleton dimension as the last dimension. So we would lose the ability to create a trivial braid of one strand, unless perhaps it is specified as a complex orbit?

[mbudisic]

Could the braid(Z) case be triggered by detecting the complex type (rather than the dimension)?

Alternatively, a fix could be to specify braid(Z) as accepting K x 1 x N (second dimension always singleton), but this may be an abomination.

[jeanluct]

Could the braid(Z) case be triggered by detecting the complex type (rather than the dimension)?

Yeah, I'm considering that but it is also unsatisfying, since real is reasonable.

Alternatively, a fix could be to specify braid(Z) as accepting K x 1 x N (second dimension always singleton), but this may be an abomination.

Nooooo!

It's such an edge case to create single-strand braids anyways. I'll try to maybe print a warning.

[jeanluct]

There might be a way out.

>> help isreal
 isreal True if input does not use complex storage.
    isreal(X) returns logical 1 (true) if X does not have an imaginary
    part, and logical 0 (false) otherwise. isreal returns logical 0 (false)
    for complex values that have zero imaginary part, since the value is
    still stored as a complex number.

    Some common related commands are:

    ~isreal(X) detects arrays that have an imaginary part, even if it is
    all zero.

    ~ANY(IMAG(X(:))) detects strictly real arrays, whether X has
    an all zero imaginary part allocated or not.

    Examples:
    1) x = magic(3);
       isreal(x)

       The result is true because x is not a complex array.

    2) y = complex(x);
       isreal(y)

       The result is false because COMPLEX returns y with an all zero
       imaginary part.

    See also real, imag, complex, i, j.

    Documentation for isreal
    Other functions named isreal

isreal returns false even if an array has 0 imaginary part, when it is created with complex.

So if a user really wants to create a single-strand braid with a complex trajectory of real numbers, they could do

>> z = [0 0]  % fixed strand
>> b = braid(complex(z))

ans = < e >

or at least that's the desired output.

[jeanluct]

Here's the example that I left as a comment in braid.m:

          %
          % Example:
          %
          % >> Z = [1 1 1 ; 2 2 2]'
          % >> braid(Z)
          %
          % will return the identity braid on one strand (and print warning).
          %
          % >> braid(complex(Z))
          %
          % will return the identity braid on two strands.
          %

[jeanluct]

Implemented in e58789b and iss151-braid-from-complex branch.