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Function Synopsis

[recon, rsv, ru, rs, rv, rb] = aorecon(mvtos, nsingin, remtiltin, nsubin)

Help text

 Usage: [recon, rsv] = aorecon(slpif, nsing, {remtilt})
     or rsv = aorecon(slpif)
 Description: Compute a least-squares reconstructor from a slope influence
    matrix. The reconstructor can include tilt or project tilt out and can
    have a user-specified number of singular values removed.
 Input Parameters:
    slpif: The 2*nsub x nact slope influence function matrix. nsub is the 
       number of subapertures and nact is the number of (master) actuators.
       The rows must be arranged such that nsub x-slopes are followed by
       nsub y-slopes.
    nsing: The number of singular values to be removed. When not specified
       this routine does not compute the reconstructor. Rather it returns
       a vector containing the singular values for the purpose of deciding
       how many to remove on a subsequent call to this routine.
    remtilt: A flag which when non-zero indicates that tilt is to be
       projected out. If not specified, tilt is projected out. To obtain a
       tilt-included reconstructor, specify zero for this argument.
 Output Parameters:
    recon: The reconstructor dimensioned the same as the transpose of slpif.
    rsv: A vector containing the singular values of slpif.
    The typical process for creating a reconstructor is:
    1. Run AOGeom to specify the adaptive optics geometry.
    2. Run AOInf to create the influence functions.
    3. Load the resulting file into a clean Matlab workspace.
    4. Execute rsv=aorecon(mvtos)
    5. Inspect rsv. Usually there is a clear breakpoint where the lowest
       few singular values are much less than all the others. It is often good
       to project these out. Determine the number to be suppressed and set the 
       variable ns to it.
    6. Execute recon=aorecon(mvtos,ns) to create the tilt-removed reconstructor.
    7. Execute reconti=aorecon(mvtos,ns,0) to create the tilt-included
    8. Save the workspace. The file can be used as input to WaveTrain (usually
       as an argument to a TasatDMModel constructor).

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