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# Abundance maps functions

## FCLS

`abundance_maps.amaps.``FCLS`(M, U)

  Performs fully constrained least squares of each pixel in M using the endmember signatures of U. Fully constrained least squares is least squares with the abundance sum-to-one constraint (ASC) and the abundance nonnegative constraint (ANC).

  Parameters:
    M: numpy array
      2D data matrix (N x p).
    U: numpy array
      2D matrix of endmembers (q x p).
  Returns: numpy array
    An abundance maps (N x q).
  References:
    Daniel Heinz, Chein-I Chang, and Mark L.G. Fully Constrained Least-Squares Based Linear Unmixing. Althouse. IEEE. 1999.
  Notes:
    Three sources were useful to build the algorithm:
      - The function hyperFclsMatlab, part of the Matlab Hyperspectral Toolbox of Isaac Gerg.
      - The Matlab (tm) help on lsqlin.
      - And the Python implementation of lsqlin by Valera Vishnevskiy, click: http://maggotroot.blogspot.ca/2013/11/constrained-linear-least-squares-in.html , it’s great code.

## NNLS

`abundance_maps.amaps.``NNLS`(M, U)

  NNLS performs non-negative constrained least squares of each pixel in M using the endmember signatures of U. Non-negative constrained least squares with the abundance nonnegative constraint (ANC). Utilizes the method of Bro.

  Parameters:
    M: numpy array
      2D data matrix (N x p).
    U: numpy array
      2D matrix of endmembers (q x p).
  Returns: numpy array
    An abundance maps (N x q).
  References:
    Bro R., de Jong S., Journal of Chemometrics, 1997, 11, 393-401.

## UCLS

`abundance_maps.amaps.``UCLS`(M, U)

  Performs unconstrained least squares abundance estimation.

  Parameters:
    M: numpy array
      2D data matrix (N x p).
    U: numpy array
      2D matrix of endmembers (q x p).
  Returns: numpy array
    An abundance maps (N x q).

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