• vLinEqn
  • vLinFitBces
  • tclLinearFits

    ABSTRACT:
    
    Routines for linear fitting:

    Given a set of nVar arrays of independent variables and one array of dependent variables, this set of tools does the linear fit and displays the result.

    
    

    vLinEqn

     C ROUTINE CALLED:
     atVLinEqn in atLinearFits.c
    
     

    DESCRIPTION: Solve a set of linear equations: A X = B, where A is a matrix composed of one vector (column) for the coeffients of each independent variable, X is the vector of unknowns which are solved for, and B is a vector containing the values of the dependent variable.

    Each vector for an independent variable contains the constans for one of the unknowns, e.g., to solve the set of equations

           2x - 3y = -13
           3x + 2y = -13
     
    pass in two vectors: a1 = (2, 3) and a2 = (-3, 2), as well as the vector B = (-13, -13). The answer can be extracted from the FUNC structure which is returned. (See ..astrotools/test/testLinearFits.tcl or the SDSSMATH home page for how to do this.)
    TCL SYNTAX:
      vLinEqn  "<dep vector>" "<ind vectors>" 
    
    TCL HELP STRING:
      Solve a set of linear equations
    
    TCL ARGUMENTS:
                     : 
      "<dep vector>" : Vector with coefficients for dependent vector
      "<ind vectors>" : List of vectors with coefficients for each independent variable
    
    

    vLinFitBces

      BCES (Bivariate Correlated Errors and intrinsic Scatter) is a linear
      regression algorithm that allows for: 
      
      The routine performs four fits: y regressed on x, x regressed on y,
      the bisector, and orthogonal errors. Which answer is the "right" one
      depends on the situation. (A simplified guide would be: if you wish
      to predict a y given an x, use y regressed on x. If you wish to learn
      about the relationship of two quantities, use the bisector. See
      Feigelson and Babu, ApJ 397, 55 1992 for details.)
      

    The algorithm and the base fortran code are from Akritas and Bershady, ApJ 470, ? 1996.

    Also returned are the results of a bootstrap ananlysis.

    The "slopeErr" and "slopeErrBoot" lists have two extra elements on them. These are variences for the bisector and orthogonal slopes calculated using a technique of wider applicability than the usual one which assumes that the residuals in Y about a line are independant of the value of X; see Isobe, Feigelson, Akritas, and Babu, ApJ 364, 104 1990)

    The covarience vector may be all zeros.

    James Annis, June 14, 1996

    C ROUTINE CALLED: atBcesFit in atLinearFits.c

    TCL SYNTAX:
      vLinFitBces  "<X>" "<XErr>" "<Y>" "<YErr>" "<XYErr>" "-nsim" "-seed" 
    
    TCL HELP STRING:
      Perform BCES linear regression of Y onto X using YErr, XErr, and
    covaraience XYErr. Return fits for Y on X, X on Y, bisector, and orthogonal.
    
    TCL ARGUMENTS:
                     : 
      "<X>"        : vector containing x values
      "<XErr>"     : vector containing x error values
      "<Y>"        : vector containing y values
      "<YErr>"     : vector containing y error values
      "<XYErr>"    : vector containing xy covariance error values
      "-nsim"        : number of bootstrap simulations [100]
      "-seed"        : integer seed for random number generator [1]