Help for IBISLSQ4

PURPOSE

   "ibislsq4" performs least squares fits on data in an IBIS interface
(tabular) file.  The solutions and/or residuals can be placed in 
specified columns of the file.  The solutions can also be output
to the terminal.  Multiple fits can be done on different parts of
one file.


EXECUTION

    This program is significantly different internally from ibislsq,
ibislsq2, ibislsq3, and ibislsq9. It is designed only for simple
linear relations of the form:

                        y = mx + b

It computes the full statistical values for the relationship,
namely, the slope, the y-intercept, the std dev of slope, the std dev
of the intercept and the residuals from the measured y values and 
those from the fitted slope.

It currently doesn't utilize weights.

Like the other least squares routines it allows for a conrol column.

For example,

     ibislsq4 INP=DATA.INT  INDCOL=1 DEPCOL=4 CONCOL=7  	     RESCOL=8  SLOPECOL=21 YINTCOL=22 SSIGCOL=10 ISIGCOL=11 'NOPRINT

    This example shows the use of all of the parameters.  The input
file, DATA.INT, is an IBIS interface file having enough columns
to handle the output columns:
The data for the independent variable is in column 1.
The data for the dependent variable is in column 4.
The control column 7 is used for multiple fits to be done in one run.

    The least square fits are done on sets of rows; a new set is 
started whenever the value in the control column changes.  If no
control column is specified then one fit is done on the whole file.

    The SLOPECOL, YINTCOL and RESCOL parameters specify in which columns, 
of the input file, the results will be put.  If either or both are
not specified then they will not be output.
The residual column can be used to 
easily calculate the deviation of the data points from the fitted line.

    Normally the solution for each set is printed to the terminal,
is printed to the terminal, but this can be turned off with the
'NOPRINT keyword.  

    The length of each set should, of course, be longer than the
number of independent variables (columns).  If it is not then the
least squares fit will not be called and values of -999.0 will be
put out for the solution.  If some columns of the independent data
are dependent then the error MATRIX RANK TOO SMALL be be printed,
and -999.0's will be put out for the solution.  If there is no
solution then zeros will be put out for the residuals.



EXAMPLES

   Suppose that columns 1 and 2 contain points (x,y) in a plane 
   and  column  7 contains a function  f(x,y).   The  following 
   sequence  will perform a quadratic least squares fit  h(x,y) 
   and place the residuals in column 8.

ibis-gen xxA nc=9 nr=9 datacols=(1,2,3)      data=(1.0,7.63,1.0, 5.0,7.11,1.0, 10.0,6.34,1.0,     15.0,5.74,1.0, 20.0,5.11,1.0, 25.0,4.52,1.0,     30.0,3.86,1.0, 35.0,3.19,1.0, 40.0,2.55,1.0)
ibislsq4 xxA indcol=1 depcol=2 concol=3 slopecol=4 yintcol=5 rescol=6 ssigcol=7 isigcol=8
ibis-l xxA cform="%10.5f %10.5f %10.5f %10.5f %10.5f %10.5f %10.5f %10.5f %10.5f" screen=132

will produce

!Number of Rows:9  Number of Columns: 9       
!File Version:IBIS-2  Organization:COLUMN  SubType:NONE
! 
!Rows: 1:9
!+----------+----------+----------+----------+----------+----------+----------+----------+---------
!        C:1        C:2        C:3        C:4        C:5        C:6        C:7        C:8       C:9
!+----------+----------+----------+----------+----------+----------+----------+----------+---------
!   1.00000    7.63000    1.00000   -0.12923    7.71557    0.04366    0.00110    0.02607    0.00000
!   5.00000    7.11000    1.00000   -0.12923    7.71557    0.04057    0.00110    0.02607    0.00000
!  10.00000    6.34000    1.00000   -0.12923    7.71557   -0.08330    0.00110    0.02607    0.00000
!  15.00000    5.74000    1.00000   -0.12923    7.71557   -0.03716    0.00110    0.02607    0.00000
!  20.00000    5.11000    1.00000   -0.12923    7.71557   -0.02103    0.00110    0.02607    0.00000
!  25.00000    4.52000    1.00000   -0.12923    7.71557    0.03511    0.00110    0.02607    0.00000
!  30.00000    3.86000    1.00000   -0.12923    7.71557    0.02125    0.00110    0.02607    0.00000
!  35.00000    3.19000    1.00000   -0.12923    7.71557   -0.00262    0.00110    0.02607    0.00000
!  40.00000    2.55000    1.00000   -0.12923    7.71557    0.00352    0.00110    0.02607    0.00000



RESTRICTIONS

Used only for least squares fits to y=mx+b.

Therefore, the maximum number of independent columns (variables) is 1.

REVISION HISTORY

Original Programmer: R. J. Bambery, 22 Jun, 2010
Current Cognizant Programmer: R. J. Bambery

Built under 64-bit linux
    2012-07-02 - RJB - replaced cartlab's zifmessage with zvmessage
                    and removed cartoVicarProto.h to make compatible
                    with transfer to MIPL
    2022-07-27 B. Crocco afids to opensource (untested)

REFERENCE

John R. Taylor, "An Introduction to Error Analysis", 2nd Ed, University Science Books, 
Sausalito CA, 1997, Chapter 8, "Least Squares Fitting".

PARAMETERS: