MYSVDFIT
Name
mysvdfit
Purpose
Perform a general least squares fit with optional error estimates.
Description
This version uses SVD. A user-supplied function or a built-in
polynomial is fit to the data.
Category
Function fitting
Calling Sequence
Result = SVDFIT(X, Y, M)
Inputs
X: A vector representing the independent variable. If this an array,
the columns are taken to be the precomputed independant vectors
and no actual function is computed here.
Y: Dependent variable vector. This vector should be same length
as X.
M: The number of coefficients in the fitting function. For
polynomials, M is equal to the degree of the polynomial + 1.
Optional Inputs
Weight: A vector of weights for Y(i). This vector should be the same
length as X and Y.
If this parameter is ommitted, 1 is assumed. The error for
each term is weighted by Weight(i) when computing the fit.
Frequently, Weight(i) = 1./Sigma(i) where Sigma is the
measurement error or standard deviation of Y(i).
Funct: A string that contains the name of an optional user-supplied
basis function with M coefficients. If omitted, polynomials
are used.
The function is called:
R = FUNCT(X,M)
where X is an N element vector, and the function value is an
(N, M) array of the N inputs, evaluated with the M basis
functions. M is analogous to the degree of the polynomial +1
if the basis function is polynomials. For example, see the
function COSINES, in the IDL User Library, which returns a
basis function of:
R(i,j) = cos(j*x(i)).
For more examples, see Numerical Recipes, page 519.
The basis function for polynomials, is R(i,j) = x(i)^j.
Outputs
SVDFIT returns a vector of M coefficients.
Optional Output Parameters
NOTE: In order for an optional keyword output parameter
to be returned, it must be defined before calling SVDFIT.
The value or structure doesn't matter. For example:
YF = 1 ;Define output variable yf.
C = SVDFIT(X, Y, M, YFIT = YF) ;Do SVD, fitted Y vector is now
;returned in variable YF.
YFIT: Vector of calculated Y's.
CHISQ: Sum of squared errors multiplied by weights if weights
are specified.
COVAR: Covariance matrix of the coefficients.
VARIANCE: Sigma squared in estimate of each coeff(M).
SINGULAR: The number of singular values returned. This value should
be 0. If not, the basis functions do not accurately
characterize the data.
Common Blocks
None.
Side Effects
None.
Modification History
Adapted from SVDFIT, from the book Numerical Recipes, Press,
et. al., Page 518.
minor error corrected April, 1992 (J.Murthy)
93/10/12, Marc W. Buie, Lowell Observatory. Added option to make this
work similar to "regress".
97/03/20, MWB, Changed to use SVDC and SVSOL and everything is now in
double precision.
2005/02/02, MWB, Changed thresh from 10^-9 to 2x10^-12
2005/06/21, MWB, added error trap keyword
2009/07/14, MWB, fixed a bug in the original covar calculation
2013/09/14, AMZ, fixed a bug for using default polynomials.