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lspoly

Calculates a set of coefficients for a weighted least squares polynomial fit to the given data.

Prototype

	function lspoly (
		x   [*] : numeric,  
		y   [*] : numeric,  
		wgt [*] : numeric,  
		n   [1] : integer   
	)

	return_val [n] :  float or double

Arguments

x

Abscissa values of the data.

y

Ordinate values of the data.

wgt

Weights for a weighted least squares model. If all data values are to be assigned equal weights, then setting the argument equal to a scalar 1.0 will result in all the weights being set to 1.0. Note: if x or y is equal to _FillValue (if present), the weight will be set to 0.0 for that coordinate pair.

n

The number of coefficients desired (i.e., n-1 will be the degree of the polynomial). Due to the method used, n should be less than or equal to five.

Return value

If either x or y are of type double, then the return array is returned as double. Otherwise, the returned coefficients are returned as type float.

Description

Given a set of data (x(i),y(i)), i = 1,...,m, lspoly calculates a set of coefficients for a weighted least squares polynomial fit to the given data. It is necessary that the number of data points) be greater than or equal to n (the number of coefficients).

Accuracy: for lower order polynomials (n .le. 5), lspoly can be expected to give satisfactory results.

Algorithm: lspoly forms the normal and solves the resulting square linear system using gaussian elimination with full pivoting.

See Also

regCoef, regline regcoef, reg_multlin

Examples

Example 1

  x = (/-4.5, -3.2, -1.4, 0.8, 2.5, 4.1/)
  y = (/ 0.7,  2.3,  3.8, 5.0, 5.5, 5.6/)

  n = 4
  c = lspoly(x,y, 1, n)    ; all weights are set to one 
  print(c)

The 3rd degree polynomial is

         Y = c(0) + c(1)*x + c(2)*x^2 + c(3)*x^3

The coefficients (which agree with those returned from Mathematica) are:

(0)      4.66863          
(1)      0.489392        
(2)     -0.0742387      
(3)      0.00267663