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lspoly_n

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

Available in version 6.2.0 and later.

Prototype

	function lspoly_n (
		x       : numeric,  
		y       : numeric,  
		wgt     : numeric,  
		n   [1] : integer,  
		dim [1] : integer   
	)

	return_val  :  float or double

Arguments

x

Abscissa values of the data.

This can be one-dimensional or multi-dimensional. If one-dimensional, it must be the same length as the rightmost dimension of y. If multi-dimensional, it must be the same dimensionality as y.

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.

This can be one-dimensional or multi-dimensional. If one-dimensional, it must be the same length as the rightmost dimension of y. If multi-dimensional, it must be the same dimensionality as y.

n

The number of coefficients desired (i.e., n-1 will be the degree of the polynomial). It is suggested that n be less than or equal to five.

dim

A scalar integer indicating which dimension of y to do the calculation on. Dimension numbering starts at 0.

Return value

The return array will have the same dimensionality as y, except the dim-th dimension will be of length n.

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_n calculates a set of coefficients for a weighted least squares polynomial fit to the given data on the given dimension. It is necessary that the number of data points) be greater than n (the number of coefficients).

Note: for NCL versions 6.4.0 and earlier, this function had a bug that caused this function to potentially return the wrong coefficients in cases where you had multiple leftmost dimensions. This has been fixed in NCL V6.5.0.

See Also

lspoly, regCoef, regline, regcoef, reg_multlin

Examples

Example 1

Note: we don't need to use lspoly_n in this example, since we are only using 1D arrays, and hence there's no reordering necessary.

  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_n(x, y, 1, n, 0)    ; 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    

Example 2

Similar as the previous example, but this time assume x and y are 3D arrays and that we want to solve the equation for the middle (dim=1) dimension:

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