Calculates a set of coefficients for a weighted least squares polynomial fit to the given data.
function lspoly ( x : numeric, y : numeric, wgt : numeric, n  : integer ) return_val : float or double
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.
This can be one-dimensional or multi-dimensional. If one-dimensional, it must be the same length as the rightmost dimension of x. If multi-dimensional, it must be the same dimensionality as x.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 computational method used, n should be less than or equal to five.
The return array will have the same dimensionality as y, except the rightmost 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.
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 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.
Note: In NCL versions 6.1.2 and earlier, this function would fail in certain cases where the input data were "scaled" down. We replaced this routine with a SLATEC version. It takes the same arguments, but uses a different algorithm under the hood. You can get the "old" (pre NCL V6.2.0) version of lspoly by using "lspoly_old", but we don't recommend it for regular use.
Use lspoly_n if you want to specify which dimension(s) to do the calculation across.
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^3The coefficients (which agree with those returned from Mathematica) are:
(0) 4.66863 (1) 0.489392 (2) -0.0742387 (3) 0.00267663