DADiSP Worksheet Functions > Function Categories > Curve Fitting > POLYFIT
Performs a Least Squares Polynomial fit.
POLYFIT(y, x, order, overwrite, form, method, "specfile")
y |
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A series or table. |
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x |
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Optional. A series or table, the explicit X values. Defaults to the X values of y. |
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order |
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An integer, the order of the polynomial fit. |
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overwrite |
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Optional. An integer, the overwrite flag for existing "specfile": |
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form |
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Optional. An integer, the polynomial coefficient form: |
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method |
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Optional. An integer, the least squares fitting method: |
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"specfile" |
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Optional. A string, the name of summary statistics file. Defaults to "polyN.fit". |
A series of coefficients.
W1: gline(100,.01,1.0,1.0)^2
W2: polyfit(W1, 3)
returns a 4 point series with values {1.0, 2.0, 1.0, 5.89E-14} as the resulting 3rd order coefficients, a[1], a[2], a[3], a[4].
W3: polygraph(W2, xvals(W1))
graphs the fit.
POLYFIT also works with XY data. For example:
W1: xy(gexp(100, 0.01), gsin(100, 0.01))
W2: polyfit(W1, 5)
W3: polyfit(W1, xvals(W1), 5)
W4: polygraph(W2, xvals(W1), 1)
W2 and W3 produce the same coefficients. The last parameter of 1 in the POLYGRAPH function creates an explicit XY graph.
polyfit(series, N) performs a least squares fit of a series to
where y is the input series and N is the order of the fit.
POLYFIT returns the coefficients, a[k], of the above power series.
If form is 1 then:
The default QR decomposition method (method = 0) is slower, but more accurate than the Gauss-Jordan elimination method and is preferred for high order fits. However, Gauss-Jordan may be preferred for low order fits where speed is an important factor.
For a tabular view of the coefficients, use the TABLEVIEW function in the Window containing the results of the POLYFIT operation.
See PFIT to fit a polynomial with error statistics.
See LINFIT to fit linear combination of arbitrary basis functions to a series using the method of least squares.
See POLYGRAPH or POLYVAL to evaluate the resulting polynomial.
See DADiSP/MatrixXL to significantly optimize POLYFIT for the QR method.