DIRECTORY IO, Histograms, LinearSystem;HistogramsOut: CEDAR DEFINITIONS = {OPEN Histograms;Stats1D: PROC [h: Histogram] RETURNS [sum0: INT, sum1, sum2, avg, stdDev: REAL, range: RealRange1];Stats2D: PROC [h: Histogram, degree: NATURAL, log: BoolPair] RETURNS [sums: Sums2D, range: RealRange2];Sums2D: TYPE ~ RECORD [degree: NATURAL _ 0,exception: BOOL _ FALSE,Sy2: REAL _ 0.0,Sxky: ColumnN _ NIL,Sxkl: MatrixN _ NIL];RowN: TYPE ~ LinearSystem.RowN;ColumnN: TYPE ~ LinearSystem.ColumnN;MatrixN: TYPE ~ LinearSystem.MatrixN;Analyze: PROC [sums: Sums2D] RETURNS [ak: ColumnN _ NIL, s, r: REAL _ 0.0];EvalError: PROC [sums: Sums2D, ak: ColumnN] RETURNS [s, r: REAL _ 0.0];WriteTo: PROC [h: Histogram, to: IO.STREAM, create, data: BOOL];}.   T  HistogramsOut.MesaCopyright c 1985 by Xerox Corporation.  All rights reserved.Last tweaked by Mike Spreitzer on June 28, 1988 3:36:10 pm PDTAn interface for getting information out of Histograms.Consider the histogram a set of <x, n> pairs, each saying that there are n counts in the bin centered on x.sum0 = S nsum1 = S n*xsum2 = S n*x2avg = sum1/sum0stdDev = SqRt[( S n*(x - avg)2 ) / ((Sn) - 1)]range.min = least x with non-zero nrange.max = greatest x with non-zero nrange.min>range.max W sum0=0Returns the sums necessary to compute a least-squares fit of the given degree.  The log argument tells whether to sum the <x,y> or their natural logarithms.If exception, there's been a floating-point exception, and the other fields are worthless.Do a least-squares fit of the sums.  The coefficients are in ak, error is s, and linear correlation is r.  If there's a floating-point exception, ak will be NIL.  s non-zero only if the number of samples exceeds the degree.  In certain degenerate cases, r will not be evaluated, and left 0.Writes descriptions of the create and/or the data.Ê/  ˜ codešœ™Kšœ
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