LinearFitBySvd (FsODE)

FsODE

Documentation for 0.0.2

LinearFitBySvd Type

Namespace: Altaxo.Calc.Regression
Assembly: AltaxoCore.Redist.dll
Base Type: obj

Performs a linear fit to a given function base using singular value decomposition.

Constructors

Constructor	Description
`LinearFitBySvd(xarr, yarr, stddev, numberOfData, numberOfParameter, evaluateFunctionBase, threshold)` Full Usage: `LinearFitBySvd(xarr, yarr, stddev, numberOfData, numberOfParameter, evaluateFunctionBase, threshold)` Parameters: xarr : `float[]` - The array of x values of the data set. yarr : `float[]` - The array of y values of the data set. stddev : `float[]` - The array of y standard deviations of the data set. Can be null if the standard deviation is unkown. numberOfData : `int` - The number of data points (may be smaller than the array sizes of the data arrays). numberOfParameter : `int` - The number of parameters to fit == size of the function base. evaluateFunctionBase : `FunctionBaseEvaluator` - The function base used to fit. threshold : `float` - A treshold value (usually 1E-5) used to chop the unimportant singular values away.	Fits a data set linear to a given function base. xarr : `float[]` The array of x values of the data set. yarr : `float[]` The array of y values of the data set. stddev : `float[]` The array of y standard deviations of the data set. Can be null if the standard deviation is unkown. numberOfData : `int` The number of data points (may be smaller than the array sizes of the data arrays). numberOfParameter : `int` The number of parameters to fit == size of the function base. evaluateFunctionBase : `FunctionBaseEvaluator` The function base used to fit. threshold : `float` A treshold value (usually 1E-5) used to chop the unimportant singular values away.
`LinearFitBySvd(xarr, yarr, stddev, numberOfData, numberOfParameter, evaluateFunctionBase, threshold)` Full Usage: `LinearFitBySvd(xarr, yarr, stddev, numberOfData, numberOfParameter, evaluateFunctionBase, threshold)` Parameters: xarr : `IReadOnlyList<float>` - The array of x values of the data set. yarr : `IReadOnlyList<float>` - The array of y values of the data set. stddev : `IReadOnlyList<float>` - The array of y standard deviations of the data set. Can be null if the standard deviation is unkown. numberOfData : `int` - The number of data points (may be smaller than the array sizes of the data arrays). numberOfParameter : `int` - The number of parameters to fit == size of the function base. evaluateFunctionBase : `FunctionBaseEvaluator` - The function base used to fit. threshold : `float` - A treshold value (usually 1E-5) used to chop the unimportant singular values away.	Fits a data set linear to a given function base. xarr : `IReadOnlyList<float>` The array of x values of the data set. yarr : `IReadOnlyList<float>` The array of y values of the data set. stddev : `IReadOnlyList<float>` The array of y standard deviations of the data set. Can be null if the standard deviation is unkown. numberOfData : `int` The number of data points (may be smaller than the array sizes of the data arrays). numberOfParameter : `int` The number of parameters to fit == size of the function base. evaluateFunctionBase : `FunctionBaseEvaluator` The function base used to fit. threshold : `float` A treshold value (usually 1E-5) used to chop the unimportant singular values away.
`LinearFitBySvd(xbase, yarr, stddev, numberOfData, numberOfParameter, threshold)` Full Usage: `LinearFitBySvd(xbase, yarr, stddev, numberOfData, numberOfParameter, threshold)` Parameters: xbase : `IROMatrix<float>` - The matrix of x values of the data set. Dimensions: numberOfData x numberOfParameters. The matrix is changed during calculation! yarr : `float[]` - The array of y values of the data set. stddev : `float[]` - The array of y standard deviations of the data set. Can be null if the standard deviation is unkown. numberOfData : `int` - The number of data points (may be smaller than the array sizes of the data arrays). numberOfParameter : `int` - The number of parameters to fit == size of the function base. threshold : `float` - A treshold value (usually 1E-5) used to chop the unimportant singular values away.	Fits a data set linear to a given x base. xbase : `IROMatrix<float>` The matrix of x values of the data set. Dimensions: numberOfData x numberOfParameters. The matrix is changed during calculation! yarr : `float[]` The array of y values of the data set. stddev : `float[]` The array of y standard deviations of the data set. Can be null if the standard deviation is unkown. numberOfData : `int` The number of data points (may be smaller than the array sizes of the data arrays). numberOfParameter : `int` The number of parameters to fit == size of the function base. threshold : `float` A treshold value (usually 1E-5) used to chop the unimportant singular values away.

Instance members

Instance member	Description
`this.AdjustedRSquared` Full Usage: `this.AdjustedRSquared` Returns: `float`	Gives the adjusted coefficient of determination. Ref. "Introduction to linear regression analysis", Wiley, p.90. Returns: `float`
`this.Calculate` Full Usage: `this.Calculate` Parameters: xbase : `IROMatrix<float>` - The matrix of x values of the data set. Dimensions: numberOfData x numberOfParameters. The matrix is changed during calculation! yarr : `IReadOnlyList<float>` - The array of y values of the data set. stddev : `IReadOnlyList<float>` - The array of y standard deviations of the data set. Can be null if the standard deviation is unkown. numberOfData : `int` - The number of data points (may be smaller than the array sizes of the data arrays). numberOfParameter : `int` - The number of parameters to fit == size of the function base. threshold : `float` - A treshold value (usually 1E-5) used to chop the unimportant singular values away. Returns: `LinearFitBySvd`	Fits a data set linear to a given x base. xbase : `IROMatrix<float>` The matrix of x values of the data set. Dimensions: numberOfData x numberOfParameters. The matrix is changed during calculation! yarr : `IReadOnlyList<float>` The array of y values of the data set. stddev : `IReadOnlyList<float>` The array of y standard deviations of the data set. Can be null if the standard deviation is unkown. numberOfData : `int` The number of data points (may be smaller than the array sizes of the data arrays). numberOfParameter : `int` The number of parameters to fit == size of the function base. threshold : `float` A treshold value (usually 1E-5) used to chop the unimportant singular values away. Returns: `LinearFitBySvd`
`this.ConditionNumber` Full Usage: `this.ConditionNumber` Returns: `float`	Gets the condition number. The decadic logarithm of the condition number is roughly the loss of precision (in digits) during the calculation. Returns: `float`
`this.Covariances` Full Usage: `this.Covariances` Returns: `float[][]`	Get the variance-covariance-matrix for the fit. Returns: `float[][]`
`this.EstimatedVariance` Full Usage: `this.EstimatedVariance` Returns: `float`	Get the estimated residual mean square, also called SigmaSquare.. The estimated mean square is defined as SumChiSquare(n-p), where n is the number of data points and p is the number of (free) parameters. Returns: `float`
`this.ExternallyStudentizedResidual` Full Usage: `this.ExternallyStudentizedResidual` Parameters: i : `int` - The index to the residual. Returns: `float` The ith externally studentized residual.	Gives the ith studentized residual, with the ith observation removed from the model. As with the studentized residual, the expected variance of this residual is 1. Since the ith observation is excluded from the model, the externally studentized residual is better suited for outlier detection than the (normal) studentized residual. Ref: Introduction to linear regression analysis, 3rd ed., Wiley, p.136 i : `int` The index to the residual. Returns: `float` The ith externally studentized residual.
`this.NumberOfData` Full Usage: `this.NumberOfData` Returns: `int`	Returns the number of data value. Returns: `int`
`this.NumberOfParameter` Full Usage: `this.NumberOfParameter` Returns: `int`	Returns the number of parameter (=Order+1) of the fit. Returns: `int`
`this.PRESSResidual` Full Usage: `this.PRESSResidual` Parameters: i : `int` - The index of the PRESS residual. Returns: `float` The ith PRESS residual.	Gives the ith PRESS residual. The PRESS residual is the prediction error of the ith value, if the ith value itself is not used in the prediction model. Ref: Introduction to linear regression analysis, 3rd ed., Wiley, p.135 i : `int` The index of the PRESS residual. Returns: `float` The ith PRESS residual.
`this.Parameter` Full Usage: `this.Parameter` Returns: `float[]`	Get the resulting parameters, so that the model y = SUM(parameter[i]*functionbase[i]) Returns: `float[]`
`this.PredictedValues` Full Usage: `this.PredictedValues` Returns: `float[]`	Gets the predicted dependent values Returns: `float[]`
`this.PredictionVariance` Full Usage: `this.PredictionVariance` Parameters: i : `int` - The index to the ith observation. Returns: `float` The variance of the ith prediction value.	Gives the variance of the prediction of the ith y-value. i : `int` The index to the ith observation. Returns: `float` The variance of the ith prediction value.
`this.RSquared` Full Usage: `this.RSquared` Returns: `float`	Gives the coefficient of determination, also called R^2, squared correlation coefficient. It is a measure, how much of the variability of the y data is accounted for by the regression model. Returns: `float`
`this.RegressionCorrectedSumOfSquares` Full Usage: `this.RegressionCorrectedSumOfSquares` Returns: `float`	Gets the regression sum of squares, i.e. SUM(yi`-ymean), where yi` is the predicted ith y value and y mean is the mean value of all y values. Returns: `float`
`this.ResidualSumOfSquares` Full Usage: `this.ResidualSumOfSquares` Returns: `float`	Gets the sum of ChiSquare for the fit. This is SUM(yi-yi`)^2, where yi is the ith y value and yi` is the ith predicted y. Returns: `float`
`this.ResidualValues` Full Usage: `this.ResidualValues` Returns: `float[]`	Gets the array of residual values defined as the difference y[i]-ypredicted[i]. Returns: `float[]`
`this.Sigma` Full Usage: `this.Sigma` Returns: `float`	Get the standard error of regression, defined as `Sqrt(SigmaSquare)`. Returns: `float`
`this.StandardErrorOfParameter` Full Usage: `this.StandardErrorOfParameter` Parameters: i : `int` - Index of the parameter. Returns: `float` The estimated standard error of parameter `i`.	Gets the estimated standard error of parameter `i`. i : `int` Index of the parameter. Returns: `float` The estimated standard error of parameter `i`.
`this.StudentizedResidual` Full Usage: `this.StudentizedResidual` Parameters: i : `int` - The index of the residual. Returns: `float` The ith studentized residual.	Gives the ith studentized residual. The studentized residual has constant variance of 1, regardless of the location of xi. Ref: Introduction to linear regression analysis, 3rd ed., Wiley, p.134 i : `int` The index of the residual. Returns: `float` The ith studentized residual.
`this.TofParameter` Full Usage: `this.TofParameter` Parameters: i : `int` Returns: `float`	i : `int` Returns: `float`
`this.TotalCorrectedSumOfSquares` Full Usage: `this.TotalCorrectedSumOfSquares` Returns: `float`	Gives the corrected sum of squares of y, i.e. SUM(yi-ymean), where yi is the ith y value and ymean is the mean of all y values. Returns: `float`

Static members

Static member	Description
`LinearFitBySvd.CorrectedSumOfSquares(x, mean, start, length)` Full Usage: `LinearFitBySvd.CorrectedSumOfSquares(x, mean, start, length)` Parameters: x : `IReadOnlyList<float>` - Array of values. mean : `float` - Mean value of the values. start : `int` - Starting index. length : `int` - Number of elements used for calculation. Returns: `float`	Calculates the corrected sum of squares of `length` elements of array x starting from index `start`. The corrected sum of squares is defined as sum of squares of the elements minus their mean value. x : `IReadOnlyList<float>` Array of values. mean : `float` Mean value of the values. start : `int` Starting index. length : `int` Number of elements used for calculation. Returns: `float`
`LinearFitBySvd.FitPolymomial(order, xValues, yValues, start, count, doRemoveNaNValues)` Full Usage: `LinearFitBySvd.FitPolymomial(order, xValues, yValues, start, count, doRemoveNaNValues)` Parameters: order : `int` - The order of the fit (1:linear, 2:quadratic, etc.) xValues : `IReadOnlyList<float>` - The column of x-values. Only those values are used, that are not NaN yValues : `IReadOnlyList<float>` - The column of y-values. start : `int` - Index of first data point to use. count : `int` - Number of data points to use. doRemoveNaNValues : `bool` - If true, value pairs containing NaN are removed before calculation of the fit. Returns: `LinearFitBySvd` The fit.	Fits data provided as xcolumn and ycolumn with a polynomial base. Here special measures are taken (scaling of the x-variable) in order to keep the precision high. order : `int` The order of the fit (1:linear, 2:quadratic, etc.) xValues : `IReadOnlyList<float>` The column of x-values. Only those values are used, that are not NaN yValues : `IReadOnlyList<float>` The column of y-values. start : `int` Index of first data point to use. count : `int` Number of data points to use. doRemoveNaNValues : `bool` If true, value pairs containing NaN are removed before calculation of the fit. Returns: `LinearFitBySvd` The fit.
`LinearFitBySvd.FitPolymomialDestructive(order, xValues, yValues, errorValues, count)` Full Usage: `LinearFitBySvd.FitPolymomialDestructive(order, xValues, yValues, errorValues, count)` Parameters: order : `int` - The order of the fit (1:linear, 2:quadratic, etc.) xValues : `float[]` - The array of x-values. The values of the array are destroyed (altered) during the evaluation! yValues : `float[]` - The array of y-values. errorValues : `float[]` - The column of errorValues. If null, errorValues are set to 1 for each element. count : `int` - Number of values to use (array[0] ... array[count-1]. Returns: `LinearFitBySvd` The fit.	Fits data provided as xcolumn and ycolumn with a polynomial base. Here special measures are taken (scaling of the x-variable) in order to keep the precision high. order : `int` The order of the fit (1:linear, 2:quadratic, etc.) xValues : `float[]` The array of x-values. The values of the array are destroyed (altered) during the evaluation! yValues : `float[]` The array of y-values. errorValues : `float[]` The column of errorValues. If null, errorValues are set to 1 for each element. count : `int` Number of values to use (array[0] ... array[count-1]. Returns: `LinearFitBySvd` The fit.
`LinearFitBySvd.GetPolynomialFunctionBase(order)` Full Usage: `LinearFitBySvd.GetPolynomialFunctionBase(order)` Parameters: order : `int` - Order of the polynomial (0: only intercept, 1: linear, 2: quadratic ... Returns: `FunctionBaseEvaluator` The function base to use with this fit.	Gets a default polynomial function base with intercept, i.e. f(y)=a+bx+cx*x ... order : `int` Order of the polynomial (0: only intercept, 1: linear, 2: quadratic ... Returns: `FunctionBaseEvaluator` The function base to use with this fit.
`LinearFitBySvd.Mean(x, start, length)` Full Usage: `LinearFitBySvd.Mean(x, start, length)` Parameters: x : `IReadOnlyList<float>` - The array of values. start : `int` - First element. length : `int` - Number of elements used for calculation. Returns: `float`	Calculates the mean value of `length` elements in array x starting from index `start`. x : `IReadOnlyList<float>` The array of values. start : `int` First element. length : `int` Number of elements used for calculation. Returns: `float`