Apache Commons Math 3.6.1 · org.apache.commons.math3.stat.regression.MillerUpdatingRegression

Field Summary

Modifier and Type	Field and Description
private final double[]	d diagonals of cross products matrix
private final double	epsilon zero tolerance
private boolean	hasIntercept boolean flag whether a regression constant is added
private final boolean[]	lindep flags for variables with linear dependency problems
private long	nobs number of observations entered
private final int	nvars number of variables in regression
private final double[]	r the off diagonal portion of the R matrix
private final double[]	rhs the elements of the R`Y
private final double[]	rss residual sum of squares for all nested regressions
private boolean	rss_set has rss been called?
private double	sserr sum of squared errors of largest regression
private double	sumsqy summation of squared Y values
private double	sumy summation of Y variable
private final double[]	tol the tolerance for each of the variables
private boolean	tol_set has the tolerance setting method been called
private final int[]	vorder order of the regressors
private final double[]	work_sing workspace for singularity method
private final double[]	work_tolset scratch space for tolerance calc
private final double[]	x_sing singular x values

Constructor Summary

Access	Constructor and Description
private	MillerUpdatingRegression() Set the default constructor to private access to prevent inadvertent instantiation
public	MillerUpdatingRegression(int number of regressors to expect, not including constant numberOfVariables, boolean include a constant automatically includeConstant, double zero tolerance, how machine zero is determined errorTolerance) This is the augmented constructor for the MillerUpdatingRegression class.
public	MillerUpdatingRegression(int maximum number of potential regressors numberOfVariables, boolean include a constant automatically includeConstant) Primary constructor for the MillerUpdatingRegression.

Method Summary

Modifier and Type	Method and Description
public void	addObservation(final double[] the array with regressor values x, final double the value of dependent variable given these regressors y) Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.addObservation. Adds an observation to the regression model.
public void	addObservations(double[][] observations on the regressors x, double[] observations on the regressand y) Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.addObservations. Adds multiple observations to the model.
public void	clear() Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.clear. As the name suggests, clear wipes the internals and reorders everything in the canonical order.
private double[]	Returns: an array with the variance covariance of the included regressors in lower triangular form cov(int how many of the regressors to include (either in canonical order, or in the current reordered state) nreq) Calculates the cov matrix assuming only the first nreq variables are included in the calculation.
public double	Returns: the diagonal element of the hatmatrix getDiagonalOfHatMatrix(double[] returns the diagonal of the hat matrix for this observation row_data) Gets the diagonal of the Hat matrix also known as the leverage matrix.
public long	Returns: number of observations getN() Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.getN. Gets the number of observations added to the regression model.
public int[]	Returns: int[] with the current order of the regressors getOrderOfRegressors() Gets the order of the regressors, useful if some type of reordering has been called.
public double[]	Returns: an array with the partial correlations of the remainder of regressors with each other and the regressand, in lower triangular form getPartialCorrelations(int how many of the regressors to include (either in canonical order, or in the current reordered state) in) In the original algorithm only the partial correlations of the regressors is returned to the user.
public boolean	Returns: true regression has an intercept, false no intercept hasIntercept() Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.hasIntercept. A getter method which determines whether a constant is included.
private void	include(final double[] observations on the regressors x, final double weight of the this observation (-1,1) wi, final double observation on the regressand yi) The include method is where the QR decomposition occurs.
private void	inverse(double[] the storage for the inverse of r rinv, int how many of the regressors to include (either in canonical order, or in the current reordered state) nreq) This internal method calculates the inverse of the upper-triangular portion of the R matrix.
private double[]	Returns: an array with the estimated slope coefficients regcf(int how many of the regressors to include (either in canonical order, or in the current reordered state) nreq) The regcf method conducts the linear regression and extracts the parameter vector.
public RegressionResults	Returns: RegressionResults the structure holding all regression results regress() Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.regress. Conducts a regression on the data in the model, using all regressors.
public RegressionResults	Returns: RegressionResults the structure holding all regression results regress(int many of the regressors to include (either in canonical order, or in the current reordered state) numberOfRegressors) Conducts a regression on the data in the model, using a subset of regressors.
public RegressionResults	Returns: RegressionResults the structure holding all regression results regress(int[] array of variables to include in regression variablesToInclude) Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.regress. Conducts a regression on the data in the model, using regressors in array Calling this method will change the internal order of the regressors and care is required in interpreting the hatmatrix.
private int	Returns: -1 error, 0 everything ok reorderRegressors(int[] the regressors to move list, int where the list will be placed pos1) ALGORITHM AS274 APPL.
private void	singcheck() The method which checks for singularities and then eliminates the offending columns.
private double	Returns: the sum of the a and b smartAdd(double - an addend a, double - an addend b) Adds to number a and b such that the contamination due to numerical smallness of one addend does not corrupt the sum.
private void	ss() Calculates the sum of squared errors for the full regression and all subsets in the following manner: rss[] ={ ResidualSumOfSquares_allNvars, ResidualSumOfSquares_FirstNvars-1, ResidualSumOfSquares_FirstNvars-2, ..., ResidualSumOfSquares_FirstVariable}
private void	tolset() This sets up tolerances for singularity testing.
private void	vmove(int initial position from, int destination to) ALGORITHM AS274 APPL.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

d	back to summary
private final double[] d diagonals of cross products matrix

epsilon	back to summary
private final double epsilon zero tolerance

hasIntercept	back to summary
private boolean hasIntercept boolean flag whether a regression constant is added

lindep	back to summary
private final boolean[] lindep flags for variables with linear dependency problems

nobs	back to summary
private long nobs number of observations entered

nvars	back to summary
private final int nvars number of variables in regression

r	back to summary
private final double[] r the off diagonal portion of the R matrix

rhs	back to summary
private final double[] rhs the elements of the R`Y

rss	back to summary
private final double[] rss residual sum of squares for all nested regressions

rss_set	back to summary
private boolean rss_set has rss been called?

sserr	back to summary
private double sserr sum of squared errors of largest regression

sumsqy	back to summary
private double sumsqy summation of squared Y values

sumy	back to summary
private double sumy summation of Y variable

tol	back to summary
private final double[] tol the tolerance for each of the variables

tol_set	back to summary
private boolean tol_set has the tolerance setting method been called

vorder	back to summary
private final int[] vorder order of the regressors

work_sing	back to summary
private final double[] work_sing workspace for singularity method

work_tolset	back to summary
private final double[] work_tolset scratch space for tolerance calc

x_sing	back to summary
private final double[] x_sing singular x values

Constructor Detail

MillerUpdatingRegression	back to summary
private MillerUpdatingRegression() Set the default constructor to private access to prevent inadvertent instantiation Annotations @SuppressWarnings:unused

MillerUpdatingRegression

back to summary

private MillerUpdatingRegression()

Set the default constructor to private access to prevent inadvertent instantiation

Annotations

@SuppressWarnings:unused

MillerUpdatingRegression back to summary

MillerUpdatingRegression	back to summary
public MillerUpdatingRegression(int numberOfVariables, boolean includeConstant, double errorTolerance) throws ModelSpecificationException This is the augmented constructor for the MillerUpdatingRegression class. Parameters numberOfVariables:int number of regressors to expect, not including constant includeConstant:boolean include a constant automatically errorTolerance:double zero tolerance, how machine zero is determined Exceptions ModelSpecificationException: if `numberOfVariables is less than 1`

public MillerUpdatingRegression(int numberOfVariables, boolean includeConstant, double errorTolerance) throws ModelSpecificationException

This is the augmented constructor for the MillerUpdatingRegression class.

Parameters

numberOfVariables:int: number of regressors to expect, not including constant
includeConstant:boolean: include a constant automatically
errorTolerance:double: zero tolerance, how machine zero is determined

Exceptions

ModelSpecificationException:: if numberOfVariables is less than 1

MillerUpdatingRegression back to summary

MillerUpdatingRegression	back to summary
public MillerUpdatingRegression(int numberOfVariables, boolean includeConstant) throws ModelSpecificationException Primary constructor for the MillerUpdatingRegression. Parameters numberOfVariables:int maximum number of potential regressors includeConstant:boolean include a constant automatically Exceptions ModelSpecificationException: if `numberOfVariables is less than 1`

public MillerUpdatingRegression(int numberOfVariables, boolean includeConstant) throws ModelSpecificationException

Primary constructor for the MillerUpdatingRegression.

Parameters

numberOfVariables:int: maximum number of potential regressors
includeConstant:boolean: include a constant automatically

Exceptions

ModelSpecificationException:: if numberOfVariables is less than 1

Method Detail

addObservation back to summary

addObservation	back to summary
public void addObservation(final double[] x, final double y) throws ModelSpecificationException Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.addObservation. Adds an observation to the regression model. Parameters x:double[] the array with regressor values y:double the value of dependent variable given these regressors Exceptions ModelSpecificationException: if the length of `x` does not equal the number of independent variables in the model

public void addObservation(final double[] x, final double y) throws ModelSpecificationException

Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.addObservation.

Adds an observation to the regression model.

Parameters

x:double[]: the array with regressor values
y:double: the value of dependent variable given these regressors

Exceptions

ModelSpecificationException:: if the length of x does not equal the number of independent variables in the model

addObservations back to summary

addObservations	back to summary
public void addObservations(double[][] x, double[] y) throws ModelSpecificationException Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.addObservations. Adds multiple observations to the model. Parameters x:double[][] observations on the regressors y:double[] observations on the regressand Exceptions ModelSpecificationException: if `x` is not rectangular, does not match the length of `y` or does not contain sufficient data to estimate the model

public void addObservations(double[][] x, double[] y) throws ModelSpecificationException

Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.addObservations.

Adds multiple observations to the model.

Parameters

x:double[][]: observations on the regressors
y:double[]: observations on the regressand

Exceptions

ModelSpecificationException:: if x is not rectangular, does not match the length of y or does not contain sufficient data to estimate the model

clear	back to summary
public void clear() Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.clear. As the name suggests, clear wipes the internals and reorders everything in the canonical order.

clear

back to summary

public void clear()

Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.clear.

As the name suggests, clear wipes the internals and reorders everything in the canonical order.

cov	back to summary
private double[] cov(int nreq) Calculates the cov matrix assuming only the first nreq variables are included in the calculation. The returned array contains a symmetric matrix stored in lower triangular form. The matrix will have ( nreq + 1 ) * nreq / 2 elements. For illustration cov = { cov_00, cov_10, cov_11, cov_20, cov_21, cov22, ... } Parameters nreq:int how many of the regressors to include (either in canonical order, or in the current reordered state) Returns:double[] an array with the variance covariance of the included regressors in lower triangular form

cov

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private double[] cov(int nreq)

Calculates the cov matrix assuming only the first nreq variables are included in the calculation. The returned array contains a symmetric matrix stored in lower triangular form. The matrix will have ( nreq + 1 ) * nreq / 2 elements. For illustration

cov =
{
 cov_00,
 cov_10, cov_11,
 cov_20, cov_21, cov22,
 ...
}

Parameters

nreq:int: how many of the regressors to include (either in canonical order, or in the current reordered state)

Returns:double[]

an array with the variance covariance of the included regressors in lower triangular form

getDiagonalOfHatMatrix	back to summary
public double getDiagonalOfHatMatrix(double[] row_data) Gets the diagonal of the Hat matrix also known as the leverage matrix. Parameters row_data:double[] returns the diagonal of the hat matrix for this observation Returns:double the diagonal element of the hatmatrix

getDiagonalOfHatMatrix

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public double getDiagonalOfHatMatrix(double[] row_data)

Gets the diagonal of the Hat matrix also known as the leverage matrix.

Parameters

row_data:double[]: returns the diagonal of the hat matrix for this observation

Returns:double

the diagonal element of the hatmatrix

getN	back to summary
public long getN() Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.getN. Gets the number of observations added to the regression model. Returns:long number of observations

getN

back to summary

public long getN()

Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.getN.

Gets the number of observations added to the regression model.

Returns:long: number of observations

getOrderOfRegressors	back to summary
public int[] getOrderOfRegressors() Gets the order of the regressors, useful if some type of reordering has been called. Calling regress with int[]{} args will trigger a reordering. Returns:int[] int[] with the current order of the regressors

getOrderOfRegressors

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public int[] getOrderOfRegressors()

Gets the order of the regressors, useful if some type of reordering has been called. Calling regress with int[]{} args will trigger a reordering.

Returns:int[]: int[] with the current order of the regressors

getPartialCorrelations	back to summary
public double[] getPartialCorrelations(int in) In the original algorithm only the partial correlations of the regressors is returned to the user. In this implementation, we have corr = { corrxx - lower triangular corrxy - bottom row of the matrix } Replaces subroutines PCORR and COR of: ALGORITHM AS274 APPL. STATIST. (1992) VOL.41, NO. 2 Calculate partial correlations after the variables in rows 1, 2, ..., IN have been forced into the regression. If IN = 1, and the first row of R represents a constant in the model, then the usual simple correlations are returned. If IN = 0, the value returned in array CORMAT for the correlation of variables Xi & Xj is: sum ( Xi.Xj ) / Sqrt ( sum (Xi^2) . sum (Xj^2) ) On return, array CORMAT contains the upper triangle of the matrix of partial correlations stored by rows, excluding the 1's on the diagonal. e.g. if IN = 2, the consecutive elements returned are: (3,4) (3,5) ... (3,ncol), (4,5) (4,6) ... (4,ncol), etc. Array YCORR stores the partial correlations with the Y-variable starting with YCORR(IN+1) = partial correlation with the variable in position (IN+1). Parameters in:int how many of the regressors to include (either in canonical order, or in the current reordered state) Returns:double[] an array with the partial correlations of the remainder of regressors with each other and the regressand, in lower triangular form

getPartialCorrelations

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public double[] getPartialCorrelations(int in)

In the original algorithm only the partial correlations of the regressors is returned to the user. In this implementation, we have

corr =
{
  corrxx - lower triangular
  corrxy - bottom row of the matrix
}
Replaces subroutines PCORR and COR of:
ALGORITHM AS274  APPL. STATIST. (1992) VOL.41, NO. 2

Calculate partial correlations after the variables in rows 1, 2, ..., IN have been forced into the regression. If IN = 1, and the first row of R represents a constant in the model, then the usual simple correlations are returned.

If IN = 0, the value returned in array CORMAT for the correlation of variables Xi & Xj is:

sum ( Xi.Xj ) / Sqrt ( sum (Xi^2) . sum (Xj^2) )

On return, array CORMAT contains the upper triangle of the matrix of partial correlations stored by rows, excluding the 1's on the diagonal. e.g. if IN = 2, the consecutive elements returned are: (3,4) (3,5) ... (3,ncol), (4,5) (4,6) ... (4,ncol), etc. Array YCORR stores the partial correlations with the Y-variable starting with YCORR(IN+1) = partial correlation with the variable in position (IN+1).

Parameters

in:int: how many of the regressors to include (either in canonical order, or in the current reordered state)

Returns:double[]

an array with the partial correlations of the remainder of regressors with each other and the regressand, in lower triangular form

hasIntercept	back to summary
public boolean hasIntercept() Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.hasIntercept. A getter method which determines whether a constant is included. Returns:boolean true regression has an intercept, false no intercept

hasIntercept

back to summary

public boolean hasIntercept()

Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.hasIntercept.

A getter method which determines whether a constant is included.

Returns:boolean: true regression has an intercept, false no intercept

include	back to summary
private void include(final double[] x, final double wi, final double yi) The include method is where the QR decomposition occurs. This statement forms all intermediate data which will be used for all derivative measures. According to the miller paper, note that in the original implementation the x vector is overwritten. In this implementation, the include method is passed a copy of the original data vector so that there is no contamination of the data. Additionally, this method differs slightly from Gentleman's method, in that the assumption is of dense design matrices, there is some advantage in using the original gentleman algorithm on sparse matrices. Parameters x:double[] observations on the regressors wi:double weight of the this observation (-1,1) yi:double observation on the regressand

include

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private void include(final double[] x, final double wi, final double yi)

The include method is where the QR decomposition occurs. This statement forms all intermediate data which will be used for all derivative measures. According to the miller paper, note that in the original implementation the x vector is overwritten. In this implementation, the include method is passed a copy of the original data vector so that there is no contamination of the data. Additionally, this method differs slightly from Gentleman's method, in that the assumption is of dense design matrices, there is some advantage in using the original gentleman algorithm on sparse matrices.

Parameters

x:double[]: observations on the regressors
wi:double: weight of the this observation (-1,1)
yi:double: observation on the regressand

inverse	back to summary
private void inverse(double[] rinv, int nreq) This internal method calculates the inverse of the upper-triangular portion of the R matrix. Parameters rinv:double[] the storage for the inverse of r nreq:int how many of the regressors to include (either in canonical order, or in the current reordered state)

inverse

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private void inverse(double[] rinv, int nreq)

This internal method calculates the inverse of the upper-triangular portion of the R matrix.

Parameters

rinv:double[]: the storage for the inverse of r
nreq:int: how many of the regressors to include (either in canonical order, or in the current reordered state)

regcf back to summary

regcf	back to summary
private double[] regcf(int nreq) throws ModelSpecificationException The regcf method conducts the linear regression and extracts the parameter vector. Notice that the algorithm can do subset regression with no alteration. Parameters nreq:int how many of the regressors to include (either in canonical order, or in the current reordered state) Returns:double[] an array with the estimated slope coefficients Exceptions ModelSpecificationException: if `nreq` is less than 1 or greater than the number of independent variables

private double[] regcf(int nreq) throws ModelSpecificationException

The regcf method conducts the linear regression and extracts the parameter vector. Notice that the algorithm can do subset regression with no alteration.

Parameters

nreq:int: how many of the regressors to include (either in canonical order, or in the current reordered state)

Returns:double[]

an array with the estimated slope coefficients

Exceptions

ModelSpecificationException:: if nreq is less than 1 or greater than the number of independent variables

regress	back to summary
public RegressionResults regress() throws ModelSpecificationException Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.regress. Conducts a regression on the data in the model, using all regressors. Returns:RegressionResults RegressionResults the structure holding all regression results Exceptions ModelSpecificationException: - thrown if number of observations is less than the number of variables

regress

back to summary

public RegressionResults regress() throws ModelSpecificationException

Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.regress.

Conducts a regression on the data in the model, using all regressors.

Returns:RegressionResults

RegressionResults the structure holding all regression results

Exceptions

ModelSpecificationException:: - thrown if number of observations is less than the number of variables

regress	back to summary
public RegressionResults regress(int numberOfRegressors) throws ModelSpecificationException Conducts a regression on the data in the model, using a subset of regressors. Parameters numberOfRegressors:int many of the regressors to include (either in canonical order, or in the current reordered state) Returns:RegressionResults RegressionResults the structure holding all regression results Exceptions ModelSpecificationException: - thrown if number of observations is less than the number of variables or number of regressors requested is greater than the regressors in the model

regress

back to summary

public RegressionResults regress(int numberOfRegressors) throws ModelSpecificationException

Conducts a regression on the data in the model, using a subset of regressors.

Parameters

numberOfRegressors:int: many of the regressors to include (either in canonical order, or in the current reordered state)

Returns:RegressionResults

RegressionResults the structure holding all regression results

Exceptions

ModelSpecificationException:: - thrown if number of observations is less than the number of variables or number of regressors requested is greater than the regressors in the model

regress	back to summary
public RegressionResults regress(int[] variablesToInclude) throws ModelSpecificationException Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.regress. Conducts a regression on the data in the model, using regressors in array Calling this method will change the internal order of the regressors and care is required in interpreting the hatmatrix. Parameters variablesToInclude:int[] array of variables to include in regression Returns:RegressionResults RegressionResults the structure holding all regression results Exceptions ModelSpecificationException: - thrown if number of observations is less than the number of variables, the number of regressors requested is greater than the regressors in the model or a regressor index in regressor array does not exist

regress

back to summary

public RegressionResults regress(int[] variablesToInclude) throws ModelSpecificationException

Implements org.apache.commons.math3.stat.regression.UpdatingMultipleLinearRegression.regress.

Conducts a regression on the data in the model, using regressors in array Calling this method will change the internal order of the regressors and care is required in interpreting the hatmatrix.

Parameters

variablesToInclude:int[]: array of variables to include in regression

Returns:RegressionResults

RegressionResults the structure holding all regression results

Exceptions

ModelSpecificationException:: - thrown if number of observations is less than the number of variables, the number of regressors requested is greater than the regressors in the model or a regressor index in regressor array does not exist

reorderRegressors	back to summary
private int reorderRegressors(int[] list, int pos1) ALGORITHM AS274 APPL. STATIST. (1992) VOL.41, NO. 2 Re-order the variables in an orthogonal reduction produced by AS75.1 so that the N variables in LIST start at position POS1, though will not necessarily be in the same order as in LIST. Any variables in VORDER before position POS1 are not moved. Auxiliary routine called: VMOVE. This internal method reorders the regressors. Parameters list:int[] the regressors to move pos1:int where the list will be placed Returns:int -1 error, 0 everything ok

reorderRegressors

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private int reorderRegressors(int[] list, int pos1)

ALGORITHM AS274 APPL. STATIST. (1992) VOL.41, NO. 2

Re-order the variables in an orthogonal reduction produced by AS75.1 so that the N variables in LIST start at position POS1, though will not necessarily be in the same order as in LIST. Any variables in VORDER before position POS1 are not moved. Auxiliary routine called: VMOVE.

This internal method reorders the regressors.

Parameters

list:int[]: the regressors to move
pos1:int: where the list will be placed

Returns:int

-1 error, 0 everything ok

singcheck	back to summary
private void singcheck() The method which checks for singularities and then eliminates the offending columns.

smartAdd	back to summary
private double smartAdd(double a, double b) Adds to number a and b such that the contamination due to numerical smallness of one addend does not corrupt the sum. Parameters a:double - an addend b:double - an addend Returns:double the sum of the a and b

smartAdd

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private double smartAdd(double a, double b)

Adds to number a and b such that the contamination due to numerical smallness of one addend does not corrupt the sum.

Parameters

a:double: - an addend
b:double: - an addend

Returns:double

the sum of the a and b

ss	back to summary
private void ss() Calculates the sum of squared errors for the full regression and all subsets in the following manner: rss[] ={ ResidualSumOfSquares_allNvars, ResidualSumOfSquares_FirstNvars-1, ResidualSumOfSquares_FirstNvars-2, ..., ResidualSumOfSquares_FirstVariable}

back to summary

private void ss()

Calculates the sum of squared errors for the full regression and all subsets in the following manner:

rss[] ={
ResidualSumOfSquares_allNvars,
ResidualSumOfSquares_FirstNvars-1,
ResidualSumOfSquares_FirstNvars-2,
..., ResidualSumOfSquares_FirstVariable}

tolset	back to summary
private void tolset() This sets up tolerances for singularity testing.

vmove	back to summary
private void vmove(int from, int to) ALGORITHM AS274 APPL. STATIST. (1992) VOL.41, NO. 2. Move variable from position FROM to position TO in an orthogonal reduction produced by AS75.1. Parameters from:int initial position to:int destination

vmove

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private void vmove(int from, int to)

ALGORITHM AS274 APPL. STATIST. (1992) VOL.41, NO. 2. Move variable from position FROM to position TO in an orthogonal reduction produced by AS75.1.

Parameters

from:int: initial position
to:int: destination

public Class MillerUpdatingRegression

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail