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Class weka.classifiers.functions.pace.PaceMatrix

java.lang.Object
    |
    +----weka.classifiers.functions.pace.Matrix
            |
            +----weka.classifiers.functions.pace.PaceMatrix

public class PaceMatrix

extends Matrix

REFERENCES

Wang, Y. (2000). "A new approach to fitting linear models in high dimensional spaces." PhD Thesis. Department of Computer Science, University of Waikato, New Zealand.

Wang, Y. and Witten, I. H. (2002). "Modeling for optimal probability prediction." Proceedings of ICML'2002. Sydney.

Version:

$Revision: 1.1 $

Author:

Yong Wang (yongwang@cs.waikato.ac.nz)

PaceMatrix(double[][])

Construct a PACE matrix from a 2-D array.

PaceMatrix(double[][], int, int)

Construct a PACE matrix quickly without checking arguments.

PaceMatrix(double[], int)

Construct a PaceMatrix from a one-dimensional packed array

PaceMatrix(DoubleVector)

Construct a PaceMatrix with a single column from a DoubleVector

PaceMatrix(int, int)

Construct an m-by-n PACE matrix of zeros.

PaceMatrix(int, int, double)

Construct an m-by-n constant PACE matrix.

PaceMatrix(Matrix)

Construct a PaceMatrix from a Matrix

backward(PaceMatrix, IntVector, int, int)

Backward ordering of columns in terms of response explanation.

cbind(PaceMatrix)

Returns a new matrix which binds two matrices with columns.

clone()

Clone the PaceMatrix object.

columnResponseExplanation(PaceMatrix, IntVector, int, int)

Returns the squared ks-th response value if the j-th column becomes the ks-th after orthogonal transformation.

forward(PaceMatrix, IntVector, int)

Forward ordering of columns in terms of response explanation.

g1(double, double)

Constructs the Givens rotation

g2(double[], int, int, int)

 

getColumn(int)

Return a DoubleVector that stores a column of the matrix

getColumn(int, int, int)

Return a DoubleVector that stores some elements of a column of the matrix

h1(int, int)

Constructs single Householder transformation for a column

h2(int, int, double, PaceMatrix, int)

Performs single Householder transformation on one column of a matrix

isEmpty()

Check if the matrix is empty

leastExplainingColumn(PaceMatrix, IntVector, int, int)

Returns the index of the column that has the smallest (squared) response, when the column is moved to become the (ks-1)-th column.

lsqr(PaceMatrix, IntVector, int)

QR transformation for a least squares problem A x = b

lsqrSelection(PaceMatrix, IntVector, int)

QR transformation for a least squares problem A x = b

main(String[])

 

maxAbs()

Returns the maximum absolute value of all elements

maxAbs(int, int, int)

Returns the maximum absolute value of some elements of a column, that is, the elements of A[i0:i1][j].

minAbs(int, int, int)

Returns the minimum absolute value of some elements of a column, that is, the elements of A[i0:i1][j].

mostExplainingColumn(PaceMatrix, IntVector, int)

Returns the index of the column that has the largest (squared) response, when each of columns pvt[ks:] is moved to become the ks-th column.

nnls(PaceMatrix, IntVector)

Solves the nonnegative linear squares problem.

nnlse(PaceMatrix, PaceMatrix, PaceMatrix, IntVector)

Solves the nonnegative least squares problem with equality constraint.

nnlse1(PaceMatrix, IntVector)

Solves the nonnegative least squares problem with equality constraint.

positiveDiagonal(PaceMatrix, IntVector)

Sets all diagonal elements to be positive (or nonnegative) without changing the least squares solution

randomNormal(int, int)

Generate matrix with standard-normally distributed random elements

rbind(PaceMatrix)

Returns a new matrix which binds two matrices together with rows.

rsolve(PaceMatrix, IntVector, int)

Solves upper-triangular equation R x = b

setColumnDimension(int)

Set the column dimenion of the matrix

setMatrix(double[], boolean)

Set the whole matrix from a 1-D array

setMatrix(int, int, int, DoubleVector)

Set the submatrix A[i0:i1][j] with the values stored in a DoubleVector

setMatrix(int, int, int, int, double)

Set the submatrix A[i0:i1][j0:j1] with a same value

setPlus(int, int, double)

Add a value to an element and reset the element

setRowDimension(int)

Set the row dimenion of the matrix

setTimes(int, int, double)

Multiply a value with an element and reset the element

steplsqr(PaceMatrix, IntVector, int, int, boolean)

Stepwise least squares QR-decomposition of the problem A x = b

sum2(boolean)

Squared sum of columns or rows of a matrix

sum2(int, int, int, boolean)

Squared sum of a column or row in a matrix

times(int, int, int, PaceMatrix, int)

Multiplication between a row (or part of a row) of the first matrix and a column (or part or a column) of the second matrix.

toString()

Converts matrix to string

toString(int, boolean)

Converts matrix to string

public PaceMatrix(int m,
                  int n)

          Construct an m-by-n PACE matrix of zeros.

Parameters:

m - Number of rows.

n - Number of colums.

public PaceMatrix(int m,
                  int n,
                  double s)

          Construct an m-by-n constant PACE matrix.

Parameters:

m - Number of rows.

n - Number of colums.

s - Fill the matrix with this scalar value.

public PaceMatrix(double A[][])

          Construct a PACE matrix from a 2-D array.

Parameters:

A - Two-dimensional array of doubles.

Throws:

java.lang.IllegalArgumentException - All rows must have the same length

public PaceMatrix(double A[][],
                  int m,
                  int n)

          Construct a PACE matrix quickly without checking arguments.

Parameters:

A - Two-dimensional array of doubles.

m - Number of rows.

n - Number of colums.

public PaceMatrix(double vals[],
                  int m)

          Construct a PaceMatrix from a one-dimensional packed array

Parameters:

vals - One-dimensional array of doubles, packed by columns (ala Fortran).

m - Number of rows.

Throws:

java.lang.IllegalArgumentException - Array length must be a multiple of m.

public PaceMatrix(DoubleVector v)

          Construct a PaceMatrix with a single column from a DoubleVector

Parameters:

v - DoubleVector

public PaceMatrix(Matrix X)

          Construct a PaceMatrix from a Matrix

Parameters:

X - Matrix

public void setRowDimension(int rowDimension)

          Set the row dimenion of the matrix

Parameters:

rowDimension - the row dimension

public void setColumnDimension(int columnDimension)

          Set the column dimenion of the matrix

Parameters:

columnDimension - the column dimension

public java.lang.Object clone()

          Clone the PaceMatrix object.

Overrides:

clone in class Matrix

public void setPlus(int i,
                    int j,
                    double s)

          Add a value to an element and reset the element

Parameters:

i - the row number of the element

j - the column number of the element

s - the double value to be added with

public void setTimes(int i,
                     int j,
                     double s)

          Multiply a value with an element and reset the element

Parameters:

i - the row number of the element

j - the column number of the element

s - the double value to be multiplied with

public void setMatrix(int i0,
                      int i1,
                      int j0,
                      int j1,
                      double s)

          Set the submatrix A[i0:i1][j0:j1] with a same value

Parameters:

i0 - the index of the first element of the column

i1 - the index of the last element of the column

j0 - the index of the first column

j1 - the index of the last column

s - the value to be set to

public void setMatrix(int i0,
                      int i1,
                      int j,
                      DoubleVector v)

          Set the submatrix A[i0:i1][j] with the values stored in a DoubleVector

Parameters:

i0 - the index of the first element of the column

i1 - the index of the last element of the column

j - the index of the column

v - the vector that stores the values

public void setMatrix(double v[],
                      boolean columnFirst)

          Set the whole matrix from a 1-D array

Parameters:

v - 1-D array of doubles

columnFirst - Whether to fill the column first or the row.

Throws:

java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

public double maxAbs()

          Returns the maximum absolute value of all elements

Returns:

the maximum value

public double maxAbs(int i0,
                     int i1,
                     int j)

          Returns the maximum absolute value of some elements of a column, that is, the elements of A[i0:i1][j].

Parameters:

i0 - the index of the first element of the column

i1 - the index of the last element of the column

j - the index of the column

Returns:

the maximum value

public double minAbs(int i0,
                     int i1,
                     int column)

          Returns the minimum absolute value of some elements of a column, that is, the elements of A[i0:i1][j].

Parameters:

i0 - the index of the first element of the column

i1 - the index of the last element of the column

j - the index of the column

Returns:

the minimum value

public boolean isEmpty()

          Check if the matrix is empty

Returns:

true if the matrix is empty

public DoubleVector getColumn(int j)

          Return a DoubleVector that stores a column of the matrix

Parameters:

j - the index of the column

public DoubleVector getColumn(int i0,
                              int i1,
                              int j)

          Return a DoubleVector that stores some elements of a column of the matrix

Parameters:

i0 - the index of the first element of the column

i1 - the index of the last element of the column

j - the index of the column

Returns:

the DoubleVector

public double times(int i,
                    int j0,
                    int j1,
                    PaceMatrix B,
                    int l)

          Multiplication between a row (or part of a row) of the first matrix and a column (or part or a column) of the second matrix.

Parameters:

i - the index of the row in the first matrix

j0 - the index of the first column in the first matrix

j1 - the index of the last column in the first matrix

B - the second matrix

l - the index of the column in the second matrix

public java.lang.String toString()

          Converts matrix to string

Overrides:

toString in class java.lang.Object

public java.lang.String toString(int digits,
                       boolean trailing)

          Converts matrix to string

Parameters:

digits - number of digits after decimal point

trailing - true if trailing zeros are padded

public double sum2(int j,
                   int i0,
                   int i1,
                   boolean col)

          Squared sum of a column or row in a matrix

Parameters:

j - the index of the column or row

i0 - the index of the first element

i1 - the index of the last element

col - if true, sum over a column; otherwise, over a row

public double[] sum2(boolean col)

          Squared sum of columns or rows of a matrix

Parameters:

col - if true, sum over columns; otherwise, over rows

public double[] h1(int j,
                   int k)

          Constructs single Householder transformation for a column

Parameters:

j - the index of the column

k - the index of the row

Returns:

d and q

public void h2(int j,
               int k,
               double q,
               PaceMatrix b,
               int l)

          Performs single Householder transformation on one column of a matrix

Parameters:

j - the index of the column

k - the index of the row

q - q = - u'u/2; must be negative

b - the matrix to be transformed

l - the column of the matrix b

public double[] g1(double a,
                   double b)

          Constructs the Givens rotation

Parameters:

a -

b -

Returns:

a double array that stores the cosine and sine values

public void g2(double cs[],
               int i0,
               int i1,
               int j)

public void forward(PaceMatrix b,
                    IntVector pvt,
                    int k0)

          Forward ordering of columns in terms of response explanation. On input, matrices A and b are already QR-transformed. The indices of transformed columns are stored in the pivoting vector.

Parameters:

b - the PaceMatrix b

pvt - the pivoting vector

k0 - the first k0 columns (in pvt) of A are not to be changed

public int mostExplainingColumn(PaceMatrix b,
                                IntVector pvt,
                                int ks)

          Returns the index of the column that has the largest (squared) response, when each of columns pvt[ks:] is moved to become the ks-th column. On input, A and b are both QR-transformed.

Parameters:

b - response

pvt - pivoting index of A

ks - columns pvt[ks:] of A are to be tested

public void backward(PaceMatrix b,
                     IntVector pvt,
                     int ks,
                     int k0)

          Backward ordering of columns in terms of response explanation. On input, matrices A and b are already QR-transformed. The indices of transformed columns are stored in the pivoting vector. A and b must have the same number of rows, being the (pseudo-)rank.

Parameters:

b - PaceMatrix b

pvt - pivoting vector

ks - number of QR-transformed columns; psuedo-rank of A

k0 - first k0 columns in pvt[] are not to be ordered.

Returns:

void

public int leastExplainingColumn(PaceMatrix b,
                                 IntVector pvt,
                                 int ks,
                                 int k0)

          Returns the index of the column that has the smallest (squared) response, when the column is moved to become the (ks-1)-th column. On input, A and b are both QR-transformed.

Parameters:

b - response

pvt - pivoting index of A

ks - psudo-rank of A

k0 - A[][pvt[0:(k0-1)]] are excluded from the testing.

public double columnResponseExplanation(PaceMatrix b,
                                        IntVector pvt,
                                        int j,
                                        int ks)

          Returns the squared ks-th response value if the j-th column becomes the ks-th after orthogonal transformation. A[][pvt[ks:j]] (or A[][pvt[j:ks]], if ks > j) and b[] are already QR-transformed on input and will remain unchanged on output. More generally, it returns the inner product of the corresponding row vector of the response PaceMatrix. (To be implemented.)

Parameters:

b - PaceMatrix b

pvt - pivoting vector

j - the column A[pvt[j]][] is to be moved

ks - the target column A[pvt[ks]][]

Returns:

the squared response value

public void lsqr(PaceMatrix b,
                 IntVector pvt,
                 int k0)

          QR transformation for a least squares problem A x = b

Parameters:

b - PaceMatrix b

pvt - pivoting vector

k0 - the first k0 columns of A (indexed by pvt) are pre-chosen. (But subject to rank examination.) For example, the constant term may be reserved, in which case k0 = 1.

Returns:

void; implicitly both A and b are transformed. pvt.size() is is the psuedo-rank of A.

public void lsqrSelection(PaceMatrix b,
                          IntVector pvt,
                          int k0)

          QR transformation for a least squares problem A x = b

Parameters:

b - PaceMatrix b

pvt - pivoting vector

k0 - the first k0 columns of A (indexed by pvt) are pre-chosen. (But subject to rank examination.) For example, the constant term may be reserved, in which case k0 = 1.

Returns:

void; implicitly both A and b are transformed. pvt.size() is is the psuedo-rank of A.

public void positiveDiagonal(PaceMatrix Y,
                             IntVector pvt)

          Sets all diagonal elements to be positive (or nonnegative) without changing the least squares solution

Parameters:

Y - the response

pvt - the pivoted column index

public void steplsqr(PaceMatrix b,
                     IntVector pvt,
                     int ks,
                     int j,
                     boolean adjoin)

          Stepwise least squares QR-decomposition of the problem A x = b

Parameters:

b - PaceMatrix b

pvt - pivoting vector

ks - number of transformed columns

j - pvt[j], the column to adjoin or delete

adjoin - to adjoin if true; otherwise, to delete

public void rsolve(PaceMatrix b,
                   IntVector pvt,
                   int kp)

          Solves upper-triangular equation R x = b

Parameters:

b - the response

pvt - the pivoting vector

kp - the number of the first columns involved

Returns:

void. On output, the solution is stored in b

public PaceMatrix rbind(PaceMatrix b)

          Returns a new matrix which binds two matrices together with rows.

Parameters:

b - the second matrix

Returns:

the combined matrix

public PaceMatrix cbind(PaceMatrix b)

          Returns a new matrix which binds two matrices with columns.

Parameters:

b - the second matrix

Returns:

the combined matrix

public DoubleVector nnls(PaceMatrix b,
                         IntVector pvt)

          Solves the nonnegative linear squares problem. That is,

min || A x - b||, subject to x >= 0.

For algorithm, refer to P161, Chapter 23 of C. L. Lawson and R. J. Hanson (1974). "Solving Least Squares Problems". Prentice-Hall.

Parameters:

b - the response

pvt - vector storing pivoting column indices

Returns:

solution

public DoubleVector nnlse(PaceMatrix b,
                          PaceMatrix c,
                          PaceMatrix d,
                          IntVector pvt)

          Solves the nonnegative least squares problem with equality constraint. That is,

min ||A x - b||, subject to x >= 0 and c x = d.

Parameters:

b - the response

c - coeficients of equality constraints

d - constants of equality constraints

pvt - vector storing pivoting column indices

public DoubleVector nnlse1(PaceMatrix b,
                           IntVector pvt)

          Solves the nonnegative least squares problem with equality constraint. That is,

min ||A x - b||, subject to x >= 0 and || x || = 1.

Parameters:

b - the response

pvt - vector storing pivoting column indices

public static Matrix randomNormal(int m,
                                  int n)

          Generate matrix with standard-normally distributed random elements

Parameters:

m - Number of rows.

n - Number of colums.

Returns:

An m-by-n matrix with random elements.

public static void main(java.lang.String args[])

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