Class PaceMatrix

java.lang.Object
weka.core.matrix.Matrix
weka.classifiers.functions.pace.PaceMatrix
All Implemented Interfaces:
Serializable, Cloneable, RevisionHandler

public class PaceMatrix extends Matrix
Class for matrix manipulation used for pace regression.

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: 1.6 $
Author:
Yong Wang (yongwang@cs.waikato.ac.nz)
See Also:
  • Constructor Details

    • PaceMatrix

      public PaceMatrix(int m, int n)
      Construct an m-by-n PACE matrix of zeros.
      Parameters:
      m - Number of rows.
      n - Number of colums.
    • PaceMatrix

      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.
    • PaceMatrix

      public PaceMatrix(double[][] A)
      Construct a PACE matrix from a 2-D array.
      Parameters:
      A - Two-dimensional array of doubles.
      Throws:
      IllegalArgumentException - All rows must have the same length
    • PaceMatrix

      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.
    • PaceMatrix

      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:
      IllegalArgumentException - Array length must be a multiple of m.
    • PaceMatrix

      public PaceMatrix(DoubleVector v)
      Construct a PaceMatrix with a single column from a DoubleVector
      Parameters:
      v - DoubleVector
    • PaceMatrix

      public PaceMatrix(Matrix X)
      Construct a PaceMatrix from a Matrix
      Parameters:
      X - Matrix
  • Method Details

    • setRowDimension

      public void setRowDimension(int rowDimension)
      Set the row dimenion of the matrix
      Parameters:
      rowDimension - the row dimension
    • setColumnDimension

      public void setColumnDimension(int columnDimension)
      Set the column dimenion of the matrix
      Parameters:
      columnDimension - the column dimension
    • clone

      public Object clone()
      Clone the PaceMatrix object.
      Overrides:
      clone in class Matrix
      Returns:
      the clone
    • setPlus

      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
    • setTimes

      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
    • setMatrix

      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
    • setMatrix

      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
    • setMatrix

      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:
      ArrayIndexOutOfBoundsException - Submatrix indices
    • maxAbs

      public double maxAbs()
      Returns the maximum absolute value of all elements
      Returns:
      the maximum value
    • maxAbs

      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
    • minAbs

      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
      column - the index of the column
      Returns:
      the minimum value
    • isEmpty

      public boolean isEmpty()
      Check if the matrix is empty
      Returns:
      true if the matrix is empty
    • getColumn

      public DoubleVector getColumn(int j)
      Return a DoubleVector that stores a column of the matrix
      Parameters:
      j - the index of the column
      Returns:
      the column
    • getColumn

      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
    • times

      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
      Returns:
      the result of the multiplication
    • toString

      public String toString()
      Converts matrix to string
      Overrides:
      toString in class Matrix
      Returns:
      the matrix as string
    • toString

      public 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
      Returns:
      the matrix as string
    • sum2

      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
      Returns:
      the squared sum
    • sum2

      public double[] sum2(boolean col)
      Squared sum of columns or rows of a matrix
      Parameters:
      col - if true, sum over columns; otherwise, over rows
      Returns:
      the squared sum
    • h1

      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
    • h2

      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
    • g1

      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
    • g2

      public void g2(double[] cs, int i0, int i1, int j)
      Performs the Givens rotation
      Parameters:
      cs - a array storing the cosine and sine values
      i0 - the index of the row of the first element
      i1 - the index of the row of the second element
      j - the index of the column
    • forward

      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
    • mostExplainingColumn

      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
      Returns:
      the index of the column
    • backward

      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.
    • leastExplainingColumn

      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.
      Returns:
      the index of the column
    • columnResponseExplanation

      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
    • lsqr

      public void lsqr(PaceMatrix b, IntVector pvt, int k0)
      QR transformation for a least squares problem
      A x = b
      implicitly both A and b are transformed. pvt.size() is the psuedo-rank of A.
      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.
    • lsqrSelection

      public void lsqrSelection(PaceMatrix b, IntVector pvt, int k0)
      QR transformation for a least squares problem
      A x = b
      implicitly both A and b are transformed. pvt.size() is the psuedo-rank of A.
      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.
    • positiveDiagonal

      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
    • steplsqr

      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
    • rsolve

      public void rsolve(PaceMatrix b, IntVector pvt, int kp)
      Solves upper-triangular equation
      R x = b
      On output, the solution is stored in b
      Parameters:
      b - the response
      pvt - the pivoting vector
      kp - the number of the first columns involved
    • rbind

      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
    • cbind

      public PaceMatrix cbind(PaceMatrix b)
      Returns a new matrix which binds two matrices with columns.
      Parameters:
      b - the second matrix
      Returns:
      the combined matrix
    • nnls

      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
    • nnlse

      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
      Returns:
      the solution
    • nnlse1

      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
      Returns:
      the solution
    • randomNormal

      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.
    • getRevision

      public String getRevision()
      Returns the revision string.
      Specified by:
      getRevision in interface RevisionHandler
      Overrides:
      getRevision in class Matrix
      Returns:
      the revision
    • main

      public static void main(String[] args)
      for testing only
      Parameters:
      args - the commandline arguments - ignored