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</DL>
<HR>

<A NAME="g1(double, double)"><!-- --></A><H3>
g1</H3>
<PRE>
public double[] <B>g1</B>(double&nbsp;a,
                   double&nbsp;b)</PRE>
<DL>
<DD>Constructs the Givens rotation
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>a</CODE> - <DD><CODE>b</CODE> - 
<DT><B>Returns:</B><DD>a double array that stores the cosine and sine values</DL>
</DD>
</DL>
<HR>

<A NAME="g2(double[], int, int, int)"><!-- --></A><H3>
g2</H3>
<PRE>
public void <B>g2</B>(double[]&nbsp;cs,
               int&nbsp;i0,
               int&nbsp;i1,
               int&nbsp;j)</PRE>
<DL>
<DD><DL>
</DL>
</DD>
</DL>
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<A NAME="forward(weka.classifiers.functions.pace.PaceMatrix, weka.classifiers.functions.pace.IntVector, int)"><!-- --></A><H3>
forward</H3>
<PRE>
public void <B>forward</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;b,
                    <A HREF="../../../../weka/classifiers/functions/pace/IntVector.html" title="class in weka.classifiers.functions.pace">IntVector</A>&nbsp;pvt,
                    int&nbsp;k0)</PRE>
<DL>
<DD>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.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - the PaceMatrix b<DD><CODE>pvt</CODE> - the pivoting vector<DD><CODE>k0</CODE> - the first k0 columns (in pvt) of A are not to be changed</DL>
</DD>
</DL>
<HR>

<A NAME="mostExplainingColumn(weka.classifiers.functions.pace.PaceMatrix, weka.classifiers.functions.pace.IntVector, int)"><!-- --></A><H3>
mostExplainingColumn</H3>
<PRE>
public int <B>mostExplainingColumn</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;b,
                                <A HREF="../../../../weka/classifiers/functions/pace/IntVector.html" title="class in weka.classifiers.functions.pace">IntVector</A>&nbsp;pvt,
                                int&nbsp;ks)</PRE>
<DL>
<DD>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.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - response<DD><CODE>pvt</CODE> - pivoting index of A<DD><CODE>ks</CODE> - columns pvt[ks:] of A are to be tested</DL>
</DD>
</DL>
<HR>

<A NAME="backward(weka.classifiers.functions.pace.PaceMatrix, weka.classifiers.functions.pace.IntVector, int, int)"><!-- --></A><H3>
backward</H3>
<PRE>
public void <B>backward</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;b,
                     <A HREF="../../../../weka/classifiers/functions/pace/IntVector.html" title="class in weka.classifiers.functions.pace">IntVector</A>&nbsp;pvt,
                     int&nbsp;ks,
                     int&nbsp;k0)</PRE>
<DL>
<DD>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.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - PaceMatrix b<DD><CODE>pvt</CODE> - pivoting vector<DD><CODE>ks</CODE> - number of QR-transformed columns; psuedo-rank of A<DD><CODE>k0</CODE> - first k0 columns in pvt[] are not to be ordered.
<DT><B>Returns:</B><DD>void</DL>
</DD>
</DL>
<HR>

<A NAME="leastExplainingColumn(weka.classifiers.functions.pace.PaceMatrix, weka.classifiers.functions.pace.IntVector, int, int)"><!-- --></A><H3>
leastExplainingColumn</H3>
<PRE>
public int <B>leastExplainingColumn</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;b,
                                 <A HREF="../../../../weka/classifiers/functions/pace/IntVector.html" title="class in weka.classifiers.functions.pace">IntVector</A>&nbsp;pvt,
                                 int&nbsp;ks,
                                 int&nbsp;k0)</PRE>
<DL>
<DD>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.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - response<DD><CODE>pvt</CODE> - pivoting index of A<DD><CODE>ks</CODE> - psudo-rank of A<DD><CODE>k0</CODE> - A[][pvt[0:(k0-1)]] are excluded from the testing.</DL>
</DD>
</DL>
<HR>

<A NAME="columnResponseExplanation(weka.classifiers.functions.pace.PaceMatrix, weka.classifiers.functions.pace.IntVector, int, int)"><!-- --></A><H3>
columnResponseExplanation</H3>
<PRE>
public double <B>columnResponseExplanation</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;b,
                                        <A HREF="../../../../weka/classifiers/functions/pace/IntVector.html" title="class in weka.classifiers.functions.pace">IntVector</A>&nbsp;pvt,
                                        int&nbsp;j,
                                        int&nbsp;ks)</PRE>
<DL>
<DD>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.)
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - PaceMatrix b<DD><CODE>pvt</CODE> - pivoting vector<DD><CODE>j</CODE> - the column A[pvt[j]][] is to be moved<DD><CODE>ks</CODE> - the target column A[pvt[ks]][]
<DT><B>Returns:</B><DD>the squared response value</DL>
</DD>
</DL>
<HR>

<A NAME="lsqr(weka.classifiers.functions.pace.PaceMatrix, weka.classifiers.functions.pace.IntVector, int)"><!-- --></A><H3>
lsqr</H3>
<PRE>
public void <B>lsqr</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;b,
                 <A HREF="../../../../weka/classifiers/functions/pace/IntVector.html" title="class in weka.classifiers.functions.pace">IntVector</A>&nbsp;pvt,
                 int&nbsp;k0)</PRE>
<DL>
<DD>QR transformation for a least squares problem
            A x = b
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - PaceMatrix b<DD><CODE>pvt</CODE> - pivoting vector<DD><CODE>k0</CODE> - 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.
<DT><B>Returns:</B><DD>void; implicitly both A and b are transformed. pvt.size() is 
            is the psuedo-rank of A.</DL>
</DD>
</DL>
<HR>

<A NAME="lsqrSelection(weka.classifiers.functions.pace.PaceMatrix, weka.classifiers.functions.pace.IntVector, int)"><!-- --></A><H3>
lsqrSelection</H3>
<PRE>
public void <B>lsqrSelection</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;b,
                          <A HREF="../../../../weka/classifiers/functions/pace/IntVector.html" title="class in weka.classifiers.functions.pace">IntVector</A>&nbsp;pvt,
                          int&nbsp;k0)</PRE>
<DL>
<DD>QR transformation for a least squares problem
            A x = b
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - PaceMatrix b<DD><CODE>pvt</CODE> - pivoting vector<DD><CODE>k0</CODE> - 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.
<DT><B>Returns:</B><DD>void; implicitly both A and b are transformed. pvt.size() is 
            is the psuedo-rank of A.</DL>
</DD>
</DL>
<HR>

<A NAME="positiveDiagonal(weka.classifiers.functions.pace.PaceMatrix, weka.classifiers.functions.pace.IntVector)"><!-- --></A><H3>
positiveDiagonal</H3>
<PRE>
public void <B>positiveDiagonal</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;Y,
                             <A HREF="../../../../weka/classifiers/functions/pace/IntVector.html" title="class in weka.classifiers.functions.pace">IntVector</A>&nbsp;pvt)</PRE>
<DL>
<DD>Sets all diagonal elements to be positive (or nonnegative) without
 changing the least squares solution
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>Y</CODE> - the response<DD><CODE>pvt</CODE> - the pivoted column index</DL>
</DD>
</DL>
<HR>

<A NAME="steplsqr(weka.classifiers.functions.pace.PaceMatrix, weka.classifiers.functions.pace.IntVector, int, int, boolean)"><!-- --></A><H3>
steplsqr</H3>
<PRE>
public void <B>steplsqr</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;b,
                     <A HREF="../../../../weka/classifiers/functions/pace/IntVector.html" title="class in weka.classifiers.functions.pace">IntVector</A>&nbsp;pvt,
                     int&nbsp;ks,
                     int&nbsp;j,
                     boolean&nbsp;adjoin)</PRE>
<DL>
<DD>Stepwise least squares QR-decomposition of the problem
	          A x = b
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - PaceMatrix b<DD><CODE>pvt</CODE> - pivoting vector<DD><CODE>ks</CODE> - number of transformed columns<DD><CODE>j</CODE> - pvt[j], the column to adjoin or delete<DD><CODE>adjoin</CODE> - to adjoin if true; otherwise, to delete</DL>
</DD>
</DL>
<HR>

<A NAME="rsolve(weka.classifiers.functions.pace.PaceMatrix, weka.classifiers.functions.pace.IntVector, int)"><!-- --></A><H3>
rsolve</H3>
<PRE>
public void <B>rsolve</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;b,
                   <A HREF="../../../../weka/classifiers/functions/pace/IntVector.html" title="class in weka.classifiers.functions.pace">IntVector</A>&nbsp;pvt,
                   int&nbsp;kp)</PRE>
<DL>
<DD>Solves upper-triangular equation
   	R x = b
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - the response<DD><CODE>pvt</CODE> - the pivoting vector<DD><CODE>kp</CODE> - the number of the first columns involved
<DT><B>Returns:</B><DD>void. On output, the solution is stored in b</DL>
</DD>
</DL>
<HR>

<A NAME="rbind(weka.classifiers.functions.pace.PaceMatrix)"><!-- --></A><H3>
rbind</H3>
<PRE>
public <A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A> <B>rbind</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;b)</PRE>
<DL>
<DD>Returns a new matrix which binds two matrices together with rows.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - the second matrix
<DT><B>Returns:</B><DD>the combined matrix</DL>
</DD>
</DL>
<HR>

<A NAME="cbind(weka.classifiers.functions.pace.PaceMatrix)"><!-- --></A><H3>
cbind</H3>
<PRE>
public <A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A> <B>cbind</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;b)</PRE>
<DL>
<DD>Returns a new matrix which binds two matrices with columns.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - the second matrix
<DT><B>Returns:</B><DD>the combined matrix</DL>
</DD>
</DL>
<HR>

<A NAME="nnls(weka.classifiers.functions.pace.PaceMatrix, weka.classifiers.functions.pace.IntVector)"><!-- --></A><H3>
nnls</H3>
<PRE>
public <A HREF="../../../../weka/classifiers/functions/pace/DoubleVector.html" title="class in weka.classifiers.functions.pace">DoubleVector</A> <B>nnls</B>(<A HREF="../../../../weka/classifiers/functions/pace/PaceMatrix.html" title="class in weka.classifiers.functions.pace">PaceMatrix</A>&nbsp;b,
                         <A HREF="../../../../weka/classifiers/functions/pace/IntVector.html" title="class in weka.classifiers.functions.pace">IntVector</A>&nbsp;pvt)</PRE>
<DL>
<DD>Solves the nonnegative linear squares problem. That is, <p>
   <center>   min || A x - b||