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LUDecompositionQuick (Colt 1.2.0 - API Specification)
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cern.colt.matrix.linalg</FONT>
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Class LUDecompositionQuick</H2>
<PRE>
<A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/Object.html" title="class or interface in java.lang">java.lang.Object</A>
<IMG SRC="../../../../resources/inherit.gif" ALT="extended by"><B>cern.colt.matrix.linalg.LUDecompositionQuick</B>
</PRE>
<DL>
<DT><B>All Implemented Interfaces:</B> <DD><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/io/Serializable.html" title="class or interface in java.io">Serializable</A></DD>
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<DT>public class <B>LUDecompositionQuick</B><DT>extends <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/Object.html" title="class or interface in java.lang">Object</A><DT>implements <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/io/Serializable.html" title="class or interface in java.io">Serializable</A></DL>
<P>
A low level version of <A HREF="../../../../cern/colt/matrix/linalg/LUDecomposition.html" title="class in cern.colt.matrix.linalg"><CODE>LUDecomposition</CODE></A>, avoiding unnecessary memory allocation and copying.
The input to <tt>decompose</tt> methods is overriden with the result (LU).
The input to <tt>solve</tt> methods is overriden with the result (X).
In addition to <tt>LUDecomposition</tt>, this class also includes a faster variant of the decomposition, specialized for tridiagonal (and hence also diagonal) matrices,
as well as a solver tuned for vectors.
Its disadvantage is that it is a bit more difficult to use than <tt>LUDecomposition</tt>.
Thus, you may want to disregard this class and come back later, if a need for speed arises.
<p>
An instance of this class remembers the result of its last decomposition.
Usage pattern is as follows: Create an instance of this class, call a decompose method,
then retrieve the decompositions, determinant, and/or solve as many equation problems as needed.
Once another matrix needs to be LU-decomposed, you need not create a new instance of this class.
Start again by calling a decompose method, then retrieve the decomposition and/or solve your equations, and so on.
In case a <tt>LU</tt> matrix is already available, call method <tt>setLU</tt> instead of <tt>decompose</tt> and proceed with solving et al.
<p>
If a matrix shall not be overriden, use <tt>matrix.copy()</tt> and hand the the copy to methods.
<p>
For an <tt>m x n</tt> matrix <tt>A</tt> with <tt>m >= n</tt>, the LU decomposition is an <tt>m x n</tt>
unit lower triangular matrix <tt>L</tt>, an <tt>n x n</tt> upper triangular matrix <tt>U</tt>,
and a permutation vector <tt>piv</tt> of length <tt>m</tt> so that <tt>A(piv,:) = L*U</tt>;
If <tt>m < n</tt>, then <tt>L</tt> is <tt>m x m</tt> and <tt>U</tt> is <tt>m x n</tt>.
<P>
The LU decomposition with pivoting always exists, even if the matrix is
singular, so the decompose methods will never fail. The primary use of the
LU decomposition is in the solution of square systems of simultaneous
linear equations.
Attempting to solve such a system will throw an exception if <tt>isNonsingular()</tt> returns false.
<p>
<P>
<P>
<DL>
<DT><B>See Also:</B><DD><A HREF="../../../../serialized-form.html#cern.colt.matrix.linalg.LUDecompositionQuick">Serialized Form</A></DL>
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<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#LUDecompositionQuick()">LUDecompositionQuick</A></B>()</CODE>
<BR>
Constructs and returns a new LU Decomposition object with default tolerance <tt>1.0E-9</tt> for singularity detection.</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#LUDecompositionQuick(double)">LUDecompositionQuick</A></B>(double tolerance)</CODE>
<BR>
Constructs and returns a new LU Decomposition object which uses the given tolerance for singularity detection;</TD>
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<CODE> void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#decompose(cern.colt.matrix.DoubleMatrix2D)">decompose</A></B>(<A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A> A)</CODE>
<BR>
Decomposes matrix <tt>A</tt> into <tt>L</tt> and <tt>U</tt> (in-place).</TD>
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<CODE> void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#decompose(cern.colt.matrix.DoubleMatrix2D, int)">decompose</A></B>(<A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A> A,
int semiBandwidth)</CODE>
<BR>
Decomposes the banded and square matrix <tt>A</tt> into <tt>L</tt> and <tt>U</tt> (in-place).</TD>
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<CODE> double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#det()">det</A></B>()</CODE>
<BR>
Returns the determinant, <tt>det(A)</tt>.</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> <A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#getL()">getL</A></B>()</CODE>
<BR>
Returns the lower triangular factor, <tt>L</tt>.</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> <A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#getLU()">getLU</A></B>()</CODE>
<BR>
Returns a copy of the combined lower and upper triangular factor, <tt>LU</tt>.</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> int[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#getPivot()">getPivot</A></B>()</CODE>
<BR>
Returns the pivot permutation vector (not a copy of it).</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> <A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#getU()">getU</A></B>()</CODE>
<BR>
Returns the upper triangular factor, <tt>U</tt>.</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#isNonsingular()">isNonsingular</A></B>()</CODE>
<BR>
Returns whether the matrix is nonsingular (has an inverse).</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#setLU(cern.colt.matrix.DoubleMatrix2D)">setLU</A></B>(<A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A> LU)</CODE>
<BR>
Sets the combined lower and upper triangular factor, <tt>LU</tt>.</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#solve(cern.colt.matrix.DoubleMatrix1D)">solve</A></B>(<A HREF="../../../../cern/colt/matrix/DoubleMatrix1D.html" title="class in cern.colt.matrix">DoubleMatrix1D</A> B)</CODE>
<BR>
Solves the system of equations <tt>A*X = B</tt> (in-place).</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#solve(cern.colt.matrix.DoubleMatrix2D)">solve</A></B>(<A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A> B)</CODE>
<BR>
Solves the system of equations <tt>A*X = B</tt> (in-place).</TD>
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<CODE> <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/String.html" title="class or interface in java.lang">String</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#toString()">toString</A></B>()</CODE>
<BR>
Returns a String with (propertyName, propertyValue) pairs.</TD>
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<A NAME="LUDecompositionQuick()"><!-- --></A><H3>
LUDecompositionQuick</H3>
<PRE>
public <B>LUDecompositionQuick</B>()</PRE>
<DL>
<DD>Constructs and returns a new LU Decomposition object with default tolerance <tt>1.0E-9</tt> for singularity detection.
<P>
</DL>
<HR>
<A NAME="LUDecompositionQuick(double)"><!-- --></A><H3>
LUDecompositionQuick</H3>
<PRE>
public <B>LUDecompositionQuick</B>(double tolerance)</PRE>
<DL>
<DD>Constructs and returns a new LU Decomposition object which uses the given tolerance for singularity detection;
<P>
</DL>
<!-- ============ METHOD DETAIL ========== -->
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<A NAME="decompose(cern.colt.matrix.DoubleMatrix2D)"><!-- --></A><H3>
decompose</H3>
<PRE>
public void <B>decompose</B>(<A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A> A)</PRE>
<DL>
<DD>Decomposes matrix <tt>A</tt> into <tt>L</tt> and <tt>U</tt> (in-place).
Upon return <tt>A</tt> is overridden with the result <tt>LU</tt>, such that <tt>L*U = A</tt>.
Uses a "left-looking", dot-product, Crout/Doolittle algorithm.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>A</CODE> - any matrix.</DL>
</DD>
</DL>
<HR>
<A NAME="decompose(cern.colt.matrix.DoubleMatrix2D, int)"><!-- --></A><H3>
decompose</H3>
<PRE>
public void <B>decompose</B>(<A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A> A,
int semiBandwidth)</PRE>
<DL>
<DD>Decomposes the banded and square matrix <tt>A</tt> into <tt>L</tt> and <tt>U</tt> (in-place).
Upon return <tt>A</tt> is overridden with the result <tt>LU</tt>, such that <tt>L*U = A</tt>.
Currently supports diagonal and tridiagonal matrices, all other cases fall through to <A HREF="../../../../cern/colt/matrix/linalg/LUDecompositionQuick.html#decompose(cern.colt.matrix.DoubleMatrix2D)"><CODE>decompose(DoubleMatrix2D)</CODE></A>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>semiBandwidth</CODE> - == 1 --> A is diagonal, == 2 --> A is tridiagonal.<DD><CODE>A</CODE> - any matrix.</DL>
</DD>
</DL>
<HR>
<A NAME="det()"><!-- --></A><H3>
det</H3>
<PRE>
public double <B>det</B>()</PRE>
<DL>
<DD>Returns the determinant, <tt>det(A)</tt>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Throws:</B>
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/IllegalArgumentException.html" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if <tt>A.rows() != A.columns()</tt> (Matrix must be square).</DL>
</DD>
</DL>
<HR>
<A NAME="getL()"><!-- --></A><H3>
getL</H3>
<PRE>
public <A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A> <B>getL</B>()</PRE>
<DL>
<DD>Returns the lower triangular factor, <tt>L</tt>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD><tt>L</tt></DL>
</DD>
</DL>
<HR>
<A NAME="getLU()"><!-- --></A><H3>
getLU</H3>
<PRE>
public <A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A> <B>getLU</B>()</PRE>
<DL>
<DD>Returns a copy of the combined lower and upper triangular factor, <tt>LU</tt>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD><tt>LU</tt></DL>
</DD>
</DL>
<HR>
<A NAME="getPivot()"><!-- --></A><H3>
getPivot</H3>
<PRE>
public int[] <B>getPivot</B>()</PRE>
<DL>
<DD>Returns the pivot permutation vector (not a copy of it).
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>piv</DL>
</DD>
</DL>
<HR>
<A NAME="getU()"><!-- --></A><H3>
getU</H3>
<PRE>
public <A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A> <B>getU</B>()</PRE>
<DL>
<DD>Returns the upper triangular factor, <tt>U</tt>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD><tt>U</tt></DL>
</DD>
</DL>
<HR>
<A NAME="isNonsingular()"><!-- --></A><H3>
isNonsingular</H3>
<PRE>
public boolean <B>isNonsingular</B>()</PRE>
<DL>
<DD>Returns whether the matrix is nonsingular (has an inverse).
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Returns:</B><DD>true if <tt>U</tt>, and hence <tt>A</tt>, is nonsingular; false otherwise.</DL>
</DD>
</DL>
<HR>
<A NAME="setLU(cern.colt.matrix.DoubleMatrix2D)"><!-- --></A><H3>
setLU</H3>
<PRE>
public void <B>setLU</B>(<A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A> LU)</PRE>
<DL>
<DD>Sets the combined lower and upper triangular factor, <tt>LU</tt>.
The parameter is not checked; make sure it is indeed a proper LU decomposition.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
</DL>
</DD>
</DL>
<HR>
<A NAME="solve(cern.colt.matrix.DoubleMatrix1D)"><!-- --></A><H3>
solve</H3>
<PRE>
public void <B>solve</B>(<A HREF="../../../../cern/colt/matrix/DoubleMatrix1D.html" title="class in cern.colt.matrix">DoubleMatrix1D</A> B)</PRE>
<DL>
<DD>Solves the system of equations <tt>A*X = B</tt> (in-place).
Upon return <tt>B</tt> is overridden with the result <tt>X</tt>, such that <tt>L*U*X = B(piv)</tt>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>B</CODE> - A vector with <tt>B.size() == A.rows()</tt>.
<DT><B>Throws:</B>
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/IllegalArgumentException.html" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if </tt>B.size() != A.rows()</tt>.
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/IllegalArgumentException.html" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if A is singular, that is, if <tt>!isNonsingular()</tt>.
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/IllegalArgumentException.html" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if <tt>A.rows() < A.columns()</tt>.</DL>
</DD>
</DL>
<HR>
<A NAME="solve(cern.colt.matrix.DoubleMatrix2D)"><!-- --></A><H3>
solve</H3>
<PRE>
public void <B>solve</B>(<A HREF="../../../../cern/colt/matrix/DoubleMatrix2D.html" title="class in cern.colt.matrix">DoubleMatrix2D</A> B)</PRE>
<DL>
<DD>Solves the system of equations <tt>A*X = B</tt> (in-place).
Upon return <tt>B</tt> is overridden with the result <tt>X</tt>, such that <tt>L*U*X = B(piv,:)</tt>.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>B</CODE> - A matrix with as many rows as <tt>A</tt> and any number of columns.
<DT><B>Throws:</B>
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/IllegalArgumentException.html" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if </tt>B.rows() != A.rows()</tt>.
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/IllegalArgumentException.html" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if A is singular, that is, if <tt>!isNonsingular()</tt>.
<DD><CODE><A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/IllegalArgumentException.html" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if <tt>A.rows() < A.columns()</tt>.</DL>
</DD>
</DL>
<HR>
<A NAME="toString()"><!-- --></A><H3>
toString</H3>
<PRE>
public <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/String.html" title="class or interface in java.lang">String</A> <B>toString</B>()</PRE>
<DL>
<DD>Returns a String with (propertyName, propertyValue) pairs.
Useful for debugging or to quickly get the rough picture.
For example,
<pre>
rank : 3
trace : 0
</pre>
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
</DL>
</DD>
</DL>
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