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<div class="subTitle">org.apache.commons.math3.linear</div>
<h2 title="Interface DecompositionSolver" class="title">Interface DecompositionSolver</h2>
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<pre>public interface <span class="strong">DecompositionSolver</span></pre>
<div class="block">Interface handling decomposition algorithms that can solve A × X = B.
<p>
Decomposition algorithms decompose an A matrix has a product of several specific
matrices from which they can solve A × X = B in least squares sense: they find X
such that ||A × X - B|| is minimal.
<p>
Some solvers like <a href="../../../../../org/apache/commons/math3/linear/LUDecomposition.html" title="class in org.apache.commons.math3.linear"><code>LUDecomposition</code></a> can only find the solution for
square matrices and when the solution is an exact linear solution, i.e. when
||A × X - B|| is exactly 0. Other solvers can also find solutions
with non-square matrix A and with non-null minimal norm. If an exact linear
solution exists it is also the minimal norm solution.</div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>2.0</dd></dl>
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<h3>Method Summary</h3>
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<caption><span>Methods</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
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<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html#getInverse()">getInverse</a></strong>()</code>
<div class="block">Get the <a href="http://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse">pseudo-inverse</a>
of the decomposed matrix.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html#isNonSingular()">isNonSingular</a></strong>()</code>
<div class="block">Check if the decomposed matrix is non-singular.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html#solve(org.apache.commons.math3.linear.RealMatrix)">solve</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> b)</code>
<div class="block">Solve the linear equation A × X = B for matrices A.</div>
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<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html#solve(org.apache.commons.math3.linear.RealVector)">solve</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b)</code>
<div class="block">Solve the linear equation A × X = B for matrices A.</div>
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<h4>solve</h4>
<pre><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> solve(<a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a> b)
throws <a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></pre>
<div class="block">Solve the linear equation A × X = B for matrices A.
<p>
The A matrix is implicit, it is provided by the underlying
decomposition algorithm.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>b</code> - right-hand side of the equation A × X = B</dd>
<dt><span class="strong">Returns:</span></dt><dd>a vector X that minimizes the two norm of A × X - B</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the matrices dimensions do not match.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if the decomposed matrix is singular.</dd></dl>
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<h4>solve</h4>
<pre><a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> solve(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> b)
throws <a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></pre>
<div class="block">Solve the linear equation A × X = B for matrices A.
<p>
The A matrix is implicit, it is provided by the underlying
decomposition algorithm.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>b</code> - right-hand side of the equation A × X = B</dd>
<dt><span class="strong">Returns:</span></dt><dd>a matrix X that minimizes the two norm of A × X - B</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the matrices dimensions do not match.</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if the decomposed matrix is singular.</dd></dl>
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<h4>isNonSingular</h4>
<pre>boolean isNonSingular()</pre>
<div class="block">Check if the decomposed matrix is non-singular.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>true if the decomposed matrix is non-singular.</dd></dl>
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<h4>getInverse</h4>
<pre><a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getInverse()
throws <a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></pre>
<div class="block">Get the <a href="http://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse">pseudo-inverse</a>
of the decomposed matrix.
<p>
<em>This is equal to the inverse of the decomposed matrix, if such an inverse exists.</em>
<p>
If no such inverse exists, then the result has properties that resemble that of an inverse.
<p>
In particular, in this case, if the decomposed matrix is A, then the system of equations
\( A x = b \) may have no solutions, or many. If it has no solutions, then the pseudo-inverse
\( A^+ \) gives the "closest" solution \( z = A^+ b \), meaning \( \left \| A z - b \right \|_2 \)
is minimized. If there are many solutions, then \( z = A^+ b \) is the smallest solution,
meaning \( \left \| z \right \|_2 \) is minimized.
<p>
Note however that some decompositions cannot compute a pseudo-inverse for all matrices.
For example, the <a href="../../../../../org/apache/commons/math3/linear/LUDecomposition.html" title="class in org.apache.commons.math3.linear"><code>LUDecomposition</code></a> is not defined for non-square matrices to begin
with. The <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear"><code>QRDecomposition</code></a> can operate on non-square matrices, but will throw
<a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear"><code>SingularMatrixException</code></a> if the decomposed matrix is singular. Refer to the javadoc
of specific decomposition implementations for more details.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>pseudo-inverse matrix (which is the inverse, if it exists),
if the decomposition can pseudo-invert the decomposed matrix</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if the decomposed matrix is singular and the decomposition
can not compute a pseudo-inverse</dd></dl>
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