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| <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> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: DecompositionSolver.java 1566017 2014-02-08 14:13:34Z tn $</dd></dl> |
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| <h3>Method Summary</h3> |
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| <caption><span>Methods</span><span class="tabEnd"> </span></caption> |
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| <th class="colFirst" scope="col">Modifier and Type</th> |
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| <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> |
| </td> |
| </tr> |
| <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> |
| </td> |
| </tr> |
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| <a name="solve(org.apache.commons.math3.linear.RealVector)"> |
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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> |
| </li> |
| </ul> |
| <a name="solve(org.apache.commons.math3.linear.RealMatrix)"> |
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| </a> |
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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> |
| </li> |
| </ul> |
| <a name="isNonSingular()"> |
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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> |
| </li> |
| </ul> |
| <a name="getInverse()"> |
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| </a> |
| <ul class="blockListLast"> |
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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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