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<div class="title">Eigen Namespace Reference<div class="ingroups"><a class="el" href="group__IterativeSolvers__Module.html">Iterative solvers module</a></div></div> </div>
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<p>iterative scaling algorithm to equilibrate rows and column norms in matrices
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<table class="memberdecls">
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Classes</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1AlignedVector3.html">AlignedVector3</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">A vectorization friendly 3D vector. <a href="classEigen_1_1AlignedVector3.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1AutoDiffScalar.html">AutoDiffScalar</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">A scalar type replacement with automatic differentation capability. <a href="classEigen_1_1AutoDiffScalar.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1BDCSVD.html">BDCSVD</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">class Bidiagonal Divide and Conquer SVD <a href="classEigen_1_1BDCSVD.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DGMRES.html">DGMRES</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">A Restarted <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems. ">GMRES</a> with deflation. This class implements a modification of the <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems. ">GMRES</a> solver for sparse linear systems. The basis is built with modified Gram-Schmidt. At each restart, a few approximated eigenvectors corresponding to the smallest eigenvalues are used to build a preconditioner for the next cycle. This preconditioner for deflation can be combined with any other preconditioner, the IncompleteLUT for instance. The preconditioner is applied at right of the matrix and the combination is multiplicative. <a href="classEigen_1_1DGMRES.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1DynamicSparseMatrix.html">DynamicSparseMatrix</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">A sparse matrix class designed for matrix assembly purpose. <a href="classEigen_1_1DynamicSparseMatrix.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1GMRES.html">GMRES</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">A <a class="el" href="classEigen_1_1GMRES.html" title="A GMRES solver for sparse square problems. ">GMRES</a> solver for sparse square problems. <a href="classEigen_1_1GMRES.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1HybridNonLinearSolver.html">HybridNonLinearSolver</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Finds a zero of a system of n nonlinear functions in n variables by a modification of the Powell hybrid method ("dogleg"). <a href="classEigen_1_1HybridNonLinearSolver.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IncompleteCholesky.html">IncompleteCholesky</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Modified Incomplete Cholesky with dual threshold. <a href="classEigen_1_1IncompleteCholesky.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1IterationController.html">IterationController</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Controls the iterations of the iterative solvers. <a href="classEigen_1_1IterationController.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiSVD.html">JacobiSVD</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Two-sided Jacobi SVD decomposition of a rectangular matrix. <a href="classEigen_1_1JacobiSVD.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1KdBVH.html">KdBVH</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">A simple bounding volume hierarchy based on AlignedBox. <a href="classEigen_1_1KdBVH.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1KroneckerProduct.html">KroneckerProduct</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Kronecker tensor product helper class for dense matrices. <a href="classEigen_1_1KroneckerProduct.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1KroneckerProductSparse.html">KroneckerProductSparse</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Kronecker tensor product helper class for sparse matrices. <a href="classEigen_1_1KroneckerProductSparse.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1LevenbergMarquardt.html">LevenbergMarquardt</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Performs non linear optimization over a non-linear function, using a variant of the Levenberg Marquardt algorithm. <a href="classEigen_1_1LevenbergMarquardt.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixExponential.html">MatrixExponential</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Class for computing the matrix exponential. <a href="classEigen_1_1MatrixExponential.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct  </td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1MatrixExponentialReturnValue.html">MatrixExponentialReturnValue</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Proxy for the matrix exponential of some matrix (expression). <a href="structEigen_1_1MatrixExponentialReturnValue.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixFunction.html">MatrixFunction</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Class for computing matrix functions. <a href="classEigen_1_1MatrixFunction.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixFunctionAtomic.html">MatrixFunctionAtomic</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Helper class for computing matrix functions of atomic matrices. <a href="classEigen_1_1MatrixFunctionAtomic.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixFunctionReturnValue.html">MatrixFunctionReturnValue</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Proxy for the matrix function of some matrix (expression). <a href="classEigen_1_1MatrixFunctionReturnValue.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixLogarithmAtomic.html">MatrixLogarithmAtomic</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Helper class for computing matrix logarithm of atomic matrices. <a href="classEigen_1_1MatrixLogarithmAtomic.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixLogarithmReturnValue.html">MatrixLogarithmReturnValue</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Proxy for the matrix logarithm of some matrix (expression). <a href="classEigen_1_1MatrixLogarithmReturnValue.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixMarketIterator.html">MatrixMarketIterator</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Iterator to browse matrices from a specified folder. <a href="classEigen_1_1MatrixMarketIterator.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixPower.html">MatrixPower</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Class for computing matrix powers. <a href="classEigen_1_1MatrixPower.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixPowerReturnValue.html">MatrixPowerReturnValue</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Proxy for the matrix power of some matrix (expression). <a href="classEigen_1_1MatrixPowerReturnValue.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixSquareRoot.html">MatrixSquareRoot</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Class for computing matrix square roots of general matrices. <a href="classEigen_1_1MatrixSquareRoot.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixSquareRootQuasiTriangular.html">MatrixSquareRootQuasiTriangular</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Class for computing matrix square roots of upper quasi-triangular matrices. <a href="classEigen_1_1MatrixSquareRootQuasiTriangular.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixSquareRootReturnValue.html">MatrixSquareRootReturnValue</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Proxy for the matrix square root of some matrix (expression). <a href="classEigen_1_1MatrixSquareRootReturnValue.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MatrixSquareRootTriangular.html">MatrixSquareRootTriangular</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Class for computing matrix square roots of upper triangular matrices. <a href="classEigen_1_1MatrixSquareRootTriangular.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1MINRES.html">MINRES</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">A minimal residual solver for sparse symmetric problems. <a href="classEigen_1_1MINRES.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1NumericalDiff.html">NumericalDiff</a></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1PolynomialSolver.html">PolynomialSolver</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">A polynomial solver. <a href="classEigen_1_1PolynomialSolver.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1PolynomialSolverBase.html">PolynomialSolverBase</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Defined to be inherited by polynomial solvers: it provides convenient methods such as. <a href="classEigen_1_1PolynomialSolverBase.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1RandomSetter.html">RandomSetter</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">The <a class="el" href="classEigen_1_1RandomSetter.html" title="The RandomSetter is a wrapper object allowing to set/update a sparse matrix with random access...">RandomSetter</a> is a wrapper object allowing to set/update a sparse matrix with random access. <a href="classEigen_1_1RandomSetter.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SkylineInplaceLU.html">SkylineInplaceLU</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Inplace LU decomposition of a skyline matrix and associated features. <a href="classEigen_1_1SkylineInplaceLU.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SkylineMatrix.html">SkylineMatrix</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">The main skyline matrix class. <a href="classEigen_1_1SkylineMatrix.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SkylineMatrixBase.html">SkylineMatrixBase</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Base class of any skyline matrices or skyline expressions. <a href="classEigen_1_1SkylineMatrixBase.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SkylineStorage.html">SkylineStorage</a></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Spline.html">Spline</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">A class representing multi-dimensional spline curves. <a href="classEigen_1_1Spline.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct  </td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1SplineFitting.html">SplineFitting</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight"><a class="el" href="classEigen_1_1Spline.html" title="A class representing multi-dimensional spline curves. ">Spline</a> fitting methods. <a href="structEigen_1_1SplineFitting.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct  </td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1SplineTraits_3_01Spline_3_01__Scalar_00_01__Dim_00_01__Degree_01_4_00_01__DerivativeOrder_01_4.html">SplineTraits< Spline< _Scalar, _Dim, _Degree >, _DerivativeOrder ></a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Compile-time attributes of the <a class="el" href="classEigen_1_1Spline.html" title="A class representing multi-dimensional spline curves. ">Spline</a> class for fixed degree. <a href="structEigen_1_1SplineTraits_3_01Spline_3_01__Scalar_00_01__Dim_00_01__Degree_01_4_00_01__DerivativeOrder_01_4.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct  </td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1SplineTraits_3_01Spline_3_01__Scalar_00_01__Dim_00_01__Degree_01_4_00_01Dynamic_01_4.html">SplineTraits< Spline< _Scalar, _Dim, _Degree >, Dynamic ></a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Compile-time attributes of the <a class="el" href="classEigen_1_1Spline.html" title="A class representing multi-dimensional spline curves. ">Spline</a> class for Dynamic degree. <a href="structEigen_1_1SplineTraits_3_01Spline_3_01__Scalar_00_01__Dim_00_01__Degree_01_4_00_01Dynamic_01_4.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct  </td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1StdMapTraits.html">StdMapTraits</a></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1StdStemFunctions.html">StdStemFunctions</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Stem functions corresponding to standard mathematical functions. <a href="classEigen_1_1StdStemFunctions.html#details">More...</a><br/></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html">SVDBase</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Mother class of SVD classes algorithms. <a href="classEigen_1_1SVDBase.html#details">More...</a><br/></td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="typedef-members"></a>
Typedefs</h2></td></tr>
<tr class="memitem:ac873daea7b3a9b6b8f7871c870d2ebe6"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ac873daea7b3a9b6b8f7871c870d2ebe6"></a>
typedef <a class="el" href="classEigen_1_1Spline.html">Spline</a>< double, 2 > </td><td class="memItemRight" valign="bottom"><a class="el" href="namespaceEigen.html#ac873daea7b3a9b6b8f7871c870d2ebe6">Spline2d</a></td></tr>
<tr class="memdesc:ac873daea7b3a9b6b8f7871c870d2ebe6"><td class="mdescLeft"> </td><td class="mdescRight">2D double B-spline with dynamic degree. <br/></td></tr>
<tr class="separator:ac873daea7b3a9b6b8f7871c870d2ebe6"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a1bd2c65ab58ac9650d544d48eb9b344f"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a1bd2c65ab58ac9650d544d48eb9b344f"></a>
typedef <a class="el" href="classEigen_1_1Spline.html">Spline</a>< float, 2 > </td><td class="memItemRight" valign="bottom"><a class="el" href="namespaceEigen.html#a1bd2c65ab58ac9650d544d48eb9b344f">Spline2f</a></td></tr>
<tr class="memdesc:a1bd2c65ab58ac9650d544d48eb9b344f"><td class="mdescLeft"> </td><td class="mdescRight">2D float B-spline with dynamic degree. <br/></td></tr>
<tr class="separator:a1bd2c65ab58ac9650d544d48eb9b344f"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:afe16609b15ce4504173a6eaabe900f35"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="afe16609b15ce4504173a6eaabe900f35"></a>
typedef <a class="el" href="classEigen_1_1Spline.html">Spline</a>< double, 3 > </td><td class="memItemRight" valign="bottom"><a class="el" href="namespaceEigen.html#afe16609b15ce4504173a6eaabe900f35">Spline3d</a></td></tr>
<tr class="memdesc:afe16609b15ce4504173a6eaabe900f35"><td class="mdescLeft"> </td><td class="mdescRight">3D double B-spline with dynamic degree. <br/></td></tr>
<tr class="separator:afe16609b15ce4504173a6eaabe900f35"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a39ab6860f203ce6726ddc9522b2826e9"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a39ab6860f203ce6726ddc9522b2826e9"></a>
typedef <a class="el" href="classEigen_1_1Spline.html">Spline</a>< float, 3 > </td><td class="memItemRight" valign="bottom"><a class="el" href="namespaceEigen.html#a39ab6860f203ce6726ddc9522b2826e9">Spline3f</a></td></tr>
<tr class="memdesc:a39ab6860f203ce6726ddc9522b2826e9"><td class="mdescLeft"> </td><td class="mdescRight">3D float B-spline with dynamic degree. <br/></td></tr>
<tr class="separator:a39ab6860f203ce6726ddc9522b2826e9"><td class="memSeparator" colspan="2"> </td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a07d8e283f082c972338f3fc4f644b2a9"><td class="memTemplParams" colspan="2">template<typename BVH , typename Intersector > </td></tr>
<tr class="memitem:a07d8e283f082c972338f3fc4f644b2a9"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceEigen.html#a07d8e283f082c972338f3fc4f644b2a9">BVIntersect</a> (const BVH &tree, Intersector &intersector)</td></tr>
<tr class="separator:a07d8e283f082c972338f3fc4f644b2a9"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ac3b8047a3ee05b5e6fec4668197a9a43"><td class="memTemplParams" colspan="2">template<typename BVH1 , typename BVH2 , typename Intersector > </td></tr>
<tr class="memitem:ac3b8047a3ee05b5e6fec4668197a9a43"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceEigen.html#ac3b8047a3ee05b5e6fec4668197a9a43">BVIntersect</a> (const BVH1 &tree1, const BVH2 &tree2, Intersector &intersector)</td></tr>
<tr class="separator:ac3b8047a3ee05b5e6fec4668197a9a43"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:adcbe73ac1482eacab0e18ee32c25508e"><td class="memTemplParams" colspan="2">template<typename BVH , typename Minimizer > </td></tr>
<tr class="memitem:adcbe73ac1482eacab0e18ee32c25508e"><td class="memTemplItemLeft" align="right" valign="top">Minimizer::Scalar </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceEigen.html#adcbe73ac1482eacab0e18ee32c25508e">BVMinimize</a> (const BVH &tree, Minimizer &minimizer)</td></tr>
<tr class="separator:adcbe73ac1482eacab0e18ee32c25508e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a915f6adc8b195c94a83c35de6a842556"><td class="memTemplParams" colspan="2">template<typename BVH1 , typename BVH2 , typename Minimizer > </td></tr>
<tr class="memitem:a915f6adc8b195c94a83c35de6a842556"><td class="memTemplItemLeft" align="right" valign="top">Minimizer::Scalar </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceEigen.html#a915f6adc8b195c94a83c35de6a842556">BVMinimize</a> (const BVH1 &tree1, const BVH2 &tree2, Minimizer &minimizer)</td></tr>
<tr class="separator:a915f6adc8b195c94a83c35de6a842556"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga375e3ea1f370fb76dfe0f43a89b95926"><td class="memTemplParams" colspan="2">template<typename Polynomial > </td></tr>
<tr class="memitem:ga375e3ea1f370fb76dfe0f43a89b95926"><td class="memTemplItemLeft" align="right" valign="top">NumTraits< typename <br class="typebreak"/>
Polynomial::Scalar >::Real </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__Polynomials__Module.html#ga375e3ea1f370fb76dfe0f43a89b95926">cauchy_max_bound</a> (const Polynomial &poly)</td></tr>
<tr class="separator:ga375e3ea1f370fb76dfe0f43a89b95926"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gab076afbdba0e9298a541cc4e8cc7506b"><td class="memTemplParams" colspan="2">template<typename Polynomial > </td></tr>
<tr class="memitem:gab076afbdba0e9298a541cc4e8cc7506b"><td class="memTemplItemLeft" align="right" valign="top">NumTraits< typename <br class="typebreak"/>
Polynomial::Scalar >::Real </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__Polynomials__Module.html#gab076afbdba0e9298a541cc4e8cc7506b">cauchy_min_bound</a> (const Polynomial &poly)</td></tr>
<tr class="separator:gab076afbdba0e9298a541cc4e8cc7506b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga1b4cbde5d98411405871accf877552d2"><td class="memTemplParams" colspan="2">template<typename PointArrayType , typename KnotVectorType > </td></tr>
<tr class="memitem:ga1b4cbde5d98411405871accf877552d2"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__Splines__Module.html#ga1b4cbde5d98411405871accf877552d2">ChordLengths</a> (const PointArrayType &pts, KnotVectorType &chord_lengths)</td></tr>
<tr class="memdesc:ga1b4cbde5d98411405871accf877552d2"><td class="mdescLeft"> </td><td class="mdescRight">Computes chord length parameters which are required for spline interpolation. <a href="group__Splines__Module.html#ga1b4cbde5d98411405871accf877552d2">More...</a><br/></td></tr>
<tr class="separator:ga1b4cbde5d98411405871accf877552d2"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga9474da5ed68bbd9a6788a999330416d6"><td class="memTemplParams" colspan="2">template<typename KnotVectorType > </td></tr>
<tr class="memitem:ga9474da5ed68bbd9a6788a999330416d6"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__Splines__Module.html#ga9474da5ed68bbd9a6788a999330416d6">KnotAveraging</a> (const KnotVectorType &parameters, DenseIndex degree, KnotVectorType &knots)</td></tr>
<tr class="memdesc:ga9474da5ed68bbd9a6788a999330416d6"><td class="mdescLeft"> </td><td class="mdescRight">Computes knot averages.The knots are computed as </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\begin{align*} u_0 & = \hdots = u_p = 0 \\ u_{m-p} & = \hdots = u_{m} = 1 \\ u_{j+p} & = \frac{1}{p}\sum_{i=j}^{j+p-1}\bar{u}_i \quad\quad j=1,\hdots,n-p \end{align*}" src="form_90.png"/>
</p>
<p> where <img class="formulaInl" alt="$p$" src="form_87.png"/> is the degree and <img class="formulaInl" alt="$m+1$" src="form_91.png"/> the number knots of the desired interpolating spline. <a href="group__Splines__Module.html#ga9474da5ed68bbd9a6788a999330416d6">More...</a><br/></td></tr>
<tr class="separator:ga9474da5ed68bbd9a6788a999330416d6"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaa8924dffc6cee7aa1e908dc395a7a167"><td class="memTemplParams" colspan="2">template<typename A , typename B > </td></tr>
<tr class="memitem:gaa8924dffc6cee7aa1e908dc395a7a167"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1KroneckerProduct.html">KroneckerProduct</a>< A, B > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__KroneckerProduct__Module.html#gaa8924dffc6cee7aa1e908dc395a7a167">kroneckerProduct</a> (const MatrixBase< A > &a, const MatrixBase< B > &b)</td></tr>
<tr class="separator:gaa8924dffc6cee7aa1e908dc395a7a167"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaca497f43cc92bcbf6eaff64984a266cc"><td class="memTemplParams" colspan="2">template<typename A , typename B > </td></tr>
<tr class="memitem:gaca497f43cc92bcbf6eaff64984a266cc"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1KroneckerProductSparse.html">KroneckerProductSparse</a>< A, B > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__KroneckerProduct__Module.html#gaca497f43cc92bcbf6eaff64984a266cc">kroneckerProduct</a> (const EigenBase< A > &a, const EigenBase< B > &b)</td></tr>
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<tr class="memitem:gadb64ffddaa9e83634e3ab0e3fd3664f5"><td class="memTemplParams" colspan="2">template<typename Polynomials , typename T > </td></tr>
<tr class="memitem:gadb64ffddaa9e83634e3ab0e3fd3664f5"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__Polynomials__Module.html#gadb64ffddaa9e83634e3ab0e3fd3664f5">poly_eval</a> (const Polynomials &poly, const T &x)</td></tr>
<tr class="separator:gadb64ffddaa9e83634e3ab0e3fd3664f5"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaadbf059bc28ce1cf94c57c1454633d40"><td class="memTemplParams" colspan="2">template<typename Polynomials , typename T > </td></tr>
<tr class="memitem:gaadbf059bc28ce1cf94c57c1454633d40"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__Polynomials__Module.html#gaadbf059bc28ce1cf94c57c1454633d40">poly_eval_horner</a> (const Polynomials &poly, const T &x)</td></tr>
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<tr class="memitem:gafbc3648f7ef67db3d5d04454fc1257fd"><td class="memTemplParams" colspan="2">template<typename RootVector , typename Polynomial > </td></tr>
<tr class="memitem:gafbc3648f7ef67db3d5d04454fc1257fd"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__Polynomials__Module.html#gafbc3648f7ef67db3d5d04454fc1257fd">roots_to_monicPolynomial</a> (const RootVector &rv, Polynomial &poly)</td></tr>
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</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>iterative scaling algorithm to equilibrate rows and column norms in matrices </p>
<p>This class can be used as a preprocessing tool to accelerate the convergence of iterative methods</p>
<p>This feature is useful to limit the pivoting amount during LU/ILU factorization The scaling strategy as presented here preserves the symmetry of the problem NOTE It is assumed that the matrix does not have empty row or column,</p>
<p>Example with key steps </p>
<div class="fragment"><div class="line">* VectorXd x(n), b(n);</div>
<div class="line">* SparseMatrix<double> A;</div>
<div class="line">* <span class="comment">// fill A and b;</span></div>
<div class="line">* IterScaling<SparseMatrix<double> > scal; </div>
<div class="line">* <span class="comment">// Compute the left and right scaling vectors. The matrix is equilibrated at output</span></div>
<div class="line">* scal.computeRef(A); </div>
<div class="line">* <span class="comment">// Scale the right hand side</span></div>
<div class="line">* b = scal.LeftScaling().cwiseProduct(b); </div>
<div class="line">* <span class="comment">// Now, solve the equilibrated linear system with any available solver</span></div>
<div class="line">* </div>
<div class="line">* <span class="comment">// Scale back the computed solution</span></div>
<div class="line">* x = scal.RightScaling().cwiseProduct(x); </div>
<div class="line">* </div>
</div><!-- fragment --><dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">_MatrixType</td><td>the type of the matrix. It should be a real square sparsematrix</td></tr>
</table>
</dd>
</dl>
<p>References : D. Ruiz and B. Ucar, A Symmetry Preserving Algorithm for Matrix Scaling, INRIA Research report RR-7552</p>
<dl class="section see"><dt>See Also</dt><dd>IncompleteLUT </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<td class="memname">void Eigen::BVIntersect </td>
<td>(</td>
<td class="paramtype">const BVH & </td>
<td class="paramname"><em>tree</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Intersector & </td>
<td class="paramname"><em>intersector</em> </td>
</tr>
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<td>)</td>
<td></td><td></td>
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<p>Given a BVH, runs the query encapsulated by <em>intersector</em>. The Intersector type must provide the following members:</p>
<div class="fragment"><div class="line"><span class="keywordtype">bool</span> intersectVolume(<span class="keyword">const</span> BVH::Volume &volume) <span class="comment">//returns true if volume intersects the query</span></div>
<div class="line"><span class="keywordtype">bool</span> intersectObject(<span class="keyword">const</span> BVH::Object &<span class="keywordtype">object</span>) <span class="comment">//returns true if the search should terminate immediately</span></div>
</div><!-- fragment -->
</div>
</div>
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<td class="memname">void Eigen::BVIntersect </td>
<td>(</td>
<td class="paramtype">const BVH1 & </td>
<td class="paramname"><em>tree1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const BVH2 & </td>
<td class="paramname"><em>tree2</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Intersector & </td>
<td class="paramname"><em>intersector</em> </td>
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<td></td>
<td>)</td>
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<p>Given two BVH's, runs the query on their Cartesian product encapsulated by <em>intersector</em>. The Intersector type must provide the following members:</p>
<div class="fragment"><div class="line"><span class="keywordtype">bool</span> intersectVolumeVolume(<span class="keyword">const</span> BVH1::Volume &v1, <span class="keyword">const</span> BVH2::Volume &v2) <span class="comment">//returns true if product of volumes intersects the query</span></div>
<div class="line"><span class="keywordtype">bool</span> intersectVolumeObject(<span class="keyword">const</span> BVH1::Volume &v1, <span class="keyword">const</span> BVH2::Object &o2) <span class="comment">//returns true if the volume-object product intersects the query</span></div>
<div class="line"><span class="keywordtype">bool</span> intersectObjectVolume(<span class="keyword">const</span> BVH1::Object &o1, <span class="keyword">const</span> BVH2::Volume &v2) <span class="comment">//returns true if the volume-object product intersects the query</span></div>
<div class="line"><span class="keywordtype">bool</span> intersectObjectObject(<span class="keyword">const</span> BVH1::Object &o1, <span class="keyword">const</span> BVH2::Object &o2) <span class="comment">//returns true if the search should terminate immediately</span></div>
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<td class="memname">Minimizer::Scalar Eigen::BVMinimize </td>
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<td class="paramtype">const BVH & </td>
<td class="paramname"><em>tree</em>, </td>
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<p>Given a BVH, runs the query encapsulated by <em>minimizer</em>. </p>
<dl class="section return"><dt>Returns</dt><dd>the minimum value. The Minimizer type must provide the following members:<div class="fragment"><div class="line"><span class="keyword">typedef</span> Scalar <span class="comment">//the numeric type of what is being minimized--not necessarily the Scalar type of the BVH (if it has one)</span></div>
<div class="line">Scalar minimumOnVolume(<span class="keyword">const</span> BVH::Volume &volume)</div>
<div class="line">Scalar minimumOnObject(<span class="keyword">const</span> BVH::Object &<span class="keywordtype">object</span>)</div>
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<td class="memname">Minimizer::Scalar Eigen::BVMinimize </td>
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<td class="paramtype">const BVH1 & </td>
<td class="paramname"><em>tree1</em>, </td>
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<td class="paramtype">const BVH2 & </td>
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<p>Given two BVH's, runs the query on their cartesian product encapsulated by <em>minimizer</em>. </p>
<dl class="section return"><dt>Returns</dt><dd>the minimum value. The Minimizer type must provide the following members:<div class="fragment"><div class="line"><span class="keyword">typedef</span> Scalar <span class="comment">//the numeric type of what is being minimized--not necessarily the Scalar type of the BVH (if it has one)</span></div>
<div class="line">Scalar minimumOnVolumeVolume(<span class="keyword">const</span> BVH1::Volume &v1, <span class="keyword">const</span> BVH2::Volume &v2)</div>
<div class="line">Scalar minimumOnVolumeObject(<span class="keyword">const</span> BVH1::Volume &v1, <span class="keyword">const</span> BVH2::Object &o2)</div>
<div class="line">Scalar minimumOnObjectVolume(<span class="keyword">const</span> BVH1::Object &o1, <span class="keyword">const</span> BVH2::Volume &v2)</div>
<div class="line">Scalar minimumOnObjectObject(<span class="keyword">const</span> BVH1::Object &o1, <span class="keyword">const</span> BVH2::Object &o2)</div>
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