doc/html/test_equilibrate.html

 // ========================================================================= //
 // This file is part of MyraMath, copyright (c) 2014-2019 by Ryan A Chilton  //
 // and distributed by MyraCore, LLC. See LICENSE.txt for license terms.      //
 // ========================================================================= //

 // Expressions.
 #include <myramath/expression/Expression.h>
 #include <myramath/expression/generators.h>
 #include <myramath/expression/arithmetic.h>
 #include <myramath/expression/functions.h>

 // Containers.
 #include <myramath/dense/DiagonalMatrix.h>
 #include <myramath/sparse/SparseMatrix.h>

 // Algorithms.
 #include <myramath/utility/random.h>
 #include <myramath/sparse/equilibrate.h>
 #include <myramath/sparse/laplacian2.h>
 #include <myramath/sparse/frobenius.h>
 #include <myramath/sparse/dimm.h>

 // Reporting.
 #include <tests/myratest.h>
 using namespace myra;

 ADD_TEST("equilibrate","[sparse]")
   {
   // Form a laplacian, rescale it randomly into D*A*D
   auto A = laplacian2<NumberD>(5,5);
   auto D = DiagonalMatrix<NumberD>::evaluate( pow(10.0,6.0*make_RandomExpression<NumberD>(A.size().first)) );
   dimm_inplace('L','N',D,A);
   dimm_inplace('R','N',D,A);
   // Make a deep copy and equilibrate it.
   auto B = A;
   auto E = equilibrate(B);
   // Verify E*B*E = A, with low relative error.
   double error = frobenius(A-E*B*E)/frobenius(A);
   myra::out() << "|A-E*B*E| = " << error << std::endl;
   REQUIRE(error < 1.0e-12);
   }

myra::pow
Expression< 1, NumberS > pow(const Expression< 1, NumberS > &A, const Expression< 1, NumberS > &B)
Returns A^B, an Expression base raised to an Expression power.
Definition: functions_power.cpp:53

generators.h
Generators for basic Expression&#39;s (constant, random, linspace, etc).

Expression.h
An interface used to fill containers from Expression&#39;s (see Matrix::evaluate(), for example)...

SparseMatrix.h
General purpose compressed-sparse-column (CSC) container.

myra
Definition: syntax.dox:1

arithmetic.h
Arithmetic operators (+,-,*,/) for Expression&#39;s.

dimm.h
Routines for multiplying by a DiagonalMatrix.

equilibrate.h
Rescales rows and columns of a symmetric SparseMatrix A, prior to direct factorization.

functions.h
Function overloads (sin, exp, etc) for Expression&#39;s.

frobenius.h
Returns frobenius norm of a SparseMatrix.

myra::Matrix::size
std::pair< int, int > size() const
Size inspector.
Definition: Matrix.cpp:116

random.h
Simplistic random number functions.

DiagonalMatrix.h
Container for a diagonal matrix, O(n) storage. Used by SVD, row/column scaling, etc.

myra::DiagonalMatrix::evaluate
static DiagonalMatrix< Number > evaluate(const Expression< 1, Number > &e)
Generates a DiagonalMatrix by evaluating an arity-1 Expression of Number.
Definition: DiagonalMatrix.cpp:258

laplacian2.h
Helper routines for reordering/filling 2D structured grids. Used by many unit tests.