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Bug of full pivoting LU for bad conditioned matrix ?

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boubalos
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#include <iostream>

#include <Eigen/Core>
#include <Eigen/LU>

using namespace Eigen;

Matrix<double,4,4> jac;
Matrix<double,4,1> x,b;

jac << 17.7198884285894e+000, 4.11883690761422e+000, 0.00000000000000e+000, -5.24617052307789e-018,
282.964019499566e+003, 8.19019146910978e+003, 610.800232848695e-006, -152.722940051182e-015,
41.4404126373160e+012, 1.19829427705403e+012, 8.00000000000000e+000, 283.033589126674e-006,
0.00000000000000e+000 , 0.00000000000000e+000, 0.00000000000000e+000, 8.00000000000000e+000;

b << 10.0000000000000e+003,
100.000000000000e+000,
1.00000000000000e+015,
10.0000000000000e+024;

x = jac.fullPivLu().solve(b); //does not give correct result
//x = jac.partialPivLu().solve(b); // give correct result, i.e. result of jac*x is equal to b; and the result is the same as that given by matlab's linsolve function


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