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working preconditioned MINRES solver
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giacomo po
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@ -34,6 +34,7 @@
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#include "src/IterativeLinearSolvers/ConjugateGradient.h"
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#include "src/IterativeLinearSolvers/BiCGSTAB.h"
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#include "src/IterativeLinearSolvers/IncompleteLUT.h"
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#include "src/IterativeLinearSolvers/MINRES.h"
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#include "src/Core/util/ReenableStupidWarnings.h"
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@ -21,7 +21,7 @@ namespace Eigen {
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* \param mat The matrix A
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* \param rhs The right hand side vector b
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* \param x On input and initial solution, on output the computed solution.
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* \param precond A preconditioner being able to efficiently solve for an
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* \param precond A right preconditioner being able to efficiently solve for an
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* approximation of Ax=b (regardless of b)
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* \param iters On input the max number of iteration, on output the number of performed iterations.
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* \param tol_error On input the tolerance error, on output an estimation of the relative error.
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@ -36,21 +36,15 @@ namespace Eigen {
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typedef typename Dest::Scalar Scalar;
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typedef Matrix<Scalar,Dynamic,1> VectorType;
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// initialize
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const int maxIters(iters); // initialize maxIters to iters
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const int N(mat.cols()); // the size of the matrix
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const RealScalar rhsNorm2(rhs.squaredNorm());
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// const RealScalar threshold(tol_error); // threshold for original convergence criterion, see below
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const RealScalar threshold2(tol_error*tol_error*rhsNorm2); // convergence threshold
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// VectorType v(VectorType::Zero(N));
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// VectorType v_hat(rhs-mat*x);
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// Compute initial residual
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VectorType residual(rhs-mat*x);
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const VectorType residual(rhs-mat*x);
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RealScalar residualNorm2(residual.squaredNorm()); // not needed for original convergnce criterion
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// Initialize preconditioned Lanczos
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VectorType v_old(N); // will be initialized inside loop
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@ -59,34 +53,25 @@ namespace Eigen {
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VectorType w(N); // will be initialized inside loop
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VectorType w_new = precond.solve(v_new); // initialize w_new
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RealScalar beta; // will be initialized inside loop
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RealScalar beta_new = sqrt(v_new.dot(w_new));
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RealScalar beta_new2 = v_new.dot(w_new);
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assert(beta_new2 >= 0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE");
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RealScalar beta_new = sqrt(beta_new2);
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RealScalar beta_one = beta_new;
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v_new /= beta_new;
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w_new /= beta_new;
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// RealScalar beta(v_hat.norm());
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// Initialize other variables
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RealScalar c(1.0); // the cosine of the Givens rotation
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RealScalar c_old(1.0);
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RealScalar s(0.0); // the sine of the Givens rotation
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RealScalar s_old(0.0); // the sine of the Givens rotation
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VectorType p_oold(VectorType::Zero(N)); // initialize p_oold=0
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VectorType p_old(p_oold); // initialize p_old=0
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VectorType p(N); // will be initialized in loop
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//RealScalar eta(beta); // CHANGE THIS
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RealScalar norm_rMR=beta;
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const RealScalar norm_r0(beta);
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VectorType p_oold(N); // will be initialized in loop
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VectorType p_old(VectorType::Zero(N)); // initialize p_old=0
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VectorType p(p_old); // initialize p=0
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RealScalar eta(1.0);
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// VectorType v_old(N), Av(N), w_oold(N); // preallocate temporaty vectors used in iteration
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RealScalar residualNorm2; // not needed for original convergnce criterion
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int n = 0;
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while ( n < maxIters ){
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// Preconditioned Lanczos
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/* Note that there are 4 variants on the Lanczos algorithm. These are
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* described in Paige, C. C. (1972). Computational variants of
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@ -105,57 +90,29 @@ namespace Eigen {
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const RealScalar alpha = v_new.dot(w);
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v_new -= alpha*v; // overwrite v_new
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w_new = precond.solve(v_new); // overwrite w_new
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beta_new = sqrt(v_new.dot(w_new)); // compute beta_new
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v_new /= beta_new; // overwrite v_new
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w_new /= beta_new; // overwrite w_new
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beta_new2 = v_new.dot(w_new); // compute beta_new
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assert(beta_new2 >= 0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE");
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beta_new = sqrt(beta_new2); // compute beta_new
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v_new /= beta_new; // overwrite v_new for next iteration
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w_new /= beta_new; // overwrite w_new for next iteration
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//
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//
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//
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//
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//
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//
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//
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//
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// // VectorType v_old(v); // now pre-allocated
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// v_old = v;
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// v=v_hat/beta;
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//// VectorType Av(mat*v); // now pre-allocated
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// Av = mat*v;
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// RealScalar alpha(v.transpose()*Av);
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// v_hat=Av-alpha*v-beta*v_old;
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// RealScalar beta_old(beta);
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// beta=v_hat.norm();
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// Apply QR
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// RealScalar c_oold(c_old); // store old-old cosine
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// c_old=c; // store old cosine
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// RealScalar s_oold(s_old); // store old-old sine
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// s_old=s; // store old sine
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// const RealScalar r1_hat=c_old *alpha-c_oold*s_old *beta_old;
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// const RealScalar r1 =std::pow(std::pow(r1_hat,2)+std::pow(beta,2),0.5);
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// Givens rotation
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const RealScalar r2 =s*alpha+c*c_old*beta; // s, s_old, c and c_old are still from previous iteration
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const RealScalar r3 =s_old*beta; // s, s_old, c and c_old are still from previous iteration
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// Compute new Givens rotation
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const RealScalar r1_hat=c*alpha-c_old*s*beta;
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const RealScalar r1 =std::pow(std::pow(r1_hat,2)+std::pow(beta_new,2),0.5);
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const RealScalar r1 =sqrt( std::pow(r1_hat,2) + std::pow(beta_new,2) );
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c_old = c; // store for next iteration
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s_old = s; // store for next iteration
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c=r1_hat/r1; // new cosine
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s=beta/r1; // new sine
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s=beta_new/r1; // new sine
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// update w
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// VectorType w_oold(w_old); // now pre-allocated
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// Update solution
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p_oold = p_old;
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p_old = p;
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p=(w-r2*p_old-r3*p_oold) /r1;
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// update x
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x += c*eta*p;
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norm_rMR *= std::fabs(s);
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x += beta_one*c*eta*p;
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residualNorm2 *= s*s;
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residualNorm2 = (mat*x-rhs).squaredNorm(); // DOES mat*x NEED TO BE RECOMPUTED ????
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//if(norm_rMR/norm_r0 < threshold){ // original convergence criterion, does not require "mat*x"
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if ( residualNorm2 < threshold2){
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break;
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}
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@ -170,7 +127,8 @@ namespace Eigen {
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}
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template< typename _MatrixType, int _UpLo=Lower,
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typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >
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typename _Preconditioner = IdentityPreconditioner>
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// typename _Preconditioner = IdentityPreconditioner<typename _MatrixType::Scalar> > // preconditioner must be positive definite
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class MINRES;
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namespace internal {
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@ -313,7 +271,7 @@ namespace Eigen {
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template<typename Rhs,typename Dest>
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void _solve(const Rhs& b, Dest& x) const
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{
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x.setOnes();
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x.setZero();
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_solveWithGuess(b,x);
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}
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