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some optimization in MINRES, not sure about convergence criterion
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@ -38,7 +38,9 @@ namespace Eigen {
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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 threshold(tol_error); // convergence threshold
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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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RealScalar beta(v_hat.norm());
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@ -52,14 +54,19 @@ namespace Eigen {
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RealScalar norm_rMR=beta;
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const RealScalar norm_r0(beta);
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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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// Lanczos
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VectorType v_old(v);
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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);
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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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@ -80,19 +87,23 @@ namespace Eigen {
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s=beta/r1;
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// update
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VectorType w_oold(w_old);
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// VectorType w_oold(w_old); // now pre-allocated
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w_oold = w_old;
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w_old=w;
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w=(v-r3*w_oold-r2*w_old) /r1;
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x += c*eta*w;
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norm_rMR *= std::fabs(s);
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eta=-s*eta;
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//if(norm_rMR/norm_r0 < threshold){
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if ( (mat*x-rhs).norm()/rhs.norm() < threshold){
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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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n++;
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}
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tol_error = (mat*x-rhs).norm()/rhs.norm(); // return error DOES mat*x NEED TO BE RECOMPUTED???
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tol_error = std::sqrt(residualNorm2 / rhsNorm2); // return error
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iters = n; // return number of iterations
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}
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