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some optimization in MINRES, not sure about convergence criterion

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giacomo po 2012-08-30 13:10:08 +02:00
parent 064f3eff95
commit 5f3880c5a8
1 changed files with 18 additions and 7 deletions
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25
Eigen/src/IterativeLinearSolvers/MINRES.h
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@ -38,7 +38,9 @@ namespace Eigen {
// initialize // initialize
const int maxIters(iters); // initialize maxIters to iters const int maxIters(iters); // initialize maxIters to iters
const int N(mat.cols()); // the size of the matrix const int N(mat.cols()); // the size of the matrix
const RealScalar threshold(tol_error); // convergence threshold const RealScalar rhsNorm2(rhs.squaredNorm());
// const RealScalar threshold(tol_error); // threshold for original convergence criterion, see below
const RealScalar threshold2(tol_error*tol_error*rhsNorm2); // convergence threshold
VectorType v(VectorType::Zero(N)); VectorType v(VectorType::Zero(N));
VectorType v_hat(rhs-mat*x); VectorType v_hat(rhs-mat*x);
RealScalar beta(v_hat.norm()); RealScalar beta(v_hat.norm());
@ -52,14 +54,19 @@ namespace Eigen {
RealScalar norm_rMR=beta; RealScalar norm_rMR=beta;
const RealScalar norm_r0(beta); const RealScalar norm_r0(beta);
VectorType v_old(N), Av(N), w_oold(N); // preallocate temporaty vectors used in iteration
RealScalar residualNorm2; // not needed for original convergnce criterion
int n = 0; int n = 0;
while ( n < maxIters ){ while ( n < maxIters ){
// Lanczos // Lanczos
VectorType v_old(v); // VectorType v_old(v); // now pre-allocated
v_old = v;
v=v_hat/beta; v=v_hat/beta;
VectorType Av(mat*v); // VectorType Av(mat*v); // now pre-allocated
Av = mat*v;
RealScalar alpha(v.transpose()*Av); RealScalar alpha(v.transpose()*Av);
v_hat=Av-alpha*v-beta*v_old; v_hat=Av-alpha*v-beta*v_old;
RealScalar beta_old(beta); RealScalar beta_old(beta);
@ -80,19 +87,23 @@ namespace Eigen {
s=beta/r1; s=beta/r1;
// update // update
VectorType w_oold(w_old); // VectorType w_oold(w_old); // now pre-allocated
w_oold = w_old;
w_old=w; w_old=w;
w=(v-r3*w_oold-r2*w_old) /r1; w=(v-r3*w_oold-r2*w_old) /r1;
x += c*eta*w; x += c*eta*w;
norm_rMR *= std::fabs(s); norm_rMR *= std::fabs(s);
eta=-s*eta; eta=-s*eta;
//if(norm_rMR/norm_r0 < threshold){
if ( (mat*x-rhs).norm()/rhs.norm() < threshold){ residualNorm2 = (mat*x-rhs).squaredNorm(); // DOES mat*x NEED TO BE RECOMPUTED ????
//if(norm_rMR/norm_r0 < threshold){ // original convergence criterion, does not require "mat*x"
if ( residualNorm2 < threshold2){
break; break;
} }
n++; n++;
} }
tol_error = (mat*x-rhs).norm()/rhs.norm(); // return error DOES mat*x NEED TO BE RECOMPUTED??? tol_error = std::sqrt(residualNorm2 / rhsNorm2); // return error
iters = n; // return number of iterations iters = n; // return number of iterations
} }