From 8c5e4fae6186004b8121276f30dd75a8b217eec9 Mon Sep 17 00:00:00 2001 From: giacomo po Date: Sat, 22 Sep 2012 15:29:00 -0700 Subject: [PATCH] working preconditioned MINRES solver --- Eigen/IterativeLinearSolvers | 1 + Eigen/src/IterativeLinearSolvers/MINRES.h | 96 +++++++---------------- 2 files changed, 28 insertions(+), 69 deletions(-) diff --git a/Eigen/IterativeLinearSolvers b/Eigen/IterativeLinearSolvers index 315c2dd1e..741bac824 100644 --- a/Eigen/IterativeLinearSolvers +++ b/Eigen/IterativeLinearSolvers @@ -34,6 +34,7 @@ #include "src/IterativeLinearSolvers/ConjugateGradient.h" #include "src/IterativeLinearSolvers/BiCGSTAB.h" #include "src/IterativeLinearSolvers/IncompleteLUT.h" +#include "src/IterativeLinearSolvers/MINRES.h" #include "src/Core/util/ReenableStupidWarnings.h" diff --git a/Eigen/src/IterativeLinearSolvers/MINRES.h b/Eigen/src/IterativeLinearSolvers/MINRES.h index 5bc4773d7..d5527a163 100644 --- a/Eigen/src/IterativeLinearSolvers/MINRES.h +++ b/Eigen/src/IterativeLinearSolvers/MINRES.h @@ -21,7 +21,7 @@ namespace Eigen { * \param mat The matrix A * \param rhs The right hand side vector b * \param x On input and initial solution, on output the computed solution. - * \param precond A preconditioner being able to efficiently solve for an + * \param precond A right preconditioner being able to efficiently solve for an * approximation of Ax=b (regardless of b) * \param iters On input the max number of iteration, on output the number of performed iterations. * \param tol_error On input the tolerance error, on output an estimation of the relative error. @@ -35,22 +35,16 @@ namespace Eigen { typedef typename Dest::RealScalar RealScalar; typedef typename Dest::Scalar Scalar; typedef Matrix VectorType; - - + // initialize const int maxIters(iters); // initialize maxIters to iters const int N(mat.cols()); // the size of the matrix 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_hat(rhs-mat*x); // Compute initial residual - VectorType residual(rhs-mat*x); - + const VectorType residual(rhs-mat*x); + RealScalar residualNorm2(residual.squaredNorm()); // not needed for original convergnce criterion // Initialize preconditioned Lanczos VectorType v_old(N); // will be initialized inside loop @@ -59,34 +53,25 @@ namespace Eigen { VectorType w(N); // will be initialized inside loop VectorType w_new = precond.solve(v_new); // initialize w_new RealScalar beta; // will be initialized inside loop - RealScalar beta_new = sqrt(v_new.dot(w_new)); + RealScalar beta_new2 = v_new.dot(w_new); + assert(beta_new2 >= 0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE"); + RealScalar beta_new = sqrt(beta_new2); + RealScalar beta_one = beta_new; v_new /= beta_new; w_new /= beta_new; - - - - // RealScalar beta(v_hat.norm()); + // Initialize other variables RealScalar c(1.0); // the cosine of the Givens rotation RealScalar c_old(1.0); RealScalar s(0.0); // the sine of the Givens rotation RealScalar s_old(0.0); // the sine of the Givens rotation - VectorType p_oold(VectorType::Zero(N)); // initialize p_oold=0 - VectorType p_old(p_oold); // initialize p_old=0 - VectorType p(N); // will be initialized in loop - - //RealScalar eta(beta); // CHANGE THIS - RealScalar norm_rMR=beta; - const RealScalar norm_r0(beta); - + VectorType p_oold(N); // will be initialized in loop + VectorType p_old(VectorType::Zero(N)); // initialize p_old=0 + VectorType p(p_old); // initialize p=0 RealScalar eta(1.0); - - // 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; while ( n < maxIters ){ - // Preconditioned Lanczos /* Note that there are 4 variants on the Lanczos algorithm. These are * described in Paige, C. C. (1972). Computational variants of @@ -105,57 +90,29 @@ namespace Eigen { const RealScalar alpha = v_new.dot(w); v_new -= alpha*v; // overwrite v_new w_new = precond.solve(v_new); // overwrite w_new - beta_new = sqrt(v_new.dot(w_new)); // compute beta_new - v_new /= beta_new; // overwrite v_new - w_new /= beta_new; // overwrite w_new + beta_new2 = v_new.dot(w_new); // compute beta_new + assert(beta_new2 >= 0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE"); + beta_new = sqrt(beta_new2); // compute beta_new + v_new /= beta_new; // overwrite v_new for next iteration + w_new /= beta_new; // overwrite w_new for next iteration -// -// -// -// -// -// -// -// -// // VectorType v_old(v); // now pre-allocated -// v_old = v; -// v=v_hat/beta; -//// VectorType Av(mat*v); // now pre-allocated -// Av = mat*v; -// RealScalar alpha(v.transpose()*Av); -// v_hat=Av-alpha*v-beta*v_old; -// RealScalar beta_old(beta); -// beta=v_hat.norm(); - - // Apply QR -// RealScalar c_oold(c_old); // store old-old cosine -// c_old=c; // store old cosine -// RealScalar s_oold(s_old); // store old-old sine -// s_old=s; // store old sine -// const RealScalar r1_hat=c_old *alpha-c_oold*s_old *beta_old; -// const RealScalar r1 =std::pow(std::pow(r1_hat,2)+std::pow(beta,2),0.5); + // Givens rotation const RealScalar r2 =s*alpha+c*c_old*beta; // s, s_old, c and c_old are still from previous iteration const RealScalar r3 =s_old*beta; // s, s_old, c and c_old are still from previous iteration - - // Compute new Givens rotation const RealScalar r1_hat=c*alpha-c_old*s*beta; - const RealScalar r1 =std::pow(std::pow(r1_hat,2)+std::pow(beta_new,2),0.5); + const RealScalar r1 =sqrt( std::pow(r1_hat,2) + std::pow(beta_new,2) ); c_old = c; // store for next iteration s_old = s; // store for next iteration c=r1_hat/r1; // new cosine - s=beta/r1; // new sine + s=beta_new/r1; // new sine - // update w - // VectorType w_oold(w_old); // now pre-allocated + // Update solution p_oold = p_old; p_old = p; p=(w-r2*p_old-r3*p_oold) /r1; - // update x - x += c*eta*p; - norm_rMR *= std::fabs(s); + x += beta_one*c*eta*p; + residualNorm2 *= s*s; - 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; } @@ -170,7 +127,8 @@ namespace Eigen { } template< typename _MatrixType, int _UpLo=Lower, - typename _Preconditioner = DiagonalPreconditioner > + typename _Preconditioner = IdentityPreconditioner> +// typename _Preconditioner = IdentityPreconditioner > // preconditioner must be positive definite class MINRES; namespace internal { @@ -313,7 +271,7 @@ namespace Eigen { template void _solve(const Rhs& b, Dest& x) const { - x.setOnes(); + x.setZero(); _solveWithGuess(b,x); }