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MINRES, bug #715: add support for zero rhs, and remove square test.

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This commit is contained in:
giacomo po 2014-03-17 16:33:52 -07:00
parent dead9085c0
commit 3e42b775ea
2 changed files with 52 additions and 27 deletions
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49
unsupported/Eigen/src/IterativeSolvers/MINRES.h
View File

@ -37,22 +37,31 @@ namespace Eigen {
typedef typename Dest::Scalar Scalar;
typedef Matrix<Scalar,Dynamic,1> VectorType;
// Check for zero rhs
const RealScalar rhsNorm2(rhs.squaredNorm());
if(rhsNorm2 == 0)
{
x.setZero();
iters = 0;
tol_error = 0;
return;
}
// 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 threshold2(tol_error*tol_error*rhsNorm2); // convergence threshold (compared to residualNorm2)
// Initialize preconditioned Lanczos
// VectorType v_old(N); // will be initialized inside loop
VectorType v_old(N); // will be initialized inside loop
VectorType v( VectorType::Zero(N) ); //initialize v
VectorType v_new(rhs-mat*x); //initialize v_new
RealScalar residualNorm2(v_new.squaredNorm());
// VectorType w(N); // will be initialized inside loop
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_new2(v_new.dot(w_new));
eigen_assert(beta_new2 >= 0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE");
eigen_assert(beta_new2 >= 0.0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE");
RealScalar beta_new(sqrt(beta_new2));
const RealScalar beta_one(beta_new);
v_new /= beta_new;
@ -62,14 +71,14 @@ namespace Eigen {
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(N); // will be initialized in loop
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);
iters = 0; // reset iters
while ( iters < maxIters ){
while ( iters < maxIters )
{
// Preconditioned Lanczos
/* Note that there are 4 variants on the Lanczos algorithm. These are
* described in Paige, C. C. (1972). Computational variants of
@ -81,17 +90,17 @@ namespace Eigen {
* A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM (1987).
*/
const RealScalar beta(beta_new);
// v_old = v; // update: at first time step, this makes v_old = 0 so value of beta doesn't matter
const VectorType v_old(v); // NOT SURE IF CREATING v_old EVERY ITERATION IS EFFICIENT
v_old = v; // update: at first time step, this makes v_old = 0 so value of beta doesn't matter
// const VectorType v_old(v); // NOT SURE IF CREATING v_old EVERY ITERATION IS EFFICIENT
v = v_new; // update
// w = w_new; // update
const VectorType w(w_new); // NOT SURE IF CREATING w EVERY ITERATION IS EFFICIENT
w = w_new; // update
// const VectorType w(w_new); // NOT SURE IF CREATING w EVERY ITERATION IS EFFICIENT
v_new.noalias() = mat*w - beta*v_old; // compute v_new
const RealScalar alpha = v_new.dot(w);
v_new -= alpha*v; // overwrite v_new
w_new = precond.solve(v_new); // overwrite w_new
beta_new2 = v_new.dot(w_new); // compute beta_new
eigen_assert(beta_new2 >= 0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE");
eigen_assert(beta_new2 >= 0.0 && "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
@ -107,28 +116,34 @@ namespace Eigen {
s=beta_new/r1; // new sine
// Update solution
// p_oold = p_old;
const VectorType p_oold(p_old); // NOT SURE IF CREATING p_oold EVERY ITERATION IS EFFICIENT
p_oold = p_old;
// const VectorType p_oold(p_old); // NOT SURE IF CREATING p_oold EVERY ITERATION IS EFFICIENT
p_old = p;
p.noalias()=(w-r2*p_old-r3*p_oold) /r1; // IS NOALIAS REQUIRED?
x += beta_one*c*eta*p;
/* Update the squared residual. Note that this is the estimated residual.
The real residual |Ax-b|^2 may be slightly larger */
residualNorm2 *= s*s;
if ( residualNorm2 < threshold2){
if ( residualNorm2 < threshold2)
{
break;
}
eta=-s*eta; // update eta
iters++; // increment iteration number (for output purposes)
}
tol_error = std::sqrt(residualNorm2 / rhsNorm2); // return error. Note that this is the estimated error. The real error |Ax-b|/|b| may be slightly larger
/* Compute error. Note that this is the estimated error. The real
error |Ax-b|/|b| may be slightly larger */
tol_error = std::sqrt(residualNorm2 / rhsNorm2);
}
}
template< typename _MatrixType, int _UpLo=Lower,
typename _Preconditioner = IdentityPreconditioner>
// typename _Preconditioner = IdentityPreconditioner<typename _MatrixType::Scalar> > // preconditioner must be positive definite
class MINRES;
namespace internal {

30
unsupported/test/minres.cpp
View File

@ -1,8 +1,8 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2012 Giacomo Po <gpo@ucla.edu>
// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
@ -14,19 +14,29 @@
template<typename T> void test_minres_T()
{
MINRES<SparseMatrix<T>, Lower, DiagonalPreconditioner<T> > minres_colmajor_diag;
MINRES<SparseMatrix<T>, Lower, IdentityPreconditioner > minres_colmajor_I;
// MINRES<SparseMatrix<T>, Lower, IncompleteLUT<T> > minres_colmajor_ilut;
//minres<SparseMatrix<T>, SSORPreconditioner<T> > minres_colmajor_ssor;
// Identity preconditioner
MINRES<SparseMatrix<T>, Lower, IdentityPreconditioner > minres_colmajor_lower_I;
MINRES<SparseMatrix<T>, Upper, IdentityPreconditioner > minres_colmajor_upper_I;
// Diagonal preconditioner
MINRES<SparseMatrix<T>, Lower, DiagonalPreconditioner<T> > minres_colmajor_lower_diag;
MINRES<SparseMatrix<T>, Upper, DiagonalPreconditioner<T> > minres_colmajor_upper_diag;
// call tests for SPD matrix
CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_lower_I) );
CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_upper_I) );
CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_lower_diag) );
CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_upper_diag) );
// TO DO: symmetric semi-definite matrix
// TO DO: symmetric indefinite matrix
CALL_SUBTEST( check_sparse_square_solving(minres_colmajor_diag) );
CALL_SUBTEST( check_sparse_spd_solving(minres_colmajor_I) );
// CALL_SUBTEST( check_sparse_square_solving(minres_colmajor_ilut) );
//CALL_SUBTEST( check_sparse_square_solving(minres_colmajor_ssor) );
}
void test_minres()
{
CALL_SUBTEST_1(test_minres_T<double>());
// CALL_SUBTEST_2(test_minres_T<std::complex<double> >());
// CALL_SUBTEST_2(test_minres_T<std::compex<double> >());
}