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some clean-up and new comments.

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This commit is contained in:
giacomo po 2012-09-24 09:20:40 -07:00
parent 18c41aa04f
commit fd0441baee
1 changed files with 8 additions and 16 deletions
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24
unsupported/Eigen/src/IterativeSolvers/MINRES.h
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@ -41,10 +41,6 @@ namespace Eigen {
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)
// // Compute initial residual
// const VectorType residual(rhs-mat*x);
// RealScalar residualNorm2(residual.squaredNorm());
// Initialize preconditioned Lanczos
// VectorType v_old(N); // will be initialized inside loop
@ -70,16 +66,14 @@ namespace Eigen {
VectorType p(p_old); // initialize p=0
RealScalar eta(1.0);
//int n = 0;
iters = 0;
// while ( n < maxIters ){
iters = 0; // reset iters
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
* the Lanczos method for the eigenproblem. IMA Journal of Applied
* Mathematics, 10(3), 373–381. The current implementation corresonds
* Mathematics, 10(3), 373–381. The current implementation corresponds
* to the case A(2,7) in the paper. It also corresponds to
* algorithm 6.14 in Y. Saad, Iterative Methods for Sparse Linear
* Systems, 2003 p.173. For the preconditioned version see
@ -87,10 +81,10 @@ namespace Eigen {
*/
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);
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);
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
@ -113,9 +107,9 @@ namespace Eigen {
// Update solution
// p_oold = p_old;
const VectorType p_oold(p_old);
const VectorType p_oold(p_old); // NOT SURE IF CREATING p_oold EVERY ITERATION IS EFFICIENT
p_old = p;
p=(w-r2*p_old-r3*p_oold) /r1;
p.noalias()=(w-r2*p_old-r3*p_oold) /r1; // IS NOALIAS REQUIRED?
x += beta_one*c*eta*p;
residualNorm2 *= s*s;
@ -124,11 +118,9 @@ namespace Eigen {
}
eta=-s*eta; // update eta
// n++; // increment iteration
iters++;
iters++; // increment iteration number (for output purposes)
}
tol_error = std::sqrt(residualNorm2 / rhsNorm2); // return error
// iters = n; // return number of iterations
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
}
}