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Some minor optimization.

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This commit is contained in:
giacomo po 2012-09-24 08:33:11 -07:00
parent dd7ff3f493
commit 18c41aa04f
1 changed files with 30 additions and 23 deletions
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53
unsupported/Eigen/src/IterativeSolvers/MINRES.h
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@ -40,23 +40,24 @@ namespace Eigen {
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 rhsNorm2(rhs.squaredNorm()); const RealScalar rhsNorm2(rhs.squaredNorm());
const RealScalar threshold2(tol_error*tol_error*rhsNorm2); // convergence threshold const RealScalar threshold2(tol_error*tol_error*rhsNorm2); // convergence threshold (compared to residualNorm2)
// Compute initial residual // // Compute initial residual
const VectorType residual(rhs-mat*x); // const VectorType residual(rhs-mat*x);
RealScalar residualNorm2(residual.squaredNorm()); // not needed for original convergnce criterion // RealScalar residualNorm2(residual.squaredNorm());
// Initialize preconditioned Lanczos // 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( VectorType::Zero(N) ); //initialize v
VectorType v_new = residual; //initialize v_new VectorType v_new(rhs-mat*x); //initialize v_new
VectorType w(N); // will be initialized inside loop RealScalar residualNorm2(v_new.squaredNorm());
VectorType w_new = precond.solve(v_new); // initialize w_new // VectorType w(N); // will be initialized inside loop
RealScalar beta; // will be initialized inside loop VectorType w_new(precond.solve(v_new)); // initialize w_new
RealScalar beta_new2 = v_new.dot(w_new); // RealScalar beta; // will be initialized inside loop
RealScalar beta_new2(v_new.dot(w_new));
assert(beta_new2 >= 0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE"); assert(beta_new2 >= 0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE");
RealScalar beta_new = sqrt(beta_new2); RealScalar beta_new(sqrt(beta_new2));
RealScalar beta_one = beta_new; const RealScalar beta_one(beta_new);
v_new /= beta_new; v_new /= beta_new;
w_new /= beta_new; w_new /= beta_new;
// Initialize other variables // Initialize other variables
@ -64,13 +65,15 @@ namespace Eigen {
RealScalar c_old(1.0); RealScalar c_old(1.0);
RealScalar s(0.0); // the sine of the Givens rotation RealScalar s(0.0); // the sine of the Givens rotation
RealScalar s_old(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_old(VectorType::Zero(N)); // initialize p_old=0
VectorType p(p_old); // initialize p=0 VectorType p(p_old); // initialize p=0
RealScalar eta(1.0); RealScalar eta(1.0);
int n = 0; //int n = 0;
while ( n < maxIters ){ iters = 0;
// while ( n < maxIters ){
while ( iters < maxIters ){
// Preconditioned Lanczos // Preconditioned Lanczos
/* Note that there are 4 variants on the Lanczos algorithm. These are /* Note that there are 4 variants on the Lanczos algorithm. These are
@ -78,14 +81,16 @@ namespace Eigen {
* the Lanczos method for the eigenproblem. IMA Journal of Applied * 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 corresonds
* to the case A(2,7) in the paper. It also corresponds to * to the case A(2,7) in the paper. It also corresponds to
* algorithm 6.14 in Y. Saad, Iterative Methods for Sparse Linear * algorithm 6.14 in Y. Saad, Iterative Methods for Sparse Linear
* Systems, 2003 p.173. For the preconditioned version see * Systems, 2003 p.173. For the preconditioned version see
* A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM (1987). * A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM (1987).
*/ */
beta = beta_new; 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 // 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);
v = v_new; // update v = v_new; // update
w = w_new; // update // w = w_new; // update
const VectorType w(w_new);
v_new.noalias() = mat*w - beta*v_old; // compute v_new v_new.noalias() = mat*w - beta*v_old; // compute v_new
const RealScalar alpha = v_new.dot(w); const RealScalar alpha = v_new.dot(w);
v_new -= alpha*v; // overwrite v_new v_new -= alpha*v; // overwrite v_new
@ -107,7 +112,8 @@ namespace Eigen {
s=beta_new/r1; // new sine s=beta_new/r1; // new sine
// Update solution // Update solution
p_oold = p_old; // p_oold = p_old;
const VectorType p_oold(p_old);
p_old = p; p_old = p;
p=(w-r2*p_old-r3*p_oold) /r1; p=(w-r2*p_old-r3*p_oold) /r1;
x += beta_one*c*eta*p; x += beta_one*c*eta*p;
@ -118,10 +124,11 @@ namespace Eigen {
} }
eta=-s*eta; // update eta eta=-s*eta; // update eta
n++; // increment iteration // n++; // increment iteration
iters++;
} }
tol_error = std::sqrt(residualNorm2 / rhsNorm2); // return error tol_error = std::sqrt(residualNorm2 / rhsNorm2); // return error
iters = n; // return number of iterations // iters = n; // return number of iterations
} }
} }