forked from lijiext/lammps
156 lines
3.5 KiB
C++
156 lines
3.5 KiB
C++
//*****************************************************************
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// Iterative template routine -- GMRES
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//
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// GMRES solves the unsymmetric linear system Ax = b using the
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// Generalized Minimum Residual method
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//
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// GMRES follows the algorithm described on p. 20 of the
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// SIAM Templates book.
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//
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// The return value indicates convergence within max_iter (input)
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// iterations (0), or no convergence within max_iter iterations (1).
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//
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// Upon successful return, output arguments have the following values:
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//
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// x -- approximate solution to Ax = b
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// max_iter -- the number of iterations performed before the
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// tolerance was reached
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// tol -- the residual after the final iteration
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//
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//*****************************************************************
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#include <cmath>
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template<class Real>
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void ApplyPlaneRotation(Real &dx, Real &dy, Real &cs, Real &sn);
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template<class Real>
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void GeneratePlaneRotation(Real &dx, Real &dy, Real &cs, Real &sn);
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template < class Matrix, class Vector >
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void
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Update(Vector &x, int k, Matrix &h, Vector &s, Vector v[])
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{
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Vector y(s);
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// Backsolve:
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for (int i = k; i >= 0; i--) {
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y(i) /= h(i,i);
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for (int j = i - 1; j >= 0; j--)
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y(j) -= h(j,i) * y(i);
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}
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for (int j = 0; j <= k; j++)
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x += v[j] * y(j);
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}
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template < class Real >
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Real
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abs(Real x)
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{
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return (x > 0 ? x : -x);
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}
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template < class Operator, class Vector, class Preconditioner,
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class Matrix, class Real >
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int
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GMRES(const Operator &A, Vector &x, const Vector &b,
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const Preconditioner &M, Matrix &H, int &m, int &max_iter,
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Real &tol)
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{
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Real resid;
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int i, j = 1, k;
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Vector s(m+1), cs(m+1), sn(m+1), w;
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Vector p = inv(M)*b;
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Real normb = p.norm();
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Vector r = inv(M) * (b - A * x);
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Real beta = r.norm();
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if (normb == 0.0)
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normb = 1;
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if ((resid = r.norm() / normb) <= tol) {
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tol = resid;
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max_iter = 0;
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return 0;
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}
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Vector *v = new Vector[m+1];
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while (j <= max_iter) {
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v[0] = r * (1.0 / beta); // ??? r / beta
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s = 0.0;
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s(0) = beta;
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for (i = 0; i < m && j <= max_iter; i++, j++) {
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w = inv(M) * (A * v[i]);
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for (k = 0; k <= i; k++) {
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H(k, i) = w.dot(v[k]);
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w -= H(k, i) * v[k];
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}
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H(i+1, i) = w.norm();
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v[i+1] = w * (1.0 / H(i+1, i)); // ??? w / H(i+1, i)
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for (k = 0; k < i; k++)
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ApplyPlaneRotation(H(k,i), H(k+1,i), cs(k), sn(k));
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GeneratePlaneRotation(H(i,i), H(i+1,i), cs(i), sn(i));
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ApplyPlaneRotation(H(i,i), H(i+1,i), cs(i), sn(i));
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ApplyPlaneRotation(s(i), s(i+1), cs(i), sn(i));
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if ((resid = abs(s(i+1)) / normb) < tol) {
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Update(x, i, H, s, v);
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tol = resid;
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max_iter = j;
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delete [] v;
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return 0;
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}
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}
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Update(x, m - 1, H, s, v);
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r = inv(M) * (b - A * x);
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beta = r.norm();
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if ((resid = beta / normb) < tol) {
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tol = resid;
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max_iter = j;
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delete [] v;
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return 0;
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}
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}
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tol = resid;
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delete [] v;
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return 1;
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}
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template<class Real>
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void GeneratePlaneRotation(Real &dx, Real &dy, Real &cs, Real &sn)
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{
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if (dy == 0.0) {
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cs = 1.0;
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sn = 0.0;
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} else if (abs(dy) > abs(dx)) {
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Real temp = dx / dy;
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sn = 1.0 / sqrt( 1.0 + temp*temp );
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cs = temp * sn;
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} else {
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Real temp = dy / dx;
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cs = 1.0 / sqrt( 1.0 + temp*temp );
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sn = temp * cs;
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}
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}
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template<class Real>
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void ApplyPlaneRotation(Real &dx, Real &dy, Real &cs, Real &sn)
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{
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Real temp = cs * dx + sn * dy;
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dy = -sn * dx + cs * dy;
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dx = temp;
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}
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