interp_laplace.h

经典numerical receip 配套代码

struct Laplace_interp : Linbcg {
	MatDoub &mat;
	Int ii,jj;
	Int nn,iter;
	VecDoub b,y,mask;

	Laplace_interp(MatDoub_IO &matrix) : mat(matrix), ii(mat.nrows()),
	jj(mat.ncols()), nn(ii*jj), iter(0), b(nn), y(nn), mask(nn) {
		Int i,j,k;
		Doub vl = 0.;
		for (k=0;k<nn;k++) {
			i = k/jj;
			j = k - i*jj;
			if (mat[i][j] < 1.e99) {
				b[k] =  y[k] = vl = mat[i][j];
				mask[k] = 1;
			} else {
				b[k] = 0.;
				y[k] = vl;
				mask[k] = 0;
			}
		}
	}

	void asolve(VecDoub_I &b, VecDoub_O &x, const Int itrnsp);
	void atimes(VecDoub_I &x, VecDoub_O &r, const Int itrnsp);

	Doub solve(Doub tol=1.e-6, Int itmax=-1) {
		Int i,j,k;
		Doub err;
		if (itmax <= 0) itmax = 2*MAX(ii,jj);
		Linbcg::solve(b,y,1,tol,itmax,iter,err);
		for (k=0,i=0;i<ii;i++) for (j=0;j<jj;j++) mat[i][j] = y[k++];
		return err;
	}
};

void Laplace_interp::asolve(VecDoub_I &b, VecDoub_O &x, const Int itrnsp) {
	Int i,n=b.size();
	for (i=0;i<n;i++) x[i] = b[i];
}

void Laplace_interp::atimes(VecDoub_I &x, VecDoub_O &r, const Int itrnsp) {
	Int i,j,k,n=r.size(),jjt,it;
	Doub del;
	for (k=0;k<n;k++) r[k] = 0.;
	for (k=0;k<n;k++) {
		i = k/jj;
		j = k - i*jj;
		if (mask[k]) {
			r[k] += x[k];
		} else if (i>0 && i<ii-1 && j>0 && j<jj-1) {
			if (itrnsp) {
				r[k] += x[k];
				del = -0.25*x[k];
				r[k-1] += del;
				r[k+1] += del;
				r[k-jj] += del;
				r[k+jj] += del;
			} else {
				r[k] = x[k] - 0.25*(x[k-1]+x[k+1]+x[k+jj]+x[k-jj]);
			}
		} else if (i>0 && i<ii-1) {
			if (itrnsp) {
				r[k] += x[k];
				del = -0.5*x[k];
				r[k-jj] += del;
				r[k+jj] += del;
			} else {
				r[k] = x[k] - 0.5*(x[k+jj]+x[k-jj]);
			}
		} else if (j>0 && j<jj-1) {
			if (itrnsp) {
				r[k] += x[k];
				del = -0.5*x[k];
				r[k-1] += del;
				r[k+1] += del;
			} else {
				r[k] = x[k] - 0.5*(x[k+1]+x[k-1]);
			}
		} else {
			jjt = i==0 ? jj : -jj;
			it = j==0 ? 1 : -1;
			if (itrnsp) {
				r[k] += x[k];
				del = -0.5*x[k];
				r[k+jjt] += del;
				r[k+it] += del;
			} else {
				r[k] = x[k] - 0.5*(x[k+jjt]+x[k+it]);
			}
		}
	}
}