Add function handles to kernel mtimes

Author: tristangdwl

chunkie/@kernel/mtimes.m

@@ -1,8 +1,225 @@
-function f = mtimes(f,g)
-% * Matrix multiplication for kernel
+function out = mtimes(f, g)
+% * Matrix multiplication for kernel objects.
 %
-% Currently only supports scalars
+% Scalar c * K or K * c: scales eval, shifted_eval, fmm (same as times).
 %
-% returns c*F or F*C for the kernel F and scalar c
-   f = times(f,g);
+% Left multiply M * K: M is a (p x m) matrix or function handle M(t)
+%   returning (p x m x nt). Output opdims = [p, K.opdims(2)].
+%
+% Right multiply K * N: N is a (q x p) matrix or function handle N(s)
+%   returning (q x p x ns), q = K.opdims(2). Output opdims = [K.opdims(1), p].
+
+% Determine which argument is the kernel and which is the multiplier.
+if isa(f, 'kernel') && isa(g, 'kernel')
+    error('KERNEL:mtimes:invalid', ...
+        'Cannot * two kernel objects; use + to combine.');
+end
+
+if ~isa(f, 'kernel')
+    [f, g] = deal(g, f);
+    side = 'left';
+elseif ~isa(g, 'kernel')
+    side = 'right';
+else
+    error('KERNEL:mtimes:invalid', 'Unexpected argument types.');
+end
+
+K = f;
+h = g;
+
+% scalar: delegate to times
+if isnumeric(h) && isscalar(h)
+    out = times(K, h);
+    return;
+end
+
+% constant matrix:
+if isnumeric(h) && ~isscalar(h)
+    A = h;
+    if strcmp(side, 'left')
+        assert(size(A,2) == K.opdims(1), ...
+            'KERNEL:mtimes: left matrix must have %d columns', K.opdims(1));
+        p = size(A, 1);
+    else
+        assert(size(A,1) == K.opdims(2), ...
+            'KERNEL:mtimes: right matrix must have %d rows', K.opdims(2));
+        p = size(A, 2);
+    end
+    h = A;
+end
+
+% only remaining option is a function handle
+if ~isa(h, 'function_handle') && ~isnumeric(h)
+    error('KERNEL:mtimes:invalid', ...
+        'Argument must be a scalar, matrix, or function handle.');
+end
+
+if isa(h, 'function_handle')
+    nargfunc = nargin(h);
+    assert(nargfunc==1, ...
+        'KERNEL:mtimes h must be a function of source or target, not both')
+end
+
+% probe h to determine output dimension p
+%
+% A function handle returning a (1 x 1 x n) array is treated as a
+% pointwise scalar multiplier
+ispointwise = false;
+if ~exist('p', 'var')
+    try
+        probe.r  = randn(2,1);  probe.d  = randn(2,1);
+        probe.d2 = randn(2,1);  probe.n  = randn(2,1);
+        hval = h(probe);
+        if size(hval,1) == 1 && size(hval,2) == 1
+            ispointwise = true;
+            if strcmp(side, 'left')
+                p = K.opdims(1);
+            else
+                p = K.opdims(2);
+            end
+        elseif strcmp(side, 'left')
+            p = size(hval, 1);
+        else
+            p = size(hval, 2);
+        end
+    catch
+        error('KERNEL:mtimes:probe', ...
+            'Could not probe function handle to determine output dimension.');
+    end
+end
+
+if ~ispointwise && exist('hval', 'var')
+    if strcmp(side, 'left')
+        assert(size(hval,2) == K.opdims(1), ...
+            'KERNEL:mtimes: left function handle must return matrices with %d columns', K.opdims(1));
+    else
+        assert(size(hval,1) == K.opdims(2), ...
+            'KERNEL:mtimes: right function handle must return matrices with %d rows', K.opdims(2));
+    end
+end
+
+Keval         = K.eval;
+Kshifted_eval = K.shifted_eval;
+Kfmm          = K.fmm;
+m             = K.opdims(1);
+q             = K.opdims(2);
+
+out      = K;
+out.type = ['custom_', K.type];
+out.name = ['custom ', K.name];
+
+    function fval = evalh(pts)
+        % h is either a constant (p x m) or (q x p) matrix
+        if isnumeric(h)
+            fval = h;
+        else
+            fval = h(pts);
+        end
+    end
+
+    function pts = shift_pts(pts, o)
+        % Translate the positions of pts by o
+        pts.r = pts.r + o(:);
+    end
+
+    function out = apply_left(fval, X)
+        if size(fval,1) == 1 && size(fval,2) == 1
+            out = fval .* X;
+        else
+            out = pagemtimes(fval, X);
+        end
+    end
+
+    function out = apply_right(X, fval)
+        if size(fval,1) == 1 && size(fval,2) == 1
+            out = X .* fval;
+        else
+            out = pagemtimes(X, fval);
+        end
+    end
+
+if strcmp(side, 'left')
+    out.opdims       = [p, q];
+    out.eval         = @eval_left;
+    out.fmm          = set_if_exist(Kfmm, @fmm_left);
+    out.shifted_eval = set_if_exist(Kshifted_eval, @shifted_eval_left);
+else
+    out.opdims       = [m, p];
+    out.eval         = @eval_right;
+    out.fmm          = set_if_exist(Kfmm, @fmm_right);
+    out.shifted_eval = set_if_exist(Kshifted_eval, @shifted_eval_right);
+end
+
+% left-multiply: h(t) * K(s,t)
+
+    function fval4 = reshape_fval_left(fval, nt)
+        % fval is either p x m x nt (per-target) or p x m (constant);
+        % reshape to p x m x nt x 1, broadcasting the constant case.
+        if size(fval, 3) == nt
+            fval4 = reshape(fval, size(fval,1), size(fval,2), nt, 1);
+        else
+            fval4 = reshape(fval, size(fval,1), size(fval,2), 1, 1);
+        end
+    end
+
+    function vals = eval_left(s, t)
+        nt   = size(t.r, 2);
+        fval = evalh(t);
+        Kmat = Keval(s, t);
+        K4   = reshape(Kmat, m, 1, nt, []);
+        out4 = apply_left(reshape_fval_left(fval, nt), K4);
+        vals = reshape(out4, p*nt, []);
+    end
+
+    function vals = shifted_eval_left(s, t, o)
+        nt   = size(t.r, 2);
+        fval = evalh(shift_pts(t, o));
+        Kmat = Kshifted_eval(s, t, o);
+        K4   = reshape(Kmat, m, 1, nt, []);
+        out4 = apply_left(reshape_fval_left(fval, nt), K4);
+        vals = reshape(out4, p*nt, []);
+    end
+
+    function out = fmm_left(eps, s, t, sigma)
+        nt    = size(t.r, 2);
+        fval  = evalh(t);
+        inner = Kfmm(eps, s, t, sigma);
+        out   = reshape(apply_left(fval, reshape(inner, m, 1, nt)), p*nt, 1);
+    end
+
+% right-multiply: K(s,t) * h(s)
+
+    function vals = eval_right(s, t)
+        ns   = size(s.r, 2);
+        nt   = size(t.r, 2);
+        fval = evalh(s);
+        Kmat = Keval(s, t);
+        K3   = reshape(Kmat, m*nt, q, ns);
+        vals = reshape(apply_right(K3, fval), m*nt, p*ns);
+    end
+
+    function vals = shifted_eval_right(s, t, o)
+        ns   = size(s.r, 2);
+        nt   = size(t.r, 2);
+        fval = evalh(shift_pts(s, o));
+        Kmat = Kshifted_eval(s, t, o);
+        K3   = reshape(Kmat, m*nt, q, ns);
+        vals = reshape(apply_right(K3, fval), m*nt, p*ns);
+    end
+
+    function out = fmm_right(eps, s, t, sigma)
+        ns     = size(s.r, 2);
+        fval   = evalh(s);
+        sig_in = reshape(apply_left(fval, reshape(sigma, p, 1, ns)), q, ns);
+        out    = Kfmm(eps, s, t, sig_in);
+    end
+
+end
+
+function out = set_if_exist(cond, val)
+if isa(cond, 'function_handle')
+    out = val;
+else
+    out = [];
+end
 end

chunkie/demo/demo_clamped_plate_scatter.m

@@ -37,18 +37,19 @@
 
 % assembling system matrix
 
-fkern =  @(s,t) chnk.flex2d.kern(zk, s, t, 'clamped_plate');
-
-kappa = signed_curvature(chnkr);
-kappa = kappa(:);
+fkern =  kernel(@(s,t) chnk.flex2d.kern(zk, s, t, 'clamped_plate'));
 
 opts = [];
 opts.sing = 'log';
 
+% Left-multiply by M(t) = [-2, 0; -4*kappa(t), -2] so that the diagonal
+% term becomes the identity, i.e. sys = M*K + I.
+Mfun = @(t) reshape([-2*ones(1,size(t.r(:,:),2)); -4*chnk.curvature2d(t); ...
+                     zeros(1,size(t.r(:,:),2)); -2*ones(1,size(t.r(:,:),2))], 2, 2, []);
+
 start = tic;
-sys = chunkermat(chnkr,fkern, opts);
-sys = sys - 0.5*eye(2*chnkr.npt);
-sys(2:2:end,1:2:end) = sys(2:2:end,1:2:end) + kappa.*eye(chnkr.npt);
+sys = chunkermat(chnkr, Mfun*fkern, opts);
+sys = sys + eye(2*chnkr.npt);
 
 t1 = toc(start);
 fprintf('%5.2e s : time to assemble matrix\n',t1)
@@ -57,19 +58,25 @@
 
 [r1, grad] = planewave(kvec, chnkr.r);
 
-nx = chnkr.n(1,:); 
+nx = chnkr.n(1,:);
 ny = chnkr.n(2,:);
 
-normalderiv = grad(:, 1).*(nx.')+ grad(:, 2).*(ny.');                                % Dirichlet and Neumann BC(Clamped BC)                         
+normalderiv = grad(:, 1).*(nx.')+ grad(:, 2).*(ny.');                                % Dirichlet and Neumann BC(Clamped BC)
 
 firstbc = -r1;
 secondbc = -normalderiv;
 
 rhs = zeros(2*chnkr.npt, 1); rhs(1:2:end) = firstbc ; rhs(2:2:end) = secondbc;
 
+% apply M(t) to the right-hand side
+ptinfo = []; ptinfo.r = chnkr.r(:,:); ptinfo.d = chnkr.d(:,:); ptinfo.d2 = chnkr.d2(:,:);
+kappa = chnk.curvature2d(ptinfo); kappa = kappa(:);
+rhs(2:2:end) = -4*kappa.*rhs(1:2:end) - 2*rhs(2:2:end);
+rhs(1:2:end) = -2*rhs(1:2:end);
+
 % Solving linear system
 
-start = tic; sol = gmres(sys,rhs,[],1e-12,100); t1 = toc(start);
+start = tic; sol = gmres(sys,rhs,[],1e-12,200); t1 = toc(start);
 fprintf('%5.2e s : time for dense gmres\n',t1)    
 
 % evaluate at targets and plot
@@ -109,7 +116,7 @@
 nexttile
 zztarg = nan(size(xxtarg));
 zztarg(out) = uin;
-h=pcolor(xxtarg,yytarg,imag(zztarg),"FaceColor","interp");
+h=pcolor(xxtarg,yytarg,imag(zztarg)); h.FaceColor="interp";
 set(h,'EdgeColor','none')
 clim([-maxu,maxu])
 colormap(redblue);
@@ -122,7 +129,7 @@
 nexttile
 zztarg = nan(size(xxtarg));
 zztarg(out) = uscat;
-h=pcolor(xxtarg,yytarg,imag(zztarg),"FaceColor","interp");
+h=pcolor(xxtarg,yytarg,imag(zztarg)); h.FaceColor="interp";
 set(h,'EdgeColor','none')
 clim([-maxu,maxu])
 colormap(redblue);
@@ -135,7 +142,7 @@
 nexttile
 zztarg = nan(size(xxtarg));
 zztarg(out) = utot;
-h=pcolor(xxtarg,yytarg,imag(zztarg),"FaceColor","interp");
+h=pcolor(xxtarg,yytarg,imag(zztarg)); h.FaceColor="interp";
 set(h,'EdgeColor','none')
 clim([-maxu,maxu])
 colormap(redblue);