Merge branch 'pre-0.1.5' into master.

+PoDoc/DefinedTerms.m

@@ -47,8 +47,8 @@ function greensC0(do)
     function thetaj(do)
         do.addln(...
             ['the mobius transformation ', ...
-            do.eqInline('\theta_j(\zeta)'), ' w.r.t. circle ', ...
-            do.eqInline('C_j'), ' by'])
+            do.eqInline('\theta_j(\zeta)'), ' w.r.t. circles ', ...
+            do.eqInline('\{C_j:j=1,\dots,m\}'), ' by'])
         do.addln(do.eqDisplay(...
             ['\theta_j(\zeta) = \delta_j + \frac{q_j^2\zeta}', ...
             '{1 - \overline{\delta_j}\zeta}']))
@@ -57,14 +57,14 @@ function thetaj(do)
     function greensCj(do)
         PoDoc.DefinedTerms.thetaj(do)
         do.addln(...
-            ['the modified Green''s function with respect to circle ', ...
-            do.eqInline('C_j'), ' as'])
+            ['the modified Green''s function with respect to circles ', ...
+            do.eqInline('\{C_j:j=1,\dots,m\}'), ' as'])
         do.addln(do.eqDisplay(...
             ['G_j(\zeta,\alpha,\overline{\alpha}) = ' ...
             '\frac{1}{2\pi\mathrm{i}}\log \left[ ' ...
             '\frac{q_j}{|\alpha - \delta_j|}', ...
             '\frac{\omega(\zeta,\alpha)}' ...
-            '{\omega(\zeta,1/\overline{\alpha})} \right]']))
+            '{\omega(\zeta,\theta_j(1/\overline{\alpha}))} \right]']))
     end
 
     function firstKindIntegral(do)

+PoTk/Evaluable.m

@@ -24,7 +24,7 @@
 % You should have received a copy of the GNU General Public License
 % along with PoTk.  If not, see <http://www.gnu.org/licenses/>.
 
-methods
+methods(Abstract)
     v = feval(obj, z)
 end
 

+PoTk/boundaryPartMake.m

@@ -0,0 +1,52 @@
+function r = boundaryPartMake(domain, f0, f1)
+% Specify different boundary conditions on unit disk c0 the other disks c_k, k > 0.
+
+% Everett Kropf, 2016
+% Rhodri Nelson, 2016
+% 
+% This file is part of the Potential Toolkit (PoTk).
+% 
+% PoTk is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+% 
+% PoTk is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+% 
+% You should have received a copy of the GNU General Public License
+% along with PoTk.  If not, see <http://www.gnu.org/licenses/>.
+
+%boundaryPartMake makes a function to evaluate points on the boundary from
+%a list of functions.
+%
+% r = boundaryPartMake(domain, f0, f1, ..., fm)
+% Takes a list of functions and returns a function r which is restricted to
+% the boundary. The function r gives f0 values for points on C0, f1 values
+% for points on C1, etc., up to fm values for points on Cm.
+
+% Everett Kropf, 2016
+
+if ~isa(domain, 'skpDomain')
+    error('First argument must be an "skpDomain" object.')
+end
+
+if ~all(cellfun(@(x) isa(x, 'function_handle'), {f0, f1}))
+    error('Expected a list of function handles following the domain.')
+end
+
+function v = reval(z)
+    v = nan(size(z));
+    [~, onj] = ison(domain, z);
+    v(onj==0)=f0(z(onj==0));
+    for j = 1:domain.m
+        ix = onj == j;
+        v(ix) = f1(z(ix));
+    end
+end
+
+r = @reval;
+
+end

+PoTk/uniformFlowBVP.m

@@ -0,0 +1,128 @@
+classdef uniformFlowBVP < bvpFun
+% Boundary value problem for a uniform flow.
+
+% Everett Kropf, 2016
+% Rhodri Nelson, 2016
+% 
+% This file is part of the Potential Toolkit (PoTk).
+% 
+% PoTk is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+% 
+% PoTk is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+% 
+% You should have received a copy of the GNU General Public License
+% along with PoTk.  If not, see <http://www.gnu.org/licenses/>.
+
+properties(SetAccess=protected)
+    parameter
+
+    ufa
+    singCorrFact
+    normConstant = 0
+end
+
+methods
+    function guf = uniformFlowBVP(beta, U, kai, a, D)
+        if ~nargin
+            sargs = {};
+        else
+            if nargin > 5
+                sargs = {D, N};
+            else
+                sargs = {D};
+            end
+        end
+
+        guf = guf@bvpFun(sargs{:});
+        if ~nargin
+            return
+        end
+
+        guf.parameter = skpParameter(beta, guf.domain);
+        beta = guf.parameter;
+        if ~beta.inUnitDomain
+            error('SKPrime:InvalidArgument', ...
+                'Parameter must have magnitude <= 1.')
+        end
+
+        if ~isempty(beta.ison) && beta.ison == 0
+            % Beta on the unit circle means.
+            ufb = @(z) ...
+                0.5*U*(a*exp(-1i*kai)*(1./(z-beta)+0.5./beta) ...
+                -conj(a)*exp(1i*kai)*(1./(conj(beta)^2*(z-1./conj(beta)))+0.5./conj(beta)));
+        elseif ~isempty(beta.ison) && beta.ison > 0
+            error('SKPrime:UndefinedState', ...
+                'The case beta on inner boundary not implemented.')
+        elseif beta == 0
+            error('SKPrime:UndefinedState', ...
+                'The case beta == 0 not yet implemented.')
+        else
+            ufb = @(z) ...
+                U*(a*exp(-1i*kai)*(1./(z-beta)+0.5./beta) ...
+                -conj(a)*exp(1i*kai)*(1./(conj(beta)^2*(z-1./conj(beta)))+0.5./conj(beta)));
+        end
+        guf.ufa = ufb;
+
+        if guf.domain.m == 0
+            % Nothing more to do.
+            return
+        end
+
+        % Known part on the boundary.   
+        if ~isempty(beta.ison) && beta.ison == 0
+            f0 = @(z) 0.0;
+            f1 = @(z) -imag(ufb(z));
+            % Note the boundary function that comes back takes care of deciding if a
+            % given point is on a boundary or not, and what boundary it is on. (Really
+            % handled in the skpDomain class code.)
+            ha = PoTk.boundaryPartMake(D, f0, f1);  
+        else
+            ha = @(z) -imag(ufb(z));
+        end
+
+        % Solve for unknown part on the boundary.
+        % TO DO: Add case when beta is on aboundary
+        guf.phiFun = solve(guf.phiFun, ha);
+
+        % Boundary function and Cauchy interpolant.
+        guf.boundaryFunction = @(z) guf.phiFun(z) + 1i*ha(z);
+        guf.continuedFunction = SKP.bmcCauchy(...
+            guf.boundaryFunction, guf.domain, 2*guf.truncation);
+
+    end
+
+    function dgufh = diffh(guf,n)
+
+        if nargin < 2
+            n = 1;
+        end
+
+        dgufh = dftDerivative(guf, @guf.hat, n);
+
+    end
+
+    function v = feval(guf, z)
+        %provides function evaluation for the Green's function.
+
+        v = guf.ufa(z) + guf.hat(z);
+    end
+
+    function v = hat(guf, z)
+        %evaluate the "analytic" part of the function.
+
+        if guf.domain.m == 0
+            v = complex(zeros(size(z)));
+            return
+        end
+
+        v = bvpEval(guf, z);
+    end
+end
+
+end