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update Octave Project Developers copyright for the new year
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author | John W. Eaton <jwe@octave.org> |
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date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 7854d5752dd2 |
children | e1788b1a315f |
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######################################################################## ## ## Copyright (C) 2016-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## This file is part of Octave. ## ## Octave 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. ## ## Octave 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 Octave; see the file COPYING. If not, see ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {[@var{t}, @var{y}] =} ode15i (@var{fun}, @var{trange}, @var{y0}, @var{yp0}) ## @deftypefnx {} {[@var{t}, @var{y}] =} ode15i (@var{fun}, @var{trange}, @var{y0}, @var{yp0}, @var{ode_opt}) ## @deftypefnx {} {[@var{t}, @var{y}, @var{te}, @var{ye}, @var{ie}] =} ode15i (@dots{}) ## @deftypefnx {} {@var{solution} =} ode15i (@dots{}) ## @deftypefnx {} {} ode15i (@dots{}) ## Solve a set of fully-implicit Ordinary Differential Equations (ODEs) or ## index 1 Differential Algebraic Equations (DAEs). ## ## @code{ode15i} uses a variable step, variable order BDF (Backward ## Differentiation Formula) method that ranges from order 1 to 5. ## ## @var{fun} is a function handle, inline function, or string containing the ## name of the function that defines the ODE: @code{0 = f(t,y,yp)}. The ## function must accept three inputs where the first is time @var{t}, the ## second is the function value @var{y} (a column vector), and the third ## is the derivative value @var{yp} (a column vector). ## ## @var{trange} specifies the time interval over which the ODE will be ## evaluated. Typically, it is a two-element vector specifying the initial and ## final times (@code{[tinit, tfinal]}). If there are more than two elements ## then the solution will also be evaluated at these intermediate time ## instances. ## ## @var{y0} and @var{yp0} contain the initial values for the unknowns @var{y} ## and @var{yp}. If they are row vectors then the solution @var{y} will be a ## matrix in which each column is the solution for the corresponding initial ## value in @var{y0} and @var{yp0}. ## ## @var{y0} and @var{yp0} must be consistent initial conditions, meaning that ## @code{f(t,y0,yp0) = 0} is satisfied. The function @code{decic} may be used ## to compute consistent initial conditions given initial guesses. ## ## The optional fifth argument @var{ode_opt} specifies non-default options to ## the ODE solver. It is a structure generated by @code{odeset}. ## ## The function typically returns two outputs. Variable @var{t} is a ## column vector and contains the times where the solution was found. The ## output @var{y} is a matrix in which each column refers to a different ## unknown of the problem and each row corresponds to a time in @var{t}. ## ## The output can also be returned as a structure @var{solution} which has a ## field @var{x} containing a row vector of times where the solution was ## evaluated and a field @var{y} containing the solution matrix such that each ## column corresponds to a time in @var{x}. Use ## @w{@code{fieldnames (@var{solution})}} to see the other fields and ## additional information returned. ## ## If no output arguments are requested, and no @qcode{"OutputFcn"} is ## specified in @var{ode_opt}, then the @qcode{"OutputFcn"} is set to ## @code{odeplot} and the results of the solver are plotted immediately. ## ## If using the @qcode{"Events"} option then three additional outputs may be ## returned. @var{te} holds the time when an Event function returned a zero. ## @var{ye} holds the value of the solution at time @var{te}. @var{ie} ## contains an index indicating which Event function was triggered in the case ## of multiple Event functions. ## ## Example: Solve @nospell{Robertson's} equations: ## ## @smallexample ## @group ## function r = robertson_dae (@var{t}, @var{y}, @var{yp}) ## r = [ -(@var{yp}(1) + 0.04*@var{y}(1) - 1e4*@var{y}(2)*@var{y}(3)) ## -(@var{yp}(2) - 0.04*@var{y}(1) + 1e4*@var{y}(2)*@var{y}(3) + 3e7*@var{y}(2)^2) ## @var{y}(1) + @var{y}(2) + @var{y}(3) - 1 ]; ## endfunction ## [@var{t},@var{y}] = ode15i (@@robertson_dae, [0, 1e3], [1; 0; 0], [-1e-4; 1e-4; 0]); ## @end group ## @end smallexample ## @seealso{decic, odeset, odeget} ## @end deftypefn function varargout = ode15i (fun, trange, y0, yp0, varargin) if (nargin < 4) print_usage (); endif solver = "ode15i"; n = numel (y0); if (nargin > 4) options = varargin{1}; else options = odeset (); endif ## Check fun, trange, y0, yp0 fun = check_default_input (fun, trange, solver, y0, yp0); if (! isempty (options.Jacobian)) if (ischar (options.Jacobian)) if (! exist (options.Jacobian)) error ("Octave:invalid-input-arg", ['ode15i: "Jacobian" function "' options.Jacobian '" not found']); endif options.Jacobian = str2func (options.Jacobian); endif endif if (! isempty (options.OutputFcn)) if (ischar (options.OutputFcn)) if (! exist (options.OutputFcn)) error ("Octave:invalid-input-arg", ['ode15i: "OutputFcn" function "' options.OutputFcn '" not found']); endif options.OutputFcn = str2func (options.OutputFcn); endif if (! is_function_handle (options.OutputFcn)) error ("Octave:invalid-input-arg", 'ode15i: "OutputFcn" must be a valid function handle'); endif endif if (! isempty (options.Events)) if (ischar (options.Events)) if (! exist (options.Events)) error ("Octave:invalid-input-arg", ['ode15i: "Events" function "' options.Events '" not found']); endif options.Events = str2func (options.Events); endif if (! is_function_handle (options.Events)) error ("Octave:invalid-input-arg", 'ode15i: "Events" must be a valid function handle'); endif endif [defaults, classes, attributes] = odedefaults (n, trange(1), trange(end)); persistent ignorefields = {"NonNegative", "Mass", ... "MStateDependence", "MvPattern", ... "MassSingular", "InitialSlope", "BDF"}; defaults = rmfield (defaults, ignorefields); classes = rmfield (classes, ignorefields); attributes = rmfield (attributes, ignorefields); classes = odeset (classes, "Vectorized", {}); attributes = odeset (attributes, "Jacobian", {}, "Vectorized", {}); options = odemergeopts ("ode15i", options, defaults, classes, attributes, solver); ## Jacobian options.havejac = false; options.havejacsparse = false; options.havejacfun = false; if (! isempty (options.Jacobian)) options.havejac = true; if (iscell (options.Jacobian)) if (numel (options.Jacobian) == 2) J1 = options.Jacobian{1}; J2 = options.Jacobian{2}; if ( ! issquare (J1) || ! issquare (J2) || rows (J1) != n || rows (J2) != n || ! isnumeric (J1) || ! isnumeric (J2) || ! isreal (J1) || ! isreal (J2)) error ("Octave:invalid-input-arg", 'ode15i: "Jacobian" matrices must be real square matrices'); endif if (issparse (J1) && issparse (J2)) options.havejacsparse = true; # Jac is sparse cell endif else error ("Octave:invalid-input-arg", 'ode15i: invalid value assigned to field "Jacobian"'); endif elseif (is_function_handle (options.Jacobian)) options.havejacfun = true; if (nargin (options.Jacobian) == 3) [J1, J2] = options.Jacobian (trange(1), y0, yp0); if ( ! issquare (J1) || rows (J1) != n || ! isnumeric (J1) || ! isreal (J1) || ! issquare (J2) || rows (J2) != n || ! isnumeric (J2) || ! isreal (J2)) error ("Octave:invalid-input-arg", 'ode15i: "Jacobian" function must evaluate to a real square matrix'); endif if (issparse (J1) && issparse (J2)) options.havejacsparse = true; # Jac is sparse fun endif else error ("Octave:invalid-input-arg", 'ode15i: invalid value assigned to field "Jacobian"'); endif else error ("Octave:invalid-input-arg", 'ode15i: "Jacobian" field must be a function handle or 2-element cell array of square matrices'); endif endif ## Abstol and Reltol options.haveabstolvec = false; if (numel (options.AbsTol) != 1 && numel (options.AbsTol) != n) error ("Octave:invalid-input-arg", 'ode15i: invalid value assigned to field "AbsTol"'); elseif (numel (options.AbsTol) == n) options.haveabstolvec = true; endif ## Stats options.havestats = strcmpi (options.Stats, "on"); ## Don't use Refine when the output is a structure if (nargout == 1) options.Refine = 1; endif ## OutputFcn and OutputSel if (isempty (options.OutputFcn) && nargout == 0) options.OutputFcn = @odeplot; options.haveoutputfunction = true; else options.haveoutputfunction = ! isempty (options.OutputFcn); endif options.haveoutputselection = ! isempty (options.OutputSel); if (options.haveoutputselection) options.OutputSel = options.OutputSel - 1; endif ## Events options.haveeventfunction = ! isempty (options.Events); ## 3 arguments in the event callback of ode15i [t, y, te, ye, ie] = __ode15__ (fun, trange, y0, yp0, options, 3); if (nargout == 2) varargout{1} = t; varargout{2} = y; elseif (nargout == 1) varargout{1}.x = t.'; # Time stamps saved in field x (row vector) varargout{1}.y = y.'; # Results are saved in field y (row vector) varargout{1}.solver = solver; if (options.haveeventfunction) varargout{1}.xe = te.'; # Time info when an event occurred varargout{1}.ye = ye.'; # Results when an event occurred varargout{1}.ie = ie.'; # Index info which event occurred endif elseif (nargout > 2) varargout = cell (1,5); varargout{1} = t; varargout{2} = y; if (options.haveeventfunction) varargout{3} = te; # Time info when an event occurred varargout{4} = ye; # Results when an event occurred varargout{5} = ie; # Index info which event occurred endif endif endfunction %!demo %! ## Solve Robertson's equations with ode15i %! fun = @(t, y, yp) [-(yp(1) + 0.04*y(1) - 1e4*y(2)*y(3)); %! -(yp(2) - 0.04*y(1) + 1e4*y(2)*y(3) + 3e7*y(2)^2); %! y(1) + y(2) + y(3) - 1]; %! %! opt = odeset ("RelTol", 1e-4, "AbsTol", [1e-8, 1e-14, 1e-6]); %! y0 = [1; 0; 0]; %! yp0 = [-1e-4; 1e-4; 0]; %! tspan = [0 4*logspace(-6, 6)]; %! %! [t, y] = ode15i (fun, tspan, y0, yp0, opt); %! %! y(:,2) = 1e4 * y(:, 2); %! figure (2); %! semilogx (t, y, "o"); %! xlabel ("time"); %! ylabel ("species concentration"); %! title ("Robertson DAE problem with a Conservation Law"); %! legend ("y1", "y2", "y3"); %!function res = rob (t, y, yp) %! res =[-(yp(1) + 0.04*y(1) - 1e4*y(2)*y(3)); %! -(yp(2) - 0.04*y(1) + 1e4*y(2)*y(3) + 3e7*y(2)^2); %! y(1) + y(2) + y(3) - 1]; %!endfunction %! %!function ref = fref () %! ref = [100, 0.617234887614937, 0.000006153591397, 0.382758958793666]; %!endfunction %! %!function ref2 = fref2 () %! ref2 = [4e6 0 0 1]; %!endfunction %! %!function [DFDY, DFDYP] = jacfundense (t, y, yp) %! DFDY = [-0.04, 1e4*y(3), 1e4*y(2); %! 0.04, -1e4*y(3)-6e7*y(2), -1e4*y(2); %! 1, 1, 1]; %! DFDYP = [-1, 0, 0; %! 0, -1, 0; %! 0, 0, 0]; %!endfunction %! %!function [DFDY, DFDYP] = jacfunsparse (t, y, yp) %! DFDY = sparse ([-0.04, 1e4*y(3), 1e4*y(2); %! 0.04, -1e4*y(3)-6e7*y(2), -1e4*y(2); %! 1, 1, 1]); %! DFDYP = sparse ([-1, 0, 0; %! 0, -1, 0; %! 0, 0, 0]); %!endfunction %! %!function [DFDY, DFDYP] = jacwrong (t, y, yp) %! DFDY = [-0.04, 1e4*y(3); %! 0.04, -1e4*y(3)-6e7*y(2)]; %! DFDYP = [-1, 0; %! 0, -1]; %!endfunction %! %!function [DFDY, DFDYP, A] = jacwrong2 (t, y, yp) %! DFDY = [-0.04, 1e4*y(3), 1e4*y(2); %! 0.04, -1e4*y(3)-6e7*y(2), -1e4*y(2); %! 1, 1, 1]; %! DFDYP = [-1, 0, 0; %! 0, -1, 0; %! 0, 0, 0]; %! A = DFDY; %!endfunction %! %!function [val, isterminal, direction] = ff (t, y, yp) %! isterminal = [0, 1]; %! if (t < 1e1) %! val = [-1, -2]; %! else %! val = [1, 3]; %! endif %! %! direction = [1, 0]; %!endfunction ## anonymous function instead of real function %!testif HAVE_SUNDIALS %! ref = 0.049787079136413; %! ff = @(t, u, udot) udot + 3 * u; %! [t, y] = ode15i (ff, 0:1, 1, -3); %! assert ([t(end), y(end)], [1, ref], 1e-3); ## function passed as string %!testif HAVE_SUNDIALS %! [t, y] = ode15i ("rob", [0, 100, 200], [1; 0; 0], [-1e-4; 1e-4; 0]); %! assert ([t(2), y(2,:)], fref, 1e-3); ## solve in intermediate step %!testif HAVE_SUNDIALS %! [t, y] = ode15i (@rob, [0, 100, 200], [1; 0; 0], [-1e-4; 1e-4; 0]); %! assert ([t(2), y(2,:)], fref, 1e-3); ## numel(trange) = 2 final value %!testif HAVE_SUNDIALS %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0]); %! assert ([t(end), y(end,:)], fref, 1e-5); ## With empty options %!testif HAVE_SUNDIALS %! opt = odeset (); %! [t, y] = ode15i (@rob, [0, 1e6, 2e6, 3e6, 4e6], [1; 0; 0], %! [-1e-4; 1e-4; 0], opt); %! assert ([t(end), y(end,:)], fref2, 1e-3); %! opt = odeset (); ## Without options %!testif HAVE_SUNDIALS %! [t, y] = ode15i (@rob, [0, 1e6, 2e6, 3e6, 4e6], [1; 0; 0],[-1e-4; 1e-4; 0]); %! assert ([t(end), y(end,:)], fref2, 1e-3); ## InitialStep option %!testif HAVE_SUNDIALS %! opt = odeset ("InitialStep", 1e-8); %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0], opt); %! assert (t(2)-t(1), 1e-8, 1e-9); ## MaxStep option %!testif HAVE_SUNDIALS %! opt = odeset ("MaxStep", 1e-3); %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0]); %! assert (t(5)-t(4), 1e-3, 1e-3); ## AbsTol scalar option %!testif HAVE_SUNDIALS %! opt = odeset ("AbsTol", 1e-8); %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0], opt); %! assert ([t(end), y(end,:)], fref, 1e-3); ## AbsTol scalar and RelTol option %!testif HAVE_SUNDIALS %! opt = odeset ("AbsTol", 1e-8, "RelTol", 1e-6); %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0], opt); %! assert ([t(end), y(end,:)], fref, 1e-3); ## AbsTol vector option %!testif HAVE_SUNDIALS %! opt = odeset ("AbsTol", [1e-8, 1e-14, 1e-6]); %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0], opt); %! assert ([t(end), y(end,:)], fref, 1e-3); ## AbsTol vector and RelTol option %!testif HAVE_SUNDIALS %! opt = odeset ("AbsTol", [1e-8, 1e-14,1e-6], "RelTol", 1e-6); %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4;1e-4;0], opt); %! assert ([t(end), y(end,:)], fref, 1e-3); ## RelTol option %!testif HAVE_SUNDIALS %! opt = odeset ("RelTol", 1e-6); %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0], opt); %! assert ([t(end), y(end,:)], fref, 1e-3); ## Jacobian fun dense %!testif HAVE_SUNDIALS %! opt = odeset ("Jacobian", @jacfundense); %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0], opt); %! assert ([t(end), y(end,:)], fref, 1e-3); ## Jacobian fun dense as string %!testif HAVE_SUNDIALS %! opt = odeset ("Jacobian", "jacfundense"); %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0], opt); %! assert ([t(end), y(end,:)], fref, 1e-3); ## Jacobian fun sparse %!testif HAVE_SUNDIALS_SUNLINSOL_KLU %! opt = odeset ("Jacobian", @jacfunsparse, "AbsTol", 1e-7, "RelTol", 1e-7); %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0], opt); %! assert ([t(end), y(end,:)], fref, 1e-3); ## Solve in backward direction starting at t=100 %!testif HAVE_SUNDIALS %! YPref = [-0.001135972751027; -0.000000027483627; 0.001136000234654]; %! Yref = [0.617234887614937, 0.000006153591397, 0.382758958793666]; %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0]); %! [t2, y2] = ode15i (@rob, [100, 0], Yref', YPref); %! assert ([t2(end), y2(end,:)], [0, 1, 0, 0], 2e-2); ## Solve in backward direction with MaxStep option #%!testif HAVE_SUNDIALS %! YPref = [-0.001135972751027; -0.000000027483627; 0.001136000234654]; %! Yref = [0.617234887614937, 0.000006153591397, 0.382758958793666]; %! opt = odeset ("MaxStep", 1e-2); %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0]); %! [t2, y2] = ode15i (@rob, [100, 0], Yref', YPref, opt); %! assert ([t2(end), y2(end,:)], [0, 1, 0, 0], 2e-2); %! assert (t2(9)-t2(10), 1e-2, 1e-2); ## Solve in backward direction starting with intermediate step #%!testif HAVE_SUNDIALS %! YPref = [-0.001135972751027; -0.000000027483627; 0.001136000234654]; %! Yref = [0.617234887614937, 0.000006153591397, 0.382758958793666]; %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0]); %! [t2, y2] = ode15i (@rob, [100, 5, 0], Yref', YPref); %! assert ([t2(end), y2(end,:)], [0, 1, 0, 0], 2e-2); ## Refine %!testif HAVE_SUNDIALS %! opt = odeset ("Refine", 3); %! [t, y] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0]); %! [t2, y2] = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0], opt); %! assert (numel (t2), numel (t) * 3, 3); ## Refine ignored if numel (trange) > 2 %!testif HAVE_SUNDIALS %! opt = odeset ("Refine", 3); %! [t, y] = ode15i (@rob, [0, 10, 100], [1; 0; 0], [-1e-4; 1e-4; 0]); %! [t2, y2] = ode15i (@rob, [0, 10, 100], [1; 0; 0], [-1e-4; 1e-4; 0], opt); %! assert (numel (t2), numel (t)); ## Events option add further elements in sol %!testif HAVE_SUNDIALS %! opt = odeset ("Events", @ff); %! sol = ode15i (@rob, [0, 100], [1; 0; 0], [-1e-4; 1e-4; 0], opt); %! assert (isfield (sol, "ie")); %! assert (sol.ie, [1, 2]); %! assert (isfield (sol, "xe")); %! assert (isfield (sol, "ye")); %! assert (sol.x(end), 10, 1); ## Events option, five output arguments %!testif HAVE_SUNDIALS %! opt = odeset ("Events", @ff); %! [t, y, te, ye, ie] = ode15i (@rob, [0, 100], [1; 0; 0], %! [-1e-4; 1e-4; 0], opt); %! assert (t(end), 10, 1); %! assert (te, [10; 10], 0.2); %! assert (ie, [1; 2]); ## Initial solutions as row vectors %!testif HAVE_SUNDIALS %! A = eye (2); %! [tout, yout] = ode15i (@(t, y, yp) A * y - A * yp, ... %! [0, 1], [1, 1], [1, 1]); %! assert (size (yout), [20, 2]); %!testif HAVE_SUNDIALS %! A = eye (2); %! [tout, yout] = ode15i (@(t, y, yp) A * y - A * yp, ... %! [0, 1], [1, 1], [1; 1]); %! assert (size (yout), [20, 2]); ## Jacobian fun wrong dimension %!testif HAVE_SUNDIALS %! opt = odeset ("Jacobian", @jacwrong); %! fail ("[t, y] = ode15i (@rob, [0, 4e6], [1; 0; 0], [-1e-4; 1e-4; 0], opt)", %! '"Jacobian" function must evaluate to a real square matrix'); ## Jacobian cell dense wrong dimension %!testif HAVE_SUNDIALS %! DFDY = [-0.04, 1; %! 0.04, 1]; %! DFDYP = [-1, 0, 0; %! 0, -1, 0; %! 0, 0, 0]; %! opt = odeset ("Jacobian", {DFDY, DFDYP}); %! fail ("[t, y] = ode15i (@rob, [0, 4e6], [1; 0; 0], [-1e-4; 1e-4; 0], opt)", %! '"Jacobian" matrices must be real square matrices'); ## Jacobian cell sparse wrong dimension %!testif HAVE_SUNDIALS_SUNLINSOL_KLU %! DFDY = sparse ([-0.04, 1; %! 0.04, 1]); %! DFDYP = sparse ([-1, 0, 0; %! 0, -1, 0; %! 0, 0, 0]); %! opt = odeset ("Jacobian", {DFDY, DFDYP}); %! fail ("[t, y] = ode15i (@rob, [0, 4e6], [1; 0; 0], [-1e-4; 1e-4; 0], opt)", %! '"Jacobian" matrices must be real square matrices'); ## Jacobian cell wrong number of matrices %!testif HAVE_SUNDIALS %! A = [1 2 3; 4 5 6; 7 8 9]; %! opt = odeset ("Jacobian", {A,A,A}); %! fail ("[t, y] = ode15i (@rob, [0, 4e6], [1; 0; 0], [-1e-4; 1e-4; 0], opt)", %! 'invalid value assigned to field "Jacobian"'); ## Jacobian single matrix %!testif HAVE_SUNDIALS %! opt = odeset ("Jacobian", [1 2 3; 4 5 6; 7 8 9]); %! fail ("[t, y] = ode15i (@rob, [0, 4e6], [1; 0; 0], [-1e-4; 1e-4; 0], opt)", %! '"Jacobian" field must be a function handle or 2-element cell array of square matrices'); ## Jacobian single matrix wrong dimension %!testif HAVE_SUNDIALS %! opt = odeset ("Jacobian", [1 2 3; 4 5 6]); %! fail ("[t, y] = ode15i (@rob, [0, 4e6], [1; 0; 0], [-1e-4; 1e-4; 0], opt)", %! '"Jacobian" field must be a function handle or 2-element cell array of square matrices'); ## Jacobian strange field %!testif HAVE_SUNDIALS %! opt = odeset ("Jacobian", "_5yVNhWVJWJn47RKnzxPsyb_"); %! fail ("[t, y] = ode15i (@rob, [0, 4e6], [1; 0; 0], [-1e-4; 1e-4; 0], opt)", %! '"Jacobian" function "_5yVNhWVJWJn47RKnzxPsyb_" not found'); %!function ydot = fun (t, y, yp) %! ydot = [y - yp]; %!endfunction %!testif HAVE_SUNDIALS %! fail ("ode15i ()", "Invalid call to ode15i"); %!testif HAVE_SUNDIALS %! fail ("ode15i (1)", "Invalid call to ode15i"); %!testif HAVE_SUNDIALS %! fail ("ode15i (1, 1)", "Invalid call to ode15i"); %!testif HAVE_SUNDIALS %! fail ("ode15i (1, 1, 1)", "Invalid call to ode15i"); %!testif HAVE_SUNDIALS %! fail ("ode15i (1, 1, 1, 1)", "ode15i: fun must be of class:"); %!testif HAVE_SUNDIALS %! fail ("ode15i (1, 1, 1, 1, 1)", "ode15i: fun must be of class:"); %!testif HAVE_SUNDIALS %! fail ("ode15i (1, 1, 1, 1, 1, 1)", "ode15i: fun must be of class:"); %!testif HAVE_SUNDIALS %! fail ("ode15i (@fun, 1, 1, 1)", %! "ode15i: invalid value assigned to field 'trange'"); %!testif HAVE_SUNDIALS %! fail ("ode15i (@fun, [1, 1], 1, 1)", %! "ode15i: invalid value assigned to field 'trange'"); %!testif HAVE_SUNDIALS %! fail ("ode15i (@fun, [1, 2], 1, [1, 2])", %! "ode15i: y0 must have 2 elements"); %!testif HAVE_SUNDIALS %! opt = odeset ("RelTol", "_5yVNhWVJWJn47RKnzxPsyb_"); %! fail ("[t, y] = ode15i (@fun, [0, 2], 2, 2, opt)", %! "ode15i: RelTol must be of class:"); %!testif HAVE_SUNDIALS %! opt = odeset ("RelTol", [1, 2]); %! fail ("[t, y] = ode15i (@fun, [0, 2], 2, 2, opt)", %! "ode15i: RelTol must be scalar"); %!testif HAVE_SUNDIALS %! opt = odeset ("RelTol", -2); %! fail ("[t, y] = ode15i (@fun, [0, 2], 2, 2, opt)", %! "ode15i: RelTol must be positive"); %!testif HAVE_SUNDIALS %! opt = odeset ("AbsTol", "_5yVNhWVJWJn47RKnzxPsyb_"); %! fail ("[t, y] = ode15i (@fun, [0, 2], 2, 2, opt)", %! "ode15i: AbsTol must be of class:"); %!testif HAVE_SUNDIALS %! opt = odeset ("AbsTol", -1); %! fail ("[t, y] = ode15i (@fun, [0, 2], 2, 2, opt)", %! "ode15i: AbsTol must be positive"); %!testif HAVE_SUNDIALS %! opt = odeset ("AbsTol", [1, 1, 1]); %! fail ("[t, y] = ode15i (@fun, [0, 2], 2, 2, opt)", %! 'ode15i: invalid value assigned to field "AbsTol"'); %!testif HAVE_SUNDIALS %! A = zeros (2); %! fail ("ode15i (@(t, y, yp) A * y - A * yp, [0, 1], eye (2), [1, 1])", %! "ode15i: Y0 must be a numeric vector"); %!testif HAVE_SUNDIALS %! A = zeros (2); %! fail ("ode15i (@(t, y, yp) A * y - A * yp, [0, 1], [1, 1], eye (2))", %! "ode15i: YP0 must be a numeric vector");