Add gradFD folder

gradFD/Example_basic_gradFD.m

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+%% Basic example of the use of the class gradFD
+% L. LAURENT --  13/04/2018 -- luc.laurent@lecnam.net
+
+% sources could be found here:
+% https://bitbucket.com/luclaurent/gradFD
+% https://github.com/luclaurent/gradFD
+%
+
+% gradFD - A toolbox to compute derivatives and hessians using finite differences
+% Copyright (C) 2018  Luc LAURENT <luc.laurent@lecnam.net>
+%
+% This program 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.
+%
+% This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% variables created for this example
+
+%specific function (peaks's Matlab function)
+funA=@(x)peaks(x(:,1),x(:,2));
+
+%1D function
+funB=@(x) exp(-x/10).*cos(x)+1/10*x;
+funDB=@(x) -exp(-x/10).*(sin(x)+1/10.*cos(x))+1/10;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% classical use of the class
+fprintf('Classical use of the class\n');
+
+%load the class with all options
+gradA=gradFD('FD1',[0 1;2 3],1e-3,funA);
+
+%extract derivatives
+gradA.GZeval
+
+%compute derivatives at other points
+gradA.Xref=[4 5;6 9; 4 5];
+
+%extract derivatives
+gradA.GZeval
+
+%change stepsizes (one per points)
+gradA.stepsDiff=[1e-2;1e-3;1e-4];
+
+%extract derivatives
+gradA.GZeval
+
+%change stepsizes (one per direction)
+gradA.stepsDiff=[1e-2 1e-3];
+
+%extract derivatives
+gradA.GZeval
+

gradFD/Example_error_gradFD.m

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+%% Advanced example of the use of the class gradFD
+% L. LAURENT --  13/04/2018 -- luc.laurent@lecnam.net
+
+% sources could be found here:
+% https://bitbucket.com/luclaurent/gradFD
+% https://github.com/luclaurent/gradFD
+%
+
+% gradFD - A toolbox to compute derivatives and hessians using finite differences
+% Copyright (C) 2018  Luc LAURENT <luc.laurent@lecnam.net>
+%
+% This program 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.
+%
+% This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% variables created for this example
+
+%1D function
+funB=@(x) exp(-x/10).*cos(x)+1/10*x;
+funDB=@(x) -exp(-x/10).*(sin(x)+1/10.*cos(x))+1/10;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Plot error due to stepsize
+fprintf('Study of the error due to the stepsize\n');
+
+%sample point
+x=5;
+%stepsize
+step=logspace(0,-13,1000);
+
+%evaluate actual derivative
+GZ=funDB(x);
+
+%compute gradients with finite differences
+errFD1=zeros(size(step));
+errBD1=zeros(size(step));
+errCD2=zeros(size(step));
+errFD2=zeros(size(step));
+errBD2=zeros(size(step));
+errCD4=zeros(size(step));
+errFD3=zeros(size(step));
+errBD3=zeros(size(step));
+errCD6=zeros(size(step));
+for itS=1:numel(step)
+    gradBFD1=gradFD('FD1',x,step(itS),funB);
+    gradBBD1=gradFD('BD1',x,step(itS),funB);
+    gradBCD2=gradFD('CD2',x,step(itS),funB);
+    gradBFD2=gradFD('FD2',x,step(itS),funB);
+    gradBBD2=gradFD('BD2',x,step(itS),funB);
+    gradBCD4=gradFD('CD4',x,step(itS),funB);
+    gradBFD3=gradFD('FD3',x,step(itS),funB);
+    gradBBD3=gradFD('BD3',x,step(itS),funB);
+    gradBCD6=gradFD('CD6',x,step(itS),funB);
+    %compute errors
+    errFD1(itS)=abs(gradBFD1.GZeval-GZ)/abs(GZ);
+    errBD1(itS)=abs(gradBBD1.GZeval-GZ)/abs(GZ);
+    errCD2(itS)=abs(gradBCD2.GZeval-GZ)/abs(GZ);
+    errFD2(itS)=abs(gradBFD2.GZeval-GZ)/abs(GZ);
+    errBD2(itS)=abs(gradBBD2.GZeval-GZ)/abs(GZ);
+    errCD4(itS)=abs(gradBCD4.GZeval-GZ)/abs(GZ);
+    errFD3(itS)=abs(gradBFD3.GZeval-GZ)/abs(GZ);
+    errBD3(itS)=abs(gradBBD3.GZeval-GZ)/abs(GZ);
+    errCD6(itS)=abs(gradBCD6.GZeval-GZ)/abs(GZ);
+end
+
+%plots
+figure
+loglog(step,errFD1,'b')
+hold on
+loglog(step,errBD1,'k')
+loglog(step,errCD2,'r')
+loglog(step,errFD2,'c')
+loglog(step,errBD2,'m')
+loglog(step,errCD4,'k-.')
+loglog(step,errFD3,'c-.')
+loglog(step,errBD3,'m-.')
+loglog(step,errCD6,'r-.')
+legend('FD1','BD1','CD2','FD2','BD2','CD4','FD3','BD3','CD6')
+title('Errors on derivatives for different FD schemes')
+xlabel('Stepsize','Interpreter','latex')
+ylabel('Error','Interpreter','latex');

gradFD/Example_external_gradFD.m

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+%% Basic example of the use of the class gradFD
+% L. LAURENT --  13/04/2018 -- luc.laurent@lecnam.net
+
+% sources could be found here:
+% https://bitbucket.com/luclaurent/gradFD
+% https://github.com/luclaurent/gradFD
+%
+
+% gradFD - A toolbox to compute derivatives and hessians using finite differences
+% Copyright (C) 2018  Luc LAURENT <luc.laurent@lecnam.net>
+%
+% This program 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.
+%
+% This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% variables created for this example
+
+%specific function (peaks's Matlab function)
+funA=@(x)peaks(x(:,1),x(:,2));
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% external use of the class
+fprintf('external use of the class\n');
+
+%load the class without specified the function
+gradExtA=gradFD('FD1',[0 1;2 3],1e-3);
+
+%extract the values of the requested points
+pointGradExtA=gradExtA.XevalG;
+
+%external evaluations of the function
+ZA=funA(pointGradExtA);
+
+%load the responses values
+gradExtA.loadZextG(ZA);
+
+%extract derivatives
+gradExtA.GZeval

gradFD/Example_plot1D_gradFD.m

@@ -0,0 +1,68 @@
+%% Advanced example of the use of the class gradFD
+% L. LAURENT --  13/04/2018 -- luc.laurent@lecnam.net
+
+% sources could be found here:
+% https://bitbucket.com/luclaurent/gradFD
+% https://github.com/luclaurent/gradFD
+%
+
+% gradFD - A toolbox to compute derivatives and hessians using finite differences
+% Copyright (C) 2018  Luc LAURENT <luc.laurent@lecnam.net>
+%
+% This program 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.
+%
+% This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% variables created for this example
+
+%1D function
+funB=@(x) exp(-x/10).*cos(x)+1/10*x;
+funDB=@(x) -exp(-x/10).*(sin(x)+1/10.*cos(x))+1/10;
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Plot derivatives
+fprintf('Study of the derivatives\n');
+
+%sample points
+x=(-1:0.1:15)';
+%stepsize
+step=1;
+
+%evaluate function and actual derivative
+Z=funB(x);
+GZ=funDB(x);
+
+%compute gradients with finite differences
+gradBFD1=gradFD('FD1',x,step,funB);
+gradBBD1=gradFD('BD1',x,step,funB);
+gradBCD2=gradFD('CD2',x,step,funB);
+gradBFD2=gradFD('FD2',x,step,funB);
+gradBBD2=gradFD('BD2',x,step,funB);
+
+%plots
+figure
+plot(x,Z,'b')
+hold on
+plot(x,GZ,'k')
+plot(x,gradBFD1.GZeval,'r')
+plot(x,gradBBD1.GZeval,'c')
+plot(x,gradBCD2.GZeval,'m')
+plot(x,gradBFD2.GZeval,'r-.')
+plot(x,gradBBD2.GZeval,'c-.')
+legend('Actual function','Actual derivative','FD1','BD1','CD2','FD2','BD2')
+title(['Derivatives with stepsize=' num2str(step)])
+xlabel('x','Interpreter','latex')
+ylabel('$f(x)$, $\frac{\partial f(x)}{\partial x}$','Interpreter','latex');

gradFD/Example_plot2D_gradFD.m

@@ -0,0 +1,83 @@
+%% Advanced example of the use of the class gradFD
+% L. LAURENT --  13/04/2018 -- luc.laurent@lecnam.net
+
+% sources could be found here:
+% https://bitbucket.com/luclaurent/gradFD
+% https://github.com/luclaurent/gradFD
+%
+
+% gradFD - A toolbox to compute derivatives and hessians using finite differences
+% Copyright (C) 2018  Luc LAURENT <luc.laurent@lecnam.net>
+%
+% This program 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.
+%
+% This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% variables created for this example
+
+%specific function (peaks's Matlab function)
+funA=@(x)peaks(x(:,1),x(:,2));
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Plot derivatives
+fprintf('Study of the derivatives\n');
+
+%sample points
+nbS=50;
+x=linspace(-3,3,nbS);
+[X,Y]=meshgrid(x);
+Xtot=[X(:) Y(:)];
+Z=funA(Xtot);
+
+%stepsize
+step=1e-4;
+
+%compute gradients with finite differences
+gradBCD2=gradFD('CD2',Xtot,step,funA);
+GZ=gradBCD2.GZeval;
+
+%reorder data
+Zsurf=reshape(Z,nbS,nbS);
+GZ1=reshape(GZ(:,1),nbS,nbS);
+GZ2=reshape(GZ(:,2),nbS,nbS);
+
+%plots
+h=figure;
+subplot(221)
+surf(X,Y,Zsurf)
+title('Peaks function')
+xlabel('x','Interpreter','latex')
+ylabel('y','Interpreter','latex')
+zlabel('f','Interpreter','latex');
+subplot(222)
+contour(X,Y,Zsurf,20)
+hold on
+quiver(X,Y,GZ1,GZ2)
+hold off
+title('Peaks function with quiver plot')
+xlabel('x','Interpreter','latex')
+ylabel('y','Interpreter','latex')
+%
+subplot(223)
+surf(X,Y,GZ1)
+xlabel('x','Interpreter','latex')
+ylabel('y','Interpreter','latex')
+zlabel('$\frac{\partial f}{\partial x_1}$','Interpreter','latex')
+subplot(224)
+surf(X,Y,GZ2)
+xlabel('x','Interpreter','latex')
+ylabel('y','Interpreter','latex')
+zlabel('$\frac{\partial f}{\partial x_1}$','Interpreter','latex')
+