Mercurial > hg > octave-lyh
changeset 6743:f11fec9c06b0
[project @ 2007-06-18 19:12:48 by dbateman]
author | dbateman |
---|---|
date | Mon, 18 Jun 2007 19:12:48 +0000 |
parents | ebf96cc00ee9 |
children | b6c6587c1fb0 |
files | doc/ChangeLog doc/interpreter/Makefile.in doc/interpreter/interp.txi doc/interpreter/interpimages.m |
diffstat | 4 files changed, 61 insertions(+), 26 deletions(-) [+] |
line wrap: on
line diff
--- a/doc/ChangeLog +++ b/doc/ChangeLog @@ -1,3 +1,10 @@ +2007-06-18 David Bateman <dbateman@free.fr> + + * interpreter/interpimages.m: Simpler images to demonstrate + the continuity of the second derivative of splines. + * interpreter/interp.txi: Also change figures here. + * interpreter/Makefile.in: and here. + 2007-06-18 Søren Hauberg <hauberg@gmail.com> * interpreter/optim.txi: Added some introductory text to each
--- a/doc/interpreter/Makefile.in +++ b/doc/interpreter/Makefile.in @@ -43,7 +43,7 @@ EXAMPLE_FILES = $(addprefix $(top_srcdir)/examples/, $(EXAMPLE_FILES_NODIR)) -INTERPIMAGES = interpft interpn interpderiv +INTERPIMAGES = interpft interpn interpderiv1 interpderiv2 INTERPIMAGES_EPS = $(addsuffix .eps, $(INTERPIMAGES)) INTERPIMAGES_PDF = $(addsuffix .pdf, $(INTERPIMAGES)) INTERPIMAGES_PNG = $(addsuffix .png, $(INTERPIMAGES))
--- a/doc/interpreter/interp.txi +++ b/doc/interpreter/interp.txi @@ -18,31 +18,49 @@ There are some important differences between the various interpolation methods. The 'spline' method enforces that both the first and second derivatives of the interpolated values have a continuous derivative, -whereas the other methods do not. This can be demonstrated by the code +whereas the other methods do not. This means that the results of the +'spline' method are generally smoother. If the function to be +interpolated is in fact smooth, then 'spline' will give excellent +results. However, if the function to be evaluated is in some manner +discontinuous, then 'pchip' interpolation might give better results. + +This can be demonstrated by the code @example @group -t = 0 : 0.3 : pi; dt = t(2)-t(1); -n = length (t); k = 100; dti = dt*n/k; -ti = t(1) + [0 : k-1]*dti; -y = sin (4*t + 0.3) .* cos (3*t - 0.1); -ddyc = diff(diff(interp1(t,y,ti,'cubic'))./dti)./dti; -ddys = diff(diff(interp1(t,y,ti,'spline'))./dti)./dti; -ddyp = diff(diff(interp1(t,y,ti,'pchip'))./dti)./dti; -plot (ti(2:end-1), ddyc,'g+',ti(2:end-1),ddys,'b*', ... - ti(2:end-1),ddyp,'c^'); -legend('cubic','spline','pchip'); +t = -2:2; +dt = 1; +ti =-2:0.025:2; +dti = 0.025; +y = sign(t); +ys = interp1(t,y,ti,'spline'); +yp = interp1(t,y,ti,'pchip'); +ddys = diff(diff(ys)./dti)./dti; +ddyp = diff(diff(yp)./dti)./dti; +figure(1); +plot (ti, ys,'r-', ti, yp,'g-'); +legend('spline','pchip',4); +figure(2); +plot (ti, ddys,'r+', ti, ddyp,'g*'); +legend('spline','pchip'); @end group @end example @ifnotinfo @noindent -The result of which can be seen in @ref{fig:interpderiv}. +The result of which can be seen in @ref{fig:interpderiv1} and +@ref{fig:interpderiv2}. -@float Figure,fig:interpderiv -@image{interpderiv,8cm} -@caption{Comparison of second derivative of interpolated values for -various interpolation methods} +@float Figure,fig:interpderiv1 +@image{interpderiv1,8cm} +@caption{Comparison of 'phcip' and 'spline' interpolation methods for a +step function} +@end float + +@float Figure,fig:interpderiv2 +@image{interpderiv2,8cm} +@caption{Comparison of the second derivate of the 'phcip' and 'spline' +interpolation methods for a step function} @end float @end ifnotinfo
--- a/doc/interpreter/interpimages.m +++ b/doc/interpreter/interpimages.m @@ -20,17 +20,27 @@ vi = interpn(x, y, z, v, xxi, yyi, zzi, 'spline'); mesh (zi, yi, squeeze (vi(1,:,:))); print (strcat (nm, ".", typ), strcat ("-d", typ)) - elseif (strcmp (nm, "interpderiv")) - t = 0 : 0.3 : pi; dt = t(2)-t(1); - n = length (t); k = 100; dti = dt*n/k; - ti = t(1) + [0 : k-1]*dti; - y = sin (4*t + 0.3) .* cos (3*t - 0.1); - ddyc = diff(diff(interp1(t,y,ti,'cubic'))./dti)./dti; + elseif (strcmp (nm, "interpderiv1")) + t = -2:2; + dt = 1; + ti =-2:0.025:2; + dti = 0.025; + y = sign(t); + ys = interp1(t,y,ti,'spline'); + yp = interp1(t,y,ti,'pchip'); + plot (ti, ys,'r-', ti, yp,'g-'); + legend('spline','pchip', 4); + print (strcat (nm, ".", typ), strcat ("-d", typ)) + elseif (strcmp (nm, "interpderiv2")) + t = -2:2; + dt = 1; + ti =-2:0.025:2; + dti = 0.025; + y = sign(t); ddys = diff(diff(interp1(t,y,ti,'spline'))./dti)./dti; ddyp = diff(diff(interp1(t,y,ti,'pchip'))./dti)./dti; - plot (ti(2:end-1), ddyc,'g+',ti(2:end-1),ddys,'b*', ... - ti(2:end-1),ddyp,'c^'); - legend('cubic','spline','pchip'); + plot (ti(2:end-1),ddys,'r*', ti(2:end-1),ddyp,'g+'); + legend('spline','pchip'); print (strcat (nm, ".", typ), strcat ("-d", typ)) endif bury_output ();