Mercurial > octave-nkf
diff scripts/ode/private/hermite_quartic_interpolation.m @ 20584:eb9e2d187ed2
maint: Use Octave coding conventions in scripts/ode/private dir.
* AbsRel_Norm.m, fuzzy_compare.m, hermite_quartic_interpolation.m,
integrate_adaptive.m, integrate_const.m, integrate_n_steps.m, kahan.m,
ode_struct_value_check.m, odepkg_event_handle.m, odepkg_structure_check.m,
runge_kutta_45_dorpri.m, starting_stepsize.m:
Wrap long lines to < 80 chars.
Use double quotes rather than single quotes where possible.
Use ';' at end of keywords "return;" and "break;"
Use '##" for stand-alone comments and '#' for end-of-line comments.
Use two spaces after period before starting new sentence.
Use '!' instead of '~' for logical negation.
Use specific form of end (endif, endfor, etc.).
Don't use line continuation marker '...' unless necessary.
| author | Rik <rik@octave.org> |
|---|---|
| date | Sun, 04 Oct 2015 22:18:54 -0700 |
| parents | 25623ef2ff4f |
| children |
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--- a/scripts/ode/private/hermite_quartic_interpolation.m Sun Oct 04 16:24:32 2015 +0100 +++ b/scripts/ode/private/hermite_quartic_interpolation.m Sun Oct 04 22:18:54 2015 -0700 @@ -17,16 +17,13 @@ ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- -## @deftypefn {Function File} {[@var{x_out}] =} hermite_quartic_interpolation (@var{t}, @var{x}, @var{der}, @var{t_out}) +## @deftypefn {Function File} {@var{x_out} =} hermite_quartic_interpolation (@var{t}, @var{x}, @var{der}, @var{t_out}) ## ## This function file can be called by an ODE solver function in order to -## interpolate the solution at the time @var{t_out} using 4th order +## interpolate the solution at the time @var{t_out} using a 4th order ## Hermite interpolation. ## -## This function must be called with one output arguments: @var{x_out} -## which contains the evaluation at @var{t_out} of the Hermite interpolant. -## -## The first input argument is the vector with two given times. +## The first input @var{t} is a vector with two given times. ## ## The second input argument is the vector with the values of the function ## to interpolate at the times specified in @var{t} and at the middle point. @@ -34,6 +31,9 @@ ## The third input argument is the value of the derivatives of the function ## evaluated at the two extreme points. ## +## The output @var{x_out} is the evaluation of the Hermite interpolant at +## @var{t_out}. +## ## @end deftypefn ## ## @seealso{linear_interpolation, quadratic_interpolation, @@ -42,18 +42,18 @@ function x_out = hermite_quartic_interpolation (t, x, der, t_out) - # Rescale time on [0,1] + ## Rescale time on [0,1] s = (t_out - t(1)) / (t(2) - t(1)); - # Hermite basis functions - # H0 = 1 - 11*s.^2 + 18*s.^3 - 8*s.^4; - # H1 = s - 4*s.^2 + 5*s.^3 - 2*s.^4; - # H2 = 16*s.^2 - 32*s.^3 + 16*s.^4; - # H3 = - 5*s.^2 + 14*s.^3 - 8*s.^4; - # H4 = s.^2 - 3*s.^3 + 2*s.^4; + ## Hermite basis functions + ## H0 = 1 - 11*s.^2 + 18*s.^3 - 8*s.^4; + ## H1 = s - 4*s.^2 + 5*s.^3 - 2*s.^4; + ## H2 = 16*s.^2 - 32*s.^3 + 16*s.^4; + ## H3 = - 5*s.^2 + 14*s.^3 - 8*s.^4; + ## H4 = s.^2 - 3*s.^3 + 2*s.^4; - x_out = zeros (size (x, 1), length (t_out)); - for ii = 1:size (x, 1) + x_out = zeros (rows (x), length (t_out)); + for ii = 1:rows (x) x_out(ii,:) = (1 - 11*s.^2 + 18*s.^3 - 8*s.^4)*x(ii,1) ... + ( s - 4*s.^2 + 5*s.^3 - 2*s.^4)*(t(2)-t(1))*der(ii,1) ... + ( 16*s.^2 - 32*s.^3 + 16*s.^4)*x(ii,2) ... @@ -63,6 +63,3 @@ endfunction -## Local Variables: *** -## mode: octave *** -## End: ***