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comparison scripts/ode/private/hermite_quartic_interpolation.m @ 20584:eb9e2d187ed2

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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
comparison
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20583:d746695bf494 20584:eb9e2d187ed2
15 ## You should have received a copy of the GNU General Public License 15 ## You should have received a copy of the GNU General Public License
16 ## along with Octave; see the file COPYING. If not, see 16 ## along with Octave; see the file COPYING. If not, see
17 ## <http://www.gnu.org/licenses/>. 17 ## <http://www.gnu.org/licenses/>.
18 18
19 ## -*- texinfo -*- 19 ## -*- texinfo -*-
20 ## @deftypefn {Function File} {[@var{x_out}] =} hermite_quartic_interpolation (@var{t}, @var{x}, @var{der}, @var{t_out}) 20 ## @deftypefn {Function File} {@var{x_out} =} hermite_quartic_interpolation (@var{t}, @var{x}, @var{der}, @var{t_out})
21 ## 21 ##
22 ## This function file can be called by an ODE solver function in order to 22 ## This function file can be called by an ODE solver function in order to
23 ## interpolate the solution at the time @var{t_out} using 4th order 23 ## interpolate the solution at the time @var{t_out} using a 4th order
24 ## Hermite interpolation. 24 ## Hermite interpolation.
25 ## 25 ##
26 ## This function must be called with one output arguments: @var{x_out} 26 ## The first input @var{t} is a vector with two given times.
27 ## which contains the evaluation at @var{t_out} of the Hermite interpolant.
28 ##
29 ## The first input argument is the vector with two given times.
30 ## 27 ##
31 ## The second input argument is the vector with the values of the function 28 ## The second input argument is the vector with the values of the function
32 ## to interpolate at the times specified in @var{t} and at the middle point. 29 ## to interpolate at the times specified in @var{t} and at the middle point.
33 ## 30 ##
34 ## The third input argument is the value of the derivatives of the function 31 ## The third input argument is the value of the derivatives of the function
35 ## evaluated at the two extreme points. 32 ## evaluated at the two extreme points.
33 ##
34 ## The output @var{x_out} is the evaluation of the Hermite interpolant at
35 ## @var{t_out}.
36 ## 36 ##
37 ## @end deftypefn 37 ## @end deftypefn
38 ## 38 ##
39 ## @seealso{linear_interpolation, quadratic_interpolation, 39 ## @seealso{linear_interpolation, quadratic_interpolation,
40 ## hermite_cubic_interpolation, hermite_quintic_interpolation, 40 ## hermite_cubic_interpolation, hermite_quintic_interpolation,
41 ## dorpri_interpolation} 41 ## dorpri_interpolation}
42 42
43 function x_out = hermite_quartic_interpolation (t, x, der, t_out) 43 function x_out = hermite_quartic_interpolation (t, x, der, t_out)
44 44
45 # Rescale time on [0,1] 45 ## Rescale time on [0,1]
46 s = (t_out - t(1)) / (t(2) - t(1)); 46 s = (t_out - t(1)) / (t(2) - t(1));
47 47
48 # Hermite basis functions 48 ## Hermite basis functions
49 # H0 = 1 - 11*s.^2 + 18*s.^3 - 8*s.^4; 49 ## H0 = 1 - 11*s.^2 + 18*s.^3 - 8*s.^4;
50 # H1 = s - 4*s.^2 + 5*s.^3 - 2*s.^4; 50 ## H1 = s - 4*s.^2 + 5*s.^3 - 2*s.^4;
51 # H2 = 16*s.^2 - 32*s.^3 + 16*s.^4; 51 ## H2 = 16*s.^2 - 32*s.^3 + 16*s.^4;
52 # H3 = - 5*s.^2 + 14*s.^3 - 8*s.^4; 52 ## H3 = - 5*s.^2 + 14*s.^3 - 8*s.^4;
53 # H4 = s.^2 - 3*s.^3 + 2*s.^4; 53 ## H4 = s.^2 - 3*s.^3 + 2*s.^4;
54 54
55 x_out = zeros (size (x, 1), length (t_out)); 55 x_out = zeros (rows (x), length (t_out));
56 for ii = 1:size (x, 1) 56 for ii = 1:rows (x)
57 x_out(ii,:) = (1 - 11*s.^2 + 18*s.^3 - 8*s.^4)*x(ii,1) ... 57 x_out(ii,:) = (1 - 11*s.^2 + 18*s.^3 - 8*s.^4)*x(ii,1) ...
58 + ( s - 4*s.^2 + 5*s.^3 - 2*s.^4)*(t(2)-t(1))*der(ii,1) ... 58 + ( s - 4*s.^2 + 5*s.^3 - 2*s.^4)*(t(2)-t(1))*der(ii,1) ...
59 + ( 16*s.^2 - 32*s.^3 + 16*s.^4)*x(ii,2) ... 59 + ( 16*s.^2 - 32*s.^3 + 16*s.^4)*x(ii,2) ...
60 + ( - 5*s.^2 + 14*s.^3 - 8*s.^4)*x(ii,3) ... 60 + ( - 5*s.^2 + 14*s.^3 - 8*s.^4)*x(ii,3) ...
61 + ( s.^2 - 3*s.^3 + 2*s.^4)*(t(2)-t(1))*der(ii,2); 61 + ( s.^2 - 3*s.^3 + 2*s.^4)*(t(2)-t(1))*der(ii,2);
62 endfor 62 endfor
63 63
64 endfunction 64 endfunction
65 65
66 ## Local Variables: ***
67 ## mode: octave ***
68 ## End: ***