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## Copyright (C) 2000-2013 Paul Kienzle
##
## 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
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{pp} =} mkpp (@var{breaks}, @var{coefs})
## @deftypefnx {Function File} {@var{pp} =} mkpp (@var{breaks}, @var{coefs}, @var{d})
##
## Construct a piecewise polynomial (pp) structure from sample points
## @var{breaks} and coefficients @var{coefs}. @var{breaks} must be a vector of
## strictly increasing values. The number of intervals is given by
## @code{@var{ni} = length (@var{breaks}) - 1}.
## When @var{m} is the polynomial order @var{coefs} must be of
## size: @var{ni} x @var{m} + 1.
##
## The i-th row of @var{coefs},
## @code{@var{coefs} (@var{i},:)}, contains the coefficients for the polynomial
## over the @var{i}-th interval, ordered from highest (@var{m}) to
## lowest (@var{0}).
##
## @var{coefs} may also be a multi-dimensional array, specifying a vector-valued
## or array-valued polynomial. In that case the polynomial order is defined
## by the length of the last dimension of @var{coefs}.
## The size of first dimension(s) are given by the scalar or
## vector @var{d}. If @var{d} is not given it is set to @code{1}.
## In any case @var{coefs} is reshaped to a 2-D matrix of
## size @code{[@var{ni}*prod(@var{d} @var{m})] }
##
## @seealso{unmkpp, ppval, spline, pchip, ppder, ppint, ppjumps}
## @end deftypefn
function pp = mkpp (x, P, d)
## check number of arguments
if (nargin < 2 || nargin > 3)
print_usage ();
endif
## check x
if (length (x) < 2)
error ("mkpp: at least one interval is needed");
endif
if (!isvector (x))
error ("mkpp: x must be a vector");
endif
len = length (x) - 1;
dP = length (size (P));
pp = struct ("form", "pp",
"breaks", x(:).',
"coefs", [],
"pieces", len,
"order", prod (size (P)) / len,
"dim", 1);
if (nargin == 3)
pp.dim = d;
pp.order /= prod (d);
endif
dim_vec = [pp.pieces * prod(pp.dim), pp.order];
pp.coefs = reshape (P, dim_vec);
endfunction
%!demo # linear interpolation
%! x = linspace (0,pi,5)';
%! t = [sin(x), cos(x)];
%! m = diff (t) ./ (x(2)-x(1));
%! b = t(1:4,:);
%! pp = mkpp (x, [m(:),b(:)]);
%! xi = linspace (0,pi,50);
%! plot (x,t,"x", xi,ppval (pp,xi));
%! legend ("control", "interp");
%!shared b,c,pp
%! b = 1:3; c = 1:24; pp = mkpp (b,c);
%!assert (pp.pieces, 2)
%!assert (pp.order, 12)
%!assert (pp.dim, 1)
%!assert (size (pp.coefs), [2,12])
%! pp = mkpp (b,c,2);
%!assert (pp.pieces, 2)
%!assert (pp.order, 6)
%!assert (pp.dim, 2)
%!assert (size (pp.coefs), [4,6])
%! pp = mkpp (b,c,3);
%!assert (pp.pieces, 2)
%!assert (pp.order, 4)
%!assert (pp.dim, 3)
%!assert (size (pp.coefs), [6,4])
%! pp = mkpp (b,c,[2,3]);
%!assert (pp.pieces, 2)
%!assert (pp.order, 2)
%!assert (pp.dim, [2,3])
%!assert (size (pp.coefs), [12,2])
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