update packages

[CreaPhase.git] / octave_packages / m / polynomial / mkpp.m

diff --git a/octave_packages/m/polynomial/mkpp.m b/octave_packages/m/polynomial/mkpp.m
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+## Copyright (C) 2000-2012 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]);