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```
## Copyright (C) 2001,2002 Kai Habel
##
## This program 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 2 of the License, or
## (at your option) any later version.
##
## This program 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 this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
## -*- texinfo -*-
## @deftypefn {Function File} {@var{pp} = } pchip (@var{x}, @var{y})
## @deftypefnx {Function File} {@var{yi} = } pchip (@var{x}, @var{y}, @var{xi})
## piecewise cubic hermite interpolating polynom.
## @var{x} must be a strictly monotonic vector (either increasing or decreasing).
## @var{y} is a vector of same length as @var{x},
## or a matrix where the number of columns must match the length
## of @var{x}. In this case the interpolating polynoms are calculated
## for each column.
## In contrast to spline, pchip preserves the monotonicity of (@var{x},@var{y}).
##
## @seealso{ppval, spline, csape}
## @} # deftypefn
## Author: Kai Habel <kai.habel@gmx.de>
## Date: 9. mar 2001
##
## S_k = a_k + b_k*x + c_k*x^2 + d_k*x^3; (spline polynom)
##
## 4 conditions:
## S_k(x_k) = y_k
## S_k(x_k+1) = y_k+1
## S_k'(x_k) = y_k'
## S_k'(x_k+1) = y_k+1'
pchip <- function(x, y, xi = NULL) {
pchip_deriv <- function(x, y) {
if (NROW(x) != NROW(y))
stop("number of rows for x and y must match")
# Octave does this for each column of y; we just assume a vector.
z <- .Fortran("dpchim",
as.integer(NROW(x)),
as.double(x),
as.double(y),
output = as.double(y),
as.integer(1),
ierr = as.integer(1),
PACKAGE = "signal")
if (z$ierr >= 0)
return(z$output)
else
stop("error")
}
n = length(x)
ry = NROW(y)
cy = NCOL(y)
h = diff(x)
if (all(h < 0)) {
x = rev(x)
h = diff(x)
y = as.matrix(y[, cy:1])
} else if (any(h<=0)) {
stop('x must be strictly monotonic')
}
if (ry != n)
stop("size of x and y must match")
if (cy > 1)
h = diff(x) %x% rep.int(1, cy) # kron multiplication
## not used: ## dy = diff(y) / h
a = y
b = pchip_deriv(x,y)
c = - (b[2:n] + 2 * b[1:(n-1)]) / h + 3 * diff(a) / h ^ 2
d = (b[1:(n-1)] + b[2:n]) / h^2 - 2 * diff(a) / h^3
d = d[1:(n-1)]; c = c[1:(n-1)]
b = b[1:(n-1)]; a = a[1:(n-1)]
coeffs = cbind(d, c, b, a)
pp = mkpp(x, coeffs)
if (is.null(xi))
ret = pp
else
ret = ppval(pp,xi)
ret
}
#xf = seq(0,10, length=500); yf = sin(2*pi*xf/5)
#xp = 0:10; yp = sin(2*pi*xp/5)
#xp = c(0:1,3:10); yp = sin(2*pi*xp/5)
#lin = pchip(xp, yp, xf)
#lin = interp1(xp, yp, xf, 'pchip')
#plot(xp, yp)
#lines(xf, lin, col = "red")
## Copyright (C) 2000 Paul Kienzle
##
## This program 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 2 of the License, or
## (at your option) any later version.
##
## This program 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 this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
## usage: pp = mkpp(x, P)
## Construct a piece-wise polynomial structure from sample points x and
## coefficients P. The ith row of P, P(i,:), contains the coefficients
## for the polynomial over the ith interval, ordered from highest to
## lowest. There must be one row for each interval in x, so
## rows(P) == length(x)-1.
##
## You can concatenate multiple polynomials of the same order over the
## same set of intervals using P = [ P1 ; P2 ; ... ; Pd ]. In this case,
## rows(P) == d*(length(x)-1).
##
## mkpp(x, P, d) is provided for compatibility, but if d is not specified
## it will be computed as round(rows(P)/(length(x)-1)) instead of defaulting
## to 1.
mkpp <- function(x, P, d = round(NROW(P)/pp$n)) {
pp = list()
pp$x = x
pp$P = P
pp$n = length(x) - 1
pp$k = NCOL(P)
pp$d = d
if (pp$n*d != NROW(P))
stop("mkpp: num intervals in x doesn't match num polynomials in P")
class(pp) = "pp"
pp
}
##%!demo # linear interpolation
#x = seq(0,pi,length=5)
#t= cbind(sin(x), cos(x))
#m = diff(t) / (x[2]-x[1])
#b = t[1:4,]
#pp = mkpp(x, cbind(as.vector(m),as.vector(b)))
#ppval(pp,x)
##%! xi=linspace(0,pi,50)
##%! plot(x,t)
## lines(xi,ppval(pp,x))
## Copyright (C) 2000 Paul Kienzle
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
## usage: yi = ppval(pp, xi)
## Evaluate piece-wise polynomial pp and points xi. If pp.d > 1,
## the returned yi will be a matrix of size rows(xi) by pp.d, or
## its transpose if xi is a row vector.
ppval = function(pp, xi) {
if (is.null(xi)) {
yi = NULL
} else {
lookup = function(x, xi) approx(x, 1:length(x), xi, method="constant", yleft=0, yright=length(x))$y
idx = lookup(pp$x[2:pp$n], xi) + 1
dx = as.matrix(xi - pp$x[idx])
dx = dx[,rep(1,pp$d)]
c = matrix(pp$P[1:(pp$n*pp$d)], pp$n, pp$d)
yi = c[idx, ]
if (pp$k > 1)
for (i in 2:pp$k) {
c = matrix(pp$P[, i], pp$n, pp$d)
yi = yi * dx + c[idx, ]
}
}
yi
}
```

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