approxfun               package:stats               R Documentation

_I_n_t_e_r_p_o_l_a_t_i_o_n _F_u_n_c_t_i_o_n_s

_D_e_s_c_r_i_p_t_i_o_n:

     Return a list of points which linearly interpolate given data
     points, or a function performing the linear (or constant)
     interpolation.

_U_s_a_g_e:

     approx   (x, y = NULL, xout, method="linear", n=50,
               yleft, yright, rule = 1, f = 0, ties = mean)

     approxfun(x, y = NULL,       method="linear",
               yleft, yright, rule = 1, f = 0, ties = mean)

_A_r_g_u_m_e_n_t_s:

    x, y: vectors giving the coordinates of the points to be
          interpolated.  Alternatively a single plotting structure can
          be specified: see 'xy.coords'.

    xout: an optional set of values specifying where interpolation is
          to take place.

  method: specifies the interpolation method to be used.  Choices are
          '"linear"' or '"constant"'.

       n: If 'xout' is not specified, interpolation takes place at 'n'
          equally spaced points spanning the interval ['min(x)',
          'max(x)'].

   yleft: the value to be returned when input 'x' values are less than
          'min(x)'. The default is defined by the value of 'rule' given
          below.

  yright: the value to be returned when input 'x' values are greater
          than 'max(x)'. The default is defined by the value of 'rule'
          given below.

    rule: an integer describing how interpolation is to take place
          outside the interval ['min(x)', 'max(x)']. If 'rule' is '1'
          then 'NA's are returned for such points and if it is '2', the
          value at the closest data extreme is used.

       f: For 'method="constant"' a number between 0 and 1 inclusive,
          indicating a compromise between left- and right-continuous
          step functions. If 'y0' and 'y1' are the values to the left
          and right of the point then the value is 'y0*(1-f)+y1*f' so
          that 'f=0' is right-continuous and 'f=1' is left-continuous.

    ties: Handling of tied 'x' values.  Either a function with a single
          vector argument returning a single number result or the
          string '"ordered"'.

_D_e_t_a_i_l_s:

     The inputs can contain missing values which are deleted, so at
     least two complete '(x, y)' pairs are required (for 'method =
     "linear"', one otherwise).  If there are duplicated (tied) 'x'
     values and 'ties' is a function it is applied to the 'y' values
     for each distinct 'x' value. Useful functions in this context
     include 'mean', 'min', and 'max'.  If 'ties="ordered"' the 'x'
     values are assumed to be already ordered.  The first 'y' value
     will be used for interpolation to the left and the last one for
     interpolation to the right.

_V_a_l_u_e:

     'approx' returns a list with components 'x' and 'y', containing
     'n' coordinates which interpolate the given data points according
     to the 'method' (and 'rule') desired.

     The function 'approxfun' returns a function performing (linear or
     constant) interpolation of the given data points.  For a given set
     of 'x' values, this function will return the corresponding
     interpolated values.  This is often more useful than 'approx'.

_R_e_f_e_r_e_n_c_e_s:

     Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) _The New S
     Language_. Wadsworth & Brooks/Cole.

_S_e_e _A_l_s_o:

     'spline' and 'splinefun' for spline interpolation.

_E_x_a_m_p_l_e_s:

     x <- 1:10
     y <- rnorm(10)
     par(mfrow = c(2,1))
     plot(x, y, main = "approx(.) and approxfun(.)")
     points(approx(x, y), col = 2, pch = "*")
     points(approx(x, y, method = "constant"), col = 4, pch = "*")

     f <- approxfun(x, y)
     curve(f(x), 0, 10, col = "green")
     points(x, y)
     is.function(fc <- approxfun(x, y, method = "const")) # TRUE
     curve(fc(x), 0, 10, col = "darkblue", add = TRUE)

     ## Show treatment of 'ties' :

     x <- c(2,2:4,4,4,5,5,7,7,7)
     y <- c(1:6, 5:4, 3:1)
     approx(x,y, xout=x)$y # warning
     (ay <- approx(x,y, xout=x, ties = "ordered")$y)
     stopifnot(ay == c(2,2,3,6,6,6,4,4,1,1,1))
     approx(x,y, xout=x, ties = min)$y
     approx(x,y, xout=x, ties = max)$y

