243 lines
7.7 KiB
Racket
243 lines
7.7 KiB
Racket
#lang scribble/manual
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@(require (for-label racket
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racket/gui/base
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plot/compat)
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plot/compat
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(only-in plot/common/contract-doc
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doc-apply))
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@title[#:tag "compat"]{Compatibility Module}
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@author["Alexander Friedman" "Jamie Raymond" "Neil Toronto"]
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@defmodule[plot/compat]
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This module provides an interface compatible with PLoT 5.1.3 and earlier.
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@; ----------------------------------------
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@section[#:tag "plot"]{Plotting}
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@doc-apply[plot]{
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Plots @racket[data] in 2D, where @racket[data] is generated by
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functions like @racket[points] or @racket[line].
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A @racket[data] value is represented as a procedure that takes a
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@racket[2d-plot-area%] instance and adds plot information to it.
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The result is a @racket[image-snip%] for the plot. If an @racket[#:out-file]
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path or port is provided, the plot is also written as a PNG image to
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the given path or port.
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The @racket[#:lncolor] keyword argument is accepted for backward compatibility, but does nothing.
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}
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@doc-apply[plot3d]{
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Plots @racket[data] in 3D, where @racket[data] is generated by a
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function like @racket[surface]. The arguments @racket[alt] and
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@racket[az] set the viewing altitude (in degrees) and the azimuth
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(also in degrees), respectively.
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A 3D @racket[data] value is represented as a procedure that takes a
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@racket[3d-plot-area%] instance and adds plot information to it.
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The @racket[#:lncolor] keyword argument is accepted for backward compatibility, but does nothing.
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}
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@doc-apply[points]{
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Creates 2D plot data (to be provided to @racket[plot]) given a list
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of points specifying locations. The @racket[sym] argument determines
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the appearance of the points. It can be a symbol, an ASCII character,
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or a small integer (between -1 and 127). The following symbols are
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known: @racket['pixel], @racket['dot], @racket['plus],
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@racket['asterisk], @racket['circle], @racket['times],
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@racket['square], @racket['triangle], @racket['oplus], @racket['odot],
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@racket['diamond], @racket['5star], @racket['6star],
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@racket['fullsquare], @racket['bullet], @racket['full5star],
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@racket['circle1], @racket['circle2], @racket['circle3],
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@racket['circle4], @racket['circle5], @racket['circle6],
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@racket['circle7], @racket['circle8], @racket['leftarrow],
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@racket['rightarrow], @racket['uparrow], @racket['downarrow].
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}
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@doc-apply[line]{
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Creates 2D plot data to draw a line.
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The line is specified in either functional, i.e. @math{y = f(x)}, or
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parametric, i.e. @math{x,y = f(t)}, mode. If the function is
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parametric, the @racket[mode] argument must be set to
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@racket['parametric]. The @racket[t-min] and @racket[t-max] arguments
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set the parameter when in parametric mode.
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}
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@doc-apply[error-bars]{
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Creates 2D plot data for error bars given a list of vectors. Each
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vector specifies the center of the error bar @math{(x,y)} as the first
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two elements and its magnitude as the third.
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}
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@doc-apply[vector-field]{
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Creates 2D plot data to draw a vector-field from a vector-valued
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function.
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}
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@doc-apply[contour]{
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Creates 2D plot data to draw contour lines, rendering a 3D function
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a 2D graph cotours (respectively) to represent the value of the
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function at that position.
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}
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@doc-apply[shade]{
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Creates 2D plot data to draw like @racket[contour], except using
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shading instead of contour lines.
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}
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@doc-apply[surface]{
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Creates 3D plot data to draw a 3D surface in a 2D box, showing only
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the @italic{top} of the surface.
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}
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@defproc[(mix [data (any/c . -> . void?)] ...)
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(any/c . -> . void?)]{
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Creates a procedure that calls each @racket[data] on its argument in
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order. Thus, this function can composes multiple plot @racket[data]s
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into a single data.
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}
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@doc-apply[plot-color?]{
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Returns @racket[#t] if @racket[v] is one of the following symbols,
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@racket[#f] otherwise:
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@racketblock[
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'white 'black 'yellow 'green 'aqua 'pink
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'wheat 'grey 'blown 'blue 'violet 'cyan
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'turquoise 'magenta 'salmon 'red
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]}
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@; ----------------------------------------
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@section[#:tag "curve-fit"]{Curve Fitting}
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The @racketmodname[plot] library uses a non-linear, least-squares fit
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algorithm to fit parameterized functions to given data.
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The code that implements the algorithm is public
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domain, and is used by the @tt{gnuplot} package.
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To fit a particular function to a curve:
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@itemize[
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@item{Set up the independent and dependent variable data. The first
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item in each vector is the independent variable, the second is the
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result. The last item is the weight of the error; we can leave it
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as @racket[1] since all the items weigh the same.
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@racketblock[
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(define data '(#(0 3 1)
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#(1 5 1)
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#(2 7 1)
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#(3 9 1)
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#(4 11 1)))
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]
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}
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@item{Set up the function to be fitted using fit. This particular
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function looks like a line. The independent variables must come
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before the parameters.
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@racketblock[
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(define fit-fun
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(lambda (x m b) (+ b (* m x))))
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]
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}
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@item{If possible, come up with some guesses for the values of the
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parameters. The guesses can be left as one, but each parameter must
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be named.}
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@item{Do the fit.
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@racketblock[
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(define fitted
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(fit fit-fun
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'((m 1) (b 1))
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data))
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]
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}
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@item{View the resulting parameters; for example,
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@racketblock[
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(fit-result-final-params fitted)
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]
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will produce @racketresultfont{(2.0 3.0)}.
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}
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@item{For some visual feedback of the fit result, plot the function
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with the new parameters. For convenience, the structure that is
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returned by the fit command has already the function.
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@racketblock[
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(plot (mix (points data)
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(line (fit-result-function fitted)))
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#:y-max 15)
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]}]
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A more realistic example can be found in
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@filepath{compat/tests/fit-demo-2.rkt} in the @filepath{plot} collection.
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@defproc[(fit [f (real? ... . -> . real?)]
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[guess-list (list/c (list symbol? real?))]
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[data (or/c (list-of (vector/c real? real? real?))
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(list-of (vector/c real? real? real? real?)))])
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fit-result?]{
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Attempts to fit a @defterm{fittable function} to the data that is
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given. The @racket[guess-list] should be a set of arguments and
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values. The more accurate your initial guesses are, the more likely
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the fit is to succeed; if there are no good values for the guesses,
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leave them as @racket[1].}
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@defstruct[fit-result ([rms real?]
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[variance real?]
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[names (listof symbol?)]
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[final-params (listof real?)]
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[std-error (listof real?)]
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[std-error-percent (listof real?)]
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[function (real? ... . -> . real?)])]{
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The @racket[params] field contains an associative list of the
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parameters specified in @racket[fit] and their values. Note that the
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values may not be correct if the fit failed to converge. For a visual
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test, use the @racket[function] field to get the function with the
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parameters in place and plot it along with the original data.}
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@; ----------------------------------------
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@section{Miscellaneous Functions}
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@defproc[(derivative [f (real? . -> . real?)] [h real? .000001])
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(real? . -> . real?)]{
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Creates a function that evaluates the numeric derivative of
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@racket[f]. The given @racket[h] is the divisor used in the
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calculation.}
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@defproc[(gradient [f (real? real? . -> . real?)] [h real? .000001])
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((vector/c real? real?) . -> . (vector/c real? real?))]{
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Creates a vector-valued function that the numeric gradient of
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@racket[f].}
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@defproc[(make-vec [fx (real? real? . -> . real?)] [fy (real? real? . -> . real?)])
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((vector/c real? real?) . -> . (vector/c real? real?))]{
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Creates a vector-values function from two parts.}
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