71 lines
2.3 KiB
Factor
71 lines
2.3 KiB
Factor
! :folding=indent:collapseFolds=0:
|
|
|
|
! $Id$
|
|
!
|
|
! Copyright (C) 2004 Slava Pestov.
|
|
!
|
|
! Redistribution and use in source and binary forms, with or without
|
|
! modification, are permitted provided that the following conditions are met:
|
|
!
|
|
! 1. Redistributions of source code must retain the above copyright notice,
|
|
! this list of conditions and the following disclaimer.
|
|
!
|
|
! 2. Redistributions in binary form must reproduce the above copyright notice,
|
|
! this list of conditions and the following disclaimer in the documentation
|
|
! and/or other materials provided with the distribution.
|
|
!
|
|
! THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
|
|
! INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
|
|
! FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
|
|
! DEVELOPERS AND CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
|
! SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
|
|
! PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
|
|
! OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
|
|
! WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
|
|
! OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
|
|
! ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
|
|
IN: math
|
|
USE: combinators
|
|
USE: kernel
|
|
USE: lists
|
|
USE: logic
|
|
USE: math
|
|
USE: stack
|
|
|
|
: multiplier ( n -- 2|4 )
|
|
odd? 4 2 ? ;
|
|
|
|
: (multipliers) ( list n -- list )
|
|
dup 2 <= [
|
|
drop
|
|
] [
|
|
dup >r multiplier swons r> pred (multipliers)
|
|
] ifte ;
|
|
|
|
: multipliers ( n -- list )
|
|
#! The value n must be odd. Makes a list like [ 1 4 2 4 1 ]
|
|
[ 1 ] swap (multipliers) 1 swons ;
|
|
|
|
: x-values ( lower upper n -- list )
|
|
#! The value n must be odd.
|
|
pred >r over - r> dup succ count [
|
|
>r 3dup r> swap / * +
|
|
] map >r 3drop r> ;
|
|
|
|
: y-values ( lower upper n quot -- values )
|
|
>r x-values r> map ;
|
|
|
|
: (simpson) ( lower upper n quot -- value )
|
|
over multipliers >r y-values r> *|+ ;
|
|
|
|
: h ( lower upper n -- h )
|
|
transp - swap pred / 3 / ;
|
|
|
|
: simpson ( lower upper n quot -- value )
|
|
#! Compute the integral between the lower and upper bound,
|
|
#! using Simpson's method with n steps. The value of n must
|
|
#! be odd. The quotation must have stack effect
|
|
#! ( x -- f(x) ).
|
|
>r 3dup r> (simpson) >r h r> * ;
|