Mon, 02 Jul 2018 16:43:07 +0100
Merge
sundar@1524 | 1 | /* |
sundar@1524 | 2 | * Copyright (c) 2015, Oracle and/or its affiliates. All rights reserved. |
sundar@1524 | 3 | * |
sundar@1524 | 4 | * Redistribution and use in source and binary forms, with or without |
sundar@1524 | 5 | * modification, are permitted provided that the following conditions |
sundar@1524 | 6 | * are met: |
sundar@1524 | 7 | * |
sundar@1524 | 8 | * - Redistributions of source code must retain the above copyright |
sundar@1524 | 9 | * notice, this list of conditions and the following disclaimer. |
sundar@1524 | 10 | * |
sundar@1524 | 11 | * - Redistributions in binary form must reproduce the above copyright |
sundar@1524 | 12 | * notice, this list of conditions and the following disclaimer in the |
sundar@1524 | 13 | * documentation and/or other materials provided with the distribution. |
sundar@1524 | 14 | * |
sundar@1524 | 15 | * - Neither the name of Oracle nor the names of its |
sundar@1524 | 16 | * contributors may be used to endorse or promote products derived |
sundar@1524 | 17 | * from this software without specific prior written permission. |
sundar@1524 | 18 | * |
sundar@1524 | 19 | * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS |
sundar@1524 | 20 | * IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, |
sundar@1524 | 21 | * THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
sundar@1524 | 22 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR |
sundar@1524 | 23 | * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
sundar@1524 | 24 | * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
sundar@1524 | 25 | * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
sundar@1524 | 26 | * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF |
sundar@1524 | 27 | * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING |
sundar@1524 | 28 | * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
sundar@1524 | 29 | * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
sundar@1524 | 30 | */ |
sundar@1524 | 31 | |
sundar@1524 | 32 | // Simple sample demonstrating "fixed point" computation with Streams |
sundar@1524 | 33 | |
sundar@1524 | 34 | // See also https://mitpress.mit.edu/sicp/chapter1/node21.html#secprocgeneralmethods |
sundar@1524 | 35 | var Stream = Java.type("java.util.stream.Stream"); |
sundar@1524 | 36 | |
sundar@1524 | 37 | // generic fixed point procedure |
sundar@1524 | 38 | function fixed_point(f, init_guess) { |
sundar@1524 | 39 | var tolerance = 0.00001; |
sundar@1524 | 40 | function close_enough(v1, v2) Math.abs(v1 - v2) < tolerance; |
sundar@1524 | 41 | |
sundar@1524 | 42 | var prev; |
sundar@1524 | 43 | return Stream.iterate(init_guess, f) |
sundar@1524 | 44 | .filter(function(x) { |
sundar@1524 | 45 | try { |
sundar@1524 | 46 | return prev == undefined? false : close_enough(prev, x); |
sundar@1524 | 47 | } finally { |
sundar@1524 | 48 | prev = x; |
sundar@1524 | 49 | } |
sundar@1524 | 50 | }) |
sundar@1524 | 51 | .findFirst() |
sundar@1524 | 52 | .get(); |
sundar@1524 | 53 | } |
sundar@1524 | 54 | |
sundar@1524 | 55 | // solution to x = cos(x) |
sundar@1524 | 56 | print(fixed_point(Math.cos, 1.0)) |
sundar@1524 | 57 | |
sundar@1524 | 58 | // solution to x = sin(x) + cos(x) |
sundar@1524 | 59 | print(fixed_point(function(x) Math.sin(x) + Math.cos(x), 1.0)); |
sundar@1524 | 60 | |
sundar@1524 | 61 | // square root by Newton's method |
sundar@1524 | 62 | // http://en.wikipedia.org/wiki/Newton's_method |
sundar@1524 | 63 | function sqrt(n) |
sundar@1524 | 64 | fixed_point(function(x) (x + n/x) / 2, 2.0); |
sundar@1524 | 65 | |
sundar@1524 | 66 | print(sqrt(2)) |
sundar@1524 | 67 | print(sqrt(3)) |
sundar@1524 | 68 | |
sundar@1524 | 69 |