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source: branches/f4grobner/utils.lisp@ 4093

Last change on this file since 4093 was 1249, checked in by Marek Rychlik, 9 years ago

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File size: 3.0 KB
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1;;; -*- Mode: Lisp -*-
2;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
3;;;
4;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
5;;;
6;;; This program is free software; you can redistribute it and/or modify
7;;; it under the terms of the GNU General Public License as published by
8;;; the Free Software Foundation; either version 2 of the License, or
9;;; (at your option) any later version.
10;;;
11;;; This program is distributed in the hope that it will be useful,
12;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
13;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14;;; GNU General Public License for more details.
15;;;
16;;; You should have received a copy of the GNU General Public License
17;;; along with this program; if not, write to the Free Software
18;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
19;;;
20;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
21
22(defpackage "UTILS"
23 (:use :cl)
24 (:export "MAKELIST-1" "MAKELIST" "SUMMATION" "INNER-PRODUCT"))
25
26(in-package :utils)
27
28;; Macros for making lists with iterators
29;;
30;; MAKELIST-1 makes a list with one iterator, while MAKELIST accepts an
31;; arbitrary number of iterators
32
33;; Sample usage:
34;; Without a step:
35;; >(makelist-1 (* 2 i) i 0 10)
36;; (0 2 4 6 8 10 12 14 16 18 20)
37;; With a step of 3:
38;; >(makelist-1 (* 2 i) i 0 10 3)
39;; (0 6 12 18)
40
41;; Generate sums of squares of numbers between 1 and 4:
42;; >(makelist (+ (* i i) (* j j)) (i 1 4) (j 1 i))
43;; (2 5 8 10 13 18 17 20 25 32)
44;; >(makelist (list i j '---> (+ (* i i) (* j j))) (i 1 4) (j 1 i))
45;; ((1 1 ---> 2) (2 1 ---> 5) (2 2 ---> 8) (3 1 ---> 10) (3 2 ---> 13)
46;; (3 3 ---> 18) (4 1 ---> 17) (4 2 ---> 20) (4 3 ---> 25) (4 4 ---> 32))
47
48;; Evaluate expression expr with variable set to lo, lo+1,... ,hi
49;; and put the results in a list.
50(defmacro makelist-1 (expr var lo hi &optional (step 1))
51 (let ((l (gensym)))
52 `(do ((,var ,lo (+ ,var ,step))
53 (,l nil (cons ,expr ,l)))
54 ((> ,var ,hi) (reverse ,l))
55 (declare (fixnum ,var)))))
56
57(defmacro makelist (expr (var lo hi &optional (step 1)) &rest more)
58 (if (endp more)
59 `(makelist-1 ,expr ,var ,lo ,hi ,step)
60 (let* ((l (gensym)))
61 `(do ((,var ,lo (+ ,var ,step))
62 (,l nil (nconc ,l `,(makelist ,expr ,@more))))
63 ((> ,var ,hi) ,l)
64 (declare (fixnum ,var))))))
65
66(defmacro summation (expr (var lo hi &optional (step 1)) &optional (add '+) (init-val 0))
67 (let ((r (gensym)))
68 `(do ((,r ,init-val)
69 (,var ,lo (+ ,var ,step)))
70 ((> ,var ,hi) ,r)
71 (setf ,r (,add ,r ,expr)))))
72
73(defmacro inner-product (x y &optional (add '+) (mult '*) (init-val 0))
74 (let ((i (gensym))
75 (xx (gensym))
76 (yy (gensym)))
77 `(let ((,xx ,x)
78 (,yy ,y))
79 (summation (,mult (elt ,xx ,i) (elt ,yy ,i))
80 (,i 0 (1- (length ,xx)))
81 ,add
82 ,init-val))))
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