source: branches/f4grobner/utils.lisp

;;; -*-  Mode: Lisp -*- 
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;;;                                                                              
;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>          
;;;                                                                              
;;;  This program is free software; you can redistribute it and/or modify        
;;;  it under the terms of the GNU General Public License as published by        
;;;  the Free Software Foundation; either version 2 of the License, or           
;;;  (at your option) any later version.                                         
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;;;  This program is distributed in the hope that it will be useful,             
;;;  but WITHOUT ANY WARRANTY; without even the implied warranty of              
;;;  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the               
;;;  GNU General Public License for more details.                                
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;;;  You should have received a copy of the GNU General Public License           
;;;  along with this program; if not, write to the Free Software                 
;;;  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  
;;;                                                                              
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(defpackage "UTILS"
  (:use :cl)
  (:export "MAKELIST-1" "MAKELIST" "SUMMATION" "INNER-PRODUCT"))

(in-package :utils)

;; Macros for making lists with iterators
;;
;; MAKELIST-1 makes a list with one iterator, while MAKELIST accepts an
;; arbitrary number of iterators

;; Sample usage:
;; Without a step:
;; >(makelist-1 (* 2 i) i 0 10)
;; (0 2 4 6 8 10 12 14 16 18 20)
;; With a step of 3:
;; >(makelist-1 (* 2 i) i 0 10 3)
;; (0 6 12 18)

;; Generate sums of squares of numbers between 1 and 4:
;; >(makelist (+ (* i i) (* j j)) (i 1 4) (j 1 i))
;; (2 5 8 10 13 18 17 20 25 32)
;; >(makelist (list i j '---> (+ (* i i) (* j j))) (i 1 4) (j 1 i))
;; ((1 1 ---> 2) (2 1 ---> 5) (2 2 ---> 8) (3 1 ---> 10) (3 2 ---> 13)
;; (3 3 ---> 18) (4 1 ---> 17) (4 2 ---> 20) (4 3 ---> 25) (4 4 ---> 32))

;; Evaluate expression expr with variable set to lo, lo+1,... ,hi
;; and put the results in a list.
(defmacro makelist-1 (expr var lo hi &optional (step 1))
  (let ((l (gensym)))
    `(do ((,var ,lo (+ ,var ,step))
          (,l nil (cons ,expr ,l)))
         ((> ,var ,hi) (reverse ,l))
       (declare (fixnum ,var)))))

(defmacro makelist (expr (var lo hi &optional (step 1)) &rest more)
  (if (endp more)
      `(makelist-1 ,expr ,var ,lo ,hi ,step)
    (let* ((l (gensym)))
      `(do ((,var ,lo (+ ,var ,step))
            (,l nil (nconc ,l `,(makelist ,expr ,@more))))
           ((> ,var ,hi) ,l)
         (declare (fixnum ,var))))))

(defmacro summation (expr (var lo hi &optional (step 1)) &optional (add '+) (init-val 0))
  (let ((r (gensym)))
    `(do ((,r ,init-val)
          (,var ,lo (+ ,var ,step)))
         ((> ,var ,hi) ,r)
       (setf ,r (,add ,r ,expr)))))

(defmacro inner-product (x y &optional (add '+) (mult '*) (init-val 0))
  (let ((i (gensym))
        (xx (gensym))
        (yy (gensym)))
    `(let ((,xx ,x)
           (,yy ,y))
       (summation (,mult (elt ,xx ,i) (elt ,yy ,i))
                  (,i 0 (1- (length ,xx)))
                  ,add 
                  ,init-val))))