[1] | 1 | head 1.4;
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| 2 | access;
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| 3 | symbols;
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| 4 | locks; strict;
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| 5 | comment @;;; @;
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| 6 |
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| 7 |
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| 8 | 1.4
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| 9 | date 2009.01.23.10.45.43; author marek; state Exp;
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| 10 | branches;
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| 11 | next 1.3;
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| 12 |
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| 13 | 1.3
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| 14 | date 2009.01.23.10.43.25; author marek; state Exp;
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| 15 | branches;
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| 16 | next 1.2;
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| 17 |
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| 18 | 1.2
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| 19 | date 2009.01.22.04.03.29; author marek; state Exp;
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| 20 | branches;
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| 21 | next 1.1;
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| 22 |
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| 23 | 1.1
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| 24 | date 2009.01.19.07.51.00; author marek; state Exp;
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| 25 | branches;
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| 26 | next ;
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| 27 |
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| 28 |
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| 29 | desc
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| 30 | @@
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| 31 |
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| 32 |
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| 33 | 1.4
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| 34 | log
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| 35 | @*** empty log message ***
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| 36 | @
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| 37 | text
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| 38 | @#|
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| 39 | $Id: makelist.lisp,v 1.3 2009/01/23 10:43:25 marek Exp marek $
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| 40 | *--------------------------------------------------------------------------*
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| 41 | | Copyright (C) 1994, Marek Rychlik (e-mail: rychlik@@math.arizona.edu) |
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| 42 | | Department of Mathematics, University of Arizona, Tucson, AZ 85721 |
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| 43 | | |
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| 44 | | Everyone is permitted to copy, distribute and modify the code in this |
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| 45 | | directory, as long as this copyright note is preserved verbatim. |
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| 46 | *--------------------------------------------------------------------------*
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| 47 | |#
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| 48 |
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| 49 | (defpackage "MAKELIST"
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| 50 | (:use "COMMON-LISP")
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| 51 | (:export makelist-1 makelist list-of set-of union-of select sum summation difference standard-vector))
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| 52 |
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| 53 | (in-package "MAKELIST")
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| 54 |
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| 55 | #+debug(proclaim '(optimize (speed 0) (debug 3)))
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| 56 | #-debug(proclaim '(optimize (speed 3) (debug 0)))
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| 57 |
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| 58 |
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| 59 | ;; Macros for making lists with iterators - an exammple of GENSYM
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| 60 | ;; MAKELIST-1 makes a list with one iterator, while MAKELIST accepts an
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| 61 | ;; arbitrary number of iterators
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| 62 |
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| 63 | ;; Sample usage:
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| 64 | ;; Without a step:
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| 65 | ;; >(makelist-1 (* 2 i) i 0 10)
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| 66 | ;; (0 2 4 6 8 10 12 14 16 18 20)
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| 67 | ;; With a step of 3:
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| 68 | ;; >(makelist-1 (* 2 i) i 0 10 3)
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| 69 | ;; (0 6 12 18)
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| 70 |
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| 71 | ;; Generate sums of squares of numbers between 1 and 4:
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| 72 | ;; >(makelist (+ (* i i) (* j j)) (i 1 4) (j 1 i))
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| 73 | ;; (2 5 8 10 13 18 17 20 25 32)
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| 74 | ;; >(makelist (list i j '---> (+ (* i i) (* j j))) (i 1 4) (j 1 i))
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| 75 | ;; ((1 1 ---> 2) (2 1 ---> 5) (2 2 ---> 8) (3 1 ---> 10) (3 2 ---> 13)
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| 76 | ;; (3 3 ---> 18) (4 1 ---> 17) (4 2 ---> 20) (4 3 ---> 25) (4 4 ---> 32))
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| 77 |
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| 78 | ;; Summation with SUM:
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| 79 | ;; Sum of squares of integers from 1 to 10:
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| 80 | ;; >(sum (expt i 2) (i 1 10))
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| 81 | ;; 385
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| 82 | ;; Sum of inverses of integers from 1 to 50:
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| 83 | ;; >(sum (/ n) (n 1 50))
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| 84 | ;; 13943237577224054960759/3099044504245996706400
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| 85 | ;; Sum of 1/(m^2+n^2) where m,n vary from 1 to 10:
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| 86 | ;; >(sum (/ (+ (expt m 2) (expt n 2))) (n 1 10) (m 1 10))
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| 87 | ;; 125085870045079516933345908893314157/42204464874461454985621846571472000
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| 88 | ;; Sum of 1/(m^2+n^2) where m,n vary from 1 to 10 and m>n:
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| 89 | ;; >(sum (/ (+ (expt m 2) (expt n 2))) (n 1 10) (m 1 (1- n)))
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| 90 | ;; 13092731173226115661182811487147/11962716801151206061684196874000
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| 91 |
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| 92 | ;; Evaluate expression expr with variable set to lo, lo+1,... ,hi
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| 93 | ;; and put the results in a list.
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| 94 | (defmacro makelist-1 (expr var lo hi &optional (step 1))
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| 95 | (let ((l (gensym)))
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| 96 | `(do ((,var ,lo (+ ,var ,step))
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| 97 | (,l nil (cons ,expr ,l)))
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| 98 | ((> ,var ,hi) (reverse ,l))
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| 99 | (declare (fixnum ,var)))))
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| 100 |
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| 101 | (defmacro makelist (expr (var lo hi &optional (step 1)) &rest more)
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| 102 | (if (endp more)
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| 103 | `(makelist-1 ,expr ,var ,lo ,hi ,step)
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| 104 | (let* ((l (gensym)))
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| 105 | `(do ((,var ,lo (+ ,var ,step))
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| 106 | (,l nil (nconc ,l `,(makelist ,expr ,@@more))))
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| 107 | ((> ,var ,hi) ,l)
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| 108 | (declare (fixnum ,var))))))
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| 109 |
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| 110 | (defmacro sum (&body body)
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| 111 | `(reduce #'+ (makelist ,@@body)))
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| 112 |
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| 113 | (defmacro summation (&body body)
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| 114 | ``(+ ,@@(makelist ,@@body)))
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| 115 |
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| 116 | (defmacro difference (&body body)
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| 117 | ``(- ,@@(makelist ,@@body)))
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| 118 |
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| 119 | ;; List of all EXPR where VAR varies over the list LST
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| 120 | (defmacro list-of (expr (var lst) &rest more)
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| 121 | (if (endp more)
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| 122 | `(list-of-1 ,expr ,var ,lst)
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| 123 | (let ((l (gensym)))
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| 124 | `(let ((,l))
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| 125 | (dolist (,var ,lst ,l)
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| 126 | (setf ,l (nconc ,l ,`(list-of ,expr ,@@more))))))))
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| 127 |
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| 128 | (defmacro list-of-1 (expr var lst)
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| 129 | (let ((l (gensym)))
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| 130 | `(let ((,l))
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| 131 | (dolist (,var ,lst (reverse ,l))
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| 132 | (setf ,l ,`(cons ,expr ,l))))))
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| 133 |
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| 134 | ;; Union of all EXPR where VAR varies over the list LST
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| 135 | (defmacro union-of (expr (var lst) &rest more)
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| 136 | (if (endp more)
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| 137 | `(union-of-1 ,expr ,var ,lst)
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| 138 | (let ((l (gensym)))
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| 139 | `(let ((,l))
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| 140 | (dolist (,var ,lst ,l)
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| 141 | (setf ,l (union ,l ,`(union-of ,expr ,@@more) :test #'equalp)))))))
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| 142 |
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| 143 | (defmacro union-of-1 (expr var lst)
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| 144 | (let ((l (gensym)))
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| 145 | `(let ((,l))
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| 146 | (dolist (,var ,lst (reverse ,l))
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| 147 | (setf ,l ,`(union ,expr ,l :test #'equalp))))))
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| 148 |
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| 149 |
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| 150 | ;; Set of all EXPR where VAR varies over the list LST
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| 151 | (defmacro set-of (expr (var lst) &rest more)
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| 152 | (if (endp more)
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| 153 | `(set-of-1 ,expr ,var ,lst)
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| 154 | (let ((l (gensym)))
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| 155 | `(let ((,l))
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| 156 | (dolist (,var ,lst ,l)
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| 157 | (setf ,l (union ,l ,`(set-of ,expr ,@@more) :test #'equalp)))))))
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| 158 |
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| 159 | (defmacro set-of-1 (expr var lst)
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| 160 | (let ((l (gensym)))
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| 161 | `(let ((,l))
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| 162 | (dolist (,var ,lst (reverse ,l))
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| 163 | (pushnew ,expr ,l :test #'equalp)))))
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| 164 |
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| 165 | ;; sublist of LST consisting of elements with indecies in IND
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| 166 | (defun select (ind lst)
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| 167 | (cond
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| 168 | ((endp ind) nil)
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| 169 | (t (cons (elt lst (car ind)) (select (cdr ind) lst)))))
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| 170 |
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| 171 | (defun standard-vector (n k &optional (coeff 1)
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| 172 | &aux (v (make-list n :initial-element 0)))
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| 173 | "Returns vector (0 0 ... 1 ... 0 0) of length N, where 1 appears on K-th place."
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| 174 | (setf (elt v k) coeff)
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| 175 | v)
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| 176 | @
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| 177 |
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| 178 |
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| 179 | 1.3
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| 180 | log
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| 181 | @*** empty log message ***
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| 182 | @
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| 183 | text
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| 184 | @d2 1
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| 185 | a2 1
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| 186 | $Id: makelist.lisp,v 1.2 2009/01/22 04:03:29 marek Exp marek $
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| 187 | d14 1
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| 188 | a14 1
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| 189 | (:export makelist-1 makelist list-of set-of union-of select sum summation difference std-vector))
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| 190 | d134 1
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| 191 | a134 1
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| 192 | (defun std-vector (n k &optional (coeff 1)
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| 193 | @
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| 194 |
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| 195 |
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| 196 | 1.2
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| 197 | log
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| 198 | @*** empty log message ***
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| 199 | @
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| 200 | text
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| 201 | @d2 1
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| 202 | a2 1
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| 203 | $Id$
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| 204 | d14 1
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| 205 | a14 1
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| 206 | (:export makelist-1 makelist list-of set-of union-of select sum summation difference standard-vector))
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| 207 | d134 1
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| 208 | a134 1
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| 209 | (defun standard-vector (n k &optional (coeff 1)
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| 210 | @
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| 211 |
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| 212 |
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| 213 | 1.1
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| 214 | log
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| 215 | @Initial revision
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| 216 | @
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| 217 | text
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| 218 | @d2 1
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| 219 | a2 1
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| 220 | $Id: makelist.lisp,v 1.12 2001/11/06 05:54:25 marek Exp $
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| 221 | d18 2
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| 222 | a19 1
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| 223 | (proclaim '(optimize (speed 0) (debug 3)))
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| 224 | @
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