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| * [http://www.lisp.org] Lisp的老巢 * [http://clisp.sourceforge.net/] CLisp 的老巢, 我目前使用的Lisp版本. * [http://www.supelec.fr/docs/cltl/cltl2.html] Common Lisp the Language, 2nd Edition 我的Lisp参考书 |
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=== 基础工具集 szcom.lisp === [[Include(/szcom.lisp)]] === LU 分解法解线性方程组 === [[Include(/LU.lisp)]] === 三对角阵的追赶法 === [[Include(/TLU.lisp)]] === 对称阵的LLT 分解法 === [[Include(/LLT.lisp)]] === 对称阵的LDLT分解法 === [[Include(/LDLT.lisp]] === SOR 迭代法解线性方程组 === [[Include(/SOR.lisp)]] ==== 次节标题1 ==== xxx == 章标题2 == === 小节标题2 === {{{ 其它 代码引用 }}} ==== 次节标题2 ==== yyy |
<<Include(/codecollect)>> |
::-- hoxide [2005-10-02 02:51:44]
Contents
1. LISP
2. 资源
- 站点
http://www.lisp.org Lisp的老巢
http://clisp.sourceforge.net/ CLisp 的老巢, 我目前使用的Lisp版本.
http://www.supelec.fr/docs/cltl/cltl2.html Common Lisp the Language, 2nd Edition 我的Lisp参考书
- 电子书 (不保证连接的可用性)
Loving Lisp - the Savy Programmer's Secret Weapon (PDF+code) 非常好的教材, 作者用lisp 20年了,还是个java程序员
The Complete Idiot’s Guide to Common Lisp Packages (PDF) 关于Lisp的 Package 使用的短文, 还讲了名字空间的问题, 看了有启发.
纸质图书 (盗链苏大图书馆了
, 都是老书 ) LISP程序设计 (美) P.H.温斯顿, B.K.P.霍恩同著 这本本书内容比较丰富, 不仅讲了lisp , 还讲了一些人工智能的东西.
LISP 语言 马希文,宋柔编著 马希文先生的全集我看过, 他是数学家, 对语言, 逻辑和计算是很有研究的, 此人已作古(没over能出全集?).
LISP语言 孙宗智,赵瑞清编著 此书比较简洁~~~
- PS: "编著"的书基本上可以断定是垃圾书, 不过不代表不能用来作为入门书籍.
- 站点
3. 代码合集
3.1. 数值分析
3.1.1. 基础工具集 szcom.lisp
;; szcom.lisp
(provide 'szcom)
(defpackage "szcom"
(:use "COMMON-LISP" "EXT")
(:export "RMAT" "PMAT" "PDMAT" "PSMAT" )
(:nicknames "SZCOM")
)
(in-package "szcom")
(defun RMAT (&optional input-stream)
(prog
((m (read input-stream))
(n (read input-stream))
tn
)
(if (not (and (integerp m)
(integerp n)))
(error "RMAT: m or n must be intergers.~%")
)
(setq A (make-array (list m n) :initial-element 0))
(loop for i from 0 below m
do
(loop for j from 0 below n
do
(setq tn (read input-stream))
(cond ((rationalp tn)
(setf (aref A i j) tn))
((null tn) (error "RMAT: unexpected steam END.~%"))
(T (error "RMAT: the member of Array must be numbers~%"))
)
)
)
(return A)
)
)
(defun PMAT (A)
(prog
((m (car (array-dimensions A)))
(n (cadr (array-dimensions A))))
(format t "~%")
(loop for i from 0 to (- m 1)
do
(loop for j from 0 to (- n 1)
do
(format t "~12,6G" (aref A i j))
)
(format t "~%" )
)
)
)
(defun PSMat (A)
(prog
((n (decf (car (array-dimensions A)))))
(loop for i from 0 to n
do
(loop for j from 0 to n
do
(format t "~12,G~^"
(let ((ind (+ (- j i) 1)))
(if (and (<= 0 ind) (< ind 3))
(aref A i ind)
0
)
)
)
)
(format t "~%")
)
)
)
(defun PDMAT (A)
(prog
((n (car (array-dimensions A))))
(format t "~%")
(loop for i from 0 to (- n 1)
do
(loop for j from 0 to (- n 1)
do
(format t "~12,6G~^" (if (= i j) (aref A i) 0)
)
)
(format t "~%" )
)
)
)
3.1.2. LU 分解法解线性方程组
;; LU.lisp
(load "szcom")
(import '(szcom:PMAT szcom:RMAT))
(defun LU-S (A LU)
(prog
((n (car (array-dimensions A)) ))
(loop for k from 0 to n
do
(loop for j from k below n
do
(setf (aref LU k j)
(- (aref A k j)
(loop for q from 0 below k
sum (* (aref LU k q) (aref LU q j))
)
)
)
)
(loop for i from (+ k 1) below n
do
(setf (aref LU i k)
(/
(- (aref A i k)
(loop for q from 0 below k
sum (* (aref LU i q) (aref LU q k))
)
)
(aref LU k k)
)
)
)
)
)
)
(defun LU-C (LU B X)
(prog
((n (car (array-dimensions LU))))
(loop for k from 0 below n
do
(setf (aref X k 0)
( - (aref B k 0)
(loop for i from 0 below k
sum (* (aref X i 0) (aref LU k i)))
)
)
)
(loop for k from (- n 1) downto 0
do
(setf (aref X k 0)
(/
(- (aref X k 0)
(loop for j from (+ k 1) below n
sum (* (aref X j 0) (aref LU k j))
)
)
(aref LU k k)
)
)
)
)
)
(setq A (RMAT))
(setq B (RMAT))
(format t "~% A : ~%")
(PMat A)
(pprint A)
(format t "~% B: ~%")
(PMat B)
(pprint B)
(format t "~%Result of LU: ~%")
;(setq LU (make-array (array-dimensions A)))
(setq LU A)
(LU-S A LU)
(PMat LU)
(format t "~%In Pairs: ~%" )
(pprint LU)
(format t "~%Result of LUS: ~%")
;(setq X (make-array (array-dimensions B)))
(setq X B)
(LU-C LU B X)
(PMat X)
(pprint X)执行结果:
bash-3.00$ cat ex2.dat 4 4 1 4 -2 3 2 2 0 4 3 0 -1 2 1 2 2 -3 4 1 6 2 1 8 bash-3.00$ ./ex2.lisp < ex2.dat A : 1.00000 4.00000 -2.00000 3.00000 2.00000 2.00000 0.000000 4.00000 3.00000 0.000000 -1.00000 2.00000 1.00000 2.00000 2.00000 -3.00000 #2A((1 4 -2 3) (2 2 0 4) (3 0 -1 2) (1 2 2 -3)) B: 6.00000 2.00000 1.00000 8.00000 #2A((6) (2) (1) (8)) Result of LU: 1.00000 4.00000 -2.00000 3.00000 2.00000 -6.00000 4.00000 -2.00000 3.00000 2.00000 -3.00000 -3.00000 1.00000 0.333333 -.888889 -8.00000 In Pairs: #2A((1 4 -2 3) (2 -6 4 -2) (3 2 -3 -3) (1 1/3 -8/9 -8)) Result of LUS: 1.00000 2.00000 0.000000 -1.00000 #2A((1) (2) (0) (-1))
3.1.3. 三对角阵的追赶法
;; TLU.lisp
(load "szcom")
(import '(szcom:PMAT szcom:PSMAT szcom:RMAT))
(defun shooting (A LU)
(prog
((n (car (array-dimensions A))))
(loop for k from 0 below n
do
(setf (aref LU k 0) (aref A k 0))
(setf (aref LU k 1)
( - (aref A k 1)
(if (> k 0)
(* (aref LU k 0)
(aref LU (- k 1) 2)
)
0)
)
)
(if (< k n)
(setf (aref LU k 2)
(/ (aref A k 2)
(aref LU k 1)
)
)
)
)
)
)
(defun shoot (LU B X)
(prog
((n (car (array-dimensions LU))))
(loop for k from 0 below n
do
(setf (aref X k 0)
(/
(- (aref B k 0)
(if (> k 0)
(* (aref LU k 0) (aref X (- k 1) 0))
0
)
)
(aref LU k 1)
)
)
)
(pprint X)
(loop for k from (- n 1) downto 0
do
(decf (aref X k 0)
(if (< k (- n 1))
(* (aref LU k 2) (aref X (+ k 1) 0))
0)
)
)
)
)
(setq A (RMAT))
(setq B (RMAT))
(format t "~% A : ~%")
(PSMat A)
(pprint A)
(format t "~% B: ~%")
(PMat B)
(pprint B)
(format t "~%Result of shooting: ~%")
(setq LU (make-array (array-dimensions A)))
(shooting A LU)
(PSMat LU)
(format t "~%In Pairs: ~%" )
(pprint LU)
(format t "~%Result of shooting result: ~%")
(setq X (make-array (array-dimensions B)))
(shoot LU B X)
(PMat X)
(pprint X)例子:
bash-3.00$ cat ex3.dat
5 3
0 13 12
11 10 9
8 7 6
5 4 3
2 1 0
5 1
3
0
-2
6
8
bash-3.00$ ./ex3.lisp < ex3.dat
A :
13. 12. 0.0 0.0 0.0
11. 10. 9. 0.0 0.0
0.0 8. 7. 6. 0.0
0.0 0.0 5. 4. 3.
0.0 0.0 0.0 2. 1.
#2A((0 13 12) (11 10 9) (8 7 6) (5 4 3) (2 1 0))
B:
3.00000
0.000000
-2.00000
6.00000
8.00000
#2A((3) (0) (-2) (6) (8))
Result of shooting:
13. .9230769 0.0 0.0 0.0
11. -.15384616 -58.5 0.0 0.0
0.0 8. 475. 1.263157900E-2 0.0
0.0 0.0 5. 3.9368422 .7620321
0.0 0.0 0.0 2. -.5240642
In Pairs:
#2A((0 13 12/13)
(11 -2/13 -117/2)
(8 475 6/475)
(5 374/95 285/374)
(2 -98/187 0))
Result of shooting result:
#2A((3/13) (33/2) (-134/475) (32/17) (-396/49))
5.71837
-5.94490
-.383673
8.04082
-8.08163
#2A((1401/245) (-2913/490) (-94/245) (394/49) (-396/49))
3.1.4. 对称阵的LLT 分解法
;; LLT.lisp
(load "szcom")
(import '(szcom:RMAT szcom:PMAT))
(defun LLT (A)
(prog
((n (car (array-dimensions A))))
(loop for k from 0 below n
do
(setf (aref A k k)
(sqrt
(- (aref A k k)
(loop for j from 0 to (- k 1)
sum (* (aref A k j)
(aref A j k)
)
)
)
)
)
(loop for i from (+ k 1) below n
do
(setf (aref A i k)
(/ (- (aref A i k)
(loop for j from 0 to (- k 1)
sum (* (aref A i j)
(aref A k j)
)
)
)
(aref A k k)
)
)
(setf (aref A k i ) (aref A i k))
)
)
)
)
(setq A (RMAT))
(setq B (RMAT))
(format t "~% A : ~%")
(PMat A)
(pprint A)
(pprint B)
(format t "~%Result of LLT: ~%")
(LLT A)
(PMat A)
(format t "~%In Pairs: ~%" )
(pprint A)
例子
bash-3.00$ cat LLT.dat
4 4
10 7 8 7
7 5 6 5
8 6 10 9
7 5 9 10
4 1
1
2
3
4bash-3.00$ ./LLT.lisp < LLT.dat
A :
10.0000 7.00000 8.00000 7.00000
7.00000 5.00000 6.00000 5.00000
8.00000 6.00000 10.0000 9.00000
7.00000 5.00000 9.00000 10.0000
#2A((10 7 8 7) (7 5 6 5) (8 6 10 9) (7 5 9 10))
#2A((1) (2) (3) (4))
Result of LLT:
3.16228 2.21359 2.52982 2.21359
2.21359 0.316228 1.26491 0.316228
2.52982 1.26491 1.41421 2.12132
2.21359 0.316228 2.12132 0.707108
In Pairs:
#2A((3.1622777 2.2135944 2.529822 2.2135944)
(2.2135944 0.3162276 1.2649105 0.3162276)
(2.529822 1.2649105 1.414214 2.1213198)
(2.2135944 0.3162276 2.1213198 0.70710814))
3.1.5. 对称阵的LDLT分解法
;; LDLT.lisp
(load "szcom")
(import '(szcom:RMAT szcom:PMAT szcom:PDMAT))
(defun LDLT (A)
(prog
((n (car (array-dimensions A))))
(setq L (make-array (list n n) :initial-element 0)
D (make-array (list n) :initial-element 0))
(loop for k from 0 below n
do
(setf (aref D k)
(- (aref A k k)
(loop for j from 0 to (- k 1)
sum (* (aref L k j)
(aref L k j)
(aref D j)
)
)
)
)
(setf (aref L k k) 1)
(loop for i from (+ k 1) below n
do
(setf (aref L i k)
(/ (- (aref A i k)
(loop for j from 0 to (- k 1)
sum (* (aref L i j)
(aref L k j)
(aref D j)
)
))
(aref D k)
)
)
)
)
(return (cons L D))
)
)
(setq A (RMAT))
(setq B (RMAT))
(format t "~% A : ~%")
(PMat A)
(pprint A)
(pprint B)
(format t "~%Result of LDLT: ~%")
(setq res (LDLT A))
(PMat (car res))
(PDMAT (cdr res))
(format t "~%In Pairs: ~%" )
(pprint res)例子:
bash-3.00$ cat LLT.dat 4 4 10 7 8 7 7 5 6 5 8 6 10 9 7 5 9 10 4 1 1 2 3 4 bash-3.00$ ./LDLT.lisp < LLT.dat A : 10.0000 7.00000 8.00000 7.00000 7.00000 5.00000 6.00000 5.00000 8.00000 6.00000 10.0000 9.00000 7.00000 5.00000 9.00000 10.0000 #2A((10 7 8 7) (7 5 6 5) (8 6 10 9) (7 5 9 10)) #2A((1) (2) (3) (4)) Result of LDLT: 1.00000 0.000000 0.000000 0.000000 0.700000 1.00000 0.000000 0.000000 0.800000 4.00000 1.00000 0.000000 0.700000 1.00000 1.50000 1.00000 10.0000 0.000000 0.000000 0.000000 0.000000 0.100000 0.000000 0.000000 0.000000 0.000000 2.00000 0.000000 0.000000 0.000000 0.000000 0.500000 In Pairs: (#2A((1 0 0 0) (7/10 1 0 0) (4/5 4 1 0) (7/10 1 3/2 1)) . #(10 1/10 2 1/
3.1.6. SOR 迭代法解线性方程组
;; SOR.lisp
(load "szcom")
(import '(szcom:PMAT szcom:RMAT))
(defun SOR (A B X &key ((:weight w) 1.0) ((:ep ep) 1.e-8 ))
(prog ((n (car (array-dimensions B)))
(k 0) (e ep) tx)
(loop until (< e ep)
do
(setf e 0)
(loop for k from 0 below n
do
(setf tx
(/
(- (aref B k 0)
(loop for j from 0 below n
sum
(if (= j k) 0
(* (aref A k j)
(aref X j 0) )
)))
(aref A k k)
)
)
(setf tx (+ (* w tx) (* (- 1 w) (aref X k 0)) ))
(setf e (max e (abs (- (aref X k 0) tx))))
(setf (aref X k 0) tx)
)
(incf k)
;(pprint X)
)
(return k)
)
)
(setq A (RMAT))
(setq B (RMAT))
(format t "~% A : ~%")
(PMat A)
(pprint A)
(format t "~% B: ~%")
(PMat B)
(pprint B)
(format t "~%Result of SOR result: ~%")
(setq X (make-array (array-dimensions B) :initial-element 0))
(setq k (SOR A B X :weight 1.3 :ep 1e-5))
(format t "~% Loop ~D time(s)" k)
(PMat X)
(pprint X)例子:
bash-3.00$ cat SOR.dat 4 4 -4 1 1 1 1 -4 1 1 1 1 -4 1 1 1 1 -4 4 1 1 1 1 1 bash-3.00$ ./SOR.lisp < SOR.dat A : -4.00000 1.00000 1.00000 1.00000 1.00000 -4.00000 1.00000 1.00000 1.00000 1.00000 -4.00000 1.00000 1.00000 1.00000 1.00000 -4.00000 #2A((-4 1 1 1) (1 -4 1 1) (1 1 -4 1) (1 1 1 -4)) B: 1.00000 1.00000 1.00000 1.00000 #2A((1) (1) (1) (1)) Result of SOR result: Loop 12 time(s) -1.00000 -.999999 -1.00000 -1.00000 #2A((-1.0000014) (-0.99999917) (-1.0) (-1.0000004))