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升级   91% TA的每日心情 | 难过 2012-8-27 18:22 |
|---|
签到天数: 1 天 [LV.1]初来乍到
 |
首先要说明的是本测试系列,除了比较编译效率外,其余所有运行效率的比较都是将matlab的首次运行排出在外,因matlab程序首次运行效率较低。理论上,Forcal程序任意次运行效率都是一样的。不过话又说回来,任意程序包含的函数,有些是需要多次运行的,而有些仅运行一次,甚至一次都不运行,故matlab函数首次运行效率较低应该是一个缺点。但如果说,matlab函数首次运行会对函数进行优化,以后运行效率会显著提高,则matlab函数首次运行效率较低就成了一个优点。9 {+ E9 z9 M, R) d; `
: R( h! o4 _& t=============" n W$ a9 B8 k$ _ q9 e. w
9 C( I2 I( s: I+ B- O- t2 C$ u本次演练要用matlab和Forcal实现两个实用函数并进行测试。当然,对脚本来说,这些函数用C/C++或Fortran来实现应是脚本的最佳选择。. {+ L/ A1 P" @5 e$ q+ `3 x
& O7 @2 b' c- G5 X2 R
=============; M- H6 `! z# x& F, L
2 U# ~5 E6 D$ Y$ ~; }6 l$ E
1、求解实系数方程组的全选主元高斯消去法:包含大量数组元素存取操作% u( U0 h) j- G0 E0 N6 t) M
! @ Q2 G+ r- X/ K
C/C++代码:- #include "stdafx.h"7 z% e8 F* E5 j3 r( z e+ C+ o
- #include <stdio.h>' y- F2 n# G# d& L
- #include <stdlib.h>1 [. y0 z( J1 a: P- J5 M, j- d2 {
- #include "time.h"
S# z. D. O8 J2 V4 k - #include "math.h"
8 }. E1 ]- d9 V4 U - 0 ^1 v1 W7 _% C, w2 Q
- int agaus(double *a,double *b,int n)
8 k3 } M6 R2 f# y8 f- b\" C - {
& f\" F0 _9 z6 ~6 S% V! ~2 c2 i% B1 p - int *js,l,k,i,j,is,p,q;
/ }! I/ c) B$ w+ q' N/ B - double d,t;# J) Y+ u, F' `- W7 X
- js=new int[n];! [) W# Y; d# h1 j$ |$ U$ ?
- l=1;7 y& t$ {\" I+ [* u
- for (k=0;k<=n-2;k++)0 T+ H$ X6 L\" f. J# v6 |
- {
: s: U2 M5 ?6 p, G; g4 L - d=0.0;
% c, ~$ k5 t* {: c& U - for (i=k;i<=n-1;i++)) `4 R( T3 G/ E5 Z/ \2 C% e: f: Q
- {; f) j# O6 {; f5 |
- for (j=k;j<=n-1;j++)+ u' {4 ^) C( B# m5 I( `- o. @2 M
- {
8 K- L6 @* W, S. e3 x& j$ q% `4 ? - t=fabs(a[i*n+j]);
\" }1 K7 C2 }' i! Z7 X; V! n: ]1 t- N7 d - if (t>d) { d=t; js[k]=j; is=i;}: r6 ?0 N\" f9 S& E
- }
8 k( t O* D; { - }5 e\" S6 g% A7 J! _$ t2 w
- if (d+1.0==1.0); w: X! j0 R; Z s\" P9 n+ |/ S
- {
% b+ t& b7 y3 N' k% y4 i - l=0;' j% z; I8 m- C5 q* o# i7 q! f
- }- e: Y5 E- p7 k0 y$ ?\" H\" r# x
- else
3 f1 L# \. j. J# N; ~6 z - {
$ v! i n# m4 ^ - if (js[k]!=k)
- ~# X( N1 v( W3 b( M - {
/ n$ K2 l8 f) S# f - for (i=0;i<=n-1;i++)/ ]+ i, K g: [- ~
- {\" F1 H' j3 e, x* \! i9 y& Q1 v) j
- p=i*n+k; q=i*n+js[k];; F+ \2 n\" U+ v: K+ J+ G
- t=a[p]; a[p]=a[q]; a[q]=t;
* p6 M j, _' I* [$ j V1 L' V - }; h4 [! l Y7 v: w; ?: y3 \3 p. [
- }% b9 L6 n/ B# m\" w7 G* |- h
- if (is!=k)
- O+ @; q5 G' w/ J7 v8 ~# l - {
, F+ n9 I9 A/ F3 H2 e2 `2 U\" s. P - for (j=k;j<=n-1;j++)1 S$ `4 P- y9 O( d1 T1 A
- {
; c2 y' O- N F! v' Y7 d# o - p=k*n+j; q=is*n+j;
( w\" ]7 E- w9 F7 _' m0 v: [ - t=a[p]; a[p]=a[q]; a[q]=t;
0 H: j* \( G: e& i# T - }
4 U: ]0 S6 ^# f0 U5 \0 T. Q; f' A! E8 s - t=b[k]; b[k]=b[is]; b[is]=t;* r# L; U- H- I2 \! ?! S( X
- }
' l# r4 G M x/ v* T- B* ` - }
6 u: L& X2 ]3 n - if (l==0)# ^\" [: f( t. s8 [, T\" {) U% X
- {
0 h t) {0 {; S: j9 E' z - delete[] js; printf("fail\n");- I: [% M: p* Y l; @
- return(0);
, C; N5 ]$ R @1 V3 s7 [ - }
/ g. @\" X- e7 J, Q( r& d6 t - d=a[k*n+k];1 @$ D9 n; e9 ]4 E
- for (j=k+1;j<=n-1;j++), S$ X5 H4 C4 M# w' I
- {
- S C2 b- B2 k7 X. S - p=k*n+j; a[p]=a[p]/d;
3 {8 n# o# v( U: q5 h - }9 e0 Z4 l! }7 i7 I. u5 a9 d
- b[k]=b[k]/d;
5 v% ]( O: |$ E) _4 T - for (i=k+1;i<=n-1;i++)
6 g1 A; z' |( s5 q8 |) v g - {
9 W' v- ^9 F% l/ O6 O4 V - for (j=k+1;j<=n-1;j++)2 {' O\" Y( ?+ k) a9 @
- {
4 ?; T& ], D+ I! i! c1 I- C - p=i*n+j;
' }/ R: ]- ]: ?0 D$ F6 ]1 Z8 @ - a[p]=a[p]-a[i*n+k]*a[k*n+j];
+ g8 t+ W$ f# W: v' ^ - }, o* m( @, I! T$ Z
- b[i]=b[i]-a[i*n+k]*b[k];\" D+ t! J2 H% Y) P0 U7 Z2 h
- }0 {- S/ h O7 l
- }& I; s\" |$ g5 [
- d=a[(n-1)*n+n-1];
5 w2 q. x3 |+ [. ] - if (fabs(d)+1.0==1.0)\" P/ B; P8 Z$ B* d. i4 |/ d% x0 a O
- {
9 D- z$ B0 f) X8 [: f8 Z - delete[] js; printf("fail\n");. C2 _4 ?* V7 F; ?! L
- return(0);5 |! H' d# @1 V& n2 ^, q# D2 p- U% i
- }
6 R% h( m2 h1 \4 s - b[n-1]=b[n-1]/d;
# K5 a0 y\" X) B4 n( I8 Z6 X a - for (i=n-2;i>=0;i--)( J( ?) D, Y\" G$ v$ u
- {. f- m; ~- p! o; v1 x
- t=0.0;8 A1 ]# J\" V( G2 V
- for (j=i+1;j<=n-1;j++)
0 I9 m& h% ]6 Y' r4 [ - {0 M/ \( y\" C0 ]\" F* e
- t=t+a[i*n+j]*b[j];: Q* b1 w G- m7 y
- }& t+ u7 w0 V q& j
- b[i]=b[i]-t;
' k; a( E. L5 C2 W - }
% ]8 U9 g4 P+ e - js[n-1]=n-1;\" `# ~( C7 a5 T' J( V
- for (k=n-1;k>=0;k--)3 O& A\" D: a* t' G, u
- {
0 Y! x) b: N6 j\" A - if (js[k]!=k)
: o2 f( Y7 u' t\" x# S# _2 n - {5 p1 x- j$ l# {8 i- N# S1 z
- t=b[k]; b[k]=b[js[k]]; b[js[k]]=t;
+ A9 h: k+ W& Z' V: y\" g\" P - }2 y\" V, s2 G1 }4 q
- }
* b6 U' M; Q3 s2 { - delete[] js;# @# [# m. E( B: ?
- return(1);
7 d6 Z) C: O4 N# V* ^0 F) z - }: y/ V1 B# x8 R9 f
- $ L% B9 l z2 K/ x# l( Z
- 0 }2 p\" [9 H9 b0 @
- int main(int argc, char *argv[])
7 j6 s& n9 d1 i E! y6 V - {
% ~9 [. b% V R7 _& L) J! C9 R- l - int i,j,k;4 w5 w- @0 } `0 j n0 y! f7 H
- double a[4][4]=% ^$ R- u. w1 Q
- { {0.2368,0.2471,0.2568,1.2671},- C1 l3 P A. k+ W/ L0 R
- {0.1968,0.2071,1.2168,0.2271},! e8 R5 g4 ]( ]& f4 _/ s
- {0.1581,1.1675,0.1768,0.1871},
: H: R; O1 X/ `# e* R/ { - {1.1161,0.1254,0.1397,0.1490} };4 \$ ^: _2 `& t& t
- double b[4]={1.8471,1.7471,1.6471,1.5471};
/ R3 n# F% z/ x\" O1 T1 q, A6 q; X - double aa[4][4],bb[4];
4 t# H* M# u2 e& [1 M8 m) _ j - clock_t tm;
! ]8 f/ U9 ?; s6 k+ L
6 W2 ], A A9 b: W( }+ |- tm=clock();- e+ B\" c& _' \: [! f/ r
- for(i=0;i<10000;i++). C( N1 J% E4 X
- {0 F. o' y5 s( f+ f9 D5 {6 }0 q
- for(j=0;j<4;j++)3 P6 B& {8 [& v( A
- {) j) M) Z$ d3 c) Y' j1 }+ V
- for(k=0;k<4;k++)
& z- z& B( P! v8 c' }: g ^5 ~# Q - {% `1 L- S* J6 X0 ]
- aa[j][k]=a[j][k];# B0 ]6 L/ D6 O' J; h
- }* M1 q& o3 H* f: d; [+ Z
- }2 m# [$ m4 H- S4 h9 v$ ]' H% g
- for(j=0;j<4;j++)1 D( D) \3 r6 b; c
- {
1 S- n/ F; @9 ]\" T - bb[j]=b[j];
2 U$ Q$ @, |3 b8 {% Z - }
! \4 c7 o z z4 Y; T2 x& ^. [% F\" E - agaus((double *)aa,bb,4);
: n7 a) e' k4 }! {: E& a9 J* W - }( O3 Q5 k8 V2 E
- printf("循环 %d 次, 耗时 %d 毫秒。\n", i,(clock()-tm));& w% G6 @3 L# O1 _, {% M
- 1 t( D4 u2 K; c
- for (i=0;i<=3;i++)) f g3 G) ?* H! \2 f3 X+ [& ]
- {( w3 ?4 R5 g! E+ C0 A {+ E! l* I
- printf("x(%d)=%e\n",i,bb[i]);% U5 { a; p) r1 T
- }
\" F* Z5 m3 t( k; \6 B( b6 \; w+ F - }
复制代码 结果:
5 q. O2 u% y3 v8 _# ~9 {循环 10000 次, 耗时 31 毫秒。, y" O+ d! H/ T$ b
x(0)=1.040577e+0005 d! G3 B' e7 X8 [, ]4 G7 {
x(1)=9.870508e-001) _8 {- e6 I G/ `$ D2 B+ ^
x(2)=9.350403e-001' V( f6 E$ A9 L2 J
x(3)=8.812823e-001
5 j0 Y4 B" {5 H* u4 K- u) F; r! [4 K3 G' x3 g- K4 G/ @2 \5 c. A: w
---------& j8 P9 a; d$ B9 d
9 j( m4 l# F* A, Mmatlab 2009a代码:- %file agaus.m
! x) K/ K6 O& j! @ n0 q - function c=agaus(a,b,n)\" C% S1 p0 u+ A# {! V
- js=linspace(0,0,n);
/ X- J2 u, t# \\" j' W) u# h - l=1;
5 [\" e9 F\" F' D# m `% m- l - for k=1:n-1# b! J* \5 U0 J0 x
- d=0.0;
8 U- \0 }; n$ e. w* g+ B - for i=k:n
( A- g! H4 y s$ A& w5 ]. b - for j=k:n# B5 ]2 ^* g# T
- t=abs(a(i,j));2 F2 Q3 o- u. f+ X) C# j! o
- if (t>d)
3 C0 d: f( `6 S# U3 @6 D - d=t; js(k)=j; is=i;
- R, \- M* D1 }) A - end: m0 J7 F: z8 |5 S$ M5 n. Y' U# b1 v
- end
3 ^) f& v0 {# ]% K3 g - end& k5 S j: S9 X
- if d+1.0==1.00 S$ [1 F/ ?) t, \
- l=0;. C' @& j9 v: e( w* p3 e2 c
- else
; c, D, w& {$ g6 p - if js(k)~=k) ?: e2 O& w4 [. g% \8 |
- for i=1:n
. ]% j+ I5 Y! R p/ U - t=a(i,k); a(i,k)=a(i,js(k)); a(i,js(k))=t;
) C; H! x. G( ?8 D% r: Y1 `7 h6 s - end
\" w1 W. p7 z, F, E - end; K% {7 M3 n\" L
- if is~=k+ H* ?$ Y; _( Z) p
- for j=k:n5 C8 n. c- I+ h# g3 p
- t=a(k,j); a(k,j)=a(is,j); a(is,j)=t;\" G# t. Z- P/ x2 E1 P q
- end
$ h8 `- H( M+ E i - t=b(k); b(k)=b(is); b(is)=t;) M! a, o/ \4 j( ]$ s0 C
- end8 W& t1 d( m9 h, ?8 c& \ I3 y
- end: r7 @7 }; g1 z( X$ G( B
- if l==0
1 |5 | e ]. P - printf('fail\n');
6 J, `4 s2 a1 x8 n- n4 e6 p - c=[];
( D' {2 d% c3 a$ V3 E' b, ~+ n+ x: U - return;
$ t\" m' S3 b2 r& ~+ g - end A$ Y) {\" i' d# e6 l
- d=a(k,k);
' Y/ }/ |/ w1 N7 e - for j=k+1:n2 E6 E! |. x7 ?# m; J
- a(k,j)=a(k,j)/d;* z9 X/ F; a\" m& w
- end+ ?% w\" a4 W8 a
- b(k)=b(k)/d;
! [# K6 D/ x H- \ - for i=k+1:n! I& I3 W: ^6 U& r0 e& U
- for j=k+1:n
, ~8 L# o( }\" C/ o' z/ c3 y - a(i,j)=a(i,j)-a(i,k)*a(k,j);
+ v$ T\" z1 K0 |9 I& C( _+ J- @& S\" @ - end/ M% v8 M$ ?2 J5 }: R8 R\" h# D' G
- b(i)=b(i)-a(i,k)*b(k);
! u! f' d: O: o; q1 h - end
& v8 S$ r/ }# Y) Z6 m - end7 H. v1 l K# ~( `- v8 o
- d=a(n,n);: _0 R: Z2 K) x# L. H( T# S8 [4 `
- if abs(d)+1.0==1.03 W: @4 l& ?1 L4 e
- printf('fail\n');
. q+ m5 L\" R! D% G# T6 z - c=[];2 E+ X3 [0 a2 ^( y* d! R& z# V
- return;* f- x( V$ j\" K4 M3 }9 u
- end5 k/ e1 k' E2 ^; _+ R
- b(n)=b(n)/d;) u/ f- r3 {0 h$ H- q\" `8 b. J
- for i=n-1:-1:1, z) j3 P2 V! M
- t=0.0;
& M4 ^1 ?/ F. f A5 W5 U% r- n( n - for j=i+1:n9 g, w& i9 H\" L
- t=t+a(i,j)*b(j);
8 Q8 V( J& u: B7 C - end( P# c; w8 ]: W' ]& C% S3 C# Q8 s
- b(i)=b(i)-t;
& E& c/ o ^( }6 F7 A3 x3 l - end8 B( H3 Y) l' [% z# H) j
- js(n)=n;8 V3 n' j( o, F5 X7 c9 G5 U9 A
- for k=n:-1:1
\" B8 D) n. E+ o/ ? - if js(k)~=k u& K7 Y( R0 j' S3 C
- t=b(k); b(k)=b(js(k)); b(js(k))=t;
! O# ~+ b, @& i( V1 p9 r. ] - end
l/ ]. C, R! F$ _5 k& A$ \ - end% i1 ?+ M- L7 o& }( M: l
- c=b;: M4 W0 _) M; _) p5 `8 [7 g
- return;
7 f* ]8 I9 ^\" h\" Z) y1 D\" k& c - end
# {5 Y, W0 x9 |4 u) p7 w\" y9 o - 7 A4 Q+ s9 p9 f$ n\" J1 g
- a=[0.2368,0.2471,0.2568,1.2671;+ D' t7 O7 p! ]2 a
- 0.1968,0.2071,1.2168,0.2271;
5 L) N& e; g- J9 T2 u& [/ j - 0.1581,1.1675,0.1768,0.1871; ]. W m\" d/ _# E+ }1 j, j2 j# P
- 1.1161,0.1254,0.1397,0.1490] ;9 F+ W7 H0 s7 R: K! b0 N' p
- b=[ 1.8471,1.7471,1.6471,1.5471];
5 f8 {/ `) e/ x. y - % V: E% e# r/ S x; ^
- tic
5 a5 ]2 w* p* | M2 Y) {/ T - for i=1:10000
1 G- N6 c8 `, W\" X6 p+ {) V7 h - c=agaus(a,b,4);6 H2 U% ]6 _' u c: y' ?+ j
- end
5 M7 d* ?# P. ^0 ^( _& P& ` - c
4 a0 R+ `# k# ^4 l4 } - toc
5 w _, L; W0 X# l2 `
+ I- y5 x5 Q% T) k1 h\" {; v c- c =
$ y% Q& N- Y5 t6 Y& N - * Y) K! a' n- f( e8 j
- 1.0406 0.9871 0.9350 0.88131 y; k* W, b4 U$ F' f
: E& c, B0 \% r' S. g- M- Elapsed time is 0.762713 seconds.
复制代码 ----------
4 f# ^ b0 h" I; T: n3 W* Z- O3 o' w7 i# X: g2 s% j& W
Forcal代码: - !using["math","sys"];
- ) ?\\" m' B, K! s/ ]' R7 L# S; ]* C
- agaus(a,b,n : js,l,k,i,j,is, d,t)=
- & g9 s/ c0 i- c. E$ t1 y) Y
- {
- # W9 t! E* Q& f4 `. }8 ]6 \8 h
- oo{ js=array(n)},
- 4 \. Y\\" \\\" @8 ^: ?3 M
- l=1, k=0,* J3 P6 n' `8 a2 L* M) n+ g
- while{ k<n-1,
- / D2 N- T$ T8 `/ u/ y S, L2 V
- d=0.0, i=k,
- ! Y3 q( _, K\\" C, i7 M: Z3 Y
- while{ i<n,7 s3 ~3 z\\" Q! A6 H
- j=k, while{j<n,' X( r, a4 Y: m: A) D+ O
- t=abs(a[i,j]),9 o, p% K' \\\" c9 A3 [
- if{t>d, d=t, js[k]=j, is=i},, s' G$ n# L1 u4 K- u6 E
- j++
- 2 \4 {% m5 |+ y- g8 @8 i3 q
- },9 e7 w. u! J$ W# _/ |( W# P! T& ]
- i++
- * H0 ]0 X\\" U3 N8 Q5 `9 c
- },3 g* X1 i\\" }6 G1 v/ @; V+ C1 y
- which{ d+1.0==1.0, l=0,
- 4 g/ }$ @; f8 p
- { if{ (js[k]!=k),' F# ] v% @ w& \
- i=0, while{i<n,. ^# y) X4 v( F) u3 ^
- t=a[i,k], a[i,k]=a[i,js[k]], a[i,js[k]]=t,\\" ~ h7 Y) E3 V
- i++
- 0 o0 ]& X l3 h$ |6 E+ ?
- }) J/ j7 s6 f/ ?6 @4 F
- },! }% [ H' C- O. y
- if{ (is!=k),4 b: a6 g! D f2 u/ s6 c) g% g
- j=k, while{j<n,% u, ?( }0 I+ O
- t=a[k,j], a[k,j]=a[is,j], a[is,j]=t,
- 6 T$ \; K- j y7 l. c1 V7 y
- j++( h5 u9 g3 v+ }/ O9 w- Q5 S0 d
- },
- ) X7 ^! W4 C# p
- t=b[k], b[k]=b[is], b[is]=t
- 2 _) o& z1 _0 ~
- }
- * N7 \7 `9 v\\" r1 t% [! `+ i
- }2 ~5 J% G6 F* d( H/ C
- },7 A. x1 w& D9 L5 T p' H
- if{ (l==0),) B. K\\" T: `: C& V1 C$ e
- printff("fail\r\n"),
- 0 g! U+ u/ v$ ~\\" c# j
- return(0)2 ^, m6 t' j e* t# D
- },8 m0 r- V4 O+ N2 T0 f
- d=a[k,k],
- d9 F: ?/ k/ X, ?. l+ T3 w
- j=k+1, while {j<n, a[k,j]=a[k,j]/d, j++},/ K; r- ?: B T2 {% l
- b[k]=b[k]/d,
- # ?7 q2 y6 r. D; x
- i=k+1, while {i<n,2 X( N) Z4 B/ F/ n9 U% ^
- j=k+1, while{j<n,3 Q. o5 T% r4 e\\" r, H0 l
- a[i,j]=a[i,j]-a[i,k]*a[k,j],
- 9 {9 U1 u& I2 ^. a) k. n2 Z1 U
- j++- o) v0 \; K2 f/ ~ {. F
- },& i7 s4 m/ t6 Z- @$ W; Y
- b[i]=b[i]-a[i,k]*b[k],\\" e4 R; N* s( e
- i++( y# ^* K. G0 G2 V7 @7 Y
- },
- 9 m1 I3 |& n( F: X( G
- k++
- 5 b0 e D4 Q* Z\\" Y4 `
- },
- * ]: Y) T5 g- u: K# z6 y* _
- d=a[(n-1),n-1],* o1 c1 R6 s+ I\\" Q
- if{ abs(d)+1.0==1.0,+ @8 R8 |; N+ U7 o1 K% b8 w
- printff("fail\r\n"),
- / l8 l# b5 a1 W
- return(0)
- ! Q2 M/ S7 z# N3 x
- },
- , ?, t' J5 V\\" s# i: |\\" e1 @- t
- b[n-1]=b[n-1]/d,
- / m& M# j\\" }+ A- Q, i8 R K
- i=n-2, while{i>=0,
- 7 `: n! ^0 Y9 p7 K. a/ X5 O
- t=0.0,* r& Q) `1 G( M( D) E6 Z
- j=i+1, while{j<n, t=t+a[i,j]*b[j], j++},
- ' O% u; K8 A2 B! k( Z3 p: t4 B
- b[i]=b[i]-t,
- 0 }\\" c( V% _( H( T
- i--
- \\" O; W7 `7 B4 [ w9 m
- },0 d3 p. U\\" i* V1 a3 I, q* n
- js[n-1]=n-1,
- * t$ I1 r: k7 t# M: J. p
- k=n-1, while{k>=0,
- ! E5 P; ~: |7 |( J; J: N4 A1 G
- if{(js[k]!=k), t=b[k], b[k]=b[js[k]], b[js[k]]=t},. t! D- W2 |0 l3 m
- k--' X F* v+ X4 J) H; S/ b& j
- },* Q$ E2 u9 u, k7 K/ T8 F, A# P
- return(1)
- * Y\\" M C$ K _
- };
- 7 F6 T9 M f4 @5 I
- , j! s) Z! _9 d3 ~( G. ]$ U# |, D
- main(:i,a,b,aa,bb,t0)=+ T$ T5 Q! j1 q# y# u/ c& a
- {7 U' f7 `2 i0 m8 o
- oo{a=arrayinit{2,4,4 :
- : _( @, Y h2 X- E, i+ Z9 s1 X
- 0.2368,0.2471,0.2568,1.2671,
- ( b) c9 I( y/ {% M M
- 0.1968,0.2071,1.2168,0.2271,
- / i' r\\" b' y% W! z2 I\\" X* X! s2 I* P' i
- 0.1581,1.1675,0.1768,0.1871,) A9 F4 L, ~4 d+ y% a: b, m) F) b
- 1.1161,0.1254,0.1397,0.1490},4 J6 F' Z1 G5 r- `( L$ W/ ^8 u
- b=arrayinit{1,4 : 1.8471,1.7471,1.6471,1.5471},
- \\" V) b. D' b$ n! m1 }
- aa=array[4,4], bb=array[4]
- , c: `! M o8 S& {. ]1 Q+ B) n
- },
- ' a: i+ s5 b; @% R5 o) Z
- t0=clock(),! S1 Z\\" g9 T) B% V x
- i=0, while{i<10000, aa.=a, bb.=b, agaus(aa,bb,4), i++},; P d1 Y/ N$ o+ h) B6 t
- outm[bb], ^' ?6 N( ~' a
- [clock()-t0]/1000
- : n' b8 l\\" I7 d# z, z
- };
结果:
- H/ s+ R) @3 o) E4 K6 u; {* G 1.04058 0.987051 0.93504 0.881282
, @0 \! w" F% l8 I' P! Q1 b+ e( M% @# x; K
2.125
$ O2 Q6 Q( }: o$ V7 p$ G. V
" L6 @: R! a+ V: D( j/ GForcal用函数sys::A()对数组元素进行存取: - !using["math","sys"];
- . `7 \. N3 f+ a+ G' j
- agaus(a,b,n : js,l,k,i,j,is, d,t)=- a/ f, z( k! C6 ]- D! f. }
- {% z* ~! N J. E, S4 M
- oo{ js=array(n)},- ?; B8 N7 z' J$ _9 K$ _9 B
- l=1, k=0,7 P4 x/ h. d0 P) ?& N0 X; B
- while{ k<n-1,7 v7 j# T6 \+ m% Q2 s
- d=0.0, i=k,0 n5 }7 }\\" y, w
- while{ i<n,
- ; H9 a, T* a! A, v$ H; c
- j=k, while{j<n,; B2 |! y3 N/ d( ?) M, w
- t=abs(A[a,i,j]),
- ) h3 H9 ~8 _5 m- K% d
- if{t>d, d=t, A[js,k]=j, is=i},
- + {$ _8 U\\" W- ~& X, k+ L
- j++. O, d# N4 k\\" w# Q
- },
- 6 L\\" w9 ]9 j1 p
- i++6 S5 {/ g R) ?2 ]0 Y
- },- q6 e- J( _3 L\\" j l
- which{ d+1.0==1.0, l=0,) X' L$ J. a5 C8 S( u( ?
- { if{ (A[js,k]!=k),9 c. q, i' H: u0 G* |: X\\" O$ n
- i=0, while{i<n,
- 1 u+ I. [) j) i1 ~7 c/ C
- t=A[a,i,k], A[a,i,k]=A[a,i,A[js,k]], A[a,i,A[js,k]]=t,
- 4 C6 G+ l; H' K/ c: n
- i++/ B\\" U9 D0 z7 A6 K, v
- }
- 6 X: u& u% f, M\\" i K2 g* U( m* K
- },, L5 H, _* Q+ ~8 j1 R4 E5 U
- if{ (is!=k),
- 8 o\\" q7 y: l9 ?; u h
- j=k, while{j<n,
- 5 R, f3 G' V2 C) F% A% i+ q0 ^$ q0 J8 K
- t=A[a,k,j], A[a,k,j]=A[a,is,j], A[a,is,j]=t,
- 0 _9 u; r3 s+ f+ ]- v/ M
- j++, m% g. A3 s1 Y. J ]- L) k
- },. @$ p\\" [5 O4 l/ K
- t=A[b,k], A[b,k]=A[b,is], A[b,is]=t K( l' _/ Z2 v, W2 J% c H
- }3 ?) E, ^/ r8 K0 F- m) d8 H
- }
- ; r0 n) [, o; Q
- },
- ! _) V c; I$ H! u6 Z. R
- if{ (l==0),
- $ G+ G: Q1 q4 m ]6 t8 `/ S
- printff("fail\r\n"),
- / U7 [2 s- o7 ^\\" A# b$ H
- return(0)
- . m2 a; `( G4 J
- },
- 8 o' c\\" n! r7 A: q
- d=A[a,k,k],
- # s# b1 J7 f! K. C. `6 b/ Q3 T
- j=k+1, while {j<n, A[a,k,j]=A[a,k,j]/d, j++},1 X9 j$ l% K$ M6 } Q/ T
- A[b,k]=A[b,k]/d,
- + y2 P8 i7 H$ P1 }7 G
- i=k+1, while {i<n,
- & Q; z( B V\\" {) w# S
- j=k+1, while{j<n,8 o- i4 X; P. M/ g: M
- A[a,i,j]=A[a,i,j]-A[a,i,k]*A[a,k,j],
- 1 F% R& Q4 v& P# ?1 `
- j++* g/ Y1 }# D\\" P4 \ q5 o
- },1 N6 p4 X' k\\" e! R+ J! g
- A[b,i]=A[b,i]-A[a,i,k]*A[b,k],
- * _: V& J7 w! S6 |0 ^
- i++
- 0 `* d4 O; M7 \+ I
- },/ X! F\\" Z; \, c( Z1 G+ _5 R- q- v
- k++
- v3 A8 q) M* O# ^9 w
- },( n1 j% n: [, ~: w$ D7 l3 ~6 R
- d=A[a,(n-1),n-1],% v+ q& M+ }5 D0 \4 ?7 m$ y, H
- if{ abs(d)+1.0==1.0,
- + V9 A, K0 x1 H/ b6 Y
- printff("fail\r\n"),$ P+ c4 S/ X6 ?2 U1 P# Z7 V( k
- return(0)
- # W q+ k+ C' P; `
- },% O+ S, ] V, ]8 E
- A[b,n-1]=A[b,n-1]/d,% p1 Q+ e6 [ Y( e
- i=n-2, while{i>=0,
- 0 x$ {7 E, J! F1 ?; a; R1 F
- t=0.0,$ M, e& F% F7 D. d
- j=i+1, while{j<n, t=t+A[a,i,j]*A[b,j], j++},
- ^% w8 h* k! a
- A[b,i]=A[b,i]-t,4 u3 P. V$ f w: v; W! o
- i--
- . `9 l$ ?& n; ^- a0 ^0 M
- },
- 5 v9 P* a. ?& J; A1 P; U( T$ Y
- A[js,n-1]=n-1,
- 2 z g/ j. Y; d0 { B/ b
- k=n-1, while{k>=0,; X' g7 _+ i/ n' K( P
- if{(A[js,k]!=k), t=A[b,k], A[b,k]=A[b,A[js,k]], A[b,A[js,k]]=t},
- ( D: s- S5 K9 n
- k--
- - A2 K) |+ U9 w* ^$ q2 X9 F
- },
- 2 V4 @1 B: N9 [/ u) N' {% L
- return(1)
- 7 O |3 ]! T% [% s
- };
- ) a& L/ t7 R# m6 Y0 e# A
- 4 C! p% s: w3 K4 l; d' i
- main(:i,a,b,aa,bb,t0)=8 X\\" R4 o, Y) D, o0 X! l
- {! e) g! D& s8 w3 T @/ i/ R
- oo{a=arrayinit{2,4,4 :
- 3 F% b; a7 E5 s! e8 @\\" R
- 0.2368,0.2471,0.2568,1.2671,' a3 M3 s0 ^# S+ Q\\" ^5 l
- 0.1968,0.2071,1.2168,0.2271,- d\\" R9 c' Y# F8 ^
- 0.1581,1.1675,0.1768,0.1871,9 b7 A3 a4 \0 M- F' B
- 1.1161,0.1254,0.1397,0.1490},3 P, P, @2 D1 _2 Q& p
- b=arrayinit{1,4 : 1.8471,1.7471,1.6471,1.5471},* w0 n1 C9 q8 f6 M4 q* }+ k* B
- aa=array[4,4], bb=array[4]4 x$ k4 M8 s\\" e% p- R
- },, u% C: e5 Q$ S\\" T2 \
- t0=clock(),
- $ t5 y1 Q4 c% J; D+ D2 H\\" T2 ?
- i=0, while{i<10000, aa.=a, bb.=b, agaus(aa,bb,4), i++},
- # x3 _6 h! }5 ^1 [+ c
- outm[bb],
- ( V! K6 }! x4 z6 }8 S
- [clock()-t0]/1000
- 0 ?) m4 N* q9 C5 d0 X: D
- };
结果:/ w, W' j% f1 w T! F& `0 O' p
1.04058 0.987051 0.93504 0.881282
3 ^: A: b0 ]! c6 }
/ `. F% s1 S4 w- h9 d; Q1.454
: g7 r- ]1 A1 |6 ]; ~* A# }; ?8 R
# n' q* }) W% i0 O% E+ ^----------
. d1 l8 O' m) e( H# z% i
! y) ~$ ]2 s) [( P可以看出C/C++、matlab、Forcal耗时之比为 1 :25:68 (Forcal不使用函数sys::A())。
/ I: H4 n( l/ i6 p5 B可以看出C/C++、matlab、Forcal耗时之比为 1 :25:47 (Forcal使用函数sys::A())。. f# S% B4 R. J1 N* o5 @9 p$ n
3 h7 E* ?5 L/ o, o8 G& J本例Forcal耗时较长的原因在于本例程序含有大量的数组元素存取操作。 |
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