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lijun0711
[专家分：0] 发布于 2005-09-28 18:45:00
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<用Doolittle分解求方阵的逆>
设A=LR,L为单位下三角阵，R为上三角阵，则A-1 =R-1 L-1，分别求出R-1和L-1，相乘即可得A-1。
(使用说明)
输入参数:
N 方阵A(N,N)的阶数。
A(N,N) N阶方阵，按行存放。
输出参数:
W 标志，W=0说明A非奇异，W=1表示A奇异，不存放A的逆。
D(N,N) 存放A的逆的元素。
中间工作单元:
C(N,N) N阶方阵
(下面有VB的程序,麻烦帮我改改成PASCAL好吗)
沙发
lijun0711 [专家分：0] 发布于 2005-09-28 18:47:00
* 用Doolittle 分解求方阵的逆 *
30 '******************************************************
50 Dim A(N, N), C(N, N), D(N, N)
60 Print Tan(3); "EG:"; Tab(8); "THE MATRIX A": Print
70 For I = 1 To N: For J = 1 To N
80 READ A(I, J): Print USING; "####.#"; A(I, J);
90 Next J: Print: Next I
100 Print: GoSub 300
110 Print Tab(5); "W="; W: Print
120 If W = 1 Then GoTo 190
130 Print Tab(15); "THE CONVERSE MATRIX OF A": Print
140 For I = 1 To N: For J = 1 To N
150 Print USING; "####.#####"; D(I, J);: Print " ";
160 Next J: Print: Next I
170 Data 1, 2, 3, 4, 1, 4, 9, 16, 1, 8, 27, 64, 1, 16, 81, 256
180 Data
190 End
300 '子程序'
310 '分解'
320 If A(1, 1) = 0 Then GoTo 890
330 For I = 2 To N: A(I, 1) = A(I, 1) / A(1, 1)
340 Next I
350 P = 0
360 For K = 2 To N: For J = K To N
370 For R = 1 To K - 1
380 P = P + A(K, R) * A(R, J)
390 Next R
400 A(K, J) = A(K, J) - P: P = 0
410 Next J
420 P = 0
430 For I = K + 1 To N: For R = 1 To K - 1
440 P = P + A(I, R) * A(R, K)
450 Next R
460 If A(K, K) = 0 Then GoTo 890
470 A(I, K) = (A(I, K) - P) / A(K, K): P = 0
480 Next I
490 Next K
500 For I = 1 To N: For J = 1 To I
510 If J = I Then C(I, I) = 1
520 If J <> I Then C(I, J) = A(I, J)
530 If J <> I Then A(I, J) = 0
540 Next J: Next I
550 '上三角求逆'
560 For K = N To 1 Step -1
570 If A(K, K) = 0 Then GoTo 890
580 A(K, K) = 1 / A(K, K)
590 For I = K - 1 To 1 Step -1
600 P = 0
610 For J = I + 1 To K
620 P = P - A(I, J) * A(J, K)
630 Next J
640 A(I, K) = P / A(I, I)
650 Next I
660 Next K
670 '下三角求逆'
680 For K = 1 To N: For I = K + 1 To N
690 P = 0
700 For J = I - 1 To K Step -1
710 P = P - C(I, J) * C(J, K)
720 Next J
730 C(I, K) = P / C(I, I)
740 Next I: Next K
750 '求A的逆'
760 For I = 1 To N: For J = I + 1 To N
770 C(I, J) = 0
780 Next J: Next I
790 For J = 1 To N: For I = J + 1 To N
800 A(I, J) = 0
810 Next I: Next J
820 For I = 1 To N: For J = 1 To N
830 D(I, J) = 0
840 For K = 1 To N
850 D(I, J) = D(I, J) + A(I, K) * C(K, J)
860 Next K
870 Next J: Next I
880 W = 0: Return
890 W = 1: Return
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