Changing for loop to backslash

3 次查看（过去 30 天）
Ruan De Beer
Ruan De Beer 2022-9-14
编辑： Torsten 2022-9-14
Ran in:
How do I change this code to not have a for loop. Hint: one backslash with multiple right-hand sides, solved simultaneously.
% Create a matrix of the coefficients
A = [6 -1 0 0 0; -3 3 0 0 0; 0 -1 9 0 0; 0 -1 -8 11 -2; -3 -1 0 0 4];
% Compute the LU Factorization
[L,U,P] = lu(A);
% Loop for each value of M from 10 to 100 with increments of 10
for M = 10 : 10 : 100
% Create a column vector of right hand side values
b = [M; 0; 160; 0; 0];
% Use the factors from LU factorization to solve
% two triangular linear systems
y = L\(P*b);
c = U\y;
% Print the solution of system of equation for current value of M
fprintf('\nSolution of system of equation for M = %d is\n', M);
disp(c);
end
Solution of system of equation for M = 10 is
2.0000 2.0000 18.0000 13.6364 2.0000
Solution of system of equation for M = 20 is
4.0000 4.0000 18.2222 14.3434 4.0000
Solution of system of equation for M = 30 is
6.0000 6.0000 18.4444 15.0505 6.0000
Solution of system of equation for M = 40 is
8.0000 8.0000 18.6667 15.7576 8.0000
Solution of system of equation for M = 50 is
10.0000 10.0000 18.8889 16.4646 10.0000
Solution of system of equation for M = 60 is
12.0000 12.0000 19.1111 17.1717 12.0000
Solution of system of equation for M = 70 is
14.0000 14.0000 19.3333 17.8788 14.0000
Solution of system of equation for M = 80 is
16.0000 16.0000 19.5556 18.5859 16.0000
Solution of system of equation for M = 90 is
18.0000 18.0000 19.7778 19.2929 18.0000
Solution of system of equation for M = 100 is
20 20 20 20 20

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采纳的回答

Torsten
Torsten 2022-9-14
编辑：Torsten 2022-9-14
Ran in:
A = [6 -1 0 0 0; -3 3 0 0 0; 0 -1 9 0 0; 0 -1 -8 11 -2; -3 -1 0 0 4];
b = [10:10:100;repmat([0; 160; 0; 0],1,10)];
dA = decomposition(A);
tic
for i=1:100000
c = dA\b;
end
toc
Elapsed time is 0.341871 seconds.
or
A = [6 -1 0 0 0; -3 3 0 0 0; 0 -1 9 0 0; 0 -1 -8 11 -2; -3 -1 0 0 4];
b = [10:10:100;repmat([0; 160; 0; 0],1,10)];
[L,U,P] = lu(A);
tic
for i=1:100000
y = L\(P*b);
c = U\y;
end
toc
Elapsed time is 0.282530 seconds.

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