Mixing
MATLAB integration of 2x2 system
I got the following matrice:
which I want to integrate with MATLAB. The obvious solution would be:
which is exactly what I am trying to achieve. I am using symbolic calculation for this. (example only for one variable)
syms aiso w w1 w2
With the matrice definition
A = [1/2/aiso 1/2; -1/2/aiso 1/2];
Now I integrate symbolically via
A = int(A,w);
Which gives me the result
A = [ w*1/(2*aiso), w*1/2; -w*1/(2*aiso), w*1/2]
That is obviously right but since I only used one symbolic variable that's not quite the case I need. I need the solution from above, which is stated in vector notation on the second picture and which should look like this in MATLAB:
A = [ (w1)*1/(2*aiso) + (w2)*1/2; (w1)*1/(2*aiso) - (w2)1/2]
Is there a way to do this in MATLAB?
Thanks a lot in advance and have a nice day!
matlab matrix integration symbolic-math
edited Nov 22 '18 at 8:18
Banghua Zhao
1,2851720
asked Nov 21 '18 at 20:27
William D.William D.
82
add a comment |
I got the following matrice:
which I want to integrate with MATLAB. The obvious solution would be:
which is exactly what I am trying to achieve. I am using symbolic calculation for this. (example only for one variable)
syms aiso w w1 w2
With the matrice definition
A = [1/2/aiso 1/2; -1/2/aiso 1/2];
Now I integrate symbolically via
A = int(A,w);
Which gives me the result
A = [ w*1/(2*aiso), w*1/2; -w*1/(2*aiso), w*1/2]
That is obviously right but since I only used one symbolic variable that's not quite the case I need. I need the solution from above, which is stated in vector notation on the second picture and which should look like this in MATLAB:
A = [ (w1)*1/(2*aiso) + (w2)*1/2; (w1)*1/(2*aiso) - (w2)1/2]
Is there a way to do this in MATLAB?
Thanks a lot in advance and have a nice day!
matlab matrix integration symbolic-math
edited Nov 22 '18 at 8:18
Banghua Zhao
1,2851720
asked Nov 21 '18 at 20:27
William D.William D.
82
You may want to createwas a symbolic vectorw = sym('w', [2,1])or integrate w.r.t[w1;w2].
– Chris H.
Nov 21 '18 at 22:10
Thanks for the reply! But this isn't working for me. When I try int(dA,[w1 w2]), MATLAB interprets it as an integration interval with lower and upper border. Any other ideas maybe?
– William D.
Nov 22 '18 at 11:23
add a comment |
I got the following matrice:
which I want to integrate with MATLAB. The obvious solution would be:
which is exactly what I am trying to achieve. I am using symbolic calculation for this. (example only for one variable)
syms aiso w w1 w2
With the matrice definition
A = [1/2/aiso 1/2; -1/2/aiso 1/2];
Now I integrate symbolically via
A = int(A,w);
Which gives me the result
A = [ w*1/(2*aiso), w*1/2; -w*1/(2*aiso), w*1/2]
That is obviously right but since I only used one symbolic variable that's not quite the case I need. I need the solution from above, which is stated in vector notation on the second picture and which should look like this in MATLAB:
A = [ (w1)*1/(2*aiso) + (w2)*1/2; (w1)*1/(2*aiso) - (w2)1/2]
Is there a way to do this in MATLAB?
Thanks a lot in advance and have a nice day!
matlab matrix integration symbolic-math
edited Nov 22 '18 at 8:18
Banghua Zhao
1,2851720
asked Nov 21 '18 at 20:27
William D.William D.
82
I got the following matrice:
which I want to integrate with MATLAB. The obvious solution would be:
which is exactly what I am trying to achieve. I am using symbolic calculation for this. (example only for one variable)
syms aiso w w1 w2
With the matrice definition
A = [1/2/aiso 1/2; -1/2/aiso 1/2];
Now I integrate symbolically via
A = int(A,w);
Which gives me the result
A = [ w*1/(2*aiso), w*1/2; -w*1/(2*aiso), w*1/2]
That is obviously right but since I only used one symbolic variable that's not quite the case I need. I need the solution from above, which is stated in vector notation on the second picture and which should look like this in MATLAB:
A = [ (w1)*1/(2*aiso) + (w2)*1/2; (w1)*1/(2*aiso) - (w2)1/2]
Is there a way to do this in MATLAB?
Thanks a lot in advance and have a nice day!
matlab matrix integration symbolic-math
matlab matrix integration symbolic-math
edited Nov 22 '18 at 8:18
Banghua Zhao
1,2851720
asked Nov 21 '18 at 20:27
William D.William D.
82
edited Nov 22 '18 at 8:18
Banghua Zhao
1,2851720
asked Nov 21 '18 at 20:27
William D.William D.
82
edited Nov 22 '18 at 8:18
Banghua Zhao
1,2851720
edited Nov 22 '18 at 8:18
Banghua Zhao
1,2851720
edited Nov 22 '18 at 8:18
Banghua Zhao
1,2851720
1,2851720
asked Nov 21 '18 at 20:27
William D.William D.
82
asked Nov 21 '18 at 20:27
William D.William D.
82
asked Nov 21 '18 at 20:27
William D.William D.
82
82
You may want to createwas a symbolic vectorw = sym('w', [2,1])or integrate w.r.t[w1;w2].
– Chris H.
Nov 21 '18 at 22:10
Thanks for the reply! But this isn't working for me. When I try int(dA,[w1 w2]), MATLAB interprets it as an integration interval with lower and upper border. Any other ideas maybe?
– William D.
Nov 22 '18 at 11:23
add a comment |
You may want to createwas a symbolic vectorw = sym('w', [2,1])or integrate w.r.t[w1;w2].
– Chris H.
Nov 21 '18 at 22:10
Thanks for the reply! But this isn't working for me. When I try int(dA,[w1 w2]), MATLAB interprets it as an integration interval with lower and upper border. Any other ideas maybe?
– William D.
Nov 22 '18 at 11:23
You may want to create
w as a symbolic vector w = sym('w', [2,1]) or integrate w.r.t [w1;w2].– Chris H.
Nov 21 '18 at 22:10
You may want to create
w as a symbolic vector w = sym('w', [2,1]) or integrate w.r.t [w1;w2].– Chris H.
Nov 21 '18 at 22:10
Thanks for the reply! But this isn't working for me. When I try int(dA,[w1 w2]), MATLAB interprets it as an integration interval with lower and upper border. Any other ideas maybe?
– William D.
Nov 22 '18 at 11:23
Thanks for the reply! But this isn't working for me. When I try int(dA,[w1 w2]), MATLAB interprets it as an integration interval with lower and upper border. Any other ideas maybe?
– William D.
Nov 22 '18 at 11:23
add a comment |
1 Answer
1
active
oldest
votes
You can integrate each component of the matrix dA to get A:
syms aiso w w1 w2
dA = [1/2/aiso 1/2; -1/2/aiso 1/2];
A = [int(dA(1,1),w1)+int(dA(1,2),w2) int(dA(2,1),w1)+int(dA(2,2),w2)]
disp(A)
Output:
[ w2/2 + w1/(2*aiso), w2/2 - w1/(2*aiso)]
It is not elegant but it works.
answered Nov 21 '18 at 22:37
Banghua ZhaoBanghua Zhao
1,2851720
This works grat for this special case. But I plan to advance to more sophisticated entries like
– William D.
Nov 22 '18 at 11:09
Thank you - I just tried it!This works great for this special case, where integration equal a simple multiplication with the vector w. But I finally plan to andvance towards matrices with entries containing dependencies like dA(1,1) = w2*w1/aiso and dA(1,2) = w1^2*w2/2; for example. So maybe there's another more general way. (?)
– William D.
Nov 22 '18 at 11:21
@WilliamD. Currently, I can only come out of this way. I will update my answer once I know more general way.
– Banghua Zhao
Nov 22 '18 at 12:47
Thanks for the effort!
– William D.
Nov 22 '18 at 15:24
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
You can integrate each component of the matrix dA to get A:
syms aiso w w1 w2
dA = [1/2/aiso 1/2; -1/2/aiso 1/2];
A = [int(dA(1,1),w1)+int(dA(1,2),w2) int(dA(2,1),w1)+int(dA(2,2),w2)]
disp(A)
Output:
[ w2/2 + w1/(2*aiso), w2/2 - w1/(2*aiso)]
It is not elegant but it works.
answered Nov 21 '18 at 22:37
Banghua ZhaoBanghua Zhao
1,2851720
This works grat for this special case. But I plan to advance to more sophisticated entries like
– William D.
Nov 22 '18 at 11:09
Thank you - I just tried it!This works great for this special case, where integration equal a simple multiplication with the vector w. But I finally plan to andvance towards matrices with entries containing dependencies like dA(1,1) = w2*w1/aiso and dA(1,2) = w1^2*w2/2; for example. So maybe there's another more general way. (?)
– William D.
Nov 22 '18 at 11:21
@WilliamD. Currently, I can only come out of this way. I will update my answer once I know more general way.
– Banghua Zhao
Nov 22 '18 at 12:47
Thanks for the effort!
– William D.
Nov 22 '18 at 15:24
add a comment |
You can integrate each component of the matrix dA to get A:
syms aiso w w1 w2
dA = [1/2/aiso 1/2; -1/2/aiso 1/2];
A = [int(dA(1,1),w1)+int(dA(1,2),w2) int(dA(2,1),w1)+int(dA(2,2),w2)]
disp(A)
Output:
[ w2/2 + w1/(2*aiso), w2/2 - w1/(2*aiso)]
It is not elegant but it works.
answered Nov 21 '18 at 22:37
Banghua ZhaoBanghua Zhao
1,2851720
This works grat for this special case. But I plan to advance to more sophisticated entries like
– William D.
Nov 22 '18 at 11:09
Thank you - I just tried it!This works great for this special case, where integration equal a simple multiplication with the vector w. But I finally plan to andvance towards matrices with entries containing dependencies like dA(1,1) = w2*w1/aiso and dA(1,2) = w1^2*w2/2; for example. So maybe there's another more general way. (?)
– William D.
Nov 22 '18 at 11:21
@WilliamD. Currently, I can only come out of this way. I will update my answer once I know more general way.
– Banghua Zhao
Nov 22 '18 at 12:47
Thanks for the effort!
– William D.
Nov 22 '18 at 15:24
add a comment |
You can integrate each component of the matrix dA to get A:
syms aiso w w1 w2
dA = [1/2/aiso 1/2; -1/2/aiso 1/2];
A = [int(dA(1,1),w1)+int(dA(1,2),w2) int(dA(2,1),w1)+int(dA(2,2),w2)]
disp(A)
Output:
[ w2/2 + w1/(2*aiso), w2/2 - w1/(2*aiso)]
It is not elegant but it works.
answered Nov 21 '18 at 22:37
Banghua ZhaoBanghua Zhao
1,2851720
You can integrate each component of the matrix dA to get A:
syms aiso w w1 w2
dA = [1/2/aiso 1/2; -1/2/aiso 1/2];
A = [int(dA(1,1),w1)+int(dA(1,2),w2) int(dA(2,1),w1)+int(dA(2,2),w2)]
disp(A)
Output:
[ w2/2 + w1/(2*aiso), w2/2 - w1/(2*aiso)]
It is not elegant but it works.
answered Nov 21 '18 at 22:37
Banghua ZhaoBanghua Zhao
1,2851720
answered Nov 21 '18 at 22:37
Banghua ZhaoBanghua Zhao
1,2851720
answered Nov 21 '18 at 22:37
Banghua ZhaoBanghua Zhao
1,2851720
answered Nov 21 '18 at 22:37
Banghua ZhaoBanghua Zhao
1,2851720
1,2851720
This works grat for this special case. But I plan to advance to more sophisticated entries like
– William D.
Nov 22 '18 at 11:09
Thank you - I just tried it!This works great for this special case, where integration equal a simple multiplication with the vector w. But I finally plan to andvance towards matrices with entries containing dependencies like dA(1,1) = w2*w1/aiso and dA(1,2) = w1^2*w2/2; for example. So maybe there's another more general way. (?)
– William D.
Nov 22 '18 at 11:21
@WilliamD. Currently, I can only come out of this way. I will update my answer once I know more general way.
– Banghua Zhao
Nov 22 '18 at 12:47
Thanks for the effort!
– William D.
Nov 22 '18 at 15:24
add a comment |
This works grat for this special case. But I plan to advance to more sophisticated entries like
– William D.
Nov 22 '18 at 11:09
Thank you - I just tried it!This works great for this special case, where integration equal a simple multiplication with the vector w. But I finally plan to andvance towards matrices with entries containing dependencies like dA(1,1) = w2*w1/aiso and dA(1,2) = w1^2*w2/2; for example. So maybe there's another more general way. (?)
– William D.
Nov 22 '18 at 11:21
@WilliamD. Currently, I can only come out of this way. I will update my answer once I know more general way.
– Banghua Zhao
Nov 22 '18 at 12:47
Thanks for the effort!
– William D.
Nov 22 '18 at 15:24
This works grat for this special case. But I plan to advance to more sophisticated entries like
– William D.
Nov 22 '18 at 11:09
This works grat for this special case. But I plan to advance to more sophisticated entries like
– William D.
Nov 22 '18 at 11:09
Thank you - I just tried it!This works great for this special case, where integration equal a simple multiplication with the vector w. But I finally plan to andvance towards matrices with entries containing dependencies like dA(1,1) = w2*w1/aiso and dA(1,2) = w1^2*w2/2; for example. So maybe there's another more general way. (?)
– William D.
Nov 22 '18 at 11:21
Thank you - I just tried it!This works great for this special case, where integration equal a simple multiplication with the vector w. But I finally plan to andvance towards matrices with entries containing dependencies like dA(1,1) = w2*w1/aiso and dA(1,2) = w1^2*w2/2; for example. So maybe there's another more general way. (?)
– William D.
Nov 22 '18 at 11:21
@WilliamD. Currently, I can only come out of this way. I will update my answer once I know more general way.
– Banghua Zhao
Nov 22 '18 at 12:47
@WilliamD. Currently, I can only come out of this way. I will update my answer once I know more general way.
– Banghua Zhao
Nov 22 '18 at 12:47
Thanks for the effort!
– William D.
Nov 22 '18 at 15:24
Thanks for the effort!
– William D.
Nov 22 '18 at 15:24
add a comment |
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You may want to create
was a symbolic vectorw = sym('w', [2,1])or integrate w.r.t[w1;w2].– Chris H.
Nov 21 '18 at 22:10
Thanks for the reply! But this isn't working for me. When I try int(dA,[w1 w2]), MATLAB interprets it as an integration interval with lower and upper border. Any other ideas maybe?
– William D.
Nov 22 '18 at 11:23