How to construct matrix from vectors?
I just started to learn some python today for first time, so be easy on me. I am having some trouble figuring how do the problem shown in this link http://12000.org/my_notes/mma_matlab_control/KERNEL/KEse44.htm Given 4 column vectors, v1,v2,v3,v4, each is 3 rows. I want to use these to construct matrix mat, which is [[v1,v2], [v3,v4]] So the resulting matrix is as shown in the link. i.e. it will be 6 rows and 2 columns. This is what I tried: import numpy as np v1=np.array([1,2,3]); v2=np.array([4,5,6]); v3=np.array([7,8,9]); v4=np.array([10,11,12]); And now I get stuck, I tried m=np.array([[v1,v2],[v3,v4]]) #no good Also m=np.array([v1,v2,v3,v4]) m.shape Out[153]: (4L, 3L) m.T array([[ 1, 4, 7, 10], [ 2, 5, 8, 11], [ 3, 6, 9, 12]]) Not what I want. I need to get the shape as in the above link, 6 rows by 2 columns, where each column vector is stacked as shown. I also tried v1=np.array([1,2,3]); v1.shape=3,1 v2=np.array([4,5,6]); v2.shape=3,1 v3=np.array([7,8,9]); v3.shape=3,1 v4=np.array([10,11,12]); v4.shape=3,1 mat=np.array([[v1,v2],[v3,v4]]) What is the correct way to do this in Python? thanks, --Nasser -- https://mail.python.org/mailman/listinfo/python-list
Re: How to construct matrix from vectors?
On 6/20/2015 9:20 PM, MRAB wrote: Here's one way, one step at a time: r1 = np.concatenate([v1, v2]) r1 array([1, 2, 3, 4, 5, 6]) r2 = np.concatenate([v3, v4]) r2 array([ 7, 8, 9, 10, 11, 12]) m = np.array([r1, r2]) m array([[ 1, 2, 3, 4, 5, 6], [ 7, 8, 9, 10, 11, 12]]) m.transpose() array([[ 1, 7], [ 2, 8], [ 3, 9], [ 4, 10], [ 5, 11], [ 6, 12]]) But your output is wrong. I did manage to find a way: - r1 =np.hstack([(v1,v2)]).T r2 =np.hstack([(v3,v4)]).T mat = np.vstack((r1,r2)) - Out[211]: array([[ 1, 4], [ 2, 5], [ 3, 6], [ 7, 10], [ 8, 11], [ 9, 12]]) But it is not as intuitive as with Matlab, where one can just write --- v1=[1,2,3]'; v2=[4,5,6]'; v3=[7,8,9]'; v4=[10,11,12]'; m=[v1 v2;v3 v4] --- --Nasser -- https://mail.python.org/mailman/listinfo/python-list
Re: How to construct matrix from vectors?
On 6/20/2015 10:47 PM, Nasser M. Abbasi wrote: I did manage to find a way: - r1 =np.hstack([(v1,v2)]).T r2 =np.hstack([(v3,v4)]).T mat = np.vstack((r1,r2)) - Out[211]: array([[ 1, 4], [ 2, 5], [ 3, 6], [ 7, 10], [ 8, 11], [ 9, 12]]) But it is not as intuitive as with Matlab, where one can just write --- v1=[1,2,3]'; v2=[4,5,6]'; v3=[7,8,9]'; v4=[10,11,12]'; m=[v1 v2;v3 v4] --- Here is a way a little closer to Matlab's method: First make all the vectors column vectors v1=np.array([(1,2,3)]).T v2=np.array([(4,5,6)]).T v3=np.array([(7,8,9)]).T v4=np.array([(10,11,12)]).T mat =np.hstack(( np.vstack((v1,v3)), np.vstack((v2,v4))) ) Out[236]: array([[ 1, 4], [ 2, 5], [ 3, 6], [ 7, 10], [ 8, 11], [ 9, 12]]) There are way too many '(([[]]))' things in Python :) -- https://mail.python.org/mailman/listinfo/python-list
Re: numpy (matrix solver) - python vs. matlab
On 04/29/2012 05:17 PM, someone wrote: I would also kindly ask about how to avoid this problem in the future, I mean, this maybe means that I have to check the condition number at all times before doing anything at all ? How to do that? I hope you'll check the condition number all the time. You could be designing a building where people will live in it. If do not check the condition number, you'll end up with a building that will fall down when a small wind hits it and many people will die all because you did not bother to check the condition number when you solved the equations you used in your design. Also, as was said, do not use INV(A) directly to solve equations. --Nasser -- http://mail.python.org/mailman/listinfo/python-list
Re: numpy (matrix solver) - python vs. matlab
On 04/29/2012 07:59 PM, someone wrote: Also, as was said, do not use INV(A) directly to solve equations. In Matlab I used x=A\b. good. I used inv(A) in python. Should I use some kind of pseudo-inverse or what do you suggest? I do not use python much myself, but a quick google showed that pyhton scipy has API for linalg, so use, which is from the documentation, the following code example X = scipy.linalg.solve(A, B) But you still need to check the cond(). If it is too large, not good. How large and all that, depends on the problem itself. But the rule of thumb, the lower the better. Less than 100 can be good in general, but I really can't give you a fixed number to use, as I am not an expert in this subjects, others who know more about it might have better recommendations. --Nasser -- http://mail.python.org/mailman/listinfo/python-list
Re: numpy (matrix solver) - python vs. matlab
On 04/29/2012 07:17 PM, someone wrote: Ok. When do you define it to be singular, btw? There are things you can see right away about a matrix A being singular without doing any computation. By just looking at it. For example, If you see a column (or row) being a linear combination of other column(s) (or row(s)) then this is a no no. In your case you have 1 2 3 111213 212223 You can see right away that if you multiply the second row by 2, and subtract from that one times the first row, then you obtain the third row. Hence the third row is a linear combination of the first row and the second row. no good. When you get a row (or a column) being a linear combination of others rows (or columns), then this means the matrix is singular. --Nasser -- http://mail.python.org/mailman/listinfo/python-list
