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POHow to compute orthogonal vector in python?
 

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  1. POHow to compute orthogonal vector in python?
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    <p>I have the following code to compute the orthogonal vectors of each vector coming as input from an i,j dimension matrix. So each row in the matrix is a vector. Here is the code:</p> <pre><code>for i in range(data.shape[0]): for j in range(data.shape[1]): s=0 #row counter set to 0 if j == data.shape[1]-1: #check if last row element has been reached for k in range(j): #compute the sum of all previous values. s=s+data2[i][k]*data[i][k] data2[i][j] = -s/data[i][k] else: data2[i][j] = random.uniform(1,random.getrandbits(10)) dot(data[i],data2[i]) </code></pre> <p>But it doesn't work as the dot function very rarely returns 0 which should be in case the vectors are orthogonal. I can't see a flow at the logic of my code. I simply fix j-1 random elements for the coefficients of the orthogonal vector and then in order to find the last coefficient i solve a simple equation which is the dot product of the previous coefficients of the random elements with the coefficients of the vector divided by the last coeffient. a1r1+a2r3+...+anrn=0. I know ai's. I fix random i-1 ri and then i solve the 1 var equation linear problem to find rn suth than ri vector would be orthogonal to a1 vector. The results from the last dot product computation i am getting are in this form:</p> <pre><code>=================================================== 8.90285882653 =================================================== 15.1275777619 =================================================== 25.0847305913 =================================================== 30.8608285102 =================================================== 35.2496752739 =================================================== -53.3796252747 =================================================== 16.302777 =================================================== 29.3607765359 =================================================== -39.8982101139 =================================================== 42.97222625 </code></pre>
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      1. POHow to compute orthogonal vector in python?
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    1. COHow big is the result of `dot`? It's unlikely that with floating point numbers you'll get a result of *exactly* zero -- Usually you get numbers on the order of epsilon for your data type (`1e-16` for double precision).
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    2. COI added the results in the question
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    3. COThe problem is that i don't even get a result close to 0
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