Based on BFS output how to select sparse matrix elements

Question

I am trying to select sparse matrix elements row-wise based on BFS output array. Suppose my BFS output is

[1, 2, 3, 6, 4, 7, 5, 8, 11, 9, 12, 10, 13, 15, 14, 16, 17, 18, 19, 20]

and I have a sparse matrix of 20x20 for example.

Now I want to use BFS output as row index and select nonzero values from the sparse matrix in same order as that of BFS output array and plot. Here is my code through which I can do some job but not perfectly what I wanted.

a = numpy.loadtxt('sparsematrix.txt', float, delimiter=',') # import data
y = numpy.reshape(a, np.size(a))
pos = np.delete(y, np.arange(0, y.size, 19))

plt.plot(pos)
plt.xlabel(sample)
plt.ylabel(position)

Problem with the above code is:

1. It selects every value in row-wise, but not in defined order of my BFS output. (it should use BFS output array as row index number to select nonzero values one-by-one)
2. It selects all the values, even zeros. - How to get only nonzero values?
3. Indexing is starting from 0 and goes to 19. I want indexing to start from 1 onwards.

Answer 1

Important Update

Now I get what you completly wanted by reading Christian's answer. I made another function to complement the one already given. See the whole program here:

sparseMatrix = ([0,4,5,0],[2,0,4,0],[0,3,3,0],[6,6,0,0])
iList = [3,1,2,4]

def AnalyzeSparseMatrix( sMatrix, iList ):
    orderedArray = [] #The array you want as output
    for i in iList:
        orderedArray += AnalyzeRowWise(sMatrix[i-1])  #Add non-zero selected line from sparse matrix
    return orderedArray #Returns a non-zero list ordered in the selected way by the BFS output list

def AnalyzeRowWise( oldArray ):
    newMatrix = []
    #Code to analize row wise
    for data in oldArray:
        if(data != 0): #Condition
            newMatrix.append(data)
    return newMatrix

#Test program
print (AnalyzeSparseMatrix(sparseMatrix, iList)) #Output: [3,3,4,5,2,4,6,6]

The new method AnalyzeSparseMatrix() takes two arguments, the first argument is the sparse matrix, the second argument is the BFS output list. The method returns a list, which is the desired list. So you can assign that list to another list you want, for example:

finalOrderedList = AnalyzeSparseMatrix( sparseMatrix, iList )

Find more details about what almost every line of code does, in the code above.

Answer 2

I've assumed that this is what you want:

bfs_output = list of row indexes where 1 is the first/top row of a matrix.
matrix m = some matrix with elements that can be 0 or non-zero
list l = a list composed of non-zero elements chosen from m

Elements from m are chosen as follows:

1. Select the row, r, in m indicated by the first/next value in bfs_output

2. Starting from the first column in r select the non-zero elements in r

3. Append the elements chosen in 2 to l

4. Repeat until no more row indexes in bfs_output

For example:

                                  0 3 1
bfs_output = [2 3 1]  &  matrix = 0 2 0    ==> list = [2 4 3 1]
                                  4 0 0

I am not sure if this is what you are after. But if it is, we can use numpy's build in selection functions to select non-zero elements from a numpy array and also to chose rows in the order we want.

from io import StringIO
import numpy as np

bfs_output = [2,3,1]
file = StringIO(u"0,3,1\n0,2,0\n4,0,0")

matrix = np.loadtxt(file, delimiter=",")

# we are subtracting 1 from all elements in bfs_output
# in order to comply with indexes starting from 1
select_rows = matrix[np.subtract(bfs_output,1)]
select_rows_1d = np.reshape(select_rows,np.size(select_rows))
list = select_rows_1d[select_rows_1d != 0]

print(list) # output = [2 4 3 1]