The MOSEK Python optimizer API manual Version 7.0 (Revision 141)

7.2. SOLVING LINEAR SYSTEMS INVOLVING THE BASIS MATRIX 89
basis variables and therefore the ordering of the columns of B is arbitrary. The ordering of the basis
variables may be retrieved by calling the function
task.initbasissolve(basis)
where basis is an array of variable indexes.
This function initializes data structures for later use and returns the indexes of the basic variables in
the array basis. The interpretation of the basis is as follows. If
basis[i] < numcon,
then the i’th basis variable is x c i . Moreover, the i ’th column in B will be the i’th column of −I. On
the other hand if
then the i ’th basis variable is variable
basis[i] ≥ numcon,
and the i ’th column of B is the column
x basis[i]−numcon
A :,(basis[i]−numcon) .
For instance if basis[0] = 4 and numcon = 5 , then since basis[0] < numcon , the first basis variable
is x c 4. Therefore, the first column of B is the fourth column of −I. Similarly, if basis[1] = 7, then the
second variable in the basis is x basis[1]−numcon = x 2 . Hence, the second column of B is identical to a :,2 .
7.2.2 An example
Consider the linear optimization problem:
minimize x 0 + x 1
subject to x 0 + 2x 1 ≤ 2,
x 0 + x 1 ≤ 6,
x 0 , x 1 ≥ 0.
(7.4)
Suppose a call to Task.initbasissolve returns an array basis so that
basis[0] = 1,
basis[1] = 2.
Then the basis variables are x c 1 and x 0 and the corresponding basis matrix B is
[
0 1
− 1 1
]
.