I have two vectors t, and delta - both of length n. I want to create a sparse DIA matrix A with that vector, and then adjust the columns: For all i, I want to move the ith entry in A by delta[i] columns to the left.
An easy way to control columns is in the COO format. Here's what I thought would work:
from scipy.sparse import diags
A = diags([t], offsets=[-1]).tocoo()
A.col = A.col - delta
However, in my example A.nnz == len(A.col) is only 216, while the length of t and delta is 239. I don't understand how that happened, given that nnz stores "Number of stored values, including explicit zeros.".
How can I tackle this problem? Here's my example data:
from numpy import np
t = np.array([ 2.655, 2.655, 2.655, 2.655, 2.655, 2.655, 2.655, 2.655,
2.655, 2.655, 2.655, 2.655, 2.655, 2.655, 2.655, 2.655,
2.655, 2.655, 2.655, 2.655, 2.655, 2.655, 2.655, 2.155,
2.155, 2.155, 2.155, 2.155, 2.155, 2.155, 2.155, 2.155,
2.155, 2.155, 2.155, 2.155, 2.155, 2.155, 2.155, 2.155,
2.155, 2.155, 2.155, 2.155, 2.155, 2.155, 2.155, 1.655,
1.655, 1.655, 1.655, 1.655, 1.655, 1.655, 1.655, 1.655,
1.655, 1.655, 1.655, 1.655, 1.655, 1.655, 1.655, 1.655,
1.655, 1.655, 1.655, 1.655, 1.655, 1.655, 1.655, 1.155,
1.155, 1.155, 1.155, 1.155, 1.155, 1.155, 1.155, 1.155,
1.155, 1.155, 1.155, 1.155, 1.155, 1.155, 1.155, 1.155,
1.155, 1.155, 1.155, 1.155, 1.155, 1.155, 1.155, 0.655,
0.655, 0.655, 0.655, 0.655, 0.655, 0.655, 0.655, 0.655,
0.655, 0.655, 0.655, 0.655, 0.655, 0.655, 0.655, 0.655,
0.655, 0.655, 0.655, 0.655, 0.655, 0.655, 0.655, 0.405,
0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405,
0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405,
0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405,
0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405,
0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405,
0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405,
0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405,
0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405,
0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405,
0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405,
0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405,
0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0.405, 0. ,
0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. , 0. , 0. ])
delta = np.array([0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5,
5, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5,
5, 5, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5,
5, 5, 5, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4,
5, 5, 5, 5, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4,
4, 5, 5, 5, 5, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4,
4, 4, 5, 5, 5, 5, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4,
4, 4, 4, 5, 5, 5, 5, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3,
4, 4, 4, 4, 5, 5, 5, 5, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3,
3, 4, 4, 4, 4, 5, 5, 5, 5, 0, 0, 0, 0, 1, 1, 1, 1, 2, 0, 2, 2, 3, 2,
1, 3, 4, 3, 0, 3, 5, 4, 1, 0])
In [29]: t = np.array([1.2, 3.2, 4, 0, 0])
In [30]: A = sparse.diags([t], offsets=[-1])
In [31]: A
Out[31]:
<6x6 sparse matrix of type '<class 'numpy.float64'>'
with 5 stored elements (1 diagonals) in DIAgonal format>
The conversion to coo strips out the 0s.
In [32]: Ac = A.tocoo()
In [33]: Ac
Out[33]:
<6x6 sparse matrix of type '<class 'numpy.float64'>'
with 3 stored elements in COOrdinate format>
Look at the code for A.tocoo (the dia to coo version). It has (self.data != 0) mask.
If I make the coo matrix directly it retains the zeros, at least temporarily:
In [58]: A.A
Out[58]:
array([[ 0. , 0. , 0. , 0. , 0. , 0. ],
[ 1.2, 0. , 0. , 0. , 0. , 0. ],
[ 0. , 3.2, 0. , 0. , 0. , 0. ],
[ 0. , 0. , 4. , 0. , 0. , 0. ],
[ 0. , 0. , 0. , 0. , 0. , 0. ],
[ 0. , 0. , 0. , 0. , 0. , 0. ]])
In [59]: M = sparse.coo_matrix((t, (np.arange(1,6),np.arange(5))),shape=(6,6))
In [60]: M
Out[60]:
<6x6 sparse matrix of type '<class 'numpy.float64'>'
with 5 stored elements in COOrdinate format>
In [61]: M.A
Out[61]:
array([[ 0. , 0. , 0. , 0. , 0. , 0. ],
[ 1.2, 0. , 0. , 0. , 0. , 0. ],
[ 0. , 3.2, 0. , 0. , 0. , 0. ],
[ 0. , 0. , 4. , 0. , 0. , 0. ],
[ 0. , 0. , 0. , 0. , 0. , 0. ],
[ 0. , 0. , 0. , 0. , 0. , 0. ]])
An inplace zero removal:
In [64]: M.eliminate_zeros()
In [65]: M
Out[65]:
<6x6 sparse matrix of type '<class 'numpy.float64'>'
with 3 stored elements in COOrdinate format>