spdiags() function not working as expected in Python
In Matlab/Octave, spdiags([-8037.500 50.000 -12.500], 0:2, 1, 51) gives following output:
(1, 1) -> -8037.5
(1, 2) -> 50
(1, 3) -> -12.500
However, when I use the following in Python, it does not produce a similar result as in Matlab/Octave:
import numpy as np
import scipy as sp
data = array([[-8037.5],
[ 50. ],
[ -12.5]])
sp.sparse.spdiags(data, np.r_[0:2 + 1].T, 1, 51).toarray()
Python's spdiags() produce following output, which is missing the 50 and -12.5 terms at 1st and 2nd indices:
array([[-8037.5, 0. , 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. , 0. , 0. ,
0. , 0. ]])
I took a look at this answer to a similar question, but I am not sure where I am going wrong.
Edit:
I am trying to build a matrix A that is made of A_diag1, A_diag2, and A_diag3 as shown below. I have defined A_diag1 and A_diag3 as suggested in the answer.
import numpy as np
import scipy as sp
A_diag1 = np.tile(np.array([-8037.500, 50, -12.5]), (3,1))
A_diag2 = np.reshape(np.repeat([1250, -18505, 1250], 49), (3, 49))
A_diag3 = np.tile(np.array([12.5, -50, 8037.500]), (3,1))
A = np.concatenate((sp.sparse.spdiags(A_diag1, np.r_[0:2 + 1], 1, 51).toarray(), \
sp.sparse.spdiags(A_diag2, np.r_[0:2 + 1], 49, 51).toarray(), \
sp.sparse.spdiags(A_diag3, np.r_[48:50 + 1], 1, 51).toarray()), axis=0)
However, five highlighted cells in last 3 rows and columns of A are showing up as zeros/singular as shown in the snapshot below. I expect those highlighted cells, currently showing as zeros, to be non-zero. [You can just copy and paste the above piece of code to reproduce A matrix from which the snapshot shown below is taken.]
EDIT2:
Following code that uses sp.sparse.diags() works as expected. Unlike sp.sparse.spdiags, input argument for the shape of the result (array dimensions) when using sp.sparse.diags() must be in a list.
import numpy as np
import scipy as sp
A_diag1 = np.array([[-8037.500], [50], [-12.5]])
A_diag2 = np.reshape(np.repeat([1250, -18505, 1250], 49), (3, 49))
A_diag3 = np.array([[12.5], [-50], [8037.500]])
A = np.concatenate((sp.sparse.diags(A_diag1, np.arange(0, 2 + 1), [1, 51]).toarray(), \
sp.sparse.diags(A_diag2, np.arange(0, 2 + 1), [49, 51]).toarray(), \
sp.sparse.diags(A_diag3, np.arange(48, 50 + 1), [1, 51]).toarray()), axis=0)
This makes a sparse matrix (51,1), with a value down each row:
In [5]: sparse.spdiags(data,[0,-1,-2],51,1)
Out[5]:
<51x1 sparse matrix of type '<class 'numpy.float64'>'
with 3 stored elements (3 diagonals) in DIAgonal format>
In [6]: print(_)
(0, 0) -8037.5
(1, 0) 50.0
(2, 0) -12.5
Notice that the spdiags definition:
data : array_like matrix diagonals stored row-wise
Sparse diagonal format stores its data in a matrix, part of which can be 'off-the-screen'. So it's a little tricky to use. I usually create matrices with the coo style of input.
In [27]: M =sparse.spdiags(data,[0,-1,-2],3,3)
In [28]: M.A
Out[28]:
array([[-8037.5, 0. , 0. ],
[ 50. , 0. , 0. ],
[ -12.5, 0. , 0. ]])
In [29]: M.data
Out[29]:
array([[-8037.5],
[ 50. ],
[ -12.5]])
In [30]: M.offsets
Out[30]: array([ 0, -1, -2], dtype=int32)
What you want is its transpose (maybe)
In [32]: Mt = M.T
In [33]: Mt.A
Out[33]:
array([[-8037.5, 50. , -12.5],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ]])
In [34]: Mt.data
Out[34]:
array([[-8037.5, 0. , 0. ],
[ 0. , 50. , 0. ],
[ 0. , 0. , -12.5]])
In [35]: Mt.offsets
Out[35]: array([0, 1, 2], dtype=int32)
So we can recreate Mt with:
sparse.spdiags(Mt.data, Mt.offsets, 3,3)
If I save the Octave matrix and load it I get:
In [40]: loadmat('diags')
Out[40]:
{'__globals__': [],
'__header__': b'MATLAB 5.0 MAT-file, written by Octave 4.0.0, 2017-10-19 01:24:58 UTC',
'__version__': '1.0',
'x': <1x51 sparse matrix of type '<class 'numpy.float64'>'
with 3 stored elements in Compressed Sparse Column format>}
In [42]: X=_['x']
In [43]: print(X)
(0, 0) -8037.5
(0, 1) 50.0
(0, 2) -12.5
And if I convert it to the dia format I get something like Mt:
In [48]: sparse.dia_matrix(X)
Out[48]:
<1x51 sparse matrix of type '<class 'numpy.float64'>'
with 3 stored elements (3 diagonals) in DIAgonal format>
In [49]: print(_)
(0, 0) -8037.5
(0, 1) 50.0
(0, 2) -12.5
In [50]: _.data, _.offsets
Out[50]:
(array([[-8037.5, 0. , 0. ],
[ 0. , 50. , 0. ],
[ 0. , 0. , -12.5]]), array([0, 1, 2]))
The sparse.diags function might be more intuitive:
In [92]: sparse.diags(data, [0,1,2],(1,3))
Out[92]:
<1x3 sparse matrix of type '<class 'numpy.float64'>'
with 3 stored elements (3 diagonals) in DIAgonal format>
In [93]: _.A
Out[93]: array([[-8037.5, 50. , -12.5]])
In [94]: print(__)
(0, 0) -8037.5
(0, 1) 50.0
(0, 2) -12.5
In [56]: sp1 = sparse.spdiags(A_diag1, np.r_[0:2 + 1], 1, 51)
In [57]: sp2 = sparse.spdiags(A_diag2, np.r_[0:2 + 1], 49, 51)
In [58]: sp3 = sparse.spdiags(A_diag3, np.r_[48:50 + 1], 1, 51)
(the r_ expressions could also be np.arange(0,3) and np.arange(48,51))
These can joined with sparse.vstack (which combines the coo format attributes)
In [69]: B = sparse.vstack((sp1,sp2,sp3))
In [72]: B
Out[72]:
<51x51 sparse matrix of type '<class 'numpy.float64'>'
with 147 stored elements in COOrdinate format>
In [75]: B.tocsr()[45:, 46:].A
Out[75]:
array([[ 1250., 0., 0., 0., 0.],
[-18505., 1250., 0., 0., 0.],
[ 1250., -18505., 1250., 0., 0.],
[ 0., 1250., -18505., 0., 0.],
[ 0., 0., 1250., 0., 0.],
[ 0., 0., 0., 0., 0.]])
matches your snapshot. (I still need to figure out what you are trying to create).
sparse.spdiags(data, diags, m, n) is just another way of calling sparse.dia_matrix((data, diags), shape=(m,n))
Going back to sparse.diags, if you want 3 diagonals, each filled with a value from data we can use:
In [111]: B = sparse.diags(data,[0,1,2],(51,51))
In [112]: B
Out[112]:
<51x51 sparse matrix of type '<class 'numpy.float64'>'
with 150 stored elements (3 diagonals) in DIAgonal format>
In [114]: B.tocsr()[:5,:5].A
Out[114]:
array([[-8037.5, 50. , -12.5, 0. , 0. ],
[ 0. , -8037.5, 50. , -12.5, 0. ],
[ 0. , 0. , -8037.5, 50. , -12.5],
[ 0. , 0. , 0. , -8037.5, 50. ],
[ 0. , 0. , 0. , 0. , -8037.5]])
In [115]: B.tocsr()[45:, 46:].A
Out[115]:
array([[ 50. , -12.5, 0. , 0. , 0. ],
[-8037.5, 50. , -12.5, 0. , 0. ],
[ 0. , -8037.5, 50. , -12.5, 0. ],
[ 0. , 0. , -8037.5, 50. , -12.5],
[ 0. , 0. , 0. , -8037.5, 50. ],
[ 0. , 0. , 0. , 0. , -8037.5]])
So the sp1 would have to look like
In [117]: B.tocsr()[0,:].todia().data
Out[117]:
array([[-8037.5, 0. , 0. ],
[ 0. , 50. , 0. ],
[ 0. , 0. , -12.5]])