SuiteSparseMatrix¶
- class probnum.problems.zoo.linalg.SuiteSparseMatrix(matid, group, name, nnz, is2d3d, isspd, psym, nsym, kind)¶
Bases:
probnum.linops.Matrix
SuiteSparse Matrix.
Sparse matrix from the SuiteSparse Matrix Collection. 1 2
- Parameters
matid (
str
) – Unique identifier for the matrix in the database.group (
str
) – Group this matrix belongs to.name (
str
) – Name of this matrix.nnz (
int
) – Number of non-zero elements.is2d3d (
bool
) – Does this matrix come from a 2D or 3D discretization?isspd (
bool
) – Is this matrix symmetric, positive definite?psym (
float
) – Degree of symmetry of the matrix pattern.nsym (
float
) – Degree of numerical symmetry of the matrix.kind (
str
) – Information of the problem domain this matrix arises from.
References
- 1
Davis, TA and Hu, Y. The University of Florida sparse matrix collection. ACM Transactions on Mathematical Software (TOMS) 38.1 ( 2011): 1-25.
- 2
Kolodziej, Scott P., et al. The SuiteSparse matrix collection website interface. Journal of Open Source Software 4.35 (2019): 1244.
Attributes Summary
Hermitian adjoint.
Transposed linear operator.
Data type of the linear operator.
Whether input dimension matches output dimension.
Number of linear operator dimensions.
Shape of the linear operator.
Methods Summary
__call__
(x[, axis])Call self as a function.
adjoint
()Hermitian adjoint.
astype
(dtype[, order, casting, subok, copy])Cast a linear operator to a different
dtype
.broadcast_matmat
(matmat)Broadcasting for a (implicitly defined) matrix-matrix product.
broadcast_matvec
(matvec)Broadcasting for a (implicitly defined) matrix-vector product.
broadcast_rmatmat
(rmatmat)broadcast_rmatvec
(rmatvec)cond
([p])Compute the condition number of the linear operator.
conj
()Complex conjugate linear operator.
Complex conjugate linear operator.
det
()Determinant of the linear operator.
eigvals
()Eigenvalue spectrum of the linear operator.
from_database_entry
(database_entry)Create a SuiteSparseMatrix object from an entry of the database index.
inv
()Inverse of the linear operator.
Log absolute determinant of the linear operator.
rank
()Rank of the linear operator.
todense
([cache])Dense matrix representation of the linear operator.
trace
()Trace of the linear operator.
Transpose this linear operator.
Attributes Documentation
- H¶
Hermitian adjoint.
- Return type
- T¶
Transposed linear operator.
- Return type
- ndim¶
Number of linear operator dimensions.
Defined analogously to
numpy.ndarray.ndim
.- Return type
- shape¶
Shape of the linear operator.
Defined as a tuple of the output and input dimension of operator.
Methods Documentation
- adjoint()¶
Hermitian adjoint.
- Return type
- astype(dtype, order='K', casting='unsafe', subok=True, copy=True)¶
Cast a linear operator to a different
dtype
.- Parameters
dtype (
Union
[dtype
,str
]) – Data type to which the linear operator is cast.order (
str
) – Memory layout order of the result.casting (
str
) – Controls what kind of data casting may occur.subok (
bool
) – If True, then sub-classes will be passed-through (default). False is currently not supported for linear operators.copy (
bool
) – Whether to return a new linear operator, even ifdtype
is the same.
- Return type
- classmethod broadcast_matmat(matmat)¶
Broadcasting for a (implicitly defined) matrix-matrix product.
Convenience function / decorator to broadcast the definition of a matrix-matrix product to vectors. This can be used to easily construct a new linear operator only from a matrix-matrix product.
- classmethod broadcast_matvec(matvec)¶
Broadcasting for a (implicitly defined) matrix-vector product.
Convenience function / decorator to broadcast the definition of a matrix-vector product. This can be used to easily construct a new linear operator only from a matrix-vector product.
- cond(p=None)¶
Compute the condition number of the linear operator.
The condition number of the linear operator with respect to the
p
norm. It measures how much the solution \(x\) of the linear system \(Ax=b\) changes with respect to small changes in \(b\).- Parameters
p ({None, 1, , 2, , inf, 'fro'}, optional) –
Order of the norm:
p
norm for matrices
None
2-norm, computed directly via singular value decomposition
’fro’
Frobenius norm
np.inf
max(sum(abs(x), axis=1))
1
max(sum(abs(x), axis=0))
2
2-norm (largest sing. value)
- Returns
The condition number of the linear operator. May be infinite.
- Return type
cond
- conj()¶
Complex conjugate linear operator.
- Return type
- conjugate()¶
Complex conjugate linear operator.
- Return type
- classmethod from_database_entry(database_entry)[source]¶
Create a SuiteSparseMatrix object from an entry of the database index.
- Parameters
database_entry (
Dict
) – Dictionary representing one entry from the SuiteSparse database index.- Return type
- inv()¶
Inverse of the linear operator.
- Return type
- rank()¶
Rank of the linear operator.
- Return type
int64
- todense(cache=True)¶
Dense matrix representation of the linear operator.
This method can be computationally very costly depending on the shape of the linear operator. Use with caution.
- Returns
matrix – Matrix representation of the linear operator.
- Return type
np.ndarray
- trace()¶
Trace of the linear operator.
Computes the trace of a square linear operator \(\text{tr}(A) = \sum_{i-1}^n A_{ii}\).
- transpose()¶
Transpose this linear operator.
Can be abbreviated self.T instead of self.transpose().
- Return type