Questions tagged [sparse-matrix]
Questions related to storage, assembly, operations, and other aspects of dealing with sparse matrices, for which only non-zero elements are stored. Questions that do not with sparse matrices directly, but other means of using sparsity should be tagged with [sparse-operator].
343 questions
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Preconditioning a separated band matrix
The Hessian matrix shown below is computed at the grid points of a discretized domain
The matrix looks like it has 3 groups of bands but upon zooming into the bands reveals that each band is actually ...
- 375
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0
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General advice on sparse matrix rank computation over GF(3)
I have a very large and very sparse matrix over the finite field GF(3). In general, its proportions are $(m\cdot 3^{m-6}) \times (6\cdot 3^{m-6})$ and its sparsity is $1/(2\cdot 3^{m-6})$ for a ...
- 121
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How to transform the matrix into a specific form
Consider a full-row rank matrix $A \in \mathbb{C}^{r \times n}$ (where the number of rows r is less than the number of columns n). How can we find a column permutation or an invertible transformation ...
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Handling defective eigenvalues in shifted block Lanczos algorithm
I’m implementing a shifted version of the block Lanczos algorithm, following the approach described in the paper by Lewis, Simon, and Grimes, to solve generalized eigenvalue problems. My ...
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How to compute eigenvalues of a large symmetric complex matrix (100k x 100k) on a GPU?
I need to compute all the eigenvalues of a large symmetric complex matrix on a GPU. The matrix has dimensions 100,000 × 100,000, with double-complex precision values. This means it requires 160GB of ...
- 21
2
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Assemble product of matrices in Finite Elements
let $A$ be the usual stiffness matrix discretising the $(\nabla u,\nabla v)_{\Omega}$, with classical Lagrangian continuous elements.
Is it possible to assemble the matrix $A^T A (= A^2)$? I don't ...
- 575
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1
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CVXPY - Convex difference of quadratic forms
I have a sparse optimization problem of the form:
$$\min_x c^T x + \| D x\|^2_2 + \| V x\|^2_2 - \| W x\|^2_2$$
$D$ is diagonal and $V$, $W$ are non-square matrices. I know that:
$$Q = D^2 + V V^T - ...
3
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1
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414
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Efficiently Updating Matrix Multiplication Result When One Matrix Changes
Suppose you have two matrices $A \in Z_q^{m\times l}$ and $B \in Z_q^{l\times n}$, and the product $A\cdot B$ has already been computed. Now, matrix $B$ remains unchanged, but a few elements in matrix ...
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ILU Preconditiner Implementation in Python
I have a question regarding the computational complexity of the ILU preconditioner in Python. I am trying to implement an ILU(0) preconditioner using the following code:
ILUfact = sla.spilu(...
- 21
3
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1
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Computing eigendecomposition of extremely large (though sparse band) matrix
I have a very large graph (about over a billion nodes) and I need to compute all the eigenvectors and eigenvalues of the graph (i.e., of the Laplacian of the adjacency matrix) for downstream analysis. ...
- 171
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Improving convergence rate of krylov schur iterations?
I am trying to implement krylov schur iterations. I am noticing that although my implementation converges, it does so really, really slowly. For a 40x40 matrix it is taking hundreds of iterations to ...
- 473
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4
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Solve Large Scale Underdetermined Linear Equation with per Element Equality Constraint
I have the following system on $\boldsymbol{x}$:
$$ \boldsymbol{A} \boldsymbol{x} = \boldsymbol{0}, \quad \text{subject to} \; {x}_{i} = {v}_{i} \; \forall i \in \mathcal{V} $$
Where $\boldsymbol{A} \...
- 767
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1
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Fast algorithm to obtain an orthogonal vector to a set of vectors
When I ask this question I am usually suggested to do things like computing the SVD decomposition of the matrix formed by the vectors. SVD decompositions are very computationally expensive.
I am also ...
- 473
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2
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Finding ALL Eingenvalues of a Sparse Integer Matrix
I would like to find ALL Eingenvalues of a huge, very sparse integer matrix. This matrix has a lot of known properties, e.g. that it is symmetric and nearly tridiagonal, with very few (max. ca. 4 per ...
3
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105
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Eliminate variables from a large system of equations
I have a large system of equations $Ax=0$. For context, the equations are invariants of some model. $A$ is sparse and typically has more columns than rows ($m < n$). The $x$ vector can be divided ...
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