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diagonal sparse matrix

Create Diagonal Matrix Object in Matrix: Sparse and Dense ...
https://rdrr.io › R-Forge › Matrix
numeric or logical; if missing, a unit diagonal n x n matrix is created. uplo. for .symDiagonal ( .trDiagonal ), the resulting sparse ...
R: Sparse Matrix diagonals
https://www.image.ucar.edu/.../fieldsCourse/Help/spamHelp/diag.html
Sparse Matrix diagonals Description Extract or replace the diagonal of a matrix, or construct a diagonal matrix. Usage # diag (x) diag (x=1, nrow, ncol) diag (x) <- value diag.spam (x=1, nrow, ncol) diag.spam (x) <- value Arguments Details Using diag (x) can have unexpected effects if x is a vector that could be of length one.
scipy.sparse.diags — SciPy v1.7.1 Manual
https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.diags.html
Construct a sparse matrix from diagonals. Parameters diagonalssequence of array_like Sequence of arrays containing the matrix diagonals, corresponding to offsets. offsetssequence of int or an int, optional Diagonals to set: k = 0 the main diagonal (default) k > 0 the kth upper diagonal k < 0 the kth lower diagonal shapetuple of int, optional
Diagonal Format (DIA) - Scipy Lecture Notes
https://scipy-lectures.org › advanced
diagonals in dense NumPy array of shape (n_diag, length). fixed length -> waste space a bit when far from main diagonal; subclass of _data_matrix (sparse matrix ...
Sparse matrix - Wikipedia
https://en.wikipedia.org › wiki › S...
A very efficient structure for an extreme case of band matrices, the diagonal matrix, is to store just the entries in the main diagonal as ...
Constructing Sparse Matrices - MATLAB & Simulink
www.mathworks.com › help › matlab
It is a tridiagonal matrix with -2s on the diagonal and 1s on the super- and subdiagonal. There are many ways to generate it—here's one possibility. n = 5; D = sparse(1:n,1:n,-2*ones(1,n),n,n); E = sparse(2:n,1:n-1,ones(1,n-1),n,n); S = E+D+E'
Constructing Sparse Matrices - MATLAB & Simulink
https://www.mathworks.com/.../math/constructing-sparse-matrices.html
Creating sparse matrices based on their diagonal elements is a common operation, so the function spdiags handles this task. Its syntax is S = spdiags (B,d,m,n) To create an output matrix S of size m -by- n with elements on p diagonals: B is a matrix of size min (m,n) -by- p. The columns of B are the values to populate the diagonals of S.
Compressed-Diagonal Storage Mode - IBM
https://www.ibm.com › reference
The storage mode used for square sparse matrices stored in compressed-diagonal storage mode has two variations, depending on whether the matrix is a general ...
Extract nonzero diagonals and create sparse band and ...
https://www.mathworks.com/help/matlab/ref/spdiags.html
S = spdiags (Bin,d,m,n) creates an m -by- n sparse matrix S by taking the columns of Bin and placing them along the diagonals specified by d. example S = spdiags (Bin,d,A) replaces the diagonals in A specified by d with the columns of Bin. Examples collapse all Create Tridiagonal Matrix Try This Example Copy Command
Constructing Sparse Matrices - MATLAB & Simulink - MathWorks
https://www.mathworks.com › math
It is a tridiagonal matrix with -2s on the diagonal and 1s on the super- and subdiagonal.
How can I extract the main diagonal of a sparse matrix?
stackoverflow.com › questions › 34870131
Jan 19, 2016 · A sparse matrix has a diagonal method: M.diagonal() http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csc_matrix.diagonal.html. The numpy diagonal is a little more powerful, allowing you to specify an off diagonal. M.A.diagonal(2)
How to create a diagonal sparse matrix in SciPy - Pretag
https://pretagteam.com › question
This function differs from spdiags in the way it handles off-diagonals.,Repeated diagonal offsets are disallowed.,Construct a sparse matrix ...
scipy.sparse.diags — SciPy v1.7.1 Manual
docs.scipy.org › generated › scipy
Construct a sparse matrix from diagonals. Parameters diagonals sequence of array_like. Sequence of arrays containing the matrix diagonals, corresponding to offsets. offsets sequence of int or an int, optional Diagonals to set: k = 0 the main diagonal (default) k > 0 the kth upper diagonal. k < 0 the kth lower diagonal. shape tuple of int, optional
How can I extract the main diagonal of a sparse matrix?
https://stackoverflow.com/questions/34870131
18.01.2016 · I want equivalent of np.diagonal(), but for sparse matrix. python python-2.7 scipy sparse-matrix. Share. Improve this question. Follow edited Apr 23 '19 at 16:38. nbro. 13.3k 23 23 gold badges 93 93 silver badges 178 178 bronze badges. asked …
Types of Sparse Matrix, Lower & Upper Triangular Sparse ...
https://quescol.com/data-structure/lower-and-upper-triangular-matrix
In a Lower triangular sparse matrix, all elements above the main diagonal have a zero value. This type of sparse matrix is also known as a lower triangular matrix. If you see its pictorial representation, then you find that all the elements having non-zero value are appear below the diagonal. In a lower triangular matrix, Arr i,j=0 where i<j.
scipy.sparse.csr_matrix.diagonal — SciPy v1.7.1 Manual
https://docs.scipy.org/.../generated/scipy.sparse.csr_matrix.diagonal.html
scipy.sparse.csr_matrix.diagonal¶ csr_matrix.diagonal(k=0)[source]¶ Returns the kth diagonal of the matrix. Parameters kint, optional Which diagonal to get, corresponding to elements a[i, i+k]. Default: 0 (the main diagonal). New in version 1.0. See also numpy.diagonal Equivalent numpy function. Examples
Solving a tridiagonal linear system
https://people.sc.fsu.edu/~jburkardt/classes/math2071_2020/tridiago…
The functions A=spline matrix(g) and [a,b,c]=spline sparse matrix(g) return dense and sparse versions of this matrix. In order to manufacture a problem, we choose a simple solution vector x and compute f = Ax. However, for the sparse matrix version, we can call f=tridiag sparse mv(a,b,c,x) to compute this product.
Efficient way to create a diagonal sparse matrix - Stack Overflow
https://stackoverflow.com › efficie...
Use scipy.sparse.spdiags (which does a lot, and so may be confusing, at first), scipy.sparse.dia_matrix and/or scipy.sparse.lil_diags .
scipy.sparse.diags — SciPy v1.7.1 Manual
https://docs.scipy.org › generated
Construct a sparse matrix from diagonals. ... This function differs from spdiags in the way it handles off-diagonals. ... Repeated diagonal offsets are disallowed.
scipy.sparse.csr_matrix.diagonal — SciPy v1.7.1 Manual
docs.scipy.org › doc › scipy
scipy.sparse.csr_matrix.diagonal¶ csr_matrix. diagonal (k = 0) [source] ¶ Returns the kth diagonal of the matrix. Parameters k int, optional. Which diagonal to get, corresponding to elements a[i, i+k]. Default: 0 (the main diagonal).
Types of Sparse Matrix, Lower & Upper Triangular Sparse ...
quescol.com › lower-and-upper-triangular-matrix
In a Lower triangular sparse matrix, all elements above the main diagonal have a zero value. This type of sparse matrix is also known as a lower triangular matrix. If you see its pictorial representation, then you find that all the elements having non-zero value are appear below the diagonal.
Sparse Arrays · The Julia Language
https://docs.julialang.org/en/v1/stdlib/SparseArrays
Construct a sparse diagonal matrix from Pairs of vectors and diagonals. Each vector kv.second will be placed on the kv.first diagonal. By default, the matrix is square and its size is inferred from kv, but a non-square size m×n (padded with zeros as needed) can be specified by passing m,n as the first arguments. Examples
Sparse matrix - Wikipedia
https://en.wikipedia.org/wiki/Sparse_matrix
An important special type of sparse matrices is band matrix, defined as follows. The lower bandwidth of a matrix A is the smallest number p such that the entry ai,j vanishes whenever i > j + p. Similarly, the upper bandwidth is the smallest number p such that ai,j = 0 whenever i < j − p (Golub & Van Loan 1996, §1.2.1). For example, a tridiagonal matrixhas lower bandwidth 1 and upper bandwidth 1. As another example, the following sparse matrix has lower and upper bandw…