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# spchol

sparse cholesky factorization

### Calling Sequence

`[R,P] = spchol(X)`

### Arguments

X

symmetric positive definite real sparse matrix

P

permutation matrix

R

cholesky factor

### Description

`[R,P] = spchol(X)` produces a lower triangular matrix `R` such that `P*R*R'*P' = X`.

### Examples

```// Factorization:
Xfull = [
3.,  0.,  0.,  2.,  0.,  0.,  2.,  0.,  2.,  0.,  0.
0.,  5.,  4.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.
0.,  4.,  5.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.
2.,  0.,  0.,  3.,  0.,  0.,  2.,  0.,  2.,  0.,  0.
0.,  0.,  0.,  0. , 5.,  0.,  0.,  0.,  0.,  0.,  4.
0.,  0.,  0.,  0.,  0.,  4.,  0.,  3.,  0.,  3.,  0.
2.,  0.,  0.,  2.,  0.,  0.,  3.,  0.,  2.,  0.,  0.
0.,  0.,  0.,  0.,  0.,  3.,  0.,  4.,  0.,  3.,  0.
2.,  0.,  0.,  2.,  0.,  0.,  2.,  0.,  3.,  0.,  0.
0.,  0.,  0.,  0.,  0.,  3.,  0.,  3.,  0.,  4.,  0.
0.,  0.,  0.,  0.,  4.,  0.,  0.,  0.,  0.,  0.,  5.];
X = sparse(Xfull);

[R, P] = spchol(X);
max(P*R*R'*P'-X)

// Factorization and solve with backslash operator:
Afull = [
2 -1  0  0  0;
-1  2 -1  0  0;
0 -1  2 -1  0;
0  0 -1  2 -1;
0  0  0 -1  2
];
A = sparse(Afull);

[L, P] = spchol(A);
max(P*L*L'*P'-A)

n = size(A, "r"); e = (1:n)'; b = A * e;
x = P*(L'\(L\(P'*b)));
A*x-b```

### See Also

• sparse — sparse matrix definition
• lusolve — sparse linear system solver
• luget — extraction of sparse LU factors
• chol — Cholesky factorization
 Report an issue << lusolve Sparse Decompositions Linear Equations (Iterative Solvers) >>

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