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Solve a System of Linear Equations (sv)
sv (defined in namespace flens::lapack) computes the solution to a real system of linear equations
\[ A X = B, \]where \(A\) is an \(n \times n\) matrix and \(X\) and \(B\) are \(n \times n_{rhs}\) matrices.
The \(LU\) decomposition with partial pivoting and row interchanges is used to factor \(A\) as
\[ A = P L U, \]where \(P\) is a permutation matrix, \(L\) is unit lower triangular, and \(U\) is upper triangular. The factored form of \(A\) is then used to solve the system of equations \(A X = B\).
Interface: Multiple Right-Hand Sides
A |
(input/output) real or complex valued GeMatrix |
piv |
(output) integer valued DenseVector |
B |
(input/output) real or complex valued GeMatrix |
Return value:
\(i=0\) |
Successfull exit. |
\(i>0\) |
\(U_{i,i}\) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed. |
Interface: Single Right-Hand Side
A |
(input/output) real or complex valued GeMatrix |
piv |
(output) integer valued DenseVector |
b |
(input/output) real or complex valued DenseVector |
Return value:
\(i=0\) |
Successfull exit. |
\(i>0\) |
\(U_{i,i}\) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed. |
Notes
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Example: lapack-gesv.
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sv is a port of dgesv and zgesv. Also this documentation is taken from there.