Condition number estimate via 1-norm: cond₁(A) = ‖A‖₁ · ‖A⁻¹‖₁. More...
#include "config.h"#include "utilities/expected.h"#include "matrix_traits.h"#include "algorithms/operations/norms.h"#include "algorithms/operations/inverse.h"
Include dependency graph for condition.h:
Go to the source code of this file.
Namespaces | |
| namespace | matrix_algorithms |
Functions | |
| template<typename T , my_size_t N> | |
| Expected< T, MatrixStatus > | matrix_algorithms::condition (const FusedMatrix< T, N, N > &A) |
| Compute the condition number of A in the 1-norm: cond₁(A) = ‖A‖₁ · ‖A⁻¹‖₁. | |
Detailed Description
Condition number estimate via 1-norm: cond₁(A) = ‖A‖₁ · ‖A⁻¹‖₁.
A condition number close to 1 means well-conditioned. Large values (>10⁶ for double, >10³ for float) indicate that solve/inverse results may lose significant digits.
ALGORITHM
- Compute ‖A‖₁ via norm1(A)
- Compute A⁻¹ via inverse(A)
- Compute ‖A⁻¹‖₁ via norm1(A⁻¹)
- Return ‖A‖₁ · ‖A⁻¹‖₁
Complexity: O(N³) for inverse, O(N²) for the two norms.
- Note
- This is the exact condition number, not a cheap estimate. A cheaper O(N²) estimate (Hager/Higham algorithm) could be added later using the LU factorization directly without forming the full inverse.
FAILURE MODES
- MatrixStatus::Singular — A is not invertible (condition = infinity)
