Condition number

Specialized interfaces

• Frobenius-norm condition number
• Infinity-norm condition number
• Max-norm condition number
• One-norm condition number
• Two-norm condition number

Vanilla interface

Header file

Implementation

The condition number of a matrix with respect to a particular norm is

\[\kappa(A) = \|A\| \|A^{-1}\|,\]

with the most common choice being the matrix two-norm.

C++ API

Base<F> Condition(const Matrix<F> &A, NormType type = TWO_NORM)

Base<F> Condition(const AbstractDistMatrix<F> &A, NormType type = TWO_NORM)

C API

ElError ElCondition_s(ElConstMatrix_s A, ElNormType normType, float* cond)

ElError ElCondition_d(ElConstMatrix_d A, ElNormType normType, double* cond)

ElError ElCondition_c(ElConstMatrix_c A, ElNormType normType, float* cond)

ElError ElCondition_z(ElConstMatrix_z A, ElNormType normType, double* cond)

ElError ElConditionDist_s(ElConstDistMatrix_s A, ElNormType normType, float* cond)

ElError ElConditionDist_d(ElConstDistMatrix_d A, ElNormType normType, double* cond)

ElError ElConditionDist_c(ElConstDistMatrix_c A, ElNormType normType, float* cond)

ElError ElConditionDist_z(ElConstDistMatrix_z A, ElNormType normType, double* cond)

Python API

Condition(A, normType=FROBENIUS_NORM)