rocsolver_sgecon Interface Reference

rocsolver_sgecon Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgecon Interface Reference

GECON estimates the reciprocal of the condition number of a general n-by-n matrix A in the 1-norm or infinity-norm. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sgecon_ (handle, norm_type, n, a, lda, anorm, rcond)

Detailed Description

GECON estimates the reciprocal of the condition number of a general n-by-n matrix A in the 1-norm or infinity-norm.

The reciprocal condition number is computed as

\[ \text{rcond} = \frac{1}{\|A\| \cdot \|A^{-1}\|} \]

where A is the matrix in its factorized form as returned by GETRF, and the norm can be the 1-norm or the infinity-norm.

The computed rcond will be a lower bound on the actual rcond. When rcond is close to zero, the matrix A is poorly conditioned (nearly singular). When rcond is close to 1, the matrix A is well conditioned.

Parameters

[in]	handle	- rocblas_handle.
[in]	norm_type	- rocsolver_norm_type. Specifies the norm to be used. The 1-norm and the infinity-norm are supported, specified by values of rocsolver_norm_type_one and rocsolver_norm_type_infinity.
[in]	n	- rocblas_int. n >= 0. The number of rows and columns of the matrix A.
[in]	A	- pointer to type. Array on the GPU of dimension lda*n. The factors L and U of the factorization \(A = PLU\) as returned by GETRF.
[in]	lda	- rocblas_int. lda >= n. The leading dimension of A.
[in]	anorm	- pointer to real type. Scalar on the GPU. The norm of the original matrix A (before factorization) as returned by LANGE.
[out]	rcond	- pointer to real type. Scalar on the GPU. The reciprocal condition number estimate.

Member Function/Subroutine Documentation