?trcon

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?trcon

Estimates the reciprocal of the condition number of a triangular matrix.

Syntax

lapack_int LAPACKE_strcon( int matrix_layout, char norm, char uplo, char diag, lapack_int n, const float* a, lapack_int lda, float* rcond );

lapack_int LAPACKE_dtrcon( int matrix_layout, char norm, char uplo, char diag, lapack_int n, const double* a, lapack_int lda, double* rcond );

lapack_int LAPACKE_ctrcon( int matrix_layout, char norm, char uplo, char diag, lapack_int n, const lapack_complex_float* a, lapack_int lda, float* rcond );

lapack_int LAPACKE_ztrcon( int matrix_layout, char norm, char uplo, char diag, lapack_int n, const lapack_complex_double* a, lapack_int lda, double* rcond );

Include Files

mkl.h

Description

The routine estimates the reciprocal of the condition number of a triangular matrix A in either the 1-norm or infinity-norm:

κ₁(A) =||A||₁ ||A^-1||₁ = κ_∞(A^T) = κ_∞(A^H)

κ_∞ (A) =||A||_∞ ||A^-1||_∞ =k₁ (A^T) = κ₁ (A^H) .

Input Parameters

matrix_layout	Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
norm	Must be '1' or 'O' or 'I'. If `norm` = '1' or 'O', then the routine estimates the condition number of matrix `A` in 1-norm. If `norm = 'I'`, then the routine estimates the condition number of matrix `A` in infinity-norm.
uplo	Must be 'U' or 'L'. Indicates whether `A` is upper or lower triangular: If `uplo = 'U'`, the array `a` stores the upper triangle of `A`, other array elements are not referenced. If `uplo = 'L'`, the array `a` stores the lower triangle of `A`, other array elements are not referenced.
diag	Must be 'N' or 'U'. If `diag = 'N'`, then `A` is not a unit triangular matrix. If `diag = 'U'`, then `A` is unit triangular: diagonal elements are assumed to be 1 and not referenced in the array `a`.
n	The order of the matrix `A`; `n`≥ 0.
a	The array `a` of size max(1, lda*n) contains the matrix `A`.
lda	The leading dimension of `a`; `lda≥ max(1, n)`.

Output Parameters

rcond

An estimate of the reciprocal of the condition number. The routine sets rcond =0 if the estimate underflows; in this case the matrix is singular (to working precision). However, anytime rcond is small compared to 1.0, for the working precision, the matrix may be poorly conditioned or even singular.

Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info = -i, parameter i had an illegal value.

Application Notes

The computed rcond is never less than r (the reciprocal of the true condition number) and in practice is nearly always less than 10r. A call to this routine involves solving a number of systems of linear equations A*x = b; the number is usually 4 or 5 and never more than 11. Each solution requires approximately n² floating-point operations for real flavors and 4n² operations for complex flavors.

Parent topic: Estimating the Condition Number: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?trcon

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