?tbcon

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?tbcon

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

Syntax

lapack_int LAPACKE_stbcon( int matrix_layout, char norm, char uplo, char diag, lapack_int n, lapack_int kd, const float* ab, lapack_int ldab, float* rcond );

lapack_int LAPACKE_dtbcon( int matrix_layout, char norm, char uplo, char diag, lapack_int n, lapack_int kd, const double* ab, lapack_int ldab, double* rcond );

lapack_int LAPACKE_ctbcon( int matrix_layout, char norm, char uplo, char diag, lapack_int n, lapack_int kd, const lapack_complex_float* ab, lapack_int ldab, float* rcond );

lapack_int LAPACKE_ztbcon( int matrix_layout, char norm, char uplo, char diag, lapack_int n, lapack_int kd, const lapack_complex_double* ab, lapack_int ldab, double* rcond );

Include Files

mkl.h

Description

The routine estimates the reciprocal of the condition number of a triangular band 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||_∞ =κ₁ (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 `ap` stores the upper triangle of `A` in packed form. If `uplo = 'L'`, the array `ap` stores the lower triangle of `A` in packed form.
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 `ab`.
n	The order of the matrix `A`; `n`≥ 0.
kd	The number of superdiagonals or subdiagonals in the matrix `A`; `kd`≥ 0.
ab	The array `ab` of size max(1, ldab*n) contains the band matrix `A`.
ldab	The leading dimension of the array `ab`. (`ldab`≥`kd` +1).

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 2*n(kd + 1) floating-point operations for real flavors and 8*n(kd + 1) 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

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