?tpcon

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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?tpcon

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

Syntax

lapack_int LAPACKE_stpcon( int matrix_layout, char norm, char uplo, char diag, lapack_int n, const float* ap, float* rcond );

lapack_int LAPACKE_dtpcon( int matrix_layout, char norm, char uplo, char diag, lapack_int n, const double* ap, double* rcond );

lapack_int LAPACKE_ctpcon( int matrix_layout, char norm, char uplo, char diag, lapack_int n, const lapack_complex_float* ap, float* rcond );

lapack_int LAPACKE_ztpcon( int matrix_layout, char norm, char uplo, char diag, lapack_int n, const lapack_complex_double* ap, double* rcond );

Include Files

mkl.h

Description

The routine estimates the reciprocal of the condition number of a packed 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||_∞ =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 `ap`.
n	The order of the matrix `A`; `n`≥ 0.
ap	The array `ap` contains the packed matrix `A`. The dimension of `ap` must be at least max(1,`n`(`n`+1)/2).

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

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