Developer Reference for Intel® oneAPI Math Kernel Library for C
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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∞(AT) = κ∞(AH)
κ∞(A) =||A||∞ ||A-1||∞ =κ1 (AT) = κ1(AH) .
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.