Visible to Intel only — GUID: GUID-55877F0D-D603-4A37-B110-F5350BB8F8C4
Visible to Intel only — GUID: GUID-55877F0D-D603-4A37-B110-F5350BB8F8C4
?gbcon
Estimates the reciprocal of the condition number of a band matrix in the 1-norm or the infinity-norm.
lapack_int LAPACKE_sgbcon( int matrix_layout, char norm, lapack_int n, lapack_int kl, lapack_int ku, const float* ab, lapack_int ldab, const lapack_int* ipiv, float anorm, float* rcond );
lapack_int LAPACKE_dgbcon( int matrix_layout, char norm, lapack_int n, lapack_int kl, lapack_int ku, const double* ab, lapack_int ldab, const lapack_int* ipiv, double anorm, double* rcond );
lapack_int LAPACKE_cgbcon( int matrix_layout, char norm, lapack_int n, lapack_int kl, lapack_int ku, const lapack_complex_float* ab, lapack_int ldab, const lapack_int* ipiv, float anorm, float* rcond );
lapack_int LAPACKE_zgbcon( int matrix_layout, char norm, lapack_int n, lapack_int kl, lapack_int ku, const lapack_complex_double* ab, lapack_int ldab, const lapack_int* ipiv, double anorm, double* rcond );
- mkl.h
The routine estimates the reciprocal of the condition number of a general band matrix A in 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).
An estimate is obtained for ||A-1||, and the reciprocal of the condition number is computed as rcond = 1 / (||A|| ||A-1||).
Before calling this routine:
compute anorm (either ||A||1 = maxjΣi |aij| or ||A||∞ = maxiΣj |aij|)
call ?gbtrf to compute the LU factorization of A.
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. |
n |
The order of the matrix A; n≥ 0. |
kl |
The number of subdiagonals within the band of A; kl≥ 0. |
ku |
The number of superdiagonals within the band of A; ku≥ 0. |
ldab |
The leading dimension of the array ab. (ldab≥ 2*kl + ku +1). |
ipiv |
Array, size at least max(1, n). The ipiv array, as returned by ?gbtrf. |
ab |
The array abof size max(1, ldab*n) contains the factored band matrix A, as returned by ?gbtrf. |
anorm |
The norm of the original matrix A(see Description). |
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. |
This function returns a value info.
If info=0, the execution is successful.
If info = -i, parameter i had an illegal value.
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 or AH*x = b; the number is usually 4 or 5 and never more than 11. Each solution requires approximately 2n(ku + 2kl) floating-point operations for real flavors and 8n(ku + 2kl) for complex flavors.