TBCON - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T>
void tbcon(char *norm, char *uplo, char *diag, integer *n, integer *kd, T *ab, integer *ldab, T *rcond, T *work, integer *iwork, integer *info)#

TBCON estimates the reciprocal of the condition number of a

triangular band matrix A.

Purpose:

  TBCON estimates the reciprocal of the condition number of a
  triangular band matrix A, in either the 1-norm or the infinity-norm.

  The norm of A is computed and an estimate is obtained for
  norm(inv(A)), then the reciprocal of the condition number is
  computed as
     RCOND = 1 / ( norm(A) * norm(inv(A))).
Parameters:
  • NORM[in]

    NORM is CHARACTER*1

    Specifies whether the 1-norm condition number or the infinity-norm condition number is required:

    = ‘1’ or ‘O’: 1-norm;

    = ‘I’: Infinity-norm.

  • UPLO[in]

    UPLO is CHARACTER*1

    = ‘U’: A is upper triangular;

    = ‘L’: A is lower triangular.
  • DIAG[in]

    DIAG is CHARACTER*1

    = ‘N’: A is non-unit triangular;

    = ‘U’: A is unit triangular.
  • N[in]

    N is INTEGER

    The order of the matrix A. N >= 0.

  • KD[in]

    KD is INTEGER

    The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.

  • AB[in]

    AB is REAL array, dimension (LDAB,N)

    The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

    if UPLO = ‘U’, AB(kd+1+i-j,j) = A(i,j) for fla_max(1,j-kd)<=i<=j;

    if UPLO = ‘L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

    If DIAG = ‘U’, the diagonal elements of A are not referenced and are assumed to be 1.
  • LDAB[in]

    LDAB is INTEGER

    The leading dimension of the array AB. LDAB >= KD+1.

  • RCOND[out]

    RCOND is REAL

    The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).

  • WORK[out] WORK is REAL array, dimension (3*N)

  • IWORK[out] IWORK is INTEGER array, dimension (N)

  • INFO[out]

    INFO is INTEGER

    = 0: successful exit

    < 0: if INFO = -i, the i-th argument had an illegal value
template<typename T, typename Ta>
void tbcon(char *norm, char *uplo, char *diag, integer *n, integer *kd, T *ab, integer *ldab, Ta *rcond, T *work, Ta *rwork, integer *info)#