zgbcon zgbtrf zgbtrs zgecon zgetrf zgetri zgetrs zgtcon zgttrf zgttrs zspcon zsptrf zsptri zsptrs zsycon zsytrf zsytri zsytrs

zgbcon() void zgbcon ( char  norm, int  n, int  kl, int  ku, int  ldab, doublecomplex  ab[], int  ipiv[], double  anorm, double *  rcond, doublecomplex  work[], double  rwork[], int *  info  ) Condition number of a complex band matrix Purpose This routine estimates the reciprocal of the condition number of a complex band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by zgbtrf. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as rcond = 1 / (norm(A) * norm(inv(A))) Parameters [in] norm Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm. = 'I': Infinity-norm. [in] n Order of the matrix A. (n >= 0) (If n = 0, returns rcond = 1) [in] kl Number of sub-diagonals within the band of A. (kl >= 0) [in] ku Number of super-diagonals within the band of A. (ku >= 0) [in] ldab Leading dimension of the two dimensional array ab[][]. (ldab >= 2kl + ku + 1) [in,out] ab[][] Array ab[lab][ldab] (lab >= n) Details of the LU factorization of the band matrix A, as computed by zgbtrf. U is stored as an upper triangular band matrix with kl+ku super-diagonals in rows 1 to kl+ku+1, and the multipliers used during the factorization are stored in rows kl+ku+2 to 2*kl+ku+1. [in] ipiv[] Array ipiv[lipiv] (lipiv >= n) Pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row ipiv[i-1]. [in] anorm norm = '1' or 'O': The 1-norm of the original matrix A. (anorm >= 0) norm = 'I': The infinity-norm of the original matrix A. (anorm >= 0) [out] rcond The reciprocal of the condition number of the matrix A, computed as rcond = 1/(norm(A) * norm(inv(A))). [out] work[] Array work[lwork] (lwork >= 2*n) Work array. [out] rwork[] Array rwork[lrwork] (lrwork >= n) Work array. [out] info = 0: Successful exit = -1: The argument norm had an illegal value (norm != '1', 'O' nor 'I') = -2: The argument n had an illegal value (n < 0) = -3: The argument kl had an illegal value (kl < 0) = -4: The argument ku had an illegal value (ku < 0) = -5: The argument ldab had an illegal value (ldab < 2kl+ku+1) = -8: The argument anorm had an illegal value (anorm < 0) Reference LAPACK