Zpbcon Zpbtrf Zpbtrs Zptcon Zpttrf Zpttrs

Zpbcon() Sub Zpbcon ( Uplo As  String, N As  Long, Kd As  Long, Ab() As  Complex, ANorm As  Double, RCond As  Double, Info As  Long  ) Condition number of a Hermitian positive definite band matrix Purpose This routine estimates the reciprocal of the condition number (in the 1-norm) of a Hermitian positive definite band matrix using the Cholesky factorization A = U^H*U or A = L*L^H computed by Zpbtrf. 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] Uplo = "U": Upper triangular factor U is stored in Ab(). = "L": Lower triangular factor L is stored in Ab(). [in] N Order of the matrix A. (N >= 0) (If N = 0, returns RCond = 1) [in] Kd Number of super-diagonals of the matrix A if Uplo = "U", or number of sub-diagonals if Uplo = "L". (Kd >= 0) [in] Ab() Array Ab(LAb1 - 1, LAb2 - 1) (LAb1 >= Kd + 1, LAb2 >= N) The triangular factor U or L from the Cholesky factorization A = U^H*U or A = L*L^H of the Hermitian positive definite band matrix A, stored in Kd+1 x N symmetric band matrix form. [in] ANorm The 1-norm (or infinity-norm) of the Hermitian positive definite band matrix A. [out] RCond The reciprocal of the condition number of the matrix A, computed as RCond = 1/(ANorm * Ainvnm), where Ainvnm is an estimate of the 1-norm of inv(A) computed in this routine. [out] Info = 0: Successful exit. = -1: The argument Uplo had an illegal value. (Uplo <> "U" nor "L") = -2: The argument N had an illegal value. (N < 0) = -3: The argument Kd had an illegal value. (Ku < 0) = -4: The argument Ab() is invalid. = -5: The argument ANorm had an illegal value. (ANorm < 0) Reference LAPACK Example Program See example of Zpbsv.