Zpbcon Zpbtrf Zpbtrs Zptcon Zpttrf Zpttrs

Zpbtrs() Sub Zpbtrs ( Uplo As  String, N As  Long, Kd As  Long, Ab() As  Complex, B() As  Complex, Info As  Long, Optional Nrhs As  Long = 1  ) Solution to factorized system of linear equations AX = B for a Hermitian positive definite band matrix Purpose This routine solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesy factorization A = U^H*U or A = L*L^H computed by Zpbtrf. Parameters [in] Uplo = "U": Upper triangle of A is stored. = "L": Lower triangle of A is stored. [in] N Number of linear equations, i.e., order of the matrix A. (N >= 0) (If N = 0, returns without computation) [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, in the Kd+1 x N symmetric band matrix form. [in,out] B() Array B(LB1 - 1, LB2 - 1) (LB1 >= max(1, N), LB2 >= Nrhs) (2D array) or B(LB - 1) (LB >= max(1, N), Nrhs = 1) (1D array) [in] N x Nrhs right hand side matrix B. [out] If Info = 0, the N x Nrhs solution matrix X. [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. (Kd < 0) = -4: The argument Ab() is invalid. = -5: The argument B() is invalid. = -7: The argument Nrhs had an illegal value. (Nrhs < 0) [in] Nrhs (Optional) Number of right hand sides, i.e., number of columns of the matrix B. (Nrhs >= 0) (If Nrhs = 0, returns without computation) (default = 1) Reference LAPACK Example Program See example of Zpbtrf.