Zpbcon Zpbtrf Zpbtrs Zptcon Zpttrf Zpttrs

Zpttrs() Sub Zpttrs ( Uplo As  String, N As  Long, D() As  Double, E() 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 tridiagonal matrix Purpose This routine solves a tridiagonal system of the form A * X = B using the factorization A = U^H*D*U or A = L*D*L^H computed by zpttrf. D is a diagonal matrix specified in the array D(), U (or L) is a unit bidiagonal matrix whose super-diagonal (sub-diagonal) is specified in the array E(), and X and B are n x nrhs matrices. Parameters [in] Uplo Specifies the form of the factorization and whether the vector E() is the super-diagonal of the upper bidiagonal factor U or the sub-diagonal of the lower bidiagonal factor L. = "U": A = U^H*D*U, E() is the super-diagonal of U. = "L": A = L*D*L^H, E() is the sub-diagonal of L. [in] N Order of the matrix A. (N >= 0) (If N = 0, returns without computation) [in] D() Array D(LD - 1) (LD >= N) N diagonal elements of the diagonal matrix D from the factorization A = U^H*D*U or A = L*D*L^H. [in] E() Array E(LE - 1) (LE >= N - 1) N-1 super-diagonal or sub-diagonal elements of the unit bidiagonal factor U or L from the factorization A = U^H*D*U or A = L*D*L^H. [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 D() is invalid. = -4: The argument E() 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 Zpttrf.