WZhesv WZhesv2 WZpbsv WZpbsv2 WZposv WZposv2 WZptsv WZptsv2

WZptsv2() Function WZptsv2 ( N As  Long, D As  Variant, E As  Variant, B As  Variant, Optional Nrhs As  Long = 1  ) Solution to system of linear equations AX = B for a Hermitian positive definite tridiagonal matrix (complex numbers in pairs of cells) Purpose WZptsv2 computes the solution to a complex system of linear equations A * X = B, where A is an N x N Hermitian positive definite tridiagonal matrix, and X and B are N x Nrhs matrices. A is factored as A = L*D*L^H, and the factored form of A is then used to solve the system of equations. To represent complex numbers, a real part and an imaginary part are stored in a pair of adjacent cells (a real part in a left cell, and an imaginary part in a right cell). The computed results are stored in the same way. Returns N+1 x 2Nrhs Column 1 Column 2 . . . Column 2Nrhs Rows 1 to N Solution matrix X (a real part and an imaginary part are stored in a pair of adjacent columns (a real part is left and an imaginary part is right)) Row N+1 Reciprocal condition number Return code . . . 0 Return code. = 0: Successful exit. = i > 0: The leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed. Parameters [in] N Number of linear equations, i.e., order of the matrix A. (N >= 1) [in] D (N) Diagonal elements of the N x N coefficient matrix A. [in] E (N-1 x 2) Subdiagonal elements of the N x N coefficient matrix A. [in] B (N x 2Nrhs) N x Nrhs right hand side matrix B. [in] Nrhs (Optional) Number of columns of right hand side matrix B. (Nrhs >= 1) (default = 1) Reference LAPACK Example Solve the system of linear equations Ax = B and estimate the reciprocal of the condition number (RCond) of A, where A is an Hermitian positive definite tridiagonal matrix and ( 2.88 0.29-0.44i 0 ) A = ( 0.29+0.44i 0.62 -0.01-0.02i ) ( 0 -0.01+0.02i 0.46 ) ( 1.6236-0.7300i ) B = ( 0.1581+0.1537i ) ( 0.1132-0.2290i )