WZgbsv WZgbsv2 WZgesv WZgesv2 WZgtsv WZgtsv2 WZsysv WZsysv2 WZtrtrs WZtrtrs2

WZgesv2() Function WZgesv2 ( N As  Long, A As  Variant, B As  Variant, Optional Nrhs As  Long = 1  ) Solution to system of linear equations AX = B for a complex matrix (complex numbers in pairs of cells) Purpose WZgesv2 computes the solution to a real system of linear equations A * X = B where A is an N x N matrix and X and B are N x Nrhs matrices. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B. 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 i-th diagonal element of the factor is zero. (Matrix A is singular) Parameters [in] N Number of linear equations, i.e., order of the matrix A. (N >= 1) [in] A (N x 2N) 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 ( 0.2-0.11i -0.93-0.32i 0.81+0.37i ) A = ( -0.8-0.92i -0.29+0.86i 0.64+0.51i ) ( 0.71+0.59i -0.15+0.19i 0.2+0.94i ) ( -0.5853-0.9457i ) B = ( -2.1697-1.0006i ) ( 0.0116-0.5094i )