WZgbsv WZgbsv2 WZgesv WZgesv2 WZgtsv WZgtsv2 WZsysv WZsysv2 WZtrtrs WZtrtrs2

WZtrtrs() Function WZtrtrs ( Uplo As  String, N As  Long, A As  Variant, B As  Variant, Optional Trans As  String = "N", Optional Nrhs As  Long = 1  ) Solution to system of linear equations AX = B, ATX = B or AHX = B for a complex triangular matrix Purpose WZtrtrs solves a triangular system of the form A * X = B, A^T * X = B or A^H * X = B where A is a triangular matrix of order N and B is an N x Nrhs matrix. A check is made to verify that A is nonsingular. To represent complex numbers in Excel cells, complex number format in Excel (e.g. 2.5+1i) is used. Worksheet function Complex can be used to input complex numbers into cells. Returns N+2 x Nrhs Column 1 Column 2 . . . Column Nrhs Rows 1 to N Solution matrix X Row N+1 Reciprocal condition number 0 . . . 0 Row N+2 Return code 0 . . . 0 Return code. = 0: Successful exit. = i > 0: The i-th diagonal element of the factor is zero. (Matrix A is singular) Parameters [in] Uplo = "U": A is upper triangular matrix. = "L": A is lower triangular matrix. [in] N Number of linear equations, i.e., order of the matrix A. (N >= 1) [in] A (N x N) N x N coefficient matrix A. (If Uplo = 0, the lower triangular part will be used. If Uplo = 1, the upper triangular part will be used) [in] B (N x Nrhs) N x Nrhs right hand side matrix B. [in] Trans (Optional) Specifies the form of the system of equations. (default = "N") = "N": A * X = B. (no transpose) = "T": A^T * X = B. (transpose) = "C": A^H * X = B. (conjugate transpose) [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 a triangular matrix and ( 0.20-0.11i 0 0 ) A = ( -0.93-0.32i 0.81+0.37i 0 ) ( -0.80-0.92i -0.29+0.86i 0.64+0.51i ) ( 0.2069+0.0399i ) B = ( -0.6633-0.6775i ) ( -0.4965-0.6057i )