WZgbsv WZgbsv2 WZgesv WZgesv2 WZgtsv WZgtsv2 WZsysv WZsysv2 WZtrtrs WZtrtrs2

WZsysv() Function WZsysv ( Uplo As  String, 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 symmetric matrix Purpose WZsysv computes the solution to a complex system of linear equations A * X = B where A is an N x N symmetric matrix and X and B are N x Nrhs matrices. The diagonal pivoting method is used to factor A as A = U * D * U^T, if Uplo = "U", or A = L * D * L^T, if Uplo = "L", where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1 x 1 and 2 x 2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B. 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": 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 >= 1) [in] A (N x N) N x N symmetric matrix A. Upper or lower triangular part is to be referenced according to Uplo. [in] B (N x Nrhs) 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 symmetric and ( 0.20-0.11i -0.93-0.32i -0.80-0.92i ) A = ( -0.93-0.32i 0.81+0.37i -0.29+0.86i ) ( -0.80-0.92i -0.29+0.86i 0.64+0.51i ) ( 1.1120-1.0248i ) B = ( -1.5297-0.7781i ) ( -0.4965-0.6057i )