WZhesv WZhesv2 WZpbsv WZpbsv2 WZposv WZposv2 WZptsv WZptsv2

WZposv() Function WZposv ( 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 Hermitian positive definite matrix (complex number representation in Excel format) Purpose WZposv computes the solution to a complex system of linear equations A * X = B, where A is an N x N Hermitian positive definite matrix and X and B are N x Nrhs matrices. The Cholesky decomposition is used to factor A as A = U^H * U, if Uplo = "U", or A = L * L^H, if Uplo = "L", where U is an upper triangular matrix and L is a lower triangular matrix. 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 Hermitian positive definite 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 an Hermitian positive definite matrix and ( 2.20 -0.11+0.93i 0.81-0.37i ) A = ( -0.11-0.93i 2.32 -0.80+0.92i ) ( 0.81+0.37i -0.80-0.92i 2.29 ) ( 1.5980+1.4644i ) B = ( 1.3498+1.4398i ) ( 2.0561-0.5441i )