Zcposv Zposv Zposvx Zppsv Zppsvx

Zposv() Sub Zposv ( Uplo As  String, N As  Long, A() As  Complex, B() As  Complex, Info As  Long, Optional Nrhs As  Long = 1  ) (Simple driver) Solution to system of linear equations AX = B for a Hermitian positive definite matrix Purpose This routine 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. 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 >= 0) (If N = 0, returns without computation) [in,out] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= N, LA2 >= N) [in] N x N Hermitian positive definite matrix A. The upper or lower triangular part is to be referenced in accordance with Uplo. [out] If Info = 0, the factor U or L from the Cholesky factorization A = U^H*U or A = L*L^H. [in,out] B() Array B(LB1 - 1, LB2 - 1) (LB1 >= max(1, N), LB2 >= Nrhs) (2D array) or B(LB - 1) (LB >= max(1, N), Nrhs = 1) (1D array) [in] N x Nrhs matrix of right hand side matrix B. [out] If Info = 0, the N x Nrhs solution matrix X. [out] Info = 0: Successful exit. = -1: The argument Uplo had an illegal value. (Uplo <> "U" nor "L") = -2: The argument N had an illegal value. (N < 0) = -3: The argument A() is invalid. = -4: The argument B() is invalid. = -6: The argument Nrhs had an illegal value. (Nrhs < 0) = 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. [in] Nrhs (Optional) Number of right hand sides, i.e., number of columns of the matrix B. (Nrhs >= 0) (If Nrhs = 0, returns without computation) (default = 1) Reference LAPACK Example Program Solve the system of linear equations Ax = B and estimate the reciprocal of the condition number (RCond) of A, where ( 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 ) Sub Ex_Zposv() Const N As Long = 3 Dim A(N - 1, N - 1) As Complex, B(N - 1) As Complex Dim ANorm As Double, RCond As Double, Info As Long A(0, 0) = Cmplx(2.2, 0) A(1, 0) = Cmplx(-0.11, -0.93): A(1, 1) = Cmplx(2.32, 0) A(2, 0) = Cmplx(0.81, 0.37): A(2, 1) = Cmplx(-0.8, -0.92): A(2, 2) = Cmplx(2.29, 0) B(0) = Cmplx(1.598, 1.4644): B(1) = Cmplx(1.3498, 1.4398): B(2) = Cmplx(2.0561, -0.5441) ANorm = Zlanhe("1", "L", N, A()) Call Zposv("L", N, A(), B(), Info) If Info = 0 Then Call Zpocon("L", N, A(), ANorm, RCond, Info) Debug.Print "X =", Debug.Print Creal(B(0)), Cimag(B(0)), Creal(B(1)), Cimag(B(1)), Creal(B(2)), Cimag(B(2)) Debug.Print "RCond =", RCond Debug.Print "Info =", Info End Sub Example Results X = 0.86 0.64 0.51 0.71 0.59 -0.15 RCond = 8.85790434328042E-02 Info = 0