Zhesv Zhesvx Zhpsv Zhpsvx

Zhesv() Sub Zhesv ( Uplo As  String, N As  Long, A() As  Complex, IPiv() As  Long, B() As  Complex, Info As  Long, Optional Nrhs As  Long = 1  ) (Simple driver) Solution to system of linear equations AX = B for a Hermitian 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 matrix and X and B are N x Nrhs matrices. The diagonal pivoting method is used to factor A as A = U * D * U^H, if Uplo = "U", or A = L * D * L^H, 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. 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 matrix A. The upper or lower triangular part is to be referenced in accordance with Uplo. [out] If Info = 0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U^H or A = L*D*L^H as computed by Zhetrf. [out] IPiv() Array IPiv(LIPiv - 1) (LIPiv >= N) Details of the interchanges and the block structure of D, as determined by Zhetrf. If IPiv(k-1) > 0, then rows and columns k and IPiv(k-1) were interchanged, and k-th diagonal of D is a 1 x 1 diagonal block.   If Uplo = "U" and IPiv(k-1) = IPiv(k-2) < 0, then rows and columns k-1 and -IPiv(k-1) were interchanged and (k-1)-th diagonal of D is a 2 x 2 diagonal block.   If Uplo = "L" and IPiv(k-1) = IPiv(k) < 0, then rows and columns k+1 and -IPiv(k-1) were interchanged and k-th diagonal of D is a 2 x 2 diagonal block. [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 IPiv() is invalid. = -5: The argument B() is invalid. = -7: The argument Nrhs had an illegal value. (Nrhs < 0) = i > 0: The i-th element of D is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be 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 ( 0.20 -0.11+0.93i 0.81-0.37i ) A = ( -0.11-0.93i -0.32 -0.80+0.92i ) ( 0.81+0.37i -0.80-0.92i -0.29 ) ( -0.1220+0.1844i ) B = ( 0.0034-0.4346i ) ( 0.5339-0.1571i ) Sub Ex_Zhesv() Const N As Long = 3 Dim A(N - 1, N - 1) As Complex, B(N - 1) As Complex, IPiv(N - 1) As Long Dim ANorm As Double, RCond As Double, Info As Long A(0, 0) = Cmplx(0.2, 0) A(1, 0) = Cmplx(-0.11, -0.93): A(1, 1) = Cmplx(-0.32, 0) A(2, 0) = Cmplx(0.81, 0.37): A(2, 1) = Cmplx(-0.8, -0.92): A(2, 2) = Cmplx(-0.29, 0) B(0) = Cmplx(-0.122, 0.1844): B(1) = Cmplx(0.0034, -0.4346): B(2) = Cmplx(0.5339, -0.1571) ANorm = Zlanhe("1", "L", N, A()) Call Zhesv("L", N, A(), IPiv(), B(), Info) If Info = 0 Then Call Zhecon("L", N, A(), IPiv(), 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 0.590000000000001 -0.15 RCond = 4.46158691608911E-02 Info = 0