Ztbcon Ztbtrs Ztpcon Ztptri Ztptrs Ztrcon Ztrtri Ztrtrs

Ztrtrs() Sub Ztrtrs ( Uplo As  String, Trans As  String, Diag As  String, N As  Long, A() As  Complex, B() As  Complex, Info As  Long, Optional Nrhs As  Long = 1  ) Solution to system of linear equations AX = B, ATX = B or AHX = B for a complex triangular matrix Purpose This routine 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. Parameters [in] Uplo = "U": A is upper triangular. = "L": A is lower triangular. [in] Trans Specifies the form of the system of equations: = "N": A * X = B. (no transpose) = "T": A^T * X = B. (transpose) = "C": A^H * X = B. (conjugate transpose) [in] Diag = "N": A is non-unit triangular. = "U": A is unit triangular. (Diagonal elements of A() are not referenced and are assumed to be 1) [in] N Order of the matrix A. (N >= 0) (If N = 0, returns without computation) [in] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= N, LA2 >= N) N x N triangular matrix A. Only the upper or lower triangular part is to be referenced in accordance with Uplo. [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 Trans had an illegal value. (Trans <> "N", "T" nor "C") = -3: The argument Diag had an illegal value. (Diag <> "N" nor "U") = -4: The argument N had an illegal value. (N < 0) = -5: The argument A() is invalid. = -6: The argument B() is invalid. = -8: The argument Nrhs had an illegal value. (Nrhs < 0) = i > 0: The i-th diagonal element of A is zero, indicating that the matrix is singular and the solutions have 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 ( 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 ) Sub Ex_Ztrtrs() Const N = 3 Dim A(N - 1, N - 1) As Complex, B(N - 1) As Complex Dim RCond As Double, Info As Long A(0, 0) = Cmplx(0.2, -0.11) A(1, 0) = Cmplx(-0.93, -0.32): A(1, 1) = Cmplx(0.81, 0.37) A(2, 0) = Cmplx(-0.8, -0.92): A(2, 1) = Cmplx(-0.29, 0.86): A(2, 2) = Cmplx(0.64, 0.51) B(0) = Cmplx(0.2069, 0.0399): B(1) = Cmplx(-0.6633, -0.6775): B(2) = Cmplx(-0.4965, -0.6057) Call Ztrtrs("L", "N", "N", N, A(), B(), Info) If Info = 0 Then Call Ztrcon("1", "L", "N", N, A(), 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 = 0.71 0.59 -0.15 0.19 0.2 0.94 RCond = 2.79371684875664E-02 Info = 0