Zgelqf Zgeqp3 Zgeqrf Zunglq Zungqr Zunmlq Zunmqr

Zunmlq() Sub Zunmlq ( Side As  String, Trans As  String, M As  Long, N As  Long, K As  Long, A() As  Complex, Tau() As  Complex, C() As  Complex, Info As  Long  ) Multiplies matrix by Q of LQ factorization of a complex matrix Purpose This routine overwrites the general complex m x n matrix C with Side = "L" Side = "R" Trans = "N": Q * C C * Q Trans = "C": Q^H * C C * Q^H where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by Dgelqf. Q is of order m if Side = "L" and of order n if Side = "R". Parameters [in] Side = "L": Apply Q or Q^H from the left. = "R": Apply Q or Q^H from the right. [in] Trans = "N": No transpose, apply Q. = "C": Conjugate transpose, apply Q^H. [in] M Number of rows of the matrix C. (M >= 0) (If M = 0, returns without computation) [in] N Number of columns of the matrix C. (N >= 0) (If N = 0, returns without computation) [in] K Number of elementary reflectors whose product defines the matrix Q. (M => K >= 0 if Side = "L", N >= K >= 0 if Side = "R") (If K = 0, returns without computation) [in] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= K, LA2 >= M (Side = "L") or N (Side = "R")) The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1, 2, ..., K, as returned by Zgelqf in the first K rows of its array argument A(). [in] Tau() Array Tau(LTau - 1) (LTau >= K) The scalar factors of the elementary reflectors H(i) as returned by Zgelqf. [in,out] C() Array C(LC1 - 1, LC2 - 1) (LC1 >= M, LC2 >= N) [in] M x N matrix C. [out] C() is overwritten by Q*C or Q^H*C or C*Q^H or C*Q. [out] Info = 0: Successful exit. = -1: The argument Side had an illegal value. (Side <> "L" nor "R") = -2: The argument Trans had an illegal value. (Trans <> "C" nor "N") = -3: The argument M had an illegal value. (M < 0) = -4: The argument N had an illegal value. (N < 0) = -5: The argument K had an illegal value. (K < 0, or K > M (Side = "L") or N (Side = "R")) = -6: The argument A() is invalid. = -7: The argument Tau() is invalid. = -8: The argument C() is invalid. Reference LAPACK Example Program Compute LQ factorization of the matrix A, and compute L*Q, where ( 0.20-0.11i -0.93-0.32i 0.81+0.37i ) A = ( -0.80-0.92i -0.29+0.86i 0.64+0.51i ) ( 0.71+0.59i -0.15+0.19i 0.20+0.94i ) Sub Ex_Zunmlq() Const M = 3, N = 3, K = N Dim A(M - 1, N - 1) As Complex, Tau(N - 1) As Complex, Info As Long Dim L(M - 1, N - 1) As Complex, I As Long, J As Long A(0, 0) = Cmplx(0.2, -0.11): A(0, 1) = Cmplx(-0.93, -0.32): A(0, 2) = Cmplx(0.81, 0.37) A(1, 0) = Cmplx(-0.8, -0.92): A(1, 1) = Cmplx(-0.29, 0.86): A(1, 2) = Cmplx(0.64, 0.51) A(2, 0) = Cmplx(0.71, 0.59): A(2, 1) = Cmplx(-0.15, 0.19): A(2, 2) = Cmplx(0.2, 0.94) Call Zgelqf(M, N, A(), Tau(), Info) For I = 0 To M - 1 For J = 0 To I L(I, J) = A(I, J) Next Next Debug.Print "L =" Debug.Print Creal(L(0, 0)), Cimag(L(0, 0)) Debug.Print Creal(L(1, 0)), Cimag(L(1, 0)), Creal(L(1, 1)), Cimag(L(1, 1)) Debug.Print Creal(L(2, 0)), Cimag(L(2, 0)), Creal(L(2, 1)), Cimag(L(2, 1)) Debug.Print Creal(L(2, 2)), Cimag(L(2, 2)) Debug.Print "Info =", Info Call Zunmlq("R", "N", M, N, K, A(), Tau(), L(), Info) Debug.Print "L*Q =" Debug.Print Creal(L(0, 0)), Cimag(L(0, 0)), Creal(L(0, 1)), Cimag(L(0, 1)), Creal(L(0, 2)), Cimag(L(0, 2)) Debug.Print Creal(L(1, 0)), Cimag(L(1, 0)), Creal(L(1, 1)), Cimag(L(1, 1)), Creal(L(1, 2)), Cimag(L(1, 2)) Debug.Print Creal(L(2, 0)), Cimag(L(2, 0)), Creal(L(2, 1)), Cimag(L(2, 1)), Creal(L(2, 2)), Cimag(L(2, 2)) Debug.Print "Info =", Info End Sub Example Results L = -1.34625406220371 -0 -0.477473025372185 0.734111062500513 1.48758208444318 -0 -0.494408907417122 -0.489357854877404 -0.116513840695564 0.106275665633282 1.15135517107319 -0 Info = 0 L*Q = 0.2 -0.11 -0.93 -0.32 0.81 0.37 -0.8 -0.92 -0.29 0.86 0.64 0.51 0.71 0.59 -0.15 0.19 0.2 0.94 Info = 0