Zgelqf Zgeqp3 Zgeqrf Zunglq Zungqr Zunmlq Zunmqr

Zunmqr() Sub Zunmqr ( 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 QR 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 complex unitary matrix defined as the product of k elementary reflectors Q = H(1) H(2) . . . H(k) as returned by Zgeqrf. Q is of order m if Side = "L" and of order n if Side = "R". Parameters [in] Side = "L": Apply Q or Q^T 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 >= M (Side = "L") or N (Side = "R"), LA2 >= K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1, 2, ..., K, as returned by Zgeqrf in the first K columns 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 Zgeqrf. [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 QR factorization of the matrix A, and compute Q*R, 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_Zunmqr() Const M = 3, N = 3, K = N Dim A(M - 1, N - 1) As Complex, Tau(N - 1) As Complex, Info As Long Dim R(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 Zgeqrf(M, N, A(), Tau(), Info) For I = 0 To M - 1 For J = I To N - 1 R(I, J) = A(I, J) Next Next Debug.Print "R =" Debug.Print Creal(R(0, 0)), Cimag(R(0, 0)), Creal(R(0, 1)), Cimag(R(0, 1)) Debug.Print Creal(R(0, 2)), Cimag(R(0, 2)) Debug.Print Creal(R(1, 1)), Cimag(R(1, 1)), Creal(R(1, 2)), Cimag(R(1, 2)) Debug.Print Creal(R(2, 2)), Cimag(R(2, 2)) Debug.Print "Info =", Info Call Zunmqr("L", "N", M, N, K, A(), Tau(), R(), Info) Debug.Print "Q*R =" Debug.Print Creal(R(0, 0)), Cimag(R(0, 0)), Creal(R(0, 1)), Cimag(R(0, 1)), Creal(R(0, 2)), Cimag(R(0, 2)) Debug.Print Creal(R(1, 0)), Cimag(R(1, 0)), Creal(R(1, 1)), Cimag(R(1, 1)), Creal(R(1, 2)), Cimag(R(1, 2)) Debug.Print Creal(R(2, 0)), Cimag(R(2, 0)), Creal(R(2, 1)), Cimag(R(2, 1)), Creal(R(2, 2)), Cimag(R(2, 2)) Debug.Print "Info =", Info End Sub Example Results R = -1.54618886297891 0 0.455571771900423 0.580588841049134 0.105614523497074 -0.57774313435356 1.14235325460067 0 -0.16000635361559 -0.558214300362838 1.30543219081149 0 Info = 0 Q*R = 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