Zgelqf Zgeqp3 Zgeqrf Zunglq Zungqr Zunmlq Zunmqr

Zgeqrf() Sub Zgeqrf ( M As  Long, N As  Long, A() As  Complex, Tau() As  Complex, Info As  Long  ) QR factorization of a complex matrix Purpose This routine computes a QR factorization of a complex m x n matrix A. A = Q * R Parameters [in] M Number of rows of the matrix A. (M >= 0) (If M = 0, returns without computation) [in] N Number of columns of the matrix A. (N >= 0) (If N = 0, returns without computation) [in,out] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= M, LA2 >= N) [in] M x N matrix A. [out] The elements on and above the diagonal of the array contains the min(M, N) x N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal, with the array Tau(), represent the unitary matrix Q as a product of min(M, N) elementary reflectors (see Further Details). [out] Tau() Array Tau(LTau - 1) (LTau >= min(M, N)) The scalar factors of the elementary reflectors (see Further Details). [out] Info = 0: Successful exit. = -1: The argument M had an illegal value. (M < 0) = -2: The argument N had an illegal value. (N < 0) = -3: The argument A() is invalid. = -4: The argument Tau() is invalid. Further Details The matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(k), where k = min(M, N). Each H(i) has the form H(i) = I - tau * v * v^H where tau is a complex scalar, and v is a complex vector with v(1 to i-1) = 0 and v(i) = 1; v(i+1 to M) is stored on exit in A(i to M-1, i-1), and tau in Tau(i-1). Reference LAPACK Example Program Compute QR factorization of the matrix A, 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_Zgeqrf() Const M = 3, N = 3, K = N Dim A(M - 1, N - 1) As Complex, Tau(N - 1) As Complex, Info 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) Debug.Print "R =" Debug.Print Creal(A(0, 0)), Cimag(A(0, 0)), Creal(A(0, 1)), Cimag(A(0, 1)) Debug.Print Creal(A(0, 2)), Cimag(A(0, 2)) Debug.Print Creal(A(1, 1)), Cimag(A(1, 1)), Creal(A(1, 2)), Cimag(A(1, 2)) Debug.Print Creal(A(2, 2)), Cimag(A(2, 2)) Debug.Print "Info =", Info Call Zungqr(M, N, K, A(), Tau(), Info) Debug.Print "Q =" Debug.Print Creal(A(0, 0)), Cimag(A(0, 0)), Creal(A(0, 1)), Cimag(A(0, 1)) Debug.Print Creal(A(1, 0)), Cimag(A(1, 0)), Creal(A(1, 1)), Cimag(A(1, 1)) Debug.Print Creal(A(2, 0)), Cimag(A(2, 0)), Creal(A(2, 1)), Cimag(A(2, 1)) Debug.Print Creal(A(0, 2)), Cimag(A(0, 2)) Debug.Print Creal(A(1, 2)), Cimag(A(1, 2)) Debug.Print Creal(A(2, 2)), Cimag(A(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 = -0.129350304344243 7.11426673893335E-02 -0.726366393673366 -0.242754372725663 0.517401217376971 0.595011399983517 -0.157793930669391 0.252577062211036 -0.459193580422062 -0.381583397815516 -0.142116660471961 0.551879456556921 0.614237041991267 -0.119926029506194 5.77211185374505E-02 0.535006158572045 0.105825585638305 0.554588344523916 Info = 0