Zgelqf Zgeqp3 Zgeqrf Zunglq Zungqr Zunmlq Zunmqr

Zgelqf() Sub Zgelqf ( M As  Long, N As  Long, A() As  Complex, Tau() As  Complex, Info As  Long  ) LQ factorization of a complex Purpose This routine computes a LQ factorization of a complex m x n matrix A. A = L * Q 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 below the diagonal of the array contains the M x min(M, N) lower trapezoidal matrix L (L is lower triangular if M <= N); the elements above the diagonal, with the array Tau(), represent the unitary matrix Q as a product of 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(k) . . . H(2) H(1), 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 N) is stored on exit in A(i-1, i to N-1), and tau in Tau(i-1). Reference LAPACK Example Program Compute LQ 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_Zgelqf() 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 Zgelqf(M, N, A(), Tau(), Info) Debug.Print "L =" Debug.Print Creal(A(0, 0)), Cimag(A(0, 0)) 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(2, 2)), Cimag(A(2, 2)) Debug.Print "Info =", Info Call Zunglq(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 L = -1.34625406220371 -0 -0.477473025372185 0.734111062500513 1.48758208444318 -0 -0.494408907417122 -0.489357854877404 -0.116513840695564 0.106275665633282 1.15135517107319 -0 Info = 0 Q = -0.148560368815241 8.17082028483825E-02 0.69080571499087 0.237696590104386 -0.545146840380333 -0.518913702352619 0.144084009371217 0.313505787318611 0.415076807108814 0.482191168043502 0.108852269075227 0.579131158086946 -0.601669493701726 -0.274836682308196 0.101479037213067 0.551542760356437 9.33352464525714E-02 0.489131616930332 Info = 0