Zgelqf Zgeqp3 Zgeqrf Zunglq Zungqr Zunmlq Zunmqr

Zgeqp3() Sub Zgeqp3 ( M As  Long, N As  Long, A() As  Complex, Jpvt() As  Long, Tau() As  Complex, Info As  Long  ) QR factorization of a complex matrix with pivoting Purpose This routine computes a QR factorization with column pivoting of a matrix A: A * P = Q * R using Level 3 BLAS. 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 upper triangle of the array contains the min(M, N) x N upper trapezoidal matrix R; the elements below the diagonal, together with the array Tau(), represent the unitary matrix Q as a product of min(M, N) elementary reflectors. [in,out] Jpvt() Array Jpvt(LJpvt - 1) (LJpvt >= N) [in] If Jpvt(j-1) <> 0, the j-th column of A is permuted to the front of A*P (a leading column); if Jpvt(j-1) = 0, the j-th column of A is a free column. [out] If Jpvt(j-1) = k, then the j-th column of A*P was the the k-th column of A. [out] Tau() Array Tau(LTau - 1) (LTau >= min(M, N)) The scalar factors of the elementary reflectors. [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 Jpvt() is invalid. = -5: The argument Tau() is invalid. 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_Zgeqp3() Const M = 3, N = 3, K = N Dim A(M - 1, N - 1) As Complex, Jpvt(N - 1) As Long, Tau(N - 1) As Complex Dim Info As Long, I 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) For I = 0 To N - 1 Jpvt(I) = 1 Next Call Zgeqp3(M, N, A(), Jpvt(), 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 "Jpvt =", Jpvt(0), Jpvt(1), Jpvt(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 Jpvt = 1 2 3 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