Dgelqf Dgeqp3 Dgeqrf Dorglq Dorgqr Dormlq Dormqr

Dgeqp3() Sub Dgeqp3 ( M As  Long, N As  Long, A() As  Double, Jpvt() As  Long, Tau() As  Double, Info As  Long  ) QR factorization 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 orthogonal 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 ( 2.20 -0.11 -0.32 ) A = ( -0.11 2.93 0.81 ) ( -0.32 0.81 2.37 ) Sub Ex_Dgeqp3() Const M = 3, N = 3, K = N Dim A(M - 1, N - 1) As Double, Jpvt(N - 1) As Long, Tau(N - 1) As Double Dim Info As Long, I As Long A(0, 0) = 0.2: A(0, 1) = -0.11: A(0, 2) = -0.93 A(1, 0) = -0.32: A(1, 1) = 0.81: A(1, 2) = 0.37 A(2, 0) = -0.8: A(2, 1) = -0.92: A(2, 2) = -0.29 For I = 0 To N - 1 Jpvt(I) = 1 Next '-- Compute QR factorization of A Call Dgeqp3(M, N, A(), Jpvt(), Tau(), Info) Debug.Print "R =" Debug.Print A(0, 0), A(0, 1), A(0, 2) Debug.Print A(1, 1), A(1, 2) Debug.Print A(2, 2) Debug.Print "Jpvt =", Jpvt(0), Jpvt(1), Jpvt(2) Debug.Print "Info =", Info '-- Compute Q Call Dorgqr(M, N, K, A(), Tau(), Info) Debug.Print "Q =" Debug.Print A(0, 0), A(0, 1), A(0, 2) Debug.Print A(1, 0), A(1, 1), A(1, 2) Debug.Print A(2, 0), A(2, 1), A(2, 2) Debug.Print "Info =", Info End Sub Example Results R = -0.884533775499839 -0.514169173181655 8.18510293279503E-02 -1.11813687057967 -0.635776616242947 -0.821576839520579 Jpvt = 1 2 3 Info = 0 Q = -0.226107815823067 0.202352390539057 0.952852961199602 0.361772505316908 -0.890778487093709 0.275016983707865 0.904431263292269 0.406899492472248 0.128206446816755 Info = 0