Dgelqf Dgeqp3 Dgeqrf Dorglq Dorgqr Dormlq Dormqr

Dormlq() Sub Dormlq ( Side As  String, Trans As  String, M As  Long, N As  Long, K As  Long, A() As  Double, Tau() As  Double, C() As  Double, Info As  Long  ) Multiplies matrix by Q of LQ factorization Purpose This routine overwrites the general real m x n matrix C with Side = "L" Side = "R" Trans = "N": Q * C C * Q Trans = "T": Q^T * C C * Q^T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by Dgelqf. 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^T from the right. [in] Trans = "N": No transpose, apply Q. = "T": Transpose, apply Q^T. [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 >= K, LA2 >= M (Side = "L") or N (Side = "R")) The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1, 2, ..., K, as returned by Dgelqf in the first K rows 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 Dgelqf. [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^T*C or C*Q^T 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 <> "T" 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 LQ factorization of the matrix A, and compute L*Q, where ( 2.20 -0.11 -0.32 ) A = ( -0.11 2.93 0.81 ) ( -0.32 0.81 2.37 ) Sub Ex_Dormlq() Const M = 3, N = 3, K = N Dim A(M - 1, N - 1) As Double, Tau(N - 1) As Double, Info As Long Dim L(M - 1, N - 1) As Double, I As Long, J 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 '-- Compute LQ factorization of A Call Dgelqf(M, N, A(), Tau(), Info) For I = 0 To M - 1 For J = 0 To I L(I, J) = A(I, J) Next Next Debug.Print "L =" Debug.Print L(0, 0), L(0, 1), L(0, 2) Debug.Print L(1, 0), L(1, 1), L(1, 2) Debug.Print L(2, 0), L(2, 1), L(2, 2) Debug.Print "Info =", Info '-- Compute L*Q Call Dormlq("R", "N", M, N, K, A(), Tau(), L(), Info) Debug.Print "L*Q =" Debug.Print L(0, 0), L(0, 1), L(0, 2) Debug.Print L(1, 0), L(1, 1), L(1, 2) Debug.Print L(2, 0), L(2, 1), L(2, 2) Debug.Print "Info =", Info End Sub Example Results L = -0.957601169589929 0 0 0.51921406926948 -0.791085804620857 0 -0.220237826244838 0.609478035393939 -1.07262846515618 Info = 0 L*Q = 0.2 -0.11 -0.93 -0.32 0.81 0.37 -0.8 -0.92 -0.29 Info = 0