LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  dlahr2 (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY) 
DLAHR2 reduces the specified number of first columns of a general rectangular matrix A so that elements below the specified subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. 
subroutine dlahr2  (  integer  N, 
integer  K,  
integer  NB,  
double precision, dimension( lda, * )  A,  
integer  LDA,  
double precision, dimension( nb )  TAU,  
double precision, dimension( ldt, nb )  T,  
integer  LDT,  
double precision, dimension( ldy, nb )  Y,  
integer  LDY  
) 
DLAHR2 reduces the specified number of first columns of a general rectangular matrix A so that elements below the specified subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A.
Download DLAHR2 + dependencies [TGZ] [ZIP] [TXT]DLAHR2 reduces the first NB columns of A real general nBY(nk+1) matrix A so that elements below the kth subdiagonal are zero. The reduction is performed by an orthogonal similarity transformation Q**T * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I  V*T*V**T, and also the matrix Y = A * V * T. This is an auxiliary routine called by DGEHRD.
[in]  N  N is INTEGER The order of the matrix A. 
[in]  K  K is INTEGER The offset for the reduction. Elements below the kth subdiagonal in the first NB columns are reduced to zero. K < N. 
[in]  NB  NB is INTEGER The number of columns to be reduced. 
[in,out]  A  A is DOUBLE PRECISION array, dimension (LDA,NK+1) On entry, the nby(nk+1) general matrix A. On exit, the elements on and above the kth subdiagonal in the first NB columns are overwritten with the corresponding elements of the reduced matrix; the elements below the kth subdiagonal, with the array TAU, represent the matrix Q as a product of elementary reflectors. The other columns of A are unchanged. See Further Details. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[out]  TAU  TAU is DOUBLE PRECISION array, dimension (NB) The scalar factors of the elementary reflectors. See Further Details. 
[out]  T  T is DOUBLE PRECISION array, dimension (LDT,NB) The upper triangular matrix T. 
[in]  LDT  LDT is INTEGER The leading dimension of the array T. LDT >= NB. 
[out]  Y  Y is DOUBLE PRECISION array, dimension (LDY,NB) The nbynb matrix Y. 
[in]  LDY  LDY is INTEGER The leading dimension of the array Y. LDY >= N. 
The matrix Q is represented as a product of nb elementary reflectors Q = H(1) H(2) . . . H(nb). Each H(i) has the form H(i) = I  tau * v * v**T where tau is a real scalar, and v is a real vector with v(1:i+k1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in A(i+k+1:n,i), and tau in TAU(i). The elements of the vectors v together form the (nk+1)bynb matrix V which is needed, with T and Y, to apply the transformation to the unreduced part of the matrix, using an update of the form: A := (I  V*T*V**T) * (A  Y*V**T). The contents of A on exit are illustrated by the following example with n = 7, k = 3 and nb = 2: ( a a a a a ) ( a a a a a ) ( a a a a a ) ( h h a a a ) ( v1 h a a a ) ( v1 v2 a a a ) ( v1 v2 a a a ) where a denotes an element of the original matrix A, h denotes a modified element of the upper Hessenberg matrix H, and vi denotes an element of the vector defining H(i). This subroutine is a slight modification of LAPACK3.0's DLAHRD incorporating improvements proposed by QuintanaOrti and Van de Gejin. Note that the entries of A(1:K,2:NB) differ from those returned by the original LAPACK3.0's DLAHRD routine. (This subroutine is not backward compatible with LAPACK3.0's DLAHRD.)
Definition at line 182 of file dlahr2.f.