zlahrd (3)  Linux Man Pages
NAME
zlahrd.f 
SYNOPSIS
Functions/Subroutines
subroutine zlahrd (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY)
ZLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below the kth subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A.
Function/Subroutine Documentation
subroutine zlahrd (integerN, integerK, integerNB, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( nb )TAU, complex*16, dimension( ldt, nb )T, integerLDT, complex*16, dimension( ldy, nb )Y, integerLDY)
ZLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below the kth subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A.
Purpose:

ZLAHRD reduces the first NB columns of a complex general nby(nk+1) matrix A so that elements below the kth subdiagonal are zero. The reduction is performed by a unitary similarity transformation Q**H * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I  V*T*V**H, and also the matrix Y = A * V * T. This is an OBSOLETE auxiliary routine. This routine will be 'deprecated' in a future release. Please use the new routine ZLAHR2 instead.
Parameters:

N
N is INTEGER The order of the matrix A.
KK is INTEGER The offset for the reduction. Elements below the kth subdiagonal in the first NB columns are reduced to zero.
NBNB is INTEGER The number of columns to be reduced.
AA is COMPLEX*16 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.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
TAUTAU is COMPLEX*16 array, dimension (NB) The scalar factors of the elementary reflectors. See Further Details.
TT is COMPLEX*16 array, dimension (LDT,NB) The upper triangular matrix T.
LDTLDT is INTEGER The leading dimension of the array T. LDT >= NB.
YY is COMPLEX*16 array, dimension (LDY,NB) The nbynb matrix Y.
LDYLDY is INTEGER The leading dimension of the array Y. LDY >= max(1,N).
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
Further Details:

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**H where tau is a complex scalar, and v is a complex 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**H) * (A  Y*V**H). The contents of A on exit are illustrated by the following example with n = 7, k = 3 and nb = 2: ( a h a a a ) ( a h a a a ) ( a h 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).
Definition at line 170 of file zlahrd.f.
Author
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