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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/DEPRECATED/zlahrd.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/DEPRECATED/zlahrd.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/DEPRECATED/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 k-th 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 (integer n, integer k, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( nb ) tau, complex*16, dimension( ldt, nb ) t, integer ldt, complex*16, dimension( ldy, nb ) y, integer ldy)

ZLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A.

Purpose:

!>
!> This routine is deprecated and has been replaced by routine ZLAHR2.
!>
!> ZLAHRD reduces the first NB columns of a complex general n-by-(n-k+1)
!> matrix A so that elements below the k-th 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.
!> 

Parameters

N

!>          N is INTEGER
!>          The order of the matrix A.
!> 

K

!>          K is INTEGER
!>          The offset for the reduction. Elements below the k-th
!>          subdiagonal in the first NB columns are reduced to zero.
!> 

NB

!>          NB is INTEGER
!>          The number of columns to be reduced.
!> 

A

!>          A is COMPLEX*16 array, dimension (LDA,N-K+1)
!>          On entry, the n-by-(n-k+1) general matrix A.
!>          On exit, the elements on and above the k-th subdiagonal in
!>          the first NB columns are overwritten with the corresponding
!>          elements of the reduced matrix; the elements below the k-th
!>          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.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!> 

TAU

!>          TAU is COMPLEX*16 array, dimension (NB)
!>          The scalar factors of the elementary reflectors. See Further
!>          Details.
!> 

T

!>          T is COMPLEX*16 array, dimension (LDT,NB)
!>          The upper triangular matrix T.
!> 

LDT

!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB.
!> 

Y

!>          Y is COMPLEX*16 array, dimension (LDY,NB)
!>          The n-by-nb matrix Y.
!> 

LDY

!>          LDY 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.

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+k-1) = 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 (n-k+1)-by-nb 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 166 of file zlahrd.f.

Author

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