# clahrd(3) [centos man page]

```clahrd.f(3)							      LAPACK							       clahrd.f(3)

NAME
clahrd.f -

SYNOPSIS
Functions/Subroutines
subroutine clahrd (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY)
CLAHRD 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 clahrd (integerN, integerK, integerNB, complex, dimension( lda, * )A, integerLDA, complex, dimension( nb )TAU, complex, dimension(
ldt, nb )T, integerLDT, complex, dimension( ldy, nb )Y, integerLDY)
CLAHRD 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:

CLAHRD 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.

This is an OBSOLETE auxiliary routine.
This routine will be 'deprecated' in a  future release.

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 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 array, dimension (NB)
The scalar factors of the elementary reflectors. See Further
Details.

T

T is COMPLEX 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 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

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+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 170 of file clahrd.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       clahrd.f(3)```
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