sqrt11()

real function sqrt11	(	integer	m,
		integer	k,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( * )	tau,
		real, dimension( lwork )	work,
		integer	lwork )

SQRT11

Purpose:

!>
!> SQRT11 computes the test ratio
!>
!>       || Q'*Q - I || / (eps * m)
!>
!> where the orthogonal matrix Q is represented as a product of
!> elementary transformations.  Each transformation has the form
!>
!>    H(k) = I - tau(k) v(k) v(k)'
!>
!> where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
!> [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
!> in A(k+1:m,k).
!> 

Parameters

[in]	M	!> M is INTEGER !> The number of rows of the matrix A. !>
[in]	K	!> K is INTEGER !> The number of columns of A whose subdiagonal entries !> contain information about orthogonal transformations. !>
[in]	A	!> A is REAL array, dimension (LDA,K) !> The (possibly partial) output of a QR reduction routine. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. !>
[in]	TAU	!> TAU is REAL array, dimension (K) !> The scaling factors tau for the elementary transformations as !> computed by the QR factorization routine. !>
[out]	WORK	!> WORK is REAL array, dimension (LWORK) !>
[in]	LWORK	!> LWORK is INTEGER !> The length of the array WORK. LWORK >= M*M + M. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 97 of file sqrt11.f.

*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            K, LDA, LWORK, M
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), TAU( * ), WORK( LWORK )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e0, one = 1.0e0 )
*     ..
*     .. Local Scalars ..
      INTEGER            INFO, J
*     ..
*     .. External Functions ..
      REAL               SLAMCH, SLANGE
      EXTERNAL           slamch, slange
*     ..
*     .. External Subroutines ..
      EXTERNAL           slaset, sorm2r, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          real
*     ..
*     .. Local Arrays ..
      REAL               RDUMMY( 1 )
*     ..
*     .. Executable Statements ..
*
      sqrt11 = zero
*
*     Test for sufficient workspace
*
      IF( lwork.LT.m*m+m ) THEN
         CALL xerbla( 'SQRT11', 7 )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.LE.0 )
     $   RETURN
*
      CALL slaset( 'Full', m, m, zero, one, work, m )
*
*     Form Q
*
      CALL sorm2r( 'Left', 'No transpose', m, m, k, a, lda, tau, work,
     $             m, work( m*m+1 ), info )
*
*     Form Q'*Q
*
      CALL sorm2r( 'Left', 'Transpose', m, m, k, a, lda, tau, work, m,
     $             work( m*m+1 ), info )
*
      DO j = 1, m
         work( ( j-1 )*m+j ) = work( ( j-1 )*m+j ) - one
      END DO
*
      sqrt11 = slange( 'One-norm', m, m, work, m, rdummy ) /
     $         ( real( m )*slamch( 'Epsilon' ) )
*
      RETURN
*
*     End of SQRT11
*

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