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.