ZQRT11
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
ZQRT11 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).
|| 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).
Arguments
| M |
(input) INTEGER
The number of rows of the matrix A.
|
| K |
(input) INTEGER
The number of columns of A whose subdiagonal entries
contain information about orthogonal transformations. |
| A |
(input) COMPLEX*16 array, dimension (LDA,K)
The (possibly partial) output of a QR reduction routine.
|
| LDA |
(input) INTEGER
The leading dimension of the array A.
|
| TAU |
(input) COMPLEX*16 array, dimension (K)
The scaling factors tau for the elementary transformations as
computed by the QR factorization routine. |
| WORK |
(workspace) COMPLEX*16 array, dimension (LWORK)
|
| LWORK |
(input) INTEGER
The length of the array WORK. LWORK >= M*M + M.
|