Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.
F06FSF generates details of a real elementary reflection
(Householder matrix),
, such that
where is orthogonal, and are real scalars, and is an -element real vector.
is given in the form
where is an -element real vector and is a real scalar. (This form is compatible with that used by LINPACK.)
If the elements of are all zero, or if the elements of are all less than in absolute value, then is set to and can be taken to be the unit matrix. Otherwise always lies in the range .
4 References
None.
5 Parameters
1: N – INTEGERInput
On entry: , the number of elements in and .
2: ALPHA – REAL (KIND=nag_wp)Input/Output
On entry: the scalar .
On exit: the scalar .
3: X() – REAL (KIND=nag_wp) arrayInput/Output
Note: the dimension of the array X
must be at least
.
On entry: the -element vector .
must be stored in , for .