HP MLIB User's Guide Vol. 1 7th Ed.

Chapter 2 Basic Vector Operations 119
Construct Givens rotation SROTG/DROTG/CROTG/ZROTG
Output a The rotated result r overwrites a.
b Not used as output by CROTG and ZROTG. In SROTG
and DROTG, the reconstruction quantity z overwrites
b. The reconstruction quantity z is useful if a matrix is
being transformed by a sequence of Givens rotations
that must be saved to be applied again. Because each z
overwrites an element that has been reduced to zero,
the transformations can be saved without using any
additional storage. The quantities c and s can be
reconstructed from z as follows:
c The rotation scalar c.
s The rotation scalar s.
Notes VECLIB also contains subprograms that construct and apply modified Givens
rotations. They are documented elsewhere in this chapter. The modified Givens
subprograms are a little more difficult to use but are more efficient.
Example Construct a Givens plane rotation that rotates vectors x and y in such a way as
to annihilate y
1
. x and y are vectors 10 elements long stored in one-dimensional
arrays X and Y of dimension 20.
REAL*8 X(20),Y(20),C,S
CALL DROTG (X(1),Y(1),C,S)
X(1) is the rotated result and Y(1) is the reconstruction quantity, so these
elements should not be rotated by a subsequent call to DROT.
if |z| = 0, set c = 0 and s =1.
if |z|<0,
set c = √(1−z
2
) ανδ σ = ζ.
if |z|>0,
set c =1/z and s = √(1−c
2
).