Can anyone point me to examples for using BLAS rotg together with rot? I think I understand rotg but not rot (applying the transformation) so well.
Basically I have a matrix A and its QR in compact LAPACK form. Now I add a row of ones to A and need to eliminate them. So the R would be e.g. 4x4 -> 5x4
x x x x 0 x x x 0 0 x x 0 0 0 x 1 1 1 1
use rotg to rotate x_11 with 1, get r1, z1, c1, s1 use rotg to rotate x_22 with 1, get r2, z2, c2, s2 use rotg to rotate x_33 with 1, get r3, z3, c3, s3 use rotg to rotate x_44 with 1, get r4, z4, c4, s4
At this point I need to apply the rotation transformation on a new vector c of dimension e.g. 5x1 using rot and this is what is not clear to me. The vector c is in the context of solving an overdetermined linear system Ax=b process where I do:
1) dormqr apply previously existing QR to b i.e. Q'*b=c 2) apply rotations using rot to c and get H1*H2*H3*H4*c=c' ... how to do this? any way to bundle them all together? 3) do the usual right substitution R*x = c'