functionhouseholderSimilarityTransformation2

Calculate the similarity transformation SAS of matrix A with householder matrix S = I - 2u*u'/(u'*u) to compute a lower Hessenberg form

Information

It is assumed, that the input vector u is a Housholder vector of the shape 
u = (u1, u2, ..., ur,0, ..., 0)
where r is an integer input. From 
S = I - 2*u*u'/u'*u = [P, 0; 0, I]
with 
dim(P) = r x r,   dim(I) = n-r x n-r
results 
S*A*S = [P*A11*P, P*A12; A21*P, A22]

Inputs

TypeNameDefaultDescription
Real[:,size(A, 1)]A
Real[size(A, 1)]uhouseholder vector
Integerr

Outputs

TypeNameDefaultDescription
Real[size(A, 1),size(A, 1)]SAS