F08FUF (ZUNMTR) multiplies an arbitrary complex matrix
C by the complex unitary matrix
Q which was determined by
F08FSF (ZHETRD) when reducing a complex Hermitian matrix to tridiagonal form.
SUBROUTINE F08FUF ( |
SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
INTEGER |
M, N, LDA, LDC, LWORK, INFO |
COMPLEX (KIND=nag_wp) |
A(LDA,*), TAU(*), C(LDC,*), WORK(max(1,LWORK)) |
CHARACTER(1) |
SIDE, UPLO, TRANS |
|
F08FUF (ZUNMTR) is intended to be used after a call to
F08FSF (ZHETRD), which reduces a complex Hermitian matrix
A to real symmetric tridiagonal form
T by a unitary similarity transformation:
A=QTQH.
F08FSF (ZHETRD) represents the unitary matrix
Q as a product of elementary reflectors.
This routine may be used to form one of the matrix products
overwriting the result on
C (which may be any complex rectangular matrix).
Golub G H and Van Loan C F (1996)
Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
The computed result differs from the exact result by a matrix
E such that
where
ε is the
machine precision.
The real analogue of this routine is
F08FGF (DORMTR).
This example computes the two smallest eigenvalues, and the associated eigenvectors, of the matrix
A, where
Here
A is Hermitian and must first be reduced to tridiagonal form
T by
F08FSF (ZHETRD). The program then calls
F08JJF (DSTEBZ) to compute the requested eigenvalues and
F08JXF (ZSTEIN) to compute the associated eigenvectors of
T. Finally F08FUF (ZUNMTR) is called to transform the eigenvectors to those of
A.