zstt21.f3
Usage
Functions/Subroutines
subroutine zstt21 (n, kband, ad, ae, sd, se, u, ldu, work, rwork, result)
ZSTT21
Function/Subroutine Documentation
subroutine zstt21 (integer n, integer kband, double precision, dimension( * ) ad, double precision, dimension( * ) ae, double precision, dimension( * ) sd, double precision, dimension( * ) se, complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, double precision, dimension( 2 ) result)
ZSTT21
Purpose:
!> !> ZSTT21 checks a decomposition of the form !> !> A = U S U**H !> !> where **H means conjugate transpose, A is real symmetric tridiagonal, !> U is unitary, and S is real and diagonal (if KBAND=0) or symmetric !> tridiagonal (if KBAND=1). Two tests are performed: !> !> RESULT(1) = | A - U S U**H | / ( |A| n ulp ) !> !> RESULT(2) = | I - U U**H | / ( n ulp ) !>
Parameters
N
!> N is INTEGER !> The size of the matrix. If it is zero, ZSTT21 does nothing. !> It must be at least zero. !>
KBAND
!> KBAND is INTEGER !> The bandwidth of the matrix S. It may only be zero or one. !> If zero, then S is diagonal, and SE is not referenced. If !> one, then S is symmetric tri-diagonal. !>
AD
!> AD is DOUBLE PRECISION array, dimension (N) !> The diagonal of the original (unfactored) matrix A. A is !> assumed to be real symmetric tridiagonal. !>
AE
!> AE is DOUBLE PRECISION array, dimension (N-1) !> The off-diagonal of the original (unfactored) matrix A. A !> is assumed to be symmetric tridiagonal. AE(1) is the (1,2) !> and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc. !>
SD
!> SD is DOUBLE PRECISION array, dimension (N) !> The diagonal of the real (symmetric tri-) diagonal matrix S. !>
SE
!> SE is DOUBLE PRECISION array, dimension (N-1) !> The off-diagonal of the (symmetric tri-) diagonal matrix S. !> Not referenced if KBSND=0. If KBAND=1, then AE(1) is the !> (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2) !> element, etc. !>
U
!> U is COMPLEX*16 array, dimension (LDU, N) !> The unitary matrix in the decomposition. !>
LDU
!> LDU is INTEGER !> The leading dimension of U. LDU must be at least N. !>
WORK
!> WORK is COMPLEX*16 array, dimension (N**2) !>
RWORK
!> RWORK is DOUBLE PRECISION array, dimension (N) !>
RESULT
!> RESULT is DOUBLE PRECISION array, dimension (2)
!> The values computed by the two tests described above. The
!> values are currently limited to 1/ulp, to avoid overflow.
!> RESULT(1) is always modified.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 131 of file zstt21.f.