TESTING/EIG/chbt21.f(3) | Library Functions Manual | TESTING/EIG/chbt21.f(3) |
NAME
TESTING/EIG/chbt21.f
SYNOPSIS
Functions/Subroutines
subroutine chbt21 (uplo, n, ka, ks, a, lda, d, e, u, ldu,
work, rwork, result)
CHBT21
Function/Subroutine Documentation
subroutine chbt21 (character uplo, integer n, integer ka, integer ks, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldu, * ) u, integer ldu, complex, dimension( * ) work, real, dimension( * ) rwork, real, dimension( 2 ) result)
CHBT21
Purpose:
CHBT21 generally checks a decomposition of the form A = U S U**H where **H means conjugate transpose, A is hermitian banded, U is unitary, and S is diagonal (if KS=0) or symmetric tridiagonal (if KS=1). Specifically: RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and RESULT(2) = | I - U U**H | / ( n ulp )
Parameters
UPLO
UPLO is CHARACTER If UPLO='U', the upper triangle of A and V will be used and the (strictly) lower triangle will not be referenced. If UPLO='L', the lower triangle of A and V will be used and the (strictly) upper triangle will not be referenced.
N
N is INTEGER The size of the matrix. If it is zero, CHBT21 does nothing. It must be at least zero.
KA
KA is INTEGER The bandwidth of the matrix A. It must be at least zero. If it is larger than N-1, then max( 0, N-1 ) will be used.
KS
KS is INTEGER The bandwidth of the matrix S. It may only be zero or one. If zero, then S is diagonal, and E is not referenced. If one, then S is symmetric tri-diagonal.
A
A is COMPLEX array, dimension (LDA, N) The original (unfactored) matrix. It is assumed to be hermitian, and only the upper (UPLO='U') or only the lower (UPLO='L') will be referenced.
LDA
LDA is INTEGER The leading dimension of A. It must be at least 1 and at least min( KA, N-1 ).
D
D is REAL array, dimension (N) The diagonal of the (symmetric tri-) diagonal matrix S.
E
E is REAL array, dimension (N-1) The off-diagonal of the (symmetric tri-) diagonal matrix S. E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and (3,2) element, etc. Not referenced if KS=0.
U
U is COMPLEX array, dimension (LDU, N) The unitary matrix in the decomposition, expressed as a dense matrix (i.e., not as a product of Householder transformations, Givens transformations, etc.)
LDU
LDU is INTEGER The leading dimension of U. LDU must be at least N and at least 1.
WORK
WORK is COMPLEX array, dimension (N**2)
RWORK
RWORK is REAL array, dimension (N)
RESULT
RESULT is REAL array, dimension (2) The values computed by the two tests described above. The values are currently limited to 1/ulp, to avoid overflow.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 150 of file chbt21.f.
Author
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