sbdt03.f - Man Page
TESTING/EIG/sbdt03.f
Synopsis
Functions/Subroutines
subroutine sbdt03 (uplo, n, kd, d, e, u, ldu, s, vt, ldvt, work, resid)
SBDT03
Function/Subroutine Documentation
subroutine sbdt03 (character uplo, integer n, integer kd, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real, dimension( * ) s, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) work, real resid)
SBDT03
Purpose:
SBDT03 reconstructs a bidiagonal matrix B from its SVD: S = U' * B * V where U and V are orthogonal matrices and S is diagonal. The test ratio to test the singular value decomposition is RESID = norm( B - U * S * VT ) / ( n * norm(B) * EPS ) where VT = V' and EPS is the machine precision.
- Parameters
UPLO
UPLO is CHARACTER*1 Specifies whether the matrix B is upper or lower bidiagonal. = 'U': Upper bidiagonal = 'L': Lower bidiagonal
N
N is INTEGER The order of the matrix B.
KD
KD is INTEGER The bandwidth of the bidiagonal matrix B. If KD = 1, the matrix B is bidiagonal, and if KD = 0, B is diagonal and E is not referenced. If KD is greater than 1, it is assumed to be 1, and if KD is less than 0, it is assumed to be 0.
D
D is REAL array, dimension (N) The n diagonal elements of the bidiagonal matrix B.
E
E is REAL array, dimension (N-1) The (n-1) superdiagonal elements of the bidiagonal matrix B if UPLO = 'U', or the (n-1) subdiagonal elements of B if UPLO = 'L'.
U
U is REAL array, dimension (LDU,N) The n by n orthogonal matrix U in the reduction B = U'*A*P.
LDU
LDU is INTEGER The leading dimension of the array U. LDU >= max(1,N)
S
S is REAL array, dimension (N) The singular values from the SVD of B, sorted in decreasing order.
VT
VT is REAL array, dimension (LDVT,N) The n by n orthogonal matrix V' in the reduction B = U * S * V'.
LDVT
LDVT is INTEGER The leading dimension of the array VT.
WORK
WORK is REAL array, dimension (2*N)
RESID
RESID is REAL The test ratio: norm(B - U * S * V') / ( n * norm(A) * EPS )
- Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 133 of file sbdt03.f.
Author
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Referenced By
The man page sbdt03(3) is an alias of sbdt03.f(3).
Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK