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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine cbdt03 | ( | character | UPLO, |
integer | N, | ||
integer | KD, | ||
real, dimension( * ) | D, | ||
real, dimension( * ) | E, | ||
complex, dimension( ldu, * ) | U, | ||
integer | LDU, | ||
real, dimension( * ) | S, | ||
complex, dimension( ldvt, * ) | VT, | ||
integer | LDVT, | ||
complex, dimension( * ) | WORK, | ||
real | RESID | ||
) |
CBDT03
CBDT03 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.
[in] | UPLO | UPLO is CHARACTER*1 Specifies whether the matrix B is upper or lower bidiagonal. = 'U': Upper bidiagonal = 'L': Lower bidiagonal |
[in] | N | N is INTEGER The order of the matrix B. |
[in] | 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. |
[in] | D | D is REAL array, dimension (N) The n diagonal elements of the bidiagonal matrix B. |
[in] | 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'. |
[in] | U | U is COMPLEX array, dimension (LDU,N) The n by n orthogonal matrix U in the reduction B = U'*A*P. |
[in] | LDU | LDU is INTEGER The leading dimension of the array U. LDU >= max(1,N) |
[in] | S | S is REAL array, dimension (N) The singular values from the SVD of B, sorted in decreasing order. |
[in] | VT | VT is COMPLEX array, dimension (LDVT,N) The n by n orthogonal matrix V' in the reduction B = U * S * V'. |
[in] | LDVT | LDVT is INTEGER The leading dimension of the array VT. |
[out] | WORK | WORK is COMPLEX array, dimension (2*N) |
[out] | RESID | RESID is REAL The test ratio: norm(B - U * S * V') / ( n * norm(A) * EPS ) |
Definition at line 137 of file cbdt03.f.