public class DBDSQR
- extends java.lang.Object
DBDSQR is a simplified interface to the JLAPACK routine dbdsqr.
This interface converts Java-style 2D row-major arrays into
the 1D column-major linearized arrays expected by the lower
level JLAPACK routines. Using this interface also allows you
to omit offset and leading dimension arguments. However, because
of these conversions, these routines will be slower than the low
level ones. Following is the description from the original Fortran
source. Contact email@example.com with any questions.
* DBDSQR computes the singular value decomposition (SVD) of a real
* N-by-N (upper or lower) bidiagonal matrix B: B = Q * S * P' (P'
* denotes the transpose of P), where S is a diagonal matrix with
* non-negative diagonal elements (the singular values of B), and Q
* and P are orthogonal matrices.
* The routine computes S, and optionally computes U * Q, P' * VT,
* or Q' * C, for given real input matrices U, VT, and C.
* See "Computing Small Singular Values of Bidiagonal Matrices With
* Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan,
* LAPACK Working Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11,
* no. 5, pp. 873-912, Sept 1990) and
* "Accurate singular values and differential qd algorithms," by
* B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics
* Department, University of California at Berkeley, July 1992
* for a detailed description of the algorithm.
* UPLO (input) CHARACTER*1
* = 'U': B is upper bidiagonal;
* = 'L': B is lower bidiagonal.
* N (input) INTEGER
* The order of the matrix B. N >= 0.
* NCVT (input) INTEGER
* The number of columns of the matrix VT. NCVT >= 0.
* NRU (input) INTEGER
* The number of rows of the matrix U. NRU >= 0.
* NCC (input) INTEGER
* The number of columns of the matrix C. NCC >= 0.
* D (input/output) DOUBLE PRECISION array, dimension (N)
* On entry, the n diagonal elements of the bidiagonal matrix B.
* On exit, if INFO=0, the singular values of B in decreasing
* E (input/output) DOUBLE PRECISION array, dimension (N)
* On entry, the elements of E contain the
* offdiagonal elements of the bidiagonal matrix whose SVD
* is desired. On normal exit (INFO = 0), E is destroyed.
* If the algorithm does not converge (INFO > 0), D and E
* will contain the diagonal and superdiagonal elements of a
* bidiagonal matrix orthogonally equivalent to the one given
* as input. E(N) is used for workspace.
* VT (input/output) DOUBLE PRECISION array, dimension (LDVT, NCVT)
* On entry, an N-by-NCVT matrix VT.
* On exit, VT is overwritten by P' * VT.
* VT is not referenced if NCVT = 0.
* LDVT (input) INTEGER
* The leading dimension of the array VT.
* LDVT >= max(1,N) if NCVT > 0; LDVT >= 1 if NCVT = 0.
* U (input/output) DOUBLE PRECISION array, dimension (LDU, N)
* On entry, an NRU-by-N matrix U.
* On exit, U is overwritten by U * Q.
* U is not referenced if NRU = 0.
* LDU (input) INTEGER
* The leading dimension of the array U. LDU >= max(1,NRU).
* C (input/output) DOUBLE PRECISION array, dimension (LDC, NCC)
* On entry, an N-by-NCC matrix C.
* On exit, C is overwritten by Q' * C.
* C is not referenced if NCC = 0.
* LDC (input) INTEGER
* The leading dimension of the array C.
* LDC >= max(1,N) if NCC > 0; LDC >=1 if NCC = 0.
* WORK (workspace) DOUBLE PRECISION array, dimension (4*N)
* INFO (output) INTEGER
* = 0: successful exit
* < 0: If INFO = -i, the i-th argument had an illegal value
* > 0: the algorithm did not converge; D and E contain the
* elements of a bidiagonal matrix which is orthogonally
* similar to the input matrix B; if INFO = i, i
* elements of E have not converged to zero.
* Internal Parameters
* TOLMUL DOUBLE PRECISION, default = max(10,min(100,EPS**(-1/8)))
* TOLMUL controls the convergence criterion of the QR loop.
* If it is positive, TOLMUL*EPS is the desired relative
* precision in the computed singular values.
* If it is negative, abs(TOLMUL*EPS*sigma_max) is the
* desired absolute accuracy in the computed singular
* values (corresponds to relative accuracy
* abs(TOLMUL*EPS) in the largest singular value.
* abs(TOLMUL) should be between 1 and 1/EPS, and preferably
* between 10 (for fast convergence) and .1/EPS
* (for there to be some accuracy in the results).
* Default is to lose at either one eighth or 2 of the
* available decimal digits in each computed singular value
* (whichever is smaller).
* MAXITR INTEGER, default = 6
* MAXITR controls the maximum number of passes of the
* algorithm through its inner loop. The algorithms stops
* (and so fails to converge) if the number of passes
* through the inner loop exceeds MAXITR*N**2.
* .. Parameters ..
|Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
public static void DBDSQR(java.lang.String uplo,