org.netlib.lapack
Class Sbdsqr
java.lang.Object
org.netlib.lapack.Sbdsqr
public class Sbdsqr
- extends java.lang.Object
Following is the description from the original
Fortran source. For each array argument, the Java
version will include an integer offset parameter, so
the arguments may not match the description exactly.
Contact seymour@cs.utk.edu with any questions.
* ..
*
* Purpose
* =======
*
* SBDSQR 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.
*
* Arguments
* =========
*
* 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) REAL 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
* order.
*
* E (input/output) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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 REAL, 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 ..
|
Method Summary |
static void |
sbdsqr(java.lang.String uplo,
int n,
int ncvt,
int nru,
int ncc,
float[] d,
int _d_offset,
float[] e,
int _e_offset,
float[] vt,
int _vt_offset,
int ldvt,
float[] u,
int _u_offset,
int ldu,
float[] c,
int _c_offset,
int Ldc,
float[] work,
int _work_offset,
intW info)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Sbdsqr
public Sbdsqr()
sbdsqr
public static void sbdsqr(java.lang.String uplo,
int n,
int ncvt,
int nru,
int ncc,
float[] d,
int _d_offset,
float[] e,
int _e_offset,
float[] vt,
int _vt_offset,
int ldvt,
float[] u,
int _u_offset,
int ldu,
float[] c,
int _c_offset,
int Ldc,
float[] work,
int _work_offset,
intW info)