org.netlib.lapack
Class DLASD2
java.lang.Object
org.netlib.lapack.DLASD2
public class DLASD2
- extends java.lang.Object
DLASD2 is a simplified interface to the JLAPACK routine dlasd2.
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 seymour@cs.utk.edu with any questions.
* ..
*
* Purpose
* =======
*
* DLASD2 merges the two sets of singular values together into a single
* sorted set. Then it tries to deflate the size of the problem.
* There are two ways in which deflation can occur: when two or more
* singular values are close together or if there is a tiny entry in the
* Z vector. For each such occurrence the order of the related secular
* equation problem is reduced by one.
*
* DLASD2 is called from DLASD1.
*
* Arguments
* =========
*
* NL (input) INTEGER
* The row dimension of the upper block. NL >= 1.
*
* NR (input) INTEGER
* The row dimension of the lower block. NR >= 1.
*
* SQRE (input) INTEGER
* = 0: the lower block is an NR-by-NR square matrix.
* = 1: the lower block is an NR-by-(NR+1) rectangular matrix.
*
* The bidiagonal matrix has N = NL + NR + 1 rows and
* M = N + SQRE >= N columns.
*
* K (output) INTEGER
* Contains the dimension of the non-deflated matrix,
* This is the order of the related secular equation. 1 <= K <=N.
*
* D (input/output) DOUBLE PRECISION array, dimension(N)
* On entry D contains the singular values of the two submatrices
* to be combined. On exit D contains the trailing (N-K) updated
* singular values (those which were deflated) sorted into
* increasing order.
*
* ALPHA (input) DOUBLE PRECISION
* Contains the diagonal element associated with the added row.
*
* BETA (input) DOUBLE PRECISION
* Contains the off-diagonal element associated with the added
* row.
*
* U (input/output) DOUBLE PRECISION array, dimension(LDU,N)
* On entry U contains the left singular vectors of two
* submatrices in the two square blocks with corners at (1,1),
* (NL, NL), and (NL+2, NL+2), (N,N).
* On exit U contains the trailing (N-K) updated left singular
* vectors (those which were deflated) in its last N-K columns.
*
* LDU (input) INTEGER
* The leading dimension of the array U. LDU >= N.
*
* Z (output) DOUBLE PRECISION array, dimension(N)
* On exit Z contains the updating row vector in the secular
* equation.
*
* DSIGMA (output) DOUBLE PRECISION array, dimension (N)
* Contains a copy of the diagonal elements (K-1 singular values
* and one zero) in the secular equation.
*
* U2 (output) DOUBLE PRECISION array, dimension(LDU2,N)
* Contains a copy of the first K-1 left singular vectors which
* will be used by DLASD3 in a matrix multiply (DGEMM) to solve
* for the new left singular vectors. U2 is arranged into four
* blocks. The first block contains a column with 1 at NL+1 and
* zero everywhere else; the second block contains non-zero
* entries only at and above NL; the third contains non-zero
* entries only below NL+1; and the fourth is dense.
*
* LDU2 (input) INTEGER
* The leading dimension of the array U2. LDU2 >= N.
*
* VT (input/output) DOUBLE PRECISION array, dimension(LDVT,M)
* On entry VT' contains the right singular vectors of two
* submatrices in the two square blocks with corners at (1,1),
* (NL+1, NL+1), and (NL+2, NL+2), (M,M).
* On exit VT' contains the trailing (N-K) updated right singular
* vectors (those which were deflated) in its last N-K columns.
* In case SQRE =1, the last row of VT spans the right null
* space.
*
* LDVT (input) INTEGER
* The leading dimension of the array VT. LDVT >= M.
*
* VT2 (output) DOUBLE PRECISION array, dimension(LDVT2,N)
* VT2' contains a copy of the first K right singular vectors
* which will be used by DLASD3 in a matrix multiply (DGEMM) to
* solve for the new right singular vectors. VT2 is arranged into
* three blocks. The first block contains a row that corresponds
* to the special 0 diagonal element in SIGMA; the second block
* contains non-zeros only at and before NL +1; the third block
* contains non-zeros only at and after NL +2.
*
* LDVT2 (input) INTEGER
* The leading dimension of the array VT2. LDVT2 >= M.
*
* IDXP (workspace) INTEGER array, dimension(N)
* This will contain the permutation used to place deflated
* values of D at the end of the array. On output IDXP(2:K)
* points to the nondeflated D-values and IDXP(K+1:N)
* points to the deflated singular values.
*
* IDX (workspace) INTEGER array, dimension(N)
* This will contain the permutation used to sort the contents of
* D into ascending order.
*
* IDXC (output) INTEGER array, dimension(N)
* This will contain the permutation used to arrange the columns
* of the deflated U matrix into three groups: the first group
* contains non-zero entries only at and above NL, the second
* contains non-zero entries only below NL+2, and the third is
* dense.
*
* COLTYP (workspace/output) INTEGER array, dimension(N)
* As workspace, this will contain a label which will indicate
* which of the following types a column in the U2 matrix or a
* row in the VT2 matrix is:
* 1 : non-zero in the upper half only
* 2 : non-zero in the lower half only
* 3 : dense
* 4 : deflated
*
* On exit, it is an array of dimension 4, with COLTYP(I) being
* the dimension of the I-th type columns.
*
* IDXQ (input) INTEGER array, dimension(N)
* This contains the permutation which separately sorts the two
* sub-problems in D into ascending order. Note that entries in
* the first hlaf of this permutation must first be moved one
* position backward; and entries in the second half
* must first have NL+1 added to their values.
*
* INFO (output) INTEGER
* = 0: successful exit.
* < 0: if INFO = -i, the i-th argument had an illegal value.
*
* Further Details
* ===============
*
* Based on contributions by
* Ming Gu and Huan Ren, Computer Science Division, University of
* California at Berkeley, USA
*
* =====================================================================
*
* .. Parameters ..
|
Method Summary |
static void |
DLASD2(int nl,
int nr,
int sqre,
intW k,
double[] d,
double[] z,
double alpha,
double beta,
double[][] u,
double[][] vt,
double[] dsigma,
double[][] u2,
double[][] vt2,
int[] idxp,
int[] idx,
int[] idxc,
int[] idxq,
int[] coltyp,
intW info)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
DLASD2
public DLASD2()
DLASD2
public static void DLASD2(int nl,
int nr,
int sqre,
intW k,
double[] d,
double[] z,
double alpha,
double beta,
double[][] u,
double[][] vt,
double[] dsigma,
double[][] u2,
double[][] vt2,
int[] idxp,
int[] idx,
int[] idxc,
int[] idxq,
int[] coltyp,
intW info)