org.netlib.lapack
Class Slasd2

java.lang.Object
  extended by org.netlib.lapack.Slasd2

public class Slasd2
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 * ======= * * SLASD2 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. * * SLASD2 is called from SLASD1. * * 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) REAL 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) REAL * Contains the diagonal element associated with the added row. * * BETA (input) REAL * Contains the off-diagonal element associated with the added * row. * * U (input/output) REAL 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) REAL array, dimension(N) * On exit Z contains the updating row vector in the secular * equation. * * DSIGMA (output) REAL array, dimension (N) * Contains a copy of the diagonal elements (K-1 singular values * and one zero) in the secular equation. * * U2 (output) REAL array, dimension(LDU2,N) * Contains a copy of the first K-1 left singular vectors which * will be used by SLASD3 in a matrix multiply (SGEMM) 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) REAL 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) REAL array, dimension(LDVT2,N) * VT2' contains a copy of the first K right singular vectors * which will be used by SLASD3 in a matrix multiply (SGEMM) 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 ..


Constructor Summary
Slasd2()
           
 
Method Summary
static void slasd2(int nl, int nr, int sqre, intW k, float[] d, int _d_offset, float[] z, int _z_offset, float alpha, float beta, float[] u, int _u_offset, int ldu, float[] vt, int _vt_offset, int ldvt, float[] dsigma, int _dsigma_offset, float[] u2, int _u2_offset, int ldu2, float[] vt2, int _vt2_offset, int ldvt2, int[] idxp, int _idxp_offset, int[] idx, int _idx_offset, int[] idxc, int _idxc_offset, int[] idxq, int _idxq_offset, int[] coltyp, int _coltyp_offset, intW info)
           
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

Slasd2

public Slasd2()
Method Detail

slasd2

public static void slasd2(int nl,
                          int nr,
                          int sqre,
                          intW k,
                          float[] d,
                          int _d_offset,
                          float[] z,
                          int _z_offset,
                          float alpha,
                          float beta,
                          float[] u,
                          int _u_offset,
                          int ldu,
                          float[] vt,
                          int _vt_offset,
                          int ldvt,
                          float[] dsigma,
                          int _dsigma_offset,
                          float[] u2,
                          int _u2_offset,
                          int ldu2,
                          float[] vt2,
                          int _vt2_offset,
                          int ldvt2,
                          int[] idxp,
                          int _idxp_offset,
                          int[] idx,
                          int _idx_offset,
                          int[] idxc,
                          int _idxc_offset,
                          int[] idxq,
                          int _idxq_offset,
                          int[] coltyp,
                          int _coltyp_offset,
                          intW info)