org.netlib.lapack
Class Dlasd1
java.lang.Object
org.netlib.lapack.Dlasd1
public class Dlasd1
- 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
* =======
*
* DLASD1 computes the SVD of an upper bidiagonal N-by-M matrix B,
* where N = NL + NR + 1 and M = N + SQRE. DLASD1 is called from DLASD0.
*
* A related subroutine DLASD7 handles the case in which the singular
* values (and the singular vectors in factored form) are desired.
*
* DLASD1 computes the SVD as follows:
*
* ( D1(in) 0 0 0 )
* B = U(in) * ( Z1' a Z2' b ) * VT(in)
* ( 0 0 D2(in) 0 )
*
* = U(out) * ( D(out) 0) * VT(out)
*
* where Z' = (Z1' a Z2' b) = u' VT', and u is a vector of dimension M
* with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros
* elsewhere; and the entry b is empty if SQRE = 0.
*
* The left singular vectors of the original matrix are stored in U, and
* the transpose of the right singular vectors are stored in VT, and the
* singular values are in D. The algorithm consists of three stages:
*
* The first stage consists of deflating the size of the problem
* when there are multiple singular values or when there are zeros in
* the Z vector. For each such occurence the dimension of the
* secular equation problem is reduced by one. This stage is
* performed by the routine DLASD2.
*
* The second stage consists of calculating the updated
* singular values. This is done by finding the square roots of the
* roots of the secular equation via the routine DLASD4 (as called
* by DLASD3). This routine also calculates the singular vectors of
* the current problem.
*
* The final stage consists of computing the updated singular vectors
* directly using the updated singular values. The singular vectors
* for the current problem are multiplied with the singular vectors
* from the overall problem.
*
* 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 row dimension N = NL + NR + 1,
* and column dimension M = N + SQRE.
*
* D (input/output) DOUBLE PRECISION array,
* dimension (N = NL+NR+1).
* On entry D(1:NL,1:NL) contains the singular values of the
* upper block; and D(NL+2:N) contains the singular values of
* the lower block. On exit D(1:N) contains the singular values
* of the modified matrix.
*
* 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(1:NL, 1:NL) contains the left singular vectors of
* the upper block; U(NL+2:N, NL+2:N) contains the left singular
* vectors of the lower block. On exit U contains the left
* singular vectors of the bidiagonal matrix.
*
* LDU (input) INTEGER
* The leading dimension of the array U. LDU >= max( 1, N ).
*
* VT (input/output) DOUBLE PRECISION array, dimension(LDVT,M)
* where M = N + SQRE.
* On entry VT(1:NL+1, 1:NL+1)' contains the right singular
* vectors of the upper block; VT(NL+2:M, NL+2:M)' contains
* the right singular vectors of the lower block. On exit
* VT' contains the right singular vectors of the
* bidiagonal matrix.
*
* LDVT (input) INTEGER
* The leading dimension of the array VT. LDVT >= max( 1, M ).
*
* IDXQ (output) INTEGER array, dimension(N)
* This contains the permutation which will reintegrate the
* subproblem just solved back into sorted order, i.e.
* D( IDXQ( I = 1, N ) ) will be in ascending order.
*
* IWORK (workspace) INTEGER array, dimension( 4 * N )
*
* WORK (workspace) DOUBLE PRECISION array, dimension( 3*M**2 + 2*M )
*
* INFO (output) INTEGER
* = 0: successful exit.
* < 0: if INFO = -i, the i-th argument had an illegal value.
* > 0: if INFO = 1, an singular value did not converge
*
* 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 |
dlasd1(int nl,
int nr,
int sqre,
double[] d,
int _d_offset,
doubleW alpha,
doubleW beta,
double[] u,
int _u_offset,
int ldu,
double[] vt,
int _vt_offset,
int ldvt,
int[] idxq,
int _idxq_offset,
int[] iwork,
int _iwork_offset,
double[] work,
int _work_offset,
intW info)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Dlasd1
public Dlasd1()
dlasd1
public static void dlasd1(int nl,
int nr,
int sqre,
double[] d,
int _d_offset,
doubleW alpha,
doubleW beta,
double[] u,
int _u_offset,
int ldu,
double[] vt,
int _vt_offset,
int ldvt,
int[] idxq,
int _idxq_offset,
int[] iwork,
int _iwork_offset,
double[] work,
int _work_offset,
intW info)