org.netlib.lapack
Class DGELSD
java.lang.Object
org.netlib.lapack.DGELSD
public class DGELSD
 extends java.lang.Object
DGELSD is a simplified interface to the JLAPACK routine dgelsd.
This interface converts Javastyle 2D rowmajor arrays into
the 1D columnmajor 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
* =======
*
* DGELSD computes the minimumnorm solution to a real linear least
* squares problem:
* minimize 2norm( b  A*x )
* using the singular value decomposition (SVD) of A. A is an MbyN
* matrix which may be rankdeficient.
*
* Several right hand side vectors b and solution vectors x can be
* handled in a single call; they are stored as the columns of the
* MbyNRHS right hand side matrix B and the NbyNRHS solution
* matrix X.
*
* The problem is solved in three steps:
* (1) Reduce the coefficient matrix A to bidiagonal form with
* Householder transformations, reducing the original problem
* into a "bidiagonal least squares problem" (BLS)
* (2) Solve the BLS using a divide and conquer approach.
* (3) Apply back all the Householder tranformations to solve
* the original least squares problem.
*
* The effective rank of A is determined by treating as zero those
* singular values which are less than RCOND times the largest singular
* value.
*
* The divide and conquer algorithm makes very mild assumptions about
* floating point arithmetic. It will work on machines with a guard
* digit in add/subtract, or on those binary machines without guard
* digits which subtract like the Cray XMP, Cray YMP, Cray C90, or
* Cray2. It could conceivably fail on hexadecimal or decimal machines
* without guard digits, but we know of none.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of A. M >= 0.
*
* N (input) INTEGER
* The number of columns of A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrices B and X. NRHS >= 0.
*
* A (input) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the MbyN matrix A.
* On exit, A has been destroyed.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,M).
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
* On entry, the MbyNRHS right hand side matrix B.
* On exit, B is overwritten by the NbyNRHS solution
* matrix X. If m >= n and RANK = n, the residual
* sumofsquares for the solution in the ith column is given
* by the sum of squares of elements n+1:m in that column.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,max(M,N)).
*
* S (output) DOUBLE PRECISION array, dimension (min(M,N))
* The singular values of A in decreasing order.
* The condition number of A in the 2norm = S(1)/S(min(m,n)).
*
* RCOND (input) DOUBLE PRECISION
* RCOND is used to determine the effective rank of A.
* Singular values S(i) <= RCOND*S(1) are treated as zero.
* If RCOND < 0, machine precision is used instead.
*
* RANK (output) INTEGER
* The effective rank of A, i.e., the number of singular values
* which are greater than RCOND*S(1).
*
* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK. LWORK must be at least 1.
* The exact minimum amount of workspace needed depends on M,
* N and NRHS. As long as LWORK is at least
* 12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2,
* if M is greater than or equal to N or
* 12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2,
* if M is less than N, the code will execute correctly.
* SMLSIZ is returned by ILAENV and is equal to the maximum
* size of the subproblems at the bottom of the computation
* tree (usually about 25), and
* NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
* For good performance, LWORK should generally be larger.
*
* If LWORK = 1, then a workspace query is assumed; the routine
* only calculates the optimal size of the WORK array, returns
* this value as the first entry of the WORK array, and no error
* message related to LWORK is issued by XERBLA.
*
* IWORK (workspace) INTEGER array, dimension (LIWORK)
* LIWORK >= 3 * MINMN * NLVL + 11 * MINMN,
* where MINMN = MIN( M,N ).
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = i, the ith argument had an illegal value.
* > 0: the algorithm for computing the SVD failed to converge;
* if INFO = i, i offdiagonal elements of an intermediate
* bidiagonal form did not converge to zero.
*
* Further Details
* ===============
*
* Based on contributions by
* Ming Gu and RenCang Li, Computer Science Division, University of
* California at Berkeley, USA
* Osni Marques, LBNL/NERSC, USA
*
* =====================================================================
*
* .. Parameters ..
Method Summary 
static void 
DGELSD(int m,
int n,
int nrhs,
double[][] a,
double[][] b,
double[] s,
doubleW rcond,
intW rank,
double[] work,
int lwork,
int[] iwork,
intW info)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
DGELSD
public DGELSD()
DGELSD
public static void DGELSD(int m,
int n,
int nrhs,
double[][] a,
double[][] b,
double[] s,
doubleW rcond,
intW rank,
double[] work,
int lwork,
int[] iwork,
intW info)