org.netlib.lapack
Class DGELSX
java.lang.Object
org.netlib.lapack.DGELSX
public class DGELSX
 extends java.lang.Object
DGELSX is a simplified interface to the JLAPACK routine dgelsx.
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
* =======
*
* This routine is deprecated and has been replaced by routine DGELSY.
*
* DGELSX computes the minimumnorm solution to a real linear least
* squares problem:
* minimize  A * X  B 
* using a complete orthogonal factorization 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 routine first computes a QR factorization with column pivoting:
* A * P = Q * [ R11 R12 ]
* [ 0 R22 ]
* with R11 defined as the largest leading submatrix whose estimated
* condition number is less than 1/RCOND. The order of R11, RANK,
* is the effective rank of A.
*
* Then, R22 is considered to be negligible, and R12 is annihilated
* by orthogonal transformations from the right, arriving at the
* complete orthogonal factorization:
* A * P = Q * [ T11 0 ] * Z
* [ 0 0 ]
* The minimumnorm solution is then
* X = P * Z' [ inv(T11)*Q1'*B ]
* [ 0 ]
* where Q1 consists of the first RANK columns of Q.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrix A. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of
* columns of matrices B and X. NRHS >= 0.
*
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the MbyN matrix A.
* On exit, A has been overwritten by details of its
* complete orthogonal factorization.
*
* 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, 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,M,N).
*
* JPVT (input/output) INTEGER array, dimension (N)
* On entry, if JPVT(i) .ne. 0, the ith column of A is an
* initial column, otherwise it is a free column. Before
* the QR factorization of A, all initial columns are
* permuted to the leading positions; only the remaining
* free columns are moved as a result of column pivoting
* during the factorization.
* On exit, if JPVT(i) = k, then the ith column of A*P
* was the kth column of A.
*
* RCOND (input) DOUBLE PRECISION
* RCOND is used to determine the effective rank of A, which
* is defined as the order of the largest leading triangular
* submatrix R11 in the QR factorization with pivoting of A,
* whose estimated condition number < 1/RCOND.
*
* RANK (output) INTEGER
* The effective rank of A, i.e., the order of the submatrix
* R11. This is the same as the order of the submatrix T11
* in the complete orthogonal factorization of A.
*
* WORK (workspace) DOUBLE PRECISION array, dimension
* (max( min(M,N)+3*N, 2*min(M,N)+NRHS )),
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = i, the ith argument had an illegal value
*
* =====================================================================
*
* .. Parameters ..
Method Summary 
static void 
DGELSX(int m,
int n,
int nrhs,
double[][] a,
double[][] b,
int[] jpvt,
double rcond,
intW rank,
double[] work,
intW info)

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