10-17-2008
awk '{if( $2 > $3) {tmp=$2; $2=$3;$3=tmp " Rev_Com";} print}' Input_File
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LEARN ABOUT REDHAT
sgelss
SGELSS(l) ) SGELSS(l)
NAME
SGELSS - compute the minimum norm solution to a real linear least squares problem
SYNOPSIS
SUBROUTINE SGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, INFO )
INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
REAL RCOND
REAL A( LDA, * ), B( LDB, * ), S( * ), WORK( * )
PURPOSE
SGELSS computes the minimum norm solution to a real linear least squares problem: Minimize 2-norm(| b - A*x |).
using the singular value decomposition (SVD) of A. A is an M-by-N matrix which may be rank-deficient.
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 M-by-NRHS
right hand side matrix B and the N-by-NRHS solution matrix X.
The effective rank of A is determined by treating as zero those singular values which are less than RCOND times the largest singular value.
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 the matrices B and X. NRHS >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A. On exit, the first min(m,n) rows of A are overwritten with its right singular vectors, stored row-
wise.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) REAL array, dimension (LDB,NRHS)
On entry, the M-by-NRHS right hand side matrix B. On exit, B is overwritten by the N-by-NRHS solution matrix X. If m >= n and
RANK = n, the residual sum-of-squares for the solution in the i-th 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) REAL array, dimension (min(M,N))
The singular values of A in decreasing order. The condition number of A in the 2-norm = S(1)/S(min(m,n)).
RCOND (input) REAL
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) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1, and also: LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ) For good perfor-
mance, 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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: the algorithm for computing the SVD failed to converge; if INFO = i, i off-diagonal elements of an intermediate bidiagonal
form did not converge to zero.
LAPACK version 3.0 15 June 2000 SGELSS(l)