
sgelsx.f(3) LAPACK sgelsx.f(3)
NAME
sgelsx.f 
SYNOPSIS
Functions/Subroutines
subroutine sgelsx (M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, WORK, INFO)
SGELSX solves overdetermined or underdetermined systems for GE matrices
Function/Subroutine Documentation
subroutine sgelsx (integerM, integerN, integerNRHS, real, dimension( lda, * )A, integerLDA,
real, dimension( ldb, * )B, integerLDB, integer, dimension( * )JPVT, realRCOND,
integerRANK, real, dimension( * )WORK, integerINFO)
SGELSX solves overdetermined or underdetermined systems for GE matrices
Purpose:
This routine is deprecated and has been replaced by routine SGELSY.
SGELSX 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**T [ inv(T11)*Q1**T*B ]
[ 0 ]
where Q1 consists of the first RANK columns of Q.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of
columns of matrices B and X. NRHS >= 0.
A
A is REAL array, dimension (LDA,N)
On entry, the MbyN matrix A.
On exit, A has been overwritten by details of its
complete orthogonal factorization.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B
B is REAL 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
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,M,N).
JPVT
JPVT is 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
RCOND is REAL
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
RANK is 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
WORK is REAL array, dimension
(max( min(M,N)+3*N, 2*min(M,N)+NRHS )),
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 178 of file sgelsx.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 sgelsx.f(3) 
