
sgelsy.f(3) LAPACK sgelsy.f(3)
NAME
sgelsy.f 
SYNOPSIS
Functions/Subroutines
subroutine sgelsy (M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, WORK, LWORK, INFO)
SGELSY solves overdetermined or underdetermined systems for GE matrices
Function/Subroutine Documentation
subroutine sgelsy (integerM, integerN, integerNRHS, real, dimension( lda, * )A, integerLDA,
real, dimension( ldb, * )B, integerLDB, integer, dimension( * )JPVT, realRCOND,
integerRANK, real, dimension( * )WORK, integerLWORK, integerINFO)
SGELSY solves overdetermined or underdetermined systems for GE matrices
Purpose:
SGELSY 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.
This routine is basically identical to the original xGELSX except
three differences:
o The call to the subroutine xGEQPF has been substituted by the
the call to the subroutine xGEQP3. This subroutine is a Blas3
version of the QR factorization with column pivoting.
o Matrix B (the right hand side) is updated with Blas3.
o The permutation of matrix B (the right hand side) is faster and
more simple.
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.
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 permuted
to the front of AP, otherwise column i is a free column.
On exit, if JPVT(i) = k, then the ith column of AP
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(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK.
The unblocked strategy requires that:
LWORK >= MAX( MN+3*N+1, 2*MN+NRHS ),
where MN = min( M, N ).
The block algorithm requires that:
LWORK >= MAX( MN+2*N+NB*(N+1), 2*MN+NB*NRHS ),
where NB is an upper bound on the blocksize returned
by ILAENV for the routines SGEQP3, STZRZF, STZRQF, SORMQR,
and SORMRZ.
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
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
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
E. QuintanaOrti, Depto. de Informatica, Universidad Jaime I, Spain
G. QuintanaOrti, Depto. de Informatica, Universidad Jaime I, Spain
Definition at line 204 of file sgelsy.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 sgelsy.f(3) 
