dgglse.f(3) [centos man page]

```dgglse.f(3)							      LAPACK							       dgglse.f(3)

NAME
dgglse.f -

SYNOPSIS
Functions/Subroutines
subroutine dgglse (M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO)
DGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Function/Subroutine Documentation
subroutine dgglse (integerM, integerN, integerP, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B,
integerLDB, double precision, dimension( * )C, double precision, dimension( * )D, double precision, dimension( * )X, double precision,
dimension( * )WORK, integerLWORK, integerINFO)
DGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Purpose:

DGGLSE solves the linear equality-constrained least squares (LSE)
problem:

minimize || c - A*x ||_2   subject to   B*x = d

where A is an M-by-N matrix, B is a P-by-N matrix, c is a given
M-vector, and d is a given P-vector. It is assumed that
P <= N <= M+P, and

rank(B) = P and  rank( (A) ) = N.
( (B) )

These conditions ensure that the LSE problem has a unique solution,
which is obtained using a generalized RQ factorization of the
matrices (B, A) given by

B = (0 R)*Q,   A = Z*T*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 matrices A and B. N >= 0.

P

P is INTEGER
The number of rows of the matrix B. 0 <= P <= N <= M+P.

A

A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix T.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).

B

B is DOUBLE PRECISION array, dimension (LDB,N)
On entry, the P-by-N matrix B.
On exit, the upper triangle of the subarray B(1:P,N-P+1:N)
contains the P-by-P upper triangular matrix R.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,P).

C

C is DOUBLE PRECISION array, dimension (M)
On entry, C contains the right hand side vector for the
least squares part of the LSE problem.
On exit, the residual sum of squares for the solution
is given by the sum of squares of elements N-P+1 to M of
vector C.

D

D is DOUBLE PRECISION array, dimension (P)
On entry, D contains the right hand side vector for the
constrained equation.
On exit, D is destroyed.

X

X is DOUBLE PRECISION array, dimension (N)
On exit, X is the solution of the LSE problem.

WORK

WORK is DOUBLE PRECISION 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. LWORK >= max(1,M+N+P).
For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB,
where NB is an upper bound for the optimal blocksizes for
DGEQRF, SGERQF, DORMQR and SORMRQ.

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 i-th argument had an illegal value.
= 1:  the upper triangular factor R associated with B in the
generalized RQ factorization of the pair (B, A) is
singular, so that rank(B) < P; the least squares
solution could not be computed.
= 2:  the (N-P) by (N-P) part of the upper trapezoidal factor
T associated with A in the generalized RQ factorization
of the pair (B, A) is singular, so that
rank( (A) ) < N; the least squares solution could not
( (B) )
be computed.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
November 2011

Definition at line 180 of file dgglse.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       dgglse.f(3)```
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