dgglse man page on Scientific

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```DGGLSE(1)	      LAPACK driver routine (version 3.2)	     DGGLSE(1)

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

SYNOPSIS
SUBROUTINE DGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK,  INFO
)

INTEGER	  INFO, LDA, LDB, LWORK, M, N, P

DOUBLE	  PRECISION  A( LDA, * ), B( LDB, * ), C( * ), D( * ),
WORK( * ), X( * )

PURPOSE
DGGLSE solves the linear equality-constrained least squares (LSE) prob‐
lem:
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-vec‐
tor, 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.

ARGUMENTS
M       (input) INTEGER
The number of rows of the matrix A.  M >= 0.

N       (input) INTEGER
The number of columns of the matrices A and B. N >= 0.

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

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

B       (input/output) 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 triangu‐
lar matrix R.

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

C       (input/output) 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 ele‐
ments N-P+1 to M of vector C.

D       (input/output) DOUBLE PRECISION array, dimension (P)
On  entry,  D  contains the right hand side vector for the con‐
strained equation.  On exit, D is destroyed.

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

WORK	 (workspace/output)   DOUBLE   PRECISION   array,    dimension
(MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK   (input) 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    (output) 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  com‐
puted.	= 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.

LAPACK driver routine (version 3November 2008			     DGGLSE(1)
```
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