sgglse.f man page

sgglse.f —

Synopsis

Functions/Subroutines

subroutine sgglse (M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO)
SGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Function/Subroutine Documentation

subroutine sgglse (integerM, integerN, integerP, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( * )C, real, dimension( * )D, real, dimension( * )X, real, dimension( * )WORK, integerLWORK, integerINFO)

SGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Purpose:

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

X

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

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. 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
SGEQRF, SGERQF, SORMQR 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

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 180 of file sgglse.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

sgglse(3) is an alias of sgglse.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK