cgglse(3)

NAME

cgglse.f –

SYNOPSIS

Functions/Subroutines

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

Function/Subroutine Documentation

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

CGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Purpose:

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

X

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

WORK

          WORK is COMPLEX 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
CGEQRF, CGERQF, CUNMQR and CUNMRQ.
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 cgglse.f.

Author

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