cgglse-f(3)

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 is INTEGER
 The number of rows of the matrix A. M >= 0.

 N is INTEGER
 The number of columns of the matrices A and B. N >= 0.

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

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

 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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