sgglse.f - Man Page

subroutine sgglse (m, n, p, a, lda, b, ldb, c, d, x, work, lwork, info)
SGGLSE solves overdetermined or underdetermined systems for OTHER matrices

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.

Definition at line 178 of file sgglse.f.