LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ cgglse()

subroutine cgglse ( integer  m,
integer  n,
integer  p,
complex, dimension( lda, * )  a,
integer  lda,
complex, dimension( ldb, * )  b,
integer  ldb,
complex, dimension( * )  c,
complex, dimension( * )  d,
complex, dimension( * )  x,
complex, dimension( * )  work,
integer  lwork,
integer  info 
)

CGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Download CGGLSE + dependencies [TGZ] [ZIP] [TXT]

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.

 Callers of this subroutine should note that the singularity/rank-deficiency checks
 implemented in this subroutine are rudimentary. The CTRTRS subroutine called by this
 subroutine only signals a failure due to singularity if the problem is exactly singular.

 It is conceivable for one (or more) of the factors involved in the generalized RQ
 factorization of the pair (B, A) to be subnormally close to singularity without this
 subroutine signalling an error. The solutions computed for such almost-rank-deficient
 problems may be less accurate due to a loss of numerical precision.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrices A and B. N >= 0.
[in]P
          P is INTEGER
          The number of rows of the matrix B. 0 <= P <= N <= M+P.
[in,out]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.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,M).
[in,out]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.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,P).
[in,out]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.
[in,out]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.
[out]X
          X is COMPLEX array, dimension (N)
          On exit, X is the solution of the LSE problem.
[out]WORK
          WORK is COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]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.
[out]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 exactly
                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 exactly 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.