.TH "SRC/sgglse.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/sgglse.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBsgglse\fP (m, n, p, a, lda, b, ldb, c, d, x, work, lwork, info)"
.br
.RI "\fB SGGLSE solves overdetermined or underdetermined systems for OTHER matrices\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine sgglse (integer m, integer n, integer p, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) c, real, dimension( * ) d, real, dimension( * ) x, real, dimension( * ) work, integer lwork, integer info)"

.PP
\fB SGGLSE solves overdetermined or underdetermined systems for OTHER matrices\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!>
!> Callers of this subroutine should note that the singularity/rank-deficiency checks
!> implemented in this subroutine are rudimentary\&. The STRTRS 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\&.
!> 
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix A\&.  M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrices A and B\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIP\fP 
.PP
.nf
!>          P is INTEGER
!>          The number of rows of the matrix B\&. 0 <= P <= N <= M+P\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&. LDA >= max(1,M)\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&. LDB >= max(1,P)\&.
!> 
.fi
.PP
.br
\fIC\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is REAL array, dimension (P)
!>          On entry, D contains the right hand side vector for the
!>          constrained equation\&.
!>          On exit, D is destroyed\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is REAL array, dimension (N)
!>          On exit, X is the solution of the LSE problem\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB188\fP of file \fBsgglse\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.