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

.in +1c
.ti -1c
.RI "subroutine \fBzggglm\fP (n, m, p, a, lda, b, ldb, d, x, y, work, lwork, info)"
.br
.RI "\fBZGGGLM\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zggglm (integer n, integer m, integer p, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) d, complex*16, dimension( * ) x, complex*16, dimension( * ) y, complex*16, dimension( * ) work, integer lwork, integer info)"

.PP
\fBZGGGLM\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZGGGLM solves a general Gauss-Markov linear model (GLM) problem:
!>
!>         minimize || y ||_2   subject to   d = A*x + B*y
!>             x
!>
!> where A is an N-by-M matrix, B is an N-by-P matrix, and d is a
!> given N-vector\&. It is assumed that M <= N <= M+P, and
!>
!>            rank(A) = M    and    rank( A B ) = N\&.
!>
!> Under these assumptions, the constrained equation is always
!> consistent, and there is a unique solution x and a minimal 2-norm
!> solution y, which is obtained using a generalized QR factorization
!> of the matrices (A, B) given by
!>
!>    A = Q*(R),   B = Q*T*Z\&.
!>          (0)
!>
!> In particular, if matrix B is square nonsingular, then the problem
!> GLM is equivalent to the following weighted linear least squares
!> problem
!>
!>              minimize || inv(B)*(d-A*x) ||_2
!>                  x
!>
!> where inv(B) denotes the inverse of B\&.
!>
!> Callers of this subroutine should note that the singularity/rank-deficiency checks
!> implemented in this subroutine are rudimentary\&. The ZTRTRS 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 QR
!> factorization of the pair (A, B) 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
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of rows of the matrices A and B\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of columns of the matrix A\&.  0 <= M <= N\&.
!> 
.fi
.PP
.br
\fIP\fP 
.PP
.nf
!>          P is INTEGER
!>          The number of columns of the matrix B\&.  P >= N-M\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension (LDA,M)
!>          On entry, the N-by-M matrix A\&.
!>          On exit, the upper triangular part of the array A contains
!>          the M-by-M upper triangular matrix R\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&. LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is COMPLEX*16 array, dimension (LDB,P)
!>          On entry, the N-by-P matrix B\&.
!>          On exit, if N <= P, the upper triangle of the subarray
!>          B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
!>          if N > P, the elements on and above the (N-P)th subdiagonal
!>          contain the N-by-P upper trapezoidal matrix T\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&. LDB >= max(1,N)\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is COMPLEX*16 array, dimension (N)
!>          On entry, D is the left hand side of the GLM equation\&.
!>          On exit, D is destroyed\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is COMPLEX*16 array, dimension (M)
!> 
.fi
.PP
.br
\fIY\fP 
.PP
.nf
!>          Y is COMPLEX*16 array, dimension (P)
!>
!>          On exit, X and Y are the solutions of the GLM problem\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 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,N+M+P)\&.
!>          For optimum performance, LWORK >= M+min(N,P)+max(N,P)*NB,
!>          where NB is an upper bound for the optimal blocksizes for
!>          ZGEQRF, ZGERQF, ZUNMQR and ZUNMRQ\&.
!>
!>          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 A in the
!>                generalized QR factorization of the pair (A, B) is exactly
!>                singular, so that rank(A) < M; the least squares
!>                solution could not be computed\&.
!>          = 2:  the bottom (N-M) by (N-M) part of the upper trapezoidal
!>                factor T associated with B in the generalized QR
!>                factorization of the pair (A, B) is exactly singular, so that
!>                rank( A B ) < N; the least squares solution could not
!>                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 \fB193\fP of file \fBzggglm\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.