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

.in +1c
.ti -1c
.RI "subroutine \fBsgels\fP (trans, m, n, nrhs, a, lda, b, ldb, work, lwork, info)"
.br
.RI "\fB SGELS solves overdetermined or underdetermined systems for GE matrices\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine sgels (character trans, integer m, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
!>
!> SGELS solves overdetermined or underdetermined real linear systems
!> involving an M-by-N matrix A, or its transpose, using a QR or LQ
!> factorization of A\&.
!>
!> It is assumed that A has full rank, and only a rudimentary protection
!> against rank-deficient matrices is provided\&. This subroutine only detects
!> exact rank-deficiency, where a diagonal element of the triangular factor
!> of A is exactly zero\&.
!>
!> It is conceivable for one (or more) of the diagonal elements of the triangular
!> factor of A to be subnormally tiny numbers without this subroutine signalling
!> an error\&. The solutions computed for such almost-rank-deficient matrices may
!> be less accurate due to a loss of numerical precision\&.
!>
!> The following options are provided:
!>
!> 1\&. If TRANS = 'N' and m >= n:  find the least squares solution of
!>    an overdetermined system, i\&.e\&., solve the least squares problem
!>                 minimize || B - A*X ||\&.
!>
!> 2\&. If TRANS = 'N' and m < n:  find the minimum norm solution of
!>    an underdetermined system A * X = B\&.
!>
!> 3\&. If TRANS = 'T' and m >= n:  find the minimum norm solution of
!>    an underdetermined system A**T * X = B\&.
!>
!> 4\&. If TRANS = 'T' and m < n:  find the least squares solution of
!>    an overdetermined system, i\&.e\&., solve the least squares problem
!>                 minimize || B - A**T * X ||\&.
!>
!> Several right hand side vectors b and solution vectors x can be
!> handled in a single call; they are stored as the columns of the
!> M-by-NRHS right hand side matrix B and the N-by-NRHS solution
!> matrix X\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          = 'N': the linear system involves A;
!>          = 'T': the linear system involves A**T\&.
!> 
.fi
.PP
.br
\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 matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
!>          NRHS is INTEGER
!>          The number of right hand sides, i\&.e\&., the number of
!>          columns of the matrices B and X\&. NRHS >=0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is REAL array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A\&.
!>          On exit,
!>            if M >= N, A is overwritten by details of its QR
!>                       factorization as returned by SGEQRF;
!>            if M <  N, A is overwritten by details of its LQ
!>                       factorization as returned by SGELQF\&.
!> 
.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,NRHS)
!>          On entry, the matrix B of right hand side vectors, stored
!>          columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS
!>          if TRANS = 'T'\&.
!>          On exit, if INFO = 0, B is overwritten by the solution
!>          vectors, stored columnwise:
!>          if TRANS = 'N' and m >= n, rows 1 to n of B contain the least
!>          squares solution vectors; the residual sum of squares for the
!>          solution in each column is given by the sum of squares of
!>          elements N+1 to M in that column;
!>          if TRANS = 'N' and m < n, rows 1 to N of B contain the
!>          minimum norm solution vectors;
!>          if TRANS = 'T' and m >= n, rows 1 to M of B contain the
!>          minimum norm solution vectors;
!>          if TRANS = 'T' and m < n, rows 1 to M of B contain the
!>          least squares solution vectors; the residual sum of squares
!>          for the solution in each column is given by the sum of
!>          squares of elements M+1 to N in that column\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&. LDB >= MAX(1,M,N)\&.
!> 
.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, MN + max( MN, NRHS ) )\&.
!>          For optimal performance,
!>          LWORK >= max( 1, MN + max( MN, NRHS )*NB )\&.
!>          where MN = min(M,N) and NB is the optimum block size\&.
!>
!>          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
!>          > 0:  if INFO =  i, the i-th diagonal element of the
!>                triangular factor of A is exactly zero, so that A does not have
!>                full rank; 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 \fB191\fP of file \fBsgels\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.