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

.in +1c
.ti -1c
.RI "subroutine \fBcgetsls\fP (trans, m, n, nrhs, a, lda, b, ldb, work, lwork, info)"
.br
.RI "\fBCGETSLS\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine cgetsls (character trans, integer m, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
 CGETSLS solves overdetermined or underdetermined complex linear systems
 involving an M-by-N matrix A, using a tall skinny QR or short wide LQ
 factorization of A\&.  It is assumed that A has full rank\&.



 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 = 'C' and m >= n:  find the minimum norm solution of
    an undetermined system A**T * X = B\&.

 4\&. If TRANS = 'C' 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;
          = 'C': the linear system involves A**H\&.
.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 COMPLEX array, dimension (LDA,N)
          On entry, the M-by-N matrix A\&.
          On exit,
          A is overwritten by details of its QR or LQ
          factorization as returned by CGEQR or CGELQ\&.
.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 COMPLEX 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 = 'C'\&.
          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\&.
          if TRANS = 'N' and m < n, rows 1 to N of B contain the
          minimum norm solution vectors;
          if TRANS = 'C' and m >= n, rows 1 to M of B contain the
          minimum norm solution vectors;
          if TRANS = 'C' and m < n, rows 1 to M of B contain the
          least squares solution vectors\&.
.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
          (workspace) COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
          or optimal, if query was assumed) LWORK\&.
          See LWORK for details\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.
          If LWORK = -1 or -2, then a workspace query is assumed\&.
          If LWORK = -1, the routine calculates optimal size of WORK for the
          optimal performance and returns this value in WORK(1)\&.
          If LWORK = -2, the routine calculates minimal size of WORK and 
          returns this value in WORK(1)\&.
.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 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 \fB160\fP of file \fBcgetsls\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.