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

.in +1c
.ti -1c
.RI "subroutine \fBzgelss\fP (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work, lwork, rwork, info)"
.br
.RI "\fB ZGELSS solves overdetermined or underdetermined systems for GE matrices\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgelss (integer m, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) s, double precision rcond, integer rank, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer info)"

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

.PP
.nf
!>
!> ZGELSS computes the minimum norm solution to a complex linear
!> least squares problem:
!>
!> Minimize 2-norm(| b - A*x |)\&.
!>
!> using the singular value decomposition (SVD) of A\&. A is an M-by-N
!> matrix which may be rank-deficient\&.
!>
!> 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\&.
!>
!> The effective rank of A is determined by treating as zero those
!> singular values which are less than RCOND times the largest singular
!> value\&.
!> 
.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 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*16 array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A\&.
!>          On exit, the first min(m,n) rows of A are overwritten with
!>          its right singular vectors, stored rowwise\&.
!> 
.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*16 array, dimension (LDB,NRHS)
!>          On entry, the M-by-NRHS right hand side matrix B\&.
!>          On exit, B is overwritten by the N-by-NRHS solution matrix X\&.
!>          If m >= n and RANK = n, the residual sum-of-squares for
!>          the solution in the i-th column is given by the sum of
!>          squares of the modulus of elements n+1:m 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
\fIS\fP 
.PP
.nf
!>          S is DOUBLE PRECISION array, dimension (min(M,N))
!>          The singular values of A in decreasing order\&.
!>          The condition number of A in the 2-norm = S(1)/S(min(m,n))\&.
!> 
.fi
.PP
.br
\fIRCOND\fP 
.PP
.nf
!>          RCOND is DOUBLE PRECISION
!>          RCOND is used to determine the effective rank of A\&.
!>          Singular values S(i) <= RCOND*S(1) are treated as zero\&.
!>          If RCOND < 0, machine precision is used instead\&.
!> 
.fi
.PP
.br
\fIRANK\fP 
.PP
.nf
!>          RANK is INTEGER
!>          The effective rank of A, i\&.e\&., the number of singular values
!>          which are greater than RCOND*S(1)\&.
!> 
.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 >= 1, and also:
!>          LWORK >=  2*min(M,N) + max(M,N,NRHS)
!>          For good performance, LWORK should generally be larger\&.
!>
!>          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
\fIRWORK\fP 
.PP
.nf
!>          RWORK is DOUBLE PRECISION array, dimension (5*min(M,N))
!> 
.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:  the algorithm for computing the SVD failed to converge;
!>                if INFO = i, i off-diagonal elements of an intermediate
!>                bidiagonal form did not converge to zero\&.
!> 
.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 \fB176\fP of file \fBzgelss\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.