.TH CGELSS 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) "
.SH NAME
CGELSS - the minimum norm solution to a complex linear least squares problem
.SH SYNOPSIS
.TP 19
SUBROUTINE CGELSS(
M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
WORK, LWORK, RWORK, INFO )
.TP 19
.ti +4
INTEGER
INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
.TP 19
.ti +4
REAL
RCOND
.TP 19
.ti +4
REAL
RWORK( * ), S( * )
.TP 19
.ti +4
COMPLEX
A( LDA, * ), B( LDB, * ), WORK( * )
.SH PURPOSE
CGELSS computes the minimum norm solution to a complex linear
least squares problem:
Minimize 2-norm(| b - A*x |).
.br
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
.br
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.
.br
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
.br
.SH ARGUMENTS
.TP 8
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
.TP 8
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
.TP 8
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
.TP 8
A (input/output) COMPLEX 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.
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
.TP 8
B (input/output) COMPLEX 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.
.TP 8
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,M,N).
.TP 8
S (output) REAL 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)).
.TP 8
RCOND (input) REAL
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.
.TP 8
RANK (output) INTEGER
The effective rank of A, i.e., the number of singular values
which are greater than RCOND*S(1).
.TP 8
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
.TP 8
LWORK (input) 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.
.TP 8
RWORK (workspace) REAL array, dimension (5*min(M,N))
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value.
.br
> 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.