CGELSS(1) LAPACK driver routine (version 3.2) CGELSS(1)NAME
CGELSS - computes the minimum norm solution to a complex linear least
squares problem
SYNOPSIS
SUBROUTINE CGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK,
LWORK, RWORK, INFO )
INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
REAL RCOND
REAL RWORK( * ), S( * )
COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
PURPOSE
CGELSS 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 singu‐
lar values which are less than RCOND times the largest singular value.
ARGUMENTS
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
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.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
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.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,M,N).
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)).
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.
RANK (output) INTEGER
The effective rank of A, i.e., the number of singular values
which are greater than RCOND*S(1).
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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.
RWORK (workspace) REAL array, dimension (5*min(M,N))
INFO (output) 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 bidiag‐
onal form did not converge to zero.
LAPACK driver routine (version 3November 2008 CGELSS(1)
