ZGELSS(l) ) ZGELSS(l)NAME
ZGELSS - compute the minimum norm solution to a complex linear least
squares problem
SYNOPSIS
SUBROUTINE ZGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK,
LWORK, RWORK, INFO )
INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
DOUBLE PRECISION RCOND
DOUBLE PRECISION RWORK( * ), S( * )
COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
PURPOSE
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 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*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.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) 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 elements
n+1:m in that column.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,M,N).
S (output) 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)).
RCOND (input) 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.
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*16 array, dimension (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) DOUBLE PRECISION 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 version 3.0 15 June 2000 ZGELSS(l)
