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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/zgelss.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/zgelss.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/zgelss.f

SYNOPSIS

Functions/Subroutines


subroutine ZGELSS (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work, lwork, rwork, info)
ZGELSS solves overdetermined or underdetermined systems for GE matrices

Function/Subroutine Documentation

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)

ZGELSS solves overdetermined or underdetermined systems for GE matrices

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
!> singular values which are less than RCOND times the largest singular
!> value.
!> 

Parameters

M

!>          M is INTEGER
!>          The number of rows of the matrix A. M >= 0.
!> 

N

!>          N is INTEGER
!>          The number of columns of the matrix A. N >= 0.
!> 

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrices B and X. NRHS >= 0.
!> 

A

!>          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.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A. LDA >= max(1,M).
!> 

B

!>          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.
!> 

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,M,N).
!> 

S

!>          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)).
!> 

RCOND

!>          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.
!> 

RANK

!>          RANK is INTEGER
!>          The effective rank of A, i.e., the number of singular values
!>          which are greater than RCOND*S(1).
!> 

WORK

!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

LWORK

!>          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.
!> 

RWORK

!>          RWORK is DOUBLE PRECISION array, dimension (5*min(M,N))
!> 

INFO

!>          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.
!> 

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 176 of file zgelss.f.

Author

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Version 3.12.0 LAPACK