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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
S(1)/S(min(m,n)).
 
        RCOND   (input) DOUBLE PRECISION
                RCOND  is  used to determine the effective rank of A.  Singular
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
RCOND*S(1).
 
        WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
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.
 

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