NAME

       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 (integerM, integerN, integerNRHS, complex*16, dimension( lda, * )A,
       integerLDA, complex*16, dimension( ldb, * )B, integerLDB, double precision, dimension( *
       )S, double precisionRCOND, integerRANK, complex*16, dimension( * )WORK, integerLWORK,
       double precision, dimension( * )RWORK, integerINFO)
        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.

       Date:
           November 2011

       Definition at line 178 of file zgelss.f.

Author

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