zgelss.f(3)

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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