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## cgelss()

subroutine cgelss | ( | integer | m,
|  | integer | n,
|  | integer | nrhs,
|  | complex, dimension( lda, * ) | a,
|  | integer | lda,
|  | complex, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | real, dimension( * ) | s,
|  | real | rcond,
|  | integer | rank,
|  | complex, dimension( * ) | work,
|  | integer | lwork,
|  | real, dimension( * ) | rwork,
|  | integer | info )

CGELSS solves overdetermined or underdetermined systems for GE matrices

Download CGELSS + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> CGELSS 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

  [in]

  M

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

  [in]

  N

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

  [in]

  NRHS

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

  [in,out]

  A

      !>          A is COMPLEX 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.
      !>

  [in]

  LDA

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

  [in,out]

  B

      !>          B is COMPLEX 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.
      !>

  [in]

  LDB

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

  [out]

  S

      !>          S is REAL 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)).
      !>

  [in]

  RCOND

      !>          RCOND is REAL
      !>          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.
      !>

  [out]

  RANK

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

  [out]

  WORK

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

  [in]

  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.
      !>

  [out]

  RWORK

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

  [out]

  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.