SRC/sgelss.f(3)

NAME
SRC/sgelss.f

SYNOPSIS

  Functions/Subroutines
subroutine sgelss (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work, lwork, info)
SGELSS solves overdetermined or underdetermined systems for GE matrices

Function/Subroutine Documentation

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

SGELSS solves overdetermined or underdetermined systems for GE matrices

Purpose:

     SGELSS computes the minimum norm solution to a real 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 REAL 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 REAL 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

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

    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)).

    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.

    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 REAL 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 >= 3*min(M,N) + max( 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.

    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 170 of file sgelss.f.

Author

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