sgetsls.f(3)

NAME
sgetsls.f

SYNOPSIS

  Functions/Subroutines
subroutine sgetsls (TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO)
SGETSLS

Function/Subroutine Documentation

  subroutine sgetsls (character TRANS, integer M, integer N, integer NRHS, real, dimension( lda, * ) A, integer LDA, real, dimension( ldb, * ) B, integer LDB, real, dimension( * ) WORK, integer LWORK, integer INFO)

Purpose:

     SGETSLS solves overdetermined or underdetermined real linear systems
     involving an M-by-N matrix A, using a tall skinny QR or short wide LQ
     factorization of A.  It is assumed that A has full rank.
     The following options are provided:
     1. If TRANS = 'N' and m >= n:  find the least squares solution of
        an overdetermined system, i.e., solve the least squares problem
                     minimize || B - A*X ||.
     2. If TRANS = 'N' and m < n:  find the minimum norm solution of
        an underdetermined system A * X = B.
     3. If TRANS = 'T' and m >= n:  find the minimum norm solution of
        an undetermined system A**T * X = B.
     4. If TRANS = 'T' and m < n:  find the least squares solution of
        an overdetermined system, i.e., solve the least squares problem
                     minimize || B - A**T * X ||.
     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.

Parameters
    TRANS

              TRANS is CHARACTER*1
              = 'N': the linear system involves A;
              = 'T': the linear system involves A**T.

    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,
              A is overwritten by details of its QR or LQ
              factorization as returned by SGEQR or SGELQ.

    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 matrix B of right hand side vectors, stored
              columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS
              if TRANS = 'T'.
              On exit, if INFO = 0, B is overwritten by the solution
              vectors, stored columnwise:
              if TRANS = 'N' and m >= n, rows 1 to n of B contain the least
              squares solution vectors.
              if TRANS = 'N' and m < n, rows 1 to N of B contain the
              minimum norm solution vectors;
              if TRANS = 'T' and m >= n, rows 1 to M of B contain the
              minimum norm solution vectors;
              if TRANS = 'T' and m < n, rows 1 to M of B contain the
              least squares solution vectors.

    LDB

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

    WORK

              (workspace) REAL array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
              or optimal, if query was assumed) LWORK.
              See LWORK for details.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If LWORK = -1 or -2, then a workspace query is assumed.
              If LWORK = -1, the routine calculates optimal size of WORK for the
              optimal performance and returns this value in WORK(1).
              If LWORK = -2, the routine calculates minimal size of WORK and
              returns this value in WORK(1).

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value
              > 0:  if INFO =  i, the i-th diagonal element of the
                    triangular factor of A is zero, so that A does not have
                    full rank; the least squares solution could not be
                    computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 160 of file sgetsls.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.