sgels.f(3)

NAME
sgels.f

SYNOPSIS

  Functions/Subroutines
subroutine sgels (TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO)
SGELS solves overdetermined or underdetermined systems for GE matrices

Function/Subroutine Documentation

  subroutine sgels (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:

     SGELS solves overdetermined or underdetermined real linear systems
     involving an M-by-N matrix A, or its transpose, using a QR or 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 underdetermined 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,
                if M >= N, A is overwritten by details of its QR
                           factorization as returned by SGEQRF;
                if M <  N, A is overwritten by details of its LQ
                           factorization as returned by SGELQF.

    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; the residual sum of squares for the
              solution in each column is given by the sum of squares of
              elements N+1 to M in that column;
              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; the residual sum of squares
              for the solution in each column is given by the sum of
              squares of elements M+1 to N in that column.

    LDB

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

    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 >= max( 1, MN + max( MN, NRHS ) ).
              For optimal performance,
              LWORK >= max( 1, MN + max( MN, NRHS )*NB ).
              where MN = min(M,N) and NB is the optimum block size.
              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:  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 181 of file sgels.f.

Author

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