SRC/DEPRECATED/dgelsx.f(3)

NAME
SRC/DEPRECATED/dgelsx.f

SYNOPSIS

  Functions/Subroutines
subroutine dgelsx (m, n, nrhs, a, lda, b, ldb, jpvt, rcond, rank, work, info)
DGELSX solves overdetermined or underdetermined systems for GE matrices

Function/Subroutine Documentation

  subroutine dgelsx (integer m, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, integer, dimension( * ) jpvt, double precision rcond, integer rank, double precision, dimension( * ) work, integer info)

DGELSX solves overdetermined or underdetermined systems for GE matrices

Purpose:

     This routine is deprecated and has been replaced by routine DGELSY.
     DGELSX computes the minimum-norm solution to a real linear least
     squares problem:
         minimize || A * X - B ||
     using a complete orthogonal factorization 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 routine first computes a QR factorization with column pivoting:
         A * P = Q * [ R11 R12 ]
                     [  0  R22 ]
     with R11 defined as the largest leading submatrix whose estimated
     condition number is less than 1/RCOND.  The order of R11, RANK,
     is the effective rank of A.
     Then, R22 is considered to be negligible, and R12 is annihilated
     by orthogonal transformations from the right, arriving at the
     complete orthogonal factorization:
        A * P = Q * [ T11 0 ] * Z
                    [  0  0 ]
     The minimum-norm solution is then
        X = P * Z**T [ inv(T11)*Q1**T*B ]
                     [        0         ]
     where Q1 consists of the first RANK columns of Q.

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 matrices B and X. NRHS >= 0.

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, A has been overwritten by details of its
              complete orthogonal factorization.

    LDA

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

    B

              B is DOUBLE PRECISION array, dimension (LDB,NRHS)
              On entry, the M-by-NRHS right hand side matrix B.
              On exit, 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,M,N).

    JPVT

              JPVT is INTEGER array, dimension (N)
              On entry, if JPVT(i) .ne. 0, the i-th column of A is an
              initial column, otherwise it is a free column.  Before
              the QR factorization of A, all initial columns are
              permuted to the leading positions; only the remaining
              free columns are moved as a result of column pivoting
              during the factorization.
              On exit, if JPVT(i) = k, then the i-th column of A*P
              was the k-th column of A.

    RCOND

              RCOND is DOUBLE PRECISION
              RCOND is used to determine the effective rank of A, which
              is defined as the order of the largest leading triangular
              submatrix R11 in the QR factorization with pivoting of A,
              whose estimated condition number < 1/RCOND.

    RANK

              RANK is INTEGER
              The effective rank of A, i.e., the order of the submatrix
              R11.  This is the same as the order of the submatrix T11
              in the complete orthogonal factorization of A.

    WORK

              WORK is DOUBLE PRECISION array, dimension
                          (max( min(M,N)+3*N, 2*min(M,N)+NRHS )),

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 176 of file dgelsx.f.

Author

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