.Modelica.Math.Matrices.LAPACK.dgels_vec

Information

Lapack documentation
    Purpose
    =======

    DGELS 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 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.

    Arguments
    =========

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

    M       (input) INTEGER
            The number of rows of the matrix A.  M >= 0.

    N       (input) INTEGER
            The number of columns of the matrix A.  N >= 0.

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

    A       (input/output) DOUBLE PRECISION 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 DGEQRF;
              if M <  N, A is overwritten by details of its LQ
                         factorization as returned by DGELQF.

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

    B       (input/output) DOUBLE PRECISION 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     (input) INTEGER
            The leading dimension of the array B. LDB >= MAX(1,M,N).

    WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK   (input) 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    (output) 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.

Interface

pure function dgels_vec
  extends Modelica.Icons.Function;
  input Real A[:, :];
  input Real b[size(A, 1)];
  output Real x[max(size(A, 1), size(A, 2))] = cat(1, b, zeros(nx - nrow)) "Solution is in first size(A,2) rows";
  output Integer info;
end dgels_vec;