MB02VD

Solution of linear equations X op(A) = B

Purpose

  To compute the solution to a real system of linear equations
     X * op(A) = B,
  where op(A) is either A or its transpose, A is an N-by-N matrix,
  and X and B are M-by-N matrices.
  The LU decomposition with partial pivoting and row interchanges,
  A = P * L * U, is used, where P is a permutation matrix, L is unit
  lower triangular, and U is upper triangular.

      SUBROUTINE MB02VD( TRANS, M, N, A, LDA, IPIV, B, LDB, INFO )
C     .. Scalar Arguments ..
      CHARACTER          TRANS
      INTEGER            INFO, LDA, LDB, M, N
C     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )

Mode Parameters

  TRANS   CHARACTER*1
          Specifies the form of op(A) to be used as follows:
          = 'N':  op(A) = A;
          = 'T':  op(A) = A';
          = 'C':  op(A) = A'.

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

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

  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the leading N-by-N part of this array must
          contain the coefficient matrix A.
          On exit, the leading N-by-N part of this array contains
          the factors L and U from the factorization A = P*L*U;
          the unit diagonal elements of L are not stored.

  LDA     INTEGER
          The leading dimension of the array A.  LDA >= MAX(1,N).

  IPIV    (output) INTEGER array, dimension (N)
          The pivot indices that define the permutation matrix P;
          row i of the matrix was interchanged with row IPIV(i).

  B       (input/output) DOUBLE PRECISION array, dimension (LDB,N)
          On entry, the leading M-by-N part of this array must
          contain the right hand side matrix B.
          On exit, if INFO = 0, the leading M-by-N part of this
          array contains the solution matrix X.

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

  INFO    (output) INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value;
          > 0:  if INFO = i, U(i,i) is exactly zero.  The
                factorization has been completed, but the factor U
                is exactly singular, so the solution could not be
                computed.

  The LU decomposition with partial pivoting and row interchanges is
  used to factor A as
     A = P * L * U,
  where P is a permutation matrix, L is unit lower triangular, and
  U is upper triangular.  The factored form of A is then used to
  solve the system of equations X * A = B or X * A' = B.

  This routine enables to solve the system X * A = B or X * A' = B
  as easily and efficiently as possible; it is similar to the LAPACK
  Library routine DGESV, which solves A * X = B.

Program Text

*     MB02VD EXAMPLE PROGRAM TEXT
*     Copyright (c) 2002-2017 NICONET e.V.
*
      INTEGER          NIN, NOUT
      PARAMETER        ( NIN = 5, NOUT = 6 )
      INTEGER          MMAX, NMAX
      PARAMETER        ( MMAX = 20, NMAX = 20 )
      INTEGER          LDA, LDB
      PARAMETER        ( LDA = NMAX, LDB = MMAX )
*     .. Local Scalars ..
      INTEGER          I, INFO, J, M, N
      CHARACTER*1      TRANS
*     .. Local Arrays ..
      DOUBLE PRECISION A(LDA,NMAX), B(LDB,NMAX)
      INTEGER          IPIV(NMAX)
*     .. External Subroutines ..
      EXTERNAL         MB02VD
*     .. Executable Statements ..
*
      WRITE ( NOUT, FMT = 99999 )
*     Skip the heading in the data file and read in the data.
      READ ( NIN, FMT = '()' )
      READ ( NIN, FMT = * ) M, N, TRANS
      IF ( N.LT.0 .OR. N.GT.NMAX ) THEN
         WRITE ( NOUT, FMT = 99995 ) N
      ELSE
         READ ( NIN, FMT = * ) ( ( A(I,J), J = 1,N ), I = 1,N )
         IF ( M.LT.0 .OR. M.GT.MMAX ) THEN
            WRITE ( NOUT, FMT = 99994 ) M
         ELSE
            READ ( NIN, FMT = * ) ( ( B(I,J), J = 1,N ), I = 1,M )
*           Solve the linear system using the LU factorization.
            CALL MB02VD( TRANS, M, N, A, LDA, IPIV, B, LDB, INFO )
*
            IF ( INFO.EQ.0 ) THEN
               WRITE ( NOUT, FMT = 99997 )
               DO 10 I = 1, M
                  WRITE ( NOUT, FMT = 99996 ) ( B(I,J), J = 1,N )
   10          CONTINUE
            ELSE
               WRITE ( NOUT, FMT = 99998 ) INFO
            END IF
         END IF
      END IF
      STOP
*
99999 FORMAT (' MB02VD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from MB02VD = ',I2)
99997 FORMAT (' The solution matrix is ')
99996 FORMAT (20(1X,F8.4))
99995 FORMAT (/' N is out of range.',/' N = ',I5)
99994 FORMAT (/' M is out of range.',/' M = ',I5)
      END

 MB02VD EXAMPLE PROGRAM DATA
   5    4      N
   1.    2.    6.    3.
  -2.   -1.   -1.    0.
   2.    3.    1.    5.
   1.   -1.    2.    0.
   0.    0.    0.    1.
   5.    5.    1.    5.
  -2.    1.    3.    1.
   0.    0.    4.    5.
   2.    1.    1.    3.

 MB02VD EXAMPLE PROGRAM RESULTS

 The solution matrix is 
  -0.0690   0.3333   0.2414   0.2529
  -0.1724  -1.6667   1.1034  -0.3678
   0.9655   0.6667  -0.3793  -0.8736
   0.3448   1.6667   0.7931   1.4023
  -0.2069   0.0000   0.7241   0.7586

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