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<HTML>
<HEAD><TITLE>MB02VD - SLICOT Library Routine Documentation</TITLE>
</HEAD>
<BODY>
<H2><A Name="MB02VD">MB02VD</A></H2>
<H3>
Solution of linear equations X op(A) = B
</H3>
<A HREF ="#Specification"><B>[Specification]</B></A>
<A HREF ="#Arguments"><B>[Arguments]</B></A>
<A HREF ="#Method"><B>[Method]</B></A>
<A HREF ="#References"><B>[References]</B></A>
<A HREF ="#Comments"><B>[Comments]</B></A>
<A HREF ="#Example"><B>[Example]</B></A>
<P>
<B><FONT SIZE="+1">Purpose</FONT></B>
<PRE>
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.
</PRE>
<A name="Specification"><B><FONT SIZE="+1">Specification</FONT></B></A>
<PRE>
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, * )
</PRE>
<A name="Arguments"><B><FONT SIZE="+1">Arguments</FONT></B></A>
<P>
<B>Mode Parameters</B>
<PRE>
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'.
</PRE>
<B>Input/Output Parameters</B>
<PRE>
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.
</PRE>
<A name="Method"><B><FONT SIZE="+1">Method</FONT></B></A>
<PRE>
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.
</PRE>
<A name="Comments"><B><FONT SIZE="+1">Further Comments</FONT></B></A>
<PRE>
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.
</PRE>
<A name="Example"><B><FONT SIZE="+1">Example</FONT></B></A>
<P>
<B>Program Text</B>
<PRE>
* MB02VD EXAMPLE PROGRAM TEXT
*
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
</PRE>
<B>Program Data</B>
<PRE>
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.
</PRE>
<B>Program Results</B>
<PRE>
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
</PRE>
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