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tridiag.f.html |
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Source file: tridiag.f
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Directory: /home/rjl/git/rjleveque/clawpack-4.x/book/chap17/advdiff
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Converted: Tue Jul 26 2011 at 12:59:07
using clawcode2html
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This documentation file will
not reflect any later changes in the source file.
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c
c LAPACK routines to solve a general tridiagonal linear system,
c used in src1.f for applying an implicit method to the diffusion equation.
c
c This file may not be needed if you already have lapack on your system.
c
c
c
SUBROUTINE DGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
* -- LAPACK routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* October 31, 1999
*
* .. Scalar Arguments ..
INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * )
* ..
*
* Purpose
* =======
*
* DGTSV solves the equation
*
* A*X = B,
*
* where A is an n by n tridiagonal matrix, by Gaussian elimination with
* partial pivoting.
*
* Note that the equation A'*X = B may be solved by interchanging the
* order of the arguments DU and DL.
*
* Arguments
* =========
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrix B. NRHS >= 0.
*
* DL (input/output) DOUBLE PRECISION array, dimension (N-1)
* On entry, DL must contain the (n-1) sub-diagonal elements of
* A.
*
* On exit, DL is overwritten by the (n-2) elements of the
* second super-diagonal of the upper triangular matrix U from
* the LU factorization of A, in DL(1), ..., DL(n-2).
*
* D (input/output) DOUBLE PRECISION array, dimension (N)
* On entry, D must contain the diagonal elements of A.
*
* On exit, D is overwritten by the n diagonal elements of U.
*
* DU (input/output) DOUBLE PRECISION array, dimension (N-1)
* On entry, DU must contain the (n-1) super-diagonal elements
* of A.
*
* On exit, DU is overwritten by the (n-1) elements of the first
* super-diagonal of U.
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
* On entry, the N by NRHS matrix of right hand side matrix B.
* On exit, if INFO = 0, the N by NRHS solution matrix X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* 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, and the solution
* has not been computed. The factorization has not been
* completed unless i = N.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J
DOUBLE PRECISION FACT, TEMP
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Executable Statements ..
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( NRHS.LT.0 ) THEN
INFO = -2
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -7
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGTSV ', -INFO )
RETURN
END IF
*
IF( N.EQ.0 )
$ RETURN
*
IF( NRHS.EQ.1 ) THEN
DO 10 I = 1, N - 2
IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
*
* No row interchange required
*
IF( D( I ).NE.ZERO ) THEN
FACT = DL( I ) / D( I )
D( I+1 ) = D( I+1 ) - FACT*DU( I )
B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 )
ELSE
INFO = I
RETURN
END IF
DL( I ) = ZERO
ELSE
*
* Interchange rows I and I+1
*
FACT = D( I ) / DL( I )
D( I ) = DL( I )
TEMP = D( I+1 )
D( I+1 ) = DU( I ) - FACT*TEMP
DL( I ) = DU( I+1 )
DU( I+1 ) = -FACT*DL( I )
DU( I ) = TEMP
TEMP = B( I, 1 )
B( I, 1 ) = B( I+1, 1 )
B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 )
END IF
10 CONTINUE
IF( N.GT.1 ) THEN
I = N - 1
IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
IF( D( I ).NE.ZERO ) THEN
FACT = DL( I ) / D( I )
D( I+1 ) = D( I+1 ) - FACT*DU( I )
B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 )
ELSE
INFO = I
RETURN
END IF
ELSE
FACT = D( I ) / DL( I )
D( I ) = DL( I )
TEMP = D( I+1 )
D( I+1 ) = DU( I ) - FACT*TEMP
DU( I ) = TEMP
TEMP = B( I, 1 )
B( I, 1 ) = B( I+1, 1 )
B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 )
END IF
END IF
IF( D( N ).EQ.ZERO ) THEN
INFO = N
RETURN
END IF
ELSE
DO 40 I = 1, N - 2
IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
*
* No row interchange required
*
IF( D( I ).NE.ZERO ) THEN
FACT = DL( I ) / D( I )
D( I+1 ) = D( I+1 ) - FACT*DU( I )
DO 20 J = 1, NRHS
B( I+1, J ) = B( I+1, J ) - FACT*B( I, J )
20 CONTINUE
ELSE
INFO = I
RETURN
END IF
DL( I ) = ZERO
ELSE
*
* Interchange rows I and I+1
*
FACT = D( I ) / DL( I )
D( I ) = DL( I )
TEMP = D( I+1 )
D( I+1 ) = DU( I ) - FACT*TEMP
DL( I ) = DU( I+1 )
DU( I+1 ) = -FACT*DL( I )
DU( I ) = TEMP
DO 30 J = 1, NRHS
TEMP = B( I, J )
B( I, J ) = B( I+1, J )
B( I+1, J ) = TEMP - FACT*B( I+1, J )
30 CONTINUE
END IF
40 CONTINUE
IF( N.GT.1 ) THEN
I = N - 1
IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
IF( D( I ).NE.ZERO ) THEN
FACT = DL( I ) / D( I )
D( I+1 ) = D( I+1 ) - FACT*DU( I )
DO 50 J = 1, NRHS
B( I+1, J ) = B( I+1, J ) - FACT*B( I, J )
50 CONTINUE
ELSE
INFO = I
RETURN
END IF
ELSE
FACT = D( I ) / DL( I )
D( I ) = DL( I )
TEMP = D( I+1 )
D( I+1 ) = DU( I ) - FACT*TEMP
DU( I ) = TEMP
DO 60 J = 1, NRHS
TEMP = B( I, J )
B( I, J ) = B( I+1, J )
B( I+1, J ) = TEMP - FACT*B( I+1, J )
60 CONTINUE
END IF
END IF
IF( D( N ).EQ.ZERO ) THEN
INFO = N
RETURN
END IF
END IF
*
* Back solve with the matrix U from the factorization.
*
IF( NRHS.LE.2 ) THEN
J = 1
70 CONTINUE
B( N, J ) = B( N, J ) / D( N )
IF( N.GT.1 )
$ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
DO 80 I = N - 2, 1, -1
B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )*
$ B( I+2, J ) ) / D( I )
80 CONTINUE
IF( J.LT.NRHS ) THEN
J = J + 1
GO TO 70
END IF
ELSE
DO 100 J = 1, NRHS
B( N, J ) = B( N, J ) / D( N )
IF( N.GT.1 )
$ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
$ D( N-1 )
DO 90 I = N - 2, 1, -1
B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )*
$ B( I+2, J ) ) / D( I )
90 CONTINUE
100 CONTINUE
END IF
*
RETURN
*
* End of DGTSV
*
END
SUBROUTINE XERBLA( SRNAME, INFO )
*
* -- LAPACK auxiliary routine (preliminary version) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER*6 SRNAME
INTEGER INFO
* ..
*
* Purpose
* =======
*
* XERBLA is an error handler for the LAPACK routines.
* It is called by an LAPACK routine if an input parameter has an
* invalid value. A message is printed and execution stops.
*
* Installers may consider modifying the STOP statement in order to
* call system-specific exception-handling facilities.
*
* Arguments
* =========
*
* SRNAME (input) CHARACTER*6
* The name of the routine which called XERBLA.
*
* INFO (input) INTEGER
* The position of the invalid parameter in the parameter list
* of the calling routine.
*
*
WRITE( *, FMT = 9999 )SRNAME, INFO
*
STOP
*
9999 FORMAT( ' ** On entry to ', A6, ' parameter number ', I2, ' had ',
$ 'an illegal value' )
*
* End of XERBLA
*
END