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DGTSV.f90
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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 ..
Real 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) Real 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) Real 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) Real 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) Real 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 ..
Real ZERO
PARAMETER ( ZERO = 0.0D+0 )
! ..
! .. Local Scalars ..
INTEGER I, J
Real FACT, TEMP
! ..
! .. Intrinsic Functions ..
INTRINSIC ABS, MAX
! ..
! .. External Subroutines ..
!c 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
!c 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