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SUBROUTINE SGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
REAL B( LDB, * ), D( * ), DL( * ), DU( * )
* ..
*
* Purpose
* =======
*
* SGTSV 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) subdiagonal elements of
* A.
* On exit, DL is overwritten by the (n-2) elements of the
* second superdiagonal 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) superdiagonal elements
* of A.
* On exit, DU is overwritten by the (n-1) elements of the first
* superdiagonal of U.
*
* B (input/output) REAL array, dimension (LDB,NRHS)
* On entry, the N-by-NRHS 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 = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER J, K
REAL MULT, 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( 'SGTSV ', -INFO )
RETURN
END IF
*
IF( N.EQ.0 )
$ RETURN
*
DO 30 K = 1, N - 1
IF( DL( K ).EQ.ZERO ) THEN
*
* Subdiagonal is zero, no elimination is required.
*
IF( D( K ).EQ.ZERO ) THEN
*
* Diagonal is zero: set INFO = K and return; a unique
* solution can not be found.
*
INFO = K
RETURN
END IF
ELSE IF( ABS( D( K ) ).GE.ABS( DL( K ) ) ) THEN
*
* No row interchange required
*
MULT = DL( K ) / D( K )
D( K+1 ) = D( K+1 ) - MULT*DU( K )
DO 10 J = 1, NRHS
B( K+1, J ) = B( K+1, J ) - MULT*B( K, J )
10 CONTINUE
IF( K.LT.( N-1 ) )
$ DL( K ) = ZERO
ELSE
*
* Interchange rows K and K+1
*
MULT = D( K ) / DL( K )
D( K ) = DL( K )
TEMP = D( K+1 )
D( K+1 ) = DU( K ) - MULT*TEMP
IF( K.LT.( N-1 ) ) THEN
DL( K ) = DU( K+1 )
DU( K+1 ) = -MULT*DL( K )
END IF
DU( K ) = TEMP
DO 20 J = 1, NRHS
TEMP = B( K, J )
B( K, J ) = B( K+1, J )
B( K+1, J ) = TEMP - MULT*B( K+1, J )
20 CONTINUE
END IF
30 CONTINUE
IF( D( N ).EQ.ZERO ) THEN
INFO = N
RETURN
END IF
*
* Back solve with the matrix U from the factorization.
*
DO 50 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 40 K = N - 2, 1, -1
B( K, J ) = ( B( K, J )-DU( K )*B( K+1, J )-DL( K )*
$ B( K+2, J ) ) / D( K )
40 CONTINUE
50 CONTINUE
*
RETURN
*
* End of SGTSV
*
END
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