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*> \brief <b> SGTSV computes the solution to system of linear equations A * X = B for GT matrices </b>
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SGTSV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgtsv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgtsv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgtsv.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
* REAL B( LDB, * ), D( * ), DL( * ), DU( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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**T*X = B may be solved by interchanging the
*> order of the arguments DU and DL.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of right hand sides, i.e., the number of columns
*> of the matrix B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in,out] DL
*> \verbatim
*> DL is 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).
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> D is 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.
*> \endverbatim
*>
*> \param[in,out] DU
*> \verbatim
*> DU is 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.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is 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.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup realGTsolve
*
* =====================================================================
SUBROUTINE SGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
* -- LAPACK driver routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
REAL B( LDB, * ), D( * ), DL( * ), DU( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO
PARAMETER ( ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, J
REAL 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( 'SGTSV ', -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 SGTSV
*
END
|
