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cgtsv.f
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*> \brief <b> CGTSV 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 CGTSV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgtsv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgtsv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgtsv.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
* COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CGTSV 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 COMPLEX 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).
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> D is COMPLEX 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 COMPLEX 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.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX 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.
*> \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 complexGTsolve
*
* =====================================================================
SUBROUTINE CGTSV( 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 ..
COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ZERO
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER J, K
COMPLEX MULT, TEMP, ZDUM
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, AIMAG, MAX, REAL
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Statement Functions ..
REAL CABS1
* ..
* .. Statement Function definitions ..
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
* ..
* .. 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( 'CGTSV ', -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( CABS1( D( K ) ).GE.CABS1( 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 CGTSV
*
END