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242 lines
6.6 KiB
242 lines
6.6 KiB
2 years ago
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*> \brief <b> ZGTSV computes the solution to system of linear equations A * X = B for GT matrices </b>
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download ZGTSV + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgtsv.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgtsv.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgtsv.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZGTSV solves the equation
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*>
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*> A*X = B,
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*>
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*> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
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*> partial pivoting.
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*>
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*> Note that the equation A**T *X = B may be solved by interchanging the
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*> order of the arguments DU and DL.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of right hand sides, i.e., the number of columns
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*> of the matrix B. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] DL
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*> \verbatim
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*> DL is COMPLEX*16 array, dimension (N-1)
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*> On entry, DL must contain the (n-1) subdiagonal elements of
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*> A.
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*> On exit, DL is overwritten by the (n-2) elements of the
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*> second superdiagonal of the upper triangular matrix U from
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*> the LU factorization of A, in DL(1), ..., DL(n-2).
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*> \endverbatim
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*>
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*> \param[in,out] D
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*> \verbatim
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*> D is COMPLEX*16 array, dimension (N)
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*> On entry, D must contain the diagonal elements of A.
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*> On exit, D is overwritten by the n diagonal elements of U.
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*> \endverbatim
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*>
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*> \param[in,out] DU
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*> \verbatim
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*> DU is COMPLEX*16 array, dimension (N-1)
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*> On entry, DU must contain the (n-1) superdiagonal elements
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*> of A.
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*> On exit, DU is overwritten by the (n-1) elements of the first
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*> superdiagonal of U.
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is COMPLEX*16 array, dimension (LDB,NRHS)
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*> On entry, the N-by-NRHS right hand side matrix B.
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*> On exit, if INFO = 0, the N-by-NRHS solution matrix X.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> > 0: if INFO = i, U(i,i) is exactly zero, and the solution
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*> has not been computed. The factorization has not been
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*> completed unless i = N.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complex16GTsolve
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*
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* =====================================================================
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SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
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*
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* -- LAPACK driver routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX*16 ZERO
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PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER J, K
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COMPLEX*16 MULT, TEMP, ZDUM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, DIMAG, MAX
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Statement Functions ..
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DOUBLE PRECISION CABS1
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* ..
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* .. Statement Function definitions ..
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CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
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* ..
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* .. Executable Statements ..
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*
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INFO = 0
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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZGTSV ', -INFO )
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RETURN
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END IF
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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DO 30 K = 1, N - 1
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IF( DL( K ).EQ.ZERO ) THEN
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*
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* Subdiagonal is zero, no elimination is required.
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*
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IF( D( K ).EQ.ZERO ) THEN
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*
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* Diagonal is zero: set INFO = K and return; a unique
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* solution can not be found.
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*
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INFO = K
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RETURN
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END IF
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ELSE IF( CABS1( D( K ) ).GE.CABS1( DL( K ) ) ) THEN
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*
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* No row interchange required
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*
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MULT = DL( K ) / D( K )
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D( K+1 ) = D( K+1 ) - MULT*DU( K )
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DO 10 J = 1, NRHS
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B( K+1, J ) = B( K+1, J ) - MULT*B( K, J )
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10 CONTINUE
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IF( K.LT.( N-1 ) )
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$ DL( K ) = ZERO
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ELSE
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*
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* Interchange rows K and K+1
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*
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MULT = D( K ) / DL( K )
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D( K ) = DL( K )
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TEMP = D( K+1 )
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D( K+1 ) = DU( K ) - MULT*TEMP
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IF( K.LT.( N-1 ) ) THEN
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DL( K ) = DU( K+1 )
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DU( K+1 ) = -MULT*DL( K )
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END IF
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DU( K ) = TEMP
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DO 20 J = 1, NRHS
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TEMP = B( K, J )
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B( K, J ) = B( K+1, J )
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B( K+1, J ) = TEMP - MULT*B( K+1, J )
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20 CONTINUE
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END IF
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30 CONTINUE
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IF( D( N ).EQ.ZERO ) THEN
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INFO = N
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RETURN
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END IF
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*
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* Back solve with the matrix U from the factorization.
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*
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DO 50 J = 1, NRHS
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B( N, J ) = B( N, J ) / D( N )
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IF( N.GT.1 )
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$ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
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DO 40 K = N - 2, 1, -1
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B( K, J ) = ( B( K, J )-DU( K )*B( K+1, J )-DL( K )*
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$ B( K+2, J ) ) / D( K )
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40 CONTINUE
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50 CONTINUE
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*
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RETURN
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*
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* End of ZGTSV
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*
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END
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