*> \brief CGTSV computes the solution to system of linear equations A * X = B for GT matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CGTSV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \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