*> \brief \b ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGTTS2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB ) * * .. Scalar Arguments .. * INTEGER ITRANS, LDB, N, NRHS * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGTTS2 solves one of the systems of equations *> A * X = B, A**T * X = B, or A**H * X = B, *> with a tridiagonal matrix A using the LU factorization computed *> by ZGTTRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] ITRANS *> \verbatim *> ITRANS is INTEGER *> Specifies the form of the system of equations. *> = 0: A * X = B (No transpose) *> = 1: A**T * X = B (Transpose) *> = 2: A**H * X = B (Conjugate transpose) *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. *> \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] DL *> \verbatim *> DL is COMPLEX*16 array, dimension (N-1) *> The (n-1) multipliers that define the matrix L from the *> LU factorization of A. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is COMPLEX*16 array, dimension (N) *> The n diagonal elements of the upper triangular matrix U from *> the LU factorization of A. *> \endverbatim *> *> \param[in] DU *> \verbatim *> DU is COMPLEX*16 array, dimension (N-1) *> The (n-1) elements of the first super-diagonal of U. *> \endverbatim *> *> \param[in] DU2 *> \verbatim *> DU2 is COMPLEX*16 array, dimension (N-2) *> The (n-2) elements of the second super-diagonal of U. *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> The pivot indices; for 1 <= i <= n, row i of the matrix was *> interchanged with row IPIV(i). IPIV(i) will always be either *> i or i+1; IPIV(i) = i indicates a row interchange was not *> required. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB,NRHS) *> On entry, the matrix of right hand side vectors B. *> On exit, B is overwritten by the solution vectors X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16GTcomputational * * ===================================================================== SUBROUTINE ZGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB ) * * -- LAPACK computational 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 ITRANS, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, J COMPLEX*16 TEMP * .. * .. Intrinsic Functions .. INTRINSIC DCONJG * .. * .. Executable Statements .. * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) \$ RETURN * IF( ITRANS.EQ.0 ) THEN * * Solve A*X = B using the LU factorization of A, * overwriting each right hand side vector with its solution. * IF( NRHS.LE.1 ) THEN J = 1 10 CONTINUE * * Solve L*x = b. * DO 20 I = 1, N - 1 IF( IPIV( I ).EQ.I ) THEN B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J ) ELSE TEMP = B( I, J ) B( I, J ) = B( I+1, J ) B( I+1, J ) = TEMP - DL( I )*B( I, J ) END IF 20 CONTINUE * * Solve U*x = b. * 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 30 I = N - 2, 1, -1 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )* \$ B( I+2, J ) ) / D( I ) 30 CONTINUE IF( J.LT.NRHS ) THEN J = J + 1 GO TO 10 END IF ELSE DO 60 J = 1, NRHS * * Solve L*x = b. * DO 40 I = 1, N - 1 IF( IPIV( I ).EQ.I ) THEN B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J ) ELSE TEMP = B( I, J ) B( I, J ) = B( I+1, J ) B( I+1, J ) = TEMP - DL( I )*B( I, J ) END IF 40 CONTINUE * * Solve U*x = b. * 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 50 I = N - 2, 1, -1 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )* \$ B( I+2, J ) ) / D( I ) 50 CONTINUE 60 CONTINUE END IF ELSE IF( ITRANS.EQ.1 ) THEN * * Solve A**T * X = B. * IF( NRHS.LE.1 ) THEN J = 1 70 CONTINUE * * Solve U**T * x = b. * B( 1, J ) = B( 1, J ) / D( 1 ) IF( N.GT.1 ) \$ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 ) DO 80 I = 3, N B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )* \$ B( I-2, J ) ) / D( I ) 80 CONTINUE * * Solve L**T * x = b. * DO 90 I = N - 1, 1, -1 IF( IPIV( I ).EQ.I ) THEN B( I, J ) = B( I, J ) - DL( I )*B( I+1, J ) ELSE TEMP = B( I+1, J ) B( I+1, J ) = B( I, J ) - DL( I )*TEMP B( I, J ) = TEMP END IF 90 CONTINUE IF( J.LT.NRHS ) THEN J = J + 1 GO TO 70 END IF ELSE DO 120 J = 1, NRHS * * Solve U**T * x = b. * B( 1, J ) = B( 1, J ) / D( 1 ) IF( N.GT.1 ) \$ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 ) DO 100 I = 3, N B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )- \$ DU2( I-2 )*B( I-2, J ) ) / D( I ) 100 CONTINUE * * Solve L**T * x = b. * DO 110 I = N - 1, 1, -1 IF( IPIV( I ).EQ.I ) THEN B( I, J ) = B( I, J ) - DL( I )*B( I+1, J ) ELSE TEMP = B( I+1, J ) B( I+1, J ) = B( I, J ) - DL( I )*TEMP B( I, J ) = TEMP END IF 110 CONTINUE 120 CONTINUE END IF ELSE * * Solve A**H * X = B. * IF( NRHS.LE.1 ) THEN J = 1 130 CONTINUE * * Solve U**H * x = b. * B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) ) IF( N.GT.1 ) \$ B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) ) / \$ DCONJG( D( 2 ) ) DO 140 I = 3, N B( I, J ) = ( B( I, J )-DCONJG( DU( I-1 ) )*B( I-1, J )- \$ DCONJG( DU2( I-2 ) )*B( I-2, J ) ) / \$ DCONJG( D( I ) ) 140 CONTINUE * * Solve L**H * x = b. * DO 150 I = N - 1, 1, -1 IF( IPIV( I ).EQ.I ) THEN B( I, J ) = B( I, J ) - DCONJG( DL( I ) )*B( I+1, J ) ELSE TEMP = B( I+1, J ) B( I+1, J ) = B( I, J ) - DCONJG( DL( I ) )*TEMP B( I, J ) = TEMP END IF 150 CONTINUE IF( J.LT.NRHS ) THEN J = J + 1 GO TO 130 END IF ELSE DO 180 J = 1, NRHS * * Solve U**H * x = b. * B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) ) IF( N.GT.1 ) \$ B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) ) \$ / DCONJG( D( 2 ) ) DO 160 I = 3, N B( I, J ) = ( B( I, J )-DCONJG( DU( I-1 ) )* \$ B( I-1, J )-DCONJG( DU2( I-2 ) )* \$ B( I-2, J ) ) / DCONJG( D( I ) ) 160 CONTINUE * * Solve L**H * x = b. * DO 170 I = N - 1, 1, -1 IF( IPIV( I ).EQ.I ) THEN B( I, J ) = B( I, J ) - DCONJG( DL( I ) )* \$ B( I+1, J ) ELSE TEMP = B( I+1, J ) B( I+1, J ) = B( I, J ) - DCONJG( DL( I ) )*TEMP B( I, J ) = TEMP END IF 170 CONTINUE 180 CONTINUE END IF END IF * * End of ZGTTS2 * END