*> \brief \b CGTTRS * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CGTTRS + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, * INFO ) * * .. Scalar Arguments .. * CHARACTER TRANS * INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CGTTRS 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 CGTTRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the form of the system of equations. *> = 'N': A * X = B (No transpose) *> = 'T': A**T * X = B (Transpose) *> = 'C': 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 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 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 array, dimension (N-1) *> The (n-1) elements of the first super-diagonal of U. *> \endverbatim *> *> \param[in] DU2 *> \verbatim *> DU2 is COMPLEX 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 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 *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complexGTcomputational * * ===================================================================== SUBROUTINE CGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, \$ INFO ) * * -- 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 .. CHARACTER TRANS INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL NOTRAN INTEGER ITRANS, J, JB, NB * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. External Subroutines .. EXTERNAL CGTTS2, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * INFO = 0 NOTRAN = ( TRANS.EQ.'N' .OR. TRANS.EQ.'n' ) IF( .NOT.NOTRAN .AND. .NOT.( TRANS.EQ.'T' .OR. TRANS.EQ. \$ 't' ) .AND. .NOT.( TRANS.EQ.'C' .OR. TRANS.EQ.'c' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( NRHS.LT.0 ) THEN INFO = -3 ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CGTTRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) \$ RETURN * * Decode TRANS * IF( NOTRAN ) THEN ITRANS = 0 ELSE IF( TRANS.EQ.'T' .OR. TRANS.EQ.'t' ) THEN ITRANS = 1 ELSE ITRANS = 2 END IF * * Determine the number of right-hand sides to solve at a time. * IF( NRHS.EQ.1 ) THEN NB = 1 ELSE NB = MAX( 1, ILAENV( 1, 'CGTTRS', TRANS, N, NRHS, -1, -1 ) ) END IF * IF( NB.GE.NRHS ) THEN CALL CGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB ) ELSE DO 10 J = 1, NRHS, NB JB = MIN( NRHS-J+1, NB ) CALL CGTTS2( ITRANS, N, JB, DL, D, DU, DU2, IPIV, B( 1, J ), \$ LDB ) 10 CONTINUE END IF * * End of CGTTRS * END