*> \brief \b CLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CLAGTM + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, * B, LDB ) * * .. Scalar Arguments .. * CHARACTER TRANS * INTEGER LDB, LDX, N, NRHS * REAL ALPHA, BETA * .. * .. Array Arguments .. * COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ), * $ X( LDX, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CLAGTM performs a matrix-vector product of the form *> *> B := alpha * A * X + beta * B *> *> where A is a tridiagonal matrix of order N, B and X are N by NRHS *> matrices, and alpha and beta are real scalars, each of which may be *> 0., 1., or -1. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the operation applied to A. *> = 'N': No transpose, B := alpha * A * X + beta * B *> = 'T': Transpose, B := alpha * A**T * X + beta * B *> = 'C': Conjugate transpose, B := alpha * A**H * X + beta * B *> \endverbatim *> *> \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 matrices X and B. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is REAL *> The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise, *> it is assumed to be 0. *> \endverbatim *> *> \param[in] DL *> \verbatim *> DL is COMPLEX array, dimension (N-1) *> The (n-1) sub-diagonal elements of T. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is COMPLEX array, dimension (N) *> The diagonal elements of T. *> \endverbatim *> *> \param[in] DU *> \verbatim *> DU is COMPLEX array, dimension (N-1) *> The (n-1) super-diagonal elements of T. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX array, dimension (LDX,NRHS) *> The N by NRHS matrix X. *> \endverbatim *> *> \param[in] LDX *> \verbatim *> LDX is INTEGER *> The leading dimension of the array X. LDX >= max(N,1). *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is REAL *> The scalar beta. BETA must be 0., 1., or -1.; otherwise, *> it is assumed to be 1. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX array, dimension (LDB,NRHS) *> On entry, the N by NRHS matrix B. *> On exit, B is overwritten by the matrix expression *> B := alpha * A * X + beta * B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(N,1). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complexOTHERauxiliary * * ===================================================================== SUBROUTINE CLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, $ B, LDB ) * * -- LAPACK auxiliary 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 LDB, LDX, N, NRHS REAL ALPHA, BETA * .. * .. Array Arguments .. COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ), $ X( LDX, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Intrinsic Functions .. INTRINSIC CONJG * .. * .. Executable Statements .. * IF( N.EQ.0 ) $ RETURN * * Multiply B by BETA if BETA.NE.1. * IF( BETA.EQ.ZERO ) THEN DO 20 J = 1, NRHS DO 10 I = 1, N B( I, J ) = ZERO 10 CONTINUE 20 CONTINUE ELSE IF( BETA.EQ.-ONE ) THEN DO 40 J = 1, NRHS DO 30 I = 1, N B( I, J ) = -B( I, J ) 30 CONTINUE 40 CONTINUE END IF * IF( ALPHA.EQ.ONE ) THEN IF( LSAME( TRANS, 'N' ) ) THEN * * Compute B := B + A*X * DO 60 J = 1, NRHS IF( N.EQ.1 ) THEN B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) ELSE B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) + $ DU( 1 )*X( 2, J ) B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) + $ D( N )*X( N, J ) DO 50 I = 2, N - 1 B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) + $ D( I )*X( I, J ) + DU( I )*X( I+1, J ) 50 CONTINUE END IF 60 CONTINUE ELSE IF( LSAME( TRANS, 'T' ) ) THEN * * Compute B := B + A**T * X * DO 80 J = 1, NRHS IF( N.EQ.1 ) THEN B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) ELSE B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) + $ DL( 1 )*X( 2, J ) B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) + $ D( N )*X( N, J ) DO 70 I = 2, N - 1 B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) + $ D( I )*X( I, J ) + DL( I )*X( I+1, J ) 70 CONTINUE END IF 80 CONTINUE ELSE IF( LSAME( TRANS, 'C' ) ) THEN * * Compute B := B + A**H * X * DO 100 J = 1, NRHS IF( N.EQ.1 ) THEN B( 1, J ) = B( 1, J ) + CONJG( D( 1 ) )*X( 1, J ) ELSE B( 1, J ) = B( 1, J ) + CONJG( D( 1 ) )*X( 1, J ) + $ CONJG( DL( 1 ) )*X( 2, J ) B( N, J ) = B( N, J ) + CONJG( DU( N-1 ) )* $ X( N-1, J ) + CONJG( D( N ) )*X( N, J ) DO 90 I = 2, N - 1 B( I, J ) = B( I, J ) + CONJG( DU( I-1 ) )* $ X( I-1, J ) + CONJG( D( I ) )* $ X( I, J ) + CONJG( DL( I ) )* $ X( I+1, J ) 90 CONTINUE END IF 100 CONTINUE END IF ELSE IF( ALPHA.EQ.-ONE ) THEN IF( LSAME( TRANS, 'N' ) ) THEN * * Compute B := B - A*X * DO 120 J = 1, NRHS IF( N.EQ.1 ) THEN B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) ELSE B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) - $ DU( 1 )*X( 2, J ) B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) - $ D( N )*X( N, J ) DO 110 I = 2, N - 1 B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) - $ D( I )*X( I, J ) - DU( I )*X( I+1, J ) 110 CONTINUE END IF 120 CONTINUE ELSE IF( LSAME( TRANS, 'T' ) ) THEN * * Compute B := B - A**T*X * DO 140 J = 1, NRHS IF( N.EQ.1 ) THEN B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) ELSE B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) - $ DL( 1 )*X( 2, J ) B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) - $ D( N )*X( N, J ) DO 130 I = 2, N - 1 B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) - $ D( I )*X( I, J ) - DL( I )*X( I+1, J ) 130 CONTINUE END IF 140 CONTINUE ELSE IF( LSAME( TRANS, 'C' ) ) THEN * * Compute B := B - A**H*X * DO 160 J = 1, NRHS IF( N.EQ.1 ) THEN B( 1, J ) = B( 1, J ) - CONJG( D( 1 ) )*X( 1, J ) ELSE B( 1, J ) = B( 1, J ) - CONJG( D( 1 ) )*X( 1, J ) - $ CONJG( DL( 1 ) )*X( 2, J ) B( N, J ) = B( N, J ) - CONJG( DU( N-1 ) )* $ X( N-1, J ) - CONJG( D( N ) )*X( N, J ) DO 150 I = 2, N - 1 B( I, J ) = B( I, J ) - CONJG( DU( I-1 ) )* $ X( I-1, J ) - CONJG( D( I ) )* $ X( I, J ) - CONJG( DL( I ) )* $ X( I+1, J ) 150 CONTINUE END IF 160 CONTINUE END IF END IF RETURN * * End of CLAGTM * END