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SUBROUTINE ZLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
$ B, LDB ) * * -- LAPACK auxiliary routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. CHARACTER TRANS INTEGER LDB, LDX, N, NRHS DOUBLE PRECISION ALPHA, BETA * .. * .. Array Arguments .. COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), $ X( LDX, * ) * .. * * Purpose * ======= * * ZLAGTM 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. * * Arguments * ========= * * TRANS (input) 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 * * N (input) INTEGER * The order of the matrix A. N >= 0. * * NRHS (input) INTEGER * The number of right hand sides, i.e., the number of columns * of the matrices X and B. * * ALPHA (input) DOUBLE PRECISION * The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise, * it is assumed to be 0. * * DL (input) COMPLEX*16 array, dimension (N-1) * The (n-1) sub-diagonal elements of T. * * D (input) COMPLEX*16 array, dimension (N) * The diagonal elements of T. * * DU (input) COMPLEX*16 array, dimension (N-1) * The (n-1) super-diagonal elements of T. * * X (input) COMPLEX*16 array, dimension (LDX,NRHS) * The N by NRHS matrix X. * LDX (input) INTEGER * The leading dimension of the array X. LDX >= max(N,1). * * BETA (input) DOUBLE PRECISION * The scalar beta. BETA must be 0., 1., or -1.; otherwise, * it is assumed to be 1. * * B (input/output) COMPLEX*16 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. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(N,1). * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Intrinsic Functions .. INTRINSIC DCONJG * .. * .. 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 ) + DCONJG( D( 1 ) )*X( 1, J ) ELSE B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J ) + $ DCONJG( DL( 1 ) )*X( 2, J ) B( N, J ) = B( N, J ) + DCONJG( DU( N-1 ) )* $ X( N-1, J ) + DCONJG( D( N ) )*X( N, J ) DO 90 I = 2, N - 1 B( I, J ) = B( I, J ) + DCONJG( DU( I-1 ) )* $ X( I-1, J ) + DCONJG( D( I ) )* $ X( I, J ) + DCONJG( 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 ) - DCONJG( D( 1 ) )*X( 1, J ) ELSE B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J ) - $ DCONJG( DL( 1 ) )*X( 2, J ) B( N, J ) = B( N, J ) - DCONJG( DU( N-1 ) )* $ X( N-1, J ) - DCONJG( D( N ) )*X( N, J ) DO 150 I = 2, N - 1 B( I, J ) = B( I, J ) - DCONJG( DU( I-1 ) )* $ X( I-1, J ) - DCONJG( D( I ) )* $ X( I, J ) - DCONJG( DL( I ) )* $ X( I+1, J ) 150 CONTINUE END IF 160 CONTINUE END IF END IF RETURN * * End of ZLAGTM * END |