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SUBROUTINE CLAPTM( UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B,
$ LDB ) * * -- LAPACK auxiliary routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDB, LDX, N, NRHS REAL ALPHA, BETA * .. * .. Array Arguments .. REAL D( * ) COMPLEX B( LDB, * ), E( * ), X( LDX, * ) * .. * * Purpose * ======= * * CLAPTM multiplies an N by NRHS matrix X by a Hermitian tridiagonal * matrix A and stores the result in a matrix B. The operation has the * form * * B := alpha * A * X + beta * B * * where alpha may be either 1. or -1. and beta may be 0., 1., or -1. * * Arguments * ========= * * UPLO (input) CHARACTER * Specifies whether the superdiagonal or the subdiagonal of the * tridiagonal matrix A is stored. * = 'U': Upper, E is the superdiagonal of A. * = 'L': Lower, E is the subdiagonal of A. * * 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) REAL * The scalar alpha. ALPHA must be 1. or -1.; otherwise, * it is assumed to be 0. * * D (input) REAL array, dimension (N) * The n diagonal elements of the tridiagonal matrix A. * * E (input) COMPLEX array, dimension (N-1) * The (n-1) subdiagonal or superdiagonal elements of A. * * X (input) COMPLEX 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) REAL * The scalar beta. BETA must be 0., 1., or -1.; otherwise, * it is assumed to be 1. * * B (input/output) 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. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(N,1). * * ===================================================================== * * .. 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 * 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( UPLO, 'U' ) ) THEN * * Compute B := B + A*X, where E is the superdiagonal of A. * 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 ) + $ E( 1 )*X( 2, J ) B( N, J ) = B( N, J ) + CONJG( E( N-1 ) )* $ X( N-1, J ) + D( N )*X( N, J ) DO 50 I = 2, N - 1 B( I, J ) = B( I, J ) + CONJG( E( I-1 ) )* $ X( I-1, J ) + D( I )*X( I, J ) + $ E( I )*X( I+1, J ) 50 CONTINUE END IF 60 CONTINUE ELSE * * Compute B := B + A*X, where E is the subdiagonal of A. * 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 ) + $ CONJG( E( 1 ) )*X( 2, J ) B( N, J ) = B( N, J ) + E( N-1 )*X( N-1, J ) + $ D( N )*X( N, J ) DO 70 I = 2, N - 1 B( I, J ) = B( I, J ) + E( I-1 )*X( I-1, J ) + $ D( I )*X( I, J ) + $ CONJG( E( I ) )*X( I+1, J ) 70 CONTINUE END IF 80 CONTINUE END IF ELSE IF( ALPHA.EQ.-ONE ) THEN IF( LSAME( UPLO, 'U' ) ) THEN * * Compute B := B - A*X, where E is the superdiagonal of A. * DO 100 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 ) - $ E( 1 )*X( 2, J ) B( N, J ) = B( N, J ) - CONJG( E( N-1 ) )* $ X( N-1, J ) - D( N )*X( N, J ) DO 90 I = 2, N - 1 B( I, J ) = B( I, J ) - CONJG( E( I-1 ) )* $ X( I-1, J ) - D( I )*X( I, J ) - $ E( I )*X( I+1, J ) 90 CONTINUE END IF 100 CONTINUE ELSE * * Compute B := B - A*X, where E is the subdiagonal of A. * 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 ) - $ CONJG( E( 1 ) )*X( 2, J ) B( N, J ) = B( N, J ) - E( N-1 )*X( N-1, J ) - $ D( N )*X( N, J ) DO 110 I = 2, N - 1 B( I, J ) = B( I, J ) - E( I-1 )*X( I-1, J ) - $ D( I )*X( I, J ) - $ CONJG( E( I ) )*X( I+1, J ) 110 CONTINUE END IF 120 CONTINUE END IF END IF RETURN * * End of CLAPTM * END |