* ************************************************************************ * SUBROUTINE ECHBMV( UPLO, N, K, ALPHA, A, LDA, X, INCX, \$ BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX ALPHA, BETA INTEGER INCX, INCY, K, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 Y( * ) COMPLEX A( LDA, * ), X( * ) * .. * * Purpose * ======= * * ECHBMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n element vectors and * A is an n by n hermitian band matrix, with k super-diagonals. * Additional precision arithmetic is used in the computation. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the band matrix A is being supplied as * follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * being supplied. * * UPLO = 'L' or 'l' The lower triangular part of A is * being supplied. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry, K specifies the number of super-diagonals of the * matrix A. K must satisfy 0 .le. K. * Unchanged on exit. * * ALPHA - COMPLEX . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * A - COMPLEX array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the hermitian matrix, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer the upper * triangular part of a hemitian band matrix from conventional * full matrix storage to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the hermitian matrix, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer the lower * triangular part of a hermitian band matrix from conventional * full matrix storage to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that the imaginary parts of the diagonal elements need * not be set and are assumed to be zero. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * ( k + 1 ). * Unchanged on exit. * * X - COMPLEX array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the * vector x. * Unchanged on exit. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX must not be zero. * Unchanged on exit. * * BETA - COMPLEX . * On entry, BETA specifies the scalar beta. * Unchanged on exit. * * Y - COMPLEX*16 array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the * vector y. On exit, Y is overwritten by the updated vector y. * At least double precision arithmetic is used in the * computation of y. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * * Level 2 Blas routine. * * -- Written on 20-July-1986. * Sven Hammarling, Nag Central Office. * Richard Hanson, Sandia National Labs. * * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCMPLX, MAX, MIN, CONJG, REAL * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO, 'U' ).AND. \$ .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = 1 ELSE IF ( N.LT.0 ) THEN INFO = 2 ELSE IF ( K.LT.0 ) THEN INFO = 3 ELSE IF ( LDA.LT.( K + 1 ) ) THEN INFO = 6 ELSE IF ( INCX.EQ.0 ) THEN INFO = 8 ELSE IF ( INCY.EQ.0 ) THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ECHBMV', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) \$ RETURN * * Start the operations. In this version the elements of the array A * are accessed sequentially with one pass through A. * * First form y := beta*y and set up the start points in X and Y if * the increments are not both unity. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN IF( BETA.NE.ONE )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, N Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, N Y( I ) = BETA*Y( I ) 20 CONTINUE END IF END IF ELSE IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( N - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( N - 1 )*INCY END IF IF( BETA.NE.ONE )THEN IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, N Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, N Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) \$ RETURN IF( LSAME( UPLO, 'U' ) )THEN * * Form y when upper triangle of A is stored. * KPLUS1 = K + 1 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N TEMP1 = DCMPLX( ALPHA )*X( J ) TEMP2 = ZERO L = KPLUS1 - J DO 50, I = MAX( 1, J - K ), J - 1 Y( I ) = Y( I ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + \$ CONJG( A( L + I, J ) )*DCMPLX( X( I ) ) 50 CONTINUE Y( J ) = Y( J ) + TEMP1*REAL( A( KPLUS1, J ) ) \$ + ALPHA*TEMP2 60 CONTINUE ELSE IX = KX - INCX DO 80, J = 1, N TEMP1 = DCMPLX( ALPHA )*X( IX + INCX ) TEMP2 = ZERO IX = KX IY = KY L = KPLUS1 - J DO 70, I = MAX( 1, J - K ), J - 1 Y( IY ) = Y( IY ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + \$ CONJG( A( L + I, J ) )*DCMPLX( X( IX ) ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( IY ) = Y( IY ) + TEMP1*REAL( A( KPLUS1, J ) ) \$ + ALPHA*TEMP2 IF( J.GT.K )THEN KX = KX + INCX KY = KY + INCY END IF 80 CONTINUE END IF ELSE * * Form y when lower triangle of A is stored. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 100, J = 1, N TEMP1 = DCMPLX( ALPHA )*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*REAL( A( 1, J ) ) L = 1 - J DO 90, I = J + 1, MIN( N, J + K ) Y( I ) = Y( I ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + \$ CONJG( A( L + I, J ) )*DCMPLX( X( I ) ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120, J = 1, N TEMP1 = DCMPLX( ALPHA )*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*REAL( A( 1, J ) ) L = 1 - J IX = JX IY = JY DO 110, I = J + 1, MIN( N, J + K ) IX = IX + INCX IY = IY + INCY Y( IY ) = Y( IY ) + TEMP1*A( L + I, J ) TEMP2 = TEMP2 + \$ CONJG( A( L + I, J ) )*DCMPLX( X( IX ) ) 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of ECHBMV. * END