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SUBROUTINE CSBMV( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y,
$ INCY ) * * -- LAPACK auxiliary routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INCX, INCY, K, LDA, N COMPLEX ALPHA, BETA * .. * .. Array Arguments .. COMPLEX A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * CSBMV 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 symmetric band matrix, with k super-diagonals. * * Arguments * ========== * * 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, 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 symmetric 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 symmetric 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 symmetric 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 symmetric 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 * * 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, 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 array, 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. * * INCY - INTEGER * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * ===================================================================== * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) COMPLEX ZERO PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L COMPLEX TEMP1, TEMP2 * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. 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( 'CSBMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) ) $ RETURN * * Set up the start points in X and Y. * 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 * * 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. * IF( BETA.NE.ONE ) THEN IF( INCY.EQ.1 ) 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 ELSE 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 = 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 + A( L+I, J )*X( I ) 50 CONTINUE Y( J ) = Y( J ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80 J = 1, N TEMP1 = ALPHA*X( JX ) 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 + A( L+I, J )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 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 = ALPHA*X( J ) TEMP2 = ZERO Y( J ) = Y( J ) + TEMP1*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 + A( L+I, J )*X( I ) 90 CONTINUE Y( J ) = Y( J ) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120 J = 1, N TEMP1 = ALPHA*X( JX ) TEMP2 = ZERO Y( JY ) = Y( JY ) + TEMP1*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 + A( L+I, J )*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 CSBMV * END |