| SUBROUTINE CSBMVF(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 |
