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SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) |
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* .. Scalar Arguments .. |
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DOUBLE PRECISION ALPHA,BETA |
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INTEGER INCX,INCY,K,LDA,N |
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CHARACTER UPLO |
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* .. |
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* .. Array Arguments .. |
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DOUBLE PRECISION A(LDA,*),X(*),Y(*) |
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* .. |
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* |
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* Purpose |
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* ======= |
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* |
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* DSBMV performs the matrix-vector operation |
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* |
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* y := alpha*A*x + beta*y, |
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* |
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* where alpha and beta are scalars, x and y are n element vectors and |
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* A is an n by n symmetric band matrix, with k super-diagonals. |
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* |
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* Arguments |
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* ========== |
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* |
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* UPLO - CHARACTER*1. |
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* On entry, UPLO specifies whether the upper or lower |
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* triangular part of the band matrix A is being supplied as |
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* follows: |
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* |
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* UPLO = 'U' or 'u' The upper triangular part of A is |
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* being supplied. |
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* |
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* UPLO = 'L' or 'l' The lower triangular part of A is |
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* being supplied. |
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* |
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* Unchanged on exit. |
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* |
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* N - INTEGER. |
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* On entry, N specifies the order of the matrix A. |
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* N must be at least zero. |
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* Unchanged on exit. |
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* |
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* K - INTEGER. |
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* On entry, K specifies the number of super-diagonals of the |
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* matrix A. K must satisfy 0 .le. K. |
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* Unchanged on exit. |
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* |
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* ALPHA - DOUBLE PRECISION. |
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* On entry, ALPHA specifies the scalar alpha. |
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* Unchanged on exit. |
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* |
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* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). |
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* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) |
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* by n part of the array A must contain the upper triangular |
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* band part of the symmetric matrix, supplied column by |
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* column, with the leading diagonal of the matrix in row |
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* ( k + 1 ) of the array, the first super-diagonal starting at |
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* position 2 in row k, and so on. The top left k by k triangle |
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* of the array A is not referenced. |
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* The following program segment will transfer the upper |
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* triangular part of a symmetric band matrix from conventional |
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* full matrix storage to band storage: |
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* |
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* DO 20, J = 1, N |
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* M = K + 1 - J |
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* DO 10, I = MAX( 1, J - K ), J |
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* A( M + I, J ) = matrix( I, J ) |
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* 10 CONTINUE |
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* 20 CONTINUE |
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* |
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* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) |
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* by n part of the array A must contain the lower triangular |
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* band part of the symmetric matrix, supplied column by |
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* column, with the leading diagonal of the matrix in row 1 of |
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* the array, the first sub-diagonal starting at position 1 in |
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* row 2, and so on. The bottom right k by k triangle of the |
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* array A is not referenced. |
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* The following program segment will transfer the lower |
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* triangular part of a symmetric band matrix from conventional |
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* full matrix storage to band storage: |
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* |
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* DO 20, J = 1, N |
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* M = 1 - J |
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* DO 10, I = J, MIN( N, J + K ) |
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* A( M + I, J ) = matrix( I, J ) |
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* 10 CONTINUE |
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* 20 CONTINUE |
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* |
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* Unchanged on exit. |
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* |
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* LDA - INTEGER. |
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* On entry, LDA specifies the first dimension of A as declared |
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* in the calling (sub) program. LDA must be at least |
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* ( k + 1 ). |
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* Unchanged on exit. |
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* |
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* X - DOUBLE PRECISION array of DIMENSION at least |
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* ( 1 + ( n - 1 )*abs( INCX ) ). |
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* Before entry, the incremented array X must contain the |
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* vector x. |
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* Unchanged on exit. |
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* |
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* INCX - INTEGER. |
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* On entry, INCX specifies the increment for the elements of |
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* X. INCX must not be zero. |
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* Unchanged on exit. |
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* |
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* BETA - DOUBLE PRECISION. |
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* On entry, BETA specifies the scalar beta. |
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* Unchanged on exit. |
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* |
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* Y - DOUBLE PRECISION array of DIMENSION at least |
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* ( 1 + ( n - 1 )*abs( INCY ) ). |
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* Before entry, the incremented array Y must contain the |
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* vector y. On exit, Y is overwritten by the updated vector y. |
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* |
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* INCY - INTEGER. |
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* On entry, INCY specifies the increment for the elements of |
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* Y. INCY must not be zero. |
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* Unchanged on exit. |
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* |
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* |
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* Level 2 Blas routine. |
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* |
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* -- Written on 22-October-1986. |
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* Jack Dongarra, Argonne National Lab. |
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* Jeremy Du Croz, Nag Central Office. |
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* Sven Hammarling, Nag Central Office. |
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* Richard Hanson, Sandia National Labs. |
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* |
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* |
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* .. Parameters .. |
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DOUBLE PRECISION ONE,ZERO |
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PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) |
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* .. |
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* .. Local Scalars .. |
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DOUBLE PRECISION TEMP1,TEMP2 |
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INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L |
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* .. |
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* .. External Functions .. |
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LOGICAL LSAME |
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EXTERNAL LSAME |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL XERBLA |
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* .. |
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* .. Intrinsic Functions .. |
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INTRINSIC MAX,MIN |
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* .. |
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* |
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* Test the input parameters. |
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* |
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INFO = 0 |
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IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN |
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INFO = 1 |
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ELSE IF (N.LT.0) THEN |
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INFO = 2 |
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ELSE IF (K.LT.0) THEN |
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INFO = 3 |
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ELSE IF (LDA.LT. (K+1)) THEN |
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INFO = 6 |
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ELSE IF (INCX.EQ.0) THEN |
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INFO = 8 |
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ELSE IF (INCY.EQ.0) THEN |
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INFO = 11 |
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END IF |
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IF (INFO.NE.0) THEN |
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CALL XERBLA('DSBMV ',INFO)
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RETURN |
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END IF |
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* |
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* Quick return if possible. |
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* |
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IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN |
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* |
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* Set up the start points in X and Y. |
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* |
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IF (INCX.GT.0) THEN |
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KX = 1 |
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ELSE |
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KX = 1 - (N-1)*INCX |
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END IF |
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IF (INCY.GT.0) THEN |
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KY = 1 |
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ELSE |
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KY = 1 - (N-1)*INCY |
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END IF |
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* |
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* Start the operations. In this version the elements of the array A |
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* are accessed sequentially with one pass through A. |
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* |
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* First form y := beta*y. |
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* |
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IF (BETA.NE.ONE) THEN |
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IF (INCY.EQ.1) THEN |
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IF (BETA.EQ.ZERO) THEN |
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DO 10 I = 1,N |
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Y(I) = ZERO |
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10 CONTINUE |
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ELSE |
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DO 20 I = 1,N |
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Y(I) = BETA*Y(I) |
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20 CONTINUE |
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END IF |
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ELSE |
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IY = KY |
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IF (BETA.EQ.ZERO) THEN |
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DO 30 I = 1,N |
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Y(IY) = ZERO |
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IY = IY + INCY |
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30 CONTINUE |
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ELSE |
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DO 40 I = 1,N |
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Y(IY) = BETA*Y(IY) |
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IY = IY + INCY |
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40 CONTINUE |
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END IF |
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END IF |
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END IF |
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IF (ALPHA.EQ.ZERO) RETURN |
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IF (LSAME(UPLO,'U')) THEN |
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* |
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* Form y when upper triangle of A is stored. |
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* |
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KPLUS1 = K + 1 |
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IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN |
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DO 60 J = 1,N |
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TEMP1 = ALPHA*X(J) |
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TEMP2 = ZERO |
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L = KPLUS1 - J |
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DO 50 I = MAX(1,J-K),J - 1 |
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Y(I) = Y(I) + TEMP1*A(L+I,J) |
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TEMP2 = TEMP2 + A(L+I,J)*X(I) |
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50 CONTINUE |
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Y(J) = Y(J) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2 |
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60 CONTINUE |
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ELSE |
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JX = KX |
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JY = KY |
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DO 80 J = 1,N |
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TEMP1 = ALPHA*X(JX) |
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TEMP2 = ZERO |
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IX = KX |
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IY = KY |
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L = KPLUS1 - J |
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DO 70 I = MAX(1,J-K),J - 1 |
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Y(IY) = Y(IY) + TEMP1*A(L+I,J) |
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TEMP2 = TEMP2 + A(L+I,J)*X(IX) |
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IX = IX + INCX |
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IY = IY + INCY |
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70 CONTINUE |
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Y(JY) = Y(JY) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2 |
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JX = JX + INCX |
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JY = JY + INCY |
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IF (J.GT.K) THEN |
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KX = KX + INCX |
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KY = KY + INCY |
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END IF |
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80 CONTINUE |
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END IF |
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ELSE |
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* |
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* Form y when lower triangle of A is stored. |
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* |
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IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN |
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DO 100 J = 1,N |
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TEMP1 = ALPHA*X(J) |
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TEMP2 = ZERO |
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Y(J) = Y(J) + TEMP1*A(1,J) |
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L = 1 - J |
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DO 90 I = J + 1,MIN(N,J+K) |
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Y(I) = Y(I) + TEMP1*A(L+I,J) |
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TEMP2 = TEMP2 + A(L+I,J)*X(I) |
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90 CONTINUE |
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Y(J) = Y(J) + ALPHA*TEMP2 |
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100 CONTINUE |
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ELSE |
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JX = KX |
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JY = KY |
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DO 120 J = 1,N |
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TEMP1 = ALPHA*X(JX) |
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TEMP2 = ZERO |
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Y(JY) = Y(JY) + TEMP1*A(1,J) |
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L = 1 - J |
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IX = JX |
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IY = JY |
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DO 110 I = J + 1,MIN(N,J+K) |
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IX = IX + INCX |
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IY = IY + INCY |
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Y(IY) = Y(IY) + TEMP1*A(L+I,J) |
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TEMP2 = TEMP2 + A(L+I,J)*X(IX) |
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110 CONTINUE |
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Y(JY) = Y(JY) + ALPHA*TEMP2 |
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JX = JX + INCX |
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JY = JY + INCY |
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120 CONTINUE |
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END IF |
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END IF |
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* |
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RETURN |
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* |
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* End of DSBMV . |
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* |
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END |