sbmv(3F)
dsbmv, ssbmv, zhbmv, chbmv - BLAS Level Two (Symmetric/Hermitian) Banded Matrix - Vector Product
As shipped in IRIX 6.5. First release of IRIX 6.5.
NAME dsbmv, ssbmv, zhbmv, chbmv - BLAS Level Two (Symmetric/Hermitian) Banded Matrix - Vector Product FORTRAN 77 SYNOPSIS subroutine dsbmv( uplo,n,k,alpha,a,lda,x,incx,beta,y,incy ) character*1 uplo integer n, k, lda, incx, incy double precision alpha, beta double precision a( lda,*), x(*), y(*) subroutine ssbmv( uplo,n,k,alpha,a,lda,x,incx,beta,y,incy ) character*1 uplo integer n, k, lda, incx, incy real alpha, beta real a( lda,*), x(*), y(*) subroutine zhbmv( uplo,n,k,alpha,a,lda,x,incx,beta,y,incy ) character*1 uplo integer n, k, lda, incx, incy double complex alpha, beta double complex a( lda,*), x(*), y(*) subroutine chbmv( uplo,n,k,alpha,a,lda,x,incx,beta,y,incy ) character*1 uplo integer n, k, lda, incx, incy complex alpha, beta complex a( lda,*), x(*), y(*) C SYNOPSIS void dsbmv( uplo,n,k,alpha,a,lda,x,incx,beta,y,incy ) MatrixTriangle uplo; Integer n, k, lda, incx, incy; double alpha, beta; double (*a)[lda*n], (*x)[ n ], (*y)[ n ]; void ssbmv( uplo,n,k,alpha,a,lda,x,incx,beta,y,incy ) MatrixTriangle uplo; Integer n, k, lda, incx, incy; float alpha, beta; float (*a)[lda*n], (*x)[ n ], (*y)[ n ]; void zhbmv( uplo,n,k,alpha,a,lda,x,incx,beta,y,incy ) MatrixTriangle uplo; Integer n, k, lda, incx, incy; Zomplex alpha, beta; Zomplex (*a)[lda*n], (*x)[ n ], (*y)[ n ]; void chbmv( uplo,n,k,alpha,a,lda,x,incx,beta,y,incy ) MatrixTriangle uplo; Integer n, k, lda, incx, incy; Complex alpha, beta; Complex (*a)[lda*n], (*x)[ n ], (*y)[ n ]; DESCRIPTION dsbmv , ssbmv , dhbmv and chbmv perform 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/hermitian band matrix, with k super-diagonals. PARAMETERS uplo On entry, uplo specifies whether the upper or lower triangular part of the matrix A is being supplied as follows: FORTRAN 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. C uplo = UpperTriangle The upper triangular part of A is being supplied. uplo = LowerTriangle The lower triangular part of A is being supplied. Unchanged on exit. n On entry, n specifies the the order of the matrix A. n must be at least zero. Unchanged on exit. alpha specifies the scalar alpha. Unchanged on exit. a An array containing the matrix A. FORTRAN Array of dimension ( lda, n ). C A pointer to an array of size lda*n. See note below about array storage convention for C. Before entry with uplo = 'U' or 'u' or , the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the symmetric/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 symmetric/hermitian band matrix from conventional full matrix storage to band storage: FORTRAN 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 C for ( j = 0; j < n; j++ ) { m = k - j; for ( i = MAX(0, j-k); i < j ) a( j*lda + m+i ) = Matrix( j*ldm + i ); } Before entry with UPLO = 'L' or 'l' or , the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the symmetric/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 symmetric/hermitian band matrix from conventional full matrix storage to band storage: FORTRAN 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 C for ( j = 0; j < n; j++ ) { m = 1 - j; for ( i = j; i < MIN( n, j+k ); i++ ) a( j*lda + m+i ) = Matrix( j*ldm + i ); } Unchanged on exit. lda 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 Array of size at least ( 1 + ( n - 1 )*abs( incx ) ). Before entry, the incremented array x must contain the n element vector x. Unchanged on exit. incx On entry, incx specifies the increment for the elements of x. incx must not be zero. Unchanged on exit. beta On entry, beta specifies the scalar beta. When beta is supplied as zero then y need not be set on input. Unchanged on exit. y Array of size at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array y must contain the n element vector y. On exit, y is overwritten by the updated vector y. incy On entry, incy specifies the increment for the elements of y. incy must not be zero. Unchanged on exit. C ARRAY STORAGE CONVENTION The matrices are assumed to be stored in a one dimensional C array in an analogous fashion as a Fortran array (column major). Therefore, the element A(i+1,j) of matrix A is stored immediately after the element A(i,j), while A(i,j+1) is lda elements apart from A(i,j). The element A(i,j) of the matrix can be accessed directly by reference to a[ (j-1)*lda + (i-1) ]. AUTHORS Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd. TUNING DSBMV and SSBMV are optimized and parallelized for SGI R3000 and R4x00 platforms. ZHBMV and CHBMV are optimized and parallelized for SGI R3000, R4x00 and R8000 platforms.