_SBMV,_HBMV(3F) _SBMV,_HBMV(3F)
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(*)
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;
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Integer n, k, lda, incx, incy;
Complex alpha, beta;
Complex (*a)[lda*n], (*x)[ n ], (*y)[ n ];
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.
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
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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 );
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_SBMV,_HBMV(3F) _SBMV,_HBMV(3F)
}
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) ].
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
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.
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