gbmv(3F)
dgbmv, sgbmv, zgbmv, cgbmv - BLAS Level Two Matrix-Vector Product
As shipped in IRIX 6.5. First release of IRIX 6.5.
NAME dgbmv, sgbmv, zgbmv, cgbmv - BLAS Level Two Matrix-Vector Product FORTRAN 77 SYNOPSIS subroutine dgbmv( trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy ) character*1 trans integer n, m, kl, ku, lda, incx, incy double precision alpha, beta double precision a( lda,*), x(*), y(*) subroutine sgbmv( trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy ) character*1 trans integer n, m, kl, ku, lda, incx, incy real alpha, beta real a( lda,*), x(*), y(*) subroutine zgbmv( trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy ) character*1 trans integer n, m, kl, ku, lda, incx, incy double complex alpha, beta double complex a( lda,*), x(*), y(*) subroutine cgbmv( trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy ) character*1 trans integer n, m, kl, ku, lda, incx, incy complex alpha, beta complex a( lda,*), x(*), y(*) C SYNOPSIS void dgbmv( trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy ) MatrixTranspose trans; Integer n, m, kl, ku, lda, incx, incy; double alpha, beta; double (*a)[lda*n], (*x)[ n ], (*y)[ n ]; void sgbmv( trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy ) MatrixTranspose trans; Integer n, m, kl, ku, lda, incx, incy; float alpha, beta; float (*a)[lda*n], (*x)[ n ], (*y)[ n ]; void zgbmv( trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy ) MatrixTranspose trans; Integer n, m, kl, ku, lda, incx, incy; Zomplex alpha, beta; Zomplex (*a)[lda*n], (*x)[ n ], (*y)[ n ]; void cgbmv( trans,m,n,kl,ku,alpha,a,lda,x,incx,beta,y,incy ) MatrixTranspose trans; Integer n, m, kl, ku, lda, incx, incy; Complex alpha, beta; Complex (*a)[lda*n], (*x)[ n ], (*y)[ n ]; DESCRIPTION dgbmv, sgbmv, zgbmv and cgbmv perform one of the matrix-vector operations: y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals. PARAMETERS trans On entry, trans specifies the operation to be performed as follows: FORTRAN trans = 'N' or 'n' y := alpha*A*x + beta*y. trans = 'T' or 't' y := alpha*A'*x + beta*y. trans = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. C trans = NoTranspose y := alpha*A*x + beta*y. trans = Transpose y := alpha*A'*x + beta*y. trans = ConjugateTranspose y := alpha*conjg( A' )*x + beta*y. Unchanged on exit. m On entry, m specifies the number of rows of rows of the matrix A. m must be at least zero. Unchanged on exit. n On entry, n specifies the order of the matrix A. n must be at least zero. Unchanged on exit. kl On entry, kl specifies the number of sub-diagonals of the matrix A. kl must satisfy 0 .le. kl. Unchanged on exit. ku On entry, ku specifies the number of super-diagonals of the matrix A. ku must satisfy 0 .le. ku. Unchanged on exit. alpha On entry, 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 containing the matrix A. See note below about array storage convention for C. Before entry, the leading ( kl + ku + 1 ) by n part of the array a must contain the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( ku + 1 ) of the array, the first super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array a that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer a band matrix from conventional full matrix storage to band storage: FORTRAN DO 20 J = 1, N K = KU + 1 - J DO 10 I = MAX( 1, J - KU ), MIN( M, J + KL ) A( K + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE C for ( j=0; j<n; j++ ) { k = ku - j; for (i = MAX(0, j-ku); i < MIN(m, j+kl); i++ ) a(j*lda+k+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 ( kl + ku + 1 ). Unchanged on exit. x Array of size at least ( 1 + ( n - 1 )*abs( incx ) ) when trans = 'N' or 'n' or NoTranspose and at least ( 1 + ( m - 1 )*abs( incx ) ) otherwise. Before entry, the incremented array x must contain the 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 + ( m - 1 )*abs( incy ) ) when trans = 'N' or 'n' or NoTranspose and at least ( 1 + ( n - 1 )*abs( incy ) ) otherwise. Before entry with beta non-zero, the incremented array y must contain the 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 Optimized and parallelized for SGI R3000, R4x00 and R8000 platforms.