DTBMV - Online Linux Manual PageSection : 1
Updated : November 2008
Source : BLAS routine
Note : BLAS routine
NAMEDTBMV - performs one of the matrix-vector operations x := A*x, or x := A'*x,

SYNOPSISSUBROUTINE DTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)    INTEGER INCX,K,LDA,N  CHARACTER DIAG,TRANS,UPLO  DOUBLE PRECISION A(LDA,*),X(*)

PURPOSEDTBMV performs one of the matrix-vector operations where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.

ARGUMENTSUPLO - CHARACTER*1.  
On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix. Unchanged on exit.
TRANS - CHARACTER*1.  
On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' x := A*x. TRANS = 'T' or 't' x := A'*x. TRANS = 'C' or 'c' x := A'*x. Unchanged on exit.
DIAG - CHARACTER*1.  
On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular. 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 with UPLO = 'U' or 'u', K specifies the number of super-diagonals of the matrix A. On entry with UPLO = 'L' or 'l', K specifies the number of sub-diagonals of the matrix A. K must satisfy 0 .le. K. Unchanged on exit.
A - DOUBLE PRECISION array of 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 matrix of coefficients, 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 an upper triangular 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 matrix of coefficients, 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 a lower triangular 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 Note that when DIAG = 'U' or 'u' the elements of the array A corresponding to the diagonal elements of the matrix are not referenced, but are assumed to be unity. 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 - DOUBLE PRECISION array of dimension at least  
( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the tranformed vector x.
INCX - INTEGER.  
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.

FURTHER DETAILSLevel 2 Blas routine. -- Written on 22-October-1986.
   Jack Dongarra, Argonne National Lab.
   Jeremy Du Croz, Nag Central Office.
   Sven Hammarling, Nag Central Office.
   Richard Hanson, Sandia National Labs.

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