Name

stbmv, dtbmv, ctbmv, ztbmv − Matrix-vector product for a triangular band matrix

FORMAT

{S,D,C,Z}TBMV (uplo, trans, diag, n, k, a, lda, x, incx)

Arguments

uplocharacter∗1
On entry, specifies whether the matrix A is an upper- or lower-triangular matrix:

If uplo = ’U’ or ’u’, A is an upper-triangular matrix. 

If uplo = ’L’ or ’l’, A is a lower-triangular matrix. 
On exit, uplo is unchanged. 

transcharacter∗1
On entry, specifies the operation to be performed:

If trans = ’N’ or ’n’, the operation is y  =  alpha∗Ax + beta∗y. 

If trans = ’T’ or ’t’, the operation is y  =  alpha∗transp(A)∗x + beta∗y. 

If trans = ’C’ or ’c’, the operation is y  =  alpha∗conjug_transp(A)∗x + beta∗y. 
On exit, trans is unchanged. 

diagcharacter∗1
On entry, specifies whether the matrix A is unit-triangular:

If diag = ’U’ or ’u’, A is a unit-triangular matrix. 

If diag = ’N’ or ’n’, A is not a unit-triangular matrix. 
On exit, diag is unchanged. 

ninteger∗4
On entry, the order of the matrix A; n >= 0.
On exit, n is unchanged. 

kinteger∗4
On entry, if uplo is equal to ’U’ or matrix A.  If uplo is equal to ’L’ or ’l’, the number of sub-diagonals k of the matrix A; k >= 0. 
On exit, k is unchanged. 

areal∗4 | real∗8 | complex∗8 | complex∗16
On entry, a two-dimensional array with dimensions lda by n.

When uplo specifies the upper portion of the matrix, the leading (k + 1) by n part of the array must contain the upper-triangular band part of the  matrix, supplied column by column. The main diagonal of the matrix is stored in row (k + 1) of the array, the first super-diagonal is stored in row k starting at position 2, and so on.  The bottom left k by k triangle of the array A is not referenced. 

When uplo specifies the lower portion of the matrix, the leading (k + 1) by n part of the array must contain the lower-triangular band part of the  matrix, supplied column by column. The main diagonal of the matrix is stored in row 1 of the array, the first sub-diagonal is stored in row 2, starting at position 1, and so on. The top right k by k triangle of the array A is not referenced. 

If diag is equal to ’U’ or diagonal elements of the matrix are not referenced, but are assumed to be unity. 
On exit, a is unchanged. 

ldainteger∗4
On entry, the first dimension of array A; lda >= (k+1).
On exit, lda is unchanged. 

xreal∗4 | real∗8 | complex∗8 | complex∗16
On entry, a one-dimensional array X of length at least (1+(n-1)∗|incx|).  Array X contains the vector x.
On exit, x is overwritten with the transformed vector x. 

incxinteger∗4
On entry, the increment for the elements of X; incx must not equal zero.
On exit, incx is unchanged. 

Description

The _TBMV subprograms compute a matrix-vector product for a triangular band matrix or its transpose:  x  =  Ax  or
 x  =  transp(A)∗x .

In addition to these operations, the CTBMV and ZTBMV subprograms compute the matrix-vector product for the conjugate transpose:
 x  =  conjug_transp(A)∗x.

x is a vector with n elements and A is an n by n band matrix, with (k + 1) diagonals. The band matrix is a unit or non-unit, upper- or lower-triangular matrix. 

Example

REAL∗4 A(5,100), X(100)
INCX = 1
LDA = 5
K = 4
N = 100
CALL STBMV(’U’,’N’,’N’,N,K,A,LDA,X,INCX)

This FORTRAN code computes the product x  =  Ax where A is an upper-triangular, non-unit diagonal matrix, with 4 superdiagonals.