Name

sgbmv, ddbmv, cgbmv, zgbmv − Matrix-vector product for a general band matrix

FORMAT

{S,D,C,Z}GBMV (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)

Arguments

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. 

minteger∗4
On entry, the number of rows of the matrix A; m >= 0.
On exit, m is unchanged. 

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

klinteger∗4
On entry, the number of sub-diagonals of the matrix A; kl >= 0.
On exit, kl is unchanged. 

kuinteger∗4
On entry, the number of super-diagonals of the matrix A; ku >= 0.
On exit, ku is unchanged. 

alphareal∗4 | real∗8 | complex∗8 | complex∗16
On entry, the scalar alpha∗.
On exit, alpha is unchanged. 

areal∗4 | real∗8 | complex∗8 | complex∗16
On entry, a two-dimensional array with dimensions lda by n. The leading m by n part of the array contains the elements of the matrix A, supplied column by column. The leading diagonal of the matrix is stored in row (ku + 1) of the array, the first super-diagonal is stored in row ku starting at position 2,  the first sub-diagonal is stored in row (ku + 2) starting at position 1,  and so on. Elements in the array A that do not correspond to elements in the matrix (such as the top left ku by ku triangle) are not referenced.
On exit, a is unchanged. 

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

xreal∗4 | real∗8 | complex∗8 | complex∗16
On entry, a one-dimensional array containing the vector x.  When trans is equal to ’N’ or (1+(n-1)∗|incx|). Otherwise, the length is at least (1+(m-1)∗|incx|). 
On exit, x is unchanged. 

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

betareal∗4 | real∗8 | complex∗8 | complex∗16
On entry, the scalar beta.
On exit, beta is unchanged. 

yreal∗4 | real∗8 | complex∗8 | complex∗16
On entry, a one-dimensional array containing the vector x.  When trans is equal to ’N’ or (1+(m-1)∗|incy|). Otherwise, the length is at least (1+(n-1)∗|incy|). 

If beta= 0, y need not be set. If beta is not equal to zero, the incremented array Y must contain the vector y. 
On exit, y is overwritten by the updated vector y. 

incyinteger∗4
On entry, the increment for the elements of Y; incy must not equal zero.
On exit, incy is unchanged. 

Description

The _GBMV subprograms compute a matrix-vector product for either a general band matrix or its transpose: y  =  alpha∗Ax + beta∗y
  y  =  alpha∗transp(A)∗x + beta∗y

In addition to these operations, the CGBMV and ZGBMV subprograms compute a matrix-vector product for the conjugate transpose:
  y  =  alpha∗conjug_transp(A)∗x + beta∗y

alphaand betaare scalars, x and y are vectors, and A is an m by n band matrix. 

Example

COMPLEX∗16 A(5,20), X(20), Y(20), alpha, beta
M = 5
N = 20
KL = 2
KU = 2
alpha = (1.0D0, 2.0D0)
LDA = 5
INCX = 1
beta = (0.0D0, 0.0D0)
INCY = 1
CALL ZGBMV(’N’,M,N,KL,KU,alpha,A,LDA,X,INCX,beta,Y,INCY)

This FORTRAN code multiplies a pentadiagonal matrix A by the vector x to get the vector y.  The operation is y  =  Ax. where A is stored in banded storage form.