## Developer Reference

• 098
• 03/30/2020
• Public Content
Contents

# ?tbmv

Computes a matrix-vector product using a triangular band matrix.

## Syntax

Include Files
• mkl.fi
,
blas.f90
Description
The
?tbmv
routines perform one of the matrix-vector operations defined as
x
:=
A
*
x
, or
x
:=
A
'*
x
, or
x
:= conjg(
A
')*
x
,
where:
x
is an
n
-element vector,
A
is an
n
-by-
n
unit, or non-unit, upper or lower triangular band matrix, with
(
k
+1)
diagonals.
Input Parameters
uplo
CHARACTER*1
.
Specifies whether the matrix
A
is an upper or lower triangular matrix:
uplo
=
'U'
or
'u'
if
uplo
=
'L'
or
'l'
, then the matrix is low triangular.
trans
CHARACTER*1
.
Specifies the operation:
if
trans
= 'N'
or
'n'
, then
x
:=
A
*
x
;
if
trans
= 'T'
or
't'
, then
x
:=
A
'*
x
;
if
trans
= 'C'
or
'c'
, then
x
:= conjg(
A
')*
x
.
diag
CHARACTER*1
.
Specifies whether the matrix
A
is unit triangular:
if
uplo
=
'U'
or
'u'
then the matrix is unit triangular;
if
diag
=
'N'
or
'n'
, then the matrix is not unit triangular.
n
INTEGER
.
Specifies the order of the matrix
A
. The value of
n
must be at least zero.
k
INTEGER
.
On entry with
uplo
=
'U'
or
'u'
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
.
The value of
k
must satisfy
0
k
.
a
REAL
for
stbmv
DOUBLE PRECISION
for
dtbmv
COMPLEX
for
ctbmv
DOUBLE COMPLEX
for
ztbmv
Array, size
(
lda
,
n
)
.
Before entry with
uplo
=
'U'
or
'u'
(
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 transfers an upper triangular band matrix from conventional full matrix storage (
matrix
) to band storage (
a
):
```       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'