Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?sbtrd

Reduces a real symmetric band matrix to tridiagonal form.

Syntax

call ssbtrd
(
vect
,
uplo
,
n
,
kd
,
ab
,
ldab
,
d
,
e
,
q
,
ldq
,
work
,
info
)
call dsbtrd
(
vect
,
uplo
,
n
,
kd
,
ab
,
ldab
,
d
,
e
,
q
,
ldq
,
work
,
info
)
call sbtrd
(
ab
[
,
q
]
[
,
vect
]
[
,
uplo
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine reduces a real symmetric band matrix
A
to symmetric tridiagonal form
T
by an orthogonal similarity transformation:
A
=
Q*T*Q
T
. The orthogonal matrix
Q
is determined as a product of Givens rotations.
If required, the routine can also form the matrix
Q
explicitly.
Input Parameters
vect
CHARACTER*1
.
Must be
'V'
,
'N'
, or
'U'
.
If
vect
=
'V'
, the routine returns the explicit matrix
Q
.
If
vect
=
'N'
, the routine does not return
Q
.
If
vect
=
'U'
, the routine updates matrix
X
by forming
X
*
Q
.
uplo
CHARACTER*1
.
Must be
'U'
or
'L'
.
If
uplo
=
'U'
,
ab
stores the upper triangular part of
A
.
If
uplo
=
'L'
,
ab
stores the lower triangular part of
A
.
n
INTEGER
.
The order of the matrix
A
(
n
0
).
kd
INTEGER
.
The number of super- or sub-diagonals in
A
(
kd
0
).
ab
,
q
,
work
REAL
for
ssbtrd
DOUBLE PRECISION
for
dsbtrd
.
ab
(
ldab
,*)
is an array containing either upper or lower triangular part of the matrix
A
(as specified by
uplo
) in band storage format.
The second dimension of
ab
must be at least max(1,
n
).
q
(
ldq
,*)
is an array.
If
vect
=
'U'
, the
q
array must contain an
n
-by-
n
matrix
X
.
If
vect
=
'N'
or
'V'
, the
q
parameter need not be set.
The second dimension of
q
must be at least max(1,
n
).
work
(*) is a workspace array.
The dimension of
work
must be at least max(1,
n
).
ldab
INTEGER
.
The leading dimension of
ab
; at least
kd
+1 .
ldq
INTEGER
.
The leading