Contents

# p?dttrsv

Computes an LU factorization of a general band matrix, using partial pivoting with row interchanges. The
function
is called by
p?dttrs
.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?dttrsv
function
solves a tridiagonal triangular system of linear equations
A
(1 :
n
,
ja
:
ja
+
n
-1)
*
X
=
B
(
ib
:
ib
+
n
-1, 1 :
nrhs
)
or
A
(1 :
n
,
ja
:
ja
+
n
-1)
T
*
X
=
B
(
ib
:
ib
+
n
-1, 1 :
nrhs
)
for real flavors;
A
(1 :
n
,
ja
:
ja
+
n
-1)
H
*
X
=
B
(
ib
:
ib
+
n
-1, 1 :
nrhs
)
for complex flavors,
where
A
(1 :
n
,
ja
:
ja
+
n
-1)
is a tridiagonal matrix factor produced by the Gaussian elimination code of
p?dttrf
and is stored in
A
(1 :
n
,
ja
:
ja
+
n
-1)
and
af
.
The matrix stored in
A
(1 :
n
,
ja
:
ja
+
n
-1)
is either upper or lower triangular according to
uplo
, and the choice of solving
A
(1 :
n
,
ja
:
ja
+
n
-1)
or
A
(1 :
n
,
ja
:
ja
+
n
-1)
T
is dictated by the user by the parameter
trans
.
The function
p?dttrf
must be called first.
Input Parameters
uplo
(global)
If
uplo
=
'U'
, the upper triangle of
A
(1:
n
,
ja
:
ja
+
n
-1)
is stored,
if
uplo
=
'L'
, the lower triangle of
A
(1:
n
,
ja
:
ja
+
n
-1)
is stored.
trans
(global)
If
trans
=
'N'
, solve with
A
(1:
n
,
ja
:
ja
+
n
-1)
,
if
trans
=
'C'
, solve with conjugate transpose
A
(1:
n
,
ja
:
ja
+
n
-1)
.
n
(global) The order of the distributed submatrix
A
;(
n
0)
.
nrhs
(global) The number of right-hand sides; the number of columns of the distributed submatrix
B
(
ib
:
ib
+
n
-1, 1:
nrhs
)
.
(
nrhs
0)
.
dl
(local).
Pointer to local part of global vector storing the lower diagonal of the matrix.
Globally,
dl

is not referenced, and
dl
must be aligned with
d
.
Must be of size
nb_a
.
d
(local).
Pointer to local part of global vector storing the main diagonal of the matrix.
du
(local).
Pointer to local part of global vector storing the upper diagonal of the matrix.
Globally,
du
[
n
-1]
is not referenced, and
du
must be aligned with
d
.
ja
(global) The index in the global matrix
A
that points to the start of the matrix to be operated on (which may be either all of
A
or a submatrix of
A
).
desca
(global and local) array of size
dlen_
.
if 1
d
type
(
dtype_a
= 501 or 502)
,
dlen
7
;
if 2
d
type
(
dtype_a
= 1)
,
dlen
9
.
The array descriptor for the distributed matrix
A
. Contains information of mapping of
A
to memory.
b
(local)
Pointer into the local memory to an array of local lead dimension
lld_b
nb
. On entry, this array contains the local pieces of the right-hand sides
B
(
ib
:
ib
+
n
-1, 1 :
nrhs
)
.
ib
(global) The row index in the global matrix
B
that points to the first row of the matrix to be operated on (which may be either all of
B
or a submatrix of
B
).
descb
(global and local) array of size
dlen_
.
if 1
d
type
(
dtype_b
= 502)
,
dlen
7
;
if 2
d
type
(
dtype_b
= 1)
,
dlen
9
.
The array descriptor for the distributed matrix
B
. Contains information of mapping
B
to memory.
laf
(local).
Size of user-input auxiliary fill-in space
af
.
laf
2*(
nb
+2)
. If
laf
is not large enough, an error code is returned and the minimum acceptable size will be returned in
af

.
work
(local).
Temporary workspace. This space may be overwritten in between
function calls
.
work
must be the size given in
lwork
.
lwork
(local or global)
Size of user-input workspace
work
. If
lwork
is too small, the minimal acceptable size will be returned in
work

and an error code is returned.
lwork
10*
npcol
+4*
nrhs
.
Output Parameters
dl
(local).
On exit, this array contains information containing the factors of the matrix.
d
On exit, this array contains information containing the factors of the matrix. Must be of size
nb_a
.
b
On exit, this contains the local piece of the solutions distributed matrix X.
af
(local).
Auxiliary fill-in space. The fill-in space is created in a call to the factorization
function
p?dttrf
and is stored in
af
. If a linear system is to be solved using
p?dttrs
after the factorization
function
,
af
must not be altered after the factorization.
work
On exit,
work
contains the minimal
lwork
.
info
(local).
If
info
=0, the execution is successful.
if
info
< 0: If the
i
-th argument is an array and the
j
-th entry
, indexed
j
-1,
info
= - (
i
*100+
j
), if the
i
-th argument is a scalar and had an illegal value, then
info
= -
i
.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.