Contents

# p?dbtrs

Solves a system of linear equations with a diagonally dominant-like banded distributed matrix using the factorization computed by
p?dbtrf
.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?dbtrs
function
solves for
X
one of the systems of equations:
sub(
A
)*
X
= sub(
B
),
(sub(
A
))
T
*
X
= sub(
B
), or
(sub(
A
))
H
*
X
= sub(
B
),
where sub(
A
) =
A
(1:
n
,
ja
:
ja
+
n
-1) is a diagonally dominant-like banded distributed matrix, and sub(
B
) denotes the distributed matrix
B
(
ib
:
ib
+
n
-1, 1:
nrhs
).
This
function
uses the
LU
factorization computed by
p?dbtrf
.
Input Parameters
trans
(global) Must be
'N'
or
'T'
or
'C'
.
Indicates the form of the equations:
If
trans
=
'N'
, then sub(
A
)*
X
= sub(
B
) is solved for
X
.
If
trans
=
'T'
, then (sub(
A
))
T
*
X
= sub(
B
) is solved for
X
.
If
trans
=
'C'
, then (sub(
A
))
H
*
X
= sub(
B
) is solved for
X
.
n
(global) The order of the distributed matrix sub(
A
)
(
n
0)
.
bwl
(global) The number of subdiagonals within the band of
A
( 0 ≤
bwl
n-1
)
.
bwu
(global) The number of superdiagonals within the band of
A
( 0 ≤
bwu
n-1
)
.
nrhs
(global) The number of right hand sides; the number of columns of the distributed matrix sub(
B
)
(
nrhs
0)
.
a
,
b
(local)
Pointers into the local memory to arrays of local sizes
lld_a
*
LOCc
(
ja
+
n
-1)
and
lld_b
*
LOCc
(
nrhs
)
, respectively.
On entry, the array
a
contains details of the
LU
factorization of the band matrix
A
, as computed by
p?dbtrf
.
On entry, the array
b
contains the local pieces of the right hand side distributed matrix sub(
B
).
ja
(global) The index in the global matrix
A
indicating 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_
. The array descriptor for the distributed matrix
A
.
If
dtype_a
= 501
, then
dlen_
7
;
else if
dtype_a
= 1
, then
dlen_
9
.
ib
(global) The row index in the global matrix
B
indicating 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_
. The array descriptor for the distributed matrix
B
.
If
dtype_b
= 502
, then
dlen_
7
;
else if
dtype_b
= 1
, then
dlen_
9
.
af
,
work
(local)
Arrays of size
laf
and
lwork
, respectively The array
af
contains auxiliary fill-in space. The fill-in space is created in a call to the factorization
function
p?dbtrf
and is stored in
af
.
The array
work
is a workspace array.
laf
(local) The size of the array
af
.
Must be
laf
NB
*(
bwl
+
bwu
)+6*(max(
bwl
,
bwu
))
2
.
If
laf
is not large enough, an error code will be returned and the minimum acceptable size will be returned in
af

.
lwork
(local or global) The size of the array
work
, must be at least
lwork
(max(
bwl
,
bwu
))
2
.
Output Parameters
b
On exit, this array contains the local pieces of the solution distributed matrix
X
.
work

On exit,
work

contains the minimum value of
lwork
required for optimum performance.
info
If
info
=0
, the execution is successful.
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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804