Contents

# p?pttrs

Solves a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal distributed matrix using the factorization computed by
p?pttrf
.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?pttrs
function
solves for
X
a system of distributed linear equations in the form:
sub(
A
)*
X
= sub(
B
) ,
where sub(
A
) =
A
(1:
n
,
ja
:
ja
+
n
-1) is an
n
-by-
n
real symmetric or complex Hermitian positive definite tridiagonal distributed matrix, and sub(
B
) denotes the distributed matrix
B
(
ib
:
ib
+
n
-1, 1:
nrhs
).
This
function
uses the factorization
sub(
A
) =
P
*
L
*
D
*
L
H
*
P
T
, or sub(
A
) =
P
*
U
H
*
D
*
U
*
P
T
computed by
p?pttrf
.
Input Parameters
uplo
(global, used in complex flavors only)
Must be
'U'
or
'L'
.
If
uplo
=
'U'
, upper triangle of sub(
A
) is stored;
If
uplo
=
'L'
, lower triangle of sub(
A
) is stored.
n
(global) The order of the distributed matrix sub(
A
)
(
n
0)
.
nrhs
(global) The number of right hand sides; the number of columns of the distributed matrix sub(
B
)
(
nrhs
0)
.
d
,
e
(local)
Pointers into the local memory to arrays of size
nb_a
each.
These arrays contain details of the factorization as returned by
p?pttrf
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
or
dtype_a
= 502
, then
dlen_
7
;
else if
dtype_a
= 1
, then
dlen_
9
.
b
(local) Same type as
d
,
e
.
Pointer into the local memory to an array of local size
lld_b
*
LOCc
(
nrhs
)
.
On entry, the array
b
contains the local pieces of the
n
-by-
nrhs
right hand side distributed matrix sub(
B
).
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?pttrf
and is stored in
af
.
The array
work
is a workspace array.
laf
(local) The size of the array
af
.
Must be
laf
nb_a
+2
.
If
laf
is not large enough, an error code is 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
(10+2*
min
(100,
nrhs
))*
NPCOL
+4*
nrhs
.
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