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

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