Contents

# p?pttrsv

Solves a single triangular linear system via frontsolve or backsolve where the triangular matrix is a factor of a tridiagonal matrix computed by
p?pttrf
.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?pttrsv
function
solves a tridiagonal triangular system of linear equations
A
(1:
n
,
ja
:
ja
+
n
-1)*
X
=
B
(
jb
:
jb+n
-1, 1:
nrhs
)
or
A
(1:
n
,
ja
:
ja
+
n
-1)
T
*
X
=
B
(
jb
:
jb+n
-1, 1:
nrhs
)
for real flavors,
A
(1:
n
,
ja
:
ja
+
n
-1)
H
*
X
=
B
(
jb
:
jb+n
-1, 1:
nrhs
)
for complex flavors,
where
A
(1:
n
,
ja
:
ja
+
n
-1)
is a tridiagonal triangular matrix factor produced by the Cholesky factorization code
p?pttrf
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
.
The function
p?pttrf
must be called first.
Input Parameters
uplo
(global) Must be
'U'
or
'L'
.
If
uplo
=
'U'
, upper triangle of
A
(1:
n
,
ja
:
ja
+
n
-1)
is stored;
If
uplo
=
'L'
, lower triangle of
A
(1:
n
,
ja
:
ja
+
n
-1)
is stored.
trans
(global) Must be
'N'
or
'C'
.
If
trans
=
'N'
, solve with
A
(1:
n
,
ja
:
ja
+
n
-1)
;
If
trans
=
'C'
(for complex flavors), solve with conjugate transpose (
A
(1:
n
,
ja
:
ja
+
n
-1)
)
H
.
n
(global)
The number of rows and columns to be operated on, that is, the order of the distributed submatrix
A
(1:
n
,
ja
:
ja
+
n
-1)
.
n
0
.
nrhs
(global)
The number of right hand sides; the number of columns of the distributed submatrix
B
(
jb
:
jb+n
-1, 1:
nrhs
);
nrhs
0
.
d
(local)
Pointer to the local part of the global vector storing the main diagonal of the matrix; must be of size
nb_a
.
e
(local)
Pointer to the local part of the global vector
du
storing the upper diagonal of the matrix; must be of size
nb_a
. Globally,
du
(
n
) 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_
. The array descriptor for the distributed matrix
A
.
If
1D type (
dtype_a
= 501 or 502)
, then
dlen
7
;
If
2D type (
dtype_a
= 1)
, then
dlen
9
.
Contains information on mapping of
A
to memory. See ScaLAPACK manual for full description and options.
b
(local)
Pointer into the local memory to an array of local lead size
lld_b
nb
.
On entry, this array contains the local pieces of the right hand sides
B
(
jb
:
jb+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_
. The array descriptor for the distributed matrix
B
.
If
1D type (
dtype_b
= 502)
, then
dlen
7
;
If
2D type (
dtype_b
= 1)
, then
dlen
9
.
Contains information on mapping of
B
to memory. See ScaLAPACK manual for full description and options.
laf
(local)
The size of user-input auxiliary fill-in space
af
. Must be
laf
(
nb
+2
*bw
)
*bw
.
If
laf
is not large enough, an error code will be returned and the minimum acceptable size will be returned in
af
[0]
.
work
(local)
The array
work
is a temporary workspace array of size
lwork
. This space may be overwritten in between
function calls
.
lwork
(local or global) The size of the user-input workspace
work
, must be at least
lwork
(10+2*min(100,
nrhs
))*
npcol
+4*
nrhs
. If
lwork
is too small, the minimal acceptable size will be returned in
work
[0]
and an error code is returned.
Output Parameters
d
,
e
(local).
On exit, these arrays contain information on the factors of the matrix.
af
(local)
The array
af
is of size
laf
. It contains auxiliary fill-in space. The fill-in space is created in a call to the factorization
function
p?pbtrf
and is stored in
af
. If a linear system is to be solved using
p?pttrs
after the factorization
function
,
af
must not be altered after the factorization.
b
On exit, this array contains the local piece of the solutions distributed matrix
X
.
work
[0]
On exit,
work
[0]
contains the minimum value of
lwork
.
info
(local)
= 0
: successful exit
< 0
: if the
i
-th argument is an array and the
j
-th entry
, indexed
j
-1,
then
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 reserverd 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