Contents

# p?trtrs

Solves a system of linear equations with a triangular distributed matrix.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?trtrs
function
solves for
X
one of the following systems of linear equations:
sub(
A
)*
X
= sub(
B
),
(sub(
A
))
T
*
X
= sub(
B
), or
(sub(
A
))
H
*
X
= sub(
B
),
where sub(
A
) =
A
(
ia
:
ia
+
n
-1,
ja
:
ja
+
n
-1) is a triangular distributed matrix of order
n
, and sub(
B
) denotes the distributed matrix
B
(
ib
:
ib
+
n
-1,
jb
:
jb
+
nrhs
-1).
A check is made to verify that sub(
A
) is nonsingular.
Input Parameters
uplo
(global) Must be
'U'
or
'L'
.
Indicates whether sub(
A
) is upper or lower triangular:
If
uplo
=
'U'
, then sub(
A
) is upper triangular.
If
uplo
=
'L'
, then sub(
A
) is lower triangular.
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
.
diag
(global) Must be
'N'
or
'U'
.
If
diag
=
'N'
, then sub(
A
) is not a unit triangular matrix.
If
diag
=
'U'
, then sub(
A
) is unit triangular.
n
(global) The order of the distributed matrix sub(
A
)
(
n
0)
.
nrhs
(global) The number of right-hand sides; i.e., 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
(
jb
+
nrhs
-1
)
, respectively.
The array
a
contains the local pieces of the distributed triangular matrix sub(
A
).
If
uplo
=
'U'
n
-by-
n
upper triangular part of sub(
A
) contains the upper triangular matrix, and the strictly lower triangular part of sub(
A
) is not referenced.
If
uplo
=
'L'
n
-by-
n
lower triangular part of sub(
A
) contains the lower triangular matrix, and the strictly upper triangular part of sub(
A
) is not referenced.
If
diag
=
'U'
, the diagonal elements of sub(
A
) are also not referenced and are assumed to be 1.
On entry, the array
b
contains the local pieces of the right hand side distributed matrix sub(
B
).
ia
,
ja
(global) The row and column indices in the global matrix
A
indicating the first row and the first column of the matrix sub(
A
), respectively.
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
ib
,
jb
(global) The row and column indices in the global matrix
B
indicating the first row and the first column of the matrix sub(
B
), respectively.
descb
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
B
.
Output Parameters
b
On exit, if
info
=0
, sub(
B
) is overwritten by the solution matrix
X
.
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
.
info
>
0
:
if
info
=
i
, the
i
-th diagonal element of sub(
A
) is zero, indicating that the submatrix is singular and the solutions
X
have not been computed.

#### 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