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'
, the leading
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'
, the leading
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,
had an illegal value, then
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

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