Contents

# p?trsv

Solves a system of linear equations whose coefficients are in a distributed triangular matrix.

## Syntax

Include Files
• mkl_pblas.h
Description
The
p?trsv
routines solve one of the systems of equations:
sub(
A
)*sub(
x
) =
b
, or
sub(
A
)'*sub(
x
) =
b
, or
conjg(sub(
A
)')*sub(
x
) =
b
,
where:
sub(
A
)
is a
n
-by-
n
unit, or non-unit, upper or lower triangular distributed matrix,
sub(
A
) =
A
(
ia
:
ia
+
n
-1,
ja
:
ja
+
n
-1)
,
b
and
sub(
x
)
are
n
-element distributed vectors,
sub(
x
)
denotes
X
(
ix
,
jx
:
jx
+
n
-1)
if
incx
=
m_x
, and
X
(
ix
:
ix
+
n
-1,
jx
)
if
incx
= 1,
.
The routine does not test for singularity or near-singularity. Such tests must be performed before calling this routine.
Input Parameters
uplo
(global) Specifies whether the distributed matrix
sub(
A
)
is upper or lower triangular:
if
uplo
=
'U'
or
'u'
, then the matrix is upper triangular;
if
uplo
=
'L'
or
'l'
, then the matrix is low triangular.
trans
(global) Specifies the form of the system of equations:
if
transa
= '
N
'
or
'
n
'
, then
sub(
A
)*sub(
x
) =
b
;
if
transa
= '
T
'
or
'
t
'
, then
sub(
A
)'*sub(
x
) =
b
;
if
transa
= '
C
'
or
'
c
'
, then
conjg(sub(
A
)')*sub(
x
) =
b
.
diag
(global) Specifies whether the matrix
sub(
A
)
is unit triangular:
if
diag
=
'U'
or
'u'
then the matrix is unit triangular;
if
diag
=
'N'
or
'n'
, then the matrix is not unit triangular.
n
(global) Specifies the order of the distributed matrix
sub(
A
)
,
n
0.
a
(local)
Array, size at least
(
lld_a
, LOCq(1,
ja
+
n
-1))
.
Before entry with
uplo
=
'U'
or
'u'
, this array contains the local entries corresponding to the entries of the upper triangular distributed matrix
sub(
A
)
, and the local entries corresponding to the entries of the strictly lower triangular part of the distributed matrix
sub(
A
)
is not referenced.
Before entry with
uplo
=
'L'
or
'l'
, this array contains the local entries corresponding to the entries of the lower triangular distributed matrix
sub(
A
)
, and the local entries corresponding to the entries of the strictly upper triangular part of the distributed matrix
sub(
A
)
is not referenced .
When
diag
=
'U'
or
'u'
, the local entries corresponding to the diagonal elements of the submatrix
sub(
A
)
are not referenced either, but are assumed to be unity.
ia
,
ja
(global) The row and column indices in the distributed matrix
A
indicating the first row and the first column of the submatrix
sub(
A
)
, respectively.
desca
(global and local) array of dimension 9. The array descriptor of the distributed matrix
A
.
x
(local)
Array, size at least
(
jx
-1)*
m_x
+
ix
+(
n
-1)*abs(
incx
))
.
This array contains the entries of the distributed vector
sub(
x
)
. Before entry,
sub(
x
)
must contain the
n
-element right-hand side distributed vector
b
.
ix
,
jx
(global) The row and column indices in the distributed matrix
X
indicating the first row and the first column of the submatrix
sub(
x
)
, respectively.
descx
(global and local) array of dimension 9. The array descriptor of the distributed matrix
X
.
incx
(global) Specifies the increment for the elements of
sub(
x
)
. Only two values are supported, namely 1 and
m_x
.
incx
must not be zero.
Output Parameters
x
Overwritten with the solution vector.

#### 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