Contents

# p?getrs

Solves a system of distributed linear equations with a general square matrix, using the
LU
factorization computed by
p?getrf
.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?getrs
function
solves a system of distributed linear equations with a general
n
-by-
n
distributed matrix sub(
A
) =
A
(
ia
:
ia
+
n
-1,
ja
:
ja
+
n
-1) using the
LU
factorization computed by
p?getrf
.
The system has one of the following forms specified by
trans
:
sub(
A
)*
X
= sub(
B
) (no transpose),
sub(
A
)
T
*
X
= sub(
B
) (transpose),
sub(
A
)
H
*
X
= sub(
B
) (conjugate transpose),
where sub(
B
) =
B
(
ib
:
ib
+
n
-1,
jb
:
jb
+
nrhs
-1).
Before calling this
function
,you must call
p?getrf
to compute the
LU
factorization of sub(
A
).
Input Parameters
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
.
n
(global) The number of linear equations; the order of the 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).
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.
On entry, the array
a
contains the local pieces of the factors
L
and
U
from the factorization sub(
A
) =
P*L*U
; the unit diagonal elements of
L
are not stored. On entry, the array
b
contains the right hand sides 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
.
ipiv
(local) Array of size of
LOCr
(
m_a
) +
mb_a
. Contains the pivoting information: local row
i
of the matrix was interchanged with the global row
ipiv
[
i
-1]
.
This array is tied to 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, overwritten by the solution distributed 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
.

#### 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