Contents

# p?gesv

Computes the solution to the system of linear equations with a square distributed matrix and multiple right-hand sides.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?gesv
function
computes the solution to a real or complex system of linear equations
sub(
A
)*
X
= sub(
B
)
, where
sub(
A
) =
A
(
ia:ia+n-1
,
ja:ja+n-1
)
is an
n
-by-
n
distributed matrix and
X
and
sub(
B
) =
B
(
ib:ib+n-1
,
jb:jb+nrhs-1
)
are
n
-by-
nrhs
distributed matrices.
The
LU
decomposition with partial pivoting and row interchanges is used to factor sub(
A
) as
sub(
A
) =
P
*
L
*
U
, where
P
is a permutation matrix,
L
is unit lower triangular, and
U
is upper triangular.
L
and
U
are stored in sub(
A
). The factored form of sub(
A
) is then used to solve the system of equations
sub(
A
)*
X
= sub(
B
)
.
Input Parameters
n
(global) The number of rows and columns to be operated on, that is, the order of the distributed submatrix
sub(
A
) (
n
0)
.
nrhs
(global) The number of right hand sides, that is, the number of columns of the distributed submatrices
B
and
X
(
nrhs
0)
.
a
,
b
(local)
Pointers into the local memory to arrays of local size
a
:
lld_a
*
LOCc
(
ja
+
n
-1)
and
b
:
lld_b
*
LOCc
(
jb+nrhs-1
)
, respectively.
On entry, the array
a
contains the local pieces of the
n
-by-
n
distributed matrix sub(
A
) to be factored.
On entry, the array
b
contains 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 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 sub(
B
), respectively.
descb
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
B
.
Output Parameters
a
Overwritten by the factors
L
and
U
from the factorization sub(
A
) =
P
*
L
*
U
; the unit diagonal elements of
L
are not stored .
b
Overwritten by the solution distributed matrix
X
.
ipiv
(local) Array of size
LOCr
(
m_a
)+
mb_a
. This array contains the pivoting information. The (local) row
i
of the matrix was interchanged with the (global) row
ipiv
[
i
- 1]
.
This array is tied to the distributed matrix
A
.
info
(global) If
info
=0
, the execution is successful.
info
< 0:
If the
i-
th argument is an array and the
j-
th entry 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
=
k
,
U
(
ia+k-1
,
ja+k-1
) is exactly zero. The factorization has been completed, but the factor
U
is exactly singular, so the solution could not be 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