Contents

# p?posv

Solves a symmetric positive definite system of linear equations.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?posv
function
computes the solution to a real/complex system of linear equations
sub(
A
)*
X
= sub(
B
)
,
where sub(
A
) denotes
A
(
ia
:
ia
+
n
-1,
ja
:
ja
+
n
-1)
and is an
n-
by-
n
symmetric/Hermitian distributed positive definite matrix and
X
and sub(
B
) denoting
B
(
ib
:
ib
+
n
-1,
jb
:
jb
+
nrhs
-1)
are
n
-by-
nrhs
distributed matrices. The Cholesky decomposition is used to factor sub(
A
) as
sub(
A
) =
U
T
*
U
, if
uplo
= 'U'
, or
sub(
A
) =
L
*
L
T
, if
uplo
= 'L'
,
where
U
is an upper triangular matrix and
L
is a lower triangular matrix. The factored form of sub(
A
) is then used to solve the system of equations.
Input Parameters
uplo
(global) Must be
'U'
or
'L'
.
Indicates whether the upper or lower triangular part of sub(
A
) is stored.
n
(global) The order of the distributed matrix sub(
A
)
(
n
0)
.
nrhs
The number of right-hand sides; the number of columns of the distributed matrix sub(
B
)
(
nrhs
0)
.
a
(local)
Pointer into the local memory to an array of size
lld_a
*
LOCc
(
ja
+
n
-1)
. On entry, this array contains the local pieces of the
n
-by-
n
symmetric distributed matrix sub(
A
) to be factored.
If
uplo
= '
U'
n
-by-
n
upper triangular part of sub(
A
) contains the upper triangular part of the matrix, and its strictly lower triangular part is not referenced.
If
uplo
= '
L'
n
-by-
n
lower triangular part of sub(
A
) contains the lower triangular part of the distributed matrix, and its strictly upper triangular part is not referenced.
ia
,
ja
(global) The row and column indices in the global matrix
A
indicating the first row and the first column of the submatrix
A
, respectively.
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
b
(local)
Pointer into the local memory to an array of size
lld_b
*
LOCc
(
jb
+
nrhs
-1)
. On entry, the local pieces of the right hand sides distributed matrix sub(
B
).
ib
,
jb
(global) The row and column indices in the global matrix
B
indicating the first row and the first column of the submatrix
B
, respectively.
descb
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
B
.
Output Parameters
a
On exit, if
info
= 0
, this array contains the local pieces of the factor
U
or
L
from the Cholesky factorization
sub(
A
) =
U
H
*
U
, or
L*L
H
.
b
On exit, if
info
= 0
, sub(
B
) is overwritten by the solution distributed matrix
X
.
info
(global)
If
info
=0
, the execution is successful.
If
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
.
If
info
> 0
: If
info
=
k
, the leading minor of order
k
,
A
(
ia
:
ia
+
k
-1,
ja
:
ja
+
k
-1)
is not positive definite, and the factorization could not be completed, and the solution has 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