Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

p?pbsv

Solves a symmetric/Hermitian positive definite banded system of linear equations.

Syntax

void
pspbsv
(
char
*uplo
,
MKL_INT
*n
,
MKL_INT
*bw
,
MKL_INT
*nrhs
,
float
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
float
*b
,
MKL_INT
*ib
,
MKL_INT
*descb
,
float
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pdpbsv
(
char
*uplo
,
MKL_INT
*n
,
MKL_INT
*bw
,
MKL_INT
*nrhs
,
double
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
double
*b
,
MKL_INT
*ib
,
MKL_INT
*descb
,
double
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pcpbsv
(
char
*uplo
,
MKL_INT
*n
,
MKL_INT
*bw
,
MKL_INT
*nrhs
,
MKL_Complex8
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_Complex8
*b
,
MKL_INT
*ib
,
MKL_INT
*descb
,
MKL_Complex8
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pzpbsv
(
char
*uplo
,
MKL_INT
*n
,
MKL_INT
*bw
,
MKL_INT
*nrhs
,
MKL_Complex16
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_Complex16
*b
,
MKL_INT
*ib
,
MKL_INT
*descb
,
MKL_Complex16
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
Include Files
  • mkl_scalapack.h
Description
The
p?pbsv
function
solves a system of linear equations
A
(1:
n
,
ja
:
ja
+
n
-1)*
X
 =
B
(
ib
:
ib
+
n
-1, 1:
nrhs
)
,
where
A
(1:
n
,
ja
:
ja
+
n
-1)
 is an
n
-by-
n
 real/complex banded symmetric positive definite distributed matrix with bandwidth
bw
.
Cholesky factorization is used to factor a reordering of the matrix into
L*L'
.
Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.
Notice revision #20201201
Input Parameters
uplo
(global) Must be
'U'
 or
'L'
.
Indicates whether the upper or lower triangular of
A
 is stored.
If
uplo
 =
'U'
, the upper triangular
A
 is stored
If
uplo
 =
'L'
, the lower triangular of
A
 is stored.
n
(global) The order of the distributed matrix
A
(
n
≥
 0)
.
bw
(global) The number of subdiagonals in
L
 or
U
.
0 ≤
bw
 ≤
n
-1
.
nrhs
(global) The number of right-hand sides; the number of columns in
B
(
nrhs
≥
 0)
.
a
(local).
Pointer into the local memory to an array with leading size
lld_a
 ≥ (
bw
+1)
 (stored in
desca
). On entry, this array contains the local pieces of the distributed matrix
sub(
A
)
 to be factored.
ja
(global) The index in the global matrix
A
 indicating the start of the matrix to be operated on (which may be either all of
A
 or a submatrix of
A
).
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 local lead size
lld_b
 ≥
nb
. On entry, this array contains the local pieces of the right hand sides
B
(
ib
:
ib
+
n
-1, 1:
nrhs
)
.
ib
(global) The row index in the global matrix
B
 indicating the first row of the matrix to be operated on (which may be either all of
b
 or a submatrix of
B
).
descb
(global and local) array of size
dlen
.
If
1D type (
dtype_b
 =502)
,
dlen
 ≥ 7
;
If
2D type (
dtype_b
 =1)
,
dlen
 ≥ 9
.
The array descriptor for the distributed matrix
B
.
Contains information of mapping of
B
 to memory.
work
(local).
Temporary workspace. This space may be overwritten in between calls to
functions
.
work
 must be the size given in
lwork
.
lwork
(local or global) Size of user-input workspace
work
. If
lwork
 is too small, the minimal acceptable size will be returned in
work
[0]
 and an error code is returned.
lwork
 ≥ (
nb
+2*
bw
)*
bw
 +max((
bw
*
nrhs
),
bw
*
bw
)
Output Parameters
a
On exit, this array contains information containing details of the factorization. Note that permutations are performed on the matrix, so that the factors returned are different from those returned by LAPACK.
b
On exit, contains the local piece of the solutions distributed matrix
X
.
work
On exit,
work
[0]
 contains the minimal
lwork
.
info
(global) If
info
=0, the execution is successful.
< 0
: If the
i
-th argument is an array and the
j
-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
.
> 0
: If
info
 =
k
 ≤
NPROCS
, the submatrix stored on processor
info
 and factored locally was not positive definite, and the factorization was not completed.
If
info
 =
k
 >
NPROCS
, the submatrix stored on processor
info
-
NPROCS
 representing interactions with other processors was not positive definite, and the factorization was not completed.

Product and Performance Information

1

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