Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.10
  • 10/21/2020
  • Public Content
Contents

cluster_sparse_solver

Calculates the solution of a set of sparse linear equations with single or multiple right-hand sides.

Syntax

void
cluster_sparse_solver
(
_MKL_DSS_HANDLE_t
pt
,
const
MKL_INT
*
maxfct
,
const
MKL_INT
*
mnum
,
const
MKL_INT
*
mtype
,
const
MKL_INT
*
phase
,
const
MKL_INT
*
n
,
const
void
*
a
,
const
MKL_INT
*
ia
,
const
MKL_INT
*
ja
,
MKL_INT
*
perm
,
const
MKL_INT
*
nrhs
,
MKL_INT
*
iparm
,
const
MKL_INT
*
msglvl
,
void
*
b
,
void
*
x
,
const
int
*
comm
,
MKL_INT
*
error
);
Include Files
  • mkl_cluster_sparse_solver.h
Description
The routine
cluster_sparse_solver
 calculates the solution of a set of sparse linear equations 
A*X = B
with single or multiple right-hand sides, using a parallel
LU
,
LDL
, or
LL
T
 factorization, where
A
 is an
n
-by-
n
 matrix, and
X
 and
B
 are
n
-by-
nrhs
 vectors or matrices.
This routine supports the Progress Routine feature. See Progress Function for details.
Input Parameters
Most of the input parameters (except for the
pt
,
phase
, and
comm
 parameters and, for the distributed format, the
a
,
ia
, and
ja
 arrays) must be set on the master MPI process only, and ignored on other processes. Other MPI processes get all required data from the master MPI process using the MPI communicator,
comm
.
pt
Array of size 64.
Handle to internal data structure. The entries must be set to zero before the first call to
cluster_sparse_solver
.
After the first call to
cluster_sparse_solver
 do not modify
pt
, as that could cause a serious memory leak.
maxfct
Ignored; assumed equal to 1.
mnum
Ignored; assumed equal to 1.
mtype
Defines the matrix type, which influences the pivoting method. The Parallel Direct Sparse Solver for Clusters solver supports the following matrices:
1
real and structurally symmetric
2
real and symmetric positive definite
-2
real and symmetric indefinite
3
complex and structurally symmetric
4
complex and Hermitian positive definite
-4
complex and Hermitian indefinite
6
complex and symmetric
11
real and nonsymmetric
13
complex and nonsymmetric
phase
Controls the execution of the solver. Usually it is a two- or three-digit integer. The first digit indicates the starting phase of execution and the second digit indicates the ending phase. Parallel Direct Sparse Solver for Clusters has the following phases of execution:
  • Phase 1: Fill-reduction analysis and symbolic factorization
  • Phase 2: Numerical factorization
  • Phase 3: Forward and Backward solve including optional iterative refinement
  • Memory release (
    phase
    = -1)
If a previous call to the routine has computed information from previous phases, execution may start at any phase. The
phase
 parameter can have the following values:
phase
Solver Execution Steps
11
Analysis
12
Analysis, numerical factorization
13
Analysis, numerical factorization, solve, iterative refinement
22
Numerical factorization
23
Numerical factorization, solve, iterative refinement
33
Solve, iterative refinement
-1
Release all internal memory for all matrices
n
Number of equations in the sparse linear systems of equations
A
*
X
 =
B
. Constraint:
n
 > 0
.
a
Array. Contains the non-zero elements of the coefficient matrix
A
 corresponding to the indices in
ja
. The coefficient matrix can be either real or complex. The matrix must be stored in the three-array variant of the compressed sparse row (CSR3) or in the three-array variant of the block compressed sparse row (BSR3) format, and the matrix must be stored with increasing values of
ja
 for each row.
For CSR3 format, the size of
a
 is the same as that of
ja
. Refer to the
values
 array description in Three Array Variation of CSR Format for more details.
For BSR3 format the size of
a
 is the size of
ja
 multiplied by the square of the block size. Refer to the
values
 array description in Three Array Variation of BSR Format for more details.
For centralized input (
iparm
[39]
=0
), provide the
a
 array for the master MPI process only. For distributed assembled input (
iparm
[39]
=1
 or
iparm
[39]
=2
), provide it for all MPI processes.
The column indices of non-zero elements of each row of the matrix
A
 must be stored in increasing order.
ia
For CSR3 format,
ia
[
i
]
 (
i
<
n
) points to the first column index of row
i
 in the array
ja
. That is,
ia
[
i
]
 gives the index of the element in array
a
 that contains the first non-zero element from row
i
 of
A
. The last element
ia
[
n
]
 is taken to be equal to the number of non-zero elements in
A
, plus one. Refer to
rowIndex
 array description in Three Array Variation of CSR Format for more details.
For BSR3 format,
ia
[
i
]
 (
i
<
n
) points to the first column index of row
i
 in the array
ja
. That is,
ia
[
i
]
 gives the index of the element in array
a
 that contains the first non-zero block from row
i
 of
A
. The last element
ia
[
n
]
 is taken to be equal to the number of non-zero blcoks in
A
, plus one. Refer to
rowIndex
 array description in Three Array Variation of BSR Format for more details.
The array
ia
 is accessed in all phases of the solution process.
Indexing of
ia
 is one-based by default, but it can be changed to zero-based by setting the appropriate value to the parameter
iparm
[34]
. For zero-based indexing, the last element
ia
[
n
]
 is assumed to be equal to the number of non-zero elements in matrix
A
.
For centralized input (
iparm
[39]
=0
), provide the
ia
 array at the master MPI process only. For distributed assembled input (
iparm
[39]
=1
 or
iparm
[39]
=2
), provide it at all MPI processes.
ja
For CSR3 format, array
ja
 contains column indices of the sparse matrix
A
. It is important that the indices are in increasing order per row. For symmetric matrices, the solver needs only the upper triangular part of the system as is shown for
columns
 array in Three Array Variation of CSR Format.
For BSR3 format, array
ja
 contains column indices of the sparse matrix
A
. It is important that the indices are in increasing order per row. For symmetric matrices, the solver needs only the upper triangular part of the system as is shown for
columns
 array in Three Array Variation of BSR Format.
The array
ja
 is accessed in all phases of the solution process.
Indexing of
ja
 is one-based by default, but it can be changed to zero-based by setting the appropriate value to the parameter
iparm
(35)
.
For centralized input (
iparm
(40)
=0)
, provide the
ja
 array at the master MPI process only. For distributed assembled input (
iparm
(40)=1
 or
iparm
(40)=2
), provide it at all MPI processes.
perm
Ignored.
nrhs
Number of right-hand sides that need to be solved for.
iparm
Array, size
64
. This array is used to pass various parameters to Parallel Direct Sparse Solver for Clusters Interface and to return some useful information after execution of the solver.
See cluster_sparse_solver iparm Parameter for more details about the
iparm
 parameters.
msglvl
Message level information. If
msglvl
 = 0
 then
cluster_sparse_solver
 generates no output, if
msglvl
 = 1
 the solver prints statistical information to the screen.
Statistics include information such as the number of non-zero elements in
L-factor
 and the timing for each phase.
Set
msglvl
 = 1
 if you report a problem with the solver, since the additional information provided can facilitate a solution.
b
Array, size
n
*
nrhs
. On entry, contains the right-hand side vector/matrix
B
, which is placed in memory contiguously. The
b
[
i
+
k
*
n
]
 must hold the
i
-th component of
k
-th right-hand side vector. Note that
b
 is only accessed in the solution phase.
comm
MPI communicator. The solver uses the Fortran MPI communicator internally.
C
onvert the MPI communicator to Fortran using the
MPI_Comm_c2f()
 function. See the examples in the
<install_dir>
/examples
 directory.
Output Parameters
pt
Handle to internal data structure.
perm
Ignored.
iparm
On output, some
iparm
 values report information such as the numbers of non-zero elements in the factors.
See cluster_sparse_solver iparm Parameter for more details about the
iparm
 parameters.
b
On output, the array is replaced with the solution if
iparm
[5]
 = 1.
x
Array, size (
n
*
nrhs
). If
iparm
[5]
=0 it contains solution vector/matrix
X
, which is placed contiguously in memory. The
x
[
i
+
k
*
n
]
 element must hold the
i
-th component of the
k
-th solution vector. Note that
x
 is only accessed in the solution phase.
error
The error indicator according to the below table:
error
Information
0
no error
-1
input inconsistent
-2
not enough memory
-3
reordering problem
-4
Zero pivot, numerical factorization or iterative refinement problem. If the error appears during the solution phase, try to change the pivoting perturbation (
iparm
[9]
) and also increase the number of iterative refinement steps. If it does not help, consider changing the scaling, matching and pivoting options (
iparm
[10]
,
iparm
[12]
,
iparm
[20]
)
-5
unclassified (internal) error
-6
reordering failed (matrix types 11 and 13 only)
-7
diagonal matrix is singular
-8
32-bit integer overflow problem
-9
not enough memory for OOC
-10
error opening OOC files
-11
read/write error with OOC files

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 specif