Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

cluster_sparse_solver iparm Parameter

The following table describes all individual components of the Parallel Direct Sparse Solver for Clusters Interface
iparm
 parameter. Components which are not used must be initialized with 0. Default values are denoted with an asterisk (*).
Component
Description
iparm
[0]
input
Use default values.
0
iparm
[1]
 -
iparm
(64)
 are filled with default values.
!=0
You must supply all values in components
iparm
[1]
 -
iparm
(64)
.
iparm
[1]
input
Fill-in reducing ordering for the input matrix.
2*
The nested dissection algorithm from the METIS package [Karypis98].
3
The parallel version of the nested dissection algorithm. It can decrease the time of computations on multi-core computers, especially when Phase 1 takes significant time.
10
The MPI version of the nested dissection and symbolic factorization algorithms. The input matrix for the reordering must be distributed among different MPI processes without any intersection. Use
iparm
[40]
 and
iparm
[41]
to set the bounds of the domain. During all of Phase 1, the entire matrix is not gathered on any one process, which can decrease computation time (especially when Phase 1 takes significant time) and decrease memory usage for each MPI process on the cluster.
If you set
iparm
[1]
 = 10
,
comm
 = -1
 (MPI communicator), and if there is one MPI process, optimization and full parallelization with the OpenMP version of the nested dissection and symbolic factorization algorithms proceeds. This can decrease computation time on multi-core computers. In this case, set
iparm
[40]
 = 1
 and
iparm
[41]
 =
n
 for one-based indexing, or to
0
 and
n
 - 1
, respectively, for zero-based indexing.
iparm
[2]
Reserved. Set to zero.
iparm[4]
input
User permutation.
This parameter controls whether user supplied fill-in reducing permutation is used instead of the integrated multiple-minimum degree or nested dissection algorithms. Another use of this parameter is to control obtaining the fill-in reducing permutation vector calculated during the reordering stage of
Intel® oneAPI Math Kernel Library
 PARDISO.
This option is useful for testing reordering algorithms, adapting the code to special applications problems (for instance, to move zero diagonal elements to the end of
P
*
A
*
P
T
), or for using the permutation vector more than once for matrices with identical sparsity structures. For definition of the permutation, see the description of the
perm
 parameter.
You can only set one of
iparm
[4]
,
iparm
[30]
, and
iparm
[35]
, so be sure that the
iparm
[30]
 (partial solution) and the
iparm
[35]
 (Schur complement) parameters are 0 if you set
iparm
[4]
.
0
User permutation in the
perm
 array is ignored.
1
Intel® oneAPI Math Kernel Library
 PARDISO uses the user supplied fill-in reducing permutation from the
perm
 array.
iparm
[1]
 is ignored.
2
Intel® oneAPI Math Kernel Library
 PARDISO returns the permutation vector computed at phase 1 in the
perm
 array.
iparm
[5]
input
Write solution on
x
.
The array
x
 is always used.
0*
The array
x
 contains the solution; right-hand side vector
b
 is kept unchanged.
1
The solver stores the solution on the right-hand side
b
.
iparm
[6]
output
Number of iterative refinement steps performed.
Reports the number of iterative refinement steps that were actually performed during the solve step.
iparm
[7]
input
Iterative refinement step.
On entry to the solve and iterative refinement step,
iparm
[7]
 must be set to the maximum number of iterative refinement steps that the solver performs.
0*
The solver automatically performs two steps of iterative refinement when perturbed pivots are obtained during the numerical factorization.
>0
Maximum number of iterative refinement steps that the solver performs. The solver performs not more than the absolute value of
iparm
[7]
 steps of iterative refinement. The solver might stop the process before the maximum number of steps if
  • a satisfactory level of accuracy of the solution in terms of backward error is achieved,
  • or if it determines that the required accuracy cannot be reached. In this case Parallel Direct Sparse Solver for Clusters Interface returns -4 in the
    error
     parameter.
The number of executed iterations is reported in
iparm
[6]
.
<0
Same as above, but the accumulation of the residuum uses extended precision real and complex data types.
Perturbed pivots result in iterative refinement (independent of
iparm
[7]
=0
) and the number of executed iterations is reported in
iparm
[6]
.
iparm
[8]
Reserved. Set to zero.
iparm
[9]
input
Pivoting perturbation.
This parameter instructs Parallel Direct Sparse Solver for Clusters Interface how to handle small pivots or zero pivots for nonsymmetric matrices (
mtype
 =11
 or
mtype
 =13
) and symmetric matrices (
mtype
 =-2
,
mtype
 =-4
, or
mtype
 =6
). For these matrices the solver uses a complete supernode pivoting approach. When the factorization algorithm reaches a point where it cannot factor the supernodes with this pivoting strategy, it uses a pivoting perturbation strategy similar to [Li99], [Schenk04].
Small pivots are perturbed with
eps = 10
-
iparm
[9]
.
The magnitude of the potential pivot is tested against a constant threshold of
alpha = eps*||
A2
||
inf
,
where
eps = 10
(-
iparm
[9]
)
,
A2
 =
P
*
P
MPS
*
D
r
*
A
*
D
c
*
P
, and
||
A2
||
inf
 is the infinity norm of the scaled and permuted matrix
A
. Any tiny pivots encountered during elimination are set to the sign
(
l
I
I
)*eps*||
A2
||
inf
, which trades off some numerical stability for the ability to keep pivots from getting too small. Small pivots are therefore perturbed with
eps = 10
(-
iparm
[9]
)
.
13*
The default value for nonsymmetric matrices(
mtype
 =11,
mtype
=13),
eps = 10
-13
.
8*
The default value for symmetric indefinite matrices (
mtype
 =-2,
mtype
=-4,
mtype
=6),
eps = 10
-8
.
iparm
[10]
input
Scaling vectors.
Parallel Direct Sparse Solver for Clusters Interface uses a maximum weight matching algorithm to permute large elements on the diagonal and to scale.
Use
iparm
[10]
 = 1 (scaling) and
iparm
[12]
 = 1 (matching) for highly indefinite symmetric matrices, for example, from interior point optimizations or saddle point problems. Note that in the analysis phase (
phase
=11
) you must provide the numerical values of the matrix
A
 in array
a
 in case of scaling and symmetric weighted matching.
0*
Disable scaling. Default for symmetric indefinite matrices.
1*
Enable scaling. Default for nonsymmetric matrices.
Scale the matrix so that the diagonal elements are equal to 1 and the absolute values of the off-diagonal entries are less or equal to 1. This scaling method is applied to nonsymmetric matrices (
mtype
 = 11,
mtype
 = 13). The scaling can also be used for symmetric indefinite matrices (
mtype
 = -2,
mtype
 = -4,
mtype
 = 6) when the symmetric weighted matchings are applied (
iparm
[12]
 = 1).
Note that in the analysis phase (
phase
=11) you must provide the numerical values of the matrix
A
 in case of scaling.
iparm
[11]
Solve with transposed or conjugate transposed matrix
A
.
For real matrices, the terms
transposed
 and
conjugate transposed
 are equivalent.
0*
Solve a linear system
AX
 =
B
.
1
Solve a conjugate transposed system
A
H
X
 =
B
 based on the factorization of the matrix
A
.
2
Solve a transposed system
A
T
X
 =
B
 based on the factorization of the matrix
A
.
iparm
[12]
input
Improved accuracy using (non-) symmetric weighted matching.
Parallel Direct Sparse Solver for Clusters Interface can use a maximum weighted matching algorithm to permute large elements close the diagonal. This strategy adds an additional level of reliability to the factorization methods and complements the alternative of using more complete pivoting techniques during the numerical factorization.
  
0*
Disable matching. Default for symmetric indefinite matrices.
1*
Enable matching. Default for nonsymmetric matrices.
Maximum weighted matching algorithm to permute large elements close to the diagonal.
It is recommended to use
iparm
[10]
 = 1 (scaling) and
iparm
[12]
= 1 (matching) for highly indefinite symmetric matrices, for example from interior point optimizations or saddle point problems.
Note that in the analysis phase (
phase
=11) you must provide the numerical values of the matrix
A
 in case of symmetric weighted matching.
iparm
[13]
output
Number of perturbed pivots.
After factorization, contains the number of perturbed pivots for the matrix types: 1, 3, 11, 13, -2, -4 and 6.
iparm
[14]
output
Peak memory on symbolic factorization.
The total peak memory in kilobytes that the solver needs during the analysis and symbolic factorization phase.
This value is only computed in phase 1.
iparm
[15]
output
Permanent memory on symbolic factorization.
Permanent memory from the analysis and symbolic factorization phase in kilobytes that the solver needs in the factorization and solve phases.
This value is only computed in phase 1.
iparm
[16]
output
Size of factors/Peak memory on numerical factorization and solution.
This parameter provides the size in kilobytes of the total memory consumed by in-core
Intel® oneAPI Math Kernel Library
 PARDISO for internal floating point arrays. This parameter is computed in phase 1. See
iparm
[62]
 for the OOC mode.
The total peak memory consumed by
Intel® oneAPI Math Kernel Library
 PARDISO is
max(
iparm
[14]
,
iparm
[15]
+
iparm
[16]
)
iparm
[17]
input/output
Report the number of non-zero elements in the factors.
<0
Enable reporting if
iparm
[17]
 < 0 on entry. The default value is -1.
>=0
Disable reporting.
iparm
[18]
 -
iparm
[19]
Reserved. Set to zero.
iparm
[20]
input
Pivoting for symmetric indefinite matrices.
0
Apply 1x1 diagonal pivoting during the factorization process.
1*
Apply 1x1 and 2x2 Bunch-Kaufman pivoting during the factorization process. Bunch-Kaufman pivoting is available for matrices of
mtype
=-2
,
mtype
=-4
, or
mtype
=6
.
iparm
[21]
output
Inertia: number of positive eigenvalues.
Intel® oneAPI Math Kernel Library
 PARDISO reports the number of positive eigenvalues for symmetric indefinite matrices.
iparm
[22]
output
Inertia: number of negative eigenvalues.
Intel® oneAPI Math Kernel Library
 PARDISO reports the number of negative eigenvalues for symmetric indefinite matrices.
iparm
[23]
 -
iparm
[25]
Reserved. Set to zero.
iparm
[26]
input
Matrix checker.
0*
Do not check the sparse matrix representation for errors.
1
Check integer arrays
ia
 and