How to find the determinant or condition number of the stiffness matrix?

General Discussion
1

Hi,profeesor How to find the determinant or condition number of the stiffness matrix?

2

You can use MUMPS, see MATSOLVERMUMPS mat_mumps_icntl_33 for the determinant. For the condition number, you can use SLEPc or ARPACK, or if the problem is not too ill-conditioned, -ksp_monitor_singular_value.

3

Be careful with the boundary condition, the tgv technique break the condition number .
And The example eigen/condition-number.edp given an example:
condition-number.edp (718 Bytes)

4

Hi,professor, I used the following command,
set(dA, sparams ="-pc_factor_mat_solver_type superlu -mat_mumps_icntl_33");
but how do I output this determinant?

5

You need to use MUMPS, not SuperLU. The determinant is displayed if you further add -ksp_view.

7

Hi，professor, I used the following command, but there is no determinant，why?
set(A, sparams =“-pc_factor_mat_solver_type mumps -mat_mumps_icntl_33 -ksp_view_determinant”);

8

What is -ksp_view_determinant?

9

I want to output determinants, but I use the following command to output conditional numbers,why？ The command “mumps -mat_mumps_icntl_33 " should the determinant.
set(A, sparams =”-pc_factor_mat_solver_type mumps -mat_mumps_icntl_33 -ksp_view_singularvalues")

10

Why are you not using the flag I told you to use in the first place?

12

Hi, however, I used the command
set(A, sparams ="-pc_factor_mat_solver_type mumps -mat_mumps_icntl_33 -ksp_view"), but Still there is any output about the determinant.

13

This is what I get, for example running diffusion-2d-PETSc.edp from examples/hpddm:

[...]
              RINFOG(3) (global estimated flops for the elimination after factorization): 1.93421e+06 
              (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (0.713452,0.)*(2^6709)
              INFOG(3) (estimated real workspace for factors on all processors after analysis): 65153
[...]

Determinant is the second line in the above snippet.

1 Like
14

Hello, I tried some examples from> examples/hpddm
, but I still didn’t output the result of determinant. The output content is basically as follows. Why？

C:\Users\weiqi>FreeFem+±mpi stokes-2d-PETSc.edp -v 0
KSP Object: 1 MPI processes
type: gmres
restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
happy breakdown tolerance 1e-30
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using PRECONDITIONED norm type for convergence test
PC Object: 1 MPI processes
type: bjacobi
number of blocks = 1
Local solver information for first block is in the following KSP and PC objects on rank 0:
Use -ksp_view ::ascii_info_detail to display information for all blocks
KSP Object: (sub_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: (sub_) 1 MPI processes
type: ilu
out-of-place factorization
0 levels of fill
tolerance for zero pivot 2.22045e-14
matrix ordering: natural
factor fill ratio given 1., needed 1.
Factored matrix follows:
Mat Object: 1 MPI processes
type: seqaij
rows=22203, cols=22203
package used to perform factorization: petsc
total: nonzeros=647409, allocated nonzeros=647409
using I-node routines: found 9835 nodes, limit used is 5
linear system matrix = precond matrix:
Mat Object: (sub_) 1 MPI processes
type: seqaij
rows=22203, cols=22203
total: nonzeros=647409, allocated nonzeros=647409
total number of mallocs used during MatSetValues calls=0
using I-node routines: found 9835 nodes, limit used is 5
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: mpiaij
rows=22203, cols=22203
total: nonzeros=647409, allocated nonzeros=647409
total number of mallocs used during MatSetValues calls=0
using I-node (on process 0) routines: found 9835 nodes, limit used is 5

15

You are not using the proper preconditioner (-pc_type).

16

Hello, professor, I still don’t quite understand what you mean. Could you please explain it in detail?

17

Explain what? -pc_type and -ksp_view are explained in the screencast I sent earlier.

18

Thank you. I see what you mean, but the determinant （examples/hpddm/bilaplace-2d-PETSc.edp)is (0, 0) * (2 ^ 0)，why？

C:\Users\weiqi>FreeFem+±mpi bilaplace-2d-PETSc.edp -v 0
KSP Object: 1 MPI processes
type: gmres
restart=30, using Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement
happy breakdown tolerance 1e-30
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using PRECONDITIONED norm type for convergence test
PC Object: 1 MPI processes
type: cholesky
out-of-place factorization
tolerance for zero pivot 2.22045e-14
matrix ordering: external
factor fill ratio given 0., needed 0.
Factored matrix follows:
Mat Object: 1 MPI processes
type: mumps
rows=6561, cols=6561
package used to perform factorization: mumps
total: nonzeros=201780, allocated nonzeros=201780
MUMPS run parameters:
SYM (matrix type): 2
PAR (host participation): 1
ICNTL(1) (output for error): 6
ICNTL(2) (output of diagnostic msg): 0
ICNTL(3) (output for global info): 0
ICNTL(4) (level of printing): 0
ICNTL(5) (input mat struct): 0
ICNTL(6) (matrix prescaling): 7
ICNTL(7) (sequential matrix ordering):7
ICNTL(8) (scaling strategy): 77
ICNTL(10) (max num of refinements): 0
ICNTL(11) (error analysis): 0
ICNTL(12) (efficiency control): 0
ICNTL(13) (sequential factorization of the root node): 0
ICNTL(14) (percentage of estimated workspace increase): 20
ICNTL(18) (input mat struct): 0
ICNTL(19) (Schur complement info): 0
ICNTL(20) (RHS sparse pattern): 0
ICNTL(21) (solution struct): 0
ICNTL(22) (in-core/out-of-core facility): 0
ICNTL(23) (max size of memory can be allocated locally):0
ICNTL(24) (detection of null pivot rows): 0
ICNTL(25) (computation of a null space basis): 0
ICNTL(26) (Schur options for RHS or solution): 0
ICNTL(27) (blocking size for multiple RHS): -32
ICNTL(28) (use parallel or sequential ordering): 1
ICNTL(29) (parallel ordering): 0
ICNTL(30) (user-specified set of entries in inv(A)): 0
ICNTL(31) (factors is discarded in the solve phase): 0
ICNTL(33) (compute determinant): 0
ICNTL(35) (activate BLR based factorization): 0
ICNTL(36) (choice of BLR factorization variant): 0
ICNTL(38) (estimated compression rate of LU factors): 333
CNTL(1) (relative pivoting threshold): 0.01
CNTL(2) (stopping criterion of refinement): 1.49012e-08
CNTL(3) (absolute pivoting threshold): 0.
CNTL(4) (value of static pivoting): -1.
CNTL(5) (fixation for null pivots): 0.
CNTL(7) (dropping parameter for BLR): 0.
RINFO(1) (local estimated flops for the elimination after analysis):
[0] 1.1037e+07
RINFO(2) (local estimated flops for the assembly after factorization):
[0] 339313.
RINFO(3) (local estimated flops for the elimination after factorization):
[0] 1.1037e+07
INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization):
[0] 4
INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization):
[0] 4
INFO(23) (num of pivots eliminated on this processor after factorization):
[0] 6561
RINFOG(1) (global estimated flops for the elimination after analysis): 1.1037e+07
RINFOG(2) (global estimated flops for the assembly after factorization): 339313.
RINFOG(3) (global estimated flops for the elimination after factorization): 1.1037e+07
(RINFOG(12) RINFOG(13))2^INFOG(34) (determinant): (0.,0.)(2^0)
INFOG(3) (estimated real workspace for factors on all processors after analysis): 228803
INFOG(4) (estimated integer workspace for factors on all processors after analysis): 121006
INFOG(5) (estimated maximum front size in the complete tree): 144
INFOG(6) (number of nodes in the complete tree): 2392
INFOG(7) (ordering option effectively used after analysis): 2
INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): 100
INFOG(9) (total real/complex workspace to store the matrix factors after factorization): 228803
INFOG(10) (total integer space store the matrix factors after factorization): 121006
INFOG(11) (order of largest frontal matrix after factorization): 144
INFOG(12) (number of off-diagonal pivots): 0
INFOG(13) (number of delayed pivots after factorization): 0
INFOG(14) (number of memory compress after factorization): 0
INFOG(15) (number of steps of iterative refinement after solution): 0
INFOG(16) (estimated size (in MB) of all MUMPS internal data for factorization after analysis: value on the most memory consuming processor): 4
INFOG(17) (estimated size of all MUMPS internal data for factorization after analysis: sum over all processors): 4
INFOG(18) (size of all MUMPS internal data allocated during factorization: value on the most memory consuming processor): 4
INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): 4
INFOG(20) (estimated number of entries in the factors): 201780
INFOG(21) (size in MB of memory effectively used during factorization - value on the most memory consuming processor): 4
INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): 4
INFOG(23) (after analysis: value of ICNTL(6) effectively used): 0
INFOG(24) (after analysis: value of ICNTL(12) effectively used): 1
INFOG(25) (after factorization: number of pivots modified by static pivoting): 0
INFOG(28) (after factorization: number of null pivots encountered): 0
INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): 201780
INFOG(30, 31) (after solution: size in Mbytes of memory used during solution phase): 3, 3
INFOG(32) (after analysis: type of analysis done): 1
INFOG(33) (value used for ICNTL(8)): 7
INFOG(34) (exponent of the determinant if determinant is requested): 0
INFOG(35) (after factorization: number of entries taking into account BLR factor compression - sum over all processors): 201780
INFOG(36) (after analysis: estimated size of all MUMPS internal data for running BLR in-core - value on the most memory consuming processor): 0
INFOG(37) (after analysis: estimated size of all MUMPS internal data for running BLR in-core - sum over all processors): 0
INFOG(38) (after analysis: estimated size of all MUMPS internal data for running BLR out-of-core - value on the most memory consuming processor): 0
INFOG(39) (after analysis: estimated size of all MUMPS internal data for running BLR out-of-core - sum over all processors): 0
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: mpiaij
rows=6561, cols=6561
total: nonzeros=74241, allocated nonzeros=74241
total number of mallocs used during MatSetValues calls=0
not using I-node (on process 0) routines

19

Here is what I get with -mat_mumps_icntl_33 1:

              (RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (0.622873,0.)*(2^79647)
20

On line 26 of this code, re-enter the following language:

set(A, sparams = “-pc_type cholesky -pc_factor_mat_solver_type mumps -mat_mumps_icntl_33 -ksp_view”);

next, Enter the following command in the command window

C:\Users\weiqi>FreeFem+±mpi bilaplace-2d-PETSc.edp -v 0

21

It is -mat_mumps_icntl_33 1, you are missing the one.

1 Like
22

Thank you very much indeed. It’s very patient of you. Thank you