Testing Matlab interface to BLOPEX

BLOPEX LOBPCG computes 4th, 5th and 6th smallest eigenpairs of the diagonal n-by-n matrix spdiags((1:n)',0,n,n), n = 10000, given the first 3 eigenvectors as initial constraints. The BLOPEX results are then compared to the Matlab version of lobpcg (lobpcg.m) results.

System configuration:

Fedora 10 OS, 4 Quad Core Opteron 2.0 Ghz CPUs, 64 GB RAM;
Open MPI version 1.2.4;
Compiler version gcc (GCC) 4.3.2 20081105 (Red Hat 4.3.2-7);
LAPACK version 3.1.1
Matlab version 7.7.0.471 (R2008b)

Setup Matlab interface with BLOPEX

We need two BLOPEX subdirectories: blopex_abstract and blopex_matlab.

Before compiling, add a search path for the Matlab mex compiler by issuing

PATH=$PATH:/opt/matlab/bin
export PATH

Then go to blopex_abstract and modify Makefile.inc by specifying the mex compiler (add line CC = mex):

CFLAGS =

AR = ar -rvcu
RANLIB = ranlib

CC = mex

Save changes to Makefile.inc and run make. This builds blopex_abstract with mex compiler.

Now shift to blopex_matlab and modify the Makefile to add LAPACK to the linking process (add -llapack):

........
driver/blopex_matlab_gateway.mexglx: blopex_matlab_gateway.c multivector_for_matlab.h matlab_interface.h \
                                     multivector_for_matlab.o matlab_interface.o
        $(CC) $(CFLAGS) $(CPPFLAGS) $< matlab_interface/c_files/multivector_for_matlab.o \
         matlab_interface/c_files/matlab_interface.o ''-llapack'' $(LIB_DIRS) $(LIBS) -outdir $(@D)
........

Save changes to Makefile and run make. This compiles the Matlab interface to BLOPEX (also with mex compiler).

Execution of tests for Matlab interface to BLOPEX

Start Matlab and add directories .../blopex/blopex_matlab/driver and .../blopex/blopex_matlab/matlab_interface/m_files to Matlab path:

>> addpath('/home/grads/.../blopex/blopex_matlab/driver')
>> addpath('/home/grads/.../blopex/blopex_matlab/matlab_interface/m_files')

Run the script .../blopex/blopex_matlab/driver/test_blopex_matlab.m:

test_blopex_matlab

The full initial guess with 10000 columns and 3 raws is detected  
The main operator is detected as a sparse matrix 
The second operator of the generalized eigenproblem 
is detected as a sparse matrix 
The preconditioner is detected as an M-function precond 
The full matrix of 3 constraints is detected 
Solving with tolerance 1.000000e-04 and maximum number of iterations 40 

Solving generalized eigenvalue problem with preconditioning

block size 3

3 constraints

...........
Eigenvalue lambda 4.0000000000002425e+00
Eigenvalue lambda 5.0000000000009530e+00
Eigenvalue lambda 6.0000000001127898e+00
Residual 3.0668655987253611e-05
Residual 5.4190180513113715e-05
Residual 8.5218964177237057e-05

15 iterations

SOLUTION TIME, blopex_matlab: 0.637745

The full initial guess with 10000 columns and 3 raws is detected  
...........
Final Eigenvalues lambda 4.0000000000000222e+00 
Final Eigenvalues lambda 5.0000000000007034e+00 
Final Eigenvalues lambda 6.0000000001121920e+00 
Final Residual Norms 2.057962e-06 
Final Residual Norms 1.494745e-05 
Final Residual Norms 8.521897e-05 

SOLUTION TIME, lobpcg.m: 0.433134

The desired tolerance (1e-4) was achieved in 15 iterations for both (Matlab-BLOPEX and Matlab-lobpcg.m) runs.

Wiki

blopex / TestBLOPEXMatlabInterfaceLinux

Testing Matlab interface to BLOPEX

Setup Matlab interface with BLOPEX

Execution of tests for Matlab interface to BLOPEX