* GEMMA performance stats

Below measurements are taken on 4x Intel(R) Core(TM) i7-6770HQ CPU @
2.60GHz with hyperthreading and 16 GB RAM with warmed up memory
buffers.

Between 0.96 and 0.97 a speed regression was [[https://github.com/genetics-statistics/GEMMA/issues/136][reported]] which resulted
in tracking of performance. It is interesting because 0.96 is a single
core Eigenlib version and 0.97 went multi-core with
openblas. Unfortunately I linked in lapack and an older BLAS which
slowed things down. In 0.98 openblas is mostly used and is faster.

Note also that the recent static versions are slower than the
dynamically linked ones. Not sure why that is.

The test commands are

#+BEGIN_SRC
# kinship
time ./bin/gemma -g ./example/mouse_hs1940.geno.txt.gz -p ./example/mouse_hs1940.pheno.txt -a ./example/mouse_hs1940.anno.txt -gk -no-check
# univariate LMM
time ./bin/gemma -g ./example/mouse_hs1940.geno.txt.gz -p ./example/mouse_hs1940.pheno.txt -n 1 -a ./example/mouse_hs1940.anno.txt -k ./output/result.cXX.txt -lmm -no-check
# multivariate LMM
time ./bin/gemma -g ./example/mouse_hs1940.geno.txt.gz -p ./example/mouse_hs1940.pheno.txt -n 1 2 -a ./example/mouse_hs1940.anno.txt -k ./output/result.cXX.txt -lmm -no-check
#+END_SRC

Currently on my laptop there is no difference in running these tests
using gcc or clang.

#+BEGIN_SRC
Clang:

real    0m25.758s
user    0m46.380s
sys     0m0.852s

real    0m22.173s
user    0m29.420s
sys     0m1.540s

GNU C

real    0m24.540s
user    0m43.948s
sys     0m1.276s

real    0m22.504s
user    0m29.768s
sys     0m1.544s
#+END_SRC

Running the GNU profiler I got K to be faster by removing the regexs

#+BEGIN_SRC
real    0m16.811s
user    0m37.788s
sys     0m2.168s
#+END_SRC

Replacing safeGetLine also made some difference

#+BEGIN_SRC
real    0m15.659s
user    0m34.896s
sys     0m1.500s
#+END_SRC

there is still some scope for improvement by changing do_strtok_safe
methods as well as less string copying during tokenization. I may get
to that at some point.

Running the GNU profiler on the MVLMM one rendered

#+BEGIN_SRC
  %   cumulative   self              self     total
 time   seconds   seconds    calls   s/call   s/call  name
 22.73      0.90     0.90    41121     0.00     0.00  CalcQi(gsl_vector const*, gsl_vector const*, gsl_matrix const*, gsl_matrix*)
 13.64      1.44     0.54    30313     0.00     0.00  CalcXHiY(gsl_vector const*, gsl_vector const*, gsl_matrix const*, gsl_matrix const*, gsl_v
ector*)
 11.87      1.91     0.47    19536     0.00     0.00  CalcSigma(char, gsl_vector const*, gsl_vector const*, gsl_matrix const*, gsl_matrix const*
, gsl_matrix const*, gsl_matrix const*, gsl_matrix const*, gsl_matrix*, gsl_matrix*)
 10.86      2.34     0.43    38621     0.00     0.00  safeGetline(std::istream&, std::__cxx11::basic_string<char, std::char_traits<char>, std::a
llocator<char> >&)
  8.33      2.67     0.33    10805     0.00     0.00  MphCalcP(gsl_vector const*, gsl_vector const*, gsl_matrix const*, gsl_matrix const*, gsl_m
atrix const*, gsl_matrix const*, gsl_matrix*, gsl_vector*, gsl_matrix*)
  6.06      2.91     0.24        1     0.24     0.43  ReadFile_geno
  5.30      3.12     0.21    19536     0.00     0.00  UpdateV(gsl_vector const*, gsl_matrix const*, gsl_matrix const*, gsl_matrix const*, gsl_ma
trix const*, gsl_matrix*, gsl_matrix*)
  5.30      3.33     0.21        1     0.21     3.27  MVLMM::AnalyzeBimbam(gsl_matrix const*, gsl_vector const*, gsl_matrix const*, gsl_matrix c
onst*)
#+END_SRC

* GEMMA 0.98 (release)

#+BEGIN_SRC bash
        libgsl.so.23 => /gnu/store/79fw0qqlgpk7n8vll6lnlc4ahahn4gbw-profile/lib/libgsl.so.23 (0x00007fcb53b1f000)
        libz.so.1 => /gnu/store/79fw0qqlgpk7n8vll6lnlc4ahahn4gbw-profile/lib/libz.so.1 (0x00007fcb53903000)
        libopenblas.so.0 => /gnu/store/79fw0qqlgpk7n8vll6lnlc4ahahn4gbw-profile/lib/libopenblas.so.0 (0x00007fcb51bfb000)
        libgfortran.so.5 => /gnu/store/79fw0qqlgpk7n8vll6lnlc4ahahn4gbw-profile/lib/libgfortran.so.5 (0x00007fcb5178c000)
        libquadmath.so.0 => /gnu/store/bmaxmigwnlbdpls20px2ipq1fll36ncd-gcc-8.2.0-lib/lib/libquadmath.so.0 (0x00007fcb5154c000)
        libstdc++.so.6 => /gnu/store/bmaxmigwnlbdpls20px2ipq1fll36ncd-gcc-8.2.0-lib/lib/libstdc++.so.6 (0x00007fcb511c4000)
        libm.so.6 => /gnu/store/l4lr0f5cjd0nbsaaf8b5dmcw1a1yypr3-glibc-2.27/lib/libm.so.6 (0x00007fcb50e2e000)
        libgcc_s.so.1 => /gnu/store/bmaxmigwnlbdpls20px2ipq1fll36ncd-gcc-8.2.0-lib/lib/libgcc_s.so.1 (0x00007fcb50c16000)
        libpthread.so.0 => /gnu/store/l4lr0f5cjd0nbsaaf8b5dmcw1a1yypr3-glibc-2.27/lib/libpthread.so.0 (0x00007fcb509f8000)
        libc.so.6 => /gnu/store/l4lr0f5cjd0nbsaaf8b5dmcw1a1yypr3-glibc-2.27/lib/libc.so.6 (0x00007fcb50645000)
        libgfortran.so.3 => /gnu/store/1yym4xrvnlsvcnbzgxy967cg6dlb19gq-gfortran-5.5.0-lib/lib/libgfortran.so.3 (0x00007fcb50322000)
        /gnu/store/l4lr0f5cjd0nbsaaf8b5dmcw1a1yypr3-glibc-2.27/lib/ld-linux-x86-64.so.2 (0x0000561ae24a8000)
#+END_SRC

#+BEGIN_SRC bash
time ./bin/gemma -g ./example/mouse_hs1940.geno.txt.gz -p ./example/mouse_hs1940.pheno.txt -a ./example/mouse_hs1940.anno.txt -gk -no-check
GEMMA 0.98 (2018-09-26) by Xiang Zhou and team (C) 2012-2018
Reading Files ...
## number of total individuals = 1940
## number of analyzed individuals = 1410
## number of covariates = 1
## number of phenotypes = 1
## number of total SNPs/var        =    12226
## number of analyzed SNPs         =    10768
Calculating Relatedness Matrix ...
================================================== 100%

real    0m7.299s
user    0m13.632s
sys     0m1.468s
#+END_SRC

#+BEGIN_SRC bash
time ./bin/gemma -g ./example/mouse_hs1940.geno.txt.gz -p ./example/mouse_hs1940.pheno.txt -n 1 -a ./example/mouse_hs1940.anno.txt -k ./output/result.cXX.txt -lmm -no-check
GEMMA 0.98 (2018-09-26) by Xiang Zhou and team (C) 2012-2018
Reading Files ...
## number of total individuals = 1940
## number of analyzed individuals = 1410
## number of covariates = 1
## number of phenotypes = 1
## number of total SNPs/var        =    12226
## number of analyzed SNPs         =    10768
Start Eigen-Decomposition...
pve estimate =0.608801
se(pve) =0.032774
================================================== 100%

real    0m12.395s
user    0m15.748s
sys     0m3.000s
#+END_SRC

Full multivariate analysis is still slow. Mostly because of CalcQi - see above profiling.

#+BEGIN_SRC bash
time ./bin/gemma -g ./example/mouse_hs1940.geno.txt.gz -p ./example/mouse_hs1940.pheno.txt -n 1 2 -a ./example/mouse_hs1940.anno.txt -k ./output/result.cXX.txt -lmm -no-check
GEMMA 0.98 (2018-09-26) by Xiang Zhou and team (C) 2012-2018
Reading Files ...
## number of total individuals = 1940
## number of analyzed individuals = 757
## number of covariates = 1
## number of phenotypes = 2
## number of total SNPs/var        =    12226
## number of analyzed SNPs         =    10775
Start Eigen-Decomposition...
REMLE estimate for Vg in the null model:
1.3270
1.3270  1.3270
se(Vg):
0.8217
0.7152  0.7198
REMLE estimate for Ve in the null model:
0.3251
0.3251  0.3251
se(Ve):
1.9191
2.6491  1.9101
REMLE likelihood = 0.0000
MLE estimate for Vg in the null model:
1.3263
1.3263  1.3263
se(Vg):
0.8217
0.7152  0.7198
MLE estimate for Ve in the null model:
0.3246
0.3246  0.3246
se(Ve):
1.9191
2.6491  1.9101
MLE likelihood = 0.0000
================================================== 100%

real    0m12.076s
user    0m13.324s
sys     0m2.260s

#+END_SRC

using GSL inline functions improved it a bit. The obvious way to
further improve things is to rejig these CalcXHiY, CalcQi and
CalcSigma functions.

* GEMMA 0.98-pre

#+BEGIN_SRC bash
/gnu/store/icz3hd36aqpjz5slyp4hhr8wsfbgiml1-bash-minimal-4.4.12/bin/bash: warning: setlocale: LC_ALL: cannot change locale (en_GB.UTF-8)
        linux-vdso.so.1 (0x00007ffe2abe1000)
        libgsl.so.23 => /home/wrk/opt/gemma-dev-env/lib/libgsl.so.23 (0x00007f685a9c0000)
        libopenblas.so.0 => /home/wrk/opt/gemma-dev-env/lib/libopenblas.so.0 (0x00007f6858422000)
        libz.so.1 => /home/wrk/opt/gemma-dev-env/lib/libz.so.1 (0x00007f6858207000)
        libgfortran.so.3 => /home/wrk/opt/gemma-dev-env/lib/libgfortran.so.3 (0x00007f6857ee6000)
        libquadmath.so.0 => /home/wrk/opt/gemma-dev-env/lib/libquadmath.so.0 (0x00007f6857ca5000)
        libstdc++.so.6 => /home/wrk/opt/gemma-dev-env/lib/libstdc++.so.6 (0x00007f685792a000)
        libm.so.6 => /home/wrk/opt/gemma-dev-env/lib/libm.so.6 (0x00007f68575de000)
        libgcc_s.so.1 => /home/wrk/opt/gemma-dev-env/lib/libgcc_s.so.1 (0x00007f68573c7000)
        libpthread.so.0 => /home/wrk/opt/gemma-dev-env/lib/libpthread.so.0 (0x00007f68571a9000)
        libc.so.6 => /home/wrk/opt/gemma-dev-env/lib/libc.so.6 (0x00007f6856df7000)
        /gnu/store/n6acaivs0jwiwpidjr551dhdni5kgpcr-glibc-2.26.105-g0890d5379c/lib/ld-linux-x86-64.so.2 => /gnu/store/gf30mz7cfx4fyj4cckgxfxwlsc3c7a8r-glibc-2.26.105-g0890d5379c/lib/ld-linux-x86-64.so.2 (0x000055ae91968000)
#+END_SRC

#+BEGIN_SRC bash
lario:~/izip/git/opensource/genenetwork/gemma$ time ./bin/gemma -g ~/tmp/mouse_hs1940/mouse_hs1940.geno.txt.gz -p ~/tmp/mouse_hs1940/mouse_hs1940.pheno.txt -a ~/tmp/mouse_hs1940/mouse_hs1940.anno.txt -gk
GEMMA 0.98-pre1 (2018/02/10) by Xiang Zhou and team (C) 2012-2018
Reading Files ...
## number of total individuals = 1940
## number of analyzed individuals = 1410
## number of covariates = 1
## number of phenotypes = 1
## number of total SNPs/var        =    12226
## number of analyzed SNPs         =    10768
Calculating Relatedness Matrix ...
================================================== 100%

real    0m15.995s
user    0m31.884s
sys     0m4.680s
#+END_SRC

#+BEGIN_SRC bash
lario:~/izip/git/opensource/genenetwork/gemma$ time bin/gemma -g ~/tmp/mouse_hs1940/mouse_hs1940.geno.txt.gz -p ~/tmp/mouse_hs1940/mouse_hs1940.pheno.txt -n 1 -a ~/tmp/mouse_hs1940/mouse_hs1940.anno.txt -k ./output/result.cXX.txt -lmm
GEMMA 0.98-pre1 (2018/02/10) by Xiang Zhou and team (C) 2012-2018
Reading Files ...
## number of total individuals = 1940
## number of analyzed individuals = 1410
## number of covariates = 1
## number of phenotypes = 1
## number of total SNPs/var        =    12226
## number of analyzed SNPs         =    10768
Start Eigen-Decomposition...
pve estimate =0.608801
se(pve) =0.032774
================================================== 100%

real    0m13.440s
user    0m20.528s
sys     0m4.324s
#+END_SRC

* GEMMA 0.97

#+BEGIN_SRC bash
lario:~/tmp/gemma-release-0.97$ ldd gemma-gn2-0.97-c760aa0-xqhsidq7h5/bin/gemma
        linux-vdso.so.1 (0x00007ffc237a8000)
        libgsl.so.23 => /home/wrk/tmp/gemma-release-0.97/gsl-2.4-as8vm64028/lib/libgsl.so.23 (0x00007f8b415f5000)
        libopenblas.so.0 => /home/wrk/tmp/gemma-release-0.97/openblas-0.2.19-f7j1vq0ncc/lib/libopenblas.so.0 (0x00007f8b3fbc3000)
        libz.so.1 => /home/wrk/tmp/gemma-release-0.97/zlib-1.2.11-sfx1wh27i6/lib/libz.so.1 (0x00007f8b3f9a8000)
        libgfortran.so.3 => /home/wrk/tmp/gemma-release-0.97/gfortran-5.4.0-lib-15plffwjdv/lib/libgfortran.so.3 (0x00007f8b3f687000)
        libquadmath.so.0 => /home/wrk/tmp/gemma-release-0.97/gcc-5.4.0-lib-3x53yv4v14/lib/libquadmath.so.0 (0x00007f8b3f448000)
        liblapack.so.3 => /home/wrk/tmp/gemma-release-0.97/lapack-3.7.1-nyd19c9ccy/lib/liblapack.so.3 (0x00007f8b3eb83000)
        libstdc++.so.6 => /home/wrk/tmp/gemma-release-0.97/gcc-5.4.0-lib-3x53yv4v14/lib/libstdc++.so.6 (0x00007f8b3e809000)
        libm.so.6 => /home/wrk/tmp/gemma-release-0.97/glibc-2.25-n6nvxlk2j8/lib/libm.so.6 (0x00007f8b3e4f7000)
        libgcc_s.so.1 => /home/wrk/tmp/gemma-release-0.97/gcc-5.4.0-lib-3x53yv4v14/lib/libgcc_s.so.1 (0x00007f8b3e2e0000)
        libpthread.so.0 => /home/wrk/tmp/gemma-release-0.97/glibc-2.25-n6nvxlk2j8/lib/libpthread.so.0 (0x00007f8b3e0c2000)
        libc.so.6 => /home/wrk/tmp/gemma-release-0.97/glibc-2.25-n6nvxlk2j8/lib/libc.so.6 (0x00007f8b3dd23000)
        libblas.so.3 => /home/wrk/tmp/gemma-release-0.97/lapack-3.7.1-nyd19c9ccy/lib/libblas.so.3 (0x00007f8b3dacb000)
        /home/wrk/tmp/gemma-release-0.97/glibc-2.25-n6nvxlk2j8/lib/ld-linux-x86-64.so.2 (0x00007f8b41a5c000)
#+END_SRC

#+BEGIN_SRC bash
lario:~/tmp/gemma-release-0.97$ time ./gemma-gn2-0.97-c760aa0-xqhsidq7h5/bin/gemma -g ~/tmp/mouse_hs1940/mouse_hs1940.geno.txt.gz -p ~/tmp/mouse_hs1940/mouse_hs1940.pheno.txt -a ~/tmp/mouse_hs1940/mouse_hs1940.anno.txt -gk
GEMMA 0.97 (2017/12/27) by Xiang Zhou and team (C) 2012-2017
Reading Files ...
## number of total individuals = 1940
## number of analyzed individuals = 1410
## number of covariates = 1
## number of phenotypes = 1
## number of total SNPs/var        =    12226
## number of analyzed SNPs         =    10768
Calculating Relatedness Matrix ...
================================================== 100%

real    0m21.389s
user    0m34.980s
sys     0m4.560s
#+END_SRC

#+BEGIN_SRC bash
lario:~/tmp/gemma-release-0.97$ time ./gemma-gn2-0.97-c760aa0-xqhsidq7h5/bin/gemma -g ~/tmp/mouse_hs1940/mouse_hs1940.geno.txt.gz -p ~/tmp/mouse_hs1940/mouse_hs1940.pheno.txt -n 1 -a ~/tmp/mouse_hs1940/mouse_hs1940.anno.txt -k ./output/result.cXX.txt -lmm
GEMMA 0.97 (2017/12/27) by Xiang Zhou and team (C) 2012-2017
Reading Files ...
## number of total individuals = 1940
## number of analyzed individuals = 1410
## number of covariates = 1
## number of phenotypes = 1
## number of total SNPs/var        =    12226
## number of analyzed SNPs         =    10768
Start Eigen-Decomposition...
pve estimate =0.608801
se(pve) =0.032774
================================================== 100%

real    0m13.296s
user    0m18.332s
sys     0m5.020s
#+END_SRC

* GEMMA 0.96

#+BEGIN_SRC bash
lario:~/tmp/gemma-release-0.96$ ldd gemma.linux
        linux-vdso.so.1 (0x00007ffd9ee8f000)
        libz.so.1 => /lib/x86_64-linux-gnu/libz.so.1 (0x00007fc2a94a1000)
        libgfortran.so.3 => /usr/lib/x86_64-linux-gnu/libgfortran.so.3 (0x00007fc2a9183000)
        libstdc++.so.6 => /usr/lib/x86_64-linux-gnu/libstdc++.so.6 (0x00007fc2a8e01000)
        libm.so.6 => /lib/x86_64-linux-gnu/libm.so.6 (0x00007fc2a8afd000)
        libgcc_s.so.1 => /lib/x86_64-linux-gnu/libgcc_s.so.1 (0x00007fc2a88e6000)
        libpthread.so.0 => /lib/x86_64-linux-gnu/libpthread.so.0 (0x00007fc2a86c9000)
        libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007fc2a832b000)
        libquadmath.so.0 => /usr/lib/x86_64-linux-gnu/libquadmath.so.0 (0x00007fc2a80ec000)
        /lib64/ld-linux-x86-64.so.2 (0x00007fc2a96bb000)
#+END_SRC

#+BEGIN_SRC bash
lario:~/tmp/gemma-release-0.96$ time ./gemma.linux -g ~/tmp/mouse_hs1940/mouse_hs1940.geno.txt.gz -p ~/tmp/mouse_hs1940/mouse_hs1940.pheno.txt -a ~/tmp/mouse_hs1940/mouse_hs1940.anno.txt -gk
Reading Files ...
## number of total individuals = 1940
## number of analyzed individuals = 1410
## number of covariates = 1
## number of phenotypes = 1
## number of total SNPs = 12226
## number of analyzed SNPs = 10768
Calculating Relatedness Matrix ...
Reading SNPs  ==================================================100.00%

real    0m16.347s
user    0m16.204s
sys     0m0.116s
#+END_SRC


#+BEGIN_SRC bash
lario:~/tmp/gemma-release-0.96$ time ./gemma.linux -g ~/tmp/mouse_hs1940/mouse_hs1940.geno.txt.gz -p ~/tmp/mouse_hs1940/mouse_hs1940.pheno.txt -n 1 -a ~/tmp/mouse_hs1940/mouse_hs1940.anno.txt -k ./output/result.cXX.txt -lmm
Reading Files ...
## number of total individuals = 1940
## number of analyzed individuals = 1410
## number of covariates = 1
## number of phenotypes = 1
## number of total SNPs = 12226
## number of analyzed SNPs = 10768
Start Eigen-Decomposition...
pve estimate =0.608801
se(pve) =0.032774
Reading SNPs  ==================================================100.00%

real    0m20.377s
user    0m20.240s
sys     0m0.132s
#+END_SRC
