Test environment: OS X Yosemite 10.10.5

Main R package used: `microbenchmark`

, `glmnet`

, `ElemStatLearn`

```
library(ElemStatLearn)
library(microbenchmark)
library(iregnet)
library(glmnet)
x.model = as.matrix(scale(prostate[,1:8]))
res.for.lasso <- microbenchmark(res.for.iregnet<-iregnet(x.model, matrix(prostate$lpsa, 97, 2), alpha=1), res.for.glmnet<-glmnet(x.model, prostate$lpsa), times=1000L)
plot(res.for.lasso)
plot(res.for.glmnet)
plot(res.for.iregnet)
```

According to the test result, two functions return a approximate result but function `glmnet`

was almost Seven times(not precise) faster than function `iregnet`

in handling a lasso problem with no censored data(using prostate cancer data set).

Test environment: OS X Yosemite 10.10.5

Main R package used: `Rperform`

```
setwd("~/Desktop/iregnet-Rperform/")
library(Rperform)
plot_branchmetrics(test_path = "tests/testthat/test_elemStatsLearn.r", metric = "time", branch1 = "optimize", branch2 = "master", save_data = F, save_plots = F)
plot_branchmetrics(test_path = "tests/testthat/get_xy.r", metric = "time", branch1 = "optimize", branch2 = "master", save_data = F, save_plots = F)
plot_branchmetrics(test_path = "tests/testthat/test_log_dist.r", metric = "time", branch1 = "optimize", branch2 = "master", save_data = F, save_plots = F)
plot_branchmetrics(test_path = "tests/testthat/test_penaltyLearning.r", metric = "time", branch1 = "optimize", branch2 = "master", save_data = F, save_plots = F)
plot_branchmetrics(test_path = "tests/testthat/test_predict.r", metric = "time", branch1 = "optimize", branch2 = "master", save_data = F, save_plots = F)
plot_branchmetrics(test_path = "tests/testthat/test_survival_glmnet.r", metric = "time", branch1 = "optimize", branch2 = "master", save_data = F, save_plots = F)
plot_branchmetrics(test_path = "tests/testthat/test_validation.r", metric = "time", branch1 = "optimize", branch2 = "master", save_data = F, save_plots = F)
plot_branchmetrics(test_path = "tests/testthat/test_zeros.r", metric = "time", branch1 = "optimize", branch2 = "master", save_data = F, save_plots = F)
```

In this test, the results from `Rperform::plot_branchmetrics`

which compare timings for the commits on the `optimize`

branch against the `master`

branch show a good performance of `optimize`

branch.

Optimizations in `optimize`

branch result in speed improvements among almost the whole test above and compare to the `master`

branch we can find that some vital part of c++ code in `iregnet_fit.cpp`

was optimized.The Hard Test below will mention the whole speed analysis of the iregnet R package.

Test environment: OS X Yosemite 10.10.5

Profiler Tool: Google-gperftools

Code Profiler: CPU profiler (1000 interrupt / second)

Analysis Tools: pprof

Group | Number of variables(row) | Number of objects(col) |
---|---|---|

The | 10 | 10000 |

Group | 10 | 100000 |

One | 10 | 1000000 |

--- | --- | --- |

The | 10 | 1000 |

Group | 100 | 1000 |

Two | 1000 | 1000 |

```
#Package iregnet version 2016.11.02 - branch master
library(iregnet)
#Prepare X&y (variables and objects is the test data)
set.seed(10)
X <- matrix(rnorm(variables*objects), objects, variables)
y <- matrix(rnorm(objects*2), objects, 2)
y <- t(apply(y, 1, sort))
#Calling the target function
#Use num_lambda=100 and family=gaussian as default parameter
iregnet(X, y, alpha = 0.5)
```

According to the text&image we can find that

- Most of time separate in
`iregnet.so`

and`libsystem_m.dylib`

node. - When more variables used, time spending in
`iregnet.so`

during the whole procedure apparently increase. - Adding more objects, the time of
`iregnet.so`

spent still close to half(even more than half).

The `iregnet.so`

file is linked to the `iregnet.o`

file which is compiled by `iregnet_fit.cpp`

file.

The libsystem_m.dylib is a dynamic library containing most of mathematics operation in OS X.

Obviously most of the time spend in iregnet R package is the `iregnet_fit.cpp`

file and for more specific information we need to analyze in this c++ file deeply.

In this way, I set up the code to time the concrete part in iregnet_fit.cpp file.I have been created a new branch called `profiler`

with timing code in `iregnet_fit.cpp`

in my iregnet repository forked from anujkhare/iregnet.

I separate the code of `iregnet_fit.cpp`

into several main parts and use the clock() function to record the them.

In the end of the procedure, the code will calculate the time spend in the percentage of all the parts and print the result.

Then build&install this local package and run two test Rscript(`test_elemStatsLearn.r`

& `test_log_dist.r`

) to analyze the result.

As the images show, we can learn that in the main process most of the time(Nearly 100%) spend in lambad loop, so

I add the code to profiling the lambda loop and the this time I find that several parts are the mainly process which spend much time during the whole procedure.

Below are the parts of code taking the most time in the iregnet R package:

(sort by desc,according to mainly result,not absolute)

```
/* calling the function defined in distributions.cpp */
loglik = compute_grad_response(w, z, &scale_update, REAL(y), REAL(y) + n_obs, eta, scale, status, n_obs, transformed_dist, NULL, debug==1 && m == 0);
```

```
sol_num = sol_denom = 0;
for (ull i = 0; i < n_obs; ++i) {
eta[i] = eta[i] - X(i, k) * beta[k];
sol_num += (w[i] * X(i, k) * (z[i] - eta[i])) / n_obs;
sol_denom += (w[i] * X(i, k) * X(i, k)) / n_obs;
}
sol_num *= -1; sol_denom *= -1;
```

```
for (ull i = 0; i < n_obs; ++i) {
eta[i] = eta[i] + X(i, k) * beta[k];
}
```

```
if (intercept && k == 0) {
beta_new = sol_num / sol_denom;
} else {
beta_new = soft_threshold(sol_num, lambda_seq[m] * alpha) /
(sol_denom + lambda_seq[m] * (1 - alpha));
}
```

```
double abs_change = fabs(beta_new - beta[k]);
if (abs_change > threshold) {
if(debug==1 && max_iter==n_iters[m])printf("iter=%d lambda=%d beta_%lld not converged, abs_change=%f > %f=threshold\n", n_iters[m], m, k, abs_change, threshold);
flag_beta_converged = 0;
beta[k] = beta_new;
}
```

In this test,I firstly use the Google-gperftools(CPU profiler) to find out which mainly process taking much time in the iregnet R package,and then I set up clock() function in separated part of `iregnet_fit.cpp`

to figure out the specific C++ code that taking the most time.

In order to speed optimizations for iregnet,the part of c++ code above in `iregnet_fit.cpp`

need to be focused and also the function defined in `distributions.cpp`

is equally important.

2017-01-26 23:56
289

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