Issues-with-covaraince-matrix.md

@@ -140,3 +140,93 @@ The 10 largest likelihood samples are chosen to compute the spread. We can find
 In our analysis, we set this threshold to be $`2.4 \times 10^{-7}`$, which corresponds to a k_max of 373 and 476 for GW190412 and GW190814 events, respectively.
 
 
+#### Sensitivity of the k_max computation using the different libraries
+
+We recently noticed that the same code on the same machine had different k_max in different virtual environments. We realized that the reason for this was that numpy was linked against different BLAS libraries in different virtual environments, which had effects on the output. However, the final on-source $`\beta`$ values are consistent with each other. Here, we describe a comparison between two virtual environments: ENV1 and ENV2. These environments are available in the CIT cluster.
+
+**ENV1**: created using `virtualenv` environment manager.
+`numpy` version: `1.16.5`
+
+`source /home/soumen.roy/HHM/o3inspiralhom/pycbc/bin/activate`
+```python
+>>> import numpy as np
+>>> np.__config__.show()
+lapack_opt_info:
+    libraries = ['openblas', 'openblas']
+    library_dirs = ['/usr/local/lib']
+    define_macros = [('HAVE_CBLAS', None)]
+    language = c
+blas_opt_info:
+    libraries = ['openblas', 'openblas']
+    library_dirs = ['/usr/local/lib']
+    define_macros = [('HAVE_CBLAS', None)]
+    language = c
+openblas_info:
+    libraries = ['openblas', 'openblas']
+    library_dirs = ['/usr/local/lib']
+    define_macros = [('HAVE_CBLAS', None)]
+    language = c
+blis_info:
+  NOT AVAILABLE
+openblas_lapack_info:
+    libraries = ['openblas', 'openblas']
+    library_dirs = ['/usr/local/lib']
+    define_macros = [('HAVE_CBLAS', None)]
+    language = c
+lapack_mkl_info:
+  NOT AVAILABLE
+blas_mkl_info:
+  NOT AVAILABLE
+
+```
+
+
+**ENV2**: created using `conda` environment manager.
+`numpy` version: `1.16.5`
+
+`source /home/haris.k/ve/anaconda2_april2020/bin/activate`
+
+```python
+>>> import numpy as np
+>>> np.__config__.show()
+lapack_opt_info:
+    libraries = ['mkl_rt', 'pthread']
+    library_dirs = ['/home/haris.k/ve/anaconda2_april2020/lib']
+    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
+    include_dirs = ['/home/haris.k/ve/anaconda2_april2020/include']
+blas_opt_info:
+    libraries = ['mkl_rt', 'pthread']
+    library_dirs = ['/home/haris.k/ve/anaconda2_april2020/lib']
+    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
+    include_dirs = ['/home/haris.k/ve/anaconda2_april2020/include']
+lapack_mkl_info:
+    libraries = ['mkl_rt', 'pthread']
+    library_dirs = ['/home/haris.k/ve/anaconda2_april2020/lib']
+    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
+    include_dirs = ['/home/haris.k/ve/anaconda2_april2020/include']
+blas_mkl_info:
+    libraries = ['mkl_rt', 'pthread']
+    library_dirs = ['/home/haris.k/ve/anaconda2_april2020/lib']
+    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
+    include_dirs = ['/home/haris.k/ve/anaconda2_april2020/include']
+mkl_info:
+    libraries = ['mkl_rt', 'pthread']
+    library_dirs = ['/home/haris.k/ve/anaconda2_april2020/lib']
+    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
+    include_dirs = ['/home/haris.k/ve/anaconda2_april2020/include']
+
+```
+
+* **Results**
+
+| Environment  | Event name  | Waveform model | k_max    |   $`\beta_{33}`$    |
+| ------------ | ----------- | -------------- | -------- | ------------------- |
+| ENV1         |  GW190814   | SEOBNRv4HM     | 476      | 10.085315670903611  |
+| ENV2         | GW190814    | SEOBNRv4HM     | 485      | 10.201704651600018  |
+| ENV1         | GW190412    | SEOBNRv4HM     | 357      | 6.111167418253159   |
+| ENV2         | GW190412    | SEOBNRv4HM     | 369      | 6.18436474734525    |
+| ENV1         | GW190412    | IMRPhenomHM    | 373      | 6.229738419184154   |
+| ENV2         | GW190412    | IMRPhenomHM    | 353      | 5.914591538278657   |
+
+
+