Project 2: Multi-location Transshipment Problem¶
In this project, we compare Stochastic Gradient Descent Vs. Bender’s Decomposition in optimizing a Two-Stage Stochastic LP.
!pip install autotime
!pip install nb-black
!pip install cvxpy
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Building wheels for collected packages: fbprophet, pyflux
Building wheel for fbprophet (setup.py) ... ?25lerror
ERROR: Command errored out with exit status 1:
command: /opt/anaconda3/envs/jeff/bin/python -u -c 'import sys, setuptools, tokenize; sys.argv[0] = '"'"'/tmp/pip-install-cyipebue/fbprophet/setup.py'"'"'; __file__='"'"'/tmp/pip-install-cyipebue/fbprophet/setup.py'"'"';f=getattr(tokenize, '"'"'open'"'"', open)(__file__);code=f.read().replace('"'"'\r\n'"'"', '"'"'\n'"'"');f.close();exec(compile(code, __file__, '"'"'exec'"'"'))' bdist_wheel -d /tmp/pip-wheel-46ektaws
cwd: /tmp/pip-install-cyipebue/fbprophet/
Complete output (38 lines):
running bdist_wheel
running build
running build_py
creating build
creating build/lib
creating build/lib/fbprophet
creating build/lib/fbprophet/stan_model
Traceback (most recent call last):
File "<string>", line 1, in <module>
File "/tmp/pip-install-cyipebue/fbprophet/setup.py", line 149, in <module>
long_description_content_type='text/markdown',
File "/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/setuptools/__init__.py", line 153, in setup
return distutils.core.setup(**attrs)
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/core.py", line 148, in setup
dist.run_commands()
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/dist.py", line 966, in run_commands
self.run_command(cmd)
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/dist.py", line 985, in run_command
cmd_obj.run()
File "/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/wheel/bdist_wheel.py", line 299, in run
self.run_command('build')
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/cmd.py", line 313, in run_command
self.distribution.run_command(command)
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/dist.py", line 985, in run_command
cmd_obj.run()
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/command/build.py", line 135, in run
self.run_command(cmd_name)
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/cmd.py", line 313, in run_command
self.distribution.run_command(command)
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/dist.py", line 985, in run_command
cmd_obj.run()
File "/tmp/pip-install-cyipebue/fbprophet/setup.py", line 48, in run
build_models(target_dir)
File "/tmp/pip-install-cyipebue/fbprophet/setup.py", line 38, in build_models
StanBackendEnum.get_backend_class(backend).build_model(target_dir, MODEL_DIR)
File "/tmp/pip-install-cyipebue/fbprophet/fbprophet/models.py", line 209, in build_model
import pystan
ModuleNotFoundError: No module named 'pystan'
----------------------------------------
ERROR: Failed building wheel for fbprophet
?25h Running setup.py clean for fbprophet
Building wheel for pyflux (setup.py) ... ?25lerror
ERROR: Command errored out with exit status 1:
command: /opt/anaconda3/envs/jeff/bin/python -u -c 'import sys, setuptools, tokenize; sys.argv[0] = '"'"'/tmp/pip-install-cyipebue/pyflux/setup.py'"'"'; __file__='"'"'/tmp/pip-install-cyipebue/pyflux/setup.py'"'"';f=getattr(tokenize, '"'"'open'"'"', open)(__file__);code=f.read().replace('"'"'\r\n'"'"', '"'"'\n'"'"');f.close();exec(compile(code, __file__, '"'"'exec'"'"'))' bdist_wheel -d /tmp/pip-wheel-qzqjec6v
cwd: /tmp/pip-install-cyipebue/pyflux/
Complete output (628 lines):
running bdist_wheel
running build
running config_cc
unifing config_cc, config, build_clib, build_ext, build commands --compiler options
running config_fc
unifing config_fc, config, build_clib, build_ext, build commands --fcompiler options
running build_src
build_src
building extension "pyflux.__check_build._check_build" sources
building extension "pyflux.arma.arma_recursions" sources
building extension "pyflux.arma.nn_architecture" sources
building extension "pyflux.families.gas_recursions" sources
building extension "pyflux.families.poisson_kalman_recursions" sources
building extension "pyflux.garch.garch_recursions" sources
building extension "pyflux.gas.gas_core_recursions" sources
building extension "pyflux.gpnarx.kernel_routines" sources
building extension "pyflux.inference.metropolis_sampler" sources
building extension "pyflux.inference.bbvi_routines" sources
building extension "pyflux.ssm.kalman" sources
building extension "pyflux.var.var_recursions" sources
build_src: building npy-pkg config files
running build_py
creating build
creating build/lib.linux-x86_64-3.7
creating build/lib.linux-x86_64-3.7/pyflux
copying pyflux/results.py -> build/lib.linux-x86_64-3.7/pyflux
copying pyflux/latent_variables.py -> build/lib.linux-x86_64-3.7/pyflux
copying pyflux/setup.py -> build/lib.linux-x86_64-3.7/pyflux
copying pyflux/data_check.py -> build/lib.linux-x86_64-3.7/pyflux
copying pyflux/__init__.py -> build/lib.linux-x86_64-3.7/pyflux
copying pyflux/tsm.py -> build/lib.linux-x86_64-3.7/pyflux
copying pyflux/covariances.py -> build/lib.linux-x86_64-3.7/pyflux
creating build/lib.linux-x86_64-3.7/pyflux/__check_build
copying pyflux/__check_build/setup.py -> build/lib.linux-x86_64-3.7/pyflux/__check_build
copying pyflux/__check_build/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/__check_build
creating build/lib.linux-x86_64-3.7/pyflux/arma
copying pyflux/arma/nnar.py -> build/lib.linux-x86_64-3.7/pyflux/arma
copying pyflux/arma/nnarx.py -> build/lib.linux-x86_64-3.7/pyflux/arma
copying pyflux/arma/arimax.py -> build/lib.linux-x86_64-3.7/pyflux/arma
copying pyflux/arma/setup.py -> build/lib.linux-x86_64-3.7/pyflux/arma
copying pyflux/arma/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/arma
copying pyflux/arma/arma.py -> build/lib.linux-x86_64-3.7/pyflux/arma
creating build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arimax_t.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arimax_poisson.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arima_cauchy.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arima_inference.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arima_normal.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arimax_skewt.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arimax_cauchy.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arimax_exponential.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arimax_laplace.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arima_poisson.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arima_laplace.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arima_t.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arima_exponential.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arimax_inference.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arimax_normal.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
copying pyflux/arma/tests/test_arima_skewt.py -> build/lib.linux-x86_64-3.7/pyflux/arma/tests
creating build/lib.linux-x86_64-3.7/pyflux/ensembles
copying pyflux/ensembles/mixture_of_experts.py -> build/lib.linux-x86_64-3.7/pyflux/ensembles
copying pyflux/ensembles/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/ensembles
creating build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/t.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/exponential.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/family.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/laplace.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/inverse_gamma.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/cauchy.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/inverse_wishart.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/normal.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/poisson.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/setup.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/flat.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/truncated_normal.py -> build/lib.linux-x86_64-3.7/pyflux/families
copying pyflux/families/skewt.py -> build/lib.linux-x86_64-3.7/pyflux/families
creating build/lib.linux-x86_64-3.7/pyflux/garch
copying pyflux/garch/egarch.py -> build/lib.linux-x86_64-3.7/pyflux/garch
copying pyflux/garch/segarchm.py -> build/lib.linux-x86_64-3.7/pyflux/garch
copying pyflux/garch/garch.py -> build/lib.linux-x86_64-3.7/pyflux/garch
copying pyflux/garch/egarchmreg.py -> build/lib.linux-x86_64-3.7/pyflux/garch
copying pyflux/garch/setup.py -> build/lib.linux-x86_64-3.7/pyflux/garch
copying pyflux/garch/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/garch
copying pyflux/garch/lmegarch.py -> build/lib.linux-x86_64-3.7/pyflux/garch
copying pyflux/garch/egarchm.py -> build/lib.linux-x86_64-3.7/pyflux/garch
copying pyflux/garch/segarch.py -> build/lib.linux-x86_64-3.7/pyflux/garch
creating build/lib.linux-x86_64-3.7/pyflux/gas
copying pyflux/gas/scores.py -> build/lib.linux-x86_64-3.7/pyflux/gas
copying pyflux/gas/gas.py -> build/lib.linux-x86_64-3.7/pyflux/gas
copying pyflux/gas/gasllt.py -> build/lib.linux-x86_64-3.7/pyflux/gas
copying pyflux/gas/gasx.py -> build/lib.linux-x86_64-3.7/pyflux/gas
copying pyflux/gas/setup.py -> build/lib.linux-x86_64-3.7/pyflux/gas
copying pyflux/gas/gasllm.py -> build/lib.linux-x86_64-3.7/pyflux/gas
copying pyflux/gas/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/gas
copying pyflux/gas/gasreg.py -> build/lib.linux-x86_64-3.7/pyflux/gas
copying pyflux/gas/gasrank.py -> build/lib.linux-x86_64-3.7/pyflux/gas
creating build/lib.linux-x86_64-3.7/pyflux/gpnarx
copying pyflux/gpnarx/gpnarx.py -> build/lib.linux-x86_64-3.7/pyflux/gpnarx
copying pyflux/gpnarx/kernels.py -> build/lib.linux-x86_64-3.7/pyflux/gpnarx
copying pyflux/gpnarx/setup.py -> build/lib.linux-x86_64-3.7/pyflux/gpnarx
copying pyflux/gpnarx/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/gpnarx
creating build/lib.linux-x86_64-3.7/pyflux/inference
copying pyflux/inference/norm_post_sim.py -> build/lib.linux-x86_64-3.7/pyflux/inference
copying pyflux/inference/stoch_optim.py -> build/lib.linux-x86_64-3.7/pyflux/inference
copying pyflux/inference/metropolis_hastings.py -> build/lib.linux-x86_64-3.7/pyflux/inference
copying pyflux/inference/bbvi.py -> build/lib.linux-x86_64-3.7/pyflux/inference
copying pyflux/inference/setup.py -> build/lib.linux-x86_64-3.7/pyflux/inference
copying pyflux/inference/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/inference
creating build/lib.linux-x86_64-3.7/pyflux/output
copying pyflux/output/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/output
copying pyflux/output/tableprinter.py -> build/lib.linux-x86_64-3.7/pyflux/output
creating build/lib.linux-x86_64-3.7/pyflux/ssm
copying pyflux/ssm/dynlin.py -> build/lib.linux-x86_64-3.7/pyflux/ssm
copying pyflux/ssm/nllt.py -> build/lib.linux-x86_64-3.7/pyflux/ssm
copying pyflux/ssm/dynamic_glm.py -> build/lib.linux-x86_64-3.7/pyflux/ssm
copying pyflux/ssm/local_level.py -> build/lib.linux-x86_64-3.7/pyflux/ssm
copying pyflux/ssm/local_trend.py -> build/lib.linux-x86_64-3.7/pyflux/ssm
copying pyflux/ssm/llt.py -> build/lib.linux-x86_64-3.7/pyflux/ssm
copying pyflux/ssm/setup.py -> build/lib.linux-x86_64-3.7/pyflux/ssm
copying pyflux/ssm/ndynlin.py -> build/lib.linux-x86_64-3.7/pyflux/ssm
copying pyflux/ssm/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/ssm
copying pyflux/ssm/nllm.py -> build/lib.linux-x86_64-3.7/pyflux/ssm
copying pyflux/ssm/dar.py -> build/lib.linux-x86_64-3.7/pyflux/ssm
copying pyflux/ssm/llm.py -> build/lib.linux-x86_64-3.7/pyflux/ssm
creating build/lib.linux-x86_64-3.7/pyflux/tests
copying pyflux/tests/nhst.py -> build/lib.linux-x86_64-3.7/pyflux/tests
copying pyflux/tests/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/tests
creating build/lib.linux-x86_64-3.7/pyflux/var
copying pyflux/var/var.py -> build/lib.linux-x86_64-3.7/pyflux/var
copying pyflux/var/setup.py -> build/lib.linux-x86_64-3.7/pyflux/var
copying pyflux/var/__init__.py -> build/lib.linux-x86_64-3.7/pyflux/var
running build_ext
customize UnixCCompiler
customize UnixCCompiler using build_ext
CCompilerOpt.cc_test_flags[999] : testing flags (-march=native)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
creating /tmp/tmp0x9e4tz_/opt
creating /tmp/tmp0x9e4tz_/opt/anaconda3
creating /tmp/tmp0x9e4tz_/opt/anaconda3/envs
creating /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff
creating /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib
creating /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7
creating /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages
creating /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy
creating /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils
creating /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-march=native'
CCompilerOpt.cc_test_flags[999] : testing flags (-O3)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-O3'
CCompilerOpt.cc_test_flags[999] : testing flags (-Werror)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-Werror'
CCompilerOpt.__init__[1674] : check requested baseline
CCompilerOpt.cc_test_flags[999] : testing flags (-msse)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse'
CCompilerOpt.cc_test_flags[999] : testing flags (-msse2)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse2'
CCompilerOpt.feature_test[1446] : testing feature 'SSE' with flags (-msse -msse2)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -Werror'
CCompilerOpt.feature_test[1446] : testing feature 'SSE2' with flags (-msse -msse2)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -Werror'
CCompilerOpt.cc_test_flags[999] : testing flags (-msse3)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse3'
CCompilerOpt.feature_test[1446] : testing feature 'SSE3' with flags (-msse -msse2 -msse3)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -Werror'
CCompilerOpt.__init__[1683] : check requested dispatch-able features
CCompilerOpt.cc_test_flags[999] : testing flags (-mssse3)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mssse3'
CCompilerOpt.cc_test_flags[999] : testing flags (-msse4.1)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse4.1'
CCompilerOpt.cc_test_flags[999] : testing flags (-mpopcnt)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mpopcnt'
CCompilerOpt.cc_test_flags[999] : testing flags (-msse4.2)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse4.2'
CCompilerOpt.cc_test_flags[999] : testing flags (-mavx)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mavx'
CCompilerOpt.feature_test[1446] : testing feature 'AVX' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -Werror'
CCompilerOpt.feature_test[1446] : testing feature 'SSSE3' with flags (-msse -msse2 -msse3 -mssse3)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -Werror'
CCompilerOpt.feature_test[1446] : testing feature 'POPCNT' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -Werror'
CCompilerOpt.feature_test[1446] : testing feature 'SSE41' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -Werror'
CCompilerOpt.cc_test_flags[999] : testing flags (-mf16c)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mf16c'
CCompilerOpt.feature_test[1446] : testing feature 'F16C' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -Werror'
CCompilerOpt.feature_test[1446] : testing feature 'SSE42' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -Werror'
CCompilerOpt.cc_test_flags[999] : testing flags (-mavx2)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mavx2'
CCompilerOpt.feature_test[1446] : testing feature 'AVX2' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mavx2)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mavx2 -Werror'
CCompilerOpt.cc_test_flags[999] : testing flags (-mfma)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mfma'
CCompilerOpt.cc_test_flags[999] : testing flags (-mavx512f)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mavx512f'
CCompilerOpt.cc_test_flags[999] : testing flags (-mavx512cd)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mavx512cd'
CCompilerOpt.cc_test_flags[999] : testing flags (-mavx512vl -mavx512bw -mavx512dq)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mavx512vl -mavx512bw -mavx512dq'
CCompilerOpt.cc_test_flags[999] : testing flags (-mavx512ifma -mavx512vbmi)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mavx512ifma -mavx512vbmi'
CCompilerOpt.feature_test[1446] : testing feature 'AVX512_CNL' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512vl -mavx512bw -mavx512dq -mavx512ifma -mavx512vbmi)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512vl -mavx512bw -mavx512dq -mavx512ifma -mavx512vbmi -Werror'
CCompilerOpt.feature_test[1446] : testing feature 'FMA3' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -Werror'
CCompilerOpt.feature_test[1446] : testing feature 'AVX512_SKX' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512vl -mavx512bw -mavx512dq)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512vl -mavx512bw -mavx512dq -Werror'
CCompilerOpt.feature_test[1446] : testing feature 'AVX512CD' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -Werror'
CCompilerOpt.feature_test[1446] : testing feature 'AVX512F' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -Werror'
CCompilerOpt.cc_test_flags[999] : testing flags (-mavx512vnni)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mavx512vnni'
CCompilerOpt.dist_test[576] : CCompilerOpt._dist_test_spawn[713] : Command (gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC -I/opt/anaconda3/envs/jeff/include/python3.7m -c /opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/test_flags.c -o /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/test_flags.o -MMD -MF /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/test_flags.o.d -mavx512vnni) failed with exit status 1 output ->
gcc: error: unrecognized command line option ‘-mavx512vnni’
CCompilerOpt.cc_test_flags[1003] : testing failed
CCompilerOpt.feature_test[1446] : testing feature 'AVX512_CLX' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512vl -mavx512bw -mavx512dq)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512vl -mavx512bw -mavx512dq -Werror'
CCompilerOpt.dist_test[576] : CCompilerOpt._dist_test_spawn[713] : Command (gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC -I/opt/anaconda3/envs/jeff/include/python3.7m -c /opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_clx.c -o /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_clx.o -MMD -MF /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_clx.o.d -msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512vl -mavx512bw -mavx512dq -Werror) failed with exit status 1 output ->
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_clx.c: In function ‘main’:
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_clx.c:6:17: error: implicit declaration of function ‘_mm512_dpbusd_epi32’ [-Werror=implicit-function-declaration]
__m512i a = _mm512_dpbusd_epi32(_mm512_setzero_si512(), _mm512_setzero_si512(), _mm512_setzero_si512());
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_clx.c:6:17: error: incompatible types when initializing type ‘__m512i {aka __vector(8) long long int}’ using type ‘int’
cc1: all warnings being treated as errors
CCompilerOpt.feature_test[1458] : testing failed
CCompilerOpt.cc_test_flags[999] : testing flags (-mavx512er -mavx512pf)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mavx512er -mavx512pf'
CCompilerOpt.feature_test[1446] : testing feature 'AVX512_KNL' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512er -mavx512pf)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512er -mavx512pf -Werror'
CCompilerOpt.cc_test_flags[999] : testing flags (-mavx5124fmaps -mavx5124vnniw -mavx512vpopcntdq)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-mavx5124fmaps -mavx5124vnniw -mavx512vpopcntdq'
CCompilerOpt.dist_test[576] : CCompilerOpt._dist_test_spawn[713] : Command (gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC -I/opt/anaconda3/envs/jeff/include/python3.7m -c /opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/test_flags.c -o /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/test_flags.o -MMD -MF /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/test_flags.o.d -mavx5124fmaps -mavx5124vnniw -mavx512vpopcntdq) failed with exit status 1 output ->
gcc: error: unrecognized command line option ‘-mavx5124fmaps’
gcc: error: unrecognized command line option ‘-mavx5124vnniw’
gcc: error: unrecognized command line option ‘-mavx512vpopcntdq’
CCompilerOpt.cc_test_flags[1003] : testing failed
CCompilerOpt.feature_test[1446] : testing feature 'AVX512_KNM' with flags (-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512er -mavx512pf)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512er -mavx512pf -Werror'
CCompilerOpt.dist_test[576] : CCompilerOpt._dist_test_spawn[713] : Command (gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC -I/opt/anaconda3/envs/jeff/include/python3.7m -c /opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_knm.c -o /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_knm.o -MMD -MF /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_knm.o.d -msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512er -mavx512pf -Werror) failed with exit status 1 output ->
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_knm.c: In function ‘main’:
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_knm.c:9:9: error: implicit declaration of function ‘_mm512_4fmadd_ps’ [-Werror=implicit-function-declaration]
b = _mm512_4fmadd_ps(b, b, b, b, b, NULL);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_knm.c:9:7: error: incompatible types when assigning to type ‘__m512 {aka __vector(16) float}’ from type ‘int’
b = _mm512_4fmadd_ps(b, b, b, b, b, NULL);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_knm.c:11:9: error: implicit declaration of function ‘_mm512_4dpwssd_epi32’ [-Werror=implicit-function-declaration]
a = _mm512_4dpwssd_epi32(a, a, a, a, a, NULL);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_knm.c:11:7: error: incompatible types when assigning to type ‘__m512i {aka __vector(8) long long int}’ from type ‘int’
a = _mm512_4dpwssd_epi32(a, a, a, a, a, NULL);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_knm.c:13:9: error: implicit declaration of function ‘_mm512_popcnt_epi64’ [-Werror=implicit-function-declaration]
a = _mm512_popcnt_epi64(a);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/cpu_avx512_knm.c:13:7: error: incompatible types when assigning to type ‘__m512i {aka __vector(8) long long int}’ from type ‘int’
a = _mm512_popcnt_epi64(a);
^
cc1: all warnings being treated as errors
CCompilerOpt.feature_test[1458] : testing failed
CCompilerOpt.__init__[1696] : skip features (SSE3 SSE SSE2) since its part of baseline
CCompilerOpt.__init__[1699] : initialize targets groups
CCompilerOpt.__init__[1701] : parse target group simd_test
CCompilerOpt._parse_target_tokens[1912] : skip targets (VSX3 ASIMD VSX FMA4 VSX2 XOP NEON) not part of baseline or dispatch-able features
CCompilerOpt._parse_policy_not_keepbase[2022] : skip baseline features (SSE2)
CCompilerOpt.generate_dispatch_header[2236] : generate CPU dispatch header: (build/src.linux-x86_64-3.7/numpy/distutils/include/npy_cpu_dispatch_config.h)
CCompilerOpt.generate_dispatch_header[2247] : dispatch header dir build/src.linux-x86_64-3.7/numpy/distutils/include does not exist, creating it
CCompilerOpt.feature_extra_checks[1519] : Testing extra checks for feature 'AVX512F' (AVX512F_REDUCE)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -Werror'
CCompilerOpt.dist_test[576] : CCompilerOpt._dist_test_spawn[713] : Command (gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC -I/opt/anaconda3/envs/jeff/include/python3.7m -c /opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c -o /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.o -MMD -MF /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.o.d -msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -Werror) failed with exit status 1 output ->
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c: In function ‘main’:
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:13:21: error: implicit declaration of function ‘_mm512_reduce_add_ps’ [-Werror=implicit-function-declaration]
float sum_ps = _mm512_reduce_add_ps(one_ps);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:14:21: error: implicit declaration of function ‘_mm512_reduce_add_pd’ [-Werror=implicit-function-declaration]
double sum_pd = _mm512_reduce_add_pd(one_pd);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:15:26: error: implicit declaration of function ‘_mm512_reduce_add_epi64’ [-Werror=implicit-function-declaration]
int sum_int = (int)_mm512_reduce_add_epi64(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:16:26: error: implicit declaration of function ‘_mm512_reduce_add_epi32’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_add_epi32(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:18:16: error: implicit declaration of function ‘_mm512_reduce_mul_ps’ [-Werror=implicit-function-declaration]
sum_ps += _mm512_reduce_mul_ps(one_ps);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:19:16: error: implicit declaration of function ‘_mm512_reduce_mul_pd’ [-Werror=implicit-function-declaration]
sum_pd += _mm512_reduce_mul_pd(one_pd);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:20:21: error: implicit declaration of function ‘_mm512_reduce_mul_epi64’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_mul_epi64(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:21:21: error: implicit declaration of function ‘_mm512_reduce_mul_epi32’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_mul_epi32(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:23:16: error: implicit declaration of function ‘_mm512_reduce_min_ps’ [-Werror=implicit-function-declaration]
sum_ps += _mm512_reduce_min_ps(one_ps);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:24:16: error: implicit declaration of function ‘_mm512_reduce_min_pd’ [-Werror=implicit-function-declaration]
sum_pd += _mm512_reduce_min_pd(one_pd);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:25:21: error: implicit declaration of function ‘_mm512_reduce_min_epi32’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_min_epi32(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:26:21: error: implicit declaration of function ‘_mm512_reduce_min_epu32’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_min_epu32(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:27:21: error: implicit declaration of function ‘_mm512_reduce_min_epi64’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_min_epi64(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:29:16: error: implicit declaration of function ‘_mm512_reduce_max_ps’ [-Werror=implicit-function-declaration]
sum_ps += _mm512_reduce_max_ps(one_ps);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:30:16: error: implicit declaration of function ‘_mm512_reduce_max_pd’ [-Werror=implicit-function-declaration]
sum_pd += _mm512_reduce_max_pd(one_pd);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:31:21: error: implicit declaration of function ‘_mm512_reduce_max_epi32’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_max_epi32(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:32:21: error: implicit declaration of function ‘_mm512_reduce_max_epu32’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_max_epu32(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:33:21: error: implicit declaration of function ‘_mm512_reduce_max_epi64’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_max_epi64(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:35:21: error: implicit declaration of function ‘_mm512_reduce_and_epi32’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_and_epi32(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:36:21: error: implicit declaration of function ‘_mm512_reduce_and_epi64’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_and_epi64(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:38:21: error: implicit declaration of function ‘_mm512_reduce_or_epi32’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_or_epi32(one_i64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512f_reduce.c:39:21: error: implicit declaration of function ‘_mm512_reduce_or_epi64’ [-Werror=implicit-function-declaration]
sum_int += (int)_mm512_reduce_or_epi64(one_i64);
^
cc1: all warnings being treated as errors
CCompilerOpt.feature_extra_checks[1537] : testing failed for checks (AVX512F_REDUCE)
CCompilerOpt.feature_extra_checks[1519] : Testing extra checks for feature 'AVX512_SKX' (AVX512BW_MASK AVX512DQ_MASK)
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512vl -mavx512bw -mavx512dq -Werror'
CCompilerOpt.dist_test[576] : CCompilerOpt._dist_test_spawn[713] : Command (gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC -I/opt/anaconda3/envs/jeff/include/python3.7m -c /opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512bw_mask.c -o /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512bw_mask.o -MMD -MF /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512bw_mask.o.d -msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512vl -mavx512bw -mavx512dq -Werror) failed with exit status 1 output ->
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512bw_mask.c: In function ‘main’:
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512bw_mask.c:12:11: error: implicit declaration of function ‘_kor_mask64’ [-Werror=implicit-function-declaration]
m64 = _kor_mask64(m64, m64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512bw_mask.c:13:11: error: implicit declaration of function ‘_kxor_mask64’ [-Werror=implicit-function-declaration]
m64 = _kxor_mask64(m64, m64);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512bw_mask.c:14:11: error: implicit declaration of function ‘_cvtu64_mask64’ [-Werror=implicit-function-declaration]
m64 = _cvtu64_mask64(_cvtmask64_u64(m64));
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512bw_mask.c:14:26: error: implicit declaration of function ‘_cvtmask64_u64’ [-Werror=implicit-function-declaration]
m64 = _cvtu64_mask64(_cvtmask64_u64(m64));
^
cc1: all warnings being treated as errors
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
compile options: '-I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512vl -mavx512bw -mavx512dq -Werror'
CCompilerOpt.dist_test[576] : CCompilerOpt._dist_test_spawn[713] : Command (gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC -I/opt/anaconda3/envs/jeff/include/python3.7m -c /opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512dq_mask.c -o /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512dq_mask.o -MMD -MF /tmp/tmp0x9e4tz_/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512dq_mask.o.d -msse -msse2 -msse3 -mssse3 -msse4.1 -mpopcnt -msse4.2 -mavx -mf16c -mfma -mavx2 -mavx512f -mavx512cd -mavx512vl -mavx512bw -mavx512dq -Werror) failed with exit status 1 output ->
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512dq_mask.c: In function ‘main’:
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512dq_mask.c:12:10: error: implicit declaration of function ‘_kor_mask8’ [-Werror=implicit-function-declaration]
m8 = _kor_mask8(m8, m8);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512dq_mask.c:13:10: error: implicit declaration of function ‘_kxor_mask8’ [-Werror=implicit-function-declaration]
m8 = _kxor_mask8(m8, m8);
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512dq_mask.c:14:10: error: implicit declaration of function ‘_cvtu32_mask8’ [-Werror=implicit-function-declaration]
m8 = _cvtu32_mask8(_cvtmask8_u32(m8));
^
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/distutils/checks/extra_avx512dq_mask.c:14:24: error: implicit declaration of function ‘_cvtmask8_u32’ [-Werror=implicit-function-declaration]
m8 = _cvtu32_mask8(_cvtmask8_u32(m8));
^
cc1: all warnings being treated as errors
CCompilerOpt.feature_extra_checks[1537] : testing failed for checks (AVX512BW_MASK AVX512DQ_MASK)
Detected changes on compiler optimizations, force rebuilding
building 'pyflux.__check_build._check_build' extension
compiling C sources
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
creating build/temp.linux-x86_64-3.7/pyflux
creating build/temp.linux-x86_64-3.7/pyflux/__check_build
compile options: '-I/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/core/include -Ibuild/src.linux-x86_64-3.7/numpy/distutils/include -I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3'
gcc: pyflux/__check_build/_check_build.c
gcc -pthread -shared -B /opt/anaconda3/envs/jeff/compiler_compat -L/opt/anaconda3/envs/jeff/lib -Wl,-rpath=/opt/anaconda3/envs/jeff/lib -Wl,--no-as-needed -Wl,--sysroot=/ build/temp.linux-x86_64-3.7/pyflux/__check_build/_check_build.o -o build/lib.linux-x86_64-3.7/pyflux/__check_build/_check_build.cpython-37m-x86_64-linux-gnu.so
building 'pyflux.arma.arma_recursions' extension
compiling C sources
C compiler: gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC
creating build/temp.linux-x86_64-3.7/pyflux/arma
compile options: '-I/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/core/include -Ibuild/src.linux-x86_64-3.7/numpy/distutils/include -I/opt/anaconda3/envs/jeff/include/python3.7m -c'
extra options: '-msse -msse2 -msse3'
gcc: pyflux/arma/arma_recursions.c
In file included from /opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/core/include/numpy/ndarraytypes.h:1944:0,
from /opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:12,
from /opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/core/include/numpy/arrayobject.h:4,
from pyflux/arma/arma_recursions.c:274:
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:17:2: warning: #warning "Using deprecated NumPy API, disable it with " "#define NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION" [-Wcpp]
#warning "Using deprecated NumPy API, disable it with " \
^
pyflux/arma/arma_recursions.c: In function ‘__Pyx__ExceptionSave’:
pyflux/arma/arma_recursions.c:19331:19: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_type’
*type = tstate->exc_type;
^
pyflux/arma/arma_recursions.c:19332:20: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_value’
*value = tstate->exc_value;
^
pyflux/arma/arma_recursions.c:19333:17: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_traceback’
*tb = tstate->exc_traceback;
^
pyflux/arma/arma_recursions.c: In function ‘__Pyx__ExceptionReset’:
pyflux/arma/arma_recursions.c:19340:22: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_type’
tmp_type = tstate->exc_type;
^
pyflux/arma/arma_recursions.c:19341:23: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_value’
tmp_value = tstate->exc_value;
^
pyflux/arma/arma_recursions.c:19342:20: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_traceback’
tmp_tb = tstate->exc_traceback;
^
pyflux/arma/arma_recursions.c:19343:11: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_type’
tstate->exc_type = type;
^
pyflux/arma/arma_recursions.c:19344:11: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_value’
tstate->exc_value = value;
^
pyflux/arma/arma_recursions.c:19345:11: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_traceback’
tstate->exc_traceback = tb;
^
pyflux/arma/arma_recursions.c: In function ‘__Pyx__GetException’:
pyflux/arma/arma_recursions.c:19400:22: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_type’
tmp_type = tstate->exc_type;
^
pyflux/arma/arma_recursions.c:19401:23: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_value’
tmp_value = tstate->exc_value;
^
pyflux/arma/arma_recursions.c:19402:20: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_traceback’
tmp_tb = tstate->exc_traceback;
^
pyflux/arma/arma_recursions.c:19403:11: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_type’
tstate->exc_type = local_type;
^
pyflux/arma/arma_recursions.c:19404:11: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_value’
tstate->exc_value = local_value;
^
pyflux/arma/arma_recursions.c:19405:11: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_traceback’
tstate->exc_traceback = local_tb;
^
pyflux/arma/arma_recursions.c: In function ‘__Pyx__ExceptionSwap’:
pyflux/arma/arma_recursions.c:19427:22: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_type’
tmp_type = tstate->exc_type;
^
pyflux/arma/arma_recursions.c:19428:23: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_value’
tmp_value = tstate->exc_value;
^
pyflux/arma/arma_recursions.c:19429:20: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_traceback’
tmp_tb = tstate->exc_traceback;
^
pyflux/arma/arma_recursions.c:19430:11: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_type’
tstate->exc_type = *type;
^
pyflux/arma/arma_recursions.c:19431:11: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_value’
tstate->exc_value = *value;
^
pyflux/arma/arma_recursions.c:19432:11: error: ‘PyThreadState {aka struct _ts}’ has no member named ‘exc_traceback’
tstate->exc_traceback = *tb;
^
In file included from /opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:21:0,
from /opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/core/include/numpy/arrayobject.h:4,
from pyflux/arma/arma_recursions.c:274:
pyflux/arma/arma_recursions.c: At top level:
/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/core/include/numpy/__multiarray_api.h:1464:1: warning: ‘_import_array’ defined but not used [-Wunused-function]
_import_array(void)
^
error: Command "gcc -pthread -B /opt/anaconda3/envs/jeff/compiler_compat -Wl,--sysroot=/ -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC -I/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/numpy/core/include -Ibuild/src.linux-x86_64-3.7/numpy/distutils/include -I/opt/anaconda3/envs/jeff/include/python3.7m -c pyflux/arma/arma_recursions.c -o build/temp.linux-x86_64-3.7/pyflux/arma/arma_recursions.o -MMD -MF build/temp.linux-x86_64-3.7/pyflux/arma/arma_recursions.o.d -msse -msse2 -msse3" failed with exit status 1
########### EXT COMPILER OPTIMIZATION ###########
Platform :
Architecture: x64
Compiler : gcc
CPU baseline :
Requested : 'min'
Enabled : SSE SSE2 SSE3
Flags : -msse -msse2 -msse3
Extra checks: none
CPU dispatch :
Requested : 'max -xop -fma4'
Enabled : SSSE3 SSE41 POPCNT SSE42 AVX F16C FMA3 AVX2 AVX512F AVX512CD AVX512_KNL AVX512_SKX AVX512_CNL
Generated : none
CCompilerOpt._cache_write[796] : write cache to path -> /tmp/pip-install-cyipebue/pyflux/build/temp.linux-x86_64-3.7/ccompiler_opt_cache_ext.py
----------------------------------------
ERROR: Failed building wheel for pyflux
?25h Running setup.py clean for pyflux
Failed to build fbprophet pyflux
Installing collected packages: fbprophet, dnntime, pyflux, autotime
Running setup.py install for fbprophet ... ?25lerror
ERROR: Command errored out with exit status 1:
command: /opt/anaconda3/envs/jeff/bin/python -u -c 'import sys, setuptools, tokenize; sys.argv[0] = '"'"'/tmp/pip-install-cyipebue/fbprophet/setup.py'"'"'; __file__='"'"'/tmp/pip-install-cyipebue/fbprophet/setup.py'"'"';f=getattr(tokenize, '"'"'open'"'"', open)(__file__);code=f.read().replace('"'"'\r\n'"'"', '"'"'\n'"'"');f.close();exec(compile(code, __file__, '"'"'exec'"'"'))' install --record /tmp/pip-record-7vad5ilk/install-record.txt --single-version-externally-managed --compile --install-headers /opt/anaconda3/envs/jeff/include/python3.7m/fbprophet
cwd: /tmp/pip-install-cyipebue/fbprophet/
Complete output (40 lines):
running install
running build
running build_py
creating build
creating build/lib
creating build/lib/fbprophet
creating build/lib/fbprophet/stan_model
Traceback (most recent call last):
File "<string>", line 1, in <module>
File "/tmp/pip-install-cyipebue/fbprophet/setup.py", line 149, in <module>
long_description_content_type='text/markdown',
File "/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/setuptools/__init__.py", line 153, in setup
return distutils.core.setup(**attrs)
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/core.py", line 148, in setup
dist.run_commands()
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/dist.py", line 966, in run_commands
self.run_command(cmd)
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/dist.py", line 985, in run_command
cmd_obj.run()
File "/opt/anaconda3/envs/jeff/lib/python3.7/site-packages/setuptools/command/install.py", line 61, in run
return orig.install.run(self)
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/command/install.py", line 545, in run
self.run_command('build')
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/cmd.py", line 313, in run_command
self.distribution.run_command(command)
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/dist.py", line 985, in run_command
cmd_obj.run()
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/command/build.py", line 135, in run
self.run_command(cmd_name)
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/cmd.py", line 313, in run_command
self.distribution.run_command(command)
File "/opt/anaconda3/envs/jeff/lib/python3.7/distutils/dist.py", line 985, in run_command
cmd_obj.run()
File "/tmp/pip-install-cyipebue/fbprophet/setup.py", line 48, in run
build_models(target_dir)
File "/tmp/pip-install-cyipebue/fbprophet/setup.py", line 38, in build_models
StanBackendEnum.get_backend_class(backend).build_model(target_dir, MODEL_DIR)
File "/tmp/pip-install-cyipebue/fbprophet/fbprophet/models.py", line 209, in build_model
import pystan
ModuleNotFoundError: No module named 'pystan'
----------------------------------------
ERROR: Command errored out with exit status 1: /opt/anaconda3/envs/jeff/bin/python -u -c 'import sys, setuptools, tokenize; sys.argv[0] = '"'"'/tmp/pip-install-cyipebue/fbprophet/setup.py'"'"'; __file__='"'"'/tmp/pip-install-cyipebue/fbprophet/setup.py'"'"';f=getattr(tokenize, '"'"'open'"'"', open)(__file__);code=f.read().replace('"'"'\r\n'"'"', '"'"'\n'"'"');f.close();exec(compile(code, __file__, '"'"'exec'"'"'))' install --record /tmp/pip-record-7vad5ilk/install-record.txt --single-version-externally-managed --compile --install-headers /opt/anaconda3/envs/jeff/include/python3.7m/fbprophet Check the logs for full command output.
WARNING: You are using pip version 20.2.4; however, version 21.1 is available.
You should consider upgrading via the '/opt/anaconda3/envs/jeff/bin/python -m pip install --upgrade pip' command.
?25hRequirement already satisfied: nb-black in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (1.0.7)
Requirement already satisfied: black>='19.3'; python_version >= "3.6" in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from nb-black) (21.4b2)
Requirement already satisfied: ipython in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from nb-black) (7.22.0)
Requirement already satisfied: regex>=2020.1.8 in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from black>='19.3'; python_version >= "3.6"->nb-black) (2021.4.4)
Requirement already satisfied: typing-extensions>=3.7.4; python_version < "3.8" in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from black>='19.3'; python_version >= "3.6"->nb-black) (3.7.4.3)
Requirement already satisfied: click>=7.1.2 in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from black>='19.3'; python_version >= "3.6"->nb-black) (7.1.2)
Requirement already satisfied: pathspec<1,>=0.8.1 in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from black>='19.3'; python_version >= "3.6"->nb-black) (0.8.1)
Requirement already satisfied: mypy-extensions>=0.4.3 in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from black>='19.3'; python_version >= "3.6"->nb-black) (0.4.3)
Requirement already satisfied: toml>=0.10.1 in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from black>='19.3'; python_version >= "3.6"->nb-black) (0.10.2)
Requirement already satisfied: appdirs in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from black>='19.3'; python_version >= "3.6"->nb-black) (1.4.4)
Requirement already satisfied: typed-ast>=1.4.2; python_version < "3.8" in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from black>='19.3'; python_version >= "3.6"->nb-black) (1.4.3)
Requirement already satisfied: prompt-toolkit!=3.0.0,!=3.0.1,<3.1.0,>=2.0.0 in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from ipython->nb-black) (3.0.18)
Requirement already satisfied: traitlets>=4.2 in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from ipython->nb-black) (5.0.5)
Requirement already satisfied: jedi>=0.16 in /opt/anaconda3/envs/jeff/lib/python3.7/site-packages (from ipython->nb-black) (0.18.0)
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# %load_ext autotime
# %load_ext nb_black
# General
import time
import numpy as np
import cvxpy as cp
import scipy as sp
import pandas as pd
import itertools
# Ignore warnings LOL
import warnings
warnings.simplefilter("ignore")
# SEED FOR RANDOMNESS
np.random.seed(420)
1. Preface¶
The type of problem we care about in this project are known as two-stage stochastic programming. Let The general formulation of it is as follows (Adapted from Wikipedia):
1.1. General Two-Stage Stochastic Program¶
1.1.1 First Stage Stochastic Program¶
(38)¶\[\begin{align}
\min_{x\in X} & \{ g(x)= f(x) + E_{\tilde{s}\sim S}[h(x, s=\tilde{s})]\}
\end{align}\]
, where \(h(x, s=\tilde{s})\) is the optimal value of the second-stage problem given a specific scenario \(\tilde{s}\). \(x \in X\) is our first-stage decision variable vector, \(S\) is a probability distribution of the scenario variables that we’re sampling from.
1.1.2 Second Stage Stochastic Program¶
For a specific \(\tilde{x}\) and \(\tilde{s}\),
(39)¶\[\begin{align}
h(x=\tilde{x}, s=\tilde{s}) = \min_{y} & \{ d(s, y) \,\vert\,C(s, x) +D(s, y) = \xi(s)\} \\
\end{align}\]
, where \(C, D, \xi\) are functions given a specific scenario \(\tilde{s}\). \(y\) is our second-stage decision variable vector.
At the first stage we optimize (minimize in the above formulation) the cost of the first-stage decision plus the expected cost of the (optimal) second-stage decision. We can view the second-stage problem simply as an optimization problem which describes our supposedly optimal behavior when the uncertain data is revealed (specific scenario \(\tilde{s}\)), or we can consider its solution as a recourse action where the term \(D(s, y)\) compensates for a possible inconsistency of the system \(C(s, x) \leq \xi(s)\) and \(d(s, y)\) is the cost of this recourse action.
1.2. Two-Stage Stochastic Linear Program¶
The stochastic linear program below is just a specific instance of the general program above, with very minor changes - e.g. functions of first-stage / second-stage decision variables are no longer general functions, but rather vectors / matrices because of constraints must be linear for a linear program.
1.2.1 First Stage Stochastic Linear Program¶
(40)¶\[\begin{align}
\min\limits_{x\in \mathbb{R}^n} & f(x)= c^\top x + E_{\tilde{s}\sim S}[h(x, s=\tilde{s})] & \\
\text{subject to}
& Ax = b &\\
& x \geq 0
\end{align}\]
, where \(h(x, s=\tilde{s})\) is the optimal value of the second-stage problem given a specific scenario \(\tilde{s}\). \(x \in \mathbb{R}^n\) is our first-stage decision variable vector, \(S\) is a probability distribution of the scenario variables that we’re sampling from., where \(h(x, s)\) is the optimal value of the second-stage problem
1.2.2 Second Stage Stochastic Linear Program¶
For a specific \(\tilde{x}\) and \(\tilde{s}\),
(41)¶\[\begin{align}
h(x=\tilde{x}, s=\tilde{s}) = \min\limits_{y\in \mathbb{R}^m}\,& d(s)^T y \\
\text{subject to }\,& C(s)x + D(s)y = \xi(s) \\
&y \geq 0
\end{align}\]
, where \(C, D, \xi\) are matrices given a specific scenario \(\tilde{s}\). \(y\) is our second-stage decision variable vector.
At the first stage we optimize (minimize in the above formulation) the cost of the first-stage decision plus the expected cost of the (optimal) second-stage decision. We can view the second-stage problem simply as an optimization problem which describes our supposedly optimal behavior when the uncertain data is revealed (specific scenario \(\tilde{s}\)), or we can consider its solution as a recourse action where the term \(D(s)y\) compensates for a possible inconsistency of the system \(C(s)x \leq \xi(s)\) and \(d(s)^\top y\) is the cost of this recourse action.
1.3. Two-Stage Stochastic Linear Program with Discretized Scenario Distribution¶
What happens if we can’t get / don’t want to sample from a continuous distribution for the scenarios? (What if \(S\) is discrete instead of continuous?). Nothing much changes other than how we calculate the expectation of the second-stage objective values.
1.3.1 First Stage Stochastic Linear Program with Discretized Scenario Distribution¶
(42)¶\[\begin{align}
\min\limits_{x\in \mathbb{R}^n}\,& f(x)= c^\top x + \underbrace{\sum_{s = \tilde{s}} p(s = \tilde{s}) h(x, s = \tilde{s})}_{E_{\tilde{s}\sim S}[h(x, s=\tilde{s})]} \\
\text{subject to }\,
& Ax = b \\
& x \geq 0
\end{align}\]
, where \(h(x, s)\) is the optimal value of the second-stage problem, and \(p(s = \tilde{s})\) is the probability of the scenario \(\tilde{s}\) occuring.
1.3.2 Second Stage Stochastic Linear Program with Discretized Scenario Distribution¶
For a specific \(\tilde{x}\) and \(\tilde{s}\),
(43)¶\[\begin{align}
h(x=\tilde{x}, s=\tilde{s}) = \min\limits_{y\in \mathbb{R}^m}\,& d(s)^T y \\
\text{subject to} & \, C(s)x + D(s)y = \xi(s) \text{, where }C(s), D(s), \xi(s) \\
& y \geq 0 \\
\end{align}\]
However, how do we go about solving this two-stage stochastic programs? The problem we face here is We will present two algorithms: Stochastic Gradient Descent and L-Shaped / Bender’s Method.
2. Method: Stochastic Gradient Descent¶
To keep things simple, we will work on using stochastic gradient descent on a stochastic linear program with s discretized scenario distribution.
First, we recall the general key update formula in gradient descent (adjusting parameter \(w_i\) in negative direction of gradient of objective \(f\)):
(44)¶\[\begin{align}
& w_i \leftarrow w_i + \alpha \frac{\partial f}{\partial w_i}\,\forall i = 0, \cdots , \text{Number of parameters} \\
\end{align}\]
Let’s recall the Lagrangian for the first stage problem :
(45)¶\[\begin{align}
\mathcal{L}(x) = c^\top x + E_{\tilde{s}\sim S}[h(x, s=\tilde{s})] - \mu
\end{align}\]
Assume we have solved the second stage problem, and have retrieved optimal primal variables \(y^*\) and dual variables \(\pi^*\) (equality constraints) and \(\lambda^*\) (inequality constraints), then recall the Lagrangian of \(h(x=\tilde{x}, s=\tilde{s})\):
(46)¶\[\begin{align}
\mathcal{L}(x) &= d(s)^\top y^* - \pi^* \left(C(s)x + D(s)y^* - \xi(s) \right) - \lambda^* y^* \\
\end{align}\]
To perform gradient descent on our obejctive function \(f(x)\), we need to find its gradient / subgradient w.r.t. \(x\):
(47)¶\[\begin{align}
f(x) &= c^\top x + \sum_s p_s h_s(x) \\
\frac{df}{dx} &= c + \frac{d \left(\sum_s p_s h_s(x)\right)}{dx} \\
&= c + \sum_s p_s\frac{d\left(h_s(x)\right)}{dx} \\
&= c + \sum_s p_s\frac{d\left(\mathcal{L}(x)\right)}{dx} \\
&= c + \sum_s p_s\frac{d\left(d^\top y_s - \pi_s \left( Dy_s - \xi_s + C_s x \right) - \lambda_s y_s \right)}{dx} \\
&= c - \sum_s p_s (\pi^\top_s C_s) \\
\end{align}\]
Stochastic Gradient Descent:
(48)¶\[\begin{align}
x &= x + \alpha \frac{df}{dx} \\
&= x + \alpha \left( c - \sum_s p_s (\pi^\top_s C_s) \right) \\
\end{align}\]
Orthogonal Projection onto intersection of half-spaces (Convex Polytope)
(49)¶\[\begin{align}
\arg \min_{x \geq 0} & \frac{1}{2} {\lVert x - y \rVert}_{2}^{2} \\
\text{subject to } & Ax \leq b
\end{align}\]
Lagrangian
(50)¶\[\begin{align}
\mathcal{L}(x, \lambda) &= \frac{1}{2} {\lVert x - y \rVert}_{2}^{2} + \lambda \left(Ax - b \right) \\
\end{align}\]
Lagrange Dual
(51)¶\[\begin{align}
\mathcal{L}(\lambda)
&= \inf_{x \geq 0} \mathcal{L}(x, \lambda) \\
&= \inf_{x \geq 0} \frac{1}{2} {\lVert x - y \rVert}_{2}^{2} + \lambda \left(Ax - b \right) \\
\end{align}\]
KKT Conditions
Stationarity:
(52)¶\[\begin{align}
\nabla_x \mathcal{L}(x, \lambda) &= 0 \\
\nabla_x \frac{1}{2} {\left( x - y \right) }^\top \left( x - y \right) + \lambda \left(Ax - b \right) &= 0 \\
\left( x - y \right) + \lambda A &= 0 \\
\lambda &= A^{-1}\left(y - x\right) \\
\end{align}\]
class StochasticGradientDescent:
@staticmethod
def projection(vector, constraints=None):
"""Find the projection of y onto the C(A) that minimizes
the euclidean norm between y and the projected vector
.. math::
\begin{align}
\arg \min_{x \geq 0} & \frac{1}{2} {\lVert x - y \rVert}_{2}^{2} \\
\text{subject to } & x \in X, \, \text{where }X\text{ is a convex set}
\end{align}
Args:
vector (np.array): Vector to be projected
Returns:
np.array: Projected vector
"""
P_positive = lambda vector: np.maximum(
vector, np.zeros(vector.shape)
) # Positive projection operator on a point
if constraints is None:
return P_positive(
vector
) # Return positive projection if there isnt a convex polytope / set constraint
proj = cp.Variable(vector.shape, nonneg=True) # Projected Vector
obj = cp.Minimize(
cp.norm2(proj - vector)
) # Minimize euclidean norm of difference between y and projection
prob = cp.Problem(obj, constraints=constraints)
prob.solve()
return proj.value
@staticmethod
def projection_dykstra(projections, x0, max_iter=1000, tol=1e-6):
"""Dykstra's Projection algorithm to find the orthogonal
projection of a point onto a convex polytope (intersection
of affine halfspaces). The algorithm below is adapted from
https://github.com/mjhough/Dykstra/blob/main/dykstra/Dykstra.py
Args:
projections
"""
assert len(x0.shape) == 1, "x0 must be a vector"
x = x0.copy()
y = np.zeros((projections.shape[0], x0.shape[0]))
n = 0
cI = np.inf
while n < max_iter and cI >= tol:
cI = 0
for i in range(projections.shape[0]):
# Update iterate
prev_x = x.copy()
x = projections[i](prev_x - y[i, :])
# Update increment
prev_y = y[i, :].copy()
y[i, :] = x - (prev_x - prev_y)
# Stop condition
cI += np.linalg.norm(prev_y - y[i, :]) ** 2
n += 1
return x
def __init__(
self, c, x0, first_stage_constraints, s_gen, n, n_iter=None, α=1e0, ε=1e-04, log=True
):
"""The Stochastic Gradient Descent method implemented here
is used to optimize the Two-Stage Stochastic Linear Program
with second-stage variables following a discrete distribution
"""
self.c = c # First-stage decision coefficient
self.x0 = x0 # Initial first-stage decision variable values
self.first_stage_constraints = first_stage_constraints # Function that gives a list of the constraints for first-stage problem
self.s_gen = s_gen # Function to generate scenario specific entities
self.n = n # Number of scenarios to generate using s_gen
self.n_iter = n_iter # Number of iterations of sgd
self.α = α # Learning rate for gradient descent
self.ε = ε # Tolerance for how close subgradient is to 0
self.log = log # Whether or not to log progress
def solve(self):
"""Solves the Two-stage Stochastic Optimization"""
f_primal_optimal, x_star, k = self.first_stage()
if self.log:
print(
f"Optimal primal objective of first stage problem: {np.round(f_primal_optimal, 3)}"
)
print(f"Optimal first-stage decision variables: {np.round(x_star, 3)}")
print(f"Number of iterations for convergence: {k}")
return f_primal_optimal, x_star, k
def first_stage(self):
"""First-stage Optimization"""
f_primal_optimal = np.inf # First-stage primal optimal objective value
x = (
np.array([0.0] * self.c.shape[0]) if self.x0 is None else self.x0.copy()
) # First-stage decision variables
# # Fix number of iterations
# for k in range(self.n_iter):
k = 0
while True:
data = list(self.s_gen(self.n)) # Random Scenarios and associated variables
# Initialize subgradient of f
ν = self.c.copy()
# Initialize expectation of h
expected_h = 0
# Accumulating subgradients
for p_s, d_s, C_s, D_s, ξ_s in data:
π_s, h_primal_optimal = self.second_stage(
x=x, d=d_s, C=C_s, D=D_s, ξ=ξ_s
)
ν -= p_s * π_s.T @ C_s # Update subgradient
expected_h += (
p_s * h_primal_optimal
) # Update expected second-stage optimal value
# Early stopping condition
if np.allclose(ν, np.zeros(self.c.shape[0]), atol=self.ε):
print("Early Stopping condition satisfied.")
break
# The current f primal optimal found
current_f_primal_optimal = self.c.T @ x + expected_h
# Updated x value [WHY TF is it a + and not a -]
x = StochasticGradientDescent.projection(
vector=x + (self.α * ν), constraints=self.first_stage_constraints
)
if self.log and k % 50 == 0:
print("=" * 20 + f" Iteration {k}" + "=" * 20)
print(
f"Current Primal Objective Found:",
np.round(current_f_primal_optimal, 3),
"|",
f"Best Primal Objective Found:",
np.round(f_primal_optimal, 3),
)
# If minimized value is better, update
if f_primal_optimal > current_f_primal_optimal:
f_primal_optimal = current_f_primal_optimal
# Update k
k += 1
return f_primal_optimal, x, k
def second_stage(self, x, d, C, D, ξ):
"""Second-stage Optimization"""
y = cp.Variable(d.shape[0], nonneg=True) # Second-stage decision variables
constraints = [C @ x + D @ y == ξ] # Second-stage constraints
obj = cp.Minimize(d @ y)
prob = cp.Problem(obj, constraints=constraints)
prob.solve()
return constraints[0].dual_value, prob.value
3. L-Shaped / Bender’s Method¶
Master Problem:
(53)¶\[\begin{align}
\underset{S \geq 0}{\min} \mu & \\
\end{align}\]
Sub Problem:
(54)¶\[\begin{align}
\underset{F}{\min} h(S=S^* = \underset{S \geq 0}{\arg\min}\,\mu, d=\tilde{d}) &= \underset{F}{\min} \sum^N_{i=1} h_i F_{B_i E_i} + \sum^N_{i=1} \sum^N_{j=1} c_{ij} F_{B_i M_j} + \sum^N_i p_i F_{RM_i} \\
\text{subject to } &S_i = F_{B_i M_i} + \sum^N_{j =1 \\ i \not= 1} F_{B_i M_j} + F_{B_i E_i}\qquad i = 1, \cdots , N, \\
&F_{B_i M_i} + \sum^N_{j = 1 \\ j \not= i} F_{B_j M_i} + F_{RM_i} = {d}_i\qquad i = 1, \cdots , N, \\
&\sum^N_{i=1} {d}_i = \sum^N_{i=1} F_{RM_i} + \sum^N_{i = 1} F_{RE_i}, \\
&F_{B_i E_i} + F_{RE_i} = S_i\qquad i = 1, \cdots , N, \\
&F_{B_i E_i}, F_{B_i M_j}, F_{RM_i}, F_{RE_i} \geq 0\qquad i = 1, \cdots , N, \\
&j = 1, \cdots , N.
\end{align}\]
Sp:
(55)¶\[\begin{align}
h_s(x) &= \underset{y_s}{\min} d^\top y_s \\
\text{subject to } Dy_s &= \xi_s - C_s x \\
y_s &\geq 0 \\
\end{align}\]
Dual Sp:
(56)¶\[\begin{align}
\underset{\pi_s, \lambda_s}{\max} & \left[\xi_s - C_s x\right]^\top \left(\pi_s, \lambda_s\right) \\
\text{subject to } & \pi_s \text{ free} \\
& \lambda_s \geq 0 \\
\end{align}\]
class Benders:
def __init__(self, c, first_stage_constraints, s_gen, ε=1e-5, log=True):
"""The Bender's method implemented here
is used to optimize the Two-Stage Stochastic Linear Program
with second-stage variables following a discrete distribution
"""
self.c = c # First-stage decision coefficient
self.first_stage_constraints = first_stage_constraints # Function that gives a list of the constraints for first-stage problem
self.s_gen = s_gen # Function to generate scenario specific entities
self.ε = ε # Tolerance between Upper Bound and Lower Bound
self.log = log # Whether or not to log progress
def solve(self):
"""Solves the Two-stage Stochastic Optimization"""
# 1. Initialize UB = infinity, LB = -infinity
UB, LB = np.inf, -np.inf
x = cp.Variable(self.c.shape, nonneg=True) # First-stage decision variables
# Master Problem
z = cp.Variable(1, nonneg=True)
MP_obj = cp.Minimize(z)
# Bender cuts that we will be adding to the master problem
cuts = (
self.first_stage_constraints
if self.first_stage_constraints is not None
else []
)
k = 0
# 2. While UB - LB > ε, we will continue adding cuts
while UB - LB > self.ε:
expected_h = 0
α, β = 0, 0 # Hyperplane of cut coefficients
# Go through all the scenarios possible
for p_s, d_s, C_s, D_s, ξ_s in self.s_gen():
# 3a. Solve the Dual of the Sub-problem for all combinations of demand \tilde{d}
# [Equivalent to solving primal since LPs have 0 duality gap]
π_optimal, h_dual_optimal, status = self.second_stage(
x=x, d=d_s, C=C_s, D=D_s, ξ=ξ_s
)
# # 4a. If dual variables are unbounded, add cut
# if status == "infeasible":
# cuts += [(ξ_s - C_s @ x).T @ π_optimal <= 0]
# # 4b. Else set UB and add cut on first stage primal optimal value
# else:
# expected_h += p_s * h_dual_optimal
# cuts += [z >= (ξ_s - C_s @ x).T @ π_optimal]
expected_h += p_s * h_dual_optimal
α += p_s * ξ_s.T @ π_optimal
β += -p_s * C_s.T @ π_optimal
# 3b. Add a new halfspace constraint
cuts += [z >= α + β.T @ x]
# 4. Update UB
UB = min(
UB,
self.c.T @ x.value + expected_h if x.value is not None else expected_h,
)
# 5. Solve Master Problem
MP_prob = cp.Problem(MP_obj, constraints=cuts)
MP_prob.solve()
# 6. Update LB
LB = MP_prob.value
if self.log:
print("=" * 20 + f" Iteration {k}" + "=" * 20)
print(
f"Lower Bound:",
np.round(LB, 3),
"|",
f"Upper Bound:",
np.round(UB, 3),
)
k += 1
if self.log:
print(f"Optimal primal objective of first stage problem: {np.round(LB, 3)}")
print(f"Optimal first-stage decision variables: {np.round(x.value, 3)}")
print(f"Number of iterations for convergence: {k}")
return LB, np.array(x.value), k
def second_stage(self, x, d, C, D, ξ):
"""Dual Form of Second-stage Optimization"""
π = cp.Variable(
ξ.shape, nonneg=False
) # Second-stage dual variables are Free since they are dual of the equality constraints
constraints = [D.T @ π <= d] # Second-stage dual constraints
obj = cp.Maximize(
(ξ - C @ (np.zeros(C.shape[1]) if x.value is None else x.value)).T @ π
)
prob = cp.Problem(obj, constraints=constraints)
prob.solve()
return π.value, prob.value, prob.status
4. Two-stage Multi-location Transshipment Problem¶
4.1. Problem Setup¶
4.1.1 First Stage Stochastic Linear Program¶
In the first stage problem, we want to figure out what the optimal order-up-to quantity \(S\) is. We formulate the first stage LP as follows, minimizing the expected (stochastic demand) transshipment cost with the order-up-to quantities \(S\) as our primal variables:
(57)¶\[\begin{align}
\underset{S \geq 0}{\min}\,& \mathbb{E}_{\tilde{d} \sim D}\left[h(S, d = \tilde{d})\right] \qquad \text{, where }D\text{ is the demand distribution} \\
\end{align}\]
4.1.2 Second Stage Stochastic Linear Program¶
In our second stage problem, given a specific order-up-to quantity \(\tilde{S}\), and a fixed demand \(\tilde{d}\), we want to solve the following constrained linear program over the primal variables \(F\) (flow to and from each node), minimziing the transshipment cost for the specific instance of \(\tilde{S}\) and \(\tilde{d}\):
(58)¶\[\begin{align}
h(S = \tilde{S}, d=\tilde{d}) = \underset{F}{\min} &\sum^N_{i=1} h_i F_{B_i E_i} + \sum^N_{i=1} \sum^N_{j=1} c_{ij} F_{B_i M_j} + \sum^N_i p_i F_{RM_i} \\
\text{subject to } & S_i = F_{B_i M_i} + \sum^N_{j =1 \\ i \not= 1} F_{B_i M_j} + F_{B_i E_i} \,\,\,\, i = 1, \cdots , N, \\
&F_{B_i M_i} + \sum^N_{j = 1 \\ j \not= i} F_{B_j M_i} + F_{RM_i} = {d}_i \,\,\,\, i = 1, \cdots , N, \\
&\sum^N_{i=1} {d}_i = \sum^N_{i=1} F_{RM_i} + \sum^N_{i = 1} F_{RE_i}, \\
&F_{B_i E_i} + F_{RE_i} = S_i \,\,\,\, i = 1, \cdots , N, \\
&F_{B_i E_i}, F_{B_i M_j}, F_{RM_i}, F_{RE_i} \geq 0 \,\,\,\, i = 1, \cdots , N, \\
&j = 1, \cdots , N.
\end{align}\]
Reformulate objective and constraints into standard form:
def get_transshipment_variables():
# Number of retailers
N = 4
# Holding cost Vector
h = np.array([1] * N)
# Shortage cost Vector
p = np.array([4] * N)
# Cost of transshipment from retailer i to retailer j Matrix
C = np.full((N, N), 0.5)
np.fill_diagonal(C, 0)
# PMF of Retailer Demand distribution
P = np.array([0.020, 0.14, 0.68, 0.14, 0.020])
# Each Retailer's Demand distribution associated with probabilities above
RETAILER_DEMANDS = np.array(
[
[60, 80, 100, 120, 140],
[100, 150, 200, 250, 300],
[90, 120, 150, 180, 210],
[70, 120, 170, 220, 270],
]
)
return N, h, p, C, P, RETAILER_DEMANDS
def random_demand(P, retailer_demands):
"""Samples a random demand vector according to demand pmf
parameters given
Args:
P (numpy.array): Array of probabilities for each demand, shape: (Number of probabilities)
retailer_demands (numpy.array): Matrix of retailer demands, shape: (Number of retailers, Number of discrete demands)
Returns:
Tuple[np.array, float]: A tuple of the (sampled Demand Vector, probability of the Sampled Demand Vector)
"""
assert np.isclose(
np.sum(P), 1
), "p must sum to 1 to be a valid probability distribution."
sampled_demand = np.array(
[np.random.choice(retailer_demand, p=P) for retailer_demand in retailer_demands]
)
p_s = np.prod(
[
P[np.argwhere(retailer_demand == D_i)[0][0]]
for retailer_demand, D_i in zip(retailer_demands, sampled_demand)
]
)
return sampled_demand, p_s
def get_second_stage_variables(s):
""""""
N, h, p, C, P, RETAILER_DEMANDS = get_transshipment_variables()
# Coefficient of Second-stage decision variables
d_s = np.concatenate(
(
h, # Coefficient of Amount of inventory that moves from begining to ending (FBE)
C.flatten(), # Coefficient of Amount of inventory to ship from current retailer to other retailers (FBM)
p, # Coefficient of Amount to ship from supplier to retailer's middle inventory (FRM)
np.array(
[0] * N
), # Coefficient of Amount to ship from supplier to retailer's ending inventory (FRE)
)
)
# Second-stage C(s) matrix
C_s = np.concatenate(
(
np.eye(N),
np.zeros(shape=(N, N)),
np.zeros(shape=(1, N)),
np.eye(N),
),
axis=0,
)
# Second-stage D(s) matrix
D_s = np.concatenate(
(
np.concatenate(
(
-np.eye(N),
np.array(
[
([-1] * N + [0] * (N * (N - 1)))[-N * idx :]
+ ([-1] * N + [0] * (N * (N - 1)))[: -N * idx]
for idx in range(N)
]
),
np.zeros(shape=(N, N)),
np.zeros(shape=(N, N)),
),
axis=1,
),
np.concatenate(
(
np.zeros(shape=(N, N)),
np.array(
[
np.array(
[
([1] + [0] * (N - 1))[-idx:]
+ ([1] + [0] * (N - 1))[:-idx]
]
* N
).flatten()
for idx in range(N)
]
),
np.eye(N),
np.zeros(shape=(N, N)),
),
axis=1,
),
np.array([[0] * N + [0] * (N * N) + [1] * N + [1] * N]),
np.concatenate(
(
-np.eye(N),
np.zeros(shape=(N, N * N)),
np.zeros(shape=(N, N)),
-np.eye(N),
),
axis=1,
),
),
axis=0,
)
# ξ(s) vector
ξ_s = np.concatenate(
(
np.zeros(N),
s,
np.array([np.sum(s)]),
np.zeros(N),
),
axis=0,
)
return d_s, C_s, D_s, ξ_s
def s_gen_sgd(n=50):
"""Function that generates the scenario dependent
second-stage variables by sampling demand
"""
N, h, p, C, P, RETAILER_DEMANDS = get_transshipment_variables()
for _ in range(n):
# Get Second-stage variables
s, p_s = random_demand(P=P, retailer_demands=RETAILER_DEMANDS)
# Get scenario-dependent variables
d_s, C_s, D_s, ξ_s = get_second_stage_variables(s)
yield p_s, d_s, C_s, D_s, ξ_s
def s_gen_benders():
"""Function that generates the scenario dependent
second-stage variables by enumerating all combinations of demand
"""
N, h, p, C, P, RETAILER_DEMANDS = get_transshipment_variables()
# Get Second-stage variables
for s in itertools.product(*RETAILER_DEMANDS):
p_s = np.prod(
[
P[np.argwhere(retailer_demand == D_i)[0][0]]
for retailer_demand, D_i in zip(RETAILER_DEMANDS, s)
]
)
# Get scenario-dependent variables
d_s, C_s, D_s, ξ_s = get_second_stage_variables(s)
yield p_s, d_s, C_s, D_s, ξ_s
4.2. Stochastic Gradient Descent¶
sgd = StochasticGradientDescent(
c=np.array([0.0] * 4),
x0=np.array([0.0] * 4),
first_stage_constraints=None,
s_gen=s_gen_sgd,
n=100,
α=1e-01,
ε=1e-01
)
sgd.solve()
==================== Iteration 0====================
Current Primal Objective Found: 15740.704 | Best Primal Objective Found: inf
==================== Iteration 50====================
Current Primal Objective Found: 2404.495 | Best Primal Objective Found: 2729.085
==================== Iteration 100====================
Current Primal Objective Found: 289.641 | Best Primal Objective Found: 264.472
==================== Iteration 150====================
Current Primal Objective Found: 262.191 | Best Primal Objective Found: 229.16
==================== Iteration 200====================
Current Primal Objective Found: 292.347 | Best Primal Objective Found: 197.497
==================== Iteration 250====================
Current Primal Objective Found: 290.276 | Best Primal Objective Found: 197.497
==================== Iteration 300====================
Current Primal Objective Found: 177.405 | Best Primal Objective Found: 167.574
==================== Iteration 350====================
Current Primal Objective Found: 165.722 | Best Primal Objective Found: 156.476
==================== Iteration 400====================
Current Primal Objective Found: 182.0 | Best Primal Objective Found: 130.407
==================== Iteration 450====================
Current Primal Objective Found: 199.385 | Best Primal Objective Found: 130.407
Early Stopping condition satisfied.
Optimal primal objective of first stage problem: 130.407
Optimal first-stage decision variables: [100.661 200.54 150.724 170.486]
Number of iterations for convergence: 499
(130.407359788351,
array([100.66088181, 200.53971283, 150.72409382, 170.48564625]),
499)
4.3. Benders¶
benders = Benders(
c=np.array([0] * 4),
first_stage_constraints=None,
s_gen=s_gen_benders,
)
benders.solve()
==================== Iteration 0====================
Lower Bound: 0.0 | Upper Bound: 2480.0
==================== Iteration 1====================
Lower Bound: 0.0 | Upper Bound: 1041.897
==================== Iteration 2====================
Lower Bound: 0.0 | Upper Bound: 115.972
==================== Iteration 3====================
Lower Bound: 0.0 | Upper Bound: 115.972
==================== Iteration 4====================
Lower Bound: 0.0 | Upper Bound: 115.972
==================== Iteration 5====================
Lower Bound: 48.645 | Upper Bound: 115.972
==================== Iteration 6====================
Lower Bound: 49.022 | Upper Bound: 115.972
==================== Iteration 7====================
Lower Bound: 51.52 | Upper Bound: 115.972
==================== Iteration 8====================
Lower Bound: 66.869 | Upper Bound: 92.555
==================== Iteration 9====================
Lower Bound: 67.483 | Upper Bound: 92.555
==================== Iteration 10====================
Lower Bound: 70.326 | Upper Bound: 92.555
==================== Iteration 11====================
Lower Bound: 71.874 | Upper Bound: 82.007
==================== Iteration 12====================
Lower Bound: 73.429 | Upper Bound: 82.007
==================== Iteration 13====================
Lower Bound: 79.194 | Upper Bound: 80.918
==================== Iteration 14====================
Lower Bound: 79.771 | Upper Bound: 80.918
==================== Iteration 15====================
Lower Bound: 80.473 | Upper Bound: 80.918
==================== Iteration 16====================
Lower Bound: 80.523 | Upper Bound: 80.918
==================== Iteration 17====================
Lower Bound: 80.523 | Upper Bound: 80.523
Optimal primal objective of first stage problem: 80.523
Optimal first-stage decision variables: [108.508 214.065 159.724 187.702]
Number of iterations for convergence: 18
(80.52286246994309,
array([108.50808924, 214.06507897, 159.7243887 , 187.70244296]),
18)
4.4. Stochastic Gradient Descent Vs. Benders¶
def run_experiment_sgd(n_scenario, α, ε):
optimal_obj_val, optimal_order_up_to_quantity, k = StochasticGradientDescent(
c=np.array([0.0] * 4),
x0=np.array([0.0] * 4),
first_stage_constraints=None,
s_gen=s_gen_sgd,
n=n_scenario,
α=α,
ε=ε,
log=False,
).solve()
return optimal_obj_val, optimal_order_up_to_quantity, k
def run_experiment_grid_sgd(
n_experiments=100, n_scenarios=[50, 100, 1000], αs=[1e0, 1e-01, 1e-02], εs=[1e-03, 1e-04, 1e-05]
):
results = []
for n_scenario in n_scenarios:
for α in αs:
for ε in εs:
(
optimal_obj_vals_sgd,
optimal_order_up_to_quantities_sgd,
n_iterations_sgd,
experiment_times,
) = ([], [], [], [])
# Run Experiments
for k in range(n_experiments):
if k % 10 == 0:
print(
f"Experimenting with n_scenario={n_scenario} | α={α} | ε={ε} | k={k}..."
)
start = time.time()
optimal_obj_val, optimal_order_up_to_quantity, n_iterations = run_experiment_sgd(
n_scenario, α, ε
)
end = time.time()
optimal_obj_vals_sgd.append(optimal_obj_val)
optimal_order_up_to_quantities_sgd.append(optimal_order_up_to_quantity)
n_iterations_sgd.append(n_iterations)
experiment_times.append(end - start)
optimal_obj_vals_sgd = np.round(np.array(optimal_obj_vals_sgd), 2)
optimal_order_up_to_quantities_sgd = np.round(np.array(
optimal_order_up_to_quantities_sgd
), 2)
n_iterations_sgd = np.array(n_iterations_sgd)
experiment_times = np.round(np.array(experiment_times), 2)
results.append(
(
n_scenario,
α,
ε,
optimal_obj_vals_sgd.mean(axis=0),
optimal_obj_vals_sgd.std(axis=0),
optimal_obj_vals_sgd.max(axis=0),
optimal_obj_vals_sgd.min(axis=0),
optimal_order_up_to_quantities_sgd.mean(axis=0),
optimal_order_up_to_quantities_sgd.std(axis=0),
optimal_order_up_to_quantities_sgd.max(axis=0),
optimal_order_up_to_quantities_sgd.min(axis=0),
n_iterations_sgd.mean(axis=0),
n_iterations_sgd.std(axis=0),
n_iterations_sgd.max(axis=0),
n_iterations_sgd.min(axis=0),
experiment_times.mean(axis=0),
experiment_times.std(axis=0),
experiment_times.max(axis=0),
experiment_times.min(axis=0),
)
)
pd.DataFrame(
results,
columns=[
"Number of Scenarios",
"Learning rate α",
"Tolerance for Subgradient Early Stopping ε",
"Mean(Objective Value)",
"Std(Objective Value)",
"Max(Objective Value)",
"Min(Objective Value)",
"Mean(Optimal Order-Up-To Quantitites)",
"Std(Optimal Order-Up-To Quantitites)",
"Max(Optimal Order-Up-To Quantitites)",
"Min(Optimal Order-Up-To Quantitites)",
"Mean(Number of Iterations)",
"Std(Number of Iterations)",
"Max(Number of Iterations)",
"Min(Number of Iterations)",
"Mean(Experiment Times)",
"Std(Experiment Times)",
"Max(Experiment Times)",
"Min(Experiment Times)",
],
).to_csv("sgd_results.csv")
return pd.DataFrame(
results,
columns=[
"Number of Scenarios",
"Learning rate α",
"Tolerance for Subgradient Early Stopping ε",
"Mean(Objective Value)",
"Std(Objective Value)",
"Max(Objective Value)",
"Min(Objective Value)",
"Mean(Optimal Order-Up-To Quantitites)",
"Std(Optimal Order-Up-To Quantitites)",
"Max(Optimal Order-Up-To Quantitites)",
"Min(Optimal Order-Up-To Quantitites)",
"Mean(Number of Iterations)",
"Std(Number of Iterations)",
"Max(Number of Iterations)",
"Min(Number of Iterations)",
"Mean(Experiment Times)",
"Std(Experiment Times)",
"Max(Experiment Times)",
"Min(Experiment Times)",
],
)
sgd_results = run_experiment_grid_sgd(
n_experiments=100, n_scenarios=[10, 50, 100, 200], αs=[1e-01], εs=[1e-01]
)
sgd_results
Experimenting with n_scenario=10 | α=0.1 | ε=0.1 | k=0...
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Experimenting with n_scenario=10 | α=0.1 | ε=0.1 | k=10...
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Experimenting with n_scenario=10 | α=0.1 | ε=0.1 | k=20...
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Experimenting with n_scenario=10 | α=0.1 | ε=0.1 | k=30...
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Experimenting with n_scenario=10 | α=0.1 | ε=0.1 | k=40...
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Experimenting with n_scenario=10 | α=0.1 | ε=0.1 | k=50...
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Experimenting with n_scenario=10 | α=0.1 | ε=0.1 | k=60...
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Experimenting with n_scenario=10 | α=0.1 | ε=0.1 | k=70...
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Experimenting with n_scenario=10 | α=0.1 | ε=0.1 | k=80...
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Experimenting with n_scenario=10 | α=0.1 | ε=0.1 | k=90...
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Experimenting with n_scenario=50 | α=0.1 | ε=0.1 | k=0...
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
Early Stopping condition satisfied.
pd.read_csv("./sgd_results.csv", index_col=[0])
| Number of Scenarios | Learning rate α | Tolerance for Subgradient Early Stopping ε | Mean(Objective Value) | Std(Objective Value) | Max(Objective Value) | Min(Objective Value) | Mean(Optimal Order-Up-To Quantitites) | Std(Optimal Order-Up-To Quantitites) | Max(Optimal Order-Up-To Quantitites) | Min(Optimal Order-Up-To Quantitites) | Mean(Number of Iterations) | Std(Number of Iterations) | Max(Number of Iterations) | Min(Number of Iterations) | Mean(Experiment Times) | Std(Experiment Times) | Max(Experiment Times) | Min(Experiment Times) | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10 | 0.1 | 0.1 | 16.5198 | 6.759651 | 55.55 | 8.53 | [148.4059 157.5988 154.6814 157.4469] | [1.96487307 2.73314115 2.02832641 2.73398928] | [150.08 162.47 156.3 162.31] | [138.58 144.07 143.93 143.92] | 684.31 | 78.390267 | 980 | 560 | 28.8340 | 3.309319 | 41.45 | 23.71 |
| 1 | 50 | 0.1 | 0.1 | 53.6970 | 4.858717 | 64.30 | 43.98 | [100.6798 200.597 150.6084 170.606 ] | [0.37629504 0.35315011 0.34831227 0.34898424] | [101.65 201.48 151.52 171.53] | [100.02 200.01 150.02 170.03] | 786.58 | 40.985163 | 915 | 729 | 166.0559 | 8.613365 | 193.08 | 153.22 |
| 2 | 100 | 0.1 | 0.1 | 127.4597 | 9.509603 | 152.36 | 103.51 | [101.2032 201.0891 151.1315 171.1326] | [0.74875481 0.63293459 0.63881668 0.62607926] | [104.29 202.48 152.68 172.56] | [100.04 200.01 150.03 170.04] | 598.64 | 205.785933 | 1469 | 360 | 253.2370 | 87.046833 | 620.72 | 152.10 |
def run_experiment_grid_benders(n_experiments=100):
results = []
(
optimal_obj_vals_benders,
optimal_order_up_to_quantities_benders,
n_iterations_benders,
experiment_times,
) = ([], [], [], [])
# Run Experiments
for k in range(n_experiments):
if k % 10 == 0:
print(f"Experimenting with k={k}...")
start = time.time()
optimal_obj_val, optimal_order_up_to_quantity, n_iterations = Benders(
c=np.array([0] * 4),
first_stage_constraints=None,
s_gen=s_gen_benders,
log=False,
).solve()
end = time.time()
optimal_obj_vals_benders.append(optimal_obj_val)
optimal_order_up_to_quantities_benders.append(optimal_order_up_to_quantity)
n_iterations_benders.append(n_iterations)
experiment_times.append(end - start)
optimal_obj_vals_benders = np.round(np.array(optimal_obj_vals_benders), 2)
optimal_order_up_to_quantities_benders = np.round(np.array(
optimal_order_up_to_quantities_benders
), 2)
n_iterations_benders = np.array(n_iterations_benders)
experiment_times = np.round(np.array(experiment_times), 2)
results.append(
(
5 ** 4,
1,
optimal_obj_vals_benders.mean(axis=0),
optimal_obj_vals_benders.std(axis=0),
optimal_obj_vals_benders.max(axis=0),
optimal_obj_vals_benders.min(axis=0),
optimal_order_up_to_quantities_benders.mean(axis=0),
optimal_order_up_to_quantities_benders.std(axis=0),
optimal_order_up_to_quantities_benders.max(axis=0),
optimal_order_up_to_quantities_benders.min(axis=0),
n_iterations_benders.mean(axis=0),
n_iterations_benders.std(axis=0),
n_iterations_benders.max(axis=0),
n_iterations_benders.min(axis=0),
experiment_times.mean(axis=0),
experiment_times.std(axis=0),
experiment_times.max(axis=0),
experiment_times.min(axis=0),
)
)
return pd.DataFrame(
results,
columns=[
"Number of Scenarios",
"Number of Iterations",
"Mean(Objective Value)",
"Std(Objective Value)",
"Max(Objective Value)",
"Min(Objective Value)",
"Mean(Optimal Order-Up-To Quantitites)",
"Std(Optimal Order-Up-To Quantitites)",
"Max(Optimal Order-Up-To Quantitites)",
"Min(Optimal Order-Up-To Quantitites)",
"Mean(Number of Iterations)",
"Std(Number of Iterations)",
"Max(Number of Iterations)",
"Min(Number of Iterations)",
"Mean(Experiment Times)",
"Std(Experiment Times)",
"Max(Experiment Times)",
"Min(Experiment Times)",
],
)
benders_results = run_experiment_grid_benders(n_experiments=100)
benders_results.to_csv("benders_results.csv")
benders_results
Experimenting with k=0...
Experimenting with k=10...
Experimenting with k=20...
Experimenting with k=30...
Experimenting with k=40...
Experimenting with k=50...
Experimenting with k=60...
Experimenting with k=70...
Experimenting with k=80...
Experimenting with k=90...
| Number of Scenarios | Number of Iterations | Mean(Objective Value) | Std(Objective Value) | Max(Objective Value) | Min(Objective Value) | Mean(Optimal Order-Up-To Quantitites) | Std(Optimal Order-Up-To Quantitites) | Max(Optimal Order-Up-To Quantitites) | Min(Optimal Order-Up-To Quantitites) | Mean(Number of Iterations) | Std(Number of Iterations) | Max(Number of Iterations) | Min(Number of Iterations) | Mean(Experiment Times) | Std(Experiment Times) | Max(Experiment Times) | Min(Experiment Times) | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 625 | 1 | 80.52 | 1.421085e-14 | 80.52 | 80.52 | [108.51000000000016, 214.0699999999998, 159.71... | [1.5631940186722204e-13, 1.9895196601282805e-1... | [108.51, 214.07, 159.72, 187.7] | [108.51, 214.07, 159.72, 187.7] | 18.0 | 0.0 | 18 | 18 | 38.7504 | 0.110408 | 39.2 | 38.53 |
4.4.1 Comparing Mean(Optimal Order-Up-To Quantities)¶
pd.options.display.max_colwidth = 100
import pandas as pd
pd.read_csv("./sgd_results.csv", index_col=[0])
| Number of Scenarios | Learning rate α | Tolerance for Subgradient Early Stopping ε | Mean(Objective Value) | Std(Objective Value) | Max(Objective Value) | Min(Objective Value) | Mean(Optimal Order-Up-To Quantitites) | Std(Optimal Order-Up-To Quantitites) | Max(Optimal Order-Up-To Quantitites) | Min(Optimal Order-Up-To Quantitites) | Mean(Number of Iterations) | Std(Number of Iterations) | Max(Number of Iterations) | Min(Number of Iterations) | Mean(Experiment Times) | Std(Experiment Times) | Max(Experiment Times) | Min(Experiment Times) | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10 | 0.1 | 0.1 | 16.5198 | 6.759651 | 55.55 | 8.53 | [148.4059 157.5988 154.6814 157.4469] | [1.96487307 2.73314115 2.02832641 2.73398928] | [150.08 162.47 156.3 162.31] | [138.58 144.07 143.93 143.92] | 684.31 | 78.390267 | 980 | 560 | 28.8340 | 3.309319 | 41.45 | 23.71 |
| 1 | 50 | 0.1 | 0.1 | 53.6970 | 4.858717 | 64.30 | 43.98 | [100.6798 200.597 150.6084 170.606 ] | [0.37629504 0.35315011 0.34831227 0.34898424] | [101.65 201.48 151.52 171.53] | [100.02 200.01 150.02 170.03] | 786.58 | 40.985163 | 915 | 729 | 166.0559 | 8.613365 | 193.08 | 153.22 |
| 2 | 100 | 0.1 | 0.1 | 127.4597 | 9.509603 | 152.36 | 103.51 | [101.2032 201.0891 151.1315 171.1326] | [0.74875481 0.63293459 0.63881668 0.62607926] | [104.29 202.48 152.68 172.56] | [100.04 200.01 150.03 170.04] | 598.64 | 205.785933 | 1469 | 360 | 253.2370 | 87.046833 | 620.72 | 152.10 |
pd.read_csv("./benders_results.csv", index_col=[0])
| Number of Scenarios | Number of Iterations | Mean(Objective Value) | Std(Objective Value) | Max(Objective Value) | Min(Objective Value) | Mean(Optimal Order-Up-To Quantitites) | Std(Optimal Order-Up-To Quantitites) | Max(Optimal Order-Up-To Quantitites) | Min(Optimal Order-Up-To Quantitites) | Mean(Number of Iterations) | Std(Number of Iterations) | Max(Number of Iterations) | Min(Number of Iterations) | Mean(Experiment Times) | Std(Experiment Times) | Max(Experiment Times) | Min(Experiment Times) | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 625 | 1 | 80.52 | 1.421085e-14 | 80.52 | 80.52 | [108.51 214.07 159.72 187.7 ] | [1.56319402e-13 1.98951966e-13 2.84217094e-13 ... | [108.51 214.07 159.72 187.7 ] | [108.51 214.07 159.72 187.7 ] | 18.0 | 0.0 | 18 | 18 | 38.7504 | 0.110408 | 39.2 | 38.53 |
4.4.2 Conclusion¶
We observe that benders goes through fewer iterations, and overall has a more accurate result.