Modified five-dimensional example

We aim to redo the Five-dimensional example from the paper draft with an out of the box 4-extended Latin Hypercube (Williamson, 2015) on [-1, 1] and compare the performance of stationary GP, our proposed nonstationary GP, TGP and CGP.

twd <- getwd()
source('BuildEmulator/BuildEmulator.R')

## Loading required package: GenSA

## Loading required package: far

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## far library : Modelization for Functional AutoRegressive processes

## version 0.6-4 (2014-12-07)

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## Type 'help( Spam)' or 'demo( spam)' for a short introduction 
## and overview of this package.
## Help for individual functions is also obtained by adding the
## suffix '.spam' to the function name, e.g. 'help( chol.spam)'.

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## Attaching package: 'spam'

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## rstan (Version 2.16.2, packaged: 2017-07-03 09:24:58 UTC, GitRev: 2e1f913d3ca3)

## For execution on a local, multicore CPU with excess RAM we recommend calling
## rstan_options(auto_write = TRUE)
## options(mc.cores = parallel::detectCores())

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## In file included from fileaa1fceb9552.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
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## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/gevv_vvv_vari.hpp:5:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/var.hpp:7:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/math/tools/config.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config.hpp:39:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config/compiler/clang.hpp:200:11: warning: 'BOOST_NO_CXX11_RVALUE_REFERENCES' macro redefined [-Wmacro-redefined]
## #  define BOOST_NO_CXX11_RVALUE_REFERENCES
##           ^
## <command line>:6:9: note: previous definition is here
## #define BOOST_NO_CXX11_RVALUE_REFERENCES 1
##         ^
## In file included from fileaa1fceb9552.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:42:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:17: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
##     static void set_zero_all_adjoints() {
##                 ^
## In file included from fileaa1fceb9552.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:43:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints_nested.hpp:17:17: warning: 'static' function 'set_zero_all_adjoints_nested' declared in header file should be declared 'static inline' [-Wunneeded-internal-declaration]
##     static void set_zero_all_adjoints_nested() {
##                 ^
## In file included from fileaa1fceb9552.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:58:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:17:14: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
##       size_t fft_next_good_size(size_t N) {
##              ^
## In file included from fileaa1fceb9552.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:298:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr.hpp:38:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr/functor/integrate_ode_rk45.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint.hpp:61:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint/util/multi_array_adaption.hpp:29:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array.hpp:21:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/base.hpp:28:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:42:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:43:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:53:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:54:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## 8 warnings generated.
## In file included from fileaa1f4365e4c1.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/gevv_vvv_vari.hpp:5:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/var.hpp:7:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/math/tools/config.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config.hpp:39:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config/compiler/clang.hpp:200:11: warning: 'BOOST_NO_CXX11_RVALUE_REFERENCES' macro redefined [-Wmacro-redefined]
## #  define BOOST_NO_CXX11_RVALUE_REFERENCES
##           ^
## <command line>:6:9: note: previous definition is here
## #define BOOST_NO_CXX11_RVALUE_REFERENCES 1
##         ^
## In file included from fileaa1f4365e4c1.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:42:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:17: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
##     static void set_zero_all_adjoints() {
##                 ^
## In file included from fileaa1f4365e4c1.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:43:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints_nested.hpp:17:17: warning: 'static' function 'set_zero_all_adjoints_nested' declared in header file should be declared 'static inline' [-Wunneeded-internal-declaration]
##     static void set_zero_all_adjoints_nested() {
##                 ^
## In file included from fileaa1f4365e4c1.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:58:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:17:14: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
##       size_t fft_next_good_size(size_t N) {
##              ^
## In file included from fileaa1f4365e4c1.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:298:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr.hpp:38:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr/functor/integrate_ode_rk45.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint.hpp:61:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint/util/multi_array_adaption.hpp:29:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array.hpp:21:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/base.hpp:28:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:42:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:43:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:53:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:54:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## 8 warnings generated.
## In file included from fileaa1f2ff4b5da.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/gevv_vvv_vari.hpp:5:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/var.hpp:7:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/math/tools/config.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config.hpp:39:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config/compiler/clang.hpp:200:11: warning: 'BOOST_NO_CXX11_RVALUE_REFERENCES' macro redefined [-Wmacro-redefined]
## #  define BOOST_NO_CXX11_RVALUE_REFERENCES
##           ^
## <command line>:6:9: note: previous definition is here
## #define BOOST_NO_CXX11_RVALUE_REFERENCES 1
##         ^
## In file included from fileaa1f2ff4b5da.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:42:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:17: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
##     static void set_zero_all_adjoints() {
##                 ^
## In file included from fileaa1f2ff4b5da.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:43:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints_nested.hpp:17:17: warning: 'static' function 'set_zero_all_adjoints_nested' declared in header file should be declared 'static inline' [-Wunneeded-internal-declaration]
##     static void set_zero_all_adjoints_nested() {
##                 ^
## In file included from fileaa1f2ff4b5da.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:58:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:17:14: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
##       size_t fft_next_good_size(size_t N) {
##              ^
## In file included from fileaa1f2ff4b5da.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:298:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr.hpp:38:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr/functor/integrate_ode_rk45.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint.hpp:61:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint/util/multi_array_adaption.hpp:29:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array.hpp:21:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/base.hpp:28:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:42:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:43:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:53:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:54:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## 8 warnings generated.

source('BuildEmulator/BuildEmulatorNSt.R')

## Loading required package: tgp

## Loading required package: CGP

## In file included from fileaa1f73aef6cb.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/gevv_vvv_vari.hpp:5:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/var.hpp:7:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/math/tools/config.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config.hpp:39:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config/compiler/clang.hpp:200:11: warning: 'BOOST_NO_CXX11_RVALUE_REFERENCES' macro redefined [-Wmacro-redefined]
## #  define BOOST_NO_CXX11_RVALUE_REFERENCES
##           ^
## <command line>:6:9: note: previous definition is here
## #define BOOST_NO_CXX11_RVALUE_REFERENCES 1
##         ^
## In file included from fileaa1f73aef6cb.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:42:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:17: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
##     static void set_zero_all_adjoints() {
##                 ^
## In file included from fileaa1f73aef6cb.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:43:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints_nested.hpp:17:17: warning: 'static' function 'set_zero_all_adjoints_nested' declared in header file should be declared 'static inline' [-Wunneeded-internal-declaration]
##     static void set_zero_all_adjoints_nested() {
##                 ^
## In file included from fileaa1f73aef6cb.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:58:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:17:14: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
##       size_t fft_next_good_size(size_t N) {
##              ^
## In file included from fileaa1f73aef6cb.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:298:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr.hpp:38:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr/functor/integrate_ode_rk45.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint.hpp:61:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint/util/multi_array_adaption.hpp:29:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array.hpp:21:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/base.hpp:28:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:42:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:43:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:53:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:54:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## 8 warnings generated.
## In file included from fileaa1f7fa5cf87.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/gevv_vvv_vari.hpp:5:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/var.hpp:7:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/math/tools/config.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config.hpp:39:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config/compiler/clang.hpp:200:11: warning: 'BOOST_NO_CXX11_RVALUE_REFERENCES' macro redefined [-Wmacro-redefined]
## #  define BOOST_NO_CXX11_RVALUE_REFERENCES
##           ^
## <command line>:6:9: note: previous definition is here
## #define BOOST_NO_CXX11_RVALUE_REFERENCES 1
##         ^
## In file included from fileaa1f7fa5cf87.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:42:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:17: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
##     static void set_zero_all_adjoints() {
##                 ^
## In file included from fileaa1f7fa5cf87.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:43:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints_nested.hpp:17:17: warning: 'static' function 'set_zero_all_adjoints_nested' declared in header file should be declared 'static inline' [-Wunneeded-internal-declaration]
##     static void set_zero_all_adjoints_nested() {
##                 ^
## In file included from fileaa1f7fa5cf87.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:58:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:17:14: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
##       size_t fft_next_good_size(size_t N) {
##              ^
## In file included from fileaa1f7fa5cf87.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:298:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr.hpp:38:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr/functor/integrate_ode_rk45.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint.hpp:61:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint/util/multi_array_adaption.hpp:29:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array.hpp:21:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/base.hpp:28:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:42:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:43:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:53:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:54:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## 8 warnings generated.
## In file included from fileaa1f74f02482.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/gevv_vvv_vari.hpp:5:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/var.hpp:7:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/math/tools/config.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config.hpp:39:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config/compiler/clang.hpp:200:11: warning: 'BOOST_NO_CXX11_RVALUE_REFERENCES' macro redefined [-Wmacro-redefined]
## #  define BOOST_NO_CXX11_RVALUE_REFERENCES
##           ^
## <command line>:6:9: note: previous definition is here
## #define BOOST_NO_CXX11_RVALUE_REFERENCES 1
##         ^
## In file included from fileaa1f74f02482.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:42:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:17: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
##     static void set_zero_all_adjoints() {
##                 ^
## In file included from fileaa1f74f02482.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:43:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints_nested.hpp:17:17: warning: 'static' function 'set_zero_all_adjoints_nested' declared in header file should be declared 'static inline' [-Wunneeded-internal-declaration]
##     static void set_zero_all_adjoints_nested() {
##                 ^
## In file included from fileaa1f74f02482.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:58:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:17:14: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
##       size_t fft_next_good_size(size_t N) {
##              ^
## In file included from fileaa1f74f02482.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:298:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr.hpp:38:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr/functor/integrate_ode_rk45.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint.hpp:61:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint/util/multi_array_adaption.hpp:29:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array.hpp:21:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/base.hpp:28:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:42:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:43:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:53:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:54:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## 8 warnings generated.
## In file included from fileaa1f296032d1.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/gevv_vvv_vari.hpp:5:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/var.hpp:7:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/math/tools/config.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config.hpp:39:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config/compiler/clang.hpp:200:11: warning: 'BOOST_NO_CXX11_RVALUE_REFERENCES' macro redefined [-Wmacro-redefined]
## #  define BOOST_NO_CXX11_RVALUE_REFERENCES
##           ^
## <command line>:6:9: note: previous definition is here
## #define BOOST_NO_CXX11_RVALUE_REFERENCES 1
##         ^
## In file included from fileaa1f296032d1.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:42:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:17: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
##     static void set_zero_all_adjoints() {
##                 ^
## In file included from fileaa1f296032d1.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:43:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints_nested.hpp:17:17: warning: 'static' function 'set_zero_all_adjoints_nested' declared in header file should be declared 'static inline' [-Wunneeded-internal-declaration]
##     static void set_zero_all_adjoints_nested() {
##                 ^
## In file included from fileaa1f296032d1.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:58:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:17:14: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
##       size_t fft_next_good_size(size_t N) {
##              ^
## In file included from fileaa1f296032d1.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:298:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr.hpp:38:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr/functor/integrate_ode_rk45.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint.hpp:61:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint/util/multi_array_adaption.hpp:29:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array.hpp:21:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/base.hpp:28:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:42:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:43:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:53:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:54:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## 8 warnings generated.
## In file included from fileaa1f75a04ae.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/gevv_vvv_vari.hpp:5:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/var.hpp:7:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/math/tools/config.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config.hpp:39:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/config/compiler/clang.hpp:200:11: warning: 'BOOST_NO_CXX11_RVALUE_REFERENCES' macro redefined [-Wmacro-redefined]
## #  define BOOST_NO_CXX11_RVALUE_REFERENCES
##           ^
## <command line>:6:9: note: previous definition is here
## #define BOOST_NO_CXX11_RVALUE_REFERENCES 1
##         ^
## In file included from fileaa1f75a04ae.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:42:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:17: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
##     static void set_zero_all_adjoints() {
##                 ^
## In file included from fileaa1f75a04ae.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:43:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints_nested.hpp:17:17: warning: 'static' function 'set_zero_all_adjoints_nested' declared in header file should be declared 'static inline' [-Wunneeded-internal-declaration]
##     static void set_zero_all_adjoints_nested() {
##                 ^
## In file included from fileaa1f75a04ae.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:58:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:17:14: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
##       size_t fft_next_good_size(size_t N) {
##              ^
## In file included from fileaa1f75a04ae.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:298:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr.hpp:38:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/StanHeaders/include/stan/math/prim/arr/functor/integrate_ode_rk45.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint.hpp:61:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/numeric/odeint/util/multi_array_adaption.hpp:29:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array.hpp:21:
## In file included from /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/base.hpp:28:
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:42:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:43:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:53:43: warning: unused typedef 'index_range' [-Wunused-local-typedef]
##       typedef typename Array::index_range index_range;
##                                           ^
## /Library/Frameworks/R.framework/Versions/3.3/Resources/library/BH/include/boost/multi_array/concept_checks.hpp:54:37: warning: unused typedef 'index' [-Wunused-local-typedef]
##       typedef typename Array::index index;
##                                     ^
## 8 warnings generated.

source('Demonstrations/5DToyExampleFun.R')

## Loading required package: DoE.wrapper

## Loading required package: FrF2

## Loading required package: DoE.base

## Loading required package: conf.design

## 
## Attaching package: 'DoE.base'

## The following objects are masked from 'package:stats':
## 
##     aov, lm

## The following object is masked from 'package:graphics':
## 
##     plot.design

## The following object is masked from 'package:base':
## 
##     lengths

## Loading required package: DiceDesign

We need to specify the regions and sub-regions for a 5D Toy function

names.row <- c("group1", "group12", "group2", "group23","group3", "group34", "group4", "group45", "group5")
Group.specification <- data.frame(cbind(c(-1.00, -0.75, -0.72, -0.44, -0.40, -0.03, -0.01, 0.27, 0.37), 
                                  c(-0.75, -0.72, -0.44, -0.40, -0.03, -0.01, 0.27, 0.37, 1.00)), 
                                  row.names = names.row)
colnames(Group.specification) <- c("x5", "x5")

# For graphical purpose: we need to plot Toy function against 5D
x.plot <- seq(-1, 1, length.out = 500)
plot.group <- list()
for(i in 1:dim(Group.specification)[1]) {
  plot.group[[i]] <- which(x.plot >= Group.specification[i, 1] & x.plot < Group.specification[i, 2])
}
plot.output <- c()
for(n in 1:length(plot.group)) {
  s <- sapply(1:length(plot.group[[n]]), function(i) 
    GeneralFunWave(x.plot[plot.group[[n]][i]], a=a.vec[n], b=b.vec[n], 
                   beta1=beta1.vec[n], beta2=beta2.vec[n]))
  plot.output <- c(plot.output, s)
}
plot.z <- cbind(unlist(plot.group), na.omit(unlist(plot.output)))
plot.z.mod <- plot.z[order(plot.z[, 1]), ]
plot.output.final <- plot.z.mod[, 2]
plot.output.final <- plot.output.final - mean(plot.output.final) # centre around zero.

par(mfrow = c(1, 1), mar = c(4, 4, 2, 1))
plot(x.plot[1:499], plot.output.final, xlim = c(-1.1, 1.1), type = 'n', 
     xlab = 'x5', ylab = 'Y')
abline(v = c(-1.00, -0.75, -0.72, -0.44, -0.40, -0.03, -0.01, 0.27, 0.37, 1.00), lty = 'dashed')
group.mixture <- c(2, 4, 6, 8)
for(i in 1:length(group.mixture)) {
  polygon(c(seq(Group.specification[group.mixture[i], 1], Group.specification[group.mixture[i], 2], length.out = 100),
            rev(seq(Group.specification[group.mixture[i], 1], Group.specification[group.mixture[i], 2], length.out = 100))),
          c(rep(-15, 100), rep(6, 100)),col="skyblue")
}
lines(x.plot[1:499], plot.output.final)

Let’s split our input matrix newExtendedNorm and simulator evaluations at input matrix output.final: and constuct stationary and nonstationary GP emulators with active prior specification for x5:

# Load the data frame that we are dealing with
load("Demonstrations/5DExampleMod.RData")
stGPFiveDToy <- nstGPFiveDToy <- MixtureFiveDToy <- list()

for(i in 1:length(LHC.data[[1]])) {
  tData5D <- data.frame(cbind(LHC.data[[1]][[i]], LHC.data[[2]][[i]]))
  names(tData5D) <- c('x1', 'x2', 'x3', 'x4', 'x5', 'y')
  cands <- names(tData5D)[1:5]
  X5V <- as.data.frame(LHC.data[[3]][[i]])
  y5V <- LHC.data[[4]][[i]]
  names(X5V) <- c('x1', 'x2', 'x3', 'x4', 'x5')
  # stationary GP emulator
  toy5D.lm <- EMULATE.lm(Response=names(tData5D)[6], tData=tData5D,
                         tcands=cands,tcanfacs=NULL,TryFouriers=TRUE,maxOrder=2,maxdf = 5)
  toy5D.lm$linModel <- lm(y ~ ., data = tData5D)
  toy5D.gp <- EMULATE.gpstan(meanResponse=toy5D.lm, tData=tData5D, additionalVariables=names(tData5D)[1:5], 
                             FastVersion = TRUE, activePrior = TRUE, activeVariables = c('x5'))
  LOOs.st <- stanLOOplot(StanEmulator = toy5D.gp, ParamNames=colnames(toy5D.gp$Design))
  NewSamplesToy5D <- EMULATOR.gpstan(X5V, Emulator=toy5D.gp, FastVersion = FALSE)
  stGPFiveDToy[[i]] <- cbind(NewSamplesToy5D$Expectation,
                             NewSamplesToy5D$Expectation-2*sqrt(NewSamplesToy5D$Variance),
                             NewSamplesToy5D$Expectation+2*sqrt(NewSamplesToy5D$Variance))
  
  # nonstationary GP emulator
  std.err <- CalStError(LOOs.st, tData5D$y)
  myem.mixture <- MIXTURE.design(y.std = std.err, X = tData5D[, 1:5], L=2)
  myem.gp.nst <- EMULATE.gpstanNSt(toy5D.lm, tData = tData5D, additionalVariables=names(tData5D)[1:5],
                                   FastVersion = TRUE, mixtureComp = myem.mixture, activePrior = TRUE, 
                                   activeVariables = c('x5'))
  MixtureFiveDToy[[i]] <- data.frame(cbind(std.err, myem.mixture$MixtureMat))
  mixture.predict <- MIXTURE.predict(x = X5V, mixtureComp = myem.mixture)
  predict.nst <- EMULATOR.gpstanNSt(X5V, Emulator = myem.gp.nst, mixturePredict = mixture.predict, 
                                    FastVersion = FALSE)
  nstGPFiveDToy[[i]] <- cbind(predict.nst$Expectation, predict.nst$Expectation-2*sqrt(predict.nst$Variance),
                              predict.nst$Expectation+2*sqrt(predict.nst$Variance))
}

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.200781549293386 using sin(pi*2*x5) and cos(pi*2*x5)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0617576631709604 using sin(pi*2*x2) and cos(pi*2*x2)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0498694521398204 using sin(pi*1*x5) and cos(pi*1*x5)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is 0.166764808207009 using x2"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0824852324226217 using sin(pi*2*x3) and cos(pi*2*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0065083873443923 using sin(pi*1*x3) and cos(pi*1*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is 0.119291216612706 using x4"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.00502433957345794 using sin(pi*2*x1) and cos(pi*2*x1)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.000315282692559204 using sin(pi*1*x3) and cos(pi*1*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is 0.0020086586342174 using x2"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.00179306292692116 using sin(pi*1*x3) and cos(pi*1*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0119648340437921 using sin(pi*1*x2) and cos(pi*1*x2)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "No permitted Fourier terms improve the fit"
## [1] "Max reduction is 0.0129783348312769 using x1"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "No permitted Fourier terms improve the fit"
## [1] "Max reduction is 0.0827019740184434 using Three Way Interactions with x2"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "No permitted Fourier terms improve the fit"
## [1] "No permitted terms improve the fit"
## 
## Call:
## lm.default(formula = y ~ x2 + I(x2^2) + x4 + x1 + I(x4 * x2) + 
##     I(x1 * x2) + I(x1 * x4) + I(sin(pi * x5 * 2)) + I(cos(pi * 
##     x5 * 2)) + I(sin(pi * x2 * 1)) + I(sin(pi * x2 * 2)) + I(cos(pi * 
##     x2 * 1)) + I(cos(pi * x2 * 2)) + I(sin(pi * x3 * 1)) + I(sin(pi * 
##     x3 * 2)) + I(cos(pi * x3 * 1)) + I(cos(pi * x3 * 2)) + I(sin(pi * 
##     x1 * 2)) + I(cos(pi * x1 * 2)) + I(x2 * x4 * x2) + I(x2 * 
##     x1 * x2) + I(x2 * x1 * x4), data = tData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.7393 -1.3860  0.4243  1.5540  4.2371 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -3.7895     3.2675  -1.160 0.251441    
## x2                    4.4448     1.4828   2.998 0.004166 ** 
## I(x2^2)              10.7932     9.7699   1.105 0.274360    
## x4                    1.5178     0.9270   1.637 0.107575    
## x1                   -1.7500     0.9660  -1.812 0.075827 .  
## I(x4 * x2)           -2.1567     1.1946  -1.805 0.076801 .  
## I(x1 * x2)           -1.8514     1.0915  -1.696 0.095834 .  
## I(x1 * x4)           -1.0556     1.1287  -0.935 0.353978    
## I(sin(pi * x5 * 2))  -0.4848     0.5216  -0.929 0.357036    
## I(cos(pi * x5 * 2))  -0.8332     0.5477  -1.521 0.134269    
## I(sin(pi * x2 * 1))  -1.5664     1.0768  -1.455 0.151755    
## I(sin(pi * x2 * 2))   2.7220     0.7629   3.568 0.000784 ***
## I(cos(pi * x2 * 1))   3.8947     3.9881   0.977 0.333302    
## I(cos(pi * x2 * 2))  -2.1246     1.1326  -1.876 0.066302 .  
## I(sin(pi * x3 * 1))   0.7247     0.4925   1.472 0.147182    
## I(sin(pi * x3 * 2))  -1.5720     0.5356  -2.935 0.004959 ** 
## I(cos(pi * x3 * 1))  -0.6102     0.5372  -1.136 0.261222    
## I(cos(pi * x3 * 2))  -0.2554     0.5981  -0.427 0.671159    
## I(sin(pi * x1 * 2))   0.3774     0.5902   0.640 0.525299    
## I(cos(pi * x1 * 2))   0.7243     0.5428   1.335 0.187853    
## I(x2 * x4 * x2)      -0.1059     2.2595  -0.047 0.962807    
## I(x2 * x1 * x2)       5.4773     2.2176   2.470 0.016834 *  
## I(x2 * x1 * x4)      -1.1870     2.1957  -0.541 0.591110    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.912 on 52 degrees of freedom
## Multiple R-squared:  0.5551, Adjusted R-squared:  0.3668 
## F-statistic: 2.949 on 22 and 52 DF,  p-value: 0.0007058
## 
## [1] "1 I(x2 * x4 * x2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "2 I(x2^2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## 
## Call:
## lm.default(formula = y ~ x2 + x4 + x1 + I(x4 * x2) + I(x1 * x2) + 
##     I(x1 * x4) + I(sin(pi * x5 * 2)) + I(cos(pi * x5 * 2)) + 
##     I(sin(pi * x2 * 1)) + I(sin(pi * x2 * 2)) + I(cos(pi * x2 * 
##     1)) + I(cos(pi * x2 * 2)) + I(sin(pi * x3 * 1)) + I(sin(pi * 
##     x3 * 2)) + I(cos(pi * x3 * 1)) + I(cos(pi * x3 * 2)) + I(sin(pi * 
##     x1 * 2)) + I(cos(pi * x1 * 2)) + I(x2 * x1 * x2) + I(x2 * 
##     x1 * x4), data = tData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.3950 -1.5133  0.3837  1.5630  4.3355 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -0.1989     0.3352  -0.593 0.555415    
## x2                    4.3705     1.4139   3.091 0.003150 ** 
## x4                    1.4718     0.6398   2.300 0.025325 *  
## x1                   -1.6426     0.9539  -1.722 0.090783 .  
## I(x4 * x2)           -1.9274     1.1658  -1.653 0.104089    
## I(x1 * x2)           -1.7120     1.0750  -1.593 0.117087    
## I(x1 * x4)           -0.9018     1.1087  -0.813 0.419551    
## I(sin(pi * x5 * 2))  -0.4020     0.5081  -0.791 0.432258    
## I(cos(pi * x5 * 2))  -0.8892     0.5370  -1.656 0.103560    
## I(sin(pi * x2 * 1))  -1.5111     1.0401  -1.453 0.152042    
## I(sin(pi * x2 * 2))   2.6658     0.7346   3.629 0.000632 ***
## I(cos(pi * x2 * 1))  -0.4735     0.5045  -0.939 0.352106    
## I(cos(pi * x2 * 2))  -1.0273     0.5408  -1.900 0.062839 .  
## I(sin(pi * x3 * 1))   0.7241     0.4886   1.482 0.144139    
## I(sin(pi * x3 * 2))  -1.6454     0.5243  -3.139 0.002751 ** 
## I(cos(pi * x3 * 1))  -0.5832     0.5295  -1.101 0.275592    
## I(cos(pi * x3 * 2))  -0.1259     0.5773  -0.218 0.828235    
## I(sin(pi * x1 * 2))   0.4264     0.5791   0.736 0.464673    
## I(cos(pi * x1 * 2))   0.8143     0.5243   1.553 0.126254    
## I(x2 * x1 * x2)       5.7103     2.1916   2.605 0.011830 *  
## I(x2 * x1 * x4)      -1.2833     2.1736  -0.590 0.557361    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.891 on 54 degrees of freedom
## Multiple R-squared:  0.5446, Adjusted R-squared:  0.3759 
## F-statistic: 3.229 on 20 and 54 DF,  p-value: 0.0003189
## 
## [1] "1 I(cos(pi * x2 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "2 I(sin(pi * x1 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "3 I(cos(pi * x3 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "4 I(x2 * x1 * x4)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "5 I(x1 * x4)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "6 I(cos(pi * x3 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "7 I(sin(pi * x2 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "8 I(sin(pi * x3 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "9 I(cos(pi * x2 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "10 I(sin(pi * x5 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "11 I(cos(pi * x1 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "12 I(x4 * x2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in all(lapply(ThreeWayInters, function(e) (all(e[variableNum, ] < :
## coercing argument of type 'list' to logical

## [1] "13 x4"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "14 I(sin(pi * x3 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "15 I(x2 * x1 * x2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## 
## Call:
## lm.default(formula = y ~ x2 + x1 + I(x1 * x2) + I(cos(pi * x5 * 
##     2)) + I(sin(pi * x2 * 2)), data = tData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -13.819  -1.218   0.396   1.701   6.601 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)   
## (Intercept)          -0.1881     0.3789  -0.496  0.62112   
## x2                    2.0609     0.7193   2.865  0.00552 **
## x1                    0.1870     0.6704   0.279  0.78112   
## I(x1 * x2)           -1.6664     1.1888  -1.402  0.16548   
## I(cos(pi * x5 * 2))  -1.7126     0.5395  -3.175  0.00224 **
## I(sin(pi * x2 * 2))   1.6162     0.6031   2.680  0.00921 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.28 on 69 degrees of freedom
## Multiple R-squared:  0.2509, Adjusted R-squared:  0.1966 
## F-statistic: 4.622 on 5 and 69 DF,  p-value: 0.001073
## 
## 
## SAMPLING FOR MODEL 'PredictLOO' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                57.4676 seconds (Sampling)
##                57.4676 seconds (Total)

## 
## SAMPLING FOR MODEL 'PredictGen' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                1.92754 seconds (Sampling)
##                1.92754 seconds (Total)
## 
## 
## SAMPLING FOR MODEL 'MixtureModPredict' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                0.032629 seconds (Sampling)
##                0.032629 seconds (Total)
## 
## 
## SAMPLING FOR MODEL 'PredictGenNGP' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                11.5447 seconds (Sampling)
##                11.5447 seconds (Total)

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.200781549293386 using sin(pi*2*x5) and cos(pi*2*x5)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0617576631709604 using sin(pi*2*x2) and cos(pi*2*x2)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0498694521398204 using sin(pi*1*x5) and cos(pi*1*x5)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is 0.166764808207009 using x2"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0824852324226217 using sin(pi*2*x3) and cos(pi*2*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0065083873443923 using sin(pi*1*x3) and cos(pi*1*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is 0.119291216612706 using x4"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.00502433957345794 using sin(pi*2*x1) and cos(pi*2*x1)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.000315282692559204 using sin(pi*1*x3) and cos(pi*1*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is 0.0020086586342174 using x2"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.00179306292692116 using sin(pi*1*x3) and cos(pi*1*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0119648340437921 using sin(pi*1*x2) and cos(pi*1*x2)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "No permitted Fourier terms improve the fit"
## [1] "Max reduction is 0.0129783348312769 using x1"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "No permitted Fourier terms improve the fit"
## [1] "Max reduction is 0.0827019740184434 using Three Way Interactions with x2"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "No permitted Fourier terms improve the fit"
## [1] "No permitted terms improve the fit"
## 
## Call:
## lm.default(formula = y ~ x2 + I(x2^2) + x4 + x1 + I(x4 * x2) + 
##     I(x1 * x2) + I(x1 * x4) + I(sin(pi * x5 * 2)) + I(cos(pi * 
##     x5 * 2)) + I(sin(pi * x2 * 1)) + I(sin(pi * x2 * 2)) + I(cos(pi * 
##     x2 * 1)) + I(cos(pi * x2 * 2)) + I(sin(pi * x3 * 1)) + I(sin(pi * 
##     x3 * 2)) + I(cos(pi * x3 * 1)) + I(cos(pi * x3 * 2)) + I(sin(pi * 
##     x1 * 2)) + I(cos(pi * x1 * 2)) + I(x2 * x4 * x2) + I(x2 * 
##     x1 * x2) + I(x2 * x1 * x4), data = tData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.7393 -1.3860  0.4243  1.5540  4.2371 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -3.7895     3.2675  -1.160 0.251441    
## x2                    4.4448     1.4828   2.998 0.004166 ** 
## I(x2^2)              10.7932     9.7699   1.105 0.274360    
## x4                    1.5178     0.9270   1.637 0.107575    
## x1                   -1.7500     0.9660  -1.812 0.075827 .  
## I(x4 * x2)           -2.1567     1.1946  -1.805 0.076801 .  
## I(x1 * x2)           -1.8514     1.0915  -1.696 0.095834 .  
## I(x1 * x4)           -1.0556     1.1287  -0.935 0.353978    
## I(sin(pi * x5 * 2))  -0.4848     0.5216  -0.929 0.357036    
## I(cos(pi * x5 * 2))  -0.8332     0.5477  -1.521 0.134269    
## I(sin(pi * x2 * 1))  -1.5664     1.0768  -1.455 0.151755    
## I(sin(pi * x2 * 2))   2.7220     0.7629   3.568 0.000784 ***
## I(cos(pi * x2 * 1))   3.8947     3.9881   0.977 0.333302    
## I(cos(pi * x2 * 2))  -2.1246     1.1326  -1.876 0.066302 .  
## I(sin(pi * x3 * 1))   0.7247     0.4925   1.472 0.147182    
## I(sin(pi * x3 * 2))  -1.5720     0.5356  -2.935 0.004959 ** 
## I(cos(pi * x3 * 1))  -0.6102     0.5372  -1.136 0.261222    
## I(cos(pi * x3 * 2))  -0.2554     0.5981  -0.427 0.671159    
## I(sin(pi * x1 * 2))   0.3774     0.5902   0.640 0.525299    
## I(cos(pi * x1 * 2))   0.7243     0.5428   1.335 0.187853    
## I(x2 * x4 * x2)      -0.1059     2.2595  -0.047 0.962807    
## I(x2 * x1 * x2)       5.4773     2.2176   2.470 0.016834 *  
## I(x2 * x1 * x4)      -1.1870     2.1957  -0.541 0.591110    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.912 on 52 degrees of freedom
## Multiple R-squared:  0.5551, Adjusted R-squared:  0.3668 
## F-statistic: 2.949 on 22 and 52 DF,  p-value: 0.0007058
## 
## [1] "1 I(x2 * x4 * x2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "2 I(x2^2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## 
## Call:
## lm.default(formula = y ~ x2 + x4 + x1 + I(x4 * x2) + I(x1 * x2) + 
##     I(x1 * x4) + I(sin(pi * x5 * 2)) + I(cos(pi * x5 * 2)) + 
##     I(sin(pi * x2 * 1)) + I(sin(pi * x2 * 2)) + I(cos(pi * x2 * 
##     1)) + I(cos(pi * x2 * 2)) + I(sin(pi * x3 * 1)) + I(sin(pi * 
##     x3 * 2)) + I(cos(pi * x3 * 1)) + I(cos(pi * x3 * 2)) + I(sin(pi * 
##     x1 * 2)) + I(cos(pi * x1 * 2)) + I(x2 * x1 * x2) + I(x2 * 
##     x1 * x4), data = tData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.3950 -1.5133  0.3837  1.5630  4.3355 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -0.1989     0.3352  -0.593 0.555415    
## x2                    4.3705     1.4139   3.091 0.003150 ** 
## x4                    1.4718     0.6398   2.300 0.025325 *  
## x1                   -1.6426     0.9539  -1.722 0.090783 .  
## I(x4 * x2)           -1.9274     1.1658  -1.653 0.104089    
## I(x1 * x2)           -1.7120     1.0750  -1.593 0.117087    
## I(x1 * x4)           -0.9018     1.1087  -0.813 0.419551    
## I(sin(pi * x5 * 2))  -0.4020     0.5081  -0.791 0.432258    
## I(cos(pi * x5 * 2))  -0.8892     0.5370  -1.656 0.103560    
## I(sin(pi * x2 * 1))  -1.5111     1.0401  -1.453 0.152042    
## I(sin(pi * x2 * 2))   2.6658     0.7346   3.629 0.000632 ***
## I(cos(pi * x2 * 1))  -0.4735     0.5045  -0.939 0.352106    
## I(cos(pi * x2 * 2))  -1.0273     0.5408  -1.900 0.062839 .  
## I(sin(pi * x3 * 1))   0.7241     0.4886   1.482 0.144139    
## I(sin(pi * x3 * 2))  -1.6454     0.5243  -3.139 0.002751 ** 
## I(cos(pi * x3 * 1))  -0.5832     0.5295  -1.101 0.275592    
## I(cos(pi * x3 * 2))  -0.1259     0.5773  -0.218 0.828235    
## I(sin(pi * x1 * 2))   0.4264     0.5791   0.736 0.464673    
## I(cos(pi * x1 * 2))   0.8143     0.5243   1.553 0.126254    
## I(x2 * x1 * x2)       5.7103     2.1916   2.605 0.011830 *  
## I(x2 * x1 * x4)      -1.2833     2.1736  -0.590 0.557361    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.891 on 54 degrees of freedom
## Multiple R-squared:  0.5446, Adjusted R-squared:  0.3759 
## F-statistic: 3.229 on 20 and 54 DF,  p-value: 0.0003189
## 
## [1] "1 I(cos(pi * x2 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "2 I(sin(pi * x1 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "3 I(cos(pi * x3 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "4 I(x2 * x1 * x4)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "5 I(x1 * x4)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "6 I(cos(pi * x3 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "7 I(sin(pi * x2 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "8 I(sin(pi * x3 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "9 I(cos(pi * x2 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "10 I(sin(pi * x5 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "11 I(cos(pi * x1 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "12 I(x4 * x2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in all(lapply(ThreeWayInters, function(e) (all(e[variableNum, ] < :
## coercing argument of type 'list' to logical

## [1] "13 x4"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "14 I(sin(pi * x3 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "15 I(x2 * x1 * x2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## 
## Call:
## lm.default(formula = y ~ x2 + x1 + I(x1 * x2) + I(cos(pi * x5 * 
##     2)) + I(sin(pi * x2 * 2)), data = tData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -13.819  -1.218   0.396   1.701   6.601 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)   
## (Intercept)          -0.1881     0.3789  -0.496  0.62112   
## x2                    2.0609     0.7193   2.865  0.00552 **
## x1                    0.1870     0.6704   0.279  0.78112   
## I(x1 * x2)           -1.6664     1.1888  -1.402  0.16548   
## I(cos(pi * x5 * 2))  -1.7126     0.5395  -3.175  0.00224 **
## I(sin(pi * x2 * 2))   1.6162     0.6031   2.680  0.00921 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.28 on 69 degrees of freedom
## Multiple R-squared:  0.2509, Adjusted R-squared:  0.1966 
## F-statistic: 4.622 on 5 and 69 DF,  p-value: 0.001073
## 
## 
## SAMPLING FOR MODEL 'PredictLOO' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                58.6065 seconds (Sampling)
##                58.6065 seconds (Total)

## 
## SAMPLING FOR MODEL 'PredictGen' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                2.15098 seconds (Sampling)
##                2.15098 seconds (Total)
## 
## 
## SAMPLING FOR MODEL 'MixtureModPredict' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                0.031853 seconds (Sampling)
##                0.031853 seconds (Total)
## 
## 
## SAMPLING FOR MODEL 'PredictGenNGP' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                11.2897 seconds (Sampling)
##                11.2897 seconds (Total)

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.200781549293386 using sin(pi*2*x5) and cos(pi*2*x5)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0617576631709604 using sin(pi*2*x2) and cos(pi*2*x2)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0498694521398204 using sin(pi*1*x5) and cos(pi*1*x5)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is 0.166764808207009 using x2"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0824852324226217 using sin(pi*2*x3) and cos(pi*2*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0065083873443923 using sin(pi*1*x3) and cos(pi*1*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is 0.119291216612706 using x4"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.00502433957345794 using sin(pi*2*x1) and cos(pi*2*x1)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.000315282692559204 using sin(pi*1*x3) and cos(pi*1*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is 0.0020086586342174 using x2"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.00179306292692116 using sin(pi*1*x3) and cos(pi*1*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0119648340437921 using sin(pi*1*x2) and cos(pi*1*x2)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "No permitted Fourier terms improve the fit"
## [1] "Max reduction is 0.0129783348312769 using x1"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "No permitted Fourier terms improve the fit"
## [1] "Max reduction is 0.0827019740184434 using Three Way Interactions with x2"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "No permitted Fourier terms improve the fit"
## [1] "No permitted terms improve the fit"
## 
## Call:
## lm.default(formula = y ~ x2 + I(x2^2) + x4 + x1 + I(x4 * x2) + 
##     I(x1 * x2) + I(x1 * x4) + I(sin(pi * x5 * 2)) + I(cos(pi * 
##     x5 * 2)) + I(sin(pi * x2 * 1)) + I(sin(pi * x2 * 2)) + I(cos(pi * 
##     x2 * 1)) + I(cos(pi * x2 * 2)) + I(sin(pi * x3 * 1)) + I(sin(pi * 
##     x3 * 2)) + I(cos(pi * x3 * 1)) + I(cos(pi * x3 * 2)) + I(sin(pi * 
##     x1 * 2)) + I(cos(pi * x1 * 2)) + I(x2 * x4 * x2) + I(x2 * 
##     x1 * x2) + I(x2 * x1 * x4), data = tData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.7393 -1.3860  0.4243  1.5540  4.2371 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -3.7895     3.2675  -1.160 0.251441    
## x2                    4.4448     1.4828   2.998 0.004166 ** 
## I(x2^2)              10.7932     9.7699   1.105 0.274360    
## x4                    1.5178     0.9270   1.637 0.107575    
## x1                   -1.7500     0.9660  -1.812 0.075827 .  
## I(x4 * x2)           -2.1567     1.1946  -1.805 0.076801 .  
## I(x1 * x2)           -1.8514     1.0915  -1.696 0.095834 .  
## I(x1 * x4)           -1.0556     1.1287  -0.935 0.353978    
## I(sin(pi * x5 * 2))  -0.4848     0.5216  -0.929 0.357036    
## I(cos(pi * x5 * 2))  -0.8332     0.5477  -1.521 0.134269    
## I(sin(pi * x2 * 1))  -1.5664     1.0768  -1.455 0.151755    
## I(sin(pi * x2 * 2))   2.7220     0.7629   3.568 0.000784 ***
## I(cos(pi * x2 * 1))   3.8947     3.9881   0.977 0.333302    
## I(cos(pi * x2 * 2))  -2.1246     1.1326  -1.876 0.066302 .  
## I(sin(pi * x3 * 1))   0.7247     0.4925   1.472 0.147182    
## I(sin(pi * x3 * 2))  -1.5720     0.5356  -2.935 0.004959 ** 
## I(cos(pi * x3 * 1))  -0.6102     0.5372  -1.136 0.261222    
## I(cos(pi * x3 * 2))  -0.2554     0.5981  -0.427 0.671159    
## I(sin(pi * x1 * 2))   0.3774     0.5902   0.640 0.525299    
## I(cos(pi * x1 * 2))   0.7243     0.5428   1.335 0.187853    
## I(x2 * x4 * x2)      -0.1059     2.2595  -0.047 0.962807    
## I(x2 * x1 * x2)       5.4773     2.2176   2.470 0.016834 *  
## I(x2 * x1 * x4)      -1.1870     2.1957  -0.541 0.591110    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.912 on 52 degrees of freedom
## Multiple R-squared:  0.5551, Adjusted R-squared:  0.3668 
## F-statistic: 2.949 on 22 and 52 DF,  p-value: 0.0007058
## 
## [1] "1 I(x2 * x4 * x2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "2 I(x2^2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## 
## Call:
## lm.default(formula = y ~ x2 + x4 + x1 + I(x4 * x2) + I(x1 * x2) + 
##     I(x1 * x4) + I(sin(pi * x5 * 2)) + I(cos(pi * x5 * 2)) + 
##     I(sin(pi * x2 * 1)) + I(sin(pi * x2 * 2)) + I(cos(pi * x2 * 
##     1)) + I(cos(pi * x2 * 2)) + I(sin(pi * x3 * 1)) + I(sin(pi * 
##     x3 * 2)) + I(cos(pi * x3 * 1)) + I(cos(pi * x3 * 2)) + I(sin(pi * 
##     x1 * 2)) + I(cos(pi * x1 * 2)) + I(x2 * x1 * x2) + I(x2 * 
##     x1 * x4), data = tData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.3950 -1.5133  0.3837  1.5630  4.3355 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -0.1989     0.3352  -0.593 0.555415    
## x2                    4.3705     1.4139   3.091 0.003150 ** 
## x4                    1.4718     0.6398   2.300 0.025325 *  
## x1                   -1.6426     0.9539  -1.722 0.090783 .  
## I(x4 * x2)           -1.9274     1.1658  -1.653 0.104089    
## I(x1 * x2)           -1.7120     1.0750  -1.593 0.117087    
## I(x1 * x4)           -0.9018     1.1087  -0.813 0.419551    
## I(sin(pi * x5 * 2))  -0.4020     0.5081  -0.791 0.432258    
## I(cos(pi * x5 * 2))  -0.8892     0.5370  -1.656 0.103560    
## I(sin(pi * x2 * 1))  -1.5111     1.0401  -1.453 0.152042    
## I(sin(pi * x2 * 2))   2.6658     0.7346   3.629 0.000632 ***
## I(cos(pi * x2 * 1))  -0.4735     0.5045  -0.939 0.352106    
## I(cos(pi * x2 * 2))  -1.0273     0.5408  -1.900 0.062839 .  
## I(sin(pi * x3 * 1))   0.7241     0.4886   1.482 0.144139    
## I(sin(pi * x3 * 2))  -1.6454     0.5243  -3.139 0.002751 ** 
## I(cos(pi * x3 * 1))  -0.5832     0.5295  -1.101 0.275592    
## I(cos(pi * x3 * 2))  -0.1259     0.5773  -0.218 0.828235    
## I(sin(pi * x1 * 2))   0.4264     0.5791   0.736 0.464673    
## I(cos(pi * x1 * 2))   0.8143     0.5243   1.553 0.126254    
## I(x2 * x1 * x2)       5.7103     2.1916   2.605 0.011830 *  
## I(x2 * x1 * x4)      -1.2833     2.1736  -0.590 0.557361    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.891 on 54 degrees of freedom
## Multiple R-squared:  0.5446, Adjusted R-squared:  0.3759 
## F-statistic: 3.229 on 20 and 54 DF,  p-value: 0.0003189
## 
## [1] "1 I(cos(pi * x2 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "2 I(sin(pi * x1 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "3 I(cos(pi * x3 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "4 I(x2 * x1 * x4)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "5 I(x1 * x4)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "6 I(cos(pi * x3 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "7 I(sin(pi * x2 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "8 I(sin(pi * x3 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "9 I(cos(pi * x2 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "10 I(sin(pi * x5 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "11 I(cos(pi * x1 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "12 I(x4 * x2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in all(lapply(ThreeWayInters, function(e) (all(e[variableNum, ] < :
## coercing argument of type 'list' to logical

## [1] "13 x4"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "14 I(sin(pi * x3 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "15 I(x2 * x1 * x2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## 
## Call:
## lm.default(formula = y ~ x2 + x1 + I(x1 * x2) + I(cos(pi * x5 * 
##     2)) + I(sin(pi * x2 * 2)), data = tData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -13.819  -1.218   0.396   1.701   6.601 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)   
## (Intercept)          -0.1881     0.3789  -0.496  0.62112   
## x2                    2.0609     0.7193   2.865  0.00552 **
## x1                    0.1870     0.6704   0.279  0.78112   
## I(x1 * x2)           -1.6664     1.1888  -1.402  0.16548   
## I(cos(pi * x5 * 2))  -1.7126     0.5395  -3.175  0.00224 **
## I(sin(pi * x2 * 2))   1.6162     0.6031   2.680  0.00921 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.28 on 69 degrees of freedom
## Multiple R-squared:  0.2509, Adjusted R-squared:  0.1966 
## F-statistic: 4.622 on 5 and 69 DF,  p-value: 0.001073
## 
## 
## SAMPLING FOR MODEL 'PredictLOO' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                58.9738 seconds (Sampling)
##                58.9738 seconds (Total)

## 
## SAMPLING FOR MODEL 'PredictGen' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                2.01916 seconds (Sampling)
##                2.01916 seconds (Total)
## 
## 
## SAMPLING FOR MODEL 'MixtureModPredict' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                0.03555 seconds (Sampling)
##                0.03555 seconds (Total)
## 
## 
## SAMPLING FOR MODEL 'PredictGenNGP' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                11.2746 seconds (Sampling)
##                11.2746 seconds (Total)

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.200781549293386 using sin(pi*2*x5) and cos(pi*2*x5)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0617576631709604 using sin(pi*2*x2) and cos(pi*2*x2)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0498694521398204 using sin(pi*1*x5) and cos(pi*1*x5)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is 0.166764808207009 using x2"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0824852324226217 using sin(pi*2*x3) and cos(pi*2*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0065083873443923 using sin(pi*1*x3) and cos(pi*1*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is 0.119291216612706 using x4"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.00502433957345794 using sin(pi*2*x1) and cos(pi*2*x1)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.000315282692559204 using sin(pi*1*x3) and cos(pi*1*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is 0.0020086586342174 using x2"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.00179306292692116 using sin(pi*1*x3) and cos(pi*1*x3)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max Fourier reduction is 0.0119648340437921 using sin(pi*1*x2) and cos(pi*1*x2)"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "Max reduction is with the Fourier term"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "No permitted Fourier terms improve the fit"
## [1] "Max reduction is 0.0129783348312769 using x1"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "No permitted Fourier terms improve the fit"
## [1] "Max reduction is 0.0827019740184434 using Three Way Interactions with x2"

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in FitLM(DataString = DataString, ResponseString =
## ResponseString, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "No permitted Fourier terms improve the fit"
## [1] "No permitted terms improve the fit"
## 
## Call:
## lm.default(formula = y ~ x2 + I(x2^2) + x4 + x1 + I(x4 * x2) + 
##     I(x1 * x2) + I(x1 * x4) + I(sin(pi * x5 * 2)) + I(cos(pi * 
##     x5 * 2)) + I(sin(pi * x2 * 1)) + I(sin(pi * x2 * 2)) + I(cos(pi * 
##     x2 * 1)) + I(cos(pi * x2 * 2)) + I(sin(pi * x3 * 1)) + I(sin(pi * 
##     x3 * 2)) + I(cos(pi * x3 * 1)) + I(cos(pi * x3 * 2)) + I(sin(pi * 
##     x1 * 2)) + I(cos(pi * x1 * 2)) + I(x2 * x4 * x2) + I(x2 * 
##     x1 * x2) + I(x2 * x1 * x4), data = tData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.7393 -1.3860  0.4243  1.5540  4.2371 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -3.7895     3.2675  -1.160 0.251441    
## x2                    4.4448     1.4828   2.998 0.004166 ** 
## I(x2^2)              10.7932     9.7699   1.105 0.274360    
## x4                    1.5178     0.9270   1.637 0.107575    
## x1                   -1.7500     0.9660  -1.812 0.075827 .  
## I(x4 * x2)           -2.1567     1.1946  -1.805 0.076801 .  
## I(x1 * x2)           -1.8514     1.0915  -1.696 0.095834 .  
## I(x1 * x4)           -1.0556     1.1287  -0.935 0.353978    
## I(sin(pi * x5 * 2))  -0.4848     0.5216  -0.929 0.357036    
## I(cos(pi * x5 * 2))  -0.8332     0.5477  -1.521 0.134269    
## I(sin(pi * x2 * 1))  -1.5664     1.0768  -1.455 0.151755    
## I(sin(pi * x2 * 2))   2.7220     0.7629   3.568 0.000784 ***
## I(cos(pi * x2 * 1))   3.8947     3.9881   0.977 0.333302    
## I(cos(pi * x2 * 2))  -2.1246     1.1326  -1.876 0.066302 .  
## I(sin(pi * x3 * 1))   0.7247     0.4925   1.472 0.147182    
## I(sin(pi * x3 * 2))  -1.5720     0.5356  -2.935 0.004959 ** 
## I(cos(pi * x3 * 1))  -0.6102     0.5372  -1.136 0.261222    
## I(cos(pi * x3 * 2))  -0.2554     0.5981  -0.427 0.671159    
## I(sin(pi * x1 * 2))   0.3774     0.5902   0.640 0.525299    
## I(cos(pi * x1 * 2))   0.7243     0.5428   1.335 0.187853    
## I(x2 * x4 * x2)      -0.1059     2.2595  -0.047 0.962807    
## I(x2 * x1 * x2)       5.4773     2.2176   2.470 0.016834 *  
## I(x2 * x1 * x4)      -1.1870     2.1957  -0.541 0.591110    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.912 on 52 degrees of freedom
## Multiple R-squared:  0.5551, Adjusted R-squared:  0.3668 
## F-statistic: 2.949 on 22 and 52 DF,  p-value: 0.0007058
## 
## [1] "1 I(x2 * x4 * x2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "2 I(x2^2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## 
## Call:
## lm.default(formula = y ~ x2 + x4 + x1 + I(x4 * x2) + I(x1 * x2) + 
##     I(x1 * x4) + I(sin(pi * x5 * 2)) + I(cos(pi * x5 * 2)) + 
##     I(sin(pi * x2 * 1)) + I(sin(pi * x2 * 2)) + I(cos(pi * x2 * 
##     1)) + I(cos(pi * x2 * 2)) + I(sin(pi * x3 * 1)) + I(sin(pi * 
##     x3 * 2)) + I(cos(pi * x3 * 1)) + I(cos(pi * x3 * 2)) + I(sin(pi * 
##     x1 * 2)) + I(cos(pi * x1 * 2)) + I(x2 * x1 * x2) + I(x2 * 
##     x1 * x4), data = tData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.3950 -1.5133  0.3837  1.5630  4.3355 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -0.1989     0.3352  -0.593 0.555415    
## x2                    4.3705     1.4139   3.091 0.003150 ** 
## x4                    1.4718     0.6398   2.300 0.025325 *  
## x1                   -1.6426     0.9539  -1.722 0.090783 .  
## I(x4 * x2)           -1.9274     1.1658  -1.653 0.104089    
## I(x1 * x2)           -1.7120     1.0750  -1.593 0.117087    
## I(x1 * x4)           -0.9018     1.1087  -0.813 0.419551    
## I(sin(pi * x5 * 2))  -0.4020     0.5081  -0.791 0.432258    
## I(cos(pi * x5 * 2))  -0.8892     0.5370  -1.656 0.103560    
## I(sin(pi * x2 * 1))  -1.5111     1.0401  -1.453 0.152042    
## I(sin(pi * x2 * 2))   2.6658     0.7346   3.629 0.000632 ***
## I(cos(pi * x2 * 1))  -0.4735     0.5045  -0.939 0.352106    
## I(cos(pi * x2 * 2))  -1.0273     0.5408  -1.900 0.062839 .  
## I(sin(pi * x3 * 1))   0.7241     0.4886   1.482 0.144139    
## I(sin(pi * x3 * 2))  -1.6454     0.5243  -3.139 0.002751 ** 
## I(cos(pi * x3 * 1))  -0.5832     0.5295  -1.101 0.275592    
## I(cos(pi * x3 * 2))  -0.1259     0.5773  -0.218 0.828235    
## I(sin(pi * x1 * 2))   0.4264     0.5791   0.736 0.464673    
## I(cos(pi * x1 * 2))   0.8143     0.5243   1.553 0.126254    
## I(x2 * x1 * x2)       5.7103     2.1916   2.605 0.011830 *  
## I(x2 * x1 * x4)      -1.2833     2.1736  -0.590 0.557361    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.891 on 54 degrees of freedom
## Multiple R-squared:  0.5446, Adjusted R-squared:  0.3759 
## F-statistic: 3.229 on 20 and 54 DF,  p-value: 0.0003189
## 
## [1] "1 I(cos(pi * x2 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "2 I(sin(pi * x1 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "3 I(cos(pi * x3 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "4 I(x2 * x1 * x4)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "5 I(x1 * x4)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "6 I(cos(pi * x3 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "7 I(sin(pi * x2 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "8 I(sin(pi * x3 * 1))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "9 I(cos(pi * x2 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "10 I(sin(pi * x5 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "11 I(cos(pi * x1 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "12 I(x4 * x2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## Warning in all(lapply(ThreeWayInters, function(e) (all(e[variableNum, ] < :
## coercing argument of type 'list' to logical

## [1] "13 x4"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "14 I(sin(pi * x3 * 2))"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## [1] "15 I(x2 * x1 * x2)"

## Warning in FitLM(dataString, responseString, Names, mainEffects,
## Interactions, : Fitting fourier basis assumes variables are on [-1,1].
## Rescale if not

## 
## Call:
## lm.default(formula = y ~ x2 + x1 + I(x1 * x2) + I(cos(pi * x5 * 
##     2)) + I(sin(pi * x2 * 2)), data = tData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -13.819  -1.218   0.396   1.701   6.601 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)   
## (Intercept)          -0.1881     0.3789  -0.496  0.62112   
## x2                    2.0609     0.7193   2.865  0.00552 **
## x1                    0.1870     0.6704   0.279  0.78112   
## I(x1 * x2)           -1.6664     1.1888  -1.402  0.16548   
## I(cos(pi * x5 * 2))  -1.7126     0.5395  -3.175  0.00224 **
## I(sin(pi * x2 * 2))   1.6162     0.6031   2.680  0.00921 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.28 on 69 degrees of freedom
## Multiple R-squared:  0.2509, Adjusted R-squared:  0.1966 
## F-statistic: 4.622 on 5 and 69 DF,  p-value: 0.001073
## 
## 
## SAMPLING FOR MODEL 'PredictLOO' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                57.2589 seconds (Sampling)
##                57.2589 seconds (Total)

## 
## SAMPLING FOR MODEL 'PredictGen' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                1.95219 seconds (Sampling)
##                1.95219 seconds (Total)
## 
## 
## SAMPLING FOR MODEL 'MixtureModPredict' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                0.037619 seconds (Sampling)
##                0.037619 seconds (Total)
## 
## 
## SAMPLING FOR MODEL 'PredictGenNGP' NOW (CHAIN 1).
## Iteration: 1 / 1 [100%]  (Sampling)
## 
##  Elapsed Time: 0 seconds (Warm-up)
##                11.2036 seconds (Sampling)
##                11.2036 seconds (Total)

MixtureFiveDToy.mod <- list()
for(i in 1:length(MixtureFiveDToy)) {
  MixtureFiveDToy.mod[[i]] <- data.frame(LHC.data[[1]][[i]], MixtureFiveDToy[[i]])
  names(MixtureFiveDToy.mod[[i]]) <- c('x1', 'x2', 'x3', 'x4', 'x5','std.err', 'red', 'blue')
}

Let’s perform similar diagnostics for TGP

TGPFiveDToy <- list()
CGPFiveDToy <- list()
for(i in 1:length(LHC.data[[1]])) {
  tData5D <- data.frame(cbind(LHC.data[[1]][[i]], LHC.data[[2]][[i]]))
  names(tData5D) <- c('x1', 'x2', 'x3', 'x4', 'x5', 'y')
  cands <- names(tData5D)[1:5]
  X5V <- as.data.frame(LHC.data[[3]][[i]])
  y5V <- LHC.data[[4]][[i]]
  names(X5V) <- c('x1', 'x2', 'x3', 'x4', 'x5')

  TGP.mod <- btgp(tData5D[, 1:5], tData5D[, 6], X5V, corr='expsep', R=2, 
                  trace=FALSE, nug.p=0, gd=c(0.01, 0.01), d = 5)
  TGPFiveDToy[[i]] <- cbind(TGP.mod$ZZ.mean, TGP.mod$ZZ.mean - 2*sqrt(TGP.mod$ZZ.s2), 
                            TGP.mod$ZZ.mean + 2*sqrt(TGP.mod$ZZ.s2))
}

## 
## burn in:
## **GROW** @depth 0: [5,0.430113], n=(33,42)
## **GROW** @depth 1: [5,0.183526], n=(15,16)
## **PRUNE** @depth 1: [5,0.413812]
## r=1000 d=[0.0605465 0.0192221 0.0650896 0.740716 0.0283082] [1.29432 0.970152 1.47972 1.04304 0.00118053]; n=(11,64)
## r=2000 d=[0.032993 0.00865194 1.08114 1.10856 0.0576937] [1.56775 0.887227 0.852031 1.64016 0.000728499]; n=(11,64)
## 
## Sampling @ nn=25 pred locs:
## r=1000 d=[0.621096 0.0463385 0.105486 0.96155 1.00405] [1.05815 1.85795 1.39642 1.17006 0.00123672]; mh=2 n=(11,64)
## r=2000 d=[0.788139 0.0177402 0.0345381 0.643599 1.13329] [1.66427 1.32608 1.39019 0.949498 0.00123626]; mh=2 n=(12,63)
## r=3000 d=[0.894452 0.21429 0.0893448 0.920921 0.79735] [1.17077 2.09113 1.12142 0.911369 0.000785596]; mh=2 n=(11,64)
## r=4000 d=[0.0681022 0.0684659 0.0124725 0.779455 1.07509] [1.55931 1.00894 1.60791 0.928669 0.000628358]; mh=2 n=(11,64)
## r=5000 d=[0.169693 0.137119 0.0812944 0.364032 0.0651202] [1.46663 1.75666 1.43811 1.56925 0.000577239]; mh=2 n=(11,64)
## Grow: 0.6116%, Prune: 0.2688%, Change: 16.45%, Swap: 100%
## finished repetition 1 of 2
## removed 2 leaves from the tree
## 
## burn in:
## **GROW** @depth 0: [5,0.820711], n=(62,13)
## **PRUNE** @depth 0: [5,0.820711]
## **GROW** @depth 0: [5,0.344811], n=(27,48)
## **GROW** @depth 1: [5,0.552085], n=(20,33)
## **PRUNE** @depth 1: [5,0.581211]
## r=1000 d=[1.08653 0.91621 0.00824779 0.890549 0.00346086] [0.693103 0.0542133 0.0487052 0.83263 0.804188]; mh=2 n=(20,55)
## r=2000 d=[1.34413 0.780668 0.0148898 1.05351 0.0149248] [1.30169 0.780212 0.0384255 0.612358 0.44801]; mh=2 n=(21,54)
## 
## Sampling @ nn=25 pred locs:
## r=1000 d=[0.684563 1.36956 0.00192423 0.123969 0.142714] [0.699166 0.16416 0.0441181 1.52844 1.00746]; mh=2 n=(22,53)
## r=2000 d=[0.747604 0.82238 0.019281 1.1503 0.042323] [1.30087 0.0895219 0.0164877 0.884983 1.49203]; mh=2 n=(21,54)
## r=3000 d=[0.891234 1.10039 0.0215422 0.944371 0.15719] [0.560554 0.100492 0.0562237 0.125332 1.50201]; mh=2 n=(21,54)
## r=4000 d=[0.671284 0.755298 0.0100473 0.0461507 2.05018] [1.1515 0.707632 0.0638653 0.0314252 0.623651]; mh=2 n=(16,59)
## r=5000 d=[0.711565 1.22558 0.00150765 0.0195069 1.30712] [0.946257 1.49261 0.0418707 0.0593632 0.231584]; mh=2 n=(16,59)
## Grow: 0.7246%, Prune: 0.4167%, Change: 40.01%, Swap: 100%
## finished repetition 2 of 2
## removed 2 leaves from the tree
## 
## 
## burn in:
## **GROW** @depth 0: [5,0.33978], n=(26,49)
## r=1000 d=[1.06346 0.0177692 1.28021 0.0900788 0.0744262] [1.05423 1.31234 0.272147 0.0331508 0.842162]; n=(19,56)
## r=2000 d=[1.31827 0.00192323 0.92468 0.053346 1.01121] [1.14681 0.0592364 0.0204913 0.537889 1.01909]; n=(23,52)
## 
## Sampling @ nn=25 pred locs:
## r=1000 d=[0.628541 0.0182114 0.647378 0.00807609 0.0303307] [0.855454 0.0961994 0.0312107 0.677671 0.596753]; mh=2 n=(21,54)
## r=2000 d=[0.116765 0.0660286 1.32014 0.00851034 0.120839] [0.78183 0.150847 0.0362207 0.151413 0.561641]; mh=2 n=(25,50)
## r=3000 d=[0.0591358 0.0127495 0.820926 0.0877641 0.0674002] [1.04264 0.698575 0.0626713 0.702924 2.08515]; mh=2 n=(22,53)
## r=4000 d=[0.049403 0.0371368 1.02436 0.00426999 0.213904] [0.973191 0.0441836 0.0310167 0.0777063 0.971423]; mh=2 n=(22,53)
## r=5000 d=[0.00512163 0.0429121 0.652173 0.000773129 0.0296328] [1.06726 0.0258725 0.0380306 0.482432 0.585435]; mh=2 n=(21,54)
## Grow: 0.2833%, Prune: 0%, Change: 61.36%, 
## finished repetition 1 of 2
## removed 2 leaves from the tree
## 
## burn in:
## **GROW** @depth 0: [5,0.501987], n=(39,36)
## **PRUNE** @depth 0: [5,0.493869]
## **GROW** @depth 0: [5,0.460392], n=(35,40)
## r=1000 d=[1.21333 1.83212 0.00611337 1.19177 0.000983039] [0.679084 0.775905 0.0169543 0.0380844 0.0448542]; mh=2 n=(30,45)
## r=2000 d=[1.0703 1.1502 0.00389772 0.73819 0.0514712] [0.476865 0.0322925 0.0238055 0.0160614 0.500029]; mh=2 n=(13,62)
## 
## Sampling @ nn=25 pred locs:
## r=1000 d=[0.703043 1.12195 0.0030708 1.06975 0.0492666] [0.251419 0.0230006 0.00658349 0.062338 0.704774]; mh=2 n=(11,64)
## r=2000 d=[1.47086 1.03125 0.028076 1.24925 0.0131784] [0.0301982 0.0318601 0.0136859 0.0068101 0.0582086]; mh=2 n=(11,64)
## r=3000 d=[0.590712 0.809766 0.0231185 0.0514177 0.0119619] [0.00988936 0.00914119 0.132018 0.0477534 0.0280505]; mh=2 n=(11,64)
## r=4000 d=[1.20818 0.0202465 0.0257286 0.0353318 0.0342453] [0.0489254 0.0275198 0.0486953 0.0552133 0.741795]; mh=2 n=(11,64)
## r=5000 d=[1.0476 0.0805119 0.00799735 0.00254732 1.14657] [0.0307823 0.0111816 0.147885 0.0867203 0.630776]; mh=2 n=(11,64)
## Grow: 0.436%, Prune: 0.1515%, Change: 46.13%, 
## finished repetition 2 of 2
## removed 2 leaves from the tree
## 
## 
## burn in:
## **GROW** @depth 0: [5,0.384741], n=(29,46)
## r=1000 d=[0.0927319 0.0251712 0.0161025 0.0303816 0.0710325] [0.124962 0.00907665 0.804733 0.983573 0.00659917]; n=(18,57)
## r=2000 d=[0.0214546 0.00281931 0.0304639 0.538953 0.0836276] [1.149 1.70874 0.653265 1.03864 0.0027776]; n=(11,64)
## 
## Sampling @ nn=25 pred locs:
## r=1000 d=[0.0529009 0.0375637 0.0304368 1.34398 0.0256487] [0.922976 1.21543 2.23125 1.1878 0.00106846]; mh=2 n=(11,64)
## r=2000 d=[0.00954868 0.0991034 0.0115659 1.37533 0.089151] [0.86094 1.12836 1.23713 1.86195 0.000656985]; mh=2 n=(11,64)
## r=3000 d=[0.0119766 0.0226935 0.0635668 1.20226 0.0367501] [0.991828 1.15538 0.996702 0.992615 0.000873469]; mh=2 n=(11,64)
## r=4000 d=[0.0301639 0.00167047 0.0234427 0.0621272 0.0499533] [1.18815 1.06219 1.33393 0.842226 0.00114346]; mh=2 n=(11,64)
## r=5000 d=[0.130478 0.0608468 1.25684 0.0168251 0.911529] [1.1884 1.65545 1.05979 1.22437 0.00113604]; mh=2 n=(11,64)
## Grow: 0.3115%, Prune: 0%, Change: 21.21%, 
## finished repetition 1 of 2
## removed 2 leaves from the tree
## 
## burn in:
## **GROW** @depth 0: [5,0.788548], n=(60,15)
## **GROW** @depth 1: [5,0.384741], n=(29,30)
## **GROW** @depth 1: [5,0.174436], n=(14,15)
## **PRUNE** @depth 2: [5,0.384741]
## **PRUNE** @depth 1: [5,0.788548]
## r=1000 d=[0.0335233 1.76433 0.00759429 0.705696 0.00527949] [1.17555 0.734501 0.0258755 0.00102492 0.977994]; mh=2 n=(11,64)
## r=2000 d=[0.0194967 0.645058 0.00314354 0.787388 0.0126035] [0.839528 1.0672 0.207174 0.000900925 0.631837]; mh=2 n=(11,64)
## 
## Sampling @ nn=25 pred locs:
## r=1000 d=[0.840218 1.61565 0.00798172 0.843816 0.0485461] [1.23963 0.675007 0.108811 0.00127121 0.559651]; mh=2 n=(11,64)
## r=2000 d=[1.60533 1.02919 0.0217828 0.833345 0.00254429] [0.656665 1.10243 0.117013 0.00566088 0.800505]; mh=2 n=(11,64)
## r=3000 d=[0.0835319 0.937953 0.0540084 0.614061 0.0589126] [1.03895 0.775029 1.43534 0.00066352 0.071205]; mh=2 n=(11,64)
## r=4000 d=[0.0204868 0.898537 0.0570232 0.962528 0.106022] [0.0313439 0.81965 1.0373 0.0818541 0.00679325]; mh=2 n=(11,64)
## r=5000 d=[0.0311836 0.584284 0.0118229 0.568132 0.0193105] [1.49254 1.56949 1.3343 0.797274 0.000878348]; mh=2 n=(11,64)
## Grow: 0.6182%, Prune: 0.2813%, Change: 17.01%, Swap: 100%
## finished repetition 2 of 2
## removed 2 leaves from the tree
## 
## 
## burn in:
## **GROW** @depth 0: [5,0.430113], n=(33,42)
## r=1000 d=[0.0822372 0.00754193 0.00342879 0.415306 0.0142463] [0.0290796 0.009245 0.132481 0.881331 0.557432]; n=(17,58)
## r=2000 d=[0.0412334 0.0341057 0.00222706 0.370499 0.469301] [0.000556556 0.0424423 0.0910712 0.762179 0.671472]; n=(11,64)
## 
## Sampling @ nn=25 pred locs:
## r=1000 d=[0.0111309 0.00530162 0.280501 0.0393792 0.599728] [0.0473288 0.0347936 0.0186048 0.162671 0.255383]; mh=2 n=(12,63)
## r=2000 d=[0.090396 0.0137437 0.00298674 0.9628 0.616203] [0.0304811 0.00990625 0.269721 1.08145 0.0293935]; mh=2 n=(11,64)
## r=3000 d=[0.0338981 0.535324 0.0287548 0.586744 0.0417069] [0.07585 0.0992628 0.835465 0.986672 0.000575373]; mh=2 n=(11,64)
## r=4000 d=[0.648364 1.05378 0.976232 0.148522 0.592404] [1.14803 1.30914 0.776615 1.16691 0.00137555]; mh=2 n=(11,64)
## r=5000 d=[0.0248001 0.92356 0.0143132 0.882848 1.42632] [0.89348 1.04433 1.41758 1.04758 0.00139482]; mh=2 n=(11,64)
## Grow: 0.2915%, Prune: 0%, Change: 22.66%, 
## finished repetition 1 of 2
## removed 2 leaves from the tree
## 
## burn in:
## **GROW** @depth 0: [5,0.501987], n=(39,36)
## **GROW** @depth 1: [5,0.1357], n=(11,20)
## **PRUNE** @depth 1: [5,0.397349]
## r=1000 d=[0.461705 0.036408 1.1193 0.00107734 0.0333787] [0.182042 0.848292 1.05399 1.07811 0.00162965]; mh=2 n=(12,63)
## r=2000 d=[0.537209 0.137513 0.139955 0.0485455 0.0321408] [1.21178 0.967087 1.60609 1.1835 0.00137423]; mh=2 n=(11,64)
## 
## Sampling @ nn=25 pred locs:
## r=1000 d=[0.0655822 1.23555 0.0297835 0.758826 0.00112996] [1.19561 1.08689 1.43853 0.909108 0.00124461]; mh=2 n=(11,64)
## r=2000 d=[0.0529913 1.20172 0.0114851 1.09123 0.00806948] [1.2508 1.1496 1.51449 1.36538 0.000869345]; mh=2 n=(11,64)
## r=3000 d=[0.0221046 1.1549 0.091406 1.04494 0.000414902] [1.08848 1.33373 1.20778 0.832776 0.00107523]; mh=2 n=(11,64)
## r=4000 d=[1.14591 1.10101 0.0100625 0.473916 0.0663845] [1.07615 1.09129 1.57751 1.35917 0.000716759]; mh=2 n=(11,64)
## r=5000 d=[0.664733 0.802741 0.00277206 1.1205 0.0292994] [1.33871 1.73067 1.52763 1.35123 0.00137654]; mh=2 n=(11,64)
## Grow: 0.4329%, Prune: 0.146%, Change: 17.61%, Swap: 100%
## finished repetition 2 of 2
## removed 2 leaves from the tree

and for CGP

for(i in 1:length(LHC.data[[1]])) {
  tData5D <- data.frame(cbind(LHC.data[[1]][[i]], LHC.data[[2]][[i]]))
  names(tData5D) <- c('x1', 'x2', 'x3', 'x4', 'x5', 'y')
  cands <- names(tData5D)[1:5]
  X5V <- as.data.frame(LHC.data[[3]][[i]])
  y5V <- LHC.data[[4]][[i]]
  names(X5V) <- c('x1', 'x2', 'x3', 'x4', 'x5')
  
  CGP.mod <- CGP(tData5D[, 1:5], tData5D[, 6])
  CGP.mod.predict <- predict(CGP.mod, X5V, PI = TRUE)
  std.dev <- (CGP.mod.predict$Y_up - CGP.mod.predict$Yp)/1.96
  CGPFiveDToy[[i]] <- cbind(CGP.mod.predict$Yp, CGP.mod.predict$Yp - 2*std.dev, 
                            CGP.mod.predict$Yp + 2*std.dev)
}

Graphical comparison of the methods.

par(mfrow = c(4, 4), mar = c(2, 2, 1, 1))
for(i in 1:4) {
  ValidPlot(stGPFiveDToy[[i]], LHC.data[[3]][[i]], LHC.data[[4]][[i]],
            axis = 5, heading = paste(" st-GP: Ens", toString(i), sep = " "), xrange = c(-1, 1), 
            interval = range(stGPFiveDToy[[i]], nstGPFiveDToy[[i]], TGPFiveDToy[[i]], CGPFiveDToy[[i]]),
            ParamNames = c("x5"))
  ValidPlot(nstGPFiveDToy[[i]],LHC.data[[3]][[i]], LHC.data[[4]][[i]], axis = 5, 
            heading = paste(" nst-GP: Ens", toString(i), sep = " "), xrange = c(-1, 1), 
            interval = range(stGPFiveDToy[[i]], nstGPFiveDToy[[i]], TGPFiveDToy[[i]], CGPFiveDToy[[i]] ),
            ParamNames = c("x5"))
  ValidPlot(TGPFiveDToy[[i]], LHC.data[[3]][[i]], LHC.data[[4]][[i]], axis = 5, 
            heading = paste(" TGP: Ens", toString(i), sep = " "), xrange = c(-1, 1), 
            interval = range(stGPFiveDToy[[i]], nstGPFiveDToy[[i]], TGPFiveDToy[[i]], CGPFiveDToy[[i]]),
            ParamNames = c("x5"))
  ValidPlot(CGPFiveDToy[[i]], LHC.data[[3]][[i]], LHC.data[[4]][[i]], axis = 5, 
            heading = paste(" CGP: Ens", toString(i), sep = " "), xrange = c(-1, 1), 
            interval = range(stGPFiveDToy[[i]], nstGPFiveDToy[[i]], TGPFiveDToy[[i]], CGPFiveDToy[[i]]),
            ParamNames = c("x5"))
}

Consider the performance of mixture model:

p1 <- ggplot(MixtureFiveDToy.mod[[1]], aes(x = x5, y = std.err, col = rgb(red = red, blue = blue, green = 0), ymin = -3.5, ymax=3.5)) +
  geom_point(size = 2) + scale_color_identity()
p2 <- ggplot(MixtureFiveDToy.mod[[2]], aes(x = x5, y = std.err, col = rgb(red = red, blue = blue, green = 0), ymin = -3.5, ymax=3.5)) +
  geom_point(size = 2) + scale_color_identity()
p3 <- ggplot(MixtureFiveDToy.mod[[3]], aes(x = x5, y = std.err, col = rgb(red = red, blue = blue, green = 0), ymin = -3.5, ymax=3.5)) +
  geom_point(size = 2) + scale_color_identity()
p4 <- ggplot(MixtureFiveDToy.mod[[4]], aes(x = x5, y = std.err, col = rgb(red = red, blue = blue, green = 0), ymin = -3.5, ymax=3.5)) +
  geom_point(size = 2) + scale_color_identity()
multiplot(p1, p2, p3, p4, cols=4)

Modified five-dimensional example

Daniel Williamson and Victoria Volodina

18/01/2018