From db8c9b3191b2fc1bfee15861a546de1afdb62aa7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Alberto=20Foss=C3=A0?= Date: Fri, 13 Sep 2024 10:32:46 -0500 Subject: [PATCH 1/4] remove duplicated error ID --- core/include/dace/daceerror.h | 1 - 1 file changed, 1 deletion(-) diff --git a/core/include/dace/daceerror.h b/core/include/dace/daceerror.h index e227d44..a28d140 100644 --- a/core/include/dace/daceerror.h +++ b/core/include/dace/daceerror.h @@ -48,7 +48,6 @@ DACE_API const errstrings DACEerr[] = { {1006, "Incorrect DA coding arrays"}, {1007, "Requested length too long"}, {1008, "Error in monomial evaluation tree construction"}, - { 8, ""}, { 9, ""}, { 10, ""}, { 911, "Order and/or variable too large"}, From 6d90264444fb49a61aab072d0f1b134442fbb907 Mon Sep 17 00:00:00 2001 From: Mauro Massari Date: Thu, 13 Mar 2025 12:21:42 +0100 Subject: [PATCH 2/4] Update od README.md and removal of tutorials --- README.md | 41 +-- Tutorials/Tutorial1/CMakeLists.txt | 67 ---- Tutorials/Tutorial1/Example1.cpp | 23 -- Tutorials/Tutorial1/Example10.cpp | 65 ---- Tutorials/Tutorial1/Example11DA.cpp | 104 ------ Tutorials/Tutorial1/Example11DARK78.cpp | 256 --------------- Tutorials/Tutorial1/Example11Pointwise.cpp | 85 ----- Tutorials/Tutorial1/Example12.cpp | 80 ----- Tutorials/Tutorial1/Example2.cpp | 28 -- Tutorials/Tutorial1/Example3.cpp | 24 -- Tutorials/Tutorial1/Example4.cpp | 30 -- Tutorials/Tutorial1/Example5.cpp | 34 -- Tutorials/Tutorial1/Example6.cpp | 38 --- Tutorials/Tutorial1/Example7.cpp | 52 --- Tutorials/Tutorial1/Example8.cpp | 54 ---- Tutorials/Tutorial1/Example9.cpp | 42 --- Tutorials/Tutorial1/Tutorial1.pdf | Bin 2512126 -> 0 bytes Tutorials/Tutorial2/1Basics-Ex.cpp | 74 ----- Tutorials/Tutorial2/2IntDiff-Ex.cpp | 114 ------- Tutorials/Tutorial2/3Evaluation-Ex.cpp | 154 --------- Tutorials/Tutorial2/4Solver-Ex.cpp | 138 -------- Tutorials/Tutorial2/5Vectors-Ex.cpp | 111 ------- Tutorials/Tutorial2/5Vectors-Ex.plot | 11 - Tutorials/Tutorial2/6Integrator-Ex.cpp | 351 --------------------- Tutorials/Tutorial2/6Integrator-Ex.plot | 61 ---- Tutorials/Tutorial2/7PID-Ex.cpp | 265 ---------------- Tutorials/Tutorial2/7PID-Ex.plot | 46 --- Tutorials/Tutorial2/CMakeLists.txt | 49 --- Tutorials/Tutorial2/Tutorial2.pdf | Bin 1601216 -> 0 bytes 29 files changed, 15 insertions(+), 2382 deletions(-) delete mode 100644 Tutorials/Tutorial1/CMakeLists.txt delete mode 100644 Tutorials/Tutorial1/Example1.cpp delete mode 100644 Tutorials/Tutorial1/Example10.cpp delete mode 100644 Tutorials/Tutorial1/Example11DA.cpp delete mode 100644 Tutorials/Tutorial1/Example11DARK78.cpp delete mode 100644 Tutorials/Tutorial1/Example11Pointwise.cpp delete mode 100644 Tutorials/Tutorial1/Example12.cpp delete mode 100644 Tutorials/Tutorial1/Example2.cpp delete mode 100644 Tutorials/Tutorial1/Example3.cpp delete mode 100644 Tutorials/Tutorial1/Example4.cpp delete mode 100644 Tutorials/Tutorial1/Example5.cpp delete mode 100644 Tutorials/Tutorial1/Example6.cpp delete mode 100644 Tutorials/Tutorial1/Example7.cpp delete mode 100644 Tutorials/Tutorial1/Example8.cpp delete mode 100644 Tutorials/Tutorial1/Example9.cpp delete mode 100644 Tutorials/Tutorial1/Tutorial1.pdf delete mode 100644 Tutorials/Tutorial2/1Basics-Ex.cpp delete mode 100644 Tutorials/Tutorial2/2IntDiff-Ex.cpp delete mode 100644 Tutorials/Tutorial2/3Evaluation-Ex.cpp delete mode 100644 Tutorials/Tutorial2/4Solver-Ex.cpp delete mode 100644 Tutorials/Tutorial2/5Vectors-Ex.cpp delete mode 100644 Tutorials/Tutorial2/5Vectors-Ex.plot delete mode 100644 Tutorials/Tutorial2/6Integrator-Ex.cpp delete mode 100644 Tutorials/Tutorial2/6Integrator-Ex.plot delete mode 100644 Tutorials/Tutorial2/7PID-Ex.cpp delete mode 100644 Tutorials/Tutorial2/7PID-Ex.plot delete mode 100644 Tutorials/Tutorial2/CMakeLists.txt delete mode 100644 Tutorials/Tutorial2/Tutorial2.pdf diff --git a/README.md b/README.md index b933d08..608e034 100644 --- a/README.md +++ b/README.md @@ -6,43 +6,32 @@ The Differential Algebra Computational Toolbox. ## Requirements To use the DACE library, you need a C++11 compatible C++ compiler. Almost all modern C++ compilers (GNU, Clang, MS Visual Studio) meet that requirement nowadays. We also highly recommend using CMake as a build system, and obviously Git as your source code management system. -On Windows, you need to download Microsoft Visual Studio (the free Community Edition is fine). On MacOS X, you need to install the Xcode package from Apple from the App Store. On Linux, you can install the compiler toolchain through your package system if they don't already come pre-installed. +On Linux, you can install the compiler toolchain through your package system if they don't already come pre-installed. On Windows it is suggested to use the WSL environment and follow the linux procedure, or download Microsoft Visual Studio (the free Community Edition is fine). On MacOS X, you need to install the Xcode package from Apple from the App Store. -To build Windows DACE library installer packages, you additionally need the NSIS installer compiler. +To build Windows DACE library installer packages, you additionally need the NSIS installer compiler. (Deprecated, will be removed soon) ## Getting started -To get started, either download one of the pre-built release packages for your platform (see the Releases tab above), or just clone the entire repository and build the library from scratch (which really is very easy). - -To use the DACE, we recommend using CMake. New DACE releases past version 2.0.1 come with a CMake package system plugin that allows very simple use of the DACE within the CMake framework. To get started, have a look at the Tutorials directories. Both of the Tutorials there are independent projects with their own stand-alone CMake file you can use as a starting point for your own programs. +To get started just clone the entire repository and build the library from scratch (which really is very easy). You can use the current development version if you want the latests improvement and bug fixes or point to the Releases page for official released versions. ## Building the DACE -To build your own version of the DACE library, simply clone this repository: +To build the DACE library, simply clone this repository: ``` -git clone "https://github.com/dacelib/dace.git" +git clone "https://github.com/dacelib/dace.git" dace ``` -Then create a build directory and run cmake, and then make to compile everything: +Then create a build directory, run cmake, and then cmake --build to compile everything: ``` -cd dace -mkdir build -cd build -cmake .. -make +mkdir dace-build +cmake -S dace/ -B dace-build/ +cmake --build dace-build/ ``` -After some compiling, you should have a sparkling new dace library ready for use. To install it directly into your system, you can just use: +After some compiling, you should have a sparkling new dace library ready for use in the dace-build folder. + +Optionally you can install the freshly built DACE library directly into your system: ``` -sudo make install +sudo cmake --install dace-build/ ``` The ```sudo``` is there to give you the required permissions to install into your system directories (usually ```/usr/local```). -## Running the Tutorials -To test if your installation was successful, you can try to build one of the Tutorials: -``` -cd ../Tutorials/Tutorial1 -mkdir build -cd build -cmake .. -make -``` -This should automatically compile all tutorials, ready to be run by you using e.g. the command ```./Example1```. +We have moved the tutorials to a different repository https://github.com/dacelib/dace-tutorials to keep the main repository clean. You can clone the tutorials repository and follow the instructions there to get started with DACE. -Also have a look at the [DACE Wiki pages](https://github.com/dacelib/dace/wiki) if you have further questions +Also have a look at the [DACE Wiki pages](https://github.com/dacelib/dace/wiki) if you have further questions. diff --git a/Tutorials/Tutorial1/CMakeLists.txt b/Tutorials/Tutorial1/CMakeLists.txt deleted file mode 100644 index f620300..0000000 --- a/Tutorials/Tutorial1/CMakeLists.txt +++ /dev/null @@ -1,67 +0,0 @@ -# DACE Examples -# -# This file shows how to use the DACE in a cmake project -# Simply import the DACE cmake package. It automatically provides the correct -# locations for headers and libraries. -# If the DACE is installed in a non-default location, tell cmake where to look: -# set(dace_DIR "/my/custom/root/usr/local/lib/cmake/dace") -# It exposes two targets: -# dace::dace (the dynamic DACE library) -# dace::dace_s (the static DACE library) -# Make sure to link your executable with one of those and include the correct -# header ( or ) in the code. -# -# On Windows only, the dace.dll dynamics library is typically expected to be -# located in the same directory as the executable using it. You can use a -# command such as the file(COPY ...) below to automatically copy the dace.dll -# from the DACE package next to your executables. - -cmake_minimum_required (VERSION 2.8.4) - -project(Examples1 CXX) - -find_package(dace 2.0.0 REQUIRED) - -if(WIN32) - get_target_property(DACEDLL dace::dace LOCATION) - file(COPY "${DACEDLL}" DESTINATION "${CMAKE_CURRENT_BINARY_DIR}") -endif(WIN32) - -add_executable(Example1 Example1.cpp) -target_link_libraries(Example1 PUBLIC dace::dace) - -add_executable(Example2 Example2.cpp) -target_link_libraries(Example2 PUBLIC dace::dace) - -add_executable(Example3 Example3.cpp) -target_link_libraries(Example3 PUBLIC dace::dace) - -add_executable(Example4 Example4.cpp) -target_link_libraries(Example4 PUBLIC dace::dace) - -add_executable(Example5 Example5.cpp) -target_link_libraries(Example5 PUBLIC dace::dace) - -add_executable(Example6 Example6.cpp) -target_link_libraries(Example6 PUBLIC dace::dace) - -add_executable(Example7 Example7.cpp) -target_link_libraries(Example7 PUBLIC dace::dace) - -add_executable(Example8 Example8.cpp) -target_link_libraries(Example8 PUBLIC dace::dace) - -add_executable(Example9 Example9.cpp) -target_link_libraries(Example9 PUBLIC dace::dace) - -add_executable(Example10 Example10.cpp) -target_link_libraries(Example10 PUBLIC dace::dace) - -add_executable(Example11Pointwise Example11Pointwise.cpp) -target_link_libraries(Example11Pointwise PUBLIC dace::dace) - -add_executable(Example11DA Example11DA.cpp) -target_link_libraries(Example11DA PUBLIC dace::dace) - -add_executable(Example12 Example12.cpp) -target_link_libraries(Example12 PUBLIC dace::dace) diff --git a/Tutorials/Tutorial1/Example1.cpp b/Tutorials/Tutorial1/Example1.cpp deleted file mode 100644 index 2ea2c49..0000000 --- a/Tutorials/Tutorial1/Example1.cpp +++ /dev/null @@ -1,23 +0,0 @@ -#include -#include -#include -#include -#include - -using namespace std; -using namespace DACE; - -int main( void ) -{ - - DA::init( 20, 1 ); // initialize DACE for 20th-order computations in 1 variable - - DA x = DA(1); // initialize x as DA - - DA y = sin(x); // compute y = sin(x) - - // print x and y to screen - cout << "x" << endl << x << endl; - cout << "y = sin(x)" << endl << y; - -} \ No newline at end of file diff --git a/Tutorials/Tutorial1/Example10.cpp b/Tutorials/Tutorial1/Example10.cpp deleted file mode 100644 index ac91a58..0000000 --- a/Tutorials/Tutorial1/Example10.cpp +++ /dev/null @@ -1,65 +0,0 @@ -#include -#include -#include -#include -#include - -using namespace std; -using namespace DACE; - - -int main( void ) -{ - - DA::init( 10, 3 ); - - const double pi = 4.0*atan(1.0); - - // initialize cyl - AlgebraicVector cyl(3); - - cyl[0] = 100.0+DA(1); - cyl[1] = (0.0+DA(2))*pi/180.0; - cyl[2] = 0.0 + DA(3); - - // initialize cart and compute transformation - AlgebraicVector cart(3); - - cart[0] = cyl[0]*cos(cyl[1]); - cart[1] = cyl[0]*sin(cyl[1]);; - cart[2] = cyl[2]; - - // subtract constant part to build DirMap - AlgebraicVector DirMap(3); - - DirMap = cart-cart.cons(); - - cout << "Direct map: from cylindric to cartesian (DirMap)" << endl << endl; - cout << DirMap << endl << endl; - - // Invert DirMap to obtain InvMap - AlgebraicVector InvMap(3); - - InvMap = DirMap.invert(); - - cout << "Invers map: from cartesian to cylindric (InvMap)" << endl << endl; - cout << InvMap << endl << endl; - - getchar(); - - // Verification - cout << "Concatenate the direct and inverse map: (DirMap) o (InvMap) = DirMap(InvMap) = I" << endl << endl; - cout << DirMap.eval(InvMap) << endl; - -} - - - - - - - - - - - diff --git a/Tutorials/Tutorial1/Example11DA.cpp b/Tutorials/Tutorial1/Example11DA.cpp deleted file mode 100644 index a41c88f..0000000 --- a/Tutorials/Tutorial1/Example11DA.cpp +++ /dev/null @@ -1,104 +0,0 @@ -#include -#include -using namespace std; -using namespace DACE; - - -template AlgebraicVector TBP( AlgebraicVector x, double t ) -{ - - AlgebraicVector pos(3), res(6); - - pos[0] = x[0]; pos[1] = x[1]; pos[2] = x[2]; - - T r = pos.vnorm(); - - const double mu = 398600; // km^3/s^2 - - res[0] = x[3]; - res[1] = x[4]; - res[2] = x[5]; - - res[3] = -mu*pos[0]/(r*r*r); - res[4] = -mu*pos[1]/(r*r*r); - res[5] = -mu*pos[2]/(r*r*r); - - return res; - -} - - -template AlgebraicVector euler( AlgebraicVector x, double t0, double t1 ) -{ - const double hmax = 0.1; - int steps = ceil((t1-t0)/hmax); - double h = (t1-t0)/steps; - double t = t0; - - for( int i = 0; i < steps; i++ ) - { - x = x + h*TBP(x,t); - t += h; - } - - return x; -} - - -int main( void ) -{ - - DA::init( 3, 6 ); - - AlgebraicVector x0(6), xf(6); - - // Set initial conditions - const double mu = 398600; - const double ecc = 0.5; - - x0[0] = 6678.0 + DA(1); // 300 km altitude - x0[1] = 0.0 + DA(2); - x0[2] = 0.0 + DA(3); - x0[3] = 0.0 + DA(4); - x0[4] = sqrt(mu/6678.0)*sqrt(1+ecc) + DA(5); - x0[5] = 0.0 + DA(6); - - // integrate for half the orbital period - - const double pi = 4.0*atan(1.0); - - double a = 6678.0/(1-ecc); - - xf = euler( x0, 0.0, pi*sqrt(a*a*a/mu)); - - // print initial and final conditions - - cout << endl << "Initial conditions:" << endl << endl; - cout << x0 << endl << endl; - - cout << endl << "Final conditions:" << endl << endl; - cout << xf << endl << endl; - - getchar(); - - // Evaluate for a displaced initial condition - - AlgebraicVector Deltax0(6); - - Deltax0[0] = 1.0; // km - Deltax0[1] = -1.0; - Deltax0[2] = 0.0; - Deltax0[3] = 0.0; - Deltax0[4] = 0.0; - Deltax0[5] = 0.0; - - cout << "Displaced Initial condition:" << endl << endl; - cout << x0.cons() + Deltax0 << endl << endl; - - cout << "Displaced Final condition:" << endl << endl; - cout << xf.eval(Deltax0) << endl; - -} - - - diff --git a/Tutorials/Tutorial1/Example11DARK78.cpp b/Tutorials/Tutorial1/Example11DARK78.cpp deleted file mode 100644 index 340be00..0000000 --- a/Tutorials/Tutorial1/Example11DARK78.cpp +++ /dev/null @@ -1,256 +0,0 @@ -#include -#include -using namespace std; -using namespace DACE; - -#warning This example only works if the DACE was built with support for the (non-default) AlgebraicMatrix type! - -double min( double a, double b ) { - - double res = a; - if(a>b){res = b;} - return res; -} - - -double max( double a, double b ) { - - double res = a; - if(b>a){res = b;} - return res; -} - - -double normtmp( int N, vector X ) { - - int I; - double res = 0.0; - - for (I=0; I AlgebraicVector RK78( int N, AlgebraicVector Y0, double X0, double X1, AlgebraicVector (*f)(AlgebraicVector,double) ) -{ - - double ERREST; - double H0 = 0.001; double HS = 0.1; double H1 = 100.0; - double EPS = 1.e-12; double BS = 20*EPS; - - AlgebraicMatrix Z(N,16); - AlgebraicVector Y1(N); - vector Y1cons(N); - - double VIHMAX = 0.0, X, H; - int I, J, K; - double RFNORM, HH0, HH1; - - double HSQR = 1.0/9.0; - vector A(13), C(13), D(13); - AlgebraicMatrix B(13,12); - - A[0] = 0.0; A[1] = 1.0/18.0; A[2] = 1.0/12.0; A[3] = 1.0/8.0; A[4] = 5.0/16.0; A[5] = 3.0/8.0; - A[6] = 59.0/400.0; A[7] = 93.0/200.0; A[8] = 5490023248.0/9719169821.0; A[9] = 13.0/20.0; A[10] = 1201146811.0/1299019798.0; A[11] = 1.0; - A[12] = 1.0; - - B.at(0,0) = 0.0; B.at(0,1) = 0.0; B.at(0,2) = 0.0; B.at(0,3) = 0.0; B.at(0,4) = 0.0; - B.at(0,5) = 0.0; B.at(0,6) = 0.0; B.at(0,7) = 0.0; B.at(0,8) = 0.0; B.at(0,9) = 0.0; - B.at(0,10) = 0.0; B.at(0,11) = 0.0; - - B.at(1,0) = 1.0/18.0; B.at(1,1) = 0.0; B.at(1,2) = 0.0; B.at(1,3) = 0.0; B.at(1,4) = 0.0; - B.at(1,5) = 0.0; B.at(1,6) = 0.0; B.at(1,7) = 0.0; B.at(1,8) = 0.0; B.at(1,9) = 0.0; - B.at(1,10) = 0.0; B.at(1,11) = 0.0; - - B.at(2,0) = 1.0/48.0; B.at(2,1) = 1.0/16.0; B.at(2,2) = 0.0; B.at(2,3) = 0.0; B.at(2,4) = 0.0; - B.at(2,5) = 0.0; B.at(2,6) = 0.0; B.at(2,7) = 0.0; B.at(2,8) = 0.0; B.at(2,9) = 0.0; - B.at(2,10) = 0.0; B.at(2,11) = 0.0; - - B.at(3,0) = 1.0/32.0; B.at(3,1) = 0.0; B.at(3,2) = 3.0/32.0; B.at(3,3) = 0.0; B.at(3,4) = 0.0; - B.at(3,5) = 0.0; B.at(3,6) = 0.0; B.at(3,7) = 0.0; B.at(3,8) = 0.0; B.at(3,9) = 0.0; - B.at(3,10) = 0.0; B.at(3,11) = 0.0; - - B.at(4,0) = 5.0/16.0; B.at(4,1) = 0.0; B.at(4,2) = -75.0/64.0; B.at(4,3) = 75.0/64.0; B.at(4,4) = 0.0; - B.at(4,5) = 0.0; B.at(4,6) = 0.0; B.at(4,7) = 0.0; B.at(4,8) = 0.0; B.at(4,9) = 0.0; - B.at(4,10) = 0.0; B.at(4,11) = 0.0; - - B.at(5,0) = 3.0/80.0; B.at(5,1) = 0.0; B.at(5,2) = 0.0; B.at(5,3) = 3.0/16.0; B.at(5,4) = 3.0/20.0; - B.at(5,5) = 0.0; B.at(5,6) = 0.0; B.at(5,7) = 0.0; B.at(5,8) = 0.0; B.at(5,9) = 0.0; - B.at(5,10) = 0.0; B.at(5,11) = 0.0; - - B.at(6,0) = 29443841.0/614563906.0; B.at(6,1) = 0.0; B.at(6,2) = 0.0; B.at(6,3) = 77736538.0/692538347.0; B.at(6,4) = -28693883.0/1125000000.0; - B.at(6,5) = 23124283.0/1800000000.0; B.at(6,6) = 0.0; B.at(6,7) = 0.0; B.at(6,8) = 0.0; B.at(6,9) = 0.0; - B.at(6,10) = 0.0; B.at(6,11) = 0.0; - - B.at(7,0) = 16016141.0/946692911.0; B.at(7,1) = 0.0; B.at(7,2) = 0.0; B.at(7,3) = 61564180.0/158732637.0; B.at(7,4) = 22789713.0/633445777.0; - B.at(7,5) = 545815736.0/2771057229.0; B.at(7,6) = -180193667.0/1043307555.0; B.at(7,7) = 0.0; B.at(7,8) = 0.0; B.at(7,9) = 0.0; - B.at(7,10) = 0.0; B.at(7,11) = 0.0; - - B.at(8,0) = 39632708.0/573591083.0; B.at(8,1) = 0.0; B.at(8,2) = 0.0; B.at(8,3) = -433636366.0/683701615.0; B.at(8,4) = -421739975.0/2616292301.0; - B.at(8,5) = 100302831.0/723423059.0; B.at(8,6) = 790204164.0/839813087.0; B.at(8,7) = 800635310.0/3783071287.0; B.at(8,8) = 0.0; B.at(8,9) = 0.0; - B.at(8,10) = 0.0; B.at(8,11) = 0.0; - - B.at(9,0) = 246121993.0/1340847787.0; B.at(9,1) = 0.0; B.at(9,2) = 0.0; B.at(9,3) = -37695042795.0/15268766246.0; B.at(9,4) = -309121744.0/1061227803.0; - B.at(9,5) = -12992083.0/490766935.0; B.at(9,6) = 6005943493.0/2108947869.0; B.at(9,7) = 393006217.0/1396673457.0; B.at(9,8) = 123872331.0/1001029789.0; B.at(9,9) = 0.0; - B.at(9,10) = 0.0; B.at(9,11) = 0.0; - - B.at(10,0) = -1028468189.0/846180014.0; B.at(10,1) = 0.0; B.at(10,2) = 0.0; B.at(10,3) = 8478235783.0/508512852.0; B.at(10,4) = 1311729495.0/1432422823.0; - B.at(10,5) = -10304129995.0/1701304382.0; B.at(10,6) = -48777925059.0/3047939560.0; B.at(10,7) = 15336726248.0/1032824649.0; B.at(10,8) = -45442868181.0/3398467696.0; B.at(10,9) = 3065993473.0/597172653.0; - B.at(10,10) = 0.0; B.at(10,11) = 0.0; - - B.at(11,0) = 185892177.0/718116043.0; B.at(11,1) = 0.0; B.at(11,2) = 0.0; B.at(11,3) = -3185094517.0/667107341.0; B.at(11,4) = -477755414.0/1098053517.0; - B.at(11,5) = -703635378.0/230739211.0; B.at(11,6) = 5731566787.0/1027545527.0; B.at(11,7) = 5232866602.0/850066563.0; B.at(11,8) = -4093664535.0/808688257.0; B.at(11,9) = 3962137247.0/1805957418.0; - B.at(11,10) = 65686358.0/487910083.0; B.at(11,11) = 0.0; - - B.at(12,0) = 403863854.0/491063109.0; B.at(12,1) = 0.0; B.at(12,2) = 0.0; B.at(12,3) = - 5068492393.0/434740067.0; B.at(12,4) = -411421997.0/543043805.0; - B.at(12,5) = 652783627.0/914296604.0; B.at(12,6) = 11173962825.0/925320556.0; B.at(12,7) = -13158990841.0/6184727034.0; B.at(12,8) = 3936647629.0/1978049680.0; B.at(12,9) = -160528059.0/685178525.0; - B.at(12,10) = 248638103.0/1413531060.0; B.at(12,11) = 0.0; - - C[0] = 14005451.0/335480064.0; C[1] = 0.0; C[2] = 0.0; C[3] = 0.0; C[4] = 0.0; C[5] = -59238493.0/1068277825.0; - C[6] = 181606767.0/758867731.0; C[7] = 561292985.0/797845732.0; C[8] = -1041891430.0/1371343529.0; C[9] = 760417239.0/1151165299.0; C[10] = 118820643.0/751138087.0; C[11] = -528747749.0/2220607170.0; - C[12] = 1.0/4.0; - - D[0] = 13451932.0/455176623.0; D[1] = 0.0; D[2] = 0.0; D[3] = 0.0; D[4] = 0.0; D[5] = -808719846.0/976000145.0; - D[6] = 1757004468.0/5645159321.0; D[7] = 656045339.0/265891186.0; D[8] = -3867574721.0/1518517206.0; D[9] = 465885868.0/322736535.0; D[10] = 53011238.0/667516719.0; D[11] = 2.0/45.0; - D[12] = 0.0; - - for( I = 0; I < N; I++ ) - { - Z.at(I,0) = Y0[I]; - Z.at(I,1) = 0.0 ; - } - - H = abs(HS) ; HH0 = abs(H0) ; HH1 = abs(H1) ; - X = X0 ; RFNORM = 0.0 ; ERREST = 0.0 ; - - while(X != X1){ - - // compute new stepsize - if (RFNORM != 0) {H = H*min(4.0,exp(HSQR*log(EPS/RFNORM)));} - if (abs(H)>abs(HH1)) { H = HH1; } else if ( abs(H)0) { H = X1-X; } - - for (J = 0; J<13; J++) { - - for (I = 0; IBS) && (abs(H/H0)>1.2)) { - H = H/3.0; - RFNORM = 0; - } - else { - for (I = 0; I AlgebraicVector rhs( AlgebraicVector x, double t ) -{ - - AlgebraicVector pos(3), res(6); - - pos[0] = x[0]; pos[1] = x[1]; pos[2] = x[2]; - - T r = pos.vnorm(); - - const double mu = 398600; // km^3/s^2 - - res[0] = x[3]; - res[1] = x[4]; - res[2] = x[5]; - - res[3] = -mu*pos[0]/(r*r*r); - res[4] = -mu*pos[1]/(r*r*r); - res[5] = -mu*pos[2]/(r*r*r); - - return res; - -} - - -int main( void ) -{ - - DA::init( 3, 6 ); - - AlgebraicVector x0(6), xf(6); - - // Set initial conditions - const double mu = 398600; - const double ecc = 0.5; - - x0[0] = 6678.0 + DA(1); // 300 km altitude - x0[1] = 0.0 + DA(2); - x0[2] = 0.0 + DA(3); - x0[3] = 0.0 + DA(4); - x0[4] = sqrt(mu/6678.0)*sqrt(1+ecc) + DA(5); - x0[5] = 0.0 + DA(6); - - // integrate for half the orbital period - - const double pi = 4.0*atan(1.0); - - double a = 6678.0/(1-ecc); - - xf = RK78( 6, x0, 0.0, pi*sqrt(a*a*a/mu), rhs ); - - // print initial and final conditions - - cout << endl << "Initial conditions:" << endl << endl; - cout << x0 << endl << endl; - - cout << endl << "Final conditions:" << endl << endl; - cout << xf << endl; - -} - - - diff --git a/Tutorials/Tutorial1/Example11Pointwise.cpp b/Tutorials/Tutorial1/Example11Pointwise.cpp deleted file mode 100644 index d0f1fc7..0000000 --- a/Tutorials/Tutorial1/Example11Pointwise.cpp +++ /dev/null @@ -1,85 +0,0 @@ -#include -#include -using namespace std; -using namespace DACE; - - -template AlgebraicVector TBP( AlgebraicVector x, double t ) -{ - - AlgebraicVector pos(3), res(6); - - pos[0] = x[0]; pos[1] = x[1]; pos[2] = x[2]; - - T r = pos.vnorm(); - - const double mu = 398600; // km^3/s^2 - - res[0] = x[3]; - res[1] = x[4]; - res[2] = x[5]; - - res[3] = -mu*pos[0]/(r*r*r); - res[4] = -mu*pos[1]/(r*r*r); - res[5] = -mu*pos[2]/(r*r*r); - - return res; - -} - - -template AlgebraicVector euler( AlgebraicVector x, double t0, double t1 ) -{ - const double hmax = 0.1; - int steps = ceil((t1-t0)/hmax); - double h = (t1-t0)/steps; - double t = t0; - - for( int i = 0; i < steps; i++ ) - { - x = x + h*TBP(x,t); - t += h; - } - - return x; -} - - - - -int main( void ) -{ - - AlgebraicVector x0(6), xf(6); - - // Set initial conditions - const double mu = 398600; - const double ecc = 0.5; - - x0[0] = 6678.0; // 300 km altitude - x0[1] = 0.0; - x0[2] = 0.0; - x0[3] = 0.0; - x0[4] = sqrt(mu/6678.0)*sqrt(1+ecc); - x0[5] = 0.0; - - // integrate for half the orbital period - - const double pi = 4.0*atan(1.0); - - double a = 6678.0/(1-ecc); - - xf = euler( x0, 0.0, pi*sqrt(a*a*a/mu)); - - // print initial and final conditions - - cout << endl << "Initial conditions:" << endl << endl; - cout << x0 << endl << endl; - - cout << endl << "Final conditions:" << endl << endl; - cout << xf << endl; - -} - - - diff --git a/Tutorials/Tutorial1/Example12.cpp b/Tutorials/Tutorial1/Example12.cpp deleted file mode 100644 index ed090ab..0000000 --- a/Tutorials/Tutorial1/Example12.cpp +++ /dev/null @@ -1,80 +0,0 @@ -#include -#include -#include -#include -#include - -using namespace std; -using namespace DACE; - - -int main( void ) -{ - - DA::init( 10, 2 ); - - const double tol = 1.0e-12; - - const double pi = 4.0*atan(1.0); - const double mu = 1.0; - - DA a = 1.0; - DA e = 0.5; - double t = pi/2.0; - - DA M = sqrt(mu/(a*a*a))*t; // real at this stage - - DA EccAn = M; //first guess - - double err = abs(EccAn - e*sin(EccAn) - M); - - // Newton's method for the reference solution - while(err>tol) - { - EccAn = EccAn - (EccAn - e*sin(EccAn) - M)/(1 - e*cos(EccAn)); - - err = abs(EccAn - e*sin(EccAn) - M); - - } - - cout << setprecision(12); - cout << "Reference solution: E = " << cons(EccAn) << endl; - - getchar(); - - a = 1.0 + DA(1); - e = 0.5 + DA(2); - - M = sqrt(mu/(a*a*a))*t; // now M is a DA - - // Newton's method for the Taylor expansion of the solution - int i = 1; - while( i <= 10){ - - EccAn = EccAn - (EccAn - e*sin(EccAn) - M)/(1 - e*cos(EccAn)); - i *= 2; - - } - - cout << "Taylor expansion of E" << cons(EccAn) << endl; - cout << EccAn << endl; - - getchar(); - - cout << "Let's verify it is the Taylor expansion of the solution:" << endl; - cout << "Evaluate (E - e*sin(E) - M) in DA" << endl; - - cout << EccAn - e*sin(EccAn) - M << endl; - -} - - - - - - - - - - - diff --git a/Tutorials/Tutorial1/Example2.cpp b/Tutorials/Tutorial1/Example2.cpp deleted file mode 100644 index 7f84f89..0000000 --- a/Tutorials/Tutorial1/Example2.cpp +++ /dev/null @@ -1,28 +0,0 @@ -#include -#include -#include -#include -#include - -using namespace std; -using namespace DACE; - -int main( void ) -{ - - DA::init( 20, 1 ); - - DA x = DA(1); - - DA y1 = sqr(sin(x)); // compute sin(x)^2 - - cout << "sin(x)^2" << endl << y1 << endl; - - DA y2 = sqr(cos(x)); // compute cos(x)^2 - - cout << "cos(x)^2" << endl << y2 << endl; - - // compute and print sin(x)^2+cos(x)^2 - cout << "sin(x)^2+cos(x)^2" << endl << y1+y2 << endl; - -} \ No newline at end of file diff --git a/Tutorials/Tutorial1/Example3.cpp b/Tutorials/Tutorial1/Example3.cpp deleted file mode 100644 index 5ea64cf..0000000 --- a/Tutorials/Tutorial1/Example3.cpp +++ /dev/null @@ -1,24 +0,0 @@ -#include -#include -#include -#include -#include - -using namespace std; -using namespace DACE; - - -int main( void ) -{ - - DA::init( 1, 1 ); // Initialize DACE for 1st-order computations in 1 variable - - DA x = 3 + DA(1); // Initialize x as DA around 3 - - cout << "x" << endl << x << endl; - - DA f = 1/(x+1/x); // Evaluate f(x) = 1/(x+1/x) - - cout << "f(x) = 1/(x+1/x)" << endl << f << endl; - -} \ No newline at end of file diff --git a/Tutorials/Tutorial1/Example4.cpp b/Tutorials/Tutorial1/Example4.cpp deleted file mode 100644 index 8c18dc8..0000000 --- a/Tutorials/Tutorial1/Example4.cpp +++ /dev/null @@ -1,30 +0,0 @@ -#include -#include -#include -#include -#include - -using namespace std; -using namespace DACE; - - -int main( void ) -{ - - DA::init( 20, 1 ); - - DA x = DA(1); - - DA y = cos(x)-1; // Compute [cos(x)-1] - - cout << "[cos(x)-1]" << endl << y << endl; - - // Compute [cos(x)-1]^11 - for ( int i = 0; i < 10; i++) - { - y = y*(cos(x)-1); - } - - cout << "[cos(x)-1]^11" << endl << y << endl; - -} \ No newline at end of file diff --git a/Tutorials/Tutorial1/Example5.cpp b/Tutorials/Tutorial1/Example5.cpp deleted file mode 100644 index 31d0748..0000000 --- a/Tutorials/Tutorial1/Example5.cpp +++ /dev/null @@ -1,34 +0,0 @@ -#include -#include -#include -#include -#include - -using namespace std; -using namespace DACE; - - -int main( void ) -{ - - DA::init( 20, 1 ); - - DA x = DA(1); - - DA y = sin(x); - - DA dy = y.deriv(1); // compute Taylor expansion of d[sin(x)]/dx - - // print d[sin(x)]/dx and cos(x) to compare - cout << "d[sin(x)]/dx" << endl << dy << endl; - cout << "cos(x)" << endl << cos(x) << endl; - - getchar(); - - DA int_y = y.integ(1); // compute Taylor expansion of int[sin(x)dx] - - // print int[sin(x)dx] and -cos(x) to compare - cout << "int[sin(x)dx]" << endl << int_y << endl; - cout << "-cos(x)" << endl << -cos(x) << endl; - -} \ No newline at end of file diff --git a/Tutorials/Tutorial1/Example6.cpp b/Tutorials/Tutorial1/Example6.cpp deleted file mode 100644 index 3fd8be5..0000000 --- a/Tutorials/Tutorial1/Example6.cpp +++ /dev/null @@ -1,38 +0,0 @@ -#include -#include -#include -#include -#include - -using namespace std; -using namespace DACE; - - -template T ErrFunc(T x) -{ - const double pi = 4.0*atan(1.0); - - T z = 1.0/sqrt(2.0*pi)*exp(-x*x/2); - return z; -} - - -int main( void ) -{ - - DA::init( 24, 1 ); // initialize DACE for 20th-order computations in 1 variable - - DA x = DA(1); - - DA y = ErrFunc(x); // compute Taylor expansion of the erf - - DA Inty = y.integ(1); // compute the Taylor expansion of the indefinite integral of erf - - double value = Inty.evalScalar(1.0)-Inty.evalScalar(-1.0); // compute int_{-1}^{+1} (erf) - - cout << "int_{-1}^{+1} (erf)" << endl; - cout << setprecision(12); - cout << "Exact result: " << 0.682689492137 << endl; - cout << "Approx result " << value << endl; - -} \ No newline at end of file diff --git a/Tutorials/Tutorial1/Example7.cpp b/Tutorials/Tutorial1/Example7.cpp deleted file mode 100644 index 3279c02..0000000 --- a/Tutorials/Tutorial1/Example7.cpp +++ /dev/null @@ -1,52 +0,0 @@ -#include -#include -#include -#include -#include - -using namespace std; -using namespace DACE; - - -template T somb(AlgebraicVector x) -{ - - return sin(sqrt(sqr(x[0]) + sqr(x[1])))/sqrt(sqr(x[0]) + sqr(x[1])); - -} - - -int main( void ) -{ - - DA::init( 10, 2 ); // initialize DACE for 10th-order computations in 2 variables - - cout << "Initialize x as two-dim DA vector around (0,0)" << endl << endl; - - AlgebraicVector x(2); - - x[0] = DA(1); - x[1] = DA(2); - - cout << "x" << endl << x << endl; - - getchar(); - - cout << "Evaluate sombrero function" << endl << endl; - - DA z = somb(x); // Evaluate sombrero function - - cout << "z" << endl << z << endl; - -} - - - - - - - - - - - diff --git a/Tutorials/Tutorial1/Example8.cpp b/Tutorials/Tutorial1/Example8.cpp deleted file mode 100644 index 5da17f0..0000000 --- a/Tutorials/Tutorial1/Example8.cpp +++ /dev/null @@ -1,54 +0,0 @@ -#include -#include -#include -#include -#include - -using namespace std; -using namespace DACE; - - -template T somb(AlgebraicVector x) -{ - - return sin(sqrt(sqr(x[0]) + sqr(x[1])))/sqrt(sqr(x[0]) + sqr(x[1])); - -} - - -int main( void ) -{ - - DA::init( 1, 2 ); // initialize DACE for 1st-order computations in 2 variables - - cout << "Initialize x as two-dim DA vector around (2,3)" << endl << endl; - - AlgebraicVector x(2); - - x[0] = 2.0 + DA(1); - x[1] = 3.0 + DA(2); - - DA z = somb(x); // Evaluate sombrero function - - cout << "Sombrero function" << endl << endl; - cout << z << endl << endl; - - AlgebraicVector grad_z(2); // Declare DA vector that will contain the gradient of sombrero function - - grad_z = z.gradient(); // Compute gradient of sombrero function - - cout << "Gradient of sombrero function" << endl << endl; - cout << grad_z << endl; - -} - - - - - - - - - - - diff --git a/Tutorials/Tutorial1/Example9.cpp b/Tutorials/Tutorial1/Example9.cpp deleted file mode 100644 index a3563ec..0000000 --- a/Tutorials/Tutorial1/Example9.cpp +++ /dev/null @@ -1,42 +0,0 @@ -#include -#include -#include -#include -#include - -using namespace std; -using namespace DACE; - - -int main( void ) -{ - - DA::init( 10, 1 ); - - DA x = DA(1); - - AlgebraicVector y(1), inv_y(1); - - y[0] = sin(x); // Compute Taylor expansion of sin(x) - - inv_y = y.invert(); // Invert Taylor polynomial - - // Compare with asin(x) - cout << "Polynomial inversion of sin(x)" << endl << endl; - cout << inv_y << endl << endl; - - cout << "asin(x)" << endl << endl; - cout << asin(x) << endl; - -} - - - - - - - - - - - diff --git a/Tutorials/Tutorial1/Tutorial1.pdf 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