ROS基于C++模型预测控制与运动规划源码+ppt文件.zip

# QDLDL A free LDL factorisation routine for quasi-definite linear systems: `Ax=b` [](https://travis-ci.org/oxfordcontrol/qdldl) [](https://ci.appveyor.com/project/bstellato/qdldl-8q1mv/branch/master) [](https://coveralls.io/github/oxfordcontrol/qdldl) ## Getting started To start using QDLDL, first clone the repository ```bash git clone https://github.com/oxfordcontrol/qdldl.git ``` ### Build To build QDLDL, you need to install [cmake](https://cmake.org/) and run ```bash mkdir build cd build cmake .. cmake --build . ``` This will generate an `out/` folder with contents: - `qdldl_example`: a **code example** from [`examples/example.c`](./examples/example.c) - `libqdldl`: a static and a dynamic versions of the library. You can include an addition option `-DUNITTESTS=ON` when calling `cmake`, which will result in an additional executable `qdldl_tester` being built in the `out/` folder to test QDLDL on a variety of problems, including those with rank deficient or otherwise ill-formatted inputs. **N.B.** All files will have file extensions appropriate to your operating system. ### Install/Uninstall To install (uninstall) the libraries and headers you can simply run `make install` (`make uninstall`) after running the `cmake` command above. ## Calling QDLDL ### Main API The QDLDL API consists of 5 functions documented in [`include/qdldl.h`](./include/qdldl.h). For more details and a working example see [`examples/example.c`](./examples/example.c). **N.B.** There is **no memory allocation** performed in these routines. The user is assumed to have the working vectors already allocated. Here is a brief summary. * `QDLDL_etree`: compute the elimination tree for the quasidefinite matrix factorization `A = LDL'` * `QDLDL_factor`: return the factors `L`, `D` and `Dinv = 1./D` * `QDLDL_solve`: solves the linear system `LDL'x = b` * `QDLDL_Lsolve`: solves `Lx = b` * `QDLDL_Ltsolve`: solves `L'x = b` In the above function calls the matrices `A` and `L` are stored in compressed sparse column (CSC) format. The matrix `A` is assumed to be symmetric and only the upper triangular portion of A should be passed to the API. The factor `L` is lower triangular with implicit ones on the diagonal (i.e. the diagonal of L is not stored as part of the CSC formatted data.) The matrices `D` and `Dinv` are both diagonal matrices, with the diagonal values stored in an array. The matrix input `A` should be quasidefinite. The API provides some (non-comprehensive) error checking to protect against non-quasidefinite or non-upper triangular inputs. ### Custom types for integer, floats and booleans QDLDL uses its own internal types for integers, floats and booleans (`QDLDL_int, QDLDL_float, QDLDL_bool`. They can be specified using the cmake options: - `DFLOAT` (default false): uses float numbers instead of doubles - `DLONG` (default true): uses long integers for indexing (for large matrices) The `QDLDL_bool` is internally defined as `unsigned char`. ## Linking QDLDL ### Basic Example A basic example appears in [`examples/example.c`](./examples/example.c) and is compiled using cmake and the `CMakeLists.txt` file in the root folder. ### Including in a cmake project You can include QDLDL in a cmake project `foo` by adding the subdirectory as ``` # Add project add_subdirectory(qdldl) ``` QDLDL can be linked using a static or dynamic linker ``` # Link static library target_link_libraries (foo qdldlstatic) # Link shared library target_link_libraries (foo qdldl) ``` for dynamic linking the shared library should be available in your path. There is also the option to include QDLDL as an object library in your project. The current `CMakeLists.txt` file creates an object library called `qdldlobject`. This can be added to your project by adding it after your sources. For example, when creating a library `foo` you can add ``` add_library(foo foo.c foo.h $<TARGET_OBJECTS:qdldlobject>) ``` for more details see the [cmake documentation](https://cmake.org/cmake/help/latest/command/add_library.html#object-libraries). ## The algorithm The algorithm is an independent implementation of the elimination tree and factorisation procedures outlined in > T. A Davis. [Algorithm 849: a concise sparse cholesky factorization package](https://dl.acm.org/citation.cfm?id=1114277). ACM Trans. Math. Softw., 31(4):587–591, 2005. ## Credits - [Paul Goulart](http://users.ox.ac.uk/~engs1373/): main development - [Bartolomeo Stellato](https://stellato.io/): code refactoring and testing - [Goran Banjac](https://people.ee.ethz.ch/~gbanjac/)