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246 CHAPTER 11. C++ LIBRARIES FOR SCIENTIFIC COMPUTING BLAS LAPACK ATLAS MUMPS . . . uBLAS ✪✪✪✪✪✪ ✧ ✧✧✧✧✧✧✧✧ ✦✦✦✦✦✦✦✦✦✦✦✦✦ MTL GLAS . . . Figure 11.1: Traditional interfaces between software BLAS LAPACK ❅ ❅❘ ❄ uBLAS ��✒ ✻ MTL ATLAS ❄ Bindings ✻ GLAS MUMPS Figure 11.2: Concept of bindings as a generic layer between linear algebra algorithms and vector and matrix software to provide a layer that uses the bindings. Figure 11.2 illustrates this philosophy. Note the difference with Figure 11.1. 11.3.1 Software bindings We now illustrate how the bindings can be used to interface external software by means of examples. BLAS bindings The BLAS are the Basic Linear Algebra Subroutines [?] [?] [?] [?] [?], whose reference implementation is available through Netlib 1 . The BLAS are subdivided in three levels : level one contains vector operations, level two matrix vector operations and level three, matrix operations. The BLAS bindings in Boost Sandbox contain interfaces to some BLAS functions. Functions are added on request. The interfaces check the input arguments using the assert command, which is only compiled when the NDEBUG compile flag is not set. The interfaces are contained in three files : blas1.hpp, blas2.hpp, and blas3.hpp in the directory boost/numeric/bindings/blas. The BLAS bindings reside in the namespace boost::numeric::bindings::blas. The BLAS provide functions for vectors and matrices with value type float, double, std::complex, and std::complex. All matrix containers have ordering type column major t,since the (FOR- TRAN) BLAS assume column major matrices. The bindings are illustrated in Figure 11.3 for the BLAS subprograms DCOPY, DSCAL, and DAXPY for objects of type std::vector. Note the include files for the bindings of the BLAS-1 subprograms and the include file that contains the specialization of vector traits for std::vector. 1 http://www.netlib.org . . . ❄ ✻ . . . � �✠
11.3. BOOST.BINDINGS 247 #include #include int main() { std::vector< double > x( 10 ), y( 10 ) ; // Fill the vector x ... bindings::blas::copy( x, y ) ; bindings::blas::scal( 2.0, y ) ; bindings::blas::axpy( −3.0, x, y ) ; return 0 ; } LAPACK bindings Figure 11.3: Example for BLAS-1 bindings and std::vector bindings traits Software for dense and banded matrices is collected in LAPACK [?]. It is a collection of FORTRAN routines mainly for solving linear systems, and eigenvalue problems, including the singular value decomposition. As for the BLAS, the Boost Sandbox does not contain a full set of interfaces to LAPACK routines, but only very commonly used subprograms. On request, more functions are added to the library. The LAPACK bindings reside in the namespace boost::numeric::bindings::lapack. Many LAPACK subroutines require auxiliary arrays, which a non-expert user does not wish to allocate for reasons of comfort. The interface allows the user to allocate auxiliary vectors using the templated Boost.Bindings class array. The LAPACK bindings verify the matrix structure to see whether the routine is the right choice. It is also checked whether the matrix arguments are column major. Every function’s return type is int. The return value is the return value of the INFO argument of the corresponding LAPACK subprogram. Figure 11.4 shows an example using GLAS. MUMPS bindings MUMPS stands for Multifrontal Massively Parallel Solver. The first version was a result from the EU project PARASOL [?, ?, ?]. The software is developed in Fortran 90 and contains a C interface. The input matrices should be given in coordinate format, i.e. storage format=coordinate t and the index numbering should start from one, i.e. sparse matrix traits::index base==1. We refer to the MUMPS Users Guide, distributed with the software [?]. The C++ interface is a generic interface to the respective C structs for the different value types that are available from the MUMPS distribution: float, double, std::complex, and std::complex. The C++ bindings also contain functions to set the pointers and sizes of the parameters in the C struct using the bindings traits classes. An example is given in Figure 11.5. The sparse matrix is the uBLAS coordinate matrix, which is a sparse matrix in
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Technische Universität Dresden Fak
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Contents I Understanding C++ 7 Intr
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CONTENTS 5 10.5 Unix and Linux . .
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Part I Understanding C ++ 7
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10 C ++ was not a reliable computer
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12 CHAPTER 1. GOOD AND BAD SCIENTIF
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20 CHAPTER 2. C++ BASICS • std::c
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22 CHAPTER 2. C++ BASICS In the fir
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24 CHAPTER 2. C++ BASICS int main (
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26 CHAPTER 2. C++ BASICS Operator A
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36 CHAPTER 2. C++ BASICS eps/= 2.0;
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56 CHAPTER 2. C++ BASICS A function
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66 CHAPTER 3. CLASSES apply symm bl
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72 CHAPTER 3. CLASSES • Compilers
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74 CHAPTER 3. CLASSES a real number
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