Example Programs for LAPACK Routines

This repository contains example programs written in Fortran 90 showing how to call double precision versions of most top-level LAPACK (driver and computational) routines.

The programs are derived from the examples used in documentation of these routines for the NAG Fortran Library, but they don't require use of that library because everything needed is here in this repository, including various auxiliary routines.

File organization

Once you've taken a copy of the repository, you'll find these items:

interface_blocks - a directory containing a few Fortran module files used when compiling the rest of the example source
auxiliary - a small set of auxiliary routines used by the example programs, for sorting and printing results
examples/source - source code of individual LAPACK examples
examples/data - input data files, one needed by each LAPACK example
examples/baseresults - expected result files (machine dependent)
examples/doc - A description of what problem each example solves
GNUmakefile - a makefile that can be used (with minor modification) to compile and run all the LAPACK examples

Available example programs

Here is a list of example programs, along with descriptions of the problems they solve.

How to build manually

We assume that you already have a library of LAPACK and BLAS routines that you can link the example programs to; they may be libraries that you have compiled yourself, from the netlib LAPACK source code, or they may be libraries obtained from elsewhere, e.g. the NAG Library, Intel's MKL, or the ARM Performance Library. These libraries must be compatible with the compiler that you use to compile the current example programs. Here we assume use of the NAG Fortran compiler, nagfor, but you can use any other modern Fortran compiler of your choice.

Go to the interface_blocks directory, and compile the file lapack_precision.f90:

    cd interface_blocks
    nagfor -c lapack_precision.f90

This module defines dp and sp, double and single precision kind types respectively, and it is needed by almost all the other Fortran files.

In the same interface_blocks directory, compile the rest of the files:

    nagfor -c *.f90

The object files produced by these compilations are not important, but the module files produced are.

Go to the auxiliary directory, and compile all the files there, using the modules in the interface_blocks directory:

    cd auxiliary
    nagfor -c -I../interface_blocks *.f90

Still in the auxiliary directory, put all the object files into a library: ar rv libaux.a *.o

Now you've done all the preparation needed before you can compile an LAPACK example program.

Let's use dgetrf_example.f90:

    cd examples/source
    nagfor -I../../interface_blocks dgetrf_example.f90 ../../auxiliary/libaux.a
      full_path_to/liblapack.a full_path_to/libblas.a -o dgetrf_example.exe

Here we assume that the LAPACK and BLAS routines are held in two separate libraries. You may have one library containing all of them.

Run the program, using the approprate data file as input:

    ./dgetrf_example.exe < ../data/dgetrf_example.d

That's it. If you had no problems, then you should be able to compile and run all the other example programs too.

How to build using the GNUmakefile

There is a GNUmakefile which contains commands to compile and run all the example programs using one of various compilers.

First of all, edit GNUmakefile and modify these two lines:

LIBLAPACK := ../lapack-3.8.0/$(compiler)/liblapack.a
LIBBLAS := ../lapack-3.8.0/$(compiler)/librefblas.a

to give the paths of your LAPACK and BLAS libraries (if you have just one library containing both LAPACK and BLAS routines, you can set them both to be the same library, or one of them to be blank).

Then a command such as:

    make compiler=nagfor

will compile all the necessary auxiliary (matrix printing) code into a library, and then compile, link and run each individual LAPACK example program. The results will be compared with a set of expected results which are located in the examples/baseresults directory.

To compile a single example, a command such as:

    make compiler=gfortran dgetrf_example.r

should work.

Test platforms

The GNUmakefile currently has knowledge of the following Fortran compilers:

NAG Fortran compiler, nagfor
GNU Fortran compiler, gfortran
Intel Fortran compiler, ifort
PGI Fortran compiler, pgf90
ARM Fortran compiler, armflang

The example programs have been shown to work with all these compilers on various 64-bit GNU/Linux operating systems, and the first three also on 64-bit Microsoft Windows.

Example program result differences

Small differences may show up between the "base" results and the results you get when you run the example programs. These can be because of small rounding differences either in the LAPACK library you're using, or because different compilers have subtle differences in the way that they print numbers (for example, in Fortran formatted output, some compilers print tiny negative numbers which round to zero when formatted as -0.0000 and other compilers print as 0.0000). Occasionally eigenvalues and eigenvectors may be produced in a different order.

numericalalgorithmsgroup / LAPACK_Examples