BLAS1_C
Basic Linear Algebra Subprograms
Level 1
Single Precision Complex Arithmetic

BLAS1_C is a MATLAB library which implements the Level 1 BLAS, or Basic Linear Algebra Subprograms.

The BLAS are a small core library of linear algebra utilities, which can be highly optimized for various architectures. Software that relies on the BLAS is thus highly portable, and will typically run very efficiently. The LINPACK and LAPACK linear algebra libraries make extensive use of the BLAS.

The Level 1 BLAS are primarily for use in vector operations. In certain cases, they may also be used to operate on the rows or columns of a two-dimensional array.

It is worth questioning whether one should try to implement the Level 1 BLAS in MATLAB: for one thing, the MATLAB language makes it very easy to carry out vector operations, even with nonunit incrementing on the vector indices. Moreover, MATLAB actually makes it more difficult to stick with the syntax of the BLAS, since it is not so easy to make a two dimensional array "look like" a vector.

In particular, if you want to work on a row of a matrix, MATLAB essentially prefers you to make a temporary vector, as in "A(3,1:N)"; in the standard BLAS, you would instead pass the location of the first entry, A(3,1), and an increment, LDA, that will lead to the next entry of the row. This is not easy or natural to do in MATLAB. Still, for consistency, I have gone ahead and tried to make a reasonable effort at implementing the Level 1 BLAS.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

BLAS1_C is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BLAS1_D, a MATLAB library which contains basic linear algebra routines for vector-vector operations, using double precision real arithmetic.

BLAS1_S, a MATLAB library which contains basic linear algebra routines for vector-vector operations, using single precision real arithmetic.

BLAS1_Z, a MATLAB library which contains basic linear algebra routines for vector-vector operations, using double precision complex arithmetic.

GSL, a C++ library which includes an implementation of the BLAS1 routines.

LAPACK_EXAMPLES, a FORTRAN90 program which demonstrates the use of the LAPACK linear algebra library.

LINPACK_C, a MATLAB library which solves linear systems using single precision complex arithmetic;

SUPER_BLAS, a C library which contains a version of some of the BLAS1 routines.

Reference:

1. Thomas Coleman, Charles vanLoan,
   Handbook for Matrix Computations,
   SIAM, 1988,
   ISBN13: 978-0-898712-27-8,
   LC: QA188.C65.
2. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
   LINPACK User's Guide,
   SIAM, 1979,
   ISBN13: 978-0-898711-72-1,
   LC: QA214.L56.
3. Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
   Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage,
   ACM Transactions on Mathematical Software,
   Volume 5, Number 3, September 1979, pages 308-323.

Source Code:

• cabs1.m, returns the L1 magnitude of a complex number;
• cabs2.m, returns the L2 magnitude of a complex number;
• caxpy.m, adds a constant times one complex vector to another.
• ccopy.m, makes a copy of a complex vector;
• cdotc.m, computes the conjugated scalar product of two complex vectors;
• cdotu.m, computes the unconjugated scalar product of two complex vectors;
• cmach.m, computes machine parameters.
• crotg.m, constructs a complex Givens plane rotation.
• cscal.m, scales a complex vector by a constant.
• csign1.m, transfer of sign to the L1 magnitude of a complex number.
• csign2.m, transfer of sign to the L2 magnitude of a complex number.
• csrot.m, applies a plane rotation to complex vectors.
• csscal.m, scale a complex vector by a real constant.
• cswap.m, interchanges two complex vectors.
• icamax.m, returns the index of the complex vector entry of greatest magnitude;
• scasum.m, sums the absolute values of the entries of a complex vector;
• scnrm2.m, computes the Euclidean norm of a complex vector.

Examples and Tests:

• blas1_c_test.m, calls all the tests;
• blas1_c_test_output.txt, the output file.
• blas1_c_test01.m, tests CABS1;
• blas1_c_test02.m, tests CABS2;
• blas1_c_test03.m, tests CAXPY;
• blas1_c_test04.m, tests CCOPY;
• blas1_c_test05.m, tests CDOTC;
• blas1_c_test06.m, tests CDOTU;
• blas1_c_test07.m, tests CMACH.
• blas1_c_test08.m, tests CROTG.
• blas1_c_test09.m, tests CSCAL;
• blas1_c_test10.m, tests CSIGN1;
• blas1_c_test11.m, tests CSIGN2;
• blas1_c_test12.m, tests CSROT;
• blas1_c_test13.m, tests CSSCAL;
• blas1_c_test14.m, tests CSWAP;
• blas1_c_test15.m, tests ICAMAX;
• blas1_c_test16.m, tests SCASUM;
• blas1_c_test17.m, tests SCNRM2;

Utility Routines:

• c4_uniform_01.m, returns a random complex value.
• lsame.m, returns .TRUE. if CA is the same letter as CB regardless of case.
• timestamp.m, prints the YMDHMS date as a timestamp.
• xerbla.m, is an error handler for the LAPACK routines.

You can go up one level to the MATLAB source codes.