BLAS1_Z
Basic Linear Algebra Subprograms
Level 1
Double Precision Complex Arithmetic

BLAS1_Z 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_Z 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_C, a MATLAB library which is a version of BLAS1 for single precision complex arithmetic.

BLAS1_D, a MATLAB library which is a version of BLAS1 for double precision real arithmetic.

BLAS1_S, a MATLAB library which is a version of BLAS1 for single precision real 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, a MATLAB library which a linear algebra package that uses the BLAS1 routines.

SUPER_BLAS, a C library which is 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:

• dzasum.m, sums the absolute values of the entries of a complex vector;
• dznrm2.m, computes the Euclidean norm of a complex vector.
• izamax.m, returns the index of the complex vector entry of greatest magnitude;
• zabs1.m, returns the L1 magnitude of a complex number;
• zabs2.m, returns the L2 magnitude of a complex number;
• zaxpy.m, adds a constant times one complex vector to another.
• zcopy.m, makes a copy of a complex vector;
• zdotc.m, computes the conjugated scalar product of two complex vectors;
• zdotu.m, computes the unconjugated scalar product of two complex vectors;
• zdrot.m, applies a plane rotation to complex vectors.
• zdscal.m, scale a complex vector by a real constant.
• zmach.m, computes machine parameters.
• zrotg.m, constructs a complex Givens plane rotation.
• zscal.m, scales a complex vector by a constant.
• zsign1.m, transfer of sign to the L1 magnitude of a complex number.
• zsign2.m, transfer of sign to the L2 magnitude of a complex number.
• zswap.m, interchanges two complex vectors.

Examples and Tests:

• blas1_z_test.m, calls all the tests;
• blas1_z_test_output.txt, the output file.
• blas1_z_test01.m, tests DZASUM;
• blas1_z_test02.m, tests DZNRM2;
• blas1_z_test03.m, tests IZAMAX;
• blas1_z_test04.m, tests ZABS1;
• blas1_z_test05.m, tests ZABS2;
• blas1_z_test06.m, tests ZAXPY;
• blas1_z_test07.m, tests ZCOPY;
• blas1_z_test08.m, tests ZDOTC;
• blas1_z_test09.m, tests ZDOTU;
• blas1_z_test10.m, tests ZDROT;
• blas1_z_test11.m, tests ZDSCAL;
• blas1_z_test12.m, tests ZMACH.
• blas1_z_test13.m, tests ZROTG;
• blas1_z_test14.m, tests ZSCAL;
• blas1_z_test15.m, tests ZSIGN1;
• blas1_z_test16.m, tests ZSIGN2;
• blas1_z_test17.m, tests ZSWAP;

Utility Routines:

• c8_uniform_01.m, returns a unit pseudorandom C8.
• 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.