TOEPLITZ
Solution of Toeplitz linear systems

TOEPLITZ is a FORTRAN77 library which solves a variety of Toeplitz and circulant linear systems.

The package can also handle circulant Toeplitz systems, and some other more complicated but related forms.

The TOEPLITZ package was written in the early 1980's by a joint working group of American and Soviet mathematicians.

The original, true, correct version of TOEPLITZ is available in the TOEPLITZ subdirectory of the NETLIB web site.

Licensing:

The toeplitz.f file is in the public domain.

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

Languages:

TOEPLITZ is available in a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

BLAS1, a FORTRAN77 library which contains the level 1 Basic Linear Algebra Subprograms.

LINPACK, a FORTRAN77 library which carries out the factorization and solution of linear systems of a variety of types.

LINPLUS, a FORTRAN77 library which includes some routines for manipulating Toeplitz matrices.

TEST_MAT, a FORTRAN77 library which includes some routines which define sample Toeplitz matrices.

TOEPLITZ_CHOLESKY, a FORTRAN77 library which computes the Cholesky factorization of a nonnegative definite symmetric Toeplitz matrix.

Reference:

1. Oleg Arushanian, MK Samarin, Valentin Voevodin, Evgeny Tyrtyshnikov, Burton Garbow, James Boyle, Wayne Cowell, Kenneth Dritz,
   The TOEPLITZ Package User's Guide,
   Argonne National Laboratory,
   ANL-83-16, 1983.
2. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
   LINPACK User's Guide,
   SIAM, 1979,
   ISBN13: 978-0-898711-72-1.
3. Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
   Basic Linear Algebra Subprograms for Fortran Usage,
   Algorithm 539,
   ACM Transactions on Mathematical Software,
   Volume 5, Number 3, September 1979, pages 308-323.

Source Code:

• toeplitz.f, the source code.
• toeplitz.sh, commands to compile the source code.

Examples and Tests:

• toeplitz_prb.f, a sample problem.
• toeplitz_prb.sh, commands to compile, link and run the sample problem.
• toeplitz_prb_output.txt, sample problem output.

List of Routines:

• CCCSLZ solves a linear system with a CCC matrix.
• CCGSLZ solves a linear system with a CCG matrix.
• CCSLZ solves a linear system with a CC matrix.
• CCTSLZ solves a linear system with a CCT matrix.
• CGSLZ solves a linear system with a CG matrix.
• CQRD computes the QR factorization of a CC matrix.
• CQRZ computes the QR factorization of a CCC matrix.
• CSLZ solves a linear system with a C matrix.
• CTGSLZ solves a linear system with a CTG matrix.
• CTSLZ solves a linear system with a CT matrix.
• DAXPY adds a multiple of one vector to another.
• DCABS1 computes the L1 norm of a complex value.
• DDOT forms the dot product of two vectors.
• DGEFA factors a general matrix.
• DGESL solves a linear system with a factored general matrix.
• DNRM2 computes the L2 norm of a vector.
• DSCAL scales a vector by a constant.
• DTRDI computes the determinant and inverse of a triangular matrix.
• DZNRM2 computes the L2 norm of a vector.
• IDAMAX locates the element of maximum absolute value in a vector.
• IZAMAX locates the element of maximum absolute value in a vector.
• SALWZ: direct or inverse discrete Fourier transform of rectangular matrix.
• TGSLD1 solves a linear system with a TG matrix.
• TGSLD solves a linear system with a TG matrix.
• TGSLZ1 solves a linear system with a TG matrix.
• TGSLZ solves a linear system with a TG matrix.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• TSLD1 solves a linear system with a T matrix.
• TSLD solves a linear system with a T matrix.
• TSLZ1 solves a linear system with a T matrix.
• TSLZ solves a linear system with a T matrix.
• ZAXPY adds a multiple of one vector to another.
• ZDOTC computes the dot product of two vectors.
• ZDSCAL scales a vector by a constant.
• ZGEFA factors a general matrix.
• ZGESL solves a linear system involving a factored general matrix.
• ZSCAL scales a vector by a constant.
• ZTRDI computes the determinant and inverse of a triangular matrix.

You can go up one level to the FORTRAN77 source codes.