Toeplitz Matrix Utilities

**R8TO**
is a Python library which
carries out some basic linear algebra operations on R8TO matrices
(real 64 bit precision Toeplitz 2*N-1 format).

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

**R8TO** is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version.

R83, a Python library which contains linear algebra routines for R83 matrices (real, 64 bit, tridiagonal 3xN format).

R83_NP, a Python library which contains linear algebra routines for R83_NP matrices (real, 64 bit, tridiagonal 3xN format, nonpivoting factorization).

R83P, a Python library which contains linear algebra routines for R83P matrices (real, 64 bit, tridiagonal periodic format).

R83S, a Python library which contains linear algebra routines for R83S matrices (real, 64 bit, tridiagonal scalar format).

R83T, a Python library which contains linear algebra routines for R83T matrices (real, 64 bit, tridiagonal Mx3 format).

R83V, a Python library which contains linear algebra routines for R83V matrices (real, 64 bit, tridiagonal three vector format).

R85, a Python library which contains linear algebra routines for R85 matrices (real, 64 bit, pentadiagonal format).

R8BB, a Python library which contains linear algebra routines for R8BB matrices (real, 64 bit, border banded format).

R8BLT, a Python library which contains linear algebra routines for R8BLT matrices (real, 64 bit, band lower triangular format).

R8BTO, a Python library which contains linear algebra routines for R8BTO matrices (real, 64 bit, block Toeplitz format).

R8BUT, a Python library which contains linear algebra routines for R8BUT matrices (real, 64 bit, band upper triangular format).

R8CC, a Python library which contains linear algebra routines for R8CC matrices (real, 64 bit, Compressed Column (Colptr,Row,Value) format).

R8CI, a Python library which contains linear algebra routines for R8CI matrices (real, 64 bit, circulant format).

R8COL, a Python library which contains utility routines for R8COL's, that is, double precision real MxN arrays, considered as N column vectors, each of length M. The data may be thought of as a matrix of multiple columns, and many operations will be carried out columnwise.

R8GB, a Python library which contains linear algebra routines for R8GB matrices (real, 64 bit, General Banded format).

R8GD, a Python library which contains linear algebra routines for R8GD matrices (real, 64 bit, general diagonal format).

R8GE, a Python library which contains linear algebra routines for R8GE matrices (real, 64 bit, General format).

R8GE_NP, a Python library which contains nonpivoting linear algebra routines for R8GE_NP matrices (real, 64 bit, General Nonpivoting format).

R8LT, a Python library which contains linear algebra routines for R8LT matrices (real, 64 bit, lower triangular format).

R8LTT, a Python library which contains linear algebra routines for R8LTT matrices (real, 64 bit, lower triangular Toeplitz format).

R8NCF, a Python library which contains linear algebra routines for R8NCF matrices (real, 64 bit, nonsymmetric coordinate format).

R8PBL, a Python library which contains linear algebra routines for R8PBL matrices (real, 64 bit, positive definite symmetric band lower format).

R8PBU, a Python library which contains linear algebra routines for R8PBU matrices (real, 64 bit, positive definite symmetric band upper format).

R8PO, a Python library which contains linear algebra routines for R8PO matrices (real, 64 bit, positive definite symmetric format).

R8PP, a Python library which contains linear algebra routines for R8PP matrices (real, 64 bit, positive definite symmetric packed format).

R8RI, a Python library which contains linear algebra routines for R8RI matrices (real, 64 bit, row indexed format).

R8ROW, a Python library which contains utility routines for R8ROW's, that is, double precision real MxN arrays, considered as M row vectors, each of length N. The data may be thought of as a matrix of multiple rows, and many operations will be carried out rowwise.

R8S3, a Python library which contains linear algebra routines for R8S3 matrices (real, 64 bit, SLAP Triad (I,J,AIJ) format).

R8SD, a Python library which contains linear algebra routines for R8SD matrices (real, 64 bit, symmetric diagonal format).

R8SM, a Python library which contains linear algebra routines for R8SM (Sherman-Morrison) matrices (real, 64 bit, A-u*v' format).

R8SP, a Python library which contains linear algebra routines for R8SP matrices (real, 64 bit, SLAP Triad (I,J,AIJ) format).

R8SR, a Python library which carries out linear algebra operations for R8SR matrices (real, 64 bit, diagonal + compressed row offdiagonal format).

R8SS, a Python library which carries out linear algebra operations for R8SS matrices (real, 64 bit, symmetric skyline format).

R8STO, a Python library which contains linear algebra routines for R8STO matrices (real, 64 bit, symmetric Toeplitz N format).

R8UT, a Python library which contains linear algebra routines for R8UT matrices (real, 64 bit, upper triangular format).

R8UTT, a Python library which contains linear algebra routines for R8UTT matrices (real, 64 bit, upper triangular Toeplitz format).

R8VM, a Python library which contains linear algebra routines for R8VM matrices (real, 64 bit, Vandermonde format).

- i4_log_10.py, returns the integer part of the logarithm base 10 of abs(X);
- r8ge.py, functions to apply to a matrix stored in R8GE matrix.
- r8to.py, functions to apply to a matrix stored in R8TO format.
- r8vec_indicator1.py, sets an R8VEC to the indicator vector;
- r8vec_print.py, prints an R8VEC;
- r8vec_uniform_01.py, sets an R8VEC to random values between 0 and 1.
- timestamp.py, prints the current YMDHMS date as a timestamp;

- r8to_test.py, calls all the tests;
- r8to_test.sh, runs all the tests;
- r8to_test_output.txt, the output from all the tests;

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