Toeplitz Matrix Utilities

**R8TO**
is a MATLAB 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 MATLAB library which contains linear algebra routines for R83 matrices (real, 64 bit, tridiagonal format).

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

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

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

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

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

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

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

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

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

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

R8CB, a MATLAB library which contains linear algebra routines for R8CB matrices (real, 64 bit, Compressed Band format).

R8CBB, a MATLAB library which contains linear algebra routines for R8CBB matrices (real, 64 bit, Compressed Border Banded format).

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

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

R8COL, a MATLAB 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 MATLAB library which contains linear algebra routines for R8GB matrices (real, 64 bit, General Banded format).

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

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

R8GE_NP, a MATLAB library which contains nonpivoting linear algebra routines for R8GE matrices (real, 64 bit, General Nonpivoting format).

R8LT, a MATLAB library which contains linear algebra routines for R8UT matrices (real, 64 bit, lower triangular format).

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

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

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

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

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

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

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

R8ROW, a MATLAB 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 MATLAB library which contains linear algebra routines for R8S3 matrices (real, 64 bit, SLAP Triad (I,J,AIJ) format).

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

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

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

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

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

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

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

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

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

- i4_log_10.m, returns the integer part of the logarithm base 10 of abs(X);
- r8ge_print.m, prints an R8GE matrix;
- r8ge_print_some.m, prints some of an R8GE matrix;
- r8to_dif2.m, returns the second difference matrix as an R8TO.
- r8to_dif2_test.m
- r8to_indicator.m, sets up an R8TO indicator matrix;
- r8to_indicator_test.m
- r8to_mtv.m, multiplies a vector times an R8TO matrix;
- r8to_mtv_test.m
- r8to_mv.m, multiplies an R8TO matrix times a vector;
- r8to_mv_test.m
- r8to_print.m, prints an R8TO matrix;
- r8to_print_test.m
- r8to_print_some.m, prints some of an R8TO matrix;
- r8to_print_some_test.m
- r8to_random.m, randomizes an R8TO matrix;
- r8to_random_test.m
- r8to_sl.m, solves A*x=b, where A is an R8TO matrix.
- r8to_sl_test.m
- r8to_slt.m, solves A'*x=b, where A is an R8TO matrix.
- r8to_slt_test.m
- r8to_to_r8ge.m, copies an R8TO matrix to an R8GE matrix;
- r8to_to_r8ge_test.m
- r8to_zeros.m, zeros an R8TO matrix;
- r8to_zeros_test.m
- r8vec_indicator1.m, sets an R8VEC to the indicator1 vector;
- r8vec_print.m, prints an R8VEC;
- r8vec_uniform_01.m, returns a random R8VEC;
- timestamp.m, prints the current YMDHMS date as a timestamp;

- r8to_test.m, runs all the tests;
- r8to_test_output.txt, the output file;

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