Upper Triangular Matrix Utilities

**R8UT**
is a Python library which
carries out some basic linear algebra operations on R8UT matrices
(real 64 bit precision upper triangular format).

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

**R8UT** 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).

R8TO, a Python library which contains linear algebra routines for R8TO matrices (real, 64 bit, Toeplitz 2*N-1 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);
- r8_uniform_01.py, is a uniform random number generator;
- r8ge_print.py, prints an R8GE matrix.
- r8ge_print_some.py, prints some of an R8GE matrix.
- r8ut.py, functions to apply to a matrix stored in R8UT format.
- r8vec_indicator1.py, sets an R8VEC to the indicator vector;
- r8vec_print.py, prints an R8VEC;
- timestamp.py, prints the current YMDHMS date as a timestamp;

- r8ut_test.py, calls all the tests;
- r8ut_test.sh, runs all the tests;
- r8ut_test_output.txt, the output from all the tests;

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