Positive Definite Symmetric Band Matrix Utilities

**R8PBU**
is a MATLAB library which
carries out some basic linear algebra operations on R8PBU matrices
(real 64 bit precision positive definite symmetric band upper format).

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

**R8PBU** is available in
a C version and
a C++ version and
a FORTRAN77 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 3xN 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 R8LT 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).

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).

R8TO, a MATLAB library which contains linear algebra routines for R8TO matrices (real, 64 bit, Toeplitz 2*N-1 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);
- r8_uniform_01.m, is a uniform random number generator;
- r8ge_det.m, computes the determinant of a factored R8GE matrix;
- r8ge_fa.m, factors an R8GE matrix;
- r8ge_print.m, prints an R8GE matrix;
- r8ge_print_some.m, prints some of an R8GE matrix;
- r8pbu_cg.m, uses the conjugate gradient method on a linear system with an R8PBU matrix;
- r8pbu_cg_test.m
- r8pbu_det.m, computes the determinant of an R8PO matrix factored by R8PBU_FA;
- r8pbu_det_test.m
- r8pbu_dif2.m, returns the DIF2 matrix in R8PBU format.
- r8pbu_dif2_test.m
- r8pbu_fa.m, factors an R8PBU matrix;
- r8pbu_fa_test.m
- r8pbu_indicator.m, returns an R8PBU indicator matrix;
- r8pbu_indicator_test.m
- r8pbu_ml.m, computes A*x or A'*x after A has been factored by R8PBU_FA;
- r8pbu_ml_test.m
- r8pbu_mv.m, multiplies an R8PBU matrix times a vector;
- r8pbu_mv_test.m
- r8pbu_print.m, prints an R8PBU matrix;
- r8pbu_print_test.m
- r8pbu_print_some.m, prints some of an R8PBU matrix;
- r8pbu_print_some_test.m
- r8pbu_random.m, randomizes an R8PBU matrix;
- r8pbu_random_test.m
- r8pbu_res.m, computes the residual R = B-A*X for R8PBU matrices.
- r8pbu_res_test.m
- r8pbu_sl.m, solves an R8PBU linear system factored by R83P_FA;
- r8pbu_sl_test.m
- r8pbu_sor.m, applies the SOR iterative method to solve a linear system with an R8PBU matrix;
- r8pbu_sor_test.m
- r8pbu_to_r8ge.m, copies an R8PBU matrix to an R8GE matrix;
- r8pbu_to_r8ge_test.m
- r8pbu_zeros.m, zeros an R8PBU matrix;
- r8pbu_zeros_test.m
- r8vec_indicator1.m, sets an R8VEC to the indicator1 vector;
- r8vec_print.m, prints an R8VEC;
- r8vec_print_some.m, prints some of an R8VEC;
- r8vec_uniform_01.m, returns a random R8VEC;
- r8vec2_print_some.m, prints some of a pair R8VEC's;
- timestamp.m, prints the current YMDHMS date as a timestamp;

- r8pbu_test.m, runs all the tests;
- r8pbu_test_output.txt, the output file;

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