**r83**,
a MATLAB code which
carries out some basic linear algebra operations on R83 matrices
(real 64 bit precision tridiagonal 3xN format).

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

**r83** is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version.

r83_np, a MATLAB code which contains linear algebra routines for r83_np matrices (real, 64 bit, tridiagonal 3xn format, nonpivoting factorization).

r83p, a MATLAB code which contains linear algebra routines for r83p matrices (real, 64 bit, tridiagonal periodic format).

r83s, a MATLAB code which contains linear algebra routines for r83s matrices (real, 64 bit, tridiagonal scalar format).

r83t, a MATLAB code which contains linear algebra routines for r83t matrices (real, 64 bit, tridiagonal mx3 format).

r83v, a MATLAB code which contains linear algebra routines for r83v matrices (real, 64 bit, tridiagonal three vector format).

r85, a MATLAB code which contains linear algebra routines for r85 matrices (real, 64 bit, pentadiagonal format).

r8bb, a MATLAB code which contains linear algebra routines for r8bb matrices (real, 64 bit, border banded format).

r8blt, a MATLAB code which contains linear algebra routines for r8blt matrices (real, 64 bit, band lower triangular format).

r8bto, a MATLAB code which contains linear algebra routines for r8bto matrices (real, 64 bit, block toeplitz format).

r8but, a MATLAB code which contains linear algebra routines for r8but matrices (real, 64 bit, band upper triangular format).

r8cb, a MATLAB code which contains linear algebra routines for r8cb matrices (real, 64 bit, compressed band format).

r8cbb, a MATLAB code which contains linear algebra routines for r8cbb matrices (real, 64 bit, compressed border banded format).

r8cc, a MATLAB code which contains linear algebra routines for r8cc matrices (real, 64 bit, compressed column (colptr,row,value) format).

r8ci, a MATLAB code which contains linear algebra routines for r8ci matrices (real, 64 bit, circulant format).

r8col, a MATLAB code 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.

r8crs, a MATLAB code which contains linear algebra routines for r8crs matrices (real, 64 bit, compressed row storage (crs) format).

r8gb, a MATLAB code which contains linear algebra routines for r8gb matrices (real, 64 bit, general banded format).

r8gd, a MATLAB code which contains linear algebra routines for r8gd matrices (real, 64 bit, general diagonal format).

r8ge, a MATLAB code which contains linear algebra routines for r8ge matrices (real, 64 bit, general format).

r8ge_np, a MATLAB code which contains nonpivoting linear algebra routines for r8ge matrices (real, 64 bit, general nonpivoting format).

r8lt, a MATLAB code which contains linear algebra routines for r8lt matrices (real, 64 bit, lower triangular format).

r8ltt, a MATLAB code which contains linear algebra routines for r8ltt matrices (real, 64 bit, lower triangular toeplitz format).

r8ncf, a MATLAB code which contains linear algebra routines for r8ncf matrices (real, 64 bit, nonsymmetric coordinate format).

r8pbl, a MATLAB code which contains linear algebra routines for r8pbl matrices (real, 64 bit, positive definite symmetric band lower format).

r8pbu, a MATLAB code which contains linear algebra routines for r8pbu matrices (real, 64 bit, positive definite symmetric band upper format).

r8po, a MATLAB code which contains linear algebra routines for r8po matrices (real, 64 bit, positive definite symmetric format).

r8pp, a MATLAB code which contains linear algebra routines for r8pp matrices (real, 64 bit, positive definite symmetric packed format).

r8ri, a MATLAB code which contains linear algebra routines for r8ri matrices (real, 64 bit, row indexed format).

r8row, a MATLAB code 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 code which contains linear algebra routines for r8s3 matrices (real, 64 bit, slap triad (i,j,aij) format).

r8sd, a MATLAB code which contains linear algebra routines for r8sd matrices (real, 64 bit, symmetric diagonal format).

r8sm, a MATLAB code which contains linear algebra routines for r8sm (sherman-morrison) matrices (real, 64 bit, a-u*v' format).

r8sp, a MATLAB code which contains linear algebra routines for r8sp matrices (real, 64 bit, slap triad (i,j,aij) format).

r8sr, a MATLAB code which carries out linear algebra operations for r8sr matrices (real, 64 bit, diagonal + compressed row offdiagonal format).

r8ss, a MATLAB code which carries out linear algebra operations for r8ss matrices (real, 64 bit, symmetric skyline format).

r8sto, a MATLAB code which contains linear algebra routines for r8sto matrices (real, 64 bit, symmetric toeplitz n format).

r8to, a MATLAB code which contains linear algebra routines for r8to matrices (real, 64 bit, toeplitz 2*n-1 format).

r8ut, a MATLAB code which contains linear algebra routines for r8ut matrices (real, 64 bit, upper triangular format).

r8utt, a MATLAB code which contains linear algebra routines for r8utt matrices (real, 64 bit, upper triangular toeplitz format).

r8vm, a MATLAB code 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, returns a pseudorandom R8.
- r83_cg.m, solves an R83 system using the conjugate gradient method.
- r83_cr_fa.m, factors an R83 system using cyclic reduction;
- r83_cr_sl.m, solves an R83 system factored by r83_cr_fa;
- r83_cr_sls.m, solves several R83 systems factored by r83_cr_fa;
- r83_dif2.m, returns the second difference matrix as an R83.
- r83_jac_sl.m, solves an R83 system using Gauss-Seidel iteration;
- r83_indicator.m, sets up an R83 indicator matrix;
- r83_jac_sl.m, solves an R83 system using Jacobi iteration;
- r83_mtv.m, multiplies a vector times an R83 matrix;
- r83_mv.m, multiplies an R83 matrix times a vector;
- r83_print.m, prints an R83 matrix;
- r83_print_some.m, prints some of an R83 matrix;
- r83_random.m, randomizes an R83 matrix;
- r83_res.m, returns the residual of an R83 linear system.
- r83_to_r8ge.m, copies an R83 matrix to an R8GE matrix;
- r83_zeros.m, zeros an R83 matrix;
- r8ge_indicator.m, returns the indicator R8GE matrix.
- r8ge_mtv.m, multiplies an R8GE matrix transposed times a vector.
- r8ge_mv.m, multiplies an R8GE matrix times a vector.
- r8ge_print.m, prints an R8GE matrix;
- r8ge_print_some.m, prints some of an R8GE matrix;
- r8vec_indicator1.m, sets an R8VEC to the indicator1 vector;
- r8vec_print.m, prints an R8VEC;
- r8vec_uniform_01.m, returns a random R8VEC;
- r8vec2_print.m, prints a pair R8VEC's;