R8LTT
Lower Triangular Toeplitz Matrix Utilities

R8LTT, a FORTRAN90 library which carries out some basic linear algebra operations on R8LTT matrices (real 64 bit precision lower triangular Toeplitz format).

Licensing:

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

Languages:

R8LTT is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version

Related Data and Programs:

R83, a FORTRAN90 library which contains linear algebra routines for R83 matrices (real, 64 bit, tridiagonal 3xN format).

R83_NP, a FORTRAN90 library which contains linear algebra routines for R83_NP matrices (real, 64 bit, tridiagonal 3xN format, nonpivoting factorization).

R83P, a FORTRAN90 library which contains linear algebra routines for R83P matrices (real, 64 bit, tridiagonal periodic format).

R83S, a FORTRAN90 library which contains linear algebra routines for R83S matrices (real, 64 bit, tridiagonal scalar format).

R83T, a FORTRAN90 library which contains linear algebra routines for R83T matrices (real, 64 bit, tridiagonal Mx3 format).

R83V, a FORTRAN90 library which contains linear algebra routines for R83V matrices (real, 64 bit, tridiagonal three vector format).

R85, a FORTRAN90 library which contains linear algebra routines for R85 matrices (real, 64 bit, pentadiagonal format).

R8BB, a FORTRAN90 library which contains linear algebra routines for R8BB matrices (real, 64 bit, border banded format).

R8BLT, a FORTRAN90 library which contains linear algebra routines for R8BLT matrices (real, 64 bit, band lower triangular format).

R8BTO, a FORTRAN90 library which contains linear algebra routines for R8BTO matrices (real, 64 bit, block Toeplitz format).

R8BUT, a FORTRAN90 library which contains linear algebra routines for R8BUT matrices (real, 64 bit, band upper triangular format).

R8CB, a FORTRAN90 library which contains linear algebra routines for R8CB matrices (real, 64 bit, Compressed Band format).

R8CBB, a FORTRAN90 library which contains linear algebra routines for R8CBB matrices (real, 64 bit, Compressed Border Banded format).

R8CC, a FORTRAN90 library which contains linear algebra routines for R8CC matrices (real, 64 bit, Compressed Column (Colptr,Row,Value) format).

R8CI, a FORTRAN90 library which contains linear algebra routines for R8CI matrices (real, 64 bit, circulant format).

R8COL, a FORTRAN90 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 FORTRAN90 library which contains linear algebra routines for R8GB matrices (real, 64 bit, General Banded format).

R8GD, a FORTRAN90 library which contains linear algebra routines for R8GD matrices (real, 64 bit, general diagonal format).

R8GE, a FORTRAN90 library which contains linear algebra routines for R8GE matrices (real, 64 bit, General format).

R8GE_NP, a FORTRAN90 library which contains nonpivoting linear algebra routines for R8GE matrices (real, 64 bit, General Nonpivoting format).

R8LT, a FORTRAN90 library which contains linear algebra routines for R8LT matrices (real, 64 bit, lower triangular format).

R8NCF, a FORTRAN90 library which contains linear algebra routines for R8NCF matrices (real, 64 bit, nonsymmetric coordinate format).

R8PBL, a FORTRAN90 library which contains linear algebra routines for R8PBL matrices (real, 64 bit, positive definite symmetric band lower format).

R8PBU, a FORTRAN90 library which contains linear algebra routines for R8PBU matrices (real, 64 bit, positive definite symmetric band upper format).

R8PO, a FORTRAN90 library which contains linear algebra routines for R8PO matrices (real, 64 bit, positive definite symmetric format).

R8PP, a FORTRAN90 library which contains linear algebra routines for R8PP matrices (real, 64 bit, positive definite symmetric packed format).

R8RI, a FORTRAN90 library which contains linear algebra routines for R8RI matrices (real, 64 bit, row indexed format).

R8ROW, a FORTRAN90 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 FORTRAN90 library which contains linear algebra routines for R8S3 matrices (real, 64 bit, SLAP Triad (I,J,AIJ) format).

R8SD, a FORTRAN90 library which contains linear algebra routines for R8SD matrices (real, 64 bit, symmetric diagonal format).

R8SM, a FORTRAN90 library which contains linear algebra routines for R8SM (Sherman-Morrison) matrices (real, 64 bit, A-u*v' format).

R8SP, a FORTRAN90 library which contains linear algebra routines for R8SP matrices (real, 64 bit, SLAP Triad (I,J,AIJ) format).

R8SR, a FORTRAN90 library which carries out linear algebra operations for R8SR matrices (real, 64 bit, diagonal + compressed row offdiagonal format).

R8SS, a FORTRAN90 library which carries out linear algebra operations for R8SS matrices (real, 64 bit, symmetric skyline format).

R8STO, a FORTRAN90 library which contains linear algebra routines for R8STO matrices (real, 64 bit, symmetric Toeplitz N format).

R8TO, a FORTRAN90 library which contains linear algebra routines for R8TO matrices (real, 64 bit, Toeplitz 2*N-1 format).

R8UT, a FORTRAN90 library which contains linear algebra routines for R8UT matrices (real, 64 bit, upper triangular format).

R8UTT, a FORTRAN90 library which contains linear algebra routines for R8UTT matrices (real, 64 bit, upper triangular Toeplitz format).

R8VM, a FORTRAN90 library which contains linear algebra routines for R8VM matrices (real, 64 bit, Vandermonde format).

Reference:

• Igor Podlubny,
  Matrix approach to discrete fractional calculus,
  Fractional Calculus and Applied Analysis,
  Volume 3, Number 4, pages 359-386, 2000.

Source Code:

• r8ltt.f90, the source code.

Examples and Tests:

• r8ltt_test.f90, a sample calling program.
• r8ltt_test.txt, the output file.

List of Routines:

• I4_LOG_10 returns the integer part of the logarithm base 10 of an I4.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8GE_PRINT prints an R8GE matrix.
• R8GE_PRINT_SOME prints some of an R8GE matrix.
• R8LTT_DET computes the determinant of a R8LTT matrix.
• R8LTT_INDICATOR sets up a R8LTT indicator matrix.
• R8LTT_INVERSE computes the inverse of a R8LTT matrix.
• R8LTT_MM computes C = A * B, where A and B are R8LTT matrices.
• R8LTT_MTM computes C = A' * B, where A and B are R8LTT matrices.
• R8LTT_MTV computes b = A'*x, where A is an R8LTT matrix.
• R8LTT_MV computes b=A*x, where A is an R8LTT matrix.
• R8LTT_PRINT prints a R8LTT matrix.
• R8LTT_PRINT_SOME prints some of a R8LTT matrix.
• R8LTT_RANDOM randomizes an R8LTT matrix.
• R8LTT_SL solves a linear system A*x=b with an R8LTT matrix.
• R8LTT_SLT solves a linear system A'*x=b with an R8LTT matrix.
• R8LTT_TO_R8GE copies an R8LTT matrix to an R8GE matrix.
• R8LTT_ZEROS zeroes an R8LTT matrix.
• R8VEC_INDICATOR1 sets an R8VEC to the indicator vector (1,2,3,...).
• R8VEC_PRINT prints an R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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