R83_NP
Tridiagonal Matrix Utilities, Nonpivoting Factorization

R83_NP is a FORTRAN90 library which carries out some basic linear algebra operations on R83_NP matrices (real 64 bit precision tridiagonal 3xN format, nonpivoting factorization).

These utilities are distinguished by the fact that an LU factorization is attempted without the use of pivoting. Such an approach will fail if a zero pivot is encountered, and will generally not be as accurate as a pivoting factorization. It is only recommended in cases where pivoting is known to be unnecessary, such as for a symmetric positive definite matrix.

Licensing:

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

Languages:

R83_NP 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).

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).

R8LTT, a FORTRAN90 library which contains linear algebra routines for R8LTT matrices (real, 64 bit, lower triangular Toeplitz 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).

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

Source Code:

• r83_np.f90, the source code.

Examples and Tests:

• r83_np_test.f90, a sample calling program.
• r83_np_test.txt, the output file.

List of Routines:

• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R83_DIF2 returns the DIF2 matrix in R83 format.
• R83_MTV computes A'*x=b, where A is an R83 matrix.
• R83_MV multiplies an R83 matrix times an R8VEC.
• R83_PRINT prints an R83 matrix.
• R83_PRINT_SOME prints some of an R83 matrix.
• R83_RANDOM randomizes an R83 matrix.
• R83_NP_DET returns the determinant of an R83 system factored by R83_NP_FA.
• R83_NP_FA factors an R83 matrix without pivoting.
• R83_NP_FS factors and solves an R83 system.
• R83_NP_FSS factors and solves multiple R83 systems.
• R83_NP_ML computes A * x or x * A, where A has been factored by R83_NP_FA.
• R83_NP_SL solves an R83 system factored by R83_NP_FA.
• R8GE_PRINT prints an R8GE matrix.
• R8GE_PRINT_SOME prints some of an R8GE matrix.
• R8VEC_INDICATOR0 sets an R8VEC to the indicator vector (0,1,2,...).
• R8VEC_INDICATOR1 sets an R8VEC to the indicator1 vector.
• R8VEC_PRINT prints an R8VEC.
• R8VEC2_PRINT_SOME prints "some" of an R8VEC2.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.